computer applications in electrical engineering

COMPUTER APPLICATIONS

IN ELECTRICAL ENGINEERING

POZNAN UNIVERSITY OF TECHNOLOGY

INSTITUTE OF ELECTRICAL ENGINEERING AND ELECTRONICS

under the auspices of

ELECTRICAL ENGINEERING COMMITTEE OF POLISH ACADEMY OF SCIENCES

and IEEE POLAND SECTION

COMPUTER APPLICATIONS

IN ELECTRICAL ENGINEERING

VOLUME 8

Edited by

Ryszard Nawrowski Poznan University of Technology

Published by POLI-GRAF-JAK

Poznan 2010

COMPUTER APPLICATIONS IN ELECTRICAL ENGINEERING

Chairman of the Programming Committee Prof. Stanisław Bolkowski, DSc

Chairman of the Organising Committee Prof. Ryszard Nawrowski, DSc

Members of the Organising Committee Prof. Wojciech Machczyński, DSc

Prof. Konrad Skowronek, DSc Krystyna Horemska, MSc

Leszek Kasprzyk, PhD

Scientific Secretary of the Conference Andrzej Tomczewski, PhD

Organising Secretary of the Conference Dorota Warchalewska-Hauser, MSc

Jarosław Jajczyk, PhD

Reviewers

Karol Bednarek Ryszard Nawrowski Stefan Brock Lech Nowak Konrad Domke Władysław Opydo Paweł Idziak Ryszard Porada GraŜyna Jastrzębska Krzysztof Siodła Leszek Kasprzyk Konrad Skowronek Andrzej Królikowski Krzysztof Sroka Józef Lorenc Wojciech Szeląg Marian Łukaniszyn Andrzej Tomczewski Kazimierz Musierowicz Maria Zielińska

Secretary of the Conference Poznan University of Technology, Institute of Electrical Engineering and Electronics

60-965 Poznań, Piotrowo 3a tel. (061) 6652388, fax. (061) 6652389

e-mail: [email protected], http://www.iee.put.poznan.pl/zkwe/

ISSN 1508-4248

ISBN 978-83-923978-9-2

Copyright by POLI-GRAF-JAK Przedsiębiorstwo Usługowo-Handlowe i Produkcyjne

ul. Jugosłowiańska 44B/2160-149 POZNAŃ All rights reserved

Poznań 2010

Contents

Preface

J. Purczyński Application of Aitken’s extrapolation in numerical analysis

1

H. Krawczyk, K. Bańczyk, J. Proficz Parallel processing of multimedia streams

9

T. Rymarczyk, S. F. Filipowicz, J. Sikora Applied multiphase level set function in image segmentation

26

M. Borysiak, Z. Krawczyk, J. Starzyński Creating patient-specific Finite Element Models with a Simple Mesh Morpher

38

J. Wiśniewski, E. Anderson, J. Karolak Susceptibility of electrical network to ferroresonance occurence

46

Z. Piątek, D Kusiak, T. Szczegielniak Reverse reaction magnetic field in two-wire high current busduct

53

M. Dąbrowski, A. Rudeński Investigation of effectiveness of α-constrained simplex method applied to design of optimal induction motors

61

M. Łukaniszyn, M. Kowol, J. Kołodziej Performance analysis of a two-module reluctance motor with an axial flux

72

G. Tarchała, T. Orłowska-Kowalska Comparative analysis of the direct sliding-mode torque control strategies of the induction motor

81

Ł. Knypiński, L. Nowak, K. Radziuk, Y. Le Menach The field-circuit analysis of the start-up operation of the brushless DC motor

93

M. Kamiński, T. Orłowska-Kowalska, K. Szabat Analysis of the dynamical performance of the two-mass drive system with the modified state controller

105

P. J. Serkies, K. Szabat, M. Dybkowski Predictive speed control of induction drive with high-frequency torsional oscillation

120

S. Banaszak, K. M. Gawrylczyk Computer modeling in the diagnostics of transformers’ windings deformations

132

I. Dolezel, V. Kotlan, B. Ulrych Study of suitable arrangement of axial electromagnetic clutch

141

A. Jastriebow, G. Słoń Accuracy of the intelligent dynamic models of relational fuzzy cognitive maps

150

W. Mazurek, T. Świeboda, M. Malinowski Design of module-based controller for solar micro combined heat and power technology

161

D. Kucharski, M. Wesołowski, R. Niedbała, J. Hauser Numerical modeling of underfloor heating system using CFD procedures with Elmer software

174

W. Grycan, B. Wnukowska, M. Kott, B. Brusiłowicz “Smart Metering” in load diagrams analysis

184

M. Kott, B. Wnukowska, W. Grycan Anticipating energy intensity of industry using software for creating econometric models

193

P. Mazurek Suppression of impulse noise in Track-Before-Detect Algorithms

201

B. Kuśnierz, J. Marlewski, A. Rybarczyk, K. Gugała BMJ2K – walking octaped robot with 24 servomechanisms

212

B. Fabiański IRp-6 industrial robot control panel

223

K. Szabat, C. T. Kowalski Fuzzy models of the biological-chemical processes in the west-water treatment plant

230

J. Tchórzewski Electric Power System from the point of view of model development

242

T. Łobos, T. Sikorski, H. Amaris, M. Alonso, D. Florez Combined monitoring and time-frequency analysis for transients in wind energy systems

260

A. Purczyński, R. Frąckowiak Calculator for Electricity Supply’s Unreliability Estimation (OZZEE)

270

R. Frąckowiak, T. Gałan Models of individual consumers load versus standard profiles; MS Excel – aided study

281

T. Wawrzyniak Wind power stations

293

AUTHORS INDEX 302

Preface

The Institute of Electrical Engineering and Electronics of the Poznan University of Technology is going, for the 15th time, to organize a Conference on Computer Applications in Electrical Engineering. The first Conference was held in 1996 and, since that time, has been held every year. Total number of 2591 lectures have been published from 1996 to 2010. During the past ten years about 2940 persons participated to the Conferences, inclusive of the workers of universities, research centres, and industry, also from Czech, Germany, Romania and Ukraine.

At the closure of the 15th ZKwE'2010 Conference the organizers decided to publish a post-conference Monograph, composed of 28 extended papers.

Monograph Computer Applications in Electrical Engineering, ed. by R. Nawrowski, in print since 2002, once per year, all papers published are selected by steering committee, reviewed and published in extended version in English.

The Conference is aimed at presenting the applications of existing computer software and original programs in the field of modelling, simulation, measurements, graphics, databases, and computer-aided scientific and engineering works related to electrical engineering.

The following thematic groups are foreseen:

1. ELECTRICAL ENGINEERING a. Electromagnetic field, electromagnetic compatibility b. Theory of circuits and signals c. Bioelectromagnetism d. Power engineering, renewable energy e. Electronics and power electronics f. Electrical engineering of vehicles g. Electrical heating h. Electrical machines, electrical drive i. Materials technology j. Mechatronics k. Electrical and electronic metrology l. Microprocessor technology and control systems m. Lighting technology

2. COMPUTER APPLICATIONS IN ENGINEERING a. Databases b. Numerical methods and algorithms c. Parallel computation d. Optimisation, genetic algorithms, neural networks and expert systems e. Computer networks, information networks f. Programming techniques g. Internet technologies h. Visualization, CAE/CAD Systems

3. DIDACTICS, EDUCATION AND SCIENTIFIC INFORMATION 4. SCIENTIFIC STUDENTS TEAM

Detailed information related to the ZKwE Conference are available on http://www.iee.put.poznan.pl/zkwe/.

Computer Applications in Electrical Engineering

1

Application of Aitken’s extrapolation in numerical analysis

Jan Purczyński

West Pomeranian University of Technology 71-126 Szczecin, ul. 26 Kwietnia 10, e-mail: [email protected]

1. Introduction

The paper is a continuation and elaboration of the subject of [5], which investigated the application of algorithm ε and Aitken’s extrapolation to solve large sets of linear equations. In this paper the application of algorithm ε [1], [2] was abandoned since in the following examples under study it yielded worse results than Aitken’s extrapolation.

The acceleration of sequence ( )nx convergence through Aitken’s extrapolation consists in creating sequence ( )nx′ given by dependence:

( )21

21

2 −−

−+−

−−=′nnn

nnnn xxx

xxxx (1)

which is convergent faster than the sequence ( )nx [1], [2], [4]. To the sequence ( )nx′ formula (1) can be once more applied, which is referred to

as multiple Aitken’s extrapolation and can be written as: nn xa =,0

( )2,1,,

21,,

,,1 2 −−

−+ +−

−−=

ninini

nininini aaa

aaaa (2)

2. Approximate solving of large sets of linear equations

The following set of equations was investigated:

BAX = (3) where: ][ ,kjJJ aA =× ; ][ jbB = .

The method of accelerating convergence was applied to the sequence of solutions obtained through Jacobi’s method [4], [6]:

dX =0 dXCX nn +⋅= −1 (4)

where: jj

jj a

bd

.= ; ( )[ ]1,

.

,, −= kj

aa

cjj

kjkj δ ; ( )kj,δ - Kronecker’s delta.

Matrix B entries were obtained using a generator of random numbers - with uniform distribution within the range (0, 1000) - installed in MathCad program.

J. Purczyński / Application of Aitken’s extrapolation in numerical analysis

2

Matrix A entries lying outside the main diagonal were determined using the same method. However, the diagonal entries satisfy the following condition:

∑≠

=kj

kjjj apa ,, (5)

Parameter p determines the spectral radius of matrix C, hence determines the convergence of results obtained in Jacobi’s method. For a sufficiently large J (matrix degree) the following approximately applies

pC 1)( =ρ (6)

In this paper the matrices under study were of a degree 1200200 ÷=J . The maximum relative error resulting from the application of (6) did not exceed the value 5102 −⋅ .

The largest characteristic value as to its absolute value (spectral radius) can be determined by the power method [4]. Having limited oneself to one iteration, an approximate formula is obtained:

1

1,1

)(S

ScC

J

kkk∑

==ρ (7)

where: ∑=

=J

kkjj cS

1, .

For the matrices under study, the relative error resulting from the application of (7) fell within the range )1010( 156 −− ÷ .

While doing the acceleration of sequence convergence of solutions obtained through Jacobi’s method, it was concluded that the best results were given by the single Aitken’s extrapolation. Formula (1) was applied vectorially, i.e. in relation to subsequent vectors nX (formula (4)). Treating the solution obtained through Gaussian elimination method as an exact one, the relative error for all solutions of the set (3) was determined and the maximum error BM was calculated. Assuming 410−=BM , an adequate number of iterations n was determined as shown in Table 1.

In accordance with (1), Aitken’s extrapolation is applied to the last three terms of a sequence. In Table 1 the values of spectral radius within the range )51( ÷ are provided which means that it is a divergent sequence of solutions obtained through Jacobi’s method (the convergence condition is 1<ρ ). For 5>ρ error

410−>BM was obtained. The results in Tab. 1 show that the application of Aitken’s extrapolation enables the abandonment of a dominant main diagonal condition with


3

reference to matrix A (formula (3)). Figure 1 presents maximum values of relative error BM depending on a number n of iteration being subject to Aitken’s extrapolation. The figure was done for J = 1000 and 4=ρ ; for other values J and ρ a similar dependence of BM on n is obtained.

Table 1. Minimum number of iterations in Jacobi’s method

Spectral radius

ρ

Number of equations in a set J

400 600 800 1000 1200 J > 1000 1 6 6 6 6 6 6 2 8 8 8 7 7 7 3 9 8 8 8 8 8 4 10 10 8 8 9 9 5 12 9 9 10 9 10

5 6 7 8 9 10 11 12 13 14 15 16 17 181 .10 8

1 .10 7

1 .10 6

1 .10 5

1 .10 4

1 .10 3

0.01

0.1

1

BMn

10 4−

n

.

Fig. 1. Maximum values of relative error BM depending on number n

of iteration being subject to Aitken’s extrapolation

3. Determining the principal value of singular integral

As an example the following singular integral was considered

∫− −

=1

1dx

axxI (8)

where ( )1,1−∈a . By calculating the integral


4

∫∫+

−

− −+

−=

1

1)(

ha

hadx

axxdx

axxhI (9)

we obtain

⎟⎠⎞

⎜⎝⎛

+−+−=

aaahhI

11ln22)( (10)

By reaching in (10) limit 0→h , the principal value of the singular integral (8) is obtained, which is given by

⎟⎠⎞

⎜⎝⎛

+−+=

aaai

11ln2 (11)

In order to apply Aitken’s extrapolation, and using the procedure of numerical integration from MathCad program, the value of the integral was determined

∫∫+

−

− −+

−=

1

2,0

2,0

1 2.02,0m

m

h

h

m dxx

xdxx

xI (12)

for m = 1, 2, 3; mmh −= 2 , and subsequently formula (1) was applied.

The value of relative error obtained for the result (in relation to (11)) equaled 15105,1 −⋅ . In the case of using the parabola method to calculate the integrals present in formula (12) the obtained value of relative error equaled 10102,1 −⋅ .

Figure 2 shows the integrand function curveax

xxf−

=)( (for a=0,2) present in

the integral (8).

1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 18

6

4

2

0

2

4

6

88

8−

fn

11− xn

.

Fig. 2. The curve of function 2,0;)( =

−= a

axxxf


5

As another example the following singular integral was considered

∫−

−=

1

1

2dx

axxI (13)

where ( )1,1−∈a . The principal value of the singular integral (13) was given by

⎟⎠⎞

⎜⎝⎛

+−+⋅=

aaaai

11ln2 2 (14)

Using the procedure of numerical integration from MathCad program, the value of the integral was determined:

∫∫+

−

−−

+−

=1 2

1

2

m

m

ha

ha

m dxax

xdxax

xI (15)

for a = -0,8; m = 1, 2, 3; mmh −= 2 , and subsequently formula (1) was applied.

The value of relative error obtained for the result equaled 151033,7 −⋅ .

4. Determining the value of improper integral

As an example the following improper integral was considered

∫∞

==0 2

sin πdxx

xI (16)

An integration interval πNx ,0∈ was divided into N sub-intervals of a size π=h . The rectangle method was used to calculate the value of function

xxxf )sin()( = in points π

212 += ixi where: i=0,1,...,N.

In accordance with the rectangle method, the value of the integral was determined for varying n; n = 0,1,...,N

∑=

=n

iin xfhS

0)( for n=0,1,...,N (17)

To the sequence of partial sums (17) multiple Aitken’s extrapolation (formula (2)) was applied and the obtained result was burdened with an error equal to 15105 −⋅ .

5. Accelerating the convergence of solution in one-point iteration method

Several methods of approximate solving of nonlinear equations boil down to the one-point iteration method, which is given by

( )nn xx φ=+1 (18)


6

Also in this case, Aitken’s extrapolation helps to accelerate the convergence of formula (18) solution.

As an example, the determination of the root of the following equation was investigated:

0)ln(2)( =+= xxxf (19)

Equation (19) can be transformed into an equivalent form )2exp(1 nn xx −=+ (20)

For the obtained sequence ( )nx , where: 5,00 =x ; 10;,...,1,0 == NNn multiple Aitken’s extrapolation is used – formula (2). The result obtained in this way is burdened with a relative error 9106,4 −⋅ . In order to obtain such accuracy while using formula (20) N=121 terms of the sequence would have to be taken into account. When considering only N=10 in (20), the obtained result is burdened with a relative error 3,38%.

Interesting qualities characterize the modified Aitken’s extrapolation method, the so called active Aitken’s extrapolation [4]. In this method, starting from value 0x , 1x and 2x are consecutively derived in accordance with formula (18). Then formula (1) is used to obtain value 2x′ . Beginning with value 2x′ the next two terms of the sequence are calculated based on formula (18).

The described algorithm can be written as

( ) ( )( ) ( )⎪

⎩

⎪⎨

⎧

≠

=+−

−−=

+++

++++

03,mod

03,mod2

212

212

23nforx

nforxxx

xxxx

nnnn

nnnn

φ (21)

Applying formula (21) to equation (20), for 5,00 =x ; 10;,...,1,0 == NNn , the solution burdened with a relative error 121083,1 −⋅− is obtained. The error is more than 1000 smaller than the error obtained in the multiple extrapolation method ( 9106,4 −⋅ ). The modified Aitken’s extrapolation method has yet another advantage, namely, it can be applied to a divergent sequence. To illustrate that, formula (19) can be used, which can be transformed into the following form

( )2

ln1

nn

xx −=+ (22)

The application of algorithm (21) to formula (22) provides the solution (N = 10) with a relative error 101028,2 −⋅ . It should be noticed that the sequence )( nx derived from formula (22) is divergent since the convergence condition ( )nxφ′ < 1 [4] is not met. A similar quality belongs to the multiple Aitken’s extrapolation method which provides solution for the divergent sequence ( )nxφ , yet it presents slower


7

convergence than the active Aitken’s extrapolation method – in the example under study the relative error of the solution is 41085,2 −⋅ .

The best effects of accelerating the convergence of the solution of formula (18) were obtained using Wegstein’s method which is given by [7]:

( )01 xx φ= ; ( ) ( )

( ) ( )nn

nnnn

nn

xxxxxxxx

φφ

φφ

−−−−=

+

+++

++

1

111

12 (23)

Applying formula (23), to both (20) and (22), the relative error of solution for N = 8 was smaller than 15101 −⋅ .

6. Conclusions

The paper investigated the application of Aitken’s extrapolation to solve selected problems of numerical analysis.

In the case of approximate solving of large sets of linear equations, Aitken’s extrapolation proved useful for the sequence of solutions obtained through Jacobi’s method. Thanks to the application of the single Aitken’s extrapolation to the last three terms of the sequence, the relative error of solutions was smaller than 4101 −⋅ . Taking into account the fact that the amount of the considered terms of the sequence did not exceed 12, the proposed method is competitive with other methods of solving the sets of linear equations with respect to calculation complexity. An additional advantage of this method is the possibility of abandoning the dominant main diagonal condition in relation to matrix A (formula (3)), which limits applicability of Jacobi’s method. Aitken’s extrapolation method can be applied to spectral radius )5,0(∈ρ .

The following two examples concerned determining the principal value of singular and improper intervals. In the case of the singular integral, the integrand function’s discontinuity within the integration interval was present. The substantial accuracy of results was reached with little calculation complexity – the relative error did not exceed the value of 10102,1 −⋅ . The fact that the integral in section IV was improper resulted from the infinity of the integration interval. The application of the multiple Aitken’s extrapolation to the sequence obtained through the rectangle method provided the result’s relative error equal to 15105 −⋅ .

In section V the acceleration of the sequence convergence of equation (18) solutions was discussed. Furthermore, the usefulness of the multiple Aitken’s extrapolation and active Aitken’s extrapolation was ascertained. Both of these methods can be used in the case when the sequence of solutions of equation (18) is a divergent sequence.


8

References [1] Brezinski C., Acceleration de la convergence en anlyse numerique. Berlin 1977. [2] Brezinski C., Algorithmes d`acceleration de la convergence. Etude numerique. Paris

1978. [3] Chua L.O. Pen- Minlin, Komputerowa analiza układów elektronicznych. Algorytmy i

metody obliczeniowe. WNT Warszawa 1981. [4] Dahlqiust G., Bjorck A., Metody numeryczne. Warszawa: PWN 1983. [5] Purczyński J., Zastosowanie algorytmu ε i ekstrapolacji Aitkena do rozwiązywania

dużych układów równań liniowych. Mat. Konf. ZkwE`97, Poznań- Kiekrz 1997, s.89-92.

[6] Stoer J., Bulirsch R., Wstęp do metod numerycznych. PWN 1975. [7] Wierzbicki W.M., Czisliennyje mietody. Wysszaja szkoła, Moskwa, 2000.


9

Parallel processing of multimedia streams

Henryk Krawczyk, Karol Bańczyk, Jerzy Proficz Gdańsk University of Technology

80-233 Gdańsk, ul. Narutowicza 11/12, e-mail: [email protected], [email protected], [email protected]

The paper presents a new multimedia processing platform: KASKADA. The design of the platform is described: the diagram of main classes, the sequence diagram illustrating their cooperation during the processing of multimedia streams, and the details of the inter-task communication mechanism. We also present the framework supporting algorithm development, a service scenario definition, and provide evaluation of the platform usability.

1. Introduction

Multimedia systems play an important role in industrial and global development. There is a need for high performance computers to process very complex algorithms, e.g., face recognition or registration (number) plate localization. The paper presents a new computational framework which is a part of Context Analysis of the Camera Data Streams for Alert Defining Applications platform (Polish abbreviation: KASKADA, i.e., cascade,l).

The platform is going to be deployed on a high-performance computational cluster 'Galera' within the Academic Computer Centre in Gdańsk – TASK [6], consisting of 672 nodes, 1344 processors and 5376 cores. The nodes are connected by 20Gbps Infiniband [9] using the fat tree technology, supporting a fast, 5000TB LUSTRE [13] file system.

streammanagement

sourcestreams

applicationservices

algorithm,service,

applicationdevelopment

developer

users

streamarchive system service repository

streams services

Internet

management of task/serviceexecution

Galera cluster

Fig. 1. The multimedia stream analysis schema for cluster computing environment

H. Krawczyk, K. Bańczyk, J. Proficz / Parallel processing of multimedia streams

10

The Fig. 1 presents the general schema of processing the multimedia streams in a computation cluster environment. The processed streams need to be received and initially pre-processed, archived in a dedicated subsystem, repacked and distributed to the cluster, where the actual analysis is performed.

The analysis algorithms are designed, programmed by the developers and should be exposed to the external users as application services accessed remotely via the user interface or an additional application using remote calls from the service repository. The above characteristics require the following core features to be provided by the system and hardware components: • Multimedia stream distribution – the incoming data including video, audio and

associated metadata should be provided to each task performing the analysis, assuming they can be scattered through the cluster nodes, high-speed networks and proper communication protocols supporting streaming need to be used. Moreover, the archiving mechanisms must be deployed for the off-line processing.

• Distributed computing – the complexity of the analysis and scalability requirement enforces its decomposition into cooperating tasks, which need to be assigned and launched on the proper cluster nodes, the efficiency of this procedure is especially important for the real-time analysis of the on-line streams.

• Quality of service – the on-line analysis requires the quality constraints to be applied at the beginning and maintained for the duration of the computation, which implies introduction of continuous cluster monitoring mechanisms controlling processor, memory, and network load, of executed tasks.

• Remote access – the general user interface needs to be provided, including access to the archive, streams, and running algorithms. Similar functionality should be provided for the client application. For both types of access the proper security policies must be applied.

• Development environment – the multimedia processing programs require proper sets of the core functions supporting their execution including stream decoding, encoding, forwarding, manipulation, meta-data gathering and the input device control, e.g. camera movement and zoom adjustment. Multimedia stream distribution can be realized using normal TCP/IP

connections; however, for the unpacked data, especially video, even fast Infiniband TCP/IP setups can be easily over-saturated. A typical solution is usage of low level RDMA [4] libraries, which are often utilized by the MPI [16] implementations. Similarly, for the stream archiving, the fast remote file systems over Infiniband are used, in this case of the ‘Galera’ cluster it’s LUSTRE [13].

Distributed computing is a key feature provided by any cluster. The usual realization is based on a queue system, enabling processor scheduling for a large number of tasks. The ‘Galera’ uses PBS [18] with a specific plugged scheduler: Maui [15]. The process of resource assignment is performed every minute, and


11

uses declared processor/memory load as an indicator of the used resources, which can be inefficient for real-time online analysis requirements.

The typical computing cluster does not usually provide any out-of-the-box quality-of-service mechanisms, some of them can be realized using special priority settings over the queue system and directly in the operating system. In our case we deployed a PBS QoS module [18] supported by a Linux quota and nice command policies.

The typical Linux cluster is accessible through a remote shell, usually SSH [20]. There is one special node – the access point, which is used for starting the tasks over the whole cluster. It manages the whole queue system including the scheduler process, and further uses SSH connections for task distribution over the computation nodes.

The typical configuration of the cluster contains the set of development tools including compilers (C++, Forthran, Java etc.), message passing libraries (usually one or more MPI implementations) and some debugging and monitoring. The multimedia processing requires, at least, installation of a proper decoder/encoder and stream transportation libraries.

In the KASKADA platform we provide a unified collection of the tools and components extending and partially replacing the (above) typical cluster solutions. The platform contains the common web interface for its management including algorithm and service repositories, on-line and archived stream control and external user/client administration.

The multimedia stream distribution is realized using fast RDMA functions, which utilise (directly) fast Infiniband networks. All multimedia processing algorithms are implemented using the same set of functions for decoding/encoding and forwarding the streams, with transparent conversion between online and archived data.

The platform provides its own way to distribute the tasks over the cluster. The proposed solution uses its own assignment algorithms and enables fast start-up of scheduled scenarios without additional overheads caused by SSH [20] protocol. The proper monitoring processes are deployed on each cluster node, they are also responsible for quality measurements and resource controlling.

Remote access is provided by the platform through the web user interface. The applications can execute and control the multimedia algorithms using typical SOA [10] approaches with the utilization of the SOAP [24] webservices. The index of the provided services is also accessible via user interface or using the UDDI [22] registry.

The platform provides sets of libraries enclosed within the framework, enabling easy development of multimedia processing algorithms in C++ language. There is provided also a unified procedure of the stream processing including decoding/encoding and metadata handling. Moreover, additional features like test streams, event monitor and service composer are provided.

The KASKADA platform provides a complete solution for multimedia processing application development: from algorithm construction, through its


12

implementation as a computational task to the exposed set of dedicated services, which can be used to solve more complex problems (e.g. person tracking), including service execution and test [3].

Each service consists of a set of cooperating tasks, described by a directed acyclic graph, where the vertices represent the tasks, and the edges indicate the data flows between them. The platform can manage multiple task graphs and return their computational results as outputs of the corresponding services. Additionally, extra tasks can be assigned for quality evaluation of the algorithms, including such factors as performance, effectiveness and scalability.

To implement a task, we need a C++ developed algorithm based on the framework library and headers. The library supports two core functionalities: audio-video stream decoding/encoding and mechanisms for inter-task communication. The latter are: object serialization, incoming data synchronization, signal handling and queue-based messaging.

The next section describes the framework design, including class and sequence diagrams. Section three contains information about task cooperation mechanisms and introduces a task graph example. In the final section, we provide conclusions, current state of development, and indicate further work to be done.

2. Framework for stream analysis

Multimedia stream processing algorithms may perform quite different types of analysis. The class of algorithms is very broad. To name just a few examples, the algorithms may perform human face recognition, voice recognition, object tracking, car registration plate detection, etc. Even though the specifics of each such algorithm are different, they all are typically built according to the same template, and they have to perform a lot of common tasks. Moreover, algorithms launched in a common environment, like KASKADA platform, need to behave according to certain rules in order to improve the whole ecosystem's manageability, stability, and so on. Also it's convenient for an algorithm developer to have the most typical and mundane tasks of a general nature solved for him, to let him concentrate on the parts that are original to his work.

KASKADA framework is a C++ library addressing these issues. It provides algorithm classes for typical algorithm types, audio/video stream decoding and encoding, C++ object serialization and inter-algorithm delivery, rtsp/file mutimedia streams handling, dynamic tasks launching and basic life-cycle management support. The framework is provided as a static Linux library with necessary headers. Additionally, the implemented algorithms can use libraries used by KASKADA which include e.g. a rich set of Boost [1] libraries and standard POSIX system features (parallelism mechanisms, including thread creation and cooperation). The user may, of course, use other algorithm needed libraries.


13

Fig. 2. The layer diagram of KASKADA framework based algorithm

The Fig. 2 shows a layer diagram of a kaskada-based algorithm. The user algorithm is always implemented as a subclass of a KASKADA framework provided abstract algorithm class. The type of user code depends on the used algorithm class. The available algorithm abstract classes are depicted in Fig. 3.

The KaskadaAlgorithm class is the most general algorithm available. It provides all basic features required from KASKADA supervised algorithms, which are related to algorithm life-cycle control. The class provides features related to input parameters parsing and XML based communication.

The KaskadaMasterAlgorithm and KaskadaSlaveAlgorithm are abstract classes for algorithms working in master-slave computational model. The master algorithm class provides methods for slave tasks starting, input/output data exchange and synchronization.

Fig. 3. The class diagram of the KASKADA framework


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The KaskadaStreamAlgorithm class is designed for on-line streams processing, where a stream is defined as a sequence of data packets available in a packet-by-packet manner. A stream algorithm can process more than one input stream and produce more than one output stream. The output streams' limitation is that all the streams must have the same content (not necessary the same protocol). The class provides an abstract callback function processDataObjects(), used as a template method pattern [7] and provides the streams' objects to the concrete algorithm implementation, e.g. MyStreamAlgorithm in Fig. 1. The method's input is a vector of objects received from input streams. Each vector position maps to an input stream number and contains the last object received from the stream. The vector is passed to the algorithm for every new object in the first stream, being the synchronization stream.

Fig. 4. Stream types handled by stream algorithm

The basic KASKADA Framework's communication protocol is kbin (standing for KASKADA Binary protocol) and is simply a network stream of serialized objects. The serialization is implemented using Boost Serialization library [2]. However, the stream algorithm class provides special functionality related to multimedia streams. It accepts and produces rtsp [19] and file multimedia streams, taking care of all the necessary decoding and encoding. The decision on used protocol types is a matter of launch configuration. Streaming capabilities of an algorithm are depicted in Fig. 4.

Fig. 5. The sequence diagram of the KASKADA framework stream algorithm


15

The framework provides classes related to the processed data. The DataObject class represents an interface of an abstract data entity. It is associated with the DataObjectInfo class containing metadata as a set of parameters. The DataObject is extended by the Image and AudioFrame classes, responsible for holding video frame and sound frame respectively.

The Fig. 5 presents typical usage of the framework. The main() function of the task creates an algorithm instance and calls the execute() method, where the main loop is invoked. During the execution, the loop provides the processed data by chunks, for video there are image frames and collected samples for audio.

In the implemented template method processDataObject(), the algorithm developer can use the sendDataObject() method for sending the processed data to the output streams, check the input parameters using the getArgs() method, or check if the task received a signal from the platform management module to finish its work using isFinished().

Each stream algorithm is also a master algorithm. Fig. 6 shows a scenario with an exemplary master task starting new slave tasks (startTasks()) and waiting for their termination. The process of starting the slaves involves communication with the management platform which launches new tasks according to available resources. The master task can suspend its activity until an unspecified slave (waitForAnyTask()) or all of slaves (waitForAllTasks()) of a set have finished. In the diagram the master algorithm is represented by the myMasterAlg class and the slave algorithm by the mySlaveAlgorithm class.

Fig. 6. The sequence diagram of the KASKADA framework master and slave algorithms

3. Execution scenarios for multimedia applications

In the KASKADA platform the term scenario is defined as an acyclic graph of

interconnected stream processing tasks extended with master-slave task cycles. A task is a running instance of a KASKADA framework based algorithm. Each


16

graph's directed edge represents data flow from a source task to a target task. A master-slave cycle is formed by a master task sending a single object to a slave task and a slave task sending back a result object. Fig. 7 shows a logical and physical view of a scenario. The logical view focuses on the stream/object logical content; str – stands for stream, obj – object, alg – stream processing algorithm (implemented, e.g. by the MyStreamAlgorithm class). Identifier #n represents nth type of stream/object/algorithm respectively. Slave algorithms are represented separately by the “slave alg #1” identifier. In the physical view, the algorithms are encapsulated symbolically by the striped frames which symbolize framework. The content types are replaced by protocol types to indicate that this type of concern is fully handled by the algorithm. Each launched algorithm instance is defined as a task. a)

b)

Fig. 7. Scenario logical (a) and physical view (b). The striped frames around algorithms in the physical view symbolize the KASKADA Framework wrap-up

Each task is capable of streaming and receiving data using the same three

protocols: rtsp, file and kbin. The algorithm “alg #1” processes a single rtsp stream and produces a single kbin stream; “alg #2” processes a single kbin stream and produces a kbin stream; “alg #3” processes a file stream and a kbin stream and produces a kbin stream. The fourth algorithm is the most complicated one; it processes two kbin streams and produces rtsp and file streams. Moreover, it acts as a master algorithm and, in some cases, it launches slave algorithms. Each slave returns the result to the master after finishing its work (the dotted edge). The graph exposes a limitation of the framework. Input rtsp streams may be handled only exclusively, i.e. every time an rtsp stream is handled, no other stream may be processed. This is, in fact, no big issue because rtsp streams are targeted only for outside world integration purposes (camera, audio-video player communication).


17

The file protocol is, on the other hand, provided mainly for archiving and debug purposes. The real world task graphs always process kbin data streams, which benefit from the fact that they utilize a much faster Infiniband RDMA [4] interface. Fig. 8 shows an effective KASKADA platform realization of the scenario taking into account the afore-mentioned issues. The connection to resources and outside world is separated from the actual algorithm by extra front and back blocks (also implemented using KASKADA Framework). The blocks are added by the platform for every scenario execution to handle all the kbin conversions (all arrows without named protocol indicate kbin) and resource communication. The resources comprise data sources (cameras, storage) and data targets (message queue, video players, storage).

Fig. 8. Scenario of an effective KASKADA platform realization

An example of a scenario is depicted in Fig. 9. The composite task performs a simplified algorithm for identification and tracking of moving objects in a camera-observed scene. Exemplary algorithms of this vast category can be found, e.g., in [21][23].

The video is first processed by the algorithm: detect blob outliers – detecting shapes surrounding the blobs, i.e. clusters of pixels representing moving objects in a picture. The frames, enriched with extra information regarding the outliers, are sent to the cut blobs algorithm. The outliers get cut out using the detected outliers and sent to two parallel feature tasks, extracting visual features of two distinct categories. They could extract, e.g. chromatic and luminance properties.

Fig. 9. An example of a scenario for object tracking and identification


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Two further parallel tasks process the features. The identify blobs task compares the features with known identities and, as a result, produces identity events, which contain significant similarity levels between objects and known identities. The track blobs task compares blob locations and features in any following frames, and generates location events describing deduced routes of objects. The identity and location events are then processed by the aggregation block, which creates events containing both object identity information and their locations.

Fig. 10 shows a more sophisticated scenario, which is built up of many identity & tracking scenarios, and three more aggregation blocks based on [11]. Video streams from n cameras are processed by the incorporated scenarios and provide object location events from multiple sources. All the events are aggregated by yet another aggregation block which converts the events to a unified form. Location values are mapped to a common space, and events describing the same objects seen by other cameras are combined. The block tries to join object trajectories crossing different view scopes in time, increasing the identification reliability based on historical results and generates improved location and identification of events from the whole area of interest.

Fig. 10. An example of a scenario for threat detection

Next, the events enter the rule-based threat detection block, which uses a knowledge base, defined as a set of rules, to identify dangerous situations. The rules could find threats, e.g. when a person belonging to a group marked “dangerous” is found or , in a corporation, when a person from a certain group spends too much time in areas not assigned to them. The rules define a, so as to say, simplistic way of thinking. Uncertainty is rounded to ones and zeros, e.g. a person who has a 0.81 probability of being X is assumed to be is X. The rules prefer false positives to false negatives (i.e. prefer to falsely call a situation a threat than to miss one). The rules provide threat events of average quality, but they manage to perform their job in real-


19

time. Every time a threat event could be sent, the block launches a slave task to refine the assessment by calculating possibly exact threat probability using Multi-Entities Bayesian Networks Logic [12], this being a first-order Bayesian logic.

The said logic is defined as a set of small Bayesian Network template frames. Based on the frames, and a given query, the logic's deduction algorithm creates Situation Specific Bayesian Networks apt to evaluate the probabilities of the query-related variables. The deduction algorithm, integrated into slave tasks, has the potential of creating very precise probability evaluations, but at the cost of unpredictable computation time. To be more exact, the algorithm refines the quality iteratively; and the more time it spends the better the quality which can be achieved. In order the find the proper time-quality trade off, the rule-based block defines the deadline in which a slave block has to provide a solution. The deadline may vary depending on the type of threat (some types of threats may have greater real-time requirements than others). The slave finishes its computation so as to meet the time requirement. On the other hand, the platform may have no resources to launch more slaves, in which case no solution will ever be provided. That's why the master block sends its own threat assessment if no slave result arrives. Each assessment has quality information. The rule-based threat assessments have always lower quality than the MEBN Logic created.

4. Scenario execution management

In KASKADA platform, scenario execution is managed on four layers:

- complex service, - simple service, - task, - processes/threads.

A complex service represents the whole scenario described as a directed acyclic graph. At this level the decomposition of the graph is performed, and the proper simple services are selected. In general cluster environments, usually these operations are performed manually by the programmer/designer during the software development.

At the simple service level, the concrete services are inspected and, according to the given quality policies, the proper tasks are selected. The result is the next graph, with the data connections as edges and the nodes represented by the algorithms to be executed as tasks. This graph is going to be assigned to the appropriate cluster nodes. In the general cluster environment, these operations are usually performer by the queue system with the support of the used scheduler.

In platform KASKADA, the task level management is performed directly by the dedicated software module: the monitor. It is implemented as a special purpose process, whose instances are running on every computation node of the cluster. Its core functions are as follow:


20

• Task start – spawning the system process and providing its proper initial environment.

• Task stop – informing the process of its finalization and stopping its execution. • Task monitoring – constant checking of the task state during its execution,

especially the usage of the resources including processor cores, memory and network load. We can distinguish three characteristic modes of the task execution: Constant

pace – where the task receives the data stream and processes its elements one by one. The source of data has low, limited, transmission rates, which is typical for multimedia streaming servers, e.g. video camera stream. Speeded up stream – where the task receives stream data as well, but it is provided as fast as the task can process it, which is typical for processing off-line data read from the archived files. One-shot data – where the whole data is provided at the beginning of the execution, which is typical for regular computing problems, e.g. text comparison. Having the above modes, we can review the typical tasks configurations in the KASKADA platform. The first category is the real-time tasks analysing the constant pace multimedia streams. The results of such processing need to be delivered immediately; and, due to the limited buffer size, every delay in the computations can cause data lost. The second category is semantically the same tasks as above, but processing is performed in the speeded-up streams mode. In this case, the time constraints are not so important, the data is already stored, so, for resource balancing purposes, its processing can be suspended. The next category is tasks analysing one-shot data; they don’t use long data streams, so their time constraints are not related to the data transmission. The above categories can be mixed as hybrid tasks, e.g. a stream analyser processing constant-pace streams and spawning one-shot slave tasks (see example in chapter V).

For the typical cluster computer: the task level management is partially performed by the queue system and other specialized software components controlling the computation nodes where the tasks are distributed, including their processor, network load, temperature etc. e.g. [8][25][5].

The lowest level of management: processes/threads is performed by the operating system, in case of the ‘Galera’ cluster: Debian Linux. At this level, tasks are represented by the system processes with the corresponding threads. The typical Unix mechanisms: priorities, quotas and tools: nice, top, ps are usually utilized for management purposes.

5. Design methodology for multimedia applications

The Fig. 11 shows a scheme of multimedia applications, scenarios and

algorithms iterrelated development in time. The arrow combined applications-scenario and scenario-algorithm pairs indicate dependencies, i.e. each scenario depends on a set of algorithms and each application depends on a set of scenarios.


21

The development may evolve along application, scenario, or algorithm path, i.e. the designers and developers may develop the applications in a top-down approach or in a bottom-up approach. The first approach assumes that the application design creates the need for a set of scenarios which in turn require a certain set of algorithms. In the second case, the development process takes the opposite direction. The applications are built based on available scenarios which are created according to available algorithms. The algorithms are then created, according rather to technical possibilities than requests from application designers. Of course many mixed approaches are possible (a scenario requires a new algorithm which, after being invented, inspires another scenario and, finally, application).

Fig. 11. The development scheme of KASKADA-based applications, scenarios and algorithms

The algorithm development process consists of seven phases as depicted in Fig.

12. The process starts with the design phase in which the algorithm is developed on the conceptual level. The author considers the problems of algorithm internal data flow and parallelization possibilities. A proper granularity level should be targeted, bearing in mind that the algorithm will (typically) be launched as computation tasks cooperating with other tasks on common problems. Too coarse-grained algorithms may be difficult to assign efficiently to computational nodes. Moreover, if algorithms have complicated specifications, it may be difficult to integrate them with other algorithms. Too-simple and fine-grained tasks may lead to too many nodes in cooperating task graphs, and to too much performance-degrading communication. The second phase is the development of a C++ algorithm based on the KASKADA Framework library. The developer has to decide which of the provided algorithm types fits best their needs, and write the algorithm with respective header files included. The header files encompass both KASKADA Framework-provided files and headers of third party libraries used by the framework. The program has to be compiled and linked. Both of the steps have to be preformed in the cluster environment, where each of the developers has their own shell account. All the necessary files required to prepare the executable are available.


22

The next phase is called simple service definition. This time the developer has to log into the User Console (UC) which is the KASKADA Platform's thin client interface. Each of the developers has their own UC account, where s/he can add and configure the prepared algorithms. The developer describes the algorithm to the platform. In this step the path to the algorithm and necessary extra parameters have to be defined. In the case of stream processing algorithms, input and output data formats have to be defined. The algorithms also get associated with the event types which they send. Independently, a simple service has to be defined grouping algorithms providing the same functionality. The service has to be associated with a set of parameters, which consist of launch and quality parameters. The launch parameters have to include all the parameters expected by the associated algorithms. The quality parameters define quality properties of the algorithms realizing the service.

Fig. 12. Seven phases of algorithm development cycle

The algorithms can, in that stage, be executed from the UC, which lets the developer perform all the test phases. First, arrives the functional tests phase. Only now, master algorithms can launch slave algorithms, and stream algorithms can be tested against the production streams (or their test copy).

If the algorithms behave according to their functional specification, quality related test phases may start. The performance tests constitute the first phase, where properties related to resources consumed by the algorithm running within a service are measured. The properties include: used memory, processors (up to 8 on one node in the Galera cluster) and processing time required to handle a data set. The second phase is related to algorithm result quality, and is called simply quality tests. This phase could provide, e.g., values of false positives and false negatives of


23

detecting a certain property. All of the properties should be set in the service quality properties in UC.

If the algorithm meets the developer’s expectations, they may contact a UC administrator who will accept the algorithm (acceptance phase). The algorithm's executable aspects and all its necessary configuration files, will be copied to a new area. The algorithm and the service will become public in UC and will become useful by the end users.

The scenario development process is similar. In the design phase a new scenario concept is inspired by the available simple services (algorithms); or new algorithm development processes are started if the targeted functionality can not be covered by the available ones. The development and service definition phases are combined into the complex service definition phase in which the graph of simple services is written into an XML document. The test phases and the acceptance phase are basically the same.

The application development process takes place outside of the KASKADA platform. Even though its progress is in no way controlled by the platform, its main phases are probably quite similar to the scenario development phases. No matter which kind of development strategy is chosen, there is surely a design, a development, and a testing phase, included. The design phase is once again focused either on seeking inspiration in the available building blocks (here scenarios) or on deciding which scenarios to develop and starting respective lower-level development phases.

6. Conclusions

The KASKADA platform supports the multimedia processing algorithms and scenarios in three dimensions: - execution supported by the scheduler, service and task components (chapter

IV), - design and implementation supported by the user console, framework libraries

and set of standard tools: C++ compiler, debugger and IDE (chapter II), - development methodology supported by the iterative and incremental process

recommendations (chapter V). The cluster computer-centric environment provides an excellent execution

environment for multimedia processing algorithms: including stream distribution, scenario decomposition, task assignment and monitoring. All these features are directly supported by both general and dedicated software and hardware components provided by the computer centre.

The developer activities, like scenario designing, algorithm implementation and testing are widely supported by the user console functionality, including test services, streams and task monitoring. Additionally, the unified framework for a programmer is provided, including a set of functionality related to the video/audio processing, encapsulated in the C++ library.


24

The described iterative and incremental methodology enables reliable multimedia application development; including algorithm design, service declaration and scenario definition and SOA [10] application implementation. The phases enable introduction of quality assurance elements and their evolution according to the CCMI or other maturity models.

We are concerned with the future work to be focused on the above three aspects of KASKADA platform development. We plan to introduce the quality measurements and evaluation [14]; including performance, reliability, security, safety and dependability factors [17].

References

[1] Boost C++ Libraries, http://www.boost.org/ [2] Boost Serialization Library http://www.boost.org/doc/libs/1_41_0/libs/

serialization/doc/index.html [3] Canfora G.., Di Penta M.: Testing Services and Service Centric Systems: Challenges

and Opportunities, IT Professional, IEEE Computer Society, March/April 2006. [4] Cohen A.: RDMA offers low overhead, high speed, Network World, March 2003,

http://www.networkworld.com/news/tech/2003/0324tech.html [5] collectd – The system statistics collection daemon, http://collectd.org/ [6] Computer Academic Center – TASK, http://www.task.gda.pl/ [7] Gamma E., Helm R., Johnson R., Vlissides J. M.: Design Patterns: Elements of

Reusable Object-Oriented Software, Addison-Wesley Professional (1994). [8] The Industry Standard In Open Source Monitoring, http://www.nagios.org/ [9] InifniBand Trade Association homepage, http://www.infinibandta.org/ [10] Krafzig D., Banke K., Slama D.: Enterprise SOA: Service-Oriented Architecture

Best Practice, Prentice Hall PTR, October 2004. [11] Krawczyk, H., Bańczyk, K.: Ontology Oriented Threat Detection System,

conference Brunów, Poland, June 2009. [12] Laskey, Kathrin B.: MEBN: A Logic for Open-World Probabilistic Reasoning,

Working Paper, C4I Papers, George Mason University, February 2006. [13] Lustre homepage, http://wiki.lustre.org/ [14] Maglio P., Srinivasan S., Kreulen J. T., Spohrer J.: Service Systems, Service

Scientists, SSME, and Innovation, Communication of the ACM, July 2006. [15] Maui scheduler homepage, http://www.clusterresources.com/products/maui/ [16] Message Passing Interface,

http://www.mcs.anl.gov/research/projects/mpi/standard.html [17] Oppenheimer D., Patterson D. A.: Architecture and Dependability of Large-Scale

Internet Services, IEEE Internet Computing, September/October 2002 [18] Portable Batch System (PBS), http://openpbs.org/ [19] Real Time Streaming Protocol (RTSP), http://www.ietf.org/rfc/rfc2326.txt, April 1998. [20] Secure Shell, http://en.wikipedia.org/wiki/Secure_Shell [21] Town, C., Ontology-Driven Bayesian Networks for Dynamic Scene Understanding,

University of Cambridge Computer Laboratory, UK, Computer Vision and Pattern Recognition Workshop, 2004. CVPRW '04.


25

[22] Universal Description Discovery and Integration, http://en.wikipedia.org/wiki/Universal_Description_Discovery_and_Integration

[23] Wang, Y., Van Dyck, R. E., Doherty, J. F., Tracking Moving Objects In Video Sequences, 2002.

[24] World Wide Web Consortium, Simple Object Access Protocol Specification, http://www.w3.org/TR/soap/

[25] xCAT Extreme Cloud Administration Toolkit, http://xcat.sourceforge.net/

The work was realized as a part of MAYDAY EURO 2012 project, Operational Program Innovative Economy 2007-2013,

Priority 2 „Infrastructure area B+R”.


26

Applied multiphase level set function in image segmentation

Tomasz Rymarczyk, Stefan F. Filipowicz, Jan Sikora

Electrical Engineering Institute 04-703 Warszawa, ul. PoŜarskiego 28, e-mail: [email protected]

The application of the level set function for the image segmentation was presented in

this paper. The image segmentation refers to the process of partitioning a digital image into multiple regions. There is typically used to locate objects and boundaries in images. The level set method is a powerful tool for representing moving or stationary interfaces. There was used the idea of the variational formulation for geometric active contours. There was used to minimization problem in image processing to compute piecewise-smooth optimal approximations of the given image. The proposed algorithm has been applied to real pictures with promising results in the image segmentation.

1. Introduction This paper presents the applications of the level set function for the image

segmentation. The level set idea, devised in Osher and Sethian [5], is known to be a powerful and versatile tool to model evolution of interfaces [4, 6, 7, 8].The original idea behind the level set method was a simple one. Given an interface Γ in Rn of dimension one, bounding an open region Ω. It was analyzed and computed its subsequent motion under a velocity field ν. This velocity can depend on position, time, the geometry of the interface (e.g. its normal or its mean curvature) and the external physical conditions. Level Set Methods is the numerical technique which can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together. The variational formulation for geometric active contours forces the level set function to be close to a signed distance function [1, 2]. This idea was used to minimization problem in image processing. For more than two phases were introduced the Mumford-Shah model [3, 9].

2. Level set method

The level set method tracks the motion of an interface by embedding the interface as the zero level set of the signed distance function. The motion of the interface is matched with the zero level set, and the resulting initial value partial differential equation for the evolution of the level set function. The idea is merely to define a smooth function )( tx,φφφφ , that represents the interface as the set where

0)( =tx,φφφφ . The motion is analyzed by the convection the ϕ values (levels) with the velocity field. The Hamilton-Jacobi equation of the form [4]:

T. Rymarczyk, S. F. Filipowicz, J. Sikora / Applied multiphase level set function…

27

0 =∇+∂∂ φφφφννννφφφφ

t (1)

where ν is the velocity on the interface. When flat or steep regions complicate the determination of the contour, the

reinitialization is necessary. This reinitialization procedure is based by replacing by another function that has the same zero level set but behaves better. This is based on following partial differential equation:

01))(S( =−∇+∂∂ φφφφφφφφφφφφt

(2)

where S(ϕ) is defined as:

>=<

=

0for 1

0for 0

0for 1-

)S(

φφφφφφφφφφφφ

φφφφ (3)

The representation of the level set function is shown on the Fig 1.

0=φ

)0( == tyxz ,,φ

Z

Y

X

0)( =yx ,φ

)( ** , yx

)( ii yx , )( 11 ++ ii yx ,

0)( >yx ,φ0)( <yx ,φ

Fig. 1. The representation of the level set function

The numerical algorithm is following (Fig. 2):

• from the level set function (initial) at a time level t, find necessary interface information 0)(0 =φ=Γ y,x ,

• calculate the velocity,

• extend velocity δφ ≤k ,

• update the level set function, • reinitialization, • check convergence.


28

START

Initialization zero

level set

Calculate velocity

Update function &

reinitialization

Condition

STOP

NO

YES

Fig. 2. The scheme of the algorithm – the level set method Figure 3 present the image segmentation by using the level set numerical

algorithm with reinitialization. The zero level set function was defined near edge of the image. It has the yellow colour on the image. The figures show the original image and the topological changes of the shape of the zero level set function after the 100, 200 and 500 iterations.

3. Mumford-shah model

For more than two phases was introduced the multiple level sets idea by Vese and Chan [9]. The algorithm set formulation and algorithm for the general Mumford-Shah minimization problem in image processing, to compute piecewise-smooth optimal approximations of a given image. The proposed model follows and fully generalizes works [3, 9], where there was proposed an active contour model without edges based on a 2-phase segmentation and level sets. The piecewise-constant segmentation of the image allows for more two segments using a new multi-phase level set formulation and partition of the image domain.


29

a) b)

c) d)

Fig. 3. The image reconstruction by the level set function: a) zero level set, b) after 100 iterations, c) after 200 iterations, d) after 500 iterations

For more than two phases was introduced the multiple level sets idea by Vese

and Chan. The algorithm sets a formulation and models for the general Mumford-Shah

minimization problem in image processing, to compute piecewise-smooth optimal approximations of a given image. The problem can be easily generalized to the case where the domain contains more than two materials.

( ) ( ) dΩsdΩssη)(ωC\Ω

2

Ω

2o ∫∫ ∇+−+= CCsF L, (4)

Coefficients c1 i c2 are mean values of points in the picture:

∫

∫

∫

∫

−

−==

Ω

Ω

o

2

Ω

Ω

o

1 ))dΩH((1

))dΩH((1sc

)dΩH(

)dΩH(sc

φφφφ

φφφφ

φφφφ

φφφφ, (5)

The material c is representing following:


30

))H((1c )H(c 21 φ−+φ= c (6) where H is the Heaviside function

0for 0H

0for 1H

<=≥=

x

x

The functional can be written as:

( ) ( ) ( ) ))dΩH(-(1csη)dΩH(csηdΩ)H(ωccΩ

22o2

Ω

21o1

Ω

21 φφφφφφφφφφφφφφφφ ∫∫∫ −+−+∇=,,F

(7) The process for minimization of the functional is the following:

( ) ( )

+−

∇∇

⋅∇=∂∂ 2

2o22

1o1ε c-sηc-sηω)(δφφφφφφφφφφφφ

φφφφt

(8)

The numerical algorithm is following (Fig. 5): • from the level set function (initial) at a time level t, find necessary interface

information, • calculate coefficients c1, c2, • update the level set function, • reinitialization, • check convergence.

The level set methods have natural flexibility to create various shapes. Model of the object is shown on the Figure 4. The Figures 6 presents the image segmentation by using the level set numerical algorithm with the Mumford-Shah model. The images show the original image and reconstruction after the 200 iterations. In the example was used the image frame as initial condition for the active contour model. The final contours have the red colour on the original image. They represent the zero value of the level set function. The segmentation gives good results, because the region borders accurately locating the object edges. An increasing numbers of iteration the quantitative results are better.

Ω ∂

1 Ω

2 Ω

2 Ω

0 Γ

0 = ∂ ∂ n ϕ

0 = ∂ ∂

n ϕ

Fig. 4. Model of the object


31

Fig. 5. The scheme of the algorithm – the level set method

Fig. 6. Image segmentation - the original images and the reconstructions after the 200 iterations


32

4. Variational level set method

The formulation of the variational level set method consists of an internal energy term that penalizes the deviation of the level set function and an external energy term that drives the motion of the zero level set toward the desired image features. When flat or steep regions complicate the determination of the contour, the reinitialization is necessary. This reinitialization procedure is based by replacing by another function that has the same zero level set but behaves better. Variational formulation for geometric active contours that forces the level set function to be close to a signed distance function, and therefore completely eliminates the need of the costly reinitialization procedure.

The resulting evolution of the level set function is the gradient flow that minimizes the overall energy functional [2]:

∫ −∇=ΩΩΩΩ

φφφφφφφφ yxdd1)(2

1)( 2P (9)

An external energy for a function ϕ(x, y) is defined as below: )()(µ)( φφφφφφφφφφφφ mΕΡΕ += (10)

where: )(φφφφP – internal energy, )(φφφφmΕ – external energy.

Denoting by φφφφ∂∂Ε

the Gateaux derivative of the functional E receiving the

following evolution equation:

φφφφφφφφ

∂∂−=

∂∂ Ε

t (11)

In the image segmentation active contours are dynamic curves that moves towards the object boundaries. Denoting letter I as an image, and g be the edge indicator function defined by:

2IG

g*σσσσ∇+

=1

1 (12)

where σσσσG is the Gaussian kernel with standard deviation σ. Total energy functional is defined by:

)(ω)(λ)(νλ,g, φφφφφφφφφφφφ gg ALΕ += (13)

where λ and ω are constant, )(φφφφgL and )(φφφφgA are defined by:

∫ ∇=Ω

dd)δ()( yxgg φφφφφφφφφφφφL (14)

∫ −=Ω

d)dH()( yxgg φφφφφφφφA (15)


33

The functional E can be written as:

)δ(ω))div(λδ)div(∆µ φφφφφφφφφφφφφφφφ


φφφφgg −

∇∇−

∇∇−−=

∂∂

(E

(16)

where ∆ is Laplace operator. The process for minimization of the functional E is the following:

)δ(ω))div(λδ()div(∆µ φφφφφφφφφφφφφφφφ


φφφφgg

t+

∇∇+

∇∇−=

∂∂

(17)

The numerical algorithm is following (Fig. 7): • from the level set function (initial) at a time level t, find necessary interface

information, • calculate H & δ, • update the level set function, • reinitialization, • check convergence.



34

Fig. 8. The image segmentation - the original image and reconstruction after the 200 iterations Figure 8 presents the image segmentation in the following iterative process. The

algorithm of the image reconstruction consists the variational level set method. The zero level set function was defined the near edge of the image (6 pixels). The final contours have the red colour on the original images. These contours represent the zero value of the level set function. The segmentation gives good results, because the region borders accurately locating the object edges. The process reconstruction is finished after the 200 iterations.

5. Variational level set method with Mumford-Shah model

An energy for a function (x, y) is defined as below: )c,c()(µ)( 21,ΕΡΕ φφφφφφφφφφφφ εεεε+= (18)

The functional can be written as:

( ) ( ) ( ) dΩudΩuuη)(ωµC\Ω

2

Ω

2o ∫∫ ∇+−++= CCuF LP, φφφφ (19)

The formulation of the variational level set method with Mumford-Shah model is following:


35

( )

( ) ( ) ))dΩH(-(1cuλ)dΩH(cuλ

dΩ)H(ωdd1)(2

1cc

Ω

22o2

Ω

21o1

Ω

221

φφφφφφφφ

φφφφφφφφφφφφΩΩΩΩ

∫∫

∫∫

−+−+

∇+−∇= yxF ,,

(20)

The process for minimization of the functional E is the following:

( ) ( )

+−

∇∇⋅∇+

∇∇−=

∂∂ 2

2o22

1o1ε c-uηc-uηω)(δ)div(∆µφφφφφφφφφφφφ


φφφφt

(21)

The numerical algorithm (Fig. 9): • from the level set function (initial) at a time level t, find necessary interface

information, • calculate coefficients c1, c2, • update the level set function, • reinitialization, • check convergence.

Figure 10 presents the roentgen images segmentation in the iterative process. The algorithm of the image reconstruction consists variational level set method and the Mumford-Shah function.



36

a)

b)

c)

d)

Fig. 10. The image segmentation: a) the oryginal image, b) after 10 iterations, c) after 50 iterations, d) after 500 iterations

6. Conclusion

The applications of the level set function for image segmentation was presented in this paper. The level set idea is known to be a powerful and versatile tool to model evolution of interfaces. The piecewise-constant segmentation of the image allows for more two segments. Variational formulation for geometric active contours that forces the level set function to be close to a signed distance function. The proposed algorithms have been used to real pictures with promising results in the roentgen images segmentation.


37

References

[1] Rymarczyk T., Filipowicz S.F., Sikora J., Tymburski M.: Variational Level Set Methods in the Roentgen Images Segmentation. COMPUMAG 2009, Florianópolis, Brasil, November 22-26, 2009.

[2] Li C., Xu C., Gui C., and M. D. Fox., “Level set evolution without re-initialization: A new variational formulation”, In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), volume 1, pages 430–436, 2005.

[3] Mumford D., Shah J.: Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., (42):577–685, 1989.

[4] Osher S., Fedkiw R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York 2003.

[5] Osher S., Sethian J.A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. J. Comput. Phys. 79, 12-49, 1988.

[6] Osher, S., Fedkiw, R.: Level Set Methods: An Overview and Some Recent Results. J. Comput. Phys. 169, 463-502, 2001.

[7] Osher S., Santosa F.: Level set methods for optimization problems involving geometry and constraints. Frequencies of a two-density inhomogeneous drum. Journal of Computational Physics, 171, pp. 272-288, 2001.

[8] Sethian J.A.: Level Set Methods and Fast Marching Methods. Cambridge Univeristy Press 1999.

[9] Vese L. Chan T.: A new multiphase level set framework for image segmentation via the Mumford and Shah model. CAM Report 01-25, UCLA Math. Dept., 2001.


38

Creating patient-specific Finite Element Models with a Simple Mesh Morpher

Michał Borysiak, Zuzanna Krawczyk, Jacek Starzyński

Warsaw University of Technology 00-662 Warszawa, ul. 75 Koszykowa, e-mail: [email protected]

The paper presents a simple 3D finite element mesh morpher aimed at creation of patient-specific models of human body parts. These models are to be used in realistic simulation of magneto- and electrotherapeutic treatment. The presented morpher uses simple algorithm of guided stretching which needs only a few measurements of patients body, but it may deform some finite elements. A public domain code Stellar is used to fix these problems.

1. Introduction

Patient specific models of bioengineering phenomena are nowadays becoming more and more popular [2,3,4]. Using them makes possible more precise investigation of bioelectromagnetic phenomena and planning of sophisticated modern therapies and evaluations. However, creation of realistic, precise finite element models of human body is usually based on the exhaustive input data. It is also a time consuming process, which cannot be yet fully automated.

In the classical approach to realistic model creation one starts with fine quality cross-section images of human body. These may be taken from a topographic scans or, in case of base, averaged models, from the available digital images datasets such as the Visible Human Project [4]. Based on such images, segmentation exhibiting the desired tissue distinction is created. Segmented images are then layered together to build a digital, voxelized model of the body. Further smoothing of the model may be necessary if the finite element mesh needs to be obtained.

The whole process takes several hours of work, even for relatively simple parts of body. The most difficult part – segmentation – is not yet fully automated, but extensive research in the picture segmentation and evaluation will probably solve these problems in the near future. However, the input data acquisition process will still remain difficult, costly, and time consuming.

2. The method

The authors would like to propose another approach, which should allow to create simplified yet quite realistic models with minor computational efforts and only a few measurements of the patient body. The presented work is a part of the larger project aimed on the creation of software which will be used by medical staff

M. Borysiak, Z. Krawczyk, J. Starzyński / Creating patient-specific Finite Elements Models…

39

in planning of electrical and magnetic therapeutic treatment. For such applications we need a tool which will quickly create a patient-similar model of body parts.

In our approach we like to minimize the input data to the absolute minimum. Thus we start with an universal, average sized fine model created using the classical procedure with fine quality input data. This fine “standard” model is created only once. Then it is used as foundation of the individualized models which are obtained by transformation of the base one. Simple measurements of external dimensions of the patients body form set of input data, which should allow to morph (shrink and/or stretch) the base model, to fit it to the given patient. This attitude will surely produce a model only roughly compatible the concrete patient but still it will be usable for presenting electric or magnetic field of external stimulator in the model similar to the patient body.

3. The implementation

The 2D implementation of the proposed methodology was shown in [1]. Here we shall present the first 3D implementation.

Fig. 1. Set of vectors V with initial points on triangular surface mesh T

Let us assume that the base model to which we apply our method has a closed,

connected external surface. Further, we assume that morphing is defined by a set of vectors V determining displacements of several characteristic points lying on the model surface to the desired position on the destination surface and the invariance point CP of the transformation. Initial points of vectors from V can be connected to create a triangular surface mesh T (Fig. 1). Each triangle of this mesh can be regarded as a face of a tetrahedron t with the opposite vertex coinciding with CP. The set of the tetrahedra defines a connected and comprehensive division D of the space, where the division of the outer space is defined by extending the tetrahedron edges beyond the triangles from T. Each of the model mesh nodes belongs to one


40

of the tetrahedron from D. The algorithm defines the displacement of a given node ni as a weighted sum of vectors (from V) corresponding to the vertices of the triangle determining the tetrahedron to which ni belongs (see Fig. 2).

Fig. 2. Details of the morphing algorithm

More precisely, for each node ni of the base model: 1. we find a triangle Tt ∈ and a point n'i belonging to t such that n'i is a

projection of ni along the the ray CP - ni , 2. we define the displacement of ni as a weighted sum of three vectors from V

which have initial points in vertices A, B and C of the found triangle t: vi =aA r AV A+aB r BV B+aC rC VC (1)

where weights are calculated as follows (P is the area of the triangle)

aA=P∆BCn'i

P∆ABC

, aB=P∆An'i C

P∆ABC

, aC=P∆An'i B

P∆ABC

(2)

CPA

CPn=r i

A −−

, CPB

CPn=r i

B −−

, CPC

CPn=r i

C −−

Practical implementation of the above algorithm requires a prior definition of the displacement vectors V and the invariance point CP. For the parts of the body the shape of which is close to spherical, the choice of CP is straightforward: it can be the center of the sphere or any point close to it, like the center of mass. An excellent example of a solid of such characteristic is a model of human head. However, due to the complicated structure of brain, internal structure of a real patient's head can differ significantly from its morphed model, even if they both


41

have similar external shape[2]. Thus, for the first implementation of the algorithm, body parts with simpler internal structure are more suitable. There are many examples of such parts, for instance arm, forearm or leg. They are however elongated and their symmetry is rather cylindrical, not spherical. In case of such elongated shapes we chose the whole axis for model mesh, which remain invariant during the transformation.

The morphing algorithm can be easily adapted to cope with this situation. After selecting the axis we adjust the length of the model mesh to the measured length of patient's body part. It is done by simple scaling the model along its axis. The set V of the displacement vectors is generated from the measured points on the patient's body. These points are the end points of the displacement vectors. The initial points are obtained as the projections of the endpoints on the model surface, perpendicular to its axis. Further, for any node ni of the original model mesh, we project it on the model axis and regard the projection as a node specific invariance point CPi. Then, we can apply the formulas given by Eq. 1 and 2 without further modifications.

We rely on the input data that is taken in two perpendicular directions in a few planes along the model axis. Only the outer dimensions are measured. To save the measurement time, the number of the points taken is rather limited and not sufficient to precisely define the morphing. Additional points are generated by assuming that each cross section in the plane perpendicular to the axis has an elliptical shape with the diameters determined by the measured points. Still further points can be obtained along the axis as a result of spline interpolation between the points from subsequent cross sections. The simplicity of input data is stressed by the graphical user interface which is shown in Fig. 2.

Fig. 3. The essence of the graphical user interface: to setup the morpher one has to measure thickness of an elongated body part into perpendicular dimensions at five planes along the part axis.

Total length of the body part is measured separately


42

For the sake of efficiency the algorithm was implemented entirely in C++ programming language. Only the ISO standard library was used which ensures program portability. The program can read and write a simple text grid format (Diffpack library standard [7]).

Fig. 4. The initial model (before applying morphing – the external mesh)

and the model after morphing (internal mesh - shaded)

Fig. 5. A part of the mesh representing bones – before applying morphing (external mesh)

and after the transformation (shaded internal mesh)

We have applied our method to an exemplary mesh in a Diffpack format representing model of a thigh and shank. The mesh has been build on the basis of scans taken as a part of The Visible Human Project [5]. It consists of two domains representing the bones and the soft tissues. The total number of tetrahedra in the mesh is 1.081.053 while the number of vertices is 186.849. The morphing transformation applied thinned the mesh by 26% along the Y axis and 18% along the Z axis.


43

As we explain in the next section, the quality of a mesh with respect to the FEM can be estimated by measuring the range of the dihedral angles of the mesh tetrahedra. The applied morphing transformation, as always, has worsen the quality of our model mesh. For the original model, the dihedral angles span a range from 3,116° to 174,6°. After the transformation it changes to: 0,0155° – 179, 97° which means that the resulting mesh contains almost planar, degenerated tetrahedra.

One can wonder how the morphing transformation, based on the measurements of the outer dimensions of the model, deforms its inner structure represented in our case with the subdomain mesh of the bones. The result is encouraging: the bones get thinned as desired. They change they shape but not significantly and one can easily recognize their characteristics shapes and arrangement.

4. Improvement of the mesh quality

According to the morphing algorithm – only vertices are moved, and it is not

taken into consideration how their displacement affects connections between vertices (tetrahedron edges and faces). Mesh morphing may cause the deterioration of the quality of some tetrahedral mesh elements which in turn may limit their usability for the Finite Element Method analysis. Bad quality elements can be defined as those tetrahedrons the shape of which significantly differs from regular tetrahedra. (Large dihedral angles have negative effect on interpolation error, too small angles cause bad stiffness matrix conditioning). We use a public domain code Stellar [6] in order to improve the quality of morphed meshes. According to the authors of Stellar, the quality of the whole mesh depends not on the average quality of its elements but on the quality of the worst element. Therefore, Stellar concentrates on improving the quality of the worst elements.

Stellar is highly configurable application. The program implements a wide choice of different mesh improvement operations, such as vertex smoothing, different topological operations including vertex insertion. Smoothing operations are moving vertices, but they do not change connections between them, topologiacal operations interfere with internal mesh structure, they may change number of verticies or faces in the mesh. According to [6], the most effective way to improve the mesh consists of applying to mesh all of the above mentioned operations, however, in principle, any set of proposed operations can be chosen. Stellar introduces four quality measures, which can be applied to mesh improvement. Quality measure t is defined as a strictly increasing function q(t), with its maximal value 1 corresponding to a regular tetrahedron. Those measures are: minimum sine – minimum sine of each of six dihedral angles of tetrahedron; biased minimum sine – sines of obtuse angles in tetrahedron are multiplied by a given coefficient, then the minimum sine is chosen; radius ratio - radius of inscribed sphere of the tetrahedron divided by the radius of circumscribed sphere of this tetrahedron, normalized in such a way that the maximum measure value equals 1;


44

volume-length ratio – volume of the tetrahedron divided by the square root of the sum of squares of tetrahedron edge lengths, with the denominator cubed. The measure is multiplied by such a coefficient that the maximum measure value equals 1.

In order to test if the way how Stellar improves meshes is useful for our application, it was applied to a number of different meshes of simple geometrical shapes. Inter alia, it has been checked how the program can cope with ellipsoids with various mesh densities and to what extent it will improve meshes which span the same shape but have different quality parameters.

In a similar way as during the morphing, meshes with poor quality were created from the good quality meshes by scaling them along one of the axes with an arbitrary factor. This straightforward procedure allowed us to obtain meshes with small and large dihedral angels.

The results have shown, that the level of improvement of meshes with good quality parameters and those of “bad” meshes is similar. Obviously, improved meshes with the initial bad quality still have worse final quality than improved meshes which have had better quality before improvement. Improvement of meshes with low quality takes Stellar more time than improvement of meshes with better quality.

It turned out that two of Stellar quality measures are more efficient than the other: biased minimum sine and volume-length ratio. Satisfactory results were also achieved by the combination of two quality measures when during the first iteration the mesh was improved with the minimum sine quality measure while during the second iteration the volume-length-ratio measure was applied.

The biased minimum sine measure does not recognize as bad ones the so called spire tetrahedrons (very long, high tetrahedrons) because value of this measure depends only on dihedral angles of the tetrahedron. This is not the case for the volume-length ratio measure. Spire tetrahedrons do not worsen discretization error or stiffness matrix conditioning, although they may cause problems because of precision of calculations in MES which is inversely proportional to the length of the longest edge of the tetrahedron.

A simple example of the application of Stellar to the ellipsoid shape has been depicted in Figure 6.

Fig. 6. Ellipsoid mesh before (a) and after (b) improving it with Stellar: the smallest dihedral angle

was improved from 9.6° to 27,4° while the largest one changed from 164,7° to 142,63°


45

Stellar can be used to improve tetrahedral models of parts of human body, although not without problems in some areas. The mesh improvement schedule in the program is designed to achieve the quality of tetrahedron that is as good as possible. Thus, the duration of the improving operation is not the most important factor. Improvement of large meshes can take a considerable long time. Moreover, Stellar does not allow to split a mesh and to form subdomain meshes which is desired in modelling parts of human body. Despite these inconveniences Stellar can be applied to improving Patient-Specific Finite Element Model.

5. Conclusion

The simple mesh morphing algorithm combined with the mesh quality improvement program allows to obtain realistic and individually shaped body models with minimal input data.

References

[1] R. Szmurło, J. Starzyński, Specimen-specific finite element models of human head

obtained with mesh-morphing, Przeglad Elektrotechniczny (Electrical Review), R. 85 NR 4/2009, pp. 47-49.

[2] M. Tada, H. Yoshida, M. Mochimaru, Geometric Modeling of Living Tissue for Subject-Specific Finite Element Analysis, Engineering in Medicine and Biology Society, 28th Annual International Conference of the IEEE, 2006, pp. 6639-6642.

[3] I. A. Sigal, M. R. Hardisty, C. M. Whyne, Mesh-morphing algorithms for specimen-specific finite element modeling, J Biomech. 2008, pp. 1381-1389.

[4] N. Inou, M. Koseki, M. Jonishi, K. Maki, Patient-Specific Finite Element Modeling of Human Skull Based on X-ray CRT Images, Proceedings of 1st AOTULE Studens Workshop and 5th KAIST-Tokyo Mechanical Engineering Workshop, Daejeon, Korea, 2007, p. 17.

[5] Visible Human Project: http://www.nlm.nih.gov/research/visible. [6] Aggressive Tetrahedral Mesh Improvement Bryan Matthew Klingner and Jonathan

Richard Shewchuk, Proceedings of the 16th International Meshing Roundtable (Seattle, Washington), pages 3–23, October 2007.

[7] H. P. Langtangen. Computational Partial Differential Equations - Numerical Methods and Diffpack Programming. Texts in Computational Science and Engineering, vol 1. Springer, and edition, 2003.

ACKNOWLEDGEMENT Research described in this was partially suported by Polish Ministry of Education grant

no. N N510 148838.


46

Susceptibility of electrical network to ferroresonance occurrence

Józef Wiśniewski

Technical University of Łódź 90-924 Łódź, ul. Stefanowskiego 18/22, e-mail: [email protected]

Edward Anderson, Janusz Karolak

Institute of Power Engineering 01-330 Warszawa, ul. Mory 8, e-mail: edward.anderson,

[email protected]

The calculations of electrical network susceptibility of chosen 110 kV, 220 kV and 400

kV networks to ferroresonance occurrence, its type and parameters were performed in the study. The influence of such parameters as voltage transformer (VT) magnetization characteristic, equivalent network capacitance, and the breaker grading capacitance on ferroresonance was investigated. The calculations were performed using the EMTP/ATP program. Some of the results were presented in this paper.

1. Introduction The ferroresonance phenomenon in the power network has been known and described for many years. However, it is difficult to investigate this phenomenon because of its significant sensitivity to even small changes in network parameters [1, 2]. Also, the form and parameters of the network equivalent scheme of devices like VT, power lines and breakers exert an effect on the phenomenon character during computer simulations. Looking for the range of network parameters, in relation to ferroresonance appearance by means of the simulation method with gradually changing network parameters, is a long-term process and does not guarantee finding a proper solution. The field measurement method aiming at finding resistance of network to ferroresonance is not effective because a slight change in investigation conditions can significantly affect obtained results. Ferroresonance in the investigated network can appear as a result of interaction between VT nonlinear inductance, network capacitance, and a breaker grading capacitance [1, 2]. The simulation investigation of susceptibility of 110 kV, 220 kV and 400 kV electrical networks to ferroresonance, its type, and parameters were carried out. The calculations were performed using the EMTP/ATP program. The influence of such parameters as VT magnetization characteristic, its burden, equivalent network capacitance and the breaker grading capacitance on the ferroresonance phenomenon was investigated. The opening of high voltage breaker was the impulse which initiated the ferroresonance.

J. Wiśniewski, E. Anderson, J. Karolak, / Susceptibility of electrical network…

47

2. Results of ferroresonance calculations The scheme of the 110 kV network, taken under consideration for ferroresonance calculation is shown in Fig. 1. After opening the breaker Q, the 110 kV network, i.e. busbars and lines replaced by capacitance CE and inductive voltage transformer VT is supplied by the grading capacitance CQ, which value depends on a breaker type within the range of few hundred to few thousand pF.

VT 110 kV

110 kV

CQ

CE Q

Fig. 1. Scheme of the 110 kV network with ferroresonance phenomenon

The magnetization characteristic of 110 kV VT used in substation is based on field measurements, Fig. 2.

0

200

400

600

800

0 0.05 0.1 0.15 0.2 0.25

i peak[A]

psi p

eak[

Wb*

turn

]

Fig. 2. The magnetization characteristic of 110 kV VT

The equivalent scheme of the investigated 110 kV network is presented in Fig. 3. The scheme can be described by the set of equations:

)1CC(RK;

RC1K);1

RR()1

CC(K

)];tcos(UC

)(i)]ana(KK[U[K/1dt

dU;U

dtd

Q

Es3

pQ2

p

s

Q

E1

mQ

21nn1321 (1)

where: -flux linkage, )tcos(mU)t(u - source voltage,

3/2*kV110mU ; k3.30sR ; 910pR .


48

u(t)

Rs

Rp

CQ

(i2)

i

i2 i1 i3

CE

VT

Q

Fig. 3. Equivalent scheme of the investigated 110 kV network taken for ferroresonance calculation

Magnetization characteristic of VT can be described by the equation:

nna1a)(2i (2)

where: 61017.31a ; 1610025.1na ; 5n . The graphical solution of the equations describing the network for steady state for chosen parameters is presented in Fig. 4. The intersection of the u vs. i network characteristic and the Um line representing the source voltage determines the possible operation points 1, 2 and 3.

-600

-400

-200

0

200

400

600

-200 -150 -100 -50 0 50 100 150 200

i[mA]

u[kV]

um 1

2

3

Fig. 4. Possible operation points. Solution for CQ=1000pF, CE=2000pF

(1 and 2 - stable operation points, 3 - unstable operation point) The graphical method, though simple, has a numerous limitations [1, 2, 3]. More precise results, more similar to those observed in the network, provide the


49

calculations by using the EMTP program. For different sets of parameters, the network behavior after the breaker opening was performed. In the investigated range of CQ and CE capacitance variation, ferroresonance did not appear or it appeared as transient short-time or stable with network frequency of fs = 50 Hz, 1/3fs, 3fs or stable with chaotic shape. For example, Fig. 5 shows the transients of phase voltages, VT currents, residual voltage and Fourier transform of phase voltages for ferroresonance with frequency of 1/3fs and Fig. 6 presents the ferroresonance with a chaotic shape.

0E+0

2E+4

4E+4

6E+4

8E+4

0 50 100

150

200

250

300

350

400

450

500

(f ile juk123_3f az.pl4; x-v ar t) v :DA v :DB v :DC 0.0 0.2 0.4 0.6 0.8 1.0 1.2[s]

-90

-45

0

45

90[kV]

(f ile juk123_3f az.pl4; x-v ar t) c:DA -EA c:DB -EB c:DC -EC 0.0 0.2 0.4 0.6 0.8 1.0 1.2[s]

-70

-35

0

35

70[mA]

(f ile juk123_3f az.pl4; x-v ar t) v :3U0_1 0.0 0.2 0.4 0.6 0.8 1.0 1.2[s]

-40

-20

0

20

40[V]

Phase voltages on VT connectors

Phase currents in VT's

Residual voltage 3U0 on VT connectors

Fourier transform of phase voltage on VT connectors

u [kV]

f [Hz]

Fig. 5. Phase voltages, VT currents, residual voltage (3U0) and Fourier transform of phase voltage on the secondary side of VT during the stable ferroresonance with frequency of 16.6 Hz

(CQ=300 pF, CE= 250 pF)


50

0E+0

2E+4

4E+4

6E+4

8E+4

0 50 100

150

200

250

300

350

400

450

500

u [kV]

f [Hz]

0.0 0.2 0.4 0.6 0.8 1.0 1.2[s]-200

-100

0

100

200[kV]

0.0 0.2 0.4 0.6 0.8 1.0 1.2[s]-0.70

-0.35

0.00

0.35

0.70[A]

0.0 0.2 0.4 0.6 0.8 1.0 1.2[s]-150

-75

0

75

150[V]

Phase voltages on VT connectors

Phase currents in VT's

Residual voltage 3U0 on VT connectors

Fourier transform of phase voltage on VT connectors

Fig. 6. Phase voltages, VT currents, residual voltage (3U0) and Fourier transform of phase voltage on the secondary side of VT during the stable chaotic ferroresonance (CQ=2000 pF, CE= 1000 pF)

The results for the complete range of investigated parameters CQ and CE were placed on the ferroresonance map, whose fragment is presented in Fig. 7. It shows the areas free of ferroresonance (N), with stable chaotic ferroresonance (T/Ch), with stable harmonic ferroresonance (e.g. T/16 Hz), or ferroresonance disappearing after a short time (e.g. Z/0.9s). The maximal observed values of ferroresonance overvoltages are also visible. The map is calculated for unloaded voltage transformers. The similar ferroresonance maps, but for voltage transformers loaded with resistance 10 (in the open triangle of secondary coils) are presented in Fig. 8. The map of ferroresonance for the 400 kV network with unloaded voltage transformers is shown in Fig. 9.


51

T/16,6Hz70

T/16,6Hz 80

T/Ch 100

T/Ch 120

Z/1 45

T/Ch 120

T/Ch 130

T/Ch 140

T/Ch 150

T/Ch 160

T/Ch 160

T/Ch 160

T/Ch 170

T/14Hz 72

T/Ch 100

Z/1 110

T/10Hz 40

T/Ch 135

T/Ch 150

T/16,6Hz 160

T/Ch 160

T/Ch 180

T/Ch 180

T/Ch 180

T/Ch 200

T/16,6Hz 80

Z/0,6 99

N T/Ch 140

N T/Ch 140

T/Ch 160

T/Ch 170

T/Ch 170

T/Ch 200

T/Ch 180

T/Ch 200

T/Ch 200

T/16,6Hz 80

N N T/Ch 140

N T/Ch 170

T/Ch 170

T/Ch 200

T/Ch 260

T/Ch 270

T/Ch 270

T/Ch 270

T/Ch 270

T/16,6Hz 100

T/Ch 100

N T/Ch 150

N N T/50Hz 250

T/50Hz 250

T/50Hz 250

T/50Hz 260

T/50Hz 260

T/50Hz 270

T/50Hz 270

N N Z/0,5 150

T/50Hz 225

T/16,6Hz 72

T/50Hz 235

T/50Hz 230

T/50Hz 250

T/50Hz 255

T/50Hz260

N T/50Hz 275

T/50Hz 280

Z/0,9 80

N T/50Hz 215

T/50Hz 200

T/16,6Hz 70

N T/50Hz 240

T/50Hz 250

T/50Hz 255

N T/50Hz 265

T/50Hz 275

T/50Hz 280

CE [pF]

CQ [pF] 250

500

1000

1500

2000

3000

1000 300

2500

600

T/Ch 130

2000 3000 4000 5000 6000 2500 3500 4500 5500 1500

Fig. 7. The ferroresonance map for the investigated 110 kV network for unloaded VT (values of overvoltage in [kV])

T/16,6Hz70

N Z/0,5 100

Z/0,8 110

N Z/0,4 120

T/Ch 140

Z/0,5 130

T/Ch 140

T/16,6Hz 130

T/Ch 140

T/Ch 170

T/Ch 160

T/16,6Hz 70

Z/0,3 90

Z/0,4 105

N T/Ch 125

T/Ch 150

T/16,6Hz 120

T/16,6Hz 120

T/Ch 165

T/Ch 180

Z/0,5 170

Z/0,5 195

T/16,6Hz 80

Z/0,4 100

T/Ch 110

T/Ch 130

N Z/0,2 140

Z/0,2 160

T/Ch 160

T/Ch 170

Z/0,3 160

Z/0,7 185

T/Ch 200

Z/0,9 210

T/16,6Hz 75

T/16,6Hz90

Z/0,2 110

Z/0,9 150

N T/Ch 145

Z/1 170

T/Ch 190

T/Ch 200

T/Ch 200

T/Ch 210

T/50 280

T/Ch 310

N Z/0,2 110

T/Ch 125

Z/0,5 160

N Z/0,4 190

Z/0,3 200

Z/0,3 190

T/50Hz 260

T/50Hz 265

T/50Hz 270

T/50Hz 270

T/50Hz 280

Z/0,4 100

N Z/0,6 145

T/50Hz 230

N T/50Hz 230

T/50Hz 245

T/50Hz 250

T/50Hz 255

T/50Hz260

T/50Hz 265

T/50Hz 275

T/50Hz 280

Z/0,4 100

Z/0,3 120

Z/0,3 180

T/50Hz 220

N T/50Hz 235

T/50Hz 240

T/50Hz 250

T/50Hz 250

T/50Hz 260

T/50Hz 270

T/50Hz 270

T/50Hz 280

CE [pF]

CQ [pF] 250

500

1000

1500

2000

3000

1000 300

2500

600

Z/0,5 120

2000 3000 4000 5000 6000 2500 3500 4500 5500 1500

Fig. 8. The ferroresonance map for the investigated 110 kV network for voltage transformers loaded with resistance 10 (in opened triangle of secondary coils)


52

CE [pF]

CQ [pF]

250

500

1000

1500

2000

3000

2500

1000 2000 3000 4000 5000 6000 600 1500 2500 3500 4500 5500 300

Z/0,2 220

T/16,6 280

T/16,6 310

T/16,6 360

N

T/16,6 390

T/16,6 420

T/16,6 440

T/16,6 470

T/16,6 490

T/Ch 390

Z/0,4 380

Z/0,4 360

T/16,6 240

T/16,6 330

T/16,6 330

T/16,6 370

N T/16,6 400

T/16,6 430

T/16,6 450

T/16,6 480

T/16,6 500

T/Ch 390

Z/1,2 380

T/50 330

T/Ch 290

T/Ch 280

Z/0,2 370

T/16,6 450

N T/16,6 420

T/16,6 440

T/16,6 470

T/16,6 490

T/16,6 510

Z/0,5 380

Z/0,2 360

T/50 340

Z/0,3 290

Z/0,1 350

N T/Ch 500

N T/Ch 540

T/Ch 540

T/16,6 490

T/16,6 500

Z/0,2 380

Z/0,2 360

Z/0,6 360

T/50 360

Z/0,3 360

N T/Ch 540

T/Ch 650

N T/Ch 610

T/Ch 620

Z/0,2 660

Z/0,3 370

T/16,6 570

T/16,6 560

Z/0,4 310

Z/0,2 310

Z/0,2 460

Z/0,4 540

Z/0,2 490

Z/0,2 720

N T/Ch 760

T/25 800

T/Ch 700

Z/0,2 320

Z/0,2 320

Z/0,2 310

Z/0,2 310

T/50 320

Z/0,3 480

Z/0,7 760

T/Ch 900

T/Ch 900

Z/0,3 310

Z/0,3 350

T/Ch 820

Z/0,2 320

Z/0,2 320

Z/0,2 320

Z/0,5 330

T/50 330

Z/0,2 320

Fig. 9. The ferroresonance map for the investigated 400 kV network for unloaded VT

(values of overvoltage in [kV])

3. Conclusions The results of the simulation calculations of the investigated phenomenon, its properties and parameters for 110 kV substation with unloaded VT were presented as ferroresonance maps. Similar calculations for 220 kV and 400 kV networks with different VT types were performed. The VT parameters were measured in the testing station or were obtained from producers. The calculated results were partly verified by comparing them to those of network measurements. The study results can be useful for planning substation work and also for explaining VT or other network devices faults occurring in the past caused by ferroresonance overvoltages.

References [1] Ferraci P., Ferroresonance. Cahier technique. No. 190, Groupe Schneider, 1998. [2] Jacobson D.: Field Testing, Modelling and Analysis of Ferroresonance in a High Voltage

Power System. Ph.D. Thesis, University of Manitoba, Winnipeg, Canada 2000. [3] Valverde V., Mazon A.J., Zamora I., Buigues G.: Ferroresonance in Voltage

Transformers: Analysis and Simulations. International Conference on Renewable Energies and Power Quality (ICREPQ'07) Sevilla, Spain.

[4] Wisniewski J., Anderson E., Karolak J.: Search for Network Parameters Preventing Ferroresonance Occurrence. 9th International Conference Electrical Power Quality and Utilisation, 2007, Barcelona, Spain.


53

Reverse reaction magnetic field in two-wire

high current busduct

Zygmunt Piątek, Dariusz Kusiak, Tomasz Sczegielniak Czestochowa University of Technology

42-200 Częstochowa, ul. Brzeźnicka 60a, e-mail: [email protected], [email protected], [email protected]

Work has shown how a reverse reaction magnetic field influences the whole magnetic field within the conductor and its vicinity. A description of this is presented in formulae for relative field values and parameters taking into account frequency, conductivity and diameter of the conductor. This has shown the field to be an elliptical field.

1. Introduction

Unshielded double-wire high current busducts with tubular conductors (Fig. 1) can be installed in switching stations NN and WN [1-3].

R2

rXY

y’ y

x’

x

d

X(r,Θ,z)

1

γ1

J21

γ1

Θ

r

R1

2 μ0

Φ

I1

ρ

R1 R2

μ0

I2

J12

Fig. 1. Two-wire high-current busduct with the currents 1I and 2I

Magnetic field )Θ,r(wH of current 1I in the first tubular conductor induces on the second neighboring parallel tubular conductor eddy currents

)Θ,r(J)Θ,r( z 2121 1J (fig.1), which in external area generate reverse reaction

magnetic field )Θ,r(rrH [4-6].

Z. Piątek, D. Kusiak, T. Szczegielniak / Reverse reaction magnetic field in two-wire…

54

2. Magnetic field in the external area of the tubular conductor

Magnetic field )Θ,r(extH in the external area ( 2Rr ) of the second tubular conductor

)Θ,r()Θ,r()Θ,r( rrwext HHH (1)

where )Θ,r(rrH is the reverse reaction magnetic field outside of the conductor.

The electric field strength )Θ,r(rrE , accompanying the magnetic field

)Θ,r(rrH in the external area of the conductor ( 2Rr ), fulfills the scalar Laplace’s equation

02 )Θ,r(E rr (2) whose solution, the separation of variablies method, has the form

nΘcosr

B)Θ,r(E)Θ,r(En

nnn

rrn

rr

11

1 (2a)

where nB is a constant, which will be calculated from boundary conditions. Applying the second Maxwell’s equation to formula (2a), we obtain the

complex form of the vector of the reverse reaction magnetic field strength outside the conductor

)Θ,r(H)Θ,r(H)Θ,r( rrΘΘ

rrrr

rr 11 H (3) where

1

10

j

n

nnrr

r nΘsinr

Bn)Θ,r(H

(3a)

and

1

10

j

n

nnrr

Θ nΘcosr

Bn)Θ,r(H

(3b)

Constant nB is [7]

cn

cnn

nn d

sdRR

RΓnI

B

2

211

10 2

j

(4)

where

)RΓ(K)RΓ(I)RΓ(K)RΓ(IRΓ)RΓ(K)RΓ(K)RΓ(I)RΓ(K)RΓ(In

)RΓ(I)RΓ(I)RΓ(Kns

nnnn

nnnnn

nnnccn

21111111121111

2112111111211

11111121

2

(4a)


55

and )RΓ(K)RΓ(I)RΓ(K)RΓ(Id nnnncn 211111111211 (4b)

where functions )RΓ(I n 11 , )RΓ(K n 11 , )RΓ(K n 21 , )RΓ(In 111 , )RΓ(Kn 111 ,

)RΓ(In 211 , )RΓ(Kn 211 , )RΓ(In 111 , )RΓ(Kn 111 , )RΓ(In 211 and

)RΓ(Kn 211 are the modified Bessel’s functions of the firsts and second kind respectively and of n, n-1 and n+1 order [8].

In the above formulas

11 j2 j4

exp[j j kkk]Γ

(5)

in which attenuation constant

12

01 k (5a)

where δ is the electrical skin depth, in an angular frequency, means electrical conductivity of conductor, and permeability of free space -17

0 mH 10 4 [9-10].

Therefore the reverse reaction magnetic field in the external area of the second tubular busbar is determined by the formula (3), where its components, after replacing the Bn constant, are

1

22

11

1

2 n cn

cnnn

rrr nΘsin

ds

dR

rR

rRΓI)Θ,r(H

(6)

and

1

22

11

1

2 n cn

cnnn

rrΘ nΘcos

ds

dR

rR

rRΓI)Θ,r(H

(6b)

If the above formulas refer to value

2

10 2 R

IH

(7)

and following introduction of the relative distance between the conductors

12

Rd

c (8)

relative variable

2Rr

(9)

and parameter


56

)RR

cc 10 ( czymprzy 2

1 (10)

Hence relative value components for the reverse reaction magnetic field are defined by the formulaes

1

11 j2

1n cn

cnn

c

n

cc

rrr nΘsin

ds)Θ,(h

(11)

and

1

11 j2

1n cn

cnn

c

n

cc

rrΘ nΘcos

ds)Θ,(h

(11a)

where 1 and 20 Θ .

The distribution of the above components within the function of parameter c are presented in Figures 2 and 3.

a)

b)

Fig. 2. The distribution of relative radial component values reverse reaction magnetic field: a) the modulus, b) the argument


57

a)

b)

Fig. 3. The distribution of relative tangent component values reverse reaction magnetic field: a) the modulus, b) the argument

3. Distribution of the reverse reaction magnetic field modulus in external area

The set of arguments for the radial and tangential field components are different and therefore at each point the study area the reverse reaction magnetic field of the conductor is elliptic field. The relative value of this field modulus, relative value of the longer ellipsis semi axis expressed by the formula

)Θ,(h)Θ,(h)Θ,(h rr 21 (12) where

)Θ,(h)Θ,(h)Θ,(h rrΘ

rrr j

21

1 (12a)

and

)Θ,(h)Θ,(h)Θ,(h *rrΘ

*rrr

2 j21

(12b)

The distribution of these values on the external surface of the second tubular busbar for various values of the c , parameter versus Θ angle is shown in Figure 4.


58

Fig. 4. The distribution of relative quantity the reverse reaction magnetic field modulus in the external area of the second busbar

For first conductor (fig. 1) the reverse reaction magnetic field has components

1

22

11

2 1 2 n cn

cnnn

nrrr nΘsin

ds

dR

rR

rRΓI)Θ,r(H

(13)

and

1

22

11

2 1 2 n cn

cnnn

nrrΘ nΘcos

ds

dR

rR

rRΓI)Θ,r(H

(13a)

Then, for relative values we have respectively

1

111 j2

1n cn

cnn

c

nn

cc

rrr nΘsin

ds)Θ,(h

(14)

and

1

111 j2

1n cn

cnn

c

nn

cc

rrΘ nΘcos

ds)Θ,(h

(14a)

The distribution of these values on the external surface of the first tubular busbar for various values of the c , parameter versus Θ angle is shown in Figure 5.

In the external area of the tubular busbar the magnetic field of reverse reaction is a field fading quickly, what is demonstrated in Figure. 6.


59

Fig. 5. The distribution of relative quantity the reverse reaction magnetic field modulus in the external area of the first busbar

Fig. 6. The module of the magnetic field of reverse reaction within the tubular busbar external area

4. Conclusions

For a two-wire non-screened busducts the magnetic field distribution in busbars

and in both internal and external area of tubular busbars is irregular, caused by the skin effect, but first of all by the proximity effect.

Figures 2 and 3 show, that the distribution of the magnetic field of reverse reaction in the external area of the busbar depends on the c parameter and is an irregular distribution with regard to the Θ angle. Consequently, the total magnetic


60

field in the busbar and around it is irregular. Figures 4 and 5 show that the reverse reaction magnetic field assumes the highest values in the nearest point of the external source of the magnetic field.

The figures presented above show that the reverse reaction magnetic field, i.e. the external proximity effect and the skin effect should be taken into consideration when the magnetic field of high-current busducts is analysed, also for power frequency applications.

References [1] Piątek Z.: Modeling of lines, cables and high-current busducts (in Polish), Wyd. Pol.

Częst., Czestochowa 2007. [2] CIGRE Brochure No 218.: Gas Insulated Transmission Lines (GIL),WG 23/21/33-

15, CIGRE, Paris, 2003. [3] Nawrowski R.: High-current air or SF6 insulated busducts (in Polish), Wyd. Pol.

Poznańskiej, Poznań 1998. [4] Piątek Z.: Impedances of Tubular High Current Busducts. Series Progress in High-

Voltage technique, Vol. 28, Polish Academy of Sciences, Committee of Electrical Engineering, Wyd. Pol. Częst., Częstochowa 2008.

[5] Baron B., Piątek Z.: Impedance and magnetic field of a tubular conductor of finite length (in Polish), XXIII IC SPETO, Gliwice-Ustroń 2000, ss. 477-484.

[6] Piątek Z., Kusiak D., Szczegielniak T.: Magnetic field of double-poles high current busduct (in Polish), Zesz. Nauk. Pol. Śl. 2009, Elektryka, z.1(209), pp. 67-87.

[7] Kusiak D.: Magnetic field of two- and three-pole high current busducts, Dissertation doctor (in Polish), Pol. Częst., Wydz. Elektryczny, Częstochowa 2008.

[8] Mc Lachan N.W.: Bessel functions for engineers (in Polish), PWN, Warsaw 1964. [9] Piątek Z.: Magnetic field in high-current isolated-phase enclosed bus ducts

surroundings, (in Polish), Zesz. Nauk. Pol. Śl. 1999, Elektryka, z. 166 [10] Piątek Z., Kusiak D., Szczegielniak T.: Magnetic field of the three phase flat high

current busduct (in Polish), Zesz. Nauk. Pol. Śl. 2009, Elektryka, z.1(209), pp. 51-65.


61

Investigation of effectiveness of α-constrained simplex method

applied to design of optimal induction motors

Mirosław Dąbrowski Poznan University of Technology

60-965 Poznań, ul. Piotrowo 3A, e-mail [email protected]

Andrzej Rudeński Institute of Electrical Engineering

04-703 Warszawa, ul. Pożaryskiego 28, e-mail [email protected]

The paper presents a modified nonlinear simplex algorithm with lexicographic order comparison of solutions and its application to the design of optimal induction motors. In the comparison of the solutions generated in the optimization process, both the objective function value and the additional parameter, called the satisfaction level of constraints, have been taken into account. The comparison method assigns some advantage degree to feasible solutions, thus allows for the control of this advantage degree during the optimization process. Special attention has been paid to the choice of the algorithm parameters and to the kind of the mutation operator. The presented algorithm has been implemented in the object-oriented software. Calculation results of the selected double-cage induction motors have been compared with the results obtained with the evolution strategy (μ+λ)-ES and with the hybrid algorithm assembled with the modified Price algorithm. An additional calculation experiment allows for the comparison of exploitation properties between the α-Constrained Simplex Method and the Modified Price Algorithm. As the investigations showed, the presented algorithm can be successively used for the optimization of the induction motors, however, with constraints, which are not very restrictive concerning respective functional parameters.

1. Introduction

Optimization of electrical machines, particularly of induction motors, consists

in a search of a solution determined by the vector of independent variables x, which leads to minimization of the value of the assumed objective function but at the same time to fulfillment of all constraints gi(x) determining the functional machine parameters. Methods of the mathematical programming as well as non-deterministic optimization methods concern tasks in the non-constrained space. In order to take the constraints into consideration several methods have been applied, between others, the methods based on the internal or external penalty function. In the case of the non-deterministic methods usually external penalty function should be applied through adding a penalty component to the objective function value. Various ways of penalty component determination have been described among other works in [7].

M. Dąbrowski, A. Rudeński / Investigation of effectiveness of α-constrained…

62

In [8] a new method for optimization in the constrained search space was proposed. It converts the constrained optimization problem into an unconstrained one. It consists in the use of the modified nonlinear simplex method by entering: first, the special order for comparing solutions and second, the mutation operator. The main modification consists in this that the solutions obtained in the optimization process are judged not only using a sum of the objective function and the penalty component but on the basis of two quantities: a new parameter, which is the constraints satisfaction level, and the objective function value, with respect to variable influence grade of one of these values on the comparison result.

Optimization procedure proposed in work [8] has been tested on several analytically expressed test functions. Very good test results in comparison to the results obtained with other optimization procedures, encouraged authors of this work to the application and examination of the described method for optimization of the induction motors. In this case the objective function is expressed using complex algorithms with many loops and recurrence-iterative procedures.

2. Comparison of solutions using lexicographic order

Comparison of the value of the objective function enlarged by the penalty

component for constraints violation in [8] has been replaced by the lexicographic assessment of solutions generated in the optimization process. These solutions have been assessed on the basis of the objective function values and on an additional parameter, namely the satisfaction level of constraints μ, calculated from the formula:

( ) ( )⎭⎬⎫

⎩⎨⎧ −=

BP xx 1,0maxμ (1)

where P(x) is the penalty component for constraints violation; B is the positive constant (an algorithm parameter).

The value of the penalty component P(x) may be expressed in various ways. Several strategies of its determination are presented in work [7].

In the minimization case, assessment of solutions is carried out on the basis of the relationship:

( ) ( )⎪⎩

⎪⎨

⎧

>=<

≥<⇔<

otherwise for ,

,for ,,,

21

2121

2121

2211

μμμμ

αμμμμ α ff

ffff (2)

where f1, f2 are the objective function values; μ1, μ2 are the satisfaction levels of constraints; α is a variable algorithm parameter.

From formula (2) appears that the solutions with the same level of constraints satisfaction and these, which have bigger or equal satisfaction level of constraints than the varying value α, are assessed only on the basis of the objective function


63

value. Whereas in the case, in which the constraints satisfaction levels of both compared solutions are smaller than α, the solution characterized by the bigger value of parameter μ. is taken as the better one. In this way the comparisons provide a possibility to favor feasible and nearly feasible solutions and to control this privilege in subsequent algorithm iterations. This guaranties support of the equilibrium between the exploration and exploitation capabilities of the optimization procedure. Through appropriate strategy of selection of the parameter μ during the optimization process the algorithm convergence is achieved together with assurance of the solutions feasibility.

In this work a strategy according to the following relationships has been applied:

( )

( ) ( )

( ) ( ) ( )

( ) ( )

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

>

≠≤<−

=≤<+−⋅−

=⎟⎠⎞

⎜⎝⎛ +

=

∑

2 if ,1

0 mod and2

0 if ,1

0mod and2

0 if ,11

0 if,max21

max

max

max

Tt

TtT

tt

TtT

tt

tN

x

t

i iii

α

α

α

βαβ

μμ

α

x (3)

where N is the number of solutions in the set; t is the subsequent number of iteration; Tmax is the maximal number of iterations (algorithm stop criterion); β , Tα are the algorithm parameters.

From relationship (3) it appears that in the first half of the optimization process a value of parameter α is corrected every Tα iterations, while in the second half of the process the solutions are assessed only on the basis of the objective function values. By such strategy of changing parameter α it is desirable to obtain the maximum number of feasible solutions in the first half of the optimization process.

3. Nonlinear simplex algorithm

Algorithm applied in work [8] is a modification of nonlinear simplex algorithm

described in paper [5]. Its essence relies on seeking new solutions inside an n+1-dimensional simplex (n is the number of the problem dimensions) created on randomly selected solutions from the processed set containing N solutions.

During every iteration three unique solutions of the vector of independent variables x: the best xb, the worst xw and the second worst xsw have been defined as follows:

( )kkb f xx min arg=

( )kkw f xx max arg= Nk .,..,2,1= (4)

( )kwksw f xx max arg≠

=


64

By selection of solutions corresponding to the simplex vertices often a selective pressure is applied in favor to better solutions. After each iteration the set of solutions is sorted in a non-growing order respectively to criterion (2). The solutions are therefore arranged from the best to the worst. In this work a selection of solutions with indices i expressed by

( )12 −= rNi (5) relationship has been applied, where r is the random number with uniform distribution in range [0, 1].

The following points are created in every algorithm iteration: the reflection point xr relative to centroid center x0 of the simplex, the expansion point xe, the contraction point xc. The worst solution is replaced by one of them.

Coordinates of the centroid center x0 have been described by formula:

∑≠

=wk

knxx 1

0 (6)

where k is the number of subsequent centroid vertex. During calculations of the centroid center coordinates, according to formula (6),

a point corresponding to the worst solution is omitted (k ≠ w). Reflection point xr, expansion point xe, and contraction point xc are created

according to formulas: ( ) 01 0 >−+= aaa wr xxx

( ) 101 0 <<−+= bbb wc xxx (7) ( ) 11 0 >−+= ccc re xxx

where xw is the worst solution; a, b, c are the constant algorithm parameters. In work [8] besides the mentioned modifications, i.e.: the application of

lexicographic order for comparison of solutions and the use of mutations, repeatedly created simplex has been introduced. The simplex is created in every algorithm iteration. In this process n+2 points participate, n+1 as simplex vertices and the worst point xw from all set of the processed solutions. Such procedure reduces a risk of obtaining wrong optimal solutions as an effect of the lack of affine independence of points corresponding to simplex vertices.

A flow-chart of the nonlinear simplex algorithm with the lexicographic order for comparison of solutions is presented in Fig. 1.


65

swwb xxx ;;

wc xx ⇒

( ) ( )( ) ( ) ( )( )wwcc ff xxxx μμ α ,, <

( ) ( )( ) ( ) ( )( )bbrr ff xxxx μμ α ,, <

wr xx ⇒

wwbc xx ⇒,

( ) ( )( ) ( ) ( )( )bbee ff xxxx μμ α ,, <

( ) ( )( ) ( ) ( )( )swswrr ff xxxx μμ α ,, ≤

rxpoint Reflection

YES

NOexpoint Expansion

NO

YES

01 x simplex,dimension −n

YES

( ) ( )( ) ( ) ( )( )wwrr ff xxxx μμ α ,, <YES

NO

NO

( ) 01 0 >−+= aaa wr xxx

( ) 11 0 >−+= ccc re xxx

( ) 101 0 <<−−= bbb wc xxxcxpoint n Contractio

we xx ⇒

wr xx ⇒

wr xx ⇒

YES NO

N search points

( ) 101, <<−−= bbb bwwbc xxxwbc ,xpoint n Contractio

Nkk ...,2,1, =x

mpa <

[ ]1,0Na =

MutationYES

NO

Fig. 1. A flow-chart of the modified nonlinear simplex algorithm with lexicographic order of solutions comparison


66

4. Mutation operator

In work [8] a mutation has been introduced to the nonlinear simplex algorithm. In every iteration with probability pm the worst solution xw from the processed set undergoes a mutation. If the mutated solution is better as the worst one in processed set, this worst solution is replaced by a new one. In opposite situation, i.e. if the mutation is not applied, normal iteration of the simplex algorithm is carried out. Applied mutation operator is similar to the boundary mutation proposed by Michalewicz in work [4]. That algorithm searched for a feasible solution for the maximal far-distant value of the randomly selected variable in a direction to either the lower or the upper limit of its variation range. In result a solution was created, which lay on the boundary of the feasible space. Whereas in this work a special mutation operator has been applied taking a small extend of feasible space into account as compared to the search space – what is distinctive in optimization of induction motors. For a randomly selected independent variable a feasible solution in the range of its variability has been searched for either bigger or smaller values than a value before mutation. If ten subsequent trials bring no success, i.e. if the feasible solution is not obtained, then as a mutated solution is accepted as the best among them. Certainly, the solutions are assessed according to relationship (2).

5. Results of computational experiments

The presented algorithm, characterized by a big number of parameters, has been

realized in an object oriented programming form. Preliminary computational experiments have been aimed to the selection of appropriate algorithm parameter values. The following aspects have been analyzed: first, the number of successful iterations, i.e. those leading to improvement of the worst solution in the processed set of N elements as a result of replacement the worst solution by a solution corresponding to a reflection, second, expansion and contraction points, third, the number of mutations, which caused improvement of the worst solution, fourth the graph of a curve, which depicted the relative number of feasible solutions in respect to all solutions in the processed set in subsequent iterations (the curve marked with arrow in fig. 2). As it turned out, the algorithm parameter values and the assumed strategy of selection of parameter α according to relationship (3), have essential influence on the graph character of this curve, i.e. on the speed of increasing the number of feasible solutions participating in the optimization process.

As a result of this analysis the following parameter values have been assumed in the calculations: B = 1000; β = 0,08; number of solutions in the processed set N = 1000; maximal number of iterations Tmax = 20000; period of change of the parameter α every Tα = 50 iterations; parameters for reflection, expansion, and


67

contraction a = 1; b = 0,75; c = 2, respectively; mutation probability pm = 0,1. Using the elaborated software six 3-phase induction double-cage motors have

been optimized. In table 1 calculation results are compared obtained by application of: the investigated α-constrained simplex algorithm (upper values); the evolution strategy (μ+λ)-ES with the number of parents μ = 200, offspring λ = 400 and the generations number g = 100 (middle values); the hybrid algorithm [1, 2, 6] compounded with the evolution strategy (μ+λ)-ES, and the modified Price algorithm (lower values). The fields in lower rows in table 1 which corresponds to the average fitness and standard deviations remain empty, because the results obtained with the hybrid algorithm are received only simple solution.

Table 1. Results of optimization calculations obtained using: α-constrained simplex algorithm, evolution strategy (μ+λ)-ES, and hybrid algorithm

Motor

Best fitness

fmin [zł]

Average fitness fav

from 20 runs fav [zł]

Standard deviation

σ [%]

Average calculation time

t [s]

PN = 7,5 kW 2p = 2

3297,25 3295,59 3292.19

3304,39 3301,20

–

0,15 0,08

–

55,3 21,9

21,9+11,9

PN = 18,5 kW 2p = 4

8102,51 8065,00 8048.61

8141,30 8078,69

–

0,29 0,12

–

83,7 50,1

50,1+25,8

PN = 22 kW 2p = 2

8889,45 8881,52 8860,66

8902,70 8886,75

–

0,11 0,04

–

72,4 34,3

34,3+21,3

PN = 22 kW 2p = 4

9185,01 9186,94 9171.64

9234,68 9230,93

–

0,24 0,30

–

80,6 49,2

49,2+15,7

PN = 75 kW 2p = 4

– 23832,07 23740.08

– 23936,99

–

– 0,18

–

– 44,9

44,9+75,4

PN = 90 kW 2p = 4

27415,11 27414,69 27351.58

27492,13 27482,63

–

0,20 0,19

–

66,3 40,2

40,2+49,4

For a motor of the rated power PN = 75 kW the examined algorithm did not find feasible solutions also with other values of the algorithm parameters.


68

Fig. 2. An example of optimization process with application of α-CSM algorithm. Curve 1 –objective function, Curve 2 – constraints satisfaction level for best solution,

Curve 3 – average constraints satisfaction level and relative number of feasible solutions (a curve depicted with an arrow)

6. Exploitation properties comparison of α-CSM and MPA algorithms

In order to compare exploitation properties of the examined algorithm (α-

CSM) and the modified Price algorithm (MPA) expressed according to [1, 2, 6], an additional computational experiment has been executed. It consisted in: – the recording of the full set of solutions (N = 1000), which has been processed

with the algorithm α-CSM to the disc file after the feasibility of all solutions has been reached. The recordings came in the nearest iterations with the indices divisible by Ta.;

– an introduction of this solution set to the MPA procedure, execution of calculation and comparison of the results with those obtained with the α-CSM procedure after the end of the work. Objective function values and differences between the objective function values of the best and the worst solutions in the obtained sets have been compared.

Additional calculations have been executed only for five motors. The motor of rated power PN = 75 kW was omitted, while for this motor α-CSM algorithm cannot find the feasible solutions.

In table 2 a comparison of results obtained with both algorithms α-CSM and the modified Price algorithm (MPA) is presented. The following denotations have been applied: fcαCSM, fcMPA –objective function values of the best solutions in sets


69

obtained from the α-CSM algorithm and the modified Price algorithm, respectively; ΔfcαCSM, ΔfcMPA –differences between the objective function values in the best and the worst solutions in these sets, respectively.

Values provided in the second column of table 2 are slight different than those in table 1. The reason is that during additional experiments single independently separated calculations have been executed. Table 1 contains the best and the average results from 20 calculations.

Table 2. Comparison of results obtained by using α-CSM and MPA algorithms

applied to the sets of feasible solutions

Motor fcαCSM [zł]

ΔfcαCSM [zł]

fcMPA [zł]

ΔfcMPA [zł]

PN = 7,5 kW 2p = 2 3302,15 2,14 3292,18 0,01

PN = 18,5 kW 2p = 4 8113,58 1,81 8083,73 0,01

PN = 22 kW 2p = 2 8903,73 9,46 8879,89 0,01

PN = 22 kW 2p = 4 9237,73 1,72 9219,54 0,01

PN = 90 kW 2p = 4 27453,53 12,55 27391,87 0,37

The stopping criterion in the modified Price algorithm is either achievement of

a very small difference between the objective function values in the first half of the processed solution set, or achievement of the maximal assumed number of iterations. This second situation takes place in case of the motor of the rated power PN = 90 kW. This explains bigger differences between objective function values in the last row of table 2.

7. Conclusions

Nonlinear simplex algorithm with lexicographic manner of solutions

comparison may be applied to the design of the optimal induction motors but only with constraints concerning exploitation and starting parameters, which are not very restrictive. For motors with weaker constraints, calculation results are comparable with those obtained by applying evolution strategy (μ+λ)-ES and only slightly poorer than those obtained with the hybrid algorithm compounded from the evolution strategy (μ+λ)-ES and the modified Price algorithm. However, the calculation time using the examined algorithm is longer.


70

The algorithm did not find feasible solutions for a motor of the rated power PN = 75 kW. This motor is characterized by very restrictive constraints concerning exploitation and starting parameters. This causes decrease of dimensions of the feasible region in comparison with the search region and its non-cohesivity. Research of feasible region structure is described in work [3]. The research results indicate that in the optimization induction motors by restrictive constraints the feasible region may be very small and non-cohesive. Probably the main reason of poorer results obtained by application of the simplex algorithm are their poor exploration abilities in comparison to the evolution strategy (μ+λ)-ES, which causes smaller diversity of solutions in the processed set.

An additional computational experiment showed that the examined algorithm α-CSM has also poorer exploitation capability than the modified Price algorithm. This is an outcome of the applied strategy of parameter α change according to relationship (3). By such strategy in the second half of the optimization process, α-CSM algorithm behaves like a classical nonlinear simplex algorithm according to [4], while in the modified Price algorithm special heuristics in target to move creation trial points closer to better solutions from the processed set are applied. In the MPA algorithm the trial point is localized on the n-dimensional line between the center of centroid and a point with the worst objective function value. Its localization also depends on the worst and the best value of the objective function and on the degree of advance of the optimization process. The trial point position is defined by a coefficient, which depends on the distance between the worst point and the centroid center. The bigger the difference between the objective function value in worst point and its value in centroid center the bigger is the distance between the trial point and the worst point. In this manner the algorithm utilizes information encoded in coordinates of all points considered in calculations. By application of the α-CSM algorithm in second half of the optimization process, the trial point positions are independent on mutual positions of the best point and the centroid center and on the degree of advance of the optimization process.

References

[1] Dainone A., Parasiliti F., Villani M., Lucidi S.: A New Method for the Design

Optimization of Three-Phase Induction Motors. I.E.E.E. Trans. on Magnetics, Vol. 34, No. 5, September 1998.

[2] Dąbrowski M., Rudeński A.: Application of non-deterministic hybrid method for optimization of three-phase induction motors by increased number of independent variables. Poznan University of Technology Academic Journals, Electrical Engineering, No. 52, 2006, pp. 145-157.

[3] Dąbrowski M., Rudeński A.: Research of feasible space structure in induction motors optimization. XLV International Symposium on Electrical Machines SME 2009, Krasiczyn, Zeszyty Problemowe BOBRME No. 82/2009, p. 123-128 (in Polish).


71

[4] Michalewich Z.: Genetic Algorithms+DataStructures=Evolution Program. Springer Verlag, Heidelberg 1992.

[5] Naelder J.A., Mead R.: A simplex method for function minimization. Comput. Journal, Vol. 7, No. 4, 1965, pp. 308-313.

[6] Price W.I.: Global optimization by controlled random search. Journal of Optimization Theory and Application, 40 (1983) pp. 333-348.

[7] Rudeński A.: Issues concerning penalty for constraints violation in design of optimal electrical machines using evolutionary methods. Przegląd Elektrotechniczny, Nr 12/2007, p. 73-78 (in Polishg).

[8] Takahama T., Sakai S.: Constrained Optimization by Applying the α Constrained Method to the Nonlinear Simplex Method with Mutations. IEEE Trans, on Evolutionary Computation, Vol. 9, No. 3, October 2005, pp 437-450.

Computer Applications in Elektrical Engineering

72

Performance analysis of a two-module reluctance motor

with an axial flux

Marian Łukaniszyn, Marcin Kowol, Janusz Kołodziej Opole University of Technology

45-272 Opole, ul. Sosnkowskiego 31, e-mail: m.lukaniszyn; m.kowol; [email protected]

The paper presents simulation results for a two-module reluctance motor (Transverse Flux Motor) with an outer rotor. The two-module TFM construction is compared with a classical, three-module one. A specific shape of teeth is used to obtain a non-zero start torque. Calculations of the magnetic field and electromagnetic torque are performed using the Flux3D package based on the finite element method. In particular, the paper analyses the influence of the new motor magnetic circuit construction on the torque produced by the motor and its pulsations. The calculations enable to determine electromechanical parameters for a specific motor under design without making its costly prototype. A number of computer simulations are carried out and the results are compared with the three-module prototype version of the motor .

1. Introduction

Transverse flux motors (TFMs) have recently attracted remarkable interest both from the academia and various industrial environments [1, 3, 5, 6, 9, 10, 11]. The low-speed motor is characterized by a high ratio of the electromagnetic torque to its volume [2, 4, 11], leading immediately to various high-torque transmission-free applications, to mention electric wind generators [1], electric (and hybrid) drives [11] and in-wheel drives [3, 9]. On the other hand, there has been a tremendous effort devoted to the problem of reduction of accompanying torque pulsations, which have been plaguing not only TFMs [2, 4, 5, 7]. Reduction of the torque pulsation is certainly welcome in the above high-torque implementations, but it is vital in modern control and robotics applications [5]. Simultaneous maximization of the average electromagnetic torque and minimization of the ripple torque is a contradicting task which can only be solved in a compromise way for a specific TFM construction.

In the previous papers by the authors [6, 8, 9], principles of operation of the three-module motor, performance prediction and an effective three-dimensional analysis of the magnetic field distribution for a TFM have been presented. Specifically, an influence of selection of various sets of three-module TFM construction parameters on the electromagnetic torque and its pulsations has been comparatively examined. The simulation results were in good agreement with

M. Lukaniszyn, M. Kowol, J. Kołodziej / Performance analysis of a two-module…

73

experimental data obtained from the prototype motor, which confirmed the usefulness of the computational approach.

In order to additionally improve electromechanical parameters and efficiency of TFMs, the new construction of a two-module reluctance motor was designed This work is an extension of the related topics presented in the area in Refs. [6, 8, 9]. This paper analyzes selected constructions of two-module TFMs. This motor structure has main defect – the start torque of the motor is equal to zero for specific rotor positions. This paper offers a new solution to this problem.

An effective tool for the calculation of motor integral parameters is the 3D FEM and an adequate modeling environment is the Flux3D program. It should be stressed that the modeling tool enables to avoid constructing and verifying a number of physical motor prototypes, which could be very expensive.

2. Construction of the two-module motor

The prototype motor structure is shown schematically in Figs. 1 and 2. The considered motor consists of two identical modules in which the stators are shifted by fifteen mechanical degrees between each either. The rotor modules are placed symmetrically. Each module has twelve teeth and includes one phase of winding in a shape of solenoidal coil. The rotor and its teeth are made of solid iron. The modules are insulated from each other with nonmagnetic separator. Two stator modules are centered along the motor shaft.

The main specifications for the motor are given in Table 1. The analysis presented in this work was carried out for a small, low-voltage

(24 V), two-phase TFM with an outer rotor. A number of turns of one phase coil was equal to 130 and the rated current value in calculation was assumed to 12A.

Fig. 1. Two-module TFM prototype


74

Fig. 2. Two-module TFM structure

Table 1. Specifications for TFM

Supply voltage Un=24V

Rated current In=12A

Rotational speed 0÷300 rpm

Winding Two-phase

Number of turns 130

External diameter of rotor 158 mm

External diameter of stator 103.5 mm

Air gap δ=0.5 mm

A simplified topology of circulation of the main flux is shown in Fig. 3, which illustrates the operation principle of the machine. The motor operates as a two-phase machine in the auto-piloted mode. The motor is supplied from a DC source through a two-pulse electric inverter (see Fig.4). Control of the motor reduces to supplying the phases with a rectangular current waveform according to the sequence A,B,A. Connection of any phase results in adequate positioning of the rotor with respect to the stator (the teeth are aligned). Since the rotor sectors are shifted between each other, the successive connection of the phases causes the rotor to rotate. The connection of the successive phases is triggered by the signals from two transoptor sensors located in the external module. The sensors co-operate with a light-reflecting disc mounted onto an inner wall of the rotor.


75

Fig. 3. Simplified topology of magnetic flux circulation

Fig. 4. One-phase half-bridge supply system and phase currents


76

It is worth mentioning that we have constructed the two-module prototype according to the state-of-the-art and using our long-year experience, also resulted from our previous, three-module prototype constructions [4, 9]. However, no formal optimization tools were available to us at the time of the construction of the prototype. The basic three-module motor will be used as a platform for verification of adequacy of a numerical model.

3. Numerical model

A precise numerical FEM model of the motor is developed in the Flux3D program [4, 9]. The 3D modeling package uses B-H characteristics to relate flux density with field intensity for all the materials. For the stator core and the rotor steel, the characteristics are defined in the first quadrant, with the initial values of B and H being both zero.

The analysis of the magnetic field in the 3-D space is performed under the following assumptions: − the field is considered to be magnetostatic, − eddy-currents in construction parts of the motors are omitted, − eddy-current losses in rotors are negligible, − the current density within the cross section of the coils is uniform, − the rotational speed of the motor is constant, − there are no magnetic couplings between individual modules of the motor.

The assumptions enable to limit the calculations to a single module only, and taking additionally account for the symmetry conditions in the motor, to 1/48 of the motor volume, which is called a calculation segment or just a segment. The structure of the two-modular motor module and the discretization mesh for the numerical model are depicted in Figs. 5 and 6, respectively. The total number of hexahedral elements in the mesh is equal to 59,053. The electromagnetic torque is calculated by the virtual work method as a derivative of the magnetic coenergy with respect to the rotation angle between the rotor and stator. The rotation of the rotor vs. stator is modeled by the sliding surface method [6, 9].

Fig. 5. Construction of TFM numerical model with boundary conditions


77

Fig. 6. Discretization mesh for TFM segment

The useful ripple torque factor ε was defined:

%100minmax ⋅−=avT

TTε (1)

where Τmax, Τmin and Tav are the maximum, minimum and average torques, respectively (in the range of a phase switch-over). A number of two-module motor numerical models with different geometry of the rotor teeth have been performed. The example of construction of the motor module with construction parameters are presented in Fig. 7. The influence of construction teeth shape (parameters: β1, β2, lw ) on electromechanical torque was analyzed for the machine with numbers of teeth in the stator and rotor being equal to 12. This was connected with a low cost of exchanging those elements in the motor and obtaining a new construction of the prototype.

The values of basic construction parameters of the motor prototype are presented in Table 2.

Table 2. Fundamental parameters of the motor prototype

r0 [mm]

r1 [mm]

r3 [mm]

r4 [mm]

lz [mm]

rm [mm]

lm [mm]

α [°]

β1

[°] β2

[°] 15 23 49,75 50,25 6 62,25 32 15 15 7,5


78

Fig. 7. Cross-section of the TFM segment

4. Results of calculations

Using Flux3D, integral parameters are calculated for the above two-module

motor model. The calculated electromagnetic torques for the considered TFM models are listed in Table 3. The rated current for which the calculations are made is equal to 12A.

Calculations of the electromagnetic torque vs. rotation angle for various TFM versions are illustrated in Fig.8. In general, a remarkable reduction in average electromagnetic torque of the two-module motor can be observed. The calculation results are in good agreement with measurements on the physical motor models.

Table 3. Calculated integral parameters for TFM models

TFM Tmax [N·m]

Tav [N·m]

γ [˚]

Two-modular 5,02 2,82 17,5

Three-modular 5,69 4,06 15


79

0 5 10 15 20 25 30-6

-4

-2

0

2

4

6

Rotor position [deg]

T e [N

⋅m]

for three-module reluctance motorfor two-module reluctance motor

Fig. 8. Electromagnetic torque vs. rotation angle for various TFMs

The main determinant of the teeth shape usefulness in the two-module motor is

obtaining the extension of a range of positive values of the electromagnetic torque produced by the motor. A larger range of angles for positive values of the electromagnetic torque guarantees the start of the motor for all rotation positions between the rotor and stator.

As can be seen from Fig. 8, the plot of electromagnetic torque for the two-module motor vs. rotor position is asymmetric. In this case (see Table 3), the extension of the electromagnetic torque range by some 2.5˚ results in the reduction of the average electromagnetic torque by as high as some 30% (as compared to the three-module motor).

It seems from the above results that the application of a two-module TFM does not have to necessarily lead to the increase in electromechanical parameters of the motor. In case of a slight improvement of the integral parameters of TFMs, construction of such types of the motor may be profitable from the viewpoint of construction costs. The model, due to its specific structure is characterized by high level of torque pulsations.

5. Conclusions

In this paper, a new construction of a two-module TFM has been analyzed. It has been shown in the calculations based on a precise 3D numerical TFM model that it was possible to determine a specific teeth shape and obtain the non zero start torque for the motor under design, without making its costly prototype. A number of computer simulations were carried out and the results were compared with those


80

for the three-module version of the motor. A selection of an appropriate configuration depends on a specific application of the motor. It is worth noticing that a number of the motor modules and their mutual rotation can also affect both the electromagnetic torque and costs.

Further improvement of integral parameters of two-module TFMs can be obtained by employing a formal construction optimization procedure, e.g. like the one in Ref. [4, 5, 8], which will be the subject of a future research work.

References

[1] Arshad W. M., Thelin P., Bäckström T., Sadarangani C.: Use of Transverse-Flux Machines in a Free-Piston Generator, IEEE Transactions on Industry Applications, July/August 2004, vol. 40, No. 4, pp. 1092÷1100.

[2] Goryca Z., Łukaniszyn M., Jagieła M., Wróbel R.: Analiza momentu elektromagnetycznego w silniku reluktancyjnym, XXXIX SME, Cedzyna/Kielce 2002, pp. 333÷339.

[3] Kastinger G.: Design of a novel transverse flux machine, ICEM 2002, Brugge, August 2002.

[4] Kowol M., Łukaniszyn M., Latawiec K.: Optimization of a Transverse Flux Motor using an evolutionary algorithm. 14th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, MMAR’2009, Międzyzdroje, Poland, 2009, Program abstract: pp. 47-48 , (full text on conf. CD).

[5] Kowol M.: Zastosowanie algorytmu ewolucyjnego do optymalizacji obwodu magnetycznego silnika reluktancyjnego ze strumieniem poprzecznym, Przegląd Elektrotechniczny, Vol. LXXXV, No. 3 Sigma-NOT, 2009, pp. 100-102.

[6] Łukaniszyn M., Kowol M.: Analiza pracy modułowego silnika reluktancyjnego z wirnikiem zewnętrznym, Śląskie Wiadomości Elektryczne, 4’2005, s. 4-7.

[7] Łukaniszyn M., Kowol M., Latawiec K.: Influence of multipolar excitation of permanent magnets on torque pulsation for TFM, Monografia PAN “Computer Applications in Electrical Engineering”, Poznań, 2009, s.180-189.

[8] Łukaniszyn M., Kowol M.: Optymalizacja obwodu magnetycznego silnika reluktancyjnego modułowego z wirnikiem zewnętrznym, XLIII Międzynarodowe Sympozjum Maszyn Elektrycznych, SME’2007, Poznań, 2007, s.191-194.

[9] Łukaniszyn M., Kowol M.: Wpływ zmian konstrukcyjnych na parametry elektromechaniczne silnika reluktancyjnego z wirnikiem zewnętrznym, Przegląd Elektrotechniczny, Vol. LXXXII, No. 11, Sigma-NOT, 2006, pp. 43-45.

[10] Peethamparam A.: Design of Transverse Flux Machines using Analytical Calculations & Finite Element Analysis, March 2001 PhD Thesis, Royal Institute of Technology, Stockholm.

[11] Ritchie E., Tutelea L.: An overview of electric vehicle in-wheel drive systems, XXXIX Międzynarodowe Sympozjum Maszyn Elektrycznych, 9-11 June 2003, Gdańsk-Jurata, pp. 1-21.


81

Comparative analysis of the direct sliding-mode torque control

strategies of the induction motor

Grzegorz Tarchała, Teresa Orłowska-Kowalska Wroclaw University of Technology

50-372 Wrocław, ul. Smoluchowskiego 19, e-mail: grzegorz.tarchala; [email protected]

The paper deals with the sliding-mode torque control of induction motor drives. Two possible control strategies are presented, with stator and with rotor flux stabilization. Mathematical model of the considered drive system and control algorithm is presented. Simulation and experimental results are demonstrated to verify the described algorithms.

1. Introduction A number of requirements are set to modern electric drives. Superb dynamic behaviour, dependable work, low cost, high power efficiency, motor parameters mismatch insensitivity, simple technical implementation are among the demands. High efficiency, dependable work and low cost can be assured by the usage of an induction motor (IM). However, quite complicated control systems must be applied in order to achieve excellent dynamic transients. This paper presents the Direct Torque Sliding-Mode Control (DTSMC), one of possible ways of controlling the induction motor drive. Sliding-mode control systems as one of variable structure systems (VSS) have been investigated in Russia from early 1930s [15]. However, first IM drive applications appeared at the turn of 1970s and 1980s as a result of Sabanovic and Izosimov works [3], [11], [12]. The following years achievements enriched the IM Sliding-Mode Control theory, among them are the important Utkin’s paper [14], the one considering position control [16] and others, [10], [18]. The subject appears to be still unexhausted and in recent years many new articles have appeared. Authors in [9] proposed a novel SMC algorithm optimizing torque response and efficiency. Conventional DTC and sliding-modes are combined in [6]. Integral nested SM controller is applied to IM in [8], [17] also for sensorless drives [1], [2]. Low and zero-speed action is concerned in [4], [9]. The exponential approach law is introduced in [13]. Second order sliding-mode, so called twisting algorithm, can be also used in IM drives [19]. This paper presents conventional Direct Torque Control taking advantage of sliding-modes, however it compares two possible control strategies assuring motor flux stabilization. Both stator and rotor fluxes can be stabilized, and these two possibilities are investigated and compared. The similarities and differences

G. Tarchała, T. Orłowska-Kowalska / Comparative analysis of the direct sliding-mode…

82

between those two methods are shown. Simulation and experimental results are presented to verify the analyzed algorithms.

2. The control strategy – theoretical basics In order to control a specific plant, like the induction motor drive, the control basics for the general plant should now be introduced. The SMC, as one of the algorithmic control strategies, requires the plant mathematical model knowledge. This model can be described by the commonly-known state equation:

),( kxx f (1) where: x, k – state variables and control signal vectors. The letter k appears here to distinguish the common control signal symbol from the motor voltage vector signal u. The next step in the control algorithm design [14] is to choose so-called switching function vector, which can be formulated as:

TNsss ],...,,[ 21s (2)

where: N – the number of available control signals. If the vector s is chosen so that its desired value is zero, the negative value of the derivative of the positive Lapunov function ensures the asymptotic convergence of switching function vector. The Lapunov standard function takes the form:

021

ssTL (3)

and its derivative: 0 ss TL (4)

It is important, at this point, to divide the derivative (4) into two parts, one dependent and one independent on the control signal, k:

Dkfs TL (5) If the control law is assumed:

Dss*s*k TT ,)sign( (6) the Lapunov function derivative can be expressed as follows:

*sfss**sfs TTTL )sign( (7)

where: 0)3(*)2(*)1(* sss*s .

If the term *s is high enough, the control purpose, i.e. zero convergence of switching functions (2) is fulfilled:

1

01

Df

Dsfs*sfs TTT

(8)

The control law (6), with the usage of the sign function, means that the control signals k=[k1,k2,…kN]T

will only take two signal states, i.e. ±1. This situation,


83

natural for the modern induction motor drives fed from the voltage-source inverter, will be described in next paragraph.

3. Mathematical model of the converter-supplied induction motor The power supply chain, commonly found in industrial applications consists of the rectifier, the voltage-source inverter (VSI) and the induction motor. These three elements are presented in Fig. 1.

A

B

C

du

Ak CkBk

N1L2L3L

IMVSIAC/DC

Fig. 1. The induction motor fed from the voltage-source inverter

The rectifier converts the alternating current (AC) into a direct current (DC) and

the ud signal can be assumed as its output. This signal needs to be measured, when the phase voltage values are needed:

C

B

Ad

C

B

A

ABC

CN

BN

AN

kkk

u

kkk

uuu

211121112

3T (9)

where: k=[kA,kB,kC]T – the VSI control signals, that become 1 when the specific phase is connected to the positive voltage, and -1 otherwise. The conventional induction motor mathematical model will be developed using voltage vector in the stationary reference frame:

CN

BN

AN

CN

BN

AN

s

s

uuu

uuu

uu

2323021211

32

T (10)

When the SMC algorithm is concerned another matrix is essential: αβABCTTT (11)


84

The last part of the presented power supply chain is the squirrel-cage induction motor, which can be described using the well-known space-vector equations expressed in the stationary frame and per unit [p.u.] system [7]: – voltage and flux equations:

srr

rss

rrr

sss

iiψiiψ

ψψi0

ψiu

mr

ms

mNr

Ns

xxxx

jdtdTr

dtdTr

(12)

– equation of motion:

sssse

oeM

m

iim

mmTdt

d

)Im(

1

s*siψ

(13)

where: rrrrssssss jjiijjiijuu rrsss ψiψi,u ,,, –

space vectors of stator voltage, current and flux, rotor flux and current, respectively, Mmrrss Txxrxr ,,,,, – induction motor parameters, stator and rotor winding resistances, reactances, magnetizing reactance and mechanical time constant, oem mm ,, – motor speed and torque, load torque, respectively,

rsmsNsNN xxxHzffT 21,50,21 .

4. SMC application to induction motor drives Taking into consideration the SMC algorithm presented in paragraph 2, the first step – the deriving of the specific plant mathematical model is now finished, and presented in previous paragraph. The second step – the switching functions selection must be now considered [5]. There are three control signals, therefore three switching functions are available:

Tsss 321 ,,s (14) Although sliding-mode theory allows to control motor position, speed or its torque, the goal of this paper is to control the last of them, and thus the first switching function is:

erefe mms 1 (15)

where: refem – torque reference value.


85

The motor can be controlled using the constant flux strategy, so the second switching function must be related to the flux; it can be both stator or rotor flux:

rrefrr

refrr

srefss

dtdTs

s

2

222 )(

(16)

where: T – flux control time constant, refr

refs , – stator and rotor flux reference

values. The third and last switching function can be the one providing the 3-phase voltage symmetry:

dtkkks CBA3 (17) For these switching functions the matrix D, necessary in the SMC control law application (6) is as follows:

111,1 rsD

D (18)

and:

TD

TD

rr

r

r

Nr

r

r

Nr

Nsr

mr

ss

sss

s

ss

Ns

TT

rTT

rTxx

x

xi

xiT

1

1122

1

1

1

(19)

where: 22 rrr – rotor flux amplitude.

Matrices D1s, D1r can be obtained substituting (15)-(17) into Lapunov derivative equation (4), (5). The f vectors, reminding after dividing the derivative of s into two parts (5) are presented in the Appendix 1. The second switching function forms (16) directly depend on the above-mentioned division to f and D matrices. The s2s form without raising to the power of two, and the s2r form without the differential part do not allow to realize this division, and thus the D matrix cannot be derived. The block diagram of the SMC structure for IM drive is presented in Fig. 2. The sliding-mode controller, relying on the information of the flux and torque errors, flux vector components (or its amplitude and angle), and additionally stator current vector, changes the control signals, i.e. transistor switches. Fluxes and torque can be calculated by one of many existing estimators [7] using the information about motor phase currents, voltages and speed. The phase voltages are calculated by (9)-(10), taking the advantage of ud and kA, kB, kC. When there is a necessity of


86

achieving speeds greater than the nominal value, the field weakening strategy must be applied.

Fig. 2. The block diagram of the direct torque SMC structure

5. Simulation results Presented above theoretical considerations are proved with simulation tests. All transients are obtained using the Matlab/Simulink software, with the fixed-step Euler method, the sampling time is 1e-6 s. The rectifier and the VSI are assumed to be ideal, i.e. the direct voltage ud is constant and there is no dead-time effect in the VSI operation. The induction motor model is formed using equations (12)-(13). Its parameters and nominal values are presented in Appendix 2. It is assumed that the flux and torque estimator works properly (Fig. 2). The drive perfect operation for control with constant stator flux is shown in Fig. 3 It can be noticed that the reference motor torque value is achieved almost immediately and stator flux is kept constant on the desired nominal level. The reference torque square wave amplitude is its nominal value (see Appendix 2). Shape of the speed transient is triangular, due to the applied torque signal. In Fig. 4 the SMC with constant rotor flux can be seen. The reference torque square wave is identical to the previous one. Likewise for the control with constant stator flux, the system dynamic behaviour is distinguished. Three different transients are shown for three different flux settling time constants Ts: 0.01s, 0.05s and 0.1s (where Ts=3T). The torque transients differ only at the beginning, and therefore its zoom is shown. The speed transients are almost identical.


87

0 0.1 0.2 0.3 0.4 0.5-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

t [s]

me,m

eref [p

.u.]

meref

me

0.42 0.421-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-0.2

-0.15

-0.1

-0.05

0

0.05

t [s]

m

, mre

f [p.u

.]

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

1.2

1.4

t [s]

sre

f ,s [p

.u.]

0 0.0025 0.0050

0.2

0.4

0.6

0.8

1

1.2

1.4

sref

s

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

s [p.u.]

s

[p.u

.]

s=f(s)

Fig. 3. Sliding-mode control of the induction motor with stator flux stabilization, simulation results

0 0.1 0.2 0.3 0.4 0.5-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

t [s]

me,m

eref [p

.u.]

0 0.005 0.01 0.015-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

meref

me

Tsi=0.05s

Ts=0.1s

Ts=0.01s

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-0.2

-0.15

-0.1

-0.05

0

0.05

t [s]

m

, mre

f [p.u

.]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.2

0.4

0.6

0.8

1

1.2

1.4

t [s]

rre

f ,r [p

.u.]

rref

r

Ts=0.1s

Ts=0.01s

Ts=0.05s

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

r [p.u.]

r

[p.u

.]

r=f( r)

Ts=0.1sTs=0.05s

Ts

=0.01s

Fig. 4. Sliding-mode control of the induction motor with rotor flux stabilization, simulation results


88

The parameter sensitivity tests were performed next, and the exemplary transient is shown in Fig. 5. Parameters used by the control system (superscript SMC) were changed in relation to real motor parameters (R). The situation with a parameter mismatch was simulated. Parameters were changed in the following way: ,5.2 R

sSMC

s rr ,5.0 Rs

SMCs xx ,5.0 R

rSMC

r rr ,5.2 Rr

SMCr xx

Rm

SMCm xx 5.1 . Comparison of the transient from Fig. 5b with the one from Fig. 5a,

proves that the SMC algorithm is insensitive to all motor parameters mismatch.

0.025 0.03 0.035 0.04 0.045 0.050.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

t [s]

me,m

eref [p

.u.]

a)

meref

me

0.025 0.03 0.035 0.04 0.045 0.05

0.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

t [s]

me,m

eref [p

.u.]

b)

meref

me

Fig. 5. Parameter sensitivity comparison, a) nominal parameters, b) parameters mismatch: Rm

SMCm

Rr

SMCr

Rr

SMCr

Rs

SMCs

Rs

SMCs xxxxrrxxrr 5.1,5.2,5.0,5.0,5.2

6. Experimental results

A number of experimental tests were performed in order to verify presented theoretical considerations. The Sliding-Mode Control algorithms were implemented in dSpace 1104 card using the dSpace software. The tests were performed with the sampling time s. The schematic diagram of a laboratory set-up is presented in Fig. 6.

Ak

CkBk

du

sAi sBi

m

Fig. 6. Experimental set-up


89

The set-up consists of the 1.5kW induction motor fed from the VSI. The load torque is provided by the DC machine. Whole control process is supervised by the dSpace 1104 card. Motor speed is measured by the incremental encoder (4096 imp./rev.). Both control methods, with stator and rotor flux stabilization, were tested. Experimental transients for the first method are presented in Fig. 7, for the second method in Fig. 8, respectively. In both cases the flux vectors were estimated by commonly used simulators [7]; the stator flux vector was estimated by the voltage-based simulator and the rotor flux – by the current-based simulator. Both control methods give almost the same results. In Fig. 7 and Fig. 8 a superb control system performance can be seen. Reference torque values are achieved almost immediately. One of the differences is that rotor flux oscillations are smaller then in stator flux signal. Speed signal is triangular due to the applied motor torque signal shape.

0 0.2 0.4 0.6 0.8 1

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

t[s]

me,m

eest [p

.u.]

meref

meest

0 0.2 0.4 0.6 0.8 1

-0.2

-0.1

0

0.1

0.2

m

[p.u

.]

t[s]

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

t[s]

ses

t , sre

f [p.u

.]

sest

sref

-1 0 1

-1

-0.5

0

0.5

1

s [p.u.]

s

[p.u

.]

Fig. 7. SMC with stator flux stabilization, experimental results


90

0 0.2 0.4 0.6 0.8 1

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

t[s]

me,m

eest [

p.u.

]

meref

meest

0 0.2 0.4 0.6 0.8 1

-0.2

-0.1

0

0.1

0.2

m

[p.u

.]

t[s]

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

t[s]

res

t , rre

f [p.u

.]

rest

rref

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

r [p.u.]

r

[p.u

.]

Fig. 8. SMC with rotor flux stabilization, experimental results

7. Conclusion

In the paper the Direct Torque Sliding Mode Control is presented. The two possible control strategies are compared – one that allows to keep stator flux constant and the second one for rotor flux. Simulation and experimental test were performed to verify described algorithms. Both control strategies give almost the same results – motor torque is controlled ideally, the reference value is achieved almost immediately and the flux is kept constant. The only difference, noticeable during experimental tests, are smaller flux oscillation for drive system operation with stabilisation of the rotor flux.

Appendix 1

The f vectors reminding after the derivative of s division (5) will be presented here, respectively for constant stator flux control:

rsrsαN

srefs

refs

smer

srs

sssssm

N

refe

s

s

iiT

r

mxxrr

xii

Tm

ff

22

11 2

2

1

(A1)

and for control with constant rotor flux:


91

emN

rss

r

mr

Nr

rr

mr

r

r

Nr

refr

refr

rsr

msrsr

r

mme

sr

srrs

Nr

r

r

mTxpaii

xxr

Tap

xxr

xr

TT

T

xxxii

xxm

xxxrxr

Tf

ff

3121

1

222

22

12

22

21

2

1

where:

m2

r

2m

rss

m

r

rm

N

m

r

rm2r

mr

s

m

r

r

Nr

r xxxrr

xx

xrx

TTx

xrxa

xxr

xx

xr

TTxra

212

,11121

21

Appendix 2

Induction motor (Indukta Sh90 L-4) parameters and its nominal values are presented in Table 1 and Table 2, respectively.

Table 1. Parameters of the IM equivalent circuit

Rs Rr Xs Xr Xm

4.8431 6.57 84.9 84.9 81.4 [] 0.0737 0.10 1.29 1.29 1.239 [p.u]

Mechanical time constant of the drive: TM=0.2s

Table 2. Motor nominal values

Power Torque Speed Voltage Current Frequency Stator flux

Rotor flux

PN MN nN UsN IsN fsN sN rN

[kW] [Nm] [rpm] [V] [A] [Hz] [Wb] [Wb]

1.5 10.2 1410 230 3.5 50 1.135 1.087 [physical

units]

0.62 0.6608 0.94 0.707 0.707 1 1.096 1.049 [p.u.]

References [1] Comanescu M., An Induction-Motor Speed Estimator Based on Integral Sliding-

Mode Current Control, IEEE Trans. Industrial Electronics, vol. 56, no. 9, September 2009, pp.3414-3423.

[2] Comanescu M., Xu L., Batzel T.D., Decoupled Current Control of Sensorless Induction-Motor Drives by Integral Sliding Mode, IEEE Trans. Industrial Electronics, vol. 55, no. 11, Nov. 2008, pp.3836-3845.


92

[3] Izosimov D. B., Matic B., et al., Using sliding modes in control of electrical drives, Dokl. ANSSSR, vol. 241, no. 4, 1978, pp. 769-772 (in Russian).

[4] Jezernik K., Speed Sensorless Variable Structure Torque Control of Induction Motor, Proc. of Int. Conf. on Industrial Technology ICIT’2009, India, 2009.

[5] Kajstura K., Orłowska-Kowalska T., Sliding-mode control of induction motor, Prace Nauk. Inst. Maszyn, Napędów i Pomiarów Elektr. Polit. Wrocł., no. 56, ser. Studia i Materiały, no. 24, 2004, pp. 279-290 (in Polish).

[6] Lascu C., Trzynadlowski A., Combining the Principles of Sliding Mode, Direct Torque Control and Space-Vector Modulation in a High-Performance Sensorless AC Drive, IEEE Trans. Industry Applications, vol. 40, no. 1, January/February 2004, pp.170-177.

[7] Orłowska-Kowalska T., Sensorless Induction Motor Drives, Wroclaw University of Technology Press, 2003 (in Polish).

[8] Rivera J., Loukianov A., Integral Nested Sliding Mode Control: Application to the Induction Motor, Proc. International Workshop on Variable Structure Systems, Italy, 2006, pp.110-114.

[9] Rodic M., Jezernik K., Sabanowic A., Speed Sensorless Sliding Mode Torque Control of Induction Motor, Proc IEEE Industry Applications Conference, vol.3, Rome, Italy, 2000, pp. 1820-1827.

[10] Sabanovic A., Bilalovic F., Sliding Mode Control of AC Drives. IEEE Trans. Industrial Applications, vol. 25, No. 1, January 1989, pp. 70-75.

[11] Sabanovic A., Izosimov D. B, Application of sliding modes to induction motor control, IEEE Trans. Industry Applications, vol. IA-17, no. 1, January/February 1981, pp. 41-49.

[12] Sabanovic A., Izosimov D. B, Music O., Bilalovic F., Sliding modes in controlled motor drives, Proc. IFAC Conference on Control in Power Electronics and Electrical Drive, Lausanne, Switzerland, 1983, pp. 133-138.

[13] Sun D., Sliding Mode Direct Torque Control for Induction Motor with Robust Stator Flux Observer, Proc. 2010 Int. Conf. on Intelligent Computation Technology and Automation, China, 2010.

[14] Utkin V., Sliding Mode Control Design Principles and Applications to Electric Drives, IEEE Trans. Industrial Electronics, vol.40, no.1, 1993, pp.23-36.

[15] Utkin V., Guldner J., Shijun M., Sliding mode control in electromechanical systems, Taylor & Francis, 1999.

[16] Veselic B., Perunicic-Drazenovic B., Milosavljevic C., High-Performance Position Control of Induction Motor Using Discrete-Time Sliding-Mode Control, IEEE Trans. Industrial Electronics, vol. 55, no. 11, November 2008, pp.3809-3817.

[17] Wang J., Li C., Li H., The Application of Integral Sliding Mode Variable Structure in Induction Motor Vector Control System, Proc. 2nd Int. Conf. on Mechanical and Electronics Engineering, Japan, 2010.

[18] Yan Z., Jin C., Utkin V., Sensorless Sliding-Mode Control of Induction Motors, IEEE Trans. Industrial Electronics, vol.47, no.6, 2000, pp.1286-1297.

[19] Zhang Z., Zhu J., Tang R., Bai B., Zhang H., Second Order Sliding Mode Control of Flux and Torque for Induction Motor, Proc. Asia-Pacific Power and Energy Engineering Conference, China, 2010.


93

The field-circuit analysis of the start-up operation

of the brushless DC motor

Łukasz Knypiński, Lech Nowak, Kazimierz Radziuk Poznan University of Technology 60 – 965 Poznań, ul. Piotrowo 3a,

e-mail: [email protected], Lech.Nowak, [email protected]

Yvonnick Le Menach

University of Science and Technologies of Lille Cité Scientifique, 59 655 Villeneuve d’Ascq, France

e-mail: [email protected]

1. Introduction Nowadays, we can observe growing concern about energy saving and the protection of natural environment. It is reflected in recent researches carried out by designers who try to find new, high, efficient machines. Therefore, development of constructions of the permanent magnet motors is being accelerated. The permanent magnet brushless DC (BLDC) motors state an important group of these types of machines. The BLDC motors have many advantages: high efficiency, high power density, wide speed range, good dynamic performance and long operational life [9, 17]. The BLDC motors are widely used in different industrial applications [1]. The further development of BLDC motors is possible owing to the development production technology and the improvement of permanent magnets parameters. Research and works connected with development of methods of simulation of transient and dynamic states in BLDC motors and advancement of optimization procedures will increase knowledge of these motors. The results of field-circuit analysis connected with optimization algorithm can show some new principle directions of the development of BLDC motor structures. In the paper an algorithm and computer code for the analysis of the outer rotor permanent magnet brushless DC motor dynamics is presented. The mathematical model of the devices includes: the equation of a electromagnetic field, the electric circuit equations and the equation of mechanical motion. The numerical implementation is based on the finite element method (FEM) and step-by-step algorithm. The nonlinear coupled field-circuit equations have been solved by using Newton-Raphson algorithm. The electric circuits of the converter during transient operation have been discussed. The computer code for dynamic simulation of the machine has been elaborated on the basis of Delphi environment. The start-up of the motor has been investigated. Selected results of the analysis are presented and discussed.

Ł. Knypiński, L. Nowak, K. Radziuk, Y. Le Menach / The field-circuit analysis…

94

2. Structure of the machine

The brushless DC motors consist of a permanent magnet rotor and stator equipped with a three phase winding. The construction of the considered motor is presented in Figure 1a. The inner stator has 12 slots. The three-phase concentrated non-overlapping winding has been applied [5]. In such constructions the ends of winding are shorter than in case of classical overlapping winding. As a result, lower copper losses can be achieved. The stator winding is star-connected. The winding configuration is shown in Figure 1b. As it can be seen, each phase have two coils connected in series. At each moment, there are two phases in conducting state and one phase in non-conducting state. In the outer rotor 10 pieces of the permanent magnet are mounted. The motor is equipped with Recoma 22 (Sm22Co17) type magnets [19]. In the discussed machine, the correlation between the number of stator slots sN and the number of pole pairs p have to satisfy relationship 22 sNp [6]. Thus, the motor has a fractional ratio of slots number to pole number. In such motors the cogging torque has lower values.

Fig. 1. The outer rotor permanent magnet brushless DC machine (a) and the stator winding configuration (b)

3. Mathematical model

In BLDC machine the magnetic field is excited by two sources: permanent magnet and stator windings. Thus, the equations describing magnetic field can be written as follows

MJJA

curlcurl (1)


95

where 1 is the magnetic reluctivity, A

is the magnetic vector potential, J

is the current density in windings, MJM

curl , Μ

is the magnetization vector

within the permanent magnet area. The electric machines are generally voltage supplied. The waveforms of currents )(),(),( 321 tititi in the stator windings are not known in advance, i.e. prior to the field calculation. Therefore, it is necessary to consider the voltage equations of the motor

uRiΨ

tdd

(2)

where Ψ is the matrix of flux linkage, R is the diagonal matrix of winding resistances, TT uuuiii ][,][ 321321 ui are the vectors of winding currents and supply voltages, respectively. The equation describing mechanical motion in rotary machine may be expressed as

loTTt

J

dd

(3)

where J – is the moment of inertia, – is the angular velocity of the rotor, T – is the electromagnetic torque, loT – is the load torque.

3. Coupled field-circuit implementation In the numerical implementation of the motor transients the finite element method (FEM) and the time stepping procedure have been applied. At the n-th time step the set of equations describing magnetic field takes the form

nMnnn ΘziΦS (4)

where nS is the stiffness matrix at time nt , nΦ is the vector of nodal potentials multiplied by the machine length [4, 14], z is the matrix of turn numbers associated with the nodes within the windings area, nMΘ is the vector of magnetomotive forces in the permanent magnets area [7, 15]. In order to solve the Kirchhoff’s equations the time stepping algorithm has been employed. After substituting n

Tn ΦzΨ [11] into equation (2), the voltage

equations describing the motor windings at ntt may be expressed in the form

nnnT

nT tt uRiΦzΦz 1 (5)

in which 1 nn ttt is the time step length.


96

The nonlinearity of the magnetic core has been taken into account. In this case, matrix nS depends on solution nΦ . In the elaborated algorithm the Newton-Raphson procedure has been applied. At the n-th time step and k-th iteration, the unknown vectors k

nΦ and kni are replaced with their

increments: 1 kn

kn

kn ΦΦΦ and 1 k

nkn

kn iii . The set of coupled field-

circuit equations can be written in the form [10]

111

11

kn

kn

Tn

Tn

kn

kn

knnM

kn

kn

T

kn

ttt RiΦzΦzuziΦSΘ

iΦ

RzzH (7)

where knH is the Hessian matrix of the Newton-Raphson process.

The value of Hessian matrix for m-th finite element is determined as follows

3

1

3

122 )()(2

qq

mqj

qq

mqimm

mji

mji SS

BSH ,,,, (8)

where ji, are the nodes of triangle finite element, m is the area of m-th element, B is the modulus of magnetic flux density in the m-th element. After solving the system (7), the vector of currents k

ni and the vector of nodal

potential knΦ can be determined. The iterative Newton-Raphson algorithm was

discussed in [8]. The movement of the rotor has been modelled by means of the method of distorted elements [3]. The value of angular position of the rotor at 1 ntt is evaluated by explicit difference formula [3]

12

1 2)(

nnlon

n JTTt (9)

where n is the angular position of the rotor at the time nt , nT is the electromagnetic torque at ntt . Finally the angular velocity of the rotor can be estimated as

t

tt nnn

15.0 (10)

4. The electrical commutation

The BLDC motors do not have brushes, instead of it, there are electrically commuted. Voltage commutation is carried out by the conventional six-switch converter. The scheme of the converter, connected with motor circuit model is shown in Figure 2.


97

Fig. 2. The conventional six-switch converter connected with motor circuit model

The stator phase voltage equations can be described as

33

333

22

222

11

111

dd

ddd

d

et

iRu

et

iRu

et

iRu

(11)

where 321 ,, eee are the back electromotive forces in the stator windings. In the studied motor, the stator windings are star-connected, so:

0321 iii (12) In such motors only two phases are voltage supplied. The third phase is not powered and is short-circuited by diode when the current is different from zero. Therefore, only two voltage equations are considered. Taking into account (12) the voltage equations (11) may be expressed in the form

3232

1323123

2121

221112

dd

ddd

dd

d

eett

iRiRRu

eett

iRiRu (13)

where 2112 uuu and 3223 uuu . Switching sequence of winding depends on the rotor position. The configuration which produces the highest torque waveform has been chosen. The rotor position is usually sensed by Hall sensors [13]. These Hall sensors are put every 120˚. The sensors generate digital signals which give information about rotor position. Using three Hall sensors and conventional six-switch converter, the six different converter states are possible. In order to produce maximum torque, the


98

converter should be commuted every 60 electric degrees. The alternative way is the sensorless method. These methods can be based on sensing currents in two phases or the determination of back electromotive forces (EMF) [2, 17]. The switching sequence of the transistor has been determined on the basis of back EMF inducted in the stator windings. The back EMF waveforms inducted in the stator winding are presented in Figure 3. The calculation have been executed for steady-state velocity equal to 504 rpm and load torque 5.2loT Nm.

Fig. 3. Calculated back EMF and voltage waveforms of load machine The switching sequence of the transistors and diodes, switching intervals and rotor position are listed in Table 1. The β is the mechanical angle. Switching intervals are presented in electrical degrees. As it can be noticed from Table 1, the transistors are conduct within 120 electrical degrees. The diodes conduct only when the phase current is switching off. The studied motor has 5 pairs of poles in the outer rotor. Therefore, in this case 360 electrical degrees correspond to 72 mechanical degrees. The five pole pairs BLDC motors need five electrical cycles to execute one rotation of the rotor. Figure 4 illustrates the electric connection of the stator windings and current direction in the six converter states. The numbers 1,2 and 3 indicate the motor windings.


99

Table 1. Switching sequence of the transistors and diodes of the converter

Converter state

Switching interval

Rotor position β [°]

Transistor ON

Diode ON

I 0˚ – 60˚ 0 – 12 T1, T6 D2 II 60˚ – 120˚ 12 – 24 T2, T6 D4 III 120˚ – 180˚ 24 – 36 T2, T4 D3 IV 180˚ – 240˚ 36 – 48 T3, T4 D5 V 240˚ – 300˚ 48 – 60 T3, T5 D1 VI 300˚ – 360˚ 60 – 72 T1, T5 D6

Fig. 4. The stator winding connection in the six converter states Two current loops are considered at each of converter state. However, in each state two different periods must be studied. It has been assumed that values of voltage 31u and 12u are given. Figure 5 illustrates equivalent electric circuit of the motor in the 4-th converter state. In this case the phase 2 is not powered. In the first period – after phase commutation, the current 2i in the switched phase 2 has value different from zero. It flows through windings 1, 2 and diode D5 (see dash dot marked current loop on Fig. 5). Then the voltages are equal to 3131 eeUu s


100

and 1212 eeu . When the current 2i achieves zero, the currents 13 ii and voltages 3131 eeUu s and )(5.0 3112 eeUu s .

Fig. 5. The equivalent electric circuit for IV stage of converter

5. The simulation of the dynamics

In this section the dynamic operation, i.e. operation with unknown varying angular velocity is investigated. In order to solve transient dynamics state, the field-circuit model (7) has been applied. Additionally, the equations describing mechanical motion (9) and (10) have been included into mathematical model of the motor. The algorithm and the computer code for simulation of the motor dynamics have been developed. The start-up of the loaded permanent magnet brushless DC motor with outer rotor has been studied. The cross section of the motor has been subdivided into 10080 triangular elements. Such number of elements ensure sufficient precision of the simulation. The switching sequence of the converter transistors has been elaborated on the basis of back electromotive forces in the stator winding and rotor position – see section 4. The motor has been controlled by using the switching algorithm presented in Table 1. The calculations have been performed for 002.0J kgm2, 0.2loT Nm, 334.0t ms and supply voltage equal to 24SU V. In order to calculate angular velocity, electromagnetic torque, back electromotive forces and currents waveforms, the coupled field-circuit non-linear and motion equations have been solved simultaneously with Newton-Raphson process. The waveforms of back EMF are shown in Figure 6.


101

Fig. 6. Back EMF waveform

Fig. 7. Phase current waveforms As it can be seen from Figure 6, the maximum values of EMF are equal to

05.9321 eee V when the velocity achieve approximately steady-state value 510 rpm. The waveforms of windings currents, angular velocity and electromagnetic torque are shown in Figures 7, 8 and 9 respectively. As it can be noticed from the figures, the maximum values of torque 8T Nm and currents 22.2121 II A have been obtained. In the torque waveform (Figure 10), and as well as in the velocity waveform (Figure 8) substantial oscillations can be observed. They are caused by cogging torque and converter commutation [19]. The cogging torque is generated by interactions between permanent magnets and stator teeth. The shape of cogging torque waveform depends on machine’s structure [14]. The reduction of this oscillations may be obtained by the optimization of machine magnetic circuit geometry. On the other hand, the examined BLDC motor is controlled by conventional six-switch converter. The phase commutation depends on the rotor position. The converter also produces oscillations in the torque waveform. These oscillations are caused by change of currents direction in the stator winding. In order to reduce such torque ripple, a RC filter connected with the input of the


102

motor can be applied [12]. When we study BLDC motor connected with converter, it is necessary to optimize the motor geometry and the control system parameters at the same time.

Fig. 8. Angular velocity waveform

Fig. 9. Torque waveform

Fig. 10. Oscillations in torque waveform


103

6. Conclusions The elaborated algorithm and the software can be successfully applied in the simulation of BLDC motors dynamics. The algorithm has been tested. It has a good convergence and is very efficient. Due to the parameterization, different structures of BLDC motors can be simulated. The algorithm can be supplemented with non-deterministic optimization procedure in the nearest future. After that, the authors want to complete the three optimization tasks. In the first one, the optimization of the geometry of the selected motor will be executed. In the second one, the parameters of supply and control system will be optimized. In the third one, the complex optimization of the motor geometry and control system will be carried out.

References

[1] Chen J., Guo Y., Zhu J., Development of a high-speed permanent-magnet brushless

DC motor for driving embroidery machines, IEEE Transactions on Magnetics, vol. 43, No. 11, pp. 4004 – 4009, 2007.

[2] Dixon J., W., Rodríguez M., Huerta R., Simplified Sensorless Control for BLDC Motor, The 19th International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium EVS-19, Busan, South Korea, pp. 1432 – 1442, 2002.

[3] Demenko A., Nowak L., Szelag W., Numerical formulation of motion equation in dynamic finite element analysis of electromechanical converters, Proceedings of International Workshop “Electric and Magnetic Fields”, Liege, Belgium, 28 - 30 September1992, pp. 610 – 616.

[4] Demenko A., Sykulski J., Wojciechowski R., Network representation of conducting regions in 3-D finite elements descriptions of electrical machines, IEEE Transactions on Magnetics, vol. 44, No. 6, pp. 714 – 717, 2008.

[5] Ishak D., Zhu Z. Q., Howe D. 2005, Permanent-magnet brushless machines with unequal tooth widths and similar slot and pole number, IEEE Transactions on Industry Applications, vol. 41, No. 2, pp. 584 – 590, 2005.

[6] Ishak D., Zhu Z. Q., Howe D., Comparative study of permanent magnet brushless motors with all teeth and alternative teeth windings, Proceedings of IEE 2nd International Conference Power Electronic, Machines and Drives, pp. 834-839, 2004.

[7] Knypiński Ł., The steady-state and transient FEM analysis of the outer-rotor permanent magnet brushless DC motor, Proceedings of X International PhD Workshop OWD 2008, Wisla, Poland, pp. 277 – 280.

[8] Knypiński Ł., Nowak L., Field-circuit simulation of the outer rotor permanent magnet brushless DC motor taking nonlinearity into account, Proceedings of XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2009, Arras, pp. 247 – 248.

[9] Lindth P. M., Jussila H. K., Niemelä M., Parviainen A., Pyrhönen J., Comparison of concentrated windings permanent magnet motors with embedded and surface mounted rotor magnets, IEEE Transactions on Magnetics, vol. 45, No. 5, pp. 2085 – 2089, 2009.


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[10] Nowak L., Dynamic operation of an electromagnetic actuator taking nonlinearity and eddy currents into account, COMPEL, vol. 18, No. 4, pp. 611 – 618, 1999.

[11] Nowak L., Radziuk K., Transient analysis of PWM-excited electromagnetic actuators, IEE Proceedings-Science, Measurement and Technology, Vol. 149, pp. 199 – 202, 2002.

[12] Rajan A. A., Vasantharatha S., Harmonics and torque ripple minimization using L-C filter for brushless DC motors, International Journal of Recent Trends in Engineering, vol. 2, No. 5, pp. 239 – 243, 2009.

[13] Samaylenko N., Han Q., Jatskevich J., Dynamics performance of brushless DC motors with unbalanced Hall sensors, IEEE Transactions on Energy Conversion, vol. 23, No. 3, pp. 752 – 763, 2008.

[14] Saied S. A., Abbaszadeh K., Hemmati S., Fadaie M., A new approach to cogging torque reduction in surface-mounted permanent-magnet motors, European Journal of Scientific Research, vol. 26, No. 4, pp. 499 – 599, 2009.

[15] Stachowiak D., Edge element analysis of brushless motors with inhomogeneously magnetized permanent magnets, COMPEL, vol. 23, No. 4, pp. 1119 – 1128, 2004.

[16] Szeląg W., Numerical method of calculation of magnetic field distribution in synchronous machine, Academic Journals of Poznan University of Technology, No. 37, 1989.

[17] Shao J., Nolan D., Teissier M., Swanson D., A novel microcontroller-based sensorless brushless DC (BLDC) motor drive for automotive fuel pumps, 37-th Industry Applications Annual Meeting IAS’02, Pittsbourgh, vol. 4, pp. 2386 – 2392, 2002.

[18] Yong Wang, Chau K. T., Chan C., C., Jiang J. Z., Transient analysis of a new outer-rotor permanent-magnet brushless DC motor drive using circuit-field-torque coupled time-stepping finite-element-method, IEEE Transactions on Magnetics, vol. 38, No. 2, pp. 1297 – 1300, 2002.

[19] Yong Liu, Zhu Z., Q., Howe D., Commutation-torque-ripple minimization in direct-torque controlled PM brushless DC drives, IEEE Transactions on Industry Applications, vol. 43, No. 3, pp. 1012 – 1021, 2007.

[20] http://www.arnoldmagnetics.com, July 2010.

Acknowledgment

This work has been financially supported by the project No. POIG.01.01.02-00-113/09.


105

Analysis of the dynamical performance of the two-mass drive

system with the modified state controller

Marcin Kamiński, Teresa Orłowska-Kowalska, Krzysztof Szabat Wroclaw University of Technology

50-372 Wrocław, ul. Smoluchowskiego 19, e-mail: marcin.kaminski, teresa.orlowska-kowalska, [email protected]

In this publication a modified state controller applied in the speed control loop of two-mass drive system is shown. A characteristic feature of this type of a drive system is an existence of oscillations of electromagnetic state variables, resulting from the finite stiffness of the connection between driven motor and the load machine. Effective damping of torsional vibrations in such a system is achieved by introducing additional feedback in the control structures of the two-mass drive. In the described control system the reduction of the feedbacks number is achieved by elimination of the one coming from the torsional torque. At the same time, it was assumed that the beneficial dynamic properties of the two-mass drive obtained in a case of the application of all possible additional feedbacks should be kept. Calculation of the controller gains was done using the pole placement method. Application of the pole placement method gives a possibility for setting the parameters of the control structure for given values of damping coefficient and resonance frequency of the close-loop system, so it is possible to influence the dynamic properties of the drive.

1. Introduction In the recent years requirements for the perfect action in steady and dynamic states of industrial electrical drives are becoming more stringent. The aim of such systems is to minimize the duration time of the transient process, the ideal tracking of the given trajectory of the speed (or position), robustness to parameter change of the controlled systems. The requirements mentioned above lead the engineers to develop new methods and control algorithms of the drives. In addition, they require accurate modeling and working conditions to obtain high precision of control, which is often connected with elimination of the simplifying assumptions. The mathematical model of the two-mass system presents phenomena occurring in many electrical drives, which can be encountered in practical industrial applications. Examples of drive systems characterized by these properties can be found in: – mill drives, – mechanisms of textile and paper machinery, – conveyors, – radio telescopes, – servo drives,

M. Kamiński, T. Orłowska-Kowalska, K. Szabat / Analysis of the dynamical

106

– drives of the robots, – positioning systems of hard disks.

A characteristic feature of this type of drive is the presence of elastic connections between the motor and the load machines. The existence of such connections in the mechanical part of the drive is the cause of generation of dynamic oscillations of the drive state variables. Such a phenomenon makes it impossible to precisely control the speed or angular position of the shaft in the drive system with elastic joint. In extreme cases, the oscillations may cause loss of stability of the controlled drive system [1]. In order to obtain a damping of torsional vibrations in the drive system with elastic joints following solutions are implemented: – modification of the mechanical part, – application of modified setting of the controllers, – extension of the classical control structures by introduction of additional

feedbacks, – implementation of advanced control techniques. The first method mentioned above relies on an introduction of additional elements in the mechanical part of the drive (i.e. introduction of mechanical dumpers); such a solution increases the cost of the drive and also its dimensions what is especially nowadays very important in industrial applications [3]. It should also be noted that the realization of such additional components is not easy and requires additional preparation. There is also possibility of modification of the control structure gains, which however cause the reduction of the electrical drive dynamics. Such a solution introduces a significant delays in the control structure, the time of speed setting in reference value is large, while system response to dynamic change of the load torque is slow. One of the most effective and the simplest in realization methods for damping of torsional vibrations in the drive system with elasticity is introduction of additional feedbacks in the classical control structure (i.e. feedbacks from torsional torque and load speed, and/or their derivatives) [1]. Suppression of state variables oscillations caused by elastic shaft between motor and load machine can be also achieved after implementation of the advanced control structures, but it should be noted, that they are computationally complex algorithms and difficult during development of the project. They are based on: – sliding mode control [4], – elements of artificial intelligence: fuzzy logic and neural networks [5], – adaptive control structures [6], – predictive controllers [7]. In this work, in order to ensure proper work of the electric drive with elastic connection, which allows high accuracy of the speed control and robustness in presence of parameter changes, a structure based on a state controller is proposed. The values of gain coefficient in this controller are calculated using pole placement


107

method [2]. A characteristic feature of such an analysis of the controller is possibility of the assumed placement of all poles of the closed structure, what allows obtaining the required dynamic properties of the controlled system. In the case of classical methods of selecting controller settings (Kessler criteria), only the dominant poles are taken into account, therefore, there are inconsistencies between reference transients and those achieved in the drive structure. In the literature exist many of examples of state controller application in drives with elastic coupling [8], [9], [10]. However, the beneficial properties of the speed control structure with the state controller are possible to obtain when information about all state variables is available. In a case of the two-mass system the most often used additional feedbacks are taken from thee torsional torque and the load-side speed. In real application full information about state variables is difficult to obtain, it requires extension of the drive and implementation of additional sensors, therefore increases the cost of a whole project. Additionally, in industrial application problems with installation of sensor systems and measurement noises can appear. For solving this problem, the special structures for estimation of the required state variables must be used. This issue is currently dominated by two trends of development: – implementation of algorithmic model for state variables reconstruction (i.e. the

Kalman filter or the Luenberger observer) [10], – neural estimators [11]. The algorithmic methods, based on the observer theory, allow obtaining very good results. However, in this case, there is a need for knowledge of the mathematical model and parameters identification of the object. On contrary, neural networks do not need any knowledge about the mathematical model and its parameters, but are characterized by high computing power requirements during operation, and time-consuming (algorithms for weight coefficient calculations) and complex design process (in a case of their structure optimization). Therefore, reasonable and very beneficial is elimination of feedbacks number used in the control structure and use minimal number of measured or estimated variables. In the case of control structure with the state controller, described below, a feedback from the torsional torque is eliminated.

Several design stages of modified state controller are presented in this publication. The results of simulation and experimental verification of the described control structures implemented for speed control of the drive system with elastic joint are presented.

2. Mathematical model of the two-mass drive and control structure

Mechanical part of the drive system consists of a motor machine – represented by electromagnetic torque me , motor speed 1 and mechanical time constant T1, connected with a load machine – represented by load torque mL, load-side speed 2


108

and mechanical time constant T2, using an elastic shaft represented by a torsional torque ms and a time constant Tc. During the analysis of such a model a simplified mathematical description based on the following equations is used:

Le

s

cc

s

mT

mT

tmtt

TT

T

T

tmtt

dtd

0

10

00

1

011

100

100

2

1

2

1

2

1

2

1

(1)

Though the power converter which supplies the motor as well as a control system are very fast, it is possible to take into account the delays of the electromagnetic torque control loop in the design process. The influence of the time constant of electromagnetic part of the drive on transients of state variables of drive is presented in [12]. This analysis shows that delays in electromagnetic control loop in the control structure described in this paper can be neglected. So in the further analysis and in the block diagram of the drive structure presented in Figure 1, an ideal electromagnetic torque control loop was assumed (there is no additional delays), which may be represented by the transfer function:

1)( sG (2)

Fig. 1. The speed control structure of the two-mass drive system based on the state controller


109

In order to determine the transfer function of the closed structure presented in Fig. 1 the following equations were used:

(3)

(4)

(5)

232112

21

22

11

kmkkdtKmdt

dmT

mmdt

dT

mmdt

dT

srie

sc

Ls

se

(6)

Introducing the Laplace operator we obtain:

(7)

(8)

(9)

232112

21

22

11

kmkkRmsmT

mmsTmmsT

sre

sc

Ls

se

(10) where:

sKR i (11)

After some calculations the following equation is obtained:

L

2c1LL2Lc1r

32212

2c1213

c212

msTTmmksmTkR

ksTkksTTkRsTsTsTTT

(12)

which enables to determine the transfer function of the closed control system:

32212

21213

21

2

ksTkksTTkRsTsTsTTTR

ccr

(13)

Taking into account expression (11) we have:

icc

i

r KkksTkTTsTTksTTTsK

3122212

213

214

2

(14)

The characteristic equation of the closed system has the following form:

c

i

ccccc TTTK

TTTk

TTTks

TTk

TTTTs

TksssH

2121

3

21

1

1

2

12

2

1

134 11

)( (15)

In order to calculate the equations defining gains of the state controller, the characteristic equation of the system (15) have to be compared to the reference polynomial of the same order. For the considerations in this project the following polynomial was taken into account:


110

4

o3or

2o

2r

2o

2or

34

2oor

22oor

2ref

4s42s4ss

s2ss2ssH

(16)

where: r, o – are required dumping factor and resonance frequency of the closed-loop system.

Comparing the elements with the same power of the Laplace operator, equations presented below can be obtained:

(17)

(18)

(19)

c

io

ccor

cccoro

or

TTTK

TTTk

TTTk

TTk

TTTT

Tk

21

4

21

3

21

13

1

2

12

222

1

1

4

1142

4

(20) and finally after a few calculations following expressions describing the gain coefficients of the state controller are obtained:

(21)

(22)

(23)

coi

orc

ccoroc

or

TTTK

kTTTk

TTTTTTk

Tk

214

13

213

12

22212

11

4

1142

4

(24)

In order to reduce the number of additional feedback in the structure, attempt of elimination of torsional torque feedback was made. Therefore in equations (21) - (24), the following assumption was introduced:

0114212

22212

ccoroc TTTT

TTk (25)

Based on (25) the formula specifying the damping coefficient r of the system with assumed resonance frequency was calculated:

221

22121

42

oc

ocr TTT

TTTTT

(26)

Obtained value is taken into account during calculation of the remaining gains of the state controller (k1, k3 and Ki, according to (21)-(24)). For maintaining the correctness of calculations and in order to obtain real value of the damping factor, the limit value of resonance frequency o was introduced:


111

co TTT

TT21

212

(27)

According to the presented approach, the dynamics of the drive system with elasticity is modeled using assumed value of parameter o. It should be noticed that the impact of this parameter is increased, in contrary to classical state controller, because at the same time increasing the resonance frequency results in decreasing the value of the damping coefficient.

3. Simulation results

For the drive system with elastic joint, working in the control structure with the state controller based on the parameters calculated in accordance with the equations presented in previous section, simulation tests in Matlab/Simulink were prepared. Following parameters of the two-mass system were assumed: T1=T2=203ms and Tc=2.6ms. For the considered parameters of the drive system the limitation of the resonance frequency, calculated according to the formula (27) takes value: o<43.5277.

In the following figures results of simulation tests are presented. All tests were done for reference speed equal 25% of the nominal speed, to demonstrate the behavior of the drive in the linear operation region, when the limitation of the electromagnetic torque is not active. After stabilization of the velocity at a reference level, at time t1=0.5s and t2=1.5s, the load torque was switched off. The control structure has been studied for different values of the resonance frequency. The results of simulation are presented in Fig. 2.

Obtained transients demonstrate the ability to influence on the system dynamics in a wide range. Increasing of the resonance frequency leads to a smaller values of the damping factor (according to the formula (26)); in result for pulsation o=40s-1 oscillation in transients of electromagnetic torque and both system speeds are observed (Fig. 2a,b). It is important that theses oscillations are diminishing, but they prolong the setting time of state variables at a reference level. For pulsation value o=30s-1 oscillations are well damped and the setting time of the system speed is short (Fig. 2e,f). For greater values of o, in the transient states of the system, bigger values of electromagnetic torque are observed, which forces the highest dynamics (Fig. 2c,d).

In the Fig. 3 analysis of the pole placement of the described control structure is presented. Changes of the design parameters (o and r) cause specific changes of the pole location on the complex plane. It should be noted that, in the control structure with state controller, where one feedback from the torsional torque is eliminated, increasing of the pulsation o moves the poles of the system in the direction of the imaginary axis. This situation is in contrary with the case when this feedback exists, and the damping factor r is constant and chosen independently.


112

a) b)

c) d)

e) f)

Fig. 2. Transients of motor and load speeds (a,c,e) and torques: electromagnetic and shaft (b,d,f) for two-mass driver system with modified state space controller, for different values of resonant

frequency and damping factor o = 40s-1, r = 0.30 (a,b), o = 35s-1, r = 0.52 (c,d) and o = 30s-1, r = 0.74 (e,f) – simulation results


113

Fig. 3. Location of poles for two-mass driver system with modified state space controller

A comparison of transients obtained for classical state controller (with feedback

form shaft torque) and modified state controller (with reduced number of feedbacks) are presented in Fig. 4. Tests were prepared for the same values of damping coefficient and resonance frequency: o = 30s-1 and r = 0.74. It is possible to observe that elimination of the analyzed feedback does not deteriorate the dynamic properties of the control structure for tested values of settings.

a) b)

Fig. 4. Comparative transients of the load speed (a) and electromagnetic torque (b) in the control structure with classical and modified state controller – simulation results for o=30s-1 and r=0.74

All the above results were obtained for the two-mass system, where the

mechanical time constants of the motor and load machine have the same value. In the last stage of simulation studies the tests of the designed control structure are made for the case of twice bigger value of the mechanical time constant (T2=2T2N).


114

a) b)

Fig. 5. Simulation results for the drive with state controller for T2=2T2N

Results of simulation are presented in Fig. 5 (for the modified state controller without feedback from shaft torque, where o=25s-1 and r=0.80). This change of T2 parameter was not taken into account during the calculations of the gains in the tested controller. For changed value of T2 the proposed control structure also enables the effective vibration suppression in the two-mass system. For the same value of o, bigger values of electromagnetic torque (and also motor current) is observed during system transients. Due to increase of the moment of inertia of the load machine, the settling time is little longer. This test presents possibility of the modified state controller and the proposed design procedure also in case of parameter changes of the drive system.

4. Experimental results For verification of the presented control structure in the real drive the laboratory

set-up shown in Fig. 6 was used. The laboratory set-up is composed of two machine motors, connected with an elastic shaft. The stiffness of connection depends on the shaft diameter. The speeds of machine and load motor are measured by incremental encoders (36000 pulses per rotation). On the laboratory set-up the LEM sensors for current measurement are implemented. Measurements data and control signals are connected with digital and analog inputs/outputs of the dSPACE 1102 card. The motor is driven by a transistor power converter.

There is no torque shaft sensor in the laboratory set-up. In order to observe the shaft torque transients in the analyzed drive, an estimator based on one of two-mass system equations was used and applied in DSP:

dtdTmm 1

1es

(28)

The idea of such estimator was presented in the application with RRC (Resonance Ratio Control) control structure [13], [14]. The model used in the


115

studies is slightly modified in comparison with the original prototype. In the equation (28) a derivative of the motor machine speed exists, so the measurement noises occurred in this signal can be intensified. For reduction of this phenomenon additional low-pass filters are used in both paths of processing, according to the diagram presented in Fig. 7.

Fig. 6. Schematic diagram of the experimental set-up, where: 1 - motor machine, 2 - load machine, 3,4 - encoders, 5 - shaft, 6 -resistor, 7 - rectifier, 8 control structure, 9 - power converter

Fig. 7. Schematic diagram of the torque shaft estimator

Output signal of the estimator is described with following equation:

1sTsT

1sTmm

q

11

q

ese

(29)

In the structure presented on Fig. 7 information about time constant of the motor machine T1 and also measurement of electromagnetic torque me and speed 1 is needed. Moreover, the problem with value of time constant Tq of the filter is appearing. But the advantage of the applied torsional torque estimator is its simplicity, which leads to small calculation power requirements.


116

a) b)

c) d)

e) f)

Fig. 8. Transients of motor and load speeds (a,c,e) and torques: electromagnetic and shaft (b,d,f) for two-mass driver system with modified state space controller, for different values of resonant

frequency and damping factor o=30s-1, r=0,74 (a,b), o=35s-1, r=0,52 (c,d) and o=40s-1, r=0,30 (e,f) – experimental results


117

As in the previous case correct work of the speed control structure with modified state controller presented in simulation were confirmed in experimental tests (Fig. 8). All researches were prepared assuming the parameters and working conditions similar as in the simulation tests. After calculations of the controller gains the large values of Ki (especially for bigger values of resonance frequency), strengthening the value of the error in the system, are obtained (according to (24)). It is advantageous because it increases the value of the output signal of the controller and therefore contributes positively to the control quality. However, in real implementation the negligible noises in the control structure can also be strengthened and interfered with the system, which feature additionally limits the maximal value of the pulsation o.

Changes of the resonant frequency and damping factor give effective changes of the dynamics in the controlled structure. Forcing a very high dynamics of the drive (large value of o and small r) leads to oscillations of state variables (Fig. 8e,f). After setting correct values of o and small r it is possible to achieve a short time of speed response of the drive system, without readjustment and state variables oscillation (Fig. 8a,b). a) b)

Fig. 9. Experimental results for the drive with state controller for T2=2T2N Also in the case of experimental tests correctness of the control structure operation for the two-mass system with doubled time constant of the load machine is presented in Fig. 9. Obtained results are similar to results from simulation tests (see Fig. 5).

5. Conclusion

The design of speed control structure with a modified state controller for the two-mass drive system simplifies the realization of such a structure in the real solution and decreases financial cost of electrical drive. The additional feedback


118

from shaft torque was eliminated, so there is no necessity of measurement or estimation of this state variable. At the same time, proposed control structure gives similar properties as a classical state controller. Comparative tests present possibility of obtaining good dynamics and damping of torsional vibrations similarly as in a case of full state controller. All presented tests were made for the natural resonance frequency of the two-mass drive equal 9.8kHz, which was caused by possibility of experimental verification of obtained results. The simulation results are confirmed by laboratory experiments.

References [1] Szabat, K., Orlowska-Kowalska, T., Vibration suppression in two-mass drive system

using PI speed controller and additional feedbacks – comparative study, IEEE Trans. Industrial Electronics, vol. 54, no. 2, pp. 1193-1206, 2007.

[2] Ogata K., Modern Control Engineering, 4-th edition, Prentice Hall, 2002. [3] Takesue N., Zhang G., Furusho J., Sakaguchi M., Precise position control of robot

arms using homogeneous ER fluid, IEEE Control Systems Magazine, vol. 19, no. 2, pp. 55-61, 1999.

[4] Korondi P., Hashimoto H., Utkin V., Discrete sliding mode control of two mass system, Proc. of the IEEE Inter. Symposium on Industrial Electronics ISIE '95, vol. 1, pp. 338 - 343, 1995.

[5] Orlowska-Kowalska T., Szabat K., Optimization of fuzzy-logic speed controller for DC drive system with elastic joints, IEEE Trans. Industry Applications, vol. 40, no. 4, pp. 1138 – 1144, 2004.

[6] Orlowska-Kowalska T., Szabat K., Control of the Drive System With Stiff and Elastic Couplings Using Adaptive Neuro-Fuzzy Approach, IEEE Trans. Industrial Electronics, vol. 54, no. 1, pp. 228-240, 2007.

[7] Cychowski M.T., Szabat K., Efficient real-time model predictive control of the drive system with elastic transmission, IET Control Theory & Applications, vol. 4 , no. 1, pp. 37-49, 2010.

[8] Kaczmarek T., Muszynski R., Damping of torsional servodrive vibration by means of the state variable feedback, Proc. of the 9th Inter. Conf. Power Electronic and Motion Control EPE-PEMC’2000, Kosice, Slovak Republic, pp. 6.225-6.228, 2000.

[9] Porumb A., Preitl S., A comparision of speed control structures of an elastic coupled drive system, Proc. of the 8th Inter. Conf. Power Electronics and Motion Control PEMC’98, pp. 4.196-4.2003, 1998.

[10] Orłowska-Kowalska T., Szabat K., Zastosowanie regulatora stanu w układzie napędowym z połączeniem sprężystym, Mat. VI Krajowej Konferencji SENE’03, pp. 679-685, 2003.

[11] Kaminski M., Orlowska-Kowalska T., FPGA Realization of the Neural Speed Estimator for the Drive System with Elastic Coupling, Proc. of 35th Annual Conference of the IEEE Industrial Electronics Society IECON 2009, Porto, Portugal, on CD, 2009.


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[12] Szabat K., Kaminski M., Design of the state controller for the two-mass drive system including the dynamic of the torque control loop, Poznan University of Technology Academic Journals Electrical Engineering, Issue 61, pp. 89-100, 2010.

[13] Yuki K., Murakami T., Ohnishi K.: Vibration control of 2 mass resonant system by resonance ratio control, Proc. of the Industrial Electronics, Control, and Instrumentation, vol. 3, pp. 2009-2014, 1993.

[14] Hori Y., Sawada H., Chun Y.: Slow resonance ratio control for vibration suppression and disturbance rejection in torsional system, IEEE Trans. Industrial Electronics, vol. 46, no. 1, pp. 162-168, 1999.


120

Predictive speed control of induction drive with high-frequency torsional oscillation

Piotr J. Serkies, Krzysztof Szabat, Mateusz Dybkowski

Wroclaw University of Technology 50-372 Wrocław, ul. Smoluchowskiego 19, e-mail: piotr.serkies,

krzysztof.szabat, mateusz.dybkowski@ pwr.wroc.pl

In the paper issues related to the use of model predictive control (MPC) of the drive system with an elastic coupling and an induction motor are presented. After a short introduction the mathematical model of the driving motor with a vector control structure and the two-mass drive system are described. Then, the idea of the MPC is introduced. Next the exact formulation of the MPC for a two-mass drive system is shown. In the MPC algorithm the constraints of the inner and control variables are taken into consideration. The results obtained in the simulation study confirm the correct work of the investigated structure.

1. Introduction

A demand for the minimalization and reducing the total moment of inertia which allows to shorten the response time of the whole system is evident in modern drives system. However, reducing the size of the mechanical elements may result in disclosure of the finite stiffness of the drive shaft, which can lead to the occurrence of torsional vibrations. This problem is common in rolling-mill drives, belt-conveyors, paper machines, robotic-arm drives including space manipulators, servo-drives and throttle systems [1] – [10].

Many control structures have been proposed for the torsional vibrations damping of the two-mass drive system [1] – [12]. The most popular approach relies on the application of additional feedback(s) from selected state variable(s) [1] – [2]. Those structures are effective in the case of the system with known and constant parameters. A drive system with changeable (or unknown) parameters requires more sophisticated control paradigms such as non-linear or adaptive control. Sliding mode based structures are proposed in [4] – [9], to achieve good level of robustness to plant parameter variations. Examples of the adaptive control structure are shown in [10] – [11].

In the recent years, model predictive control (MPC) has been widely investigated for its potential in controlling modern electrical drives and power electronics circuits [12] – [14]. Predictive control presents several advantages that make it suitable for the control of power converters and drives. The central feature of MPC is that it enables the process operating and physical constraints (due to e.g.

P. J. Serkies, K. Szabat, M. Dybkowski / Predictive speed control of induction drive…

121

resource limitations, operational or safety concerns as well as limits arising from various economic objectives) to be taken directly into consideration in the control problem formulation so that any potential constraint violations are anticipated and prevented. Additionally, as the control input is obtained by solving an optimization problem at each sampling time, it can ensure truly optimal performance of the closed-loop control system.

The main goal of this paper is to present and discuss simulation results related to the MPC of a two-mass system. Contrary to some previous works [13], [14], the DC driving machine has been replaced in this work with an induction motor. Although the mechanical part of the drive system remains the same, the change of the torque control loop from the simple one (DC motor) to very complicated (field-oriented controlled induction motor) can influence the properties of the whole control structure. Additionally, the frequency of torsional oscillations is more than ten times higher than in [13]. The main goal of the paper is to investigate how these two factors influence the system performance.

2. The induction motor drive with field oriented control structure

Induction motors (IM) are used more and more widely in different industrial

installations. IM are durable, they do not need much servicing and are relatively cheap, yet they are nonlinear objects and thus require advanced control methods. The direct field-oriented control structure (DFOC), presented in Fig. 1, is recently commonly used IM control scheme. It needs information about the rotor flux vector magnitude and position to perform precise direct flux control and the transformation from a-b-c to x-y as well as α-β reference frames and vice versa. Field-oriented control [16] makes it possible to separate control of the rotor flux – by means of the stator current vector component isx and electromagnetic torque control – by means of the second current component isy. It utilises a similar torque control method as in the separately excited DC machine. The rotor flux vector of IM has to be calculated on the basis of suitable estimator [16] using measured stator currents and voltages as well as IM parameters. Errors in all those factors influence the computed value of the rotor flux vector and thus accuracy of the whole torque control loop in a negative way. They can also reduce the performance of the outer (speed) loop.

Usually the external speed controller for two-mass system with additional feedbacks is designed with the assumption, that the internal torque control loop is very fast and reacts without any delay [2]. In the case of the DFOC induction motor drive the internal torque control loop contains relatively complicated structure, which can cause some delay (and nonlinearities) in the torque control (in comparison with very simple DC drive case). Thus the effectiveness of the external MPC speed controller, designed in the same way as for linear system without internal delay, is tested based on the estimated state variables.


122

Fig. 1. The block diagram of DFOC

3. Two-mass drive system

Many industrial drive systems can be modelled as two-mass systems, where the first mass represents the moment of inertia of the motor and the second mass refers to the moment of inertia of the load machine. In this paper, the commonly used inertia-free-shaft dual-mass system model will be employed, which is described by the following normalized differential equations [2]:

11

( ) ( ) ( )e sd tT m t m t

dt

(1)

22

( ) ( ) ( )s Ld tT m t m t

dt

(2)

1 2( )

( ) ( )sc

dm tT t t

dt (3)

where: 1 ,2 – motor and load speeds, me, ms, mL – electromagnetic, shaft ad load torques, T1, T2 – mechanical time constant of the motor and the load machine, Tc – stiffness time constant and T – position time constant.

The schematic diagram of a dual-mass system is shown in Fig. 2.


123

2 Lmem 1 smsm

Fig. 2. The ideal diagram of the two-mass system

In most cases, the internal damping coefficient d is very small and can be neglected in the synthesis of the control system.

The resonant fr and antiresonant far frequencies of the two-mass system are defined as follows:

21

21cr JJ

JJK

21f

,

2

car J

K21f

(4)

The value of the resonant frequency depends on the type of the drive and can vary from a few hertz in a paper machine section [17], through dozens of hertz in a rolling-mill drive [18], and can exceed hundreds hertz in a modern servo-drives [14]. The value of the antiresonant frequency can be even ten times smaller than the resonant one in a dryer [2], but usually the difference is much smaller (smaller than two).

The next parameter commonly provided for analysis of the two-mass system is inertia ratio defined as:

1

2

1

2TT

JJR (5)

4. MPC-based control structure

In model predictive control, an explicit model of the plant is used to predict the

effect of future actions of the manipulated variables on the process output. The performance of the system (whether predicted or actual) will be assessed through a cost function [19], [20]:

0kk

Tkk

Tk RuuQyyJ (6)

where Q 0 and R > 0 are the weighting matrices. In (6), yk denotes the value of the output vector at a future time k, given an input sequence uk, an initial state x0 of the system. At each time step k an MPC algorithm attempts to optimize future plant behavior while respecting the system input/output constraints by computing a sequence of control actions.


124

The MPC algorithm based on problem (6) can be implemented in two ways. The traditional approach relies on solving the optimization problem on-line for a given x(k) in a receding-horizon fashion. This means that, at the current time k, only the first element control signal uk of the optimal input sequence is actually implemented to the plant and the rest of the control moves uk+I are discarded. At the next time step, the whole procedure is repeated for the new measured or estimated state x(k+1) [20]. This strategy can be computationally demanding for systems requiring fast sampling or low-performance computers and hence greatly restricting the scope of applicability to systems with relatively slow dynamics. In the second approach, the problem (6) is first solved off-line for all state realizations x Xf with the use of multi-parametric programming [20]. Specifically, by treating the state vector x(k) as a parameter vector, it can be shown that the parameter space Xf can be subdivided into characteristic regions, where the optimizer is given as an explicit function of the parameters. This profile is a piecewise affine state feedback law:

r,rr PxgxKxU (7) where Pr are polyhedral sets defined as:

rrrn

r N,...1r,dxH|xP (8) Algorithms for the construction of a polyhedral partition of the state space and

computation of a PWA control law are given in [20] – [24]. In its simplest form, the PWA control law (7) – (8) can be evaluated by searching for a region containing current state x in its interior and applying the affine control law associated with this region. More efficient search strategies which offer a logarithmic-type complexity with respect to the total number of regions Nr in the partition have also been developed. Nonetheless, the implementation of the explicit MPC control law can often be several orders of magnitude more efficient than solving the optimization problem (6) directly. This gain in efficiency is crucial for demanding applications with fast dynamics or high sampling rates in the milli/micro second range, such as the drive system considered in this paper. A more exact description of the MPC strategy and its explicit solution is presented [20] – [24].

The block diagram of the considered control structure presented in Fig. 3.

emrem

refLs mm ˆ,ˆ,ˆ,ˆ 21

1

2 Lmem 1 smsm

Fig. 3. The block diagram of the analysed control structure with MPC speed controller


125

It consists of the following blocks:

− a dual-mass system, − a DFOC torque control loop, − a predictive speed controller, − a Luenberger observer used for estimation of the system state variables (it is

assumed that only the motor torque and the motor speed are available for control purposes).

The original state vector of the two-mass drive system has been extended by three additional variables which describ the dynamic of the load torque, reference value and the electromagentic torque. The dynamics of the two variables mentioned firstly is unknown so it is assumed:

0Lmdtd

(9)

0ref

dtd (10)

The dynamics of the electromagnetic torque transients is described by the following equations:

re

mee m

Tm

dtd 1

(11)

Taking into account the abovementioned variables, the analyzed state vector has the following form:

TrefLsec mmmX 21 (12)

The model described by eq. (1), (9) – (11) has been transformed to a discrete model with sampling time Ts. The following constraints are imposed for all k:

5.15.1

33

smm e

(13)

The vector y used in (6) has the following form:

.,,,

214

3

22

11

ymmy

yy

Ls

ref

ref

(14)

The first and the second terms of (14) minimize the difference between the motor and load speed and the reference value while the third term minimizes the difference between the shaft and the load torque and the last term calculates the difference between the two speeds.

The resulting formulation of (6) can be given in the following form:


126

1Nc

1j

2re

N

0k

244

233

222

211

1Ncu,,2u,1u

jmr

kyqkyqkyqkyqmin

(15)

where: q1 … q4 – weights for the victor y, r – weight for control signal, N – length of the horizon window, Nc – control horizon.

5. Results

In order to validate the feasibility and effectiveness of the proposed approach, a comprehensive simulation study has been carried out. In this synopsis, only a number of selected transients are presented. The study has been done with the help of the Matlab-Simulink simulation packet. The used model has different sampling times. The fastest sampling period has the induction motor and the two mass system model – 2 s. The observer has been calculated with the period 100 s; and the predictive controller with 500 s. The parameters of the mechanical part of the drive have been as follows: the stiffness time constant Tc = 100 s and the mechanical time constant of the driving motor T1 = 100 ms. The mechanical time constant of the load machine has been changing between 25 and 200 ms. As mentioned in the previous section, the maximal allowed value of the electromagnetic torque has been set to 3, and for the shaft torque to 1.5 of its nominal value. The frequency characteristic of the analyzed system for different value of R are shown in Fig. 4.

As can be concluded from Fig. 4, the resonant frequency of the systems exceed hundreds of Hertz, contrary to some previous works [13] – [14] where frequency of torsional vibration was much smaller.

First the correctness of the work of the DFOC control structure has been examined. In Fig. 5 the electromagnetic torque responses as well as the flux responses of the induction motor to the step changes of the reference torque are shown.

As can be concluded from the presented transients, the response time of the modulus of the rotor flux is about 10ms (Fig. 5b). Therefore, in the next study the induction motor is first excited (the flux is set to the nominal value) and then the drive is ready to work. Rapid changes of the electromagnetic torque have almost no influence on the transients of the flux. Transients of the electromagnetic torque under rapid changes of its reference value is shown in Fig. 5a. The torque follows its reference value without oscillations and with the setting time approximately 800s (for the step changes equal to the nominal value). So, the presented figures confirm the correct work of the DFOC control structure.


127

-200

-150

-100

-50

0

50

100

150

Mag

nitu

de (d

B)

101

102

103

104

-2

-1

0

1

2

Phas

e (r

ad)

Frequency (rad/sec)

R=2rez=387.3rad/sare=223.6rad/s

R=1rez=447.2rad/sare=316.2rad/s

R=0.25rez=707.1rad/sare=632.4rad/s

Fig. 4. Frequency characteristic of the analyzed systems

0 0.02 0.04 0.06 0.08 0.1 0.12

-2

0

2

time [s]

m [p

.u]

0 0.02 0.04 0.06 0.08 0.1 0.120

0.2

0.4

0.6

time [s]

| r| [

p.u]

meref

me

|rref|

|r|

a) b)

Fig. 5. Responses of the electromagnetic torque (a) , and the modulus of the rotor flux (b) in DFOC control structure to the step changes of the reference value

Then, the whole control structure including the DFOC scheme and the

predictive speed controller working with the Luenberger observer has been investigated. The two-mass drive system with different inertia ratio R = 2 (ωrez = 387.3rad/s), R = 1 (ωrez = 447.2/s), and R = 4 (ωrez = 707.1rad/s) has been tested. The parameters of the predictive control strategy used for the different inertia ratio are shown in Table 1.

Table 1. The utilized parameters of the MPC for different inertia ratio

diag(Q) r N Nc

R = 2 [10500 10500 8 1000] 2 10 2 R = 1 [550 550 8 1000] 2 10 2

R = 0.25 [430 430 80 10] 8 20 2


128

The explicit MPC controller has been computed using the Multi-Parametric Toolbox (MPT). In Fig. 6 two-dimensional cuts through the polyhedral partition corresponding to [2, ms ] and [me,1 ] are depicted for illustration.

-0.1 -0.05 0 0.05 0.1

-1

0

1

me=0 1=0 mL=0 ref=0.75

2 [p.u]

ms [p

.u]

-2 0 2-0.1

0

0.12=0 ms=0 mL=0 ref=0.75

me [p.u]

1 [p.u

]ref =0 =0 m =0 m =0

a) b)

Fig. 6. Closed-loop partitions defined over [ms ω2] (a), [ω1 me] (b)

The tested system has the following operation scheme. At time t1 = 0.05s the reference value of the speed is set to 0.75 of its nominal value. As can be seen in Fig. 7a, the electromagnetic torque response is very fast. It is clearly visible in the some figure that there are no validation in the shaft torque transient. The start-up takes approximately 0.16 s. The load torque is applied at the time t2 = 0.2 s, which causes the small but visible disruption in the speeds transients. The transients of the isx and the isy in DFOC control structure is presented in Fig. 7c and the active controller region in Fig. 7d. The transients of the system with different inertia ratio R = 1 and R = 0.25 are presented in Fig. 8 and 9 respectively.

0 0.05 0.1 0.15 0.2 0.25 0.3-1

0

1

2

3

time [s]

m [p

.u]

0 0.05 0.1 0.15 0.2 0.25 0.30

0.25

0.5

0.75

time [s]

[p

.u]

0 0.05 0.1 0.15 0.2 0.25 0.3-10

0

10

20

times [s]

i s [p.u

]

0 0.05 0.1 0.15 0.2 0.25 0.30

50

100

times [s]

regi

on

ref

2

1

mT

me

isx is

y

mL

a)

b)

c) d)

Fig. 7. Transients of the system for R = 2: a) torques, b) speeds, c) currents in axis x and y,

d) actives regions


129

0 0.05 0.1 0.15 0.2 0.25 0.3-1

0

1

2

3

time [s]

m [p

.u]

0 0.05 0.1 0.15 0.2 0.25 0.30

0.25

0.5

0.75

time [s]

[p

.u]

0 0.05 0.1 0.15 0.2 0.25 0.3-10

0

10

20

times [s]

i s [p.u

]

0 0.05 0.1 0.15 0.2 0.25 0.30

50

100

times [s]

regi

on

ref

1

2

mL

mT

me

isyis

x

a)

b)

c) d)

Fig. 8. Transients of the system for R = 1: a) torques, b) speeds, c) currents in axis x and y,

d) actives regions

0 0.05 0.1 0.15 0.2 0.25 0.30

1

2

3

time [s]

m [p

.u]

0 0.05 0.1 0.15 0.2 0.25 0.30

0.25

0.5

0.75

time [s]

[p

.u]

0 0.05 0.1 0.15 0.2 0.25 0.3-10

0

10

20

times [s]

i s [p.u

]

0 0.05 0.1 0.15 0.2 0.25 0.31

1.5

2

times [s]

regi

on

isx

a)

b)

c)

me mT

mL

isy

2

1

ref

d)

Fig. 9. Transients of the system for R = 0.25: a) torques, b) speeds, c) currents in axis x and y,

d) actives regions

As can be concluded from presented transients the proposed control structure works in a correctly. The torsional vibrations are effectively damped in both examined systems. In the case of the big value of the inertia ratio (R = 2) the decrease of the system dynamic is visible. It comes from the fact that the total moment of inertia of such system is much bigger than the moment of inertia of the system with smaller value of the inertia ratio. The system can become faster by suitable increase the values of q1 and q2.


130

6. Conclusion

In the paper issues related to the application of the MPC control structure to the drive system with an induction motor and the two-mass system are presented. The DFOC control structure has been applied to control the electromagnetic torque. The predictive speed controller works with the Luenberger observer which is used to estimate the non-measurable state variables of the system.

As can be concluded from the presented results, the drive system works correctly for different configuration of the mechanical part of the drive. The sets of the control constraints related to the shaft torque and electromagnetic torque are not validated. It means that the control structure based on the MPC can ensure safe work in a drive system with elastic transmission. The replace of the simple electromagnetic torque control loop (DC motor) by the much more complicated one (DFOC) does not influence the properties of the drive.

The future work will be devoted to designing of an MPC control structure robust to parameter variation with respect to the shape of its transients. Also an experimental verification of the proposed solution is one of the main point of the future work.

References

[1] Orlowska-Kowalska T., Szabat K., Control of the Drive System with Stiff and

Elastic Couplings Using Adaptive Neuro-Fuzzy Approach, IEEE Trans. on Industrial Electronics, vol. 54, no.1, pp. 228-240, 2007.

[2] Szabat K., Struktury sterowania elektrycznych układów napędowych z połączeniem sprężystym. Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej nr 61, Wrocław 2008.

[3] Korondi P., H. Hashimoto H., Utkin V., Direct torsion control of flexible shaft in an observer-based discrete-time sliding mode, IEEE Trans. on Ind. Electronics, pp. 291-296, vol. 45, no.2, 1998.

[4] Szabat K., Orlowska-Kowalska T., Performance Improvement of Industrial Drives with Mechanical Elasticity Using Nonlinear Adaptive Kalman Filter, IEEE Trans. on Industrial Electronics, vol. 55, no. 3, pp. 1075-1084, 2008.

[5] Hace A., Jezernik K., Sabanovic A., Improved Design of VSS Controller for a Linear Belt-Driven Servomechanism, IEEE/ASME Trans. on Mechatronics, pp 385-390, vol. 10, no.4, 2005.

[6] Ryvkin S., Izosimov D., Bayda S., Flex mechanical digital control design, Proceedings of IEEE International Conference on Industrial Technology, IEEE ICIT'03, vol.1, 2003, pp. 298-302.

[9] Vittek J., Makys P., Stulrajter M., Dodds S.J., Perryman R., Comparison of sliding mode and forced dynamics control of electric drive with a flexible coupling employing PMSM, IEEE Int. Conf. on Industrial Technology ICIT 2008, 2008, on CD, China.


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[10] Szabat, K., Orlowska-Kowalska T., “Performance Improvement of Industrial Drives with Mechanical Elasticity using Nonlinear Adaptive Kalman Filter”, IEEE Trans. Industrial Electronics, vol.55, no. 3, 2008, pp.1075-1084.

[11] Hirovonen M., Pyrhonen O., Handroos H., “Adaptive nonlinear velocity controller for a flexible mechanism of a linear motor”, Mechatronics, Elsevier, vol. 16, no. 5, 2006, pp.279-290.

[12] Cortés P., Kazmierkowski M.P., Kennel R.M., Quevedo D.E., Rodriguez J., Predictive control in power electronics and drives, IEEE Trans. Industrial Electronics, vol. 55, no. 12, pp. 4312–4324, Dec. 2008.

[13] Szabat K., Serkies P., Zastosowanie sterowania predykcyjnego w układzie napędowym z połączeniem sprężystym. Przegląd Elektrotechniczny vol. 86, no. 2, pp. 380–383, 2010.

[14] Szabat K., Serkies P., Nalepa R, Cychowski M., Predictive Position Control of Elastic Dual-Mass Drives under Torque and Speed Constraints, International Conference and Exhibition on Power Electronics and Motion Control- EPE-PEMC' 2010 Ohrid Macedonia.

[15] Vašak M., Baotić M., Petrović I., Perić N., Hybrid Theory-Based Time-Optimal Control of an Electronic Throttle, IEEE Trans. on Industrial Electronics, pp. 1483-1494, vol. 43, no.3 , 2007.

[16] Orłowska-Kowalska T., Bezczujnikowe układy napedowe z silnikami indukcyjnymi Oficyna Wydaw. PWr, Wrocław, 2003.

[17] Valenzuela M.A., Bentley J.M., Lorenz R.D., Evaluation of Torsional Oscillations in Paper Machine Sections, IEEE Trans. on Industry Applications, vol. 41, no.2 , pp. 493-501, 2005.

[18] Wang J., Zhang Y., Xu L., Jing Y., Zhang S., Torsional vibration suppression of rolling mill with constrained model predictive control, 6th World Congress on Intelligent Control and Automation, 2006, pp. 6401-6405, China.

[19] Maciejowski J.M., Predictive Control with Constraints, Prentice Hall, UK, 2002. [20] Cychowski M.T., Robust Model Predictive Control, VDM Verlag, 2009. [21] Kvasnica M., Grieder P., Baotic M., Morari M., Multi-Parametric Toolbox (MPT),

HSCC (Hybrid Systems: Computation and Control), Lecture Notes in Computer Science, vol. 2993, 2004, pp. 448-46.

[22] Tøndel P., Johansen T.A., Bemporad A., An algorithm for multi-parametric quadratic programming and explicit MPC solutions, Automatica, 2003, 39, (3), pp. 489-497.

[23] Spjøtvold J., Kerrigan E.C., Jones C.N., Tøndel P., Johansen T.A., On the facet-to-facet property of solutions to convex parametric quadratic programs, Automatica, 2006, 42, (12), pp. 2209-2214.

[24] Bemporad A., Morari M., Dua V., Pistikopoulos E. N., The explicit linear quadratic regulator for constrained systems, Automatica, vol. 38, no. 1, pp. 3–20, Jan. 2002.

Acknowledgment

This research work is supported in part by the Ministry of Science and Higher Education (Poland) under Grant N N510 352936 (2009-2011).


132

Computer modeling in the diagnostics

of transformers’ windings deformations

Szymon Banaszak, Konstanty Marek Gawrylczyk West Pomeranian University of Technology in Szczecin

70 - 310 Szczecin, ul. Gen. Sikorskiego 37, e-mail: [email protected], [email protected]

The diagnostics of power transformers is very important in order to plan repairs and replacements of aged population of transformers operated in Poland and Europe. One of these methods is Frequency Response Analysis – FRA. It can detect any mechanical changes in active part of transformer, which may even lead to serious faults of units in service. As the method is based on comparison of measured curves, which are not always available from previous measurements the computer modeling was applied to create models of windings’ response. The paper presents examples of models created for simple windings and also for real transformer with some deformations of windings simulated.

1. Introduction

The average age of power transformers operated in Poland and other European countries is constantly growing. At present over half of them are operated over 25 years. In addition there are not sufficient possibilities of producing new units in short period of time. Therefore it is very important to recognize transformers’ technical condition. One of diagnostic methods used for this purpose is Frequency Response Analysis – FRA. The method, already applied in industry, is based on the correlation of the geometry of windings and their transfer function, usually in the range from 10 Hz to 2 MHz. The FRA method is used for detection of deformations in windings – radial buckling, axial displacement or inter-winding short-circuits and others. These deformations result from electrodynamic forces coming from short circuits, transient overvoltages, ageing of solid insulation in transformer and also during transportation of units. Slightly damaged winding doesn’t lead directly to catastrophic fault of transformer, as it can be still operated for longer time, e.g. to next overvoltage, which could breakdown the weakened insulation and generate fault of unit [1].

2. Assessment of FRA results

At this stage of FRA development results of measurements are given as damping of windings to sine signal in frequency range, according to formula:

S. Banaszak, K. M. Gawrylczyk / Computer modeling in the diagnostics …

133

in

outUU

log20]dB[FRA (1)

where: Uin – voltage signal applied to winding, Uout – voltage signal measured. The measurement can be taken either on two ends of the winding (with secondary

winding open or shortened and grounded) or between windings of the same phase. The typical FRA curves measured on the power transformer are shown on the Fig. 1. The assessment is currently based mainly on visual comparison of curves recorded between three phases of unit, between sister units or for measurements taken earlier for the same unit. The last option is giving the full information on changes in transformer’s active part, however it is not possible to obtain FRA “fingerprints” for transformers produced 20-25 years ago. Therefore additional direction in development of FRA method is computer modeling of transformer response.

The comparison can be also performed with automated computer algorithms, there are two of them applied in industrial practice (Chinese Standard DL/T911-2004 and NCEPRI method). These algorithms are based on calculating differences between two curves in given frequency ranges, responsible for various phenomena in transformer, but cannot be used without additional help of experienced specialist.

Fig. 1. Example of differences in FRA measurements The identified frequency ranges are related to core magnetism influence, obvious

or slight deformations and set-up of connections and leads [2].

3. Modeling of FRA response

In industrial practice there are often cases of transformers which are difficult to be assessed due to lack of earlier “fingerprints”. Usually it is difficult to find sister unit of the same construction operated in the same working conditions with the same history of service. The comparison between phases is not always very reliable as there are always differences between middle phase and side phases as there is


134

different magnetic flux distribution. Additionally in some transformers there are differences between phases which are known to be typical for given type, e.g. related to leads set-up in the tank or position of bushing versus windings. In such cases the best option seems to be creation of computer model of “healthy” winding and simulation of various defects or even creation of a tool analyzing and comparing response of phases and model and giving possible causes for observed differences.

Fig. 2. Examples of models of single winding compared to reference measurement

Some examples of models’ responses compared to measured data are given on Fig. 2. These were calculated for the small single winding of 15/0.4 low power transformer. The computer model, rather simple at the beginning of experiment, had new elements been added at subsequent stages, resulting in good conformity to real measurements at the end. It was necessary to take into consideration not only basic series and parallel RLC elements but also couplings, leakage currents and other factors not constant in the frequency range. There is also the problem with obtaining actual sizes of all simulated elements and their exact material properties, as these values are used for model generation. It is not possible to open every transformer to measure internal sizes, so the modeling is based on information given in technical documentation of transformer, not always containing all details as they are. All these elements create the circuit model through which the same FRA signal is transferred as for real object giving more or less similar result.


135

At the current stage of modeling it is not possible yet to create complete models giving exactly the same response as this of modeled transformers. However these are still developed and can simulate some basic faults. Models of winding’s FRA response consist of basic RLC elements and additional couplings. The total number of elements directly influences the accuracy of model. The model used for presented simulations was based on 156 RLC elements and over 300 additional couplings. These were put as a net of series and parallel capacitances, series inductances, magnetic couplings and series and parallel resistances [3]. The second presented model was created for the winding used for previous controlled deformations tests for 15/0.4 kV, 16 MVA transformer [1]. The winding was taken out of tank and some basic deformations were carried out with FRA measurements taken at all stages. It allowed to identify the basic ranges and types of changes in registered curves related to given type and size of deformation. Such experiment will be repeated in the next couple of months in laboratory conditions (previous one was in field conditions before scraping the transformer) and will possible give even more detailed relations. All tests were performed for winding without tank and oil. Therefore also model is based on calculations considering these facts. Such model cannot be considered as a tool providing the response of complete transformer and was used only for these tests, as it was the easiest way to compare real measurements before and after deformation with different approaches of model. Also the geometry of winding wasn’t typical as there was no tap changer mounted, leaving regulation winding open, but still having influence on parallel parameters of model [2]. The first stage of modeling was to prepare model of the ‘healthy’ winding – before introducing controlled deformations. There were several approaches undertaken, each of them containing additional elements, leading to modeled curve similar in shape to the real one (Fig. 3). However, all of these parameters are always just a simplification of real phenomena and properties, therefore there will be always some errors in model generation and further interpretation of results. Such errors may be comparable or even higher than differences between healthy and slightly damaged phase, therefore it will be not always possible to use computer modeling for automated analysis of the FRA results. In the above example the curves look similar, having number, position and type of resonances comparable, however using any automated tool for assessment would generate obvious deformation results. The next approach was generated for the winding after conducting deformation. The deformation was big in scale, not possible to occur in the real transformer, but as the model used for the experiment was simple, consisting of only ten circuit levels it was necessary to introduce deformation giving clear differences possible to simulate in one of ten circuit levels. Changes of RLC parameters in the model were considered according to real deformation size and new parameters for model were obtained. After model recalculation the new simulation had been created (Fig. 4b).


136

Fig. 3. The comparison of measurement and modeling of 16 MVA winding

Fig. 4. The comparison of measurements (a) before and after deformation and simulations, (b) corresponding to them


137

At first it seemed that such slight change in the model wouldn’t give noticeable and correct response, but results showed that the model worked, giving changes similar to real measurements on deformed winding. It can be seen that character of changes for simulation of deformation in model is similar to real measurements before and after deformation. Both frequency ranges and amplitude shifts occur in similar areas. Of course differences between models and real winding’s response are still too large and in the normal conditions it would be identified as rough deformation, but this example shows that it is possible to obtain models giving response similar to real objects after simulating deformations [4]. The Fig. 4a presents real measurement before and after deformation. The most important differences between curves can be observed in the frequency range from 10 kHz to 100 kHz. This range is related to changes in windings geometry. In the Fig. 4b corresponding model is presented. It can be seen that in the mentioned range changes of FRA curve are similar in size, position and type to measured ones. In higher frequencies differences are bigger, as it is not possible to simulate the whole frequency range with one model. In addition there are many factors influencing this part of FRA curves, which cannot be easily identified, generalized and modeled in a simple way.

4. 3D FEM-model for analysis of electromagnetic field

The described model shows the possibility of modeling the electromagnetic field of the transformer windings using finite elements. For this aim the COMSOL Multiphysics 3.5A package was used. The analyzed model is shown in Fig. 5.

Fig. 5. Simplified 3D-FEM model of transformer windings with ports


138

The modeling was done by discretization of the analyzed area on 91k tetrahedral finite elements, using a quadratic approximation within the elements. Number of degrees of freedom in analyzed model exceeded 800k, and the size of problem to be solved ranged from 6 to 8 GB of computer memory. Analysis time for a single frequency value exceeded 20 minutes (with CPU I7 / 2.67 MHz, 9GB RAM, Windows 7 64bit).

For description of 3D electromagnetic field A-V formulation was chosen, because of its convenience for solving of models with forced voltage supply. The shape of these equations is as follows:

0divgradV)j(div)j( r0r02 A

(2)

0gradV)j(rot1)j( r0r0

r02

ArotA

while the material parameters were following: − windings: μr = 1, εr = 1, γ = 5.998107 [S/m], − core (steel sheets): μr = 1000, εr = 1, γ = 10 [S/m], − air: μr = 1, εr = 1, γ = 1 [S/m].

Assumption of non-zero value of γ for the air was dictated by the need to improve the convergence of the solution. Fig. 6 shows the distribution of current density on the surface of the windings in the presence of a short circuit at a frequency of f = 1000 Hz. The brighter color shows a significant amount of current in the short turn.

Fig. 6. Current density in short turns of the winding


139

The results obtained from simulation for the frequency range 50 Hz – 100 kHz were used to provide similar characteristics as those obtained by the analyzer FRA. Due to the scale of the assumed model and a small number of coil turns, measuring resistance R0 was reduced to a value having neglible impact on the current in the circuit, i.e. 0.1 Ω. Acquired amplitude and phase characteristics are shown in the drawings below. Darker characteristics correspond to the state without a short circuit.

Fig. 7. Frequency characteristics of output voltage in presence of short circuit

It should be noted that due to large dimension of finite elements in relation to the skin

depth for the copper, the results are reliable only until the frequency of f = 20 kHz.

5. Summary

The FRA method is an important diagnostic tool for detection of mechanical deformations of windings. The way of taking measurements, connection set-ups and properties of devices used for recording FRA curves are being standardized (e.g. IEC group PT 60076-18). There is still problem with full analysis of results and identification of existing faults in windings, their scale or exact position. One of tools, which may be used for analysis of results are computer models of FRA response. After obtaining simulated curves similar to real measurements, based on


140

parameters of modeled windings or transformer, it will be possible to simulate various types and sizes of deformations and check their influence on the shape of recorded curve. For preparing the models it is necessary to consider many details of construction and parameters of windings, however examples presented in the paper show, that it is possible to create models having response similar to real measurements. In addition, these models were based on rather simple approaches, having the winding divided into ten level circuit. Preparing more complex model will lead to more detailed models. It is planned to perform deformation measurements on recently obtained transformer in laboratory conditions and prepare computer models allowing to simulate created deformations.

References [1] “Mechanical-Condition Assessment of Transformer Windings Using Frequency

Response Analysis (FRA)”, Report of CIGRE Working Group A2.26, (2008). [2] Banaszak Sz. “Conformity of Models and Measurements of Windings Deformations

in Frequency Response Analysis Method”, New Electrical and Electronic Technologies and Their Industrial Implementation, Przeglad Elektrotechniczny 7'2010, pp. 278-280.

[3] Banaszak Sz., Szrot M.: „Pomiary odpowiedzi częstotliwościowej uzwojeń transformatora w warunkach kontrolowanej deformacji”, IX Sympozjum Inżynieria Wysokich Napięć IW-2008, Będlewo, czerwiec 2008, Przegląd Elektrotechniczny 10/2008, pp. 128-131.

[4] Banaszak Sz.: „Modelowanie odpowiedzi częstotliwościowej uzwojeń transformatora”, IX Sympozjum Inżynieria Wysokich Napięć IW-2008, Będlewo, VI.2008, Przegląd Elektrotechniczny 10/2008, pp. 124-127.


141

Study of suitable arrangement of axial electromagnetic clutch

Ivo Doležel

Czech Technical University 166 27 Praha 6, Technicka 2, e-mail: [email protected]

Václav Kotlan, Bohus Ulrych University of West Bohemia

306 14 Plzen, Univerzitni 26, e-mail: [email protected], [email protected])

A methodology of designing axial magnetic clutch is presented. Except for the prescribed force, the clutch must satisfy certain requirements concerning its temperature rise and several other aspects. The methodology is illustrated by two examples.

1. Introduction The paper deals with the design of an electromagnetic friction clutch for a

combined electromagnetic-thermoelastic actuator. The task of the clutch is to fix the position of its plunger. The complete device (that is intended for an accurate setting of position [1–2]) is depicted in Fig. 1 and works in two successive steps.

Fig. 1. A combined electromagnetic-thermoelastic actuator: 1 – friction clutch 2 – plunger (2.1 – its ferromagnetic part, 2.2 – nonferromagnetic (thermoelastic) part, 3 – field coil of the

actuator consisting of several sections, 4 – shell of the actuator, 5 – return spring, 6 – photoelectric sensor of position of the plunger controlling operation of the friction clutch 1,

7 – frame of the machine

I. Doležel, V. Kotlan, B. Ulrych / Study of suitable arrangement of axial…

142

A. Electromagnetic regime The field coil 3 (that may consist of one or rather several sections) carries direct

current ext,DCI of density ext,DCJ . This current generates in the system

quasistationary magnetic field DCB that produces force mF acting on the ferromagnetic part 2.1 of the plunger 2. This force pulls the plunger into the field coil 3 and must be higher than the sum of the force sF produced by the return spring 5 and possible external force extF . After reaching the desired shift ,mzu (fast, but only approximately) controlled by the photoelectric sensor 6 with wide light trace, the electromagnetic friction clutch 1 switches on, while the field coil 3 is disconnected from the DC source. Now the position of the plunger 2 is fixed, but still it may exhibit some error. B. Thermoelastic regime

Selected sections of the coil 3 start carrying harmonic current of density

ext,ACJ and frequency f that generates in the device periodic magnetic field

ACB . This field induces in the plunger 2 (mainly in its nonferromagnetic part 2.2) eddy currents of density eddyJ that cause its heating and consequent dilatation

,z Tu with respect to its fixed part – friction surface of the clutch 1. This fine dilatation is again checked by the photosensor 6, now with narrow light trace. Even this shift may be fixed by another friction clutch (that is not present in Fig. 1).

The aim of paper is to describe and model the operation of the electromagnetic clutch 1 for massive and hollow ferromagnetic part 2.2 of the plunger.

2. Description of the device

The investigated clutch is depicted in Fig. 2. It consists of two principal parts–

magnetic circuit 1 and field coil 4. When the field coil is connected to a DC source, magnetic flux starts flowing through the magnetic circuit 1 and ferromagnetic part 3 of the plunger. This produces attractive magnetic force between these parts and its normal component in the space of jaws produces a friction force that prevents part 3 from further movement.


143

Fig. 2. Basic arrangement of the considered friction clutch: 1–ferromagnetic (carbon steel 12 040) movable frame of the clutch, 2–ferromagnetic part of the plunger whose position is to be fixed,

3–friction relining of jaws of the clutch, 4–field coil

3. Mathematical model of the pump The mathematical model of the clutch consists of two partial differential

equations describing the distribution of the magnetic and temperature fields. The stationary magnetic field in the clutch is expressed in terms of the magnetic

vector potential A and obeys the equation [3]

ext1curl curl

A J (1)

where symbol stands for the magnetic permeability and extJ is the field current density. The field produces magnetic force mF acting between the magnetic circuit 1 and cylinder 2 (see Fig. 2) whose value is expressed by the integral

m1 ( ) ( ) ( ) d2 S

S F H n B B n H n H BŃ (2)

where H and B are vectors of the magnetic field and n denotes the unit vector of the outward normal. Finally, S is the surface of the magnetic circuit 1 of the clutch.

The normal component m,nF of the force mF with respect to the jaws then

produces the axial friction force f,aF between the jaws of the clutch and fixed cylinder, whose value is

f,a m,n F f F (3) The nonstationary temperature field in the clutch is described by the equation [4]

Jdiv grad = TT c wt

(4)


144

where stands for the thermal conductivity, is the specific mass, c denotes the specific heat, and Jw denotes the specific ohmic losses produced by the field coil given by the formula

2ext

JJw

(5)

being the electrical conductivity of material of the coil.

4. Computer model The numerical solution was realized using the FEM-based program QuickField

(version 5.6 [5]) supplemented with a number of own procedures and scripts. The aim was to quickly obtain information about the approximate, but sufficiently accurate distributions of magnetic and temperature fields. A great attention was paid to monitoring of the convergence of solution in the dependence on some important parameters (position of the artificial boundary) and density of the discretization mesh.

After extensive testing we decided that it would be sufficient to solve a 2D model instead of a full 3D model. The error due to neglecting the front effects seems to be lower than about 8 %. In order to obtain values with three valid digits for the magnetic field, the corresponding mesh had to consist of more than 180 000 elements; for the temperature field this number could be substantially lower (as the corresponding definition area is smaller) – about 150 000 elements.

5. Illustrative examples

We present the most important results of two examples. The magnetic clutch is

always the same, while in the former case the ferromagnetic part of the plunger is hollow and in the latter one massive (Fig. 3).

The principal dimensions of the friction clutch (see Figs. 2 and 3) are: 0 50l mm, 0 30D mm, 1 20D mm. The magnetic circuit of the clutch as well

as the ferromagnetic part of the plunger are made from carbon steel CSN 12 040. Its magnetization characteristic and temperature dependence of its important physical parameters are depicted in Figs. 4 and 5.

The field coil is made from copper, number of turns c 250N , diameter of the conductor 1d mm, factor of filling 0.7853 , maximum admissible temperature of insulation being max 200T °C.


145

D 0D 0

D1

Fig. 3. Arrangement of the magnetic friction clutch: a) with hollow cylindrical ferromagnetic plunger, b) with massive cylindrical ferromagnetic plunger

0.00.30.50.81.01.31.51.82.0

0.0 2.5 5.0 7.5 10.0 12.5 15.0H (kA/m)

B(T

)

Fig. 4. Magnetization characteristic B H of carbon steel 12 040

0

10

20

30

40

50

60

0 100 200 300 400 500T (°C)

(W

/mK

)

Fig. 5. Dependence T for carbon steel 12 040


146

First, several figures containing results for the hollow ferromagnetic plunger will be presented. Figure 6 depicts the distribution of magnetic field in the system for field current of density 6

ext 8 10J A/m2. In this case the upper part of the plunger is

oversaturated ( max 1.95B T), which deteriorates the operation parameters of the clutch – the magnetic force between the jaws and plunger decreases.

For the same value of the field current density Fig. 7 shows the distribution of the steady-state temperature field in the system. The maximum temperature of the system field coil – magnetic circuit max 210T °C occurs mainly in the field coil and neighboring parts of the yokes. But due to good thermal conductivity of carbon steel (the relining of jaws of the clutch is very thin) the temperature in the system is distributed highly uniformly and its lowest value min 194T °C.

The most crucial, however, are the results that allow determining the most suitable arrangement of the clutch from the viewpoint of the friction force f,aF . For the initial arrangement (see Fig. 3a) Fig. 8 shows the dependence of magnetic force m1F (acting on one jaw of the clutch), friction force f,aF and maximum

temperature maxT in the system for varying values of extJ in the field coil.

Fig. 6. Force lines of the magnetic field in the system for 6

ext 8 10J A/m2

(maximum magnetic flux density in the yoke max 2.01B T)


147

Fig. 7. Isothermal lines of the steady-state temperature field for 6ext 8 10J A/m2

(difference between neighbor isotherms 0.8T °C)

The distribution of magnetic and temperature fields for massive ferromagnetic plunger is quite analogous to Figs. 6 and 7. But magnetic field in the massive plunger is more uniform, which results in higher normal and friction forces. The highest and lowest temperatures in the system are somewhat lower than those in the previous case. The principal results are depicted in graphs in Fig. 9.

0

20

40

60

80

100

120

140

0 2 4 6 8 10J ext (106 A/m2)

Fm

,1, F

f,a (N

)

0

50

100

150

200

250

300

350

Tm

ax (°

C)

1234

Fig. 8. Operation characteristics of the friction clutch acting on the hollow plunger (Fig. 3a), 1 – normal component of magnetic force m1F acting on one jaw of the clutch, 2 – total friction force

f,aF acting on all two jaws of the clutch, 3 – maximum acceptable temperature cT of the field coil,

4 – actual maximum temperature maxT in the system


148

0

50

100

150

200

250

0 2 4 6 8 10J ext (106 A/m2)

Fm

1, F

f,a (N

)

0

50

100

150

200

250

300

350

Tm

ax (°

C)

1234

Fig. 9. Operation characteristics of the friction clutch acting on the massive plunger (Fig. 3b), 1 – normal component of magnetic force m1F acting on one jaw of the clutch, 2 – total friction force

f,aF acting on all two jaws of the clutch, 3 – maximum acceptable temperature cT of the field coil,

4 – actual maximum temperature maxT in the system

6. Conclusion The aim of the paper was to evaluate the operation parameters and

characteristics of an axial magnetic clutch intended for fixing the plunger (that is partly ferromagnetic) in a combined electromagnetic-thermoelastic actuator proposed by the authors. The total friction force f,aF exerted by the clutch must be higher than counterforce exerted by the return spring and possible external force, as explained in paragraph 1.

In case of massive plunger the friction forces are higher due to more uniform distribution of magnetic field in the system. On the other hand, the massive plunger is heavier and higher force has to be exerted to pull it into field coil 3 of the actuator. The final decision about whether to use the hollow or massive plunger depends also on a complete economical analysis and technological possibilities of the producer.

References

[1] Doležel, I., Ulrych, B., and Kotlan, V.: Combined electromagnetic-thermoelastic

actuator for accurate setting of position. Proc. EPNC 2010, Essen, Germany, 2010, Book of abstracts.

[2] Doležel, I., Kotlan, V., and Ulrych, B.: Electromagnetic-thermoelastic actuator for wide-range setting of position. Proc. CPEE 2010, Kynžvart, Czech Republic, 2010, CD-ROM.


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[3] Stratton, J. A.: Electromagnetic Theory. John Wiley & Sons, Inc., Hoboken, NJ, 2007. [4] Holman, J. P.: Heat Transfer. McGrawHill, New York, NY, 2001. [5] www.quickfield.com.

Acknowledgment

The financial support of the Grant Agency of the Czech Republic (project No. 102/09/1305), Research Plan MSM 6840770017 and project KONTAKT MEB051041 is gratefully acknowledged.


150

Accuracy of the intelligent dynamic models

of relational fuzzy cognitive maps

Aleksander Jastriebow, Grzegorz Słoń Kielce University of Technology

25-314 Kielce, Al. Tysiąclecia P. P. 7, e-mail: [email protected]

Applying fuzzy relational cognitive maps in dynamic modelling work of the systems involves restrictions deriving from the assumed model parameters. The selection of these parameters depends mostly on abilities of calculating equipment used for the simulation and on the modelling purposes. In most cases it is necessary to balance between increasing the mapping accuracy (which is connected with the calculation time lengthening) and shortening the calculation time (which, in consequence, worsens the accuracy). Additionally, aiming at the accuracy maximization not always can really improve it, but is always connected with the growing of the computational load. In this chapter the analysis of the intelligent cognitive maps work accuracy in the realization dynamic models is elaborated. As a result of the numerical analysis there was shown the existence of certain optimal parameters of analyzed signals fuzzyfication and connected with them sampling parameters in fuzzy arithmetical operations performed during the modelling processes.

1. Introduction

In works [1-5] there were introduced and analyzed applying static and dynamic

models of fuzzy relational cognitive maps in decisional monitoring low-structural objects. The research results showed the existence of certain dependencies between accuracy of such models work, selected parameters of fuzzy cognitive maps and the length of the sampling step chosen for numerical calculation. It is specially demonstrated in dynamic models, where the stabilization of the system after stimulating by external signals needs certain number of the cycles of the signals flow through feedbacks.

In the chapter, the results of the simulation analysis of the relationship between actions accuracy, membership functions parameters and fuzziness measure of the applied signals, will be presented on the example of chosen fuzzy relational cognitive map. The results will be shown in the form of appropriate diagrams, derive from which the existence of certain optimal parameters of the models fuzzyfication.

2. Model of the analyzed cognitive map

Generally speaking, a cognitive map can be presented as following pair of sets:

<X, R> (1) where: X = [X1, ..., XN]T – the set of values of the map concepts (state vector),

R = Rij – matrix of relations between variables Xi and Xj (i,j = 1, ..., N).

A. Jastriebow, G. Słoń / Accuracy of the intelligent dynamic models…

151

Figure 1 presents graphical model fuzzy relational cognitive map chosen for numerical analysis.

Fig. 1. The explored cognitive map graphical model (N = 5)

Dynamic model of fuzzy relational cognitive maps for the object from Fig. 1 can be presented in the form (2) [4]:

)()1( tXtX kk )([5

1tX i

i

kii RtX ,)]1( (2)

where: Xk – the k-th concept value (k = 1, ..., 5), t – discrete time, – operation of fuzzy addition, – operation of fuzzy subtraction, Ri,k – individual fuzzy relation between fuzzy concepts numbered i and k, – operation of max-min fuzzy composition.

Matching fuzzy parameters, it should be considered: the type of membership function, according to which individual concepts will be fuzzyfied (Fig. 2), universum domain (which depends on the expected concept values) and the number of the universum sampling points.

The essential question is also determining the method of normalization of concepts, which is necessary owing to their distinct physical characteristics. For the needs of this analysis there was chosen non-dimensional normalization to the domain [-1, 1].

For fuzzyfication, according to the algorithm presented in [3, 4], Gauss type function (3) whose graphical representation (for selected parameters) is presented in Fig. 3, was chosen.

2)(

)(

cx

ex (3) where: µ(x) – membership function, x – argument, c – µ(x) function centre, σ – µ(x) function width coefficient.


152

Gauss type membership function

0,0

0,2

0,4

0,6

0,8

1,0

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0u

µ(u

)

Triangular membership function

0,0

0,2

0,4

0,6

0,8

1,0

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0u

µ(u

)

Trapezoidal membership function

0,0

0,2

0,4

0,6

0,8

1,0

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0u

µ(u

)

Fig. 2. Examples of membership functions, which can be used for fuzzyfication of cognitive map

concepts, u – universum, µ(u) – membership function


153

Fig. 3. Hypothetical course of one of input signals, marked as X1 (after Gauss type fuzzyfication with σ = 0.2), with momentary value (centre) equals to 0.35 (after non-dimensional normalization

to domain [-1, 1])

Similarly to fuzzyfication of concepts, also at the choosing of fuzzy relation characteristics one can use different membership functions, which can be the base for creating such the relations (Fig. 4).

For the needs of present simulation there were chosen the Gauss type relations, strengths of which were corresponding with values of the crisp relations presented in (2).

During the process of determining the universum domain, two concepts should be taken into consideration: normalization domain boundaries and width coefficient of the membership function – σ. Normalization domain boundaries should be chosen in the way which secures maximal symmetry of fuzzy concepts shapes in full range of normalized values. It means e.g. that if σ < 0.8 for normalization range [0, 1], universum domain can amount from -1 to 2, but for normalization range [-1, 1], universum domain should be wider – from -2 to 2. Generally, for higher values of σ the universum should be wider owing to necessity of keeping the above mentioned symmetry. Finally the universum with domain [-2, 2] was chosen.

In the further part of the chapter there will be presented results of the research on dependency of the accuracy of fuzzy relational cognitive map activities on membership function parameter σ (fuzziness degree FUZ) of the model presented in (4)-(5) [6] and on sampling step Δx of the fuzzy sets universum X = [-2, 2] (xk = -2 + Δx·k, k = 0, ..., K).

))((11)( 221 xμDK

XFUZiXi (4)

K

kkXX xμxμD

ii0

22 1)(2))(( (5)

where: )(xμiX – membership function of fuzzy set Xi type (3), i = 1, ..., 5.


154

-2,0-1,0

0,01,0

2,0

0,0

0,2

0,4

0,6

0,8

1,0

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0

u2

µ(r,

u 1,u

2)

u1

Gaussoidal relation

-2,0-1,0

0,01,0

2,0

0,0

0,2

0,4

0,6

0,8

1,0

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0

u2

µ(r,

u 1,u

2)

u1

Triangular relation

-2,0-1,0

0,01,0

2,0

0,0

0,2

0,4

0,6

0,8

1,0

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0

u2

µ(r,

u 1,u

2)

u1

Trapezoidal relation

Fig. 4. Examples of fuzzy relations built on the basis of different kinds of membership functions;

u1, u2 – universum variables, µ(r,u1,u2) – membership function of the relation


155

3. Selected results of simulation analysis

Matrix of relations r = ri,k (i, k = 1, ..., 5) was determined as follow (according to Fig. 1):

005,04,03,00001,02,01,01,00004,03,00004,06,0000

r (6)

Elements of matrix r are values of reference for the constructing individual fuzzy relations [3, 4], which can be designed by experts or during the learning process. These relations are elements of the fuzzy relations matrix R, which is the basis of the operating of the relational fuzzy cognitive map used in the tested model.

It was assumed that the system will be acting under influence of one-shot forcing selected concepts to certain values. These values are shown in Table 1.

Table 1. Values of stimulating signals

Concept number 1 2 3 4 5

Stimulating value (normalized) 0.5 0.4 0 0 0

In consecutive calculation steps the system obtains a certain state of equilibrium, which is the basis for the conclusion. The simulation was carried out for 200 steps of discrete time.

A. Comparative results of analysis for crisp and defuzzyfied courses of concepts

presented in Fig. 1, according to matrix R from (6) – for σ = 0.2 and different values of K

In Fig. 4 there is presented comparison of time courses of tested system

concepts in dynamic crisp model and fuzzy model for different number of sampling points of the universum (after defuzzyfication with weighted average method).

From Fig. 4 results that the lower number of the universum sampling points the larger differences between time courses of the fuzzy model concepts. Further research also shows dependency of this difference on the value of σ coefficient (Fig. 5).

Therefore it can be stated that accuracy of fuzzy models depends on the number of the universum sampling points K (which is identical with the number of linguistic functions selected for fuzzyfication) and the coefficient of the membership function width σ. It is quite intuitive assessment, based on visual comparison of time courses, but the conclusions objectification bears the presentation numerical criterion, which would allow to appraise the accuracy of the mapping more accurately and to point the sufficient level of this accuracy.


156

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

Fig. 4. Time courses of concepts for different models. a) crisp system, b) – e) fuzzy systems with different numbers of linguistic functions (K) on the universum domain (with constant value

of the coefficient σ = 0.2): b) K = 101, c) K = 65, d) K = 41, e) K = 33

a)

b)

e)

c)

d)


157

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

-0,2

0,0

0,2

0,4

0,6

1 19 37 55 73 91 109 127 145 163 181 199

t

Time courses

X1X2X3X4X5

Fig. 5. Time courses of concepts for different models. a) crisp system, b) – e) fuzzy systems with

different values of σ coefficient (with constant number of the linguistic functions on the universum domain K = 41): b) σ = 0.3, c) σ = 0.4, d) σ = 0.5, e) σ = 0.7

a)

b)

e)

c)

d)


158

B. Results of numerical appraisal of the criterion of nearness between crisp and defuzzyfied values

Appraisal of the accuracy level of the mapping of courses by fuzzy model was

performed using nearness criterion (7) considering deviation between fuzzy course and crisp course that was taken as the comparison base. The aim of the studying of the above mentioned criterion is an attempt at finding the number of the universum K sampling points and the membership function width coefficient σ that secure the minimal value of the criterion (7) in specific circumstances.

FUZn

oi

wi nXnXFUZJ min)()(

2001)(

200

0

2

(7)

where: )(nX wi – defuzzyfied course of i-th concept of the cognitive map (1),

)(nX oi – crisp course of i-th concept of the cognitive map (in equation (1) fuzzy

operators was replaced with arithmetical operators), i = 1, ..., 5. Determining the course of function J(FUZ) allows to discover its minimum for

given value of K. This minimum can take different values for different values of K, moreover it also depends on earlier assumed limitations of the calculating system (e.g. on the universum u domain boundaries). It should be also considered that such research is carried out independently for each concept and its results can be different for different concepts.

Figs. 6 and 7 present diagrams of function J(FUZ) for concept X1 for two different values of K. It should be noticed that “de facto” they present dependency on the membership function with coefficient σ because FUZ is function of σ.

Fig. 6. The course of function J(FUZ) values of concept X1 for K = 33


159

Fig. 7. The course of function J(FUZ) values of concept X1 for K = 41

The comparison of courses from figs. 6 and 7 leads to the observation that minimal value of the nearness criterion J(FUZ) can occur for different values of the fuzziness degree FUZ of given concept and its location depends on the assumed technical parameters of calculating system (number of the universum K sampling steps and, indirectly, the universum u domain width). Therefore it can be stated that for a constant value of K (or Δx) there is optimal value FUZ* dependent on the parameter σ. According to this there can be formulated the problem of finding up the optimal value of σ.

Generally, analyzing the results of A. and B. it can be stated that there is a problem of the optimization of the selecting parameters σ, Δx and R, which can be solved by using different optimization algorithms (e.g. gradient or genetic) [7].

4. Conclusions

Results of the partial numerical analysis of the accuracy of intelligent dynamic

models of fuzzy cognitive maps presented in the work, lead to existence of certain optimal parameters of the fuzzyfication with using max-min composition between fuzzy concepts and appropriate fuzzy relations.

The problem of seeking optimal parameters of the model is connected not only with the modelled system parameters themselves. It also requires consideration of the calculating equipment technical abilities and expected calculation time.

For finding optimal parameters there is proposed using certain optimization methods based on gradient or genetic algorithms that will be presented in further works.

References

[1] Borisov V. V., Kruglov V. V., Fiedulov A. C. Fuzzy models and networks. Telekom,

Moscow 2007 (in Russian). [2] Jastriebow A., Gad S., Słoń G., Analysis of the fuzzy cognitive maps dynamics in

diagnostic monitoring of systems. Proc. of XIV Scientific Conference Computer Applications in Electrical Engineering ZKwE’2009, Poznan 2009, pp. 287-288 (in Polish).


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[3] Jastriebow A., Słoń G., Fuzzy cognitive maps in relational modelling of low-structural systems. In: Jastriebow A. (red.) Computer Science in XXI Century. Information Technologies in Science, Technology and Education. Science Publishing House of Institute of Exploitation Technology – National Research Institute, Radom 2009, pp. 35-38 (in Polish).

[4] Jastriebow A., Słoń G., Fuzzy cognitive maps in relational modelling of monitoring systems. In: Kowalczuk Z. (red.) Systems of faults detection, analysis and toleration. PWNT, Gdansk 2009, str. 217-224 (in Polish).

[5] Kosko B., Fuzzy cognitive maps. Int. Journal of Man-Machine Studies, Vol. 24. pp. 65-75, 1986.

[6] Osowski S., Neural networks for the information processing. Printing house of Warsaw University of Technology, Warszawa 2000 (in Polish).

[7] Stach W., Kurgan L., Pedrycz W., Reformat M., Genetic Learning of Fuzzy Cognitive Maps, Fuzzy Sets and Systems, Vol. 153, August 2005, pp. 371-401.


161

Design of module-based controller for solar micro combined heat

and power technology

Wojciech Mazurek, Tymoteusz Świeboda, Marek Malinowski

Electrotechnical Institute 50-369 Wrocław, ul. M. Skłodowskiej-Curie 55/61, e-mail: [email protected]

Control and Data Acquisition System for the micro-CHP unit has been designed as a new approach to the microgeneration system supplied by energy of the Sun. This paper describes only the part of the system which is intended for controlling and measurement data collecting. Owing to the Unit, in a households, radiation absorbed by collectors can be used for heating of water, generation of electricity or obtaining the cold for air-conditioning. This top-down engineering approach are implemented by three independent subsystems. In order to manage whole station Programmable Automation Controller has been mounted. The System equipped in a proper number of flow meters, pressure and temperature sensors and liquid pumps according to an algorithm is able to control the heat distribution, calculate thermal power display these data and actual state of the unit. In addition, using LabVIEW software special programs have been written. These programs make possible to display and control states of the Unit. The entire controlling system is supplied by the 1 kW using PV Panels Subsystem. In case of the sun’s energy is not sufficient, the PV system has an ability of over-switching on supply from the power network.

1. Introduction

Currently, the main electricity suppliers, intended for the industries and households are commercial power plants, which utilize fossil fuels as energy sources. Due to limited resources, serious environmental impacts and rising energy consumption these fuels will have to be replaced by renewable and coal-free energy forms. There are different methods to obtain “green” energy. Wind, solar, hydrologic or biomass – all methods accomplish common feature i.e. they can be used both in large power plants and next to typical dwellings facilities for small-scale generators. That is why huge power electric market could be efficiently covered regardless of distance from the power plants, amount of customers or their requirements. Current model for production of the electricity is one of the significant reason why there are so many “black” areas for instance in “third world” countries. The response for this problems is cogeneration which provides to large distribution of small power stations. Furthermore, due to worldwide shortage of electrical capacity and because of the costs of power transmissions and inconvenience in constructions of the new electrical lines small-scale heat and power generation plants have been becoming technically and economically advantageous. A possible method for improving of availability of the electricity could become micro-CHP which is the kind of microgeneration technology. Micro

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Combined Heat and Power (micro-CHP) technology is an alternative idea of cogeneration for the private houses, dwellings or small office buildings. Small, useful micro-CHP unit supplied by renewable energy sources can be assemble in location according to the needs of the customers. The energy is delivered on demand as a heat and an electricity. This solution has significant advantages in comparison to the conventional power plants therefore can be used as the method in areas where the costs of the electrifying exceed the profitability of the investment or in places where are the needs to implement the energy saving process.

The other form of energy which is utilized for domestic or industrial purposes is a heat. Similarly to electricity, the heat can be transferred from power plants or produced locally. As well-known, the efficiency of the energy conversion is limited by physical laws regardless of methods which involve these conversions. Traditional combustion, nuclear fission or direct transformation in fuel cells lead to excess of the heat generation which is treated as a waste in typical power plants. In many of large power stations this heat can not be spent due to different economic and technical reasons. An idea to produce useful heat with electricity generation directly for the customers, meaningfully rises conversion efficiency. The results are lower costs and fuel utilization at carbon mitigation. The brilliant advantage of micro-CHP in terms of principle of operation is possible intermittent generation. The unit of µ-CHP is capable to achieve certain amount of energy according to current consumption, avoiding, thereby, redundant losses.

Plenty of advantages of CHP units in comparison to commercial power plants have been scaling up their involvement. In spite of different economic problems, the CHP technology is being especially developed for small-scale applications. Furthermore, the climate changes and environmental problems increase the interests for renewable energy sources which have been successfully beginning to replace fossil fuels. The association of small-scale CHP with green energy sources creates excellent opportunity to propagate the cogeneration around the world. Nomenclature µ-CHP C&DA PAC WHS

micro Combined Heat and Power Control and Data Acquisition Programmable Automation Controller Water Heating System

ORC CAU VCU PV

Organic Rankine Cycle Cooling Absorption Unit Vapor Compression Unit Photovoltaic

However, to realize above conceptions different technical conditions have to be fulfilled. One of these is completely automatic and reliable operation of the installed units. This is the main term to implement micro-CHP for domestic and small-industrial facilities. Utilization of green energy as for example the energy from the sun or wind which magnitudes are quite unpredictable is the answer on question why microcontroller control systems have to be used to guarantee reliable operation. This paper first of all describes the adequate system which works in


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accordance with digital algorithm acquiring the data from measurement instruments. The control and data acquisition (C&DA) system has been constructed to efficiently manage µ-CHP unit supplied by solar energy.

2. Construction of the Micro-CHP system

For proper description of C&DA System, construction of the µ-CHP Unit should to be introduced. One of the significant issues to obtain the best method for energy conversions is suitable investigation. Simple calculations and/or simulations can not give sufficient answer when there are a lot of unknowns. Due to adequate reason multistage conversion structure of the Unit has been made to evaluate which form of energy is the most suitable when the main source are solar collectors. The sun’s energy can by utilize as a coolness, heat and an electricity. According to Carnot cycle principles, the absorbed energy is converted for heat engine or refrigerating system. The structure scheme of the micro-CHP unit is illustrated in Fig. 1. For supplying the system upper and lower heat sources are utilized. As the upper heat source flat-plate solar collectors have been mounted. The collectors can provide up to 30 kW of total thermal power. This thermal energy is utilized for heating of water, generation of electricity and obtaining the cold for air-conditioning. For lower heat source surrounding is used where the heat from the condenser is dissipated for refrigeration purposes.

Fig. 1. Configuration of the µ-CHP system with subsystems: WHS – Water Heating System, ORC - Organic Rankine Cycle, CAU – Cooling Absorption Unit,

VCU – Vapor Compression Unit; all additionally supplied by photovoltaic panels (PV)

The main subsystems which have been created to achieve various form of energy from solar collectors, are: ORC – Organic Rankine Cycle [1] for generation an electricity, CAU – Cooling Absorption Unit [4] and VCU – Vapor Compression


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Unit for obtaining a cool [6] and WHS – Water Heating System. These subsystems can be used independently according to current requirements.

Apart from solar collectors and ORC, photovoltaic panels (PV) are mounted in order to deliver electricity for Control and Data Acquisition System and circulating pumps i.e. for all electric devices in the Station which require power supply. The PV system has an ability of providing up to 1 kW of power and over-switching on supply from the power network in case when the sun’s energy is not sufficient.

Microgeneration Unit is supplied by vacuum flat solar collectors connected in serial-parallel way which work even up to 90 – 100°C. The active surface of single collector is app. 1,9 m2 thus for whole solar station the surface is about 38 m2. Placed inside the collectors working medium is made of aluminum nitrate which accomplishes high absorption coefficient of 0,95 and low emission factor of 0,05. Depending on the intensity of the radiation these values allow to achieve sufficient efficiency of the entire solar power station. Absorbed energy is transported from solar collectors to particulars subsystems of micro-CHP by a main fluid of the Unit which bases on 1,2-propylene glycol.

ORC subsystem have been created to prepare indirect generation of the electricity basing on thermodynamic conversions of heat into work. The organic fluid allows an energetic conversion at a low temperature of the resource, a better collecting efficiency and hence the possibility of reducing the size of the solar field. Furthermore, at low temperatures, organic working fluids lead to higher cycle efficiency than a water.

Two independent refrigerating subsystems (CAU and VCU) allow transfer the heat from a space into the surroundings. They can be successful used for air-conditioning aims, mainly due to great connection between them and a space being cooled: the bigger radiation from the Sun and temperature of the environment, the higher efficiency of the refrigeration.

The simplest method to utilize solar energy is a heating of water. By virtue of this Water Heating Subsystem has been built. The system makes possible of convenient raising the temperature of water to the useful value of 60°C.

2. 1. Control and Data Acquisition System The proper managing of whole solar power station requires suitable devices intended for automation, reliable, and remote operation. This operation basing on input measurement data is depended on current state of the Unit and has to be correctly programmed with prediction of all possible regular and emergency events. To realize such a conception independent microcontroller system had to be consider. For the Solar Power Station Programmable Automation Controller (PAC) have been chosen as a main core of the Control and Data Acquisition System. PAC offers the flexibility and ease of a PC and the reliability of a programmable logic controller for each connected measuring/controlling instrument. The controller


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have 400 MHz real-time processor and 256 MB of SDRAM which is absolutely enough for these quite not exacting purposes. It uses TCP/IP protocol for communication interface. The real-time PAC connected to 8-slot solid backplane controls a wide variety of hot-swappable I/O modules. The modular I/O architecture with built-in signal conditioning and isolation provides direct connectivity to temperature, pressure and flow meters, DAC and ADC circuits. The I/O modules filter, calibrate and scale raw sensor signals to engineering and perform self-diagnostic to search for problems, such as open thermocouple or out-of-range events. Unsophisticated scheme in Fig. 2 depicts fundamental principles for PAC, modules and intended components.

Fig. 2. Illustration of connections in C&DA system

Various modules are used to manage the station. 8-channel, 16-bit thermocouple and 4-wire RTD modules are mounted to record the temperature from thermocouples and resistive thermal devices. The only targets for above sensors and dedicated modules are the working fluid of solar station and a water that is heated by WHS subsystem. One of the most important parameter which is crucial to characterize the efficiency of µ-CHP unit is a stream of the heat-carrying agent. Pressure and flow of the fluids have been measuring to evaluate the stream. This is realized by implementation of 8-channel Analog Voltage Input Module and 12 to 24 V Sinking Counter Module dedicated for pressure transmitters and flow meters, respectively. Programmable Automation Controller converts the voltages in range from 0 to 12 V in order to process the pressure and counts voltage impulses


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to achieve the flow values. There is only one way which affords the control system to manage the power transmissions of the Unit. The widely-used circulating pumps are controlled, switched on and managed by the different I/O modules. 8-channel Analog Voltage Output Module controls the speed of the pumps by applying of appropriate potential difference in range from 0 to 10 V. Sending by circulating pumps emergency signals accomplishes 24 VDC Sinking Digital Input Module. When control algorithm changes current state of the Unit (e.g. from electricity production to air-conditioning or scaling up or down of power transmission) 16-channel Sourcing Digital Output Module switches chosen pumps to obtain suitable state.

2.2. Electric driver design

Both electronic control signals and measurement data are sent through the

constructed electrical driver being part of C&DA system. The main driver with visible PAC device and different modules are shown in Fig. 3. In addition there is circuit diagram presented in Fig. 4. Two various electrical components of the µCHP unit are switched by particular relays built into the driver. According to circuit diagram the circulating pumps and cooling radiator intended for Lower Heat Source are indirectly switched on and off by the modules due to supply of ~230 V. The rest of C&DA system’s equipments are directly managed with aid of dedicated modules.

Fig. 3. C&DA system’s driver


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One of the sophisticated feature of C&DA system is a fully automatic and reliable operation. Due to necessary testing, improvement and maintenance manual control option has been also implemented. Two depicted figures illustrate this option – for instance as the knobs being visible in the Fig. 3 and as a part of the circuit diagram shown in Fig. 4. Manual controlling, basing on real or user program settings, have been enabled to improve an algorithm written into PAC. From this point of view manual control option is crucial during development of the solar station while it could be passed over in final commercial version of the µ-CHP Unit.

Fig. 4. Detail of the driver logic schematic

2.3. Control Algorithm Implementation During power plant’s operation various events can occur. Hence, software development was as important task as engineering design and construction. The development has been lead in graphical environment NI LabVIEW – created for programming of measurement test control systems. Schematic representation of the algorithm is shown in Fig. 5. The meaning of C&DA’s algorithm is as follows. Loop structure control program bases on priorities, i.e. there are built-in loops which are firstly executed in comparison to the others. An example is flow meters’ reading function. This loop counts the voltage impulses sending in time by


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intended module. The loss of certain impulses caused due to non-hierarchy structure of the algorithm would has an influence on current magnitude of the flow. From this point of view a loop such as above is outside a main complex loop depicted in Fig. 5 and has the highest priority. The main loop clarifies the principles of operation of control algorithm. Firstly Read/Write I/O module function is executed. It means the reading of measurement data and/or writing configuration settings into circulating pumps or fun (radiator) using particular I/O modules. Basing on captured data proper rotational speed of chosen pumps is calculated. These velocities have to fulfill specific conditions in terms of power distribution for active subsystems. In other words to enable chosen energy conversion (from solar energy to heat, coolness or electricity) and/or keep conversion efficiency the PAC should switch on and set suitable speed of circulating pumps.

Fig. 5. Diagram of the control algorithm intended for Programmable Logic Controller

In the next stage of the algorithm State of Emergency Check function is executed. The aim of the function is a searching of emergency states which car appear during µ-CHP unit operation and start-up an alarm procedure in case of any emergency events. According to principles of operation following events may be found: collector temperature over range, organic working fluid over pressure, water pressure over pressure, circulating pumps failure.

Looking for above problems Emergency Check function aids to avoid serious crash of µ-CHP unit such as uncontrolled rise of pressure or temperature of various


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fluids. The same stage contains an option of Manual/Automatic mode. In the automatic mode The PAC with the algorithm manages the station while in manual the user has an ability to control the micro-CHP unit. Creating of Clusters Containing All Variables function is due to the LabVIEW structure. The cluster aids to put in order a huge amount of data which are sent in C&DA system. The last stage in the main loop is Read Operating Panel Settings option which is active in manual mode. In this mode the control algorithm is passed over.

2. 4. User program description Regardless of control algorithm implementation, different user programs have been written to display the working of the Unit. Using these programs testing, improvement and illustration of states of the operation is possible. The main user program contains six bookmarks which depict the main heat source with WHS subsystem and necessary tools for the manual management. Fig. 6 shows Heat Source bookmark. There are four banks of solar panels (6a), plenty of points of temperature measurements (6b), data of flows (6c), values of pressure (6d) and circulating pumps settings (6e) in the figure. In addition the window depicts current value of thermal power achieved from solar collectors (6f).

Fig. 6. The main user program with Heat Source bookmark: solar collectors (a), points of temperature measurements (b), data of flows (c), values of pressure (d), circulating pumps settings (e)

and current value of thermal power (f)


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The other functions of the program are as follows: water warming (fig. 7), which illustrates a connection between water heated by

µ-CHP and the water received from commercial thermal power plant, displaying of measurement data of whole solar station, alarm window, that displays emergency states, circulating pumps settings function which allows to set the pumps in manual

way, other settings which for instance allow to force certain temperature of heated

water or the speed of the power transmission. Similar to heat source with WHS windows the other subsystems found their

graphical implementations in LabVIEW programs. Such a window of ORC subsystem is presented in Fig. 9. The window illustrates components of the subsystems i.e. shell-and-tube JAD-type heat exchanger (9a), expander with generator (9b), heat regenerator (9c), condenser (9d), condensate vessel (9e), electric boiler (9f) and circulating pumps (9g). In addition there are different measurement data such as temperature and pressure of working fluid in various parts of the subsystem. The user program aids to investigate ORC subsystem by tracing and displaying of particular stages of the operation.

Cooling Absorption Unit subsystem with its user program is shown in Fig 8. Likewise was written above the window reflects the structure of the subsystem, thus facilitates technical and scientific researches.

Both user program have a function to enable 9 kW 3-phase electric boiler with volume of 3 dm3. Hence, in manual mode this external heat source is used when solar radiation is not sufficient.

Fig. 7. Water warming bookmark


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Fig. 8. Cooling Absorption Unit window

Fig. 9. ORC subsystem user program: shell-and-tube JAD-type heat exchanger (a), expander with generator (b), heat regenerator (c), condenser (d), condensate vessel (e), electric boiler (f)

and circulating pumps (g)

3. Exemplary results from C&DA system Various data are captured mainly due to controlling of the solar station. However, from a scientific point of view acquiring measurement data is also very important. Investigating micro-CHP unit through analyzing values of magnitudes such as temperatures, pressures and flows makes possible to confirm and prove that the idea of combined heat and power is quite successful and can be use in typical domestic or industrial applications. The graphs placed bellow show temperature values of working fluid that have been measured during operation of the micro-CHP unit.


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0,0

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120,0

2009-07-09 2009-07-10 2009-07-11 2009-07-12 2009-07-13 2009-07-14

date

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]

Fig. 10. Temperature of working fluid collected during a few sunny days of summer

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Fig. 11. Temperature of working fluid collected during a few sunny days of winter

Some conclusions can be considered when the above data are analyzed. During sunny days, regardless of a season of the year similar temperatures can be obtained. First of all a reason is the construction of vacuum solar collectors and the chemical composition of working fluid which lead to excellent absorption coefficient. In addition these collectors are mounted on the roof at an angle of 60° which is as acceptable in winter as in summer. The result is that µ-CHP unit is able to work whole year and support or replace classic methods of heating of water or even of obtaining an electricity or a coldness.

4. Conclusions

Control and Data Acquisition System has been made to provide automatic or manual regulation of the micro Combined Heat and Power unit supplied from solar collectors. The system makes possible to efficiently manage entire unit by controlling the stream of the heat with the aid of the Programmable Automation


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Controller and LabVIEW programs. This control is being realized on the basis of primary data from pressure and temperature sensors and flow meters which are assembled in the different subsystems of the micro-CHP. The data which have been collected within a period of work are used to evaluate the most appropriate method for thermal energy conversion in typical habitable facilities.

References [1] Devotta S., Holland F.: Comparison of theoretical Rankine power cycle performance

data for 24 working fluids. Heat Recovery Systems & CHP, 5 (6), 503–510, 1995. [2] Dong L., Liu H., Riffat S.: Development of small-scale and micro-scale biomass-

fuelled CHP systems – A literature review. Applied Thermal Engineering, 29, 2119–2126, 2009.

[3] Mallik A., Gupta S.: Modelling of MEMS based temperature sensor and temperature control in a petrochemical industry using LabVIEW. International Conference on Computer and Automation Engineering, 287 – 292, 2009.

[4] Srikhirin P., Aphornratana S., Chungpaibulpatana S.: A review of absorption refrigeration Technologies. Renewable & Sustainable Energy Reviews, 5, 343–372, 2001.

[5] Swain N. K., Anderson J. A., Singh A., Swain M., Fullon M., Garrett J., Tucker O.: Remote Data Acquisition, Control and Analysis using LabVIEW Front Panel and Real Time Engine. SoutheastCon, 2003. Proceedings. IEEE, 1-6, 2003.

[6] Zhai X. Q., Wang R. Z., Wu J. Y., Dai Y. J., Ma Q.: Design and performance of a solar powered air conditioning system In a Green building. Applied Energy, 85, 297–311, 2008.


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Numerical modeling of underfloor heating system using CFD

procedures with Elmer software

Daniel Kucharski, Marcin Wesołowski, Ryszard Niedbała Warsaw University of Technology

00-662 Warszawa, ul. Koszykowa 75, e-mail: [email protected]

Jacek Hauser Poznan University of Technology

60-965 Poznań, ul. Piotrowo 3A, e-mail: [email protected]

In the paper, the usage of multiphysical simulation software Elmer for simulating underfloor heating systems in a building is presented. Calculations were carried out in areas of solid elements of the model of the room, with the behavior of air and its temperature distribution was also taken into account. Results were compared with those obtained from other model based on a study of the temperature field only in solids, where the room’s temperature is known, or its change is given.

1. Introduction

Numerical simulation allows observation of physical phenomena on a computer

screen, with a possibility of detailed analysis of each of the parts of the modeled world. To achieve desired results of calculations, two approaches are used – creating your own computational procedures and using commercial programs like Ansys, Flow 3D, or Nisa. The first method gives a possibility of experiencing the wealth of numerical algorithms, which allows us to simulate our physical world, to understand the beauty of mathematical formulas, and to feel both their complexity, and also simplicity and elegance of form. Unfortunately, creating your own algorithms and their programming is very time consuming. The prices of commercial computational systems that use the best available models describing the physical phenomena are very high. Consequently, small research teams or individual scientist cannot afford them.

The solution to this problem that combines the two mentioned above methods are programs released under GNU General Public License (http://www.gnu.org/). The user receives not only the executable program, but also its source code. That gives the possibility of making modifications in software and of implementing your own procedures without having to write that program from scratch. However, the most important reasons for using GNU GPL programs are that they are often free of charge and at the same time, they have similar computation potential like commercial programs.

This paper proposes the usage of finite element software package Elmer [2, 7]. The creation of this program has been started in 1995 in Finland. It is a result of a

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scientific project for the development of a research tool for solving Computational Fluid Dynamics problems. Nowadays, further development of Elmer is in the hands of CSC - IT Center for Science, and their distribution is based on the GNU license, under which Linux operating system is also released. Initially, the program was intended only for the CFD problems, but it has been expanded over time to describe the thermal, electrostatic, and electromagnetic phenomena, diffusion, mechanical deformations, acoustics and even quantum processes [7]. Elmer has been verified in many simulation problems, such as Magnetic Czochralski method for monocrystalline silicon growth [8]. From mathematical point of view, it is a very a complicated process, which combines mass transfer, temperature field and crystallization of the material from liquid silicon, and also magnetic field affecting the crystallization process.

Many researchers have worked on the problem of numerical simulation of heating entire buildings or individual rooms [1, 4, 5, 6]. In simplified calculation models, this problem is reduced to determining only the temperature distributions in solid elements (walls, floors, ceilings) of the building. Newton's Law of Cooling equation (4) is used to describe heat transfer between solid elements and ambient air [4]. Advanced model describes also the temperature field of air in the room, with its movement, according to location of heat source and ventilation efficiency. Moreover, this model was presented in many scientific works [1, 5, 6]. The disadvantages of this approach are: complexity of the model, which forces you to use highly advanced computer systems, and the fact that its solution is extremely time consuming.

The design of the underfloor heating system is usually based on the determination of energy balance in a steady-state in different areas of the building, assuming minimum outside temperature for a given area of the country. This method might be insufficient for heating systems that are characterized by slowly response of the temperature field to changing weather conditions. Storage underfloor heating systems, which works intermittently and accumulates heat at certain times of the day, while in the remaining periods use this energy to heat, are particularly this types of systems.

2. Mathematical models

The geometry of the modeled object has been based on typical construction of

buildings, heated by a heat source located under the floor surface. Two-dimensional model of the room was considered, without any windows or doors. There was not any force ventilation in room, so air movement was solely the result of a natural convection. Heat was transferred through the exterior wall, which was composed of two materials - styrofoam and cellular concrete. Used materials, together with their thermal parameters, are listed in Table 1.

The geometry of the sample object was created using Gmsh software (http://www.geuz.org/gmsh/) [3]. This free program is a finite element mesh


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generator with very interesting capabilities. The reason for using this program is lack of this type of advanced software in the Elmer system. Fortunately, one of the Elmer programs, ElmerGrid to be exact, was designed to transform one of several popular mesh file formats created in other programs (inter alia Ansys or Gid) to the one that is understood by ElmerSolver.

Gmsh works on a similar principle as interpreted programming language. It is possible to define the variables that describe the model width, height or diameter of the heating cables. The existence of a loop conditional is a very interesting feature. Model of an element could be created with that feature, in the way a computer program is normally created, for example: ten cables of the same shapes, which are located in close distance. It allows you to apply modifications to the structure of geometry quickly, without having to make many operations as in typical GUI type programs. It is possible to generate mesh using various algorithms (Delaunay, Frontal). Gmsh can generate mesh with various polygon sizes in different areas of the model of the room, as can be seen in Fig. 1.

Fig. 1. Model geometry created with Gmsh After creating the model geometry and its polygon mesh, solver input file (file

extension is sif) needs to be created. That requires selecting mathematical equations that govern physical phenomena. The definition of parameters of all materials is also required. Very interesting feature of Elmer is that one can have influence on the way in which Elmer procedures of solving differential equations actually work. It is possible to use direct linear system solvers that use Umfpack or Lapack libraries, iterative Krylov solvers, multigrid solvers, and many more [2, 7]. Multitude of Elmer’s options is really overwhelming.

Calculations were performed in transient state. The calculations were carried out in steps of 1 s for the first 3600 s of simulation time, the rest of the simulation uses step of a 2 s range. The calculation that was run on PC Intel Quad Duo lasted


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approximately 200,000 s, so more than two days. An important advantage of Elmer is its ability to interrupt the calculations and run them again from the moment they were interrupted.

Table 1. Materials used in calculations

Material cw k ρ - [J/kgK] [W/mK] [kg/m3]

Floor concrete F311 Knauf 837 1,660 2100

Cellular concrete Ytong 700 type (for wall) 840 0,200 700

Styrofoam PS-E FS 15 (thermal insulation of the wall) 1500 0,042 15

Styrofoam PS-E FS 20 (thermal insulation of the floor) 1500 0,038 20

It was mentioned in the preface that two different methods of solving the

problem have been applied in this research. Figure 1 shows both geometry of the same room model connected with these two approaches. On the left side of Figure 1, shape of the model with its polygon mesh for solving coupled velocity and temperature field were presented. In the area defined as air, the program will solve the Navier-Stokes equations (velocity and pressure fields) and Fourier-Kirchoff equation in solid elements of room. On the right side of Figure 1 is the same model, however without mesh in the air area of the room. The result of these calculations is the temperature field only in solid elements.

Three different equations are required for finding velocity, temperature, and pressure fields in air: continuity equation, Navier-Stokes equation (2), and Fourier-Kirchoff, which is also called heat equation (1). Elmer can perform calculations for three compressibility model of simulated flow: incompressible, artificial compressible and perfect gas [2]. Thermal incompressible flow of Newtonian fluid was chosen, because it models well the airflow in a heated room. In incompressible flow, fluid density ρ=const is assumed and conservation of mass (the continuity equation) simplifies to form of 0=⋅∇ u . Temperature field is a result of Fourier-Kirchoff equation, given in form:

vp pρ=tktu+τtρc ⋅∇⋅∇−⎟

⎠⎞

⎜⎝⎛ ∇⋅

∂∂ )()( r (1)

where: cp – specific heat for given pressure, ρ - density, u – velocity vector, k – thermal conductivity, pv – heat source density, t – temperature field, τ - time.

( ) ( ) f=p+μuu+τuρ

rrrr

∇⋅∇−⎟⎠⎞

⎜⎝⎛ ∇⋅

∂∂ T2 (2)


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Boussinesq approximation is very important for presented calculations (3). We assumed thermal incompressible that ρ=const, but of course when we think about natural convection, density of the fluid needs to be changing with temperature, which cause buoyancy force. Equation (3) requires knowledge of the value of volume expansion coefficient β, which was defined for air in 273 K, β = 0,00343 1/K. Another simplification of these very complicated and time-consuming calculations is that it was assumed that the air is a Newtonian fluid, which means that the dynamic viscosity is constant, independent of the speed of fluid motion. It was also assumed constant with temperature.

))(1( 00 ttgρ=f −− βr

(3) In case of calculations that were performed only for solid elements, temperature

field cannot be solved for air. Typical way to approach in this case is to use Newton’s Law of Cooling (heat transfer is proportional to temperature difference between surface and ambient temperature) (4). We assume that the surfaces of walls and floors are exchanging heat with ambient air, and rate of this process is described by heat transfer coefficient α. This is a very basic approach with computation time very short if compared to second method, but ambient temperature has to be assumed, which is in some way wrong. Calculation of this temperature is the main issue of many scientific problems. For example, this temperature might be an unknown in a given shape of a room, structure of the wall, used materials, and heat system efficiency.

)( ptt=q −⋅α (4) One of many interesting feature of Elmer is the possibility of using internal

programming language for mathematical operations called Matc. Values of material parameters or the power of the heat source can be a function of every physical quantity, which are the results of a calculation. That gives a possibility of defining thermal conductivity as a function of temperature or the heat source value as an impulse function: Body Force 1 Name = "cables" Heat Source = Variable Time matc "if ( tx >0 & tx<25000 ) 300; else 0;" End

In above example of part of sif file, the manner in which the heat source works is defined. Between 0 s and 25,000 s of calculation time, heat source (electric underfloor heating cables) generates 300 W per 1 kg of mass. For the rest of simulation time, heat was not provided. In the same way, the temperature controller can be modeled, defining value of generated heat as a function of temperature of heat source.


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3. Results

Although calculations of an advanced model are extremely time-consuming, a number of them were carried out. In case of calculations of a simpler model, in which air behavior was not considered, equations (1) and (4) were used. This approach was marked by the "FK", the abbreviation of the name of the Fourier-Kirchoff equation. The second approach is governed by the equations (1) and (2), and it was marked by the “FK-NS”, because it uses both Fourier-Kirchoff and Navier-Stokes equations. Two-dimensional distribution of thermal, velocity and pressure fields was a solution for this model. Temperature field of the model is presented in Fig. 2 for different time moments. At first, the air temperature was uniform, which cause irregular flow of mass of air. It can be see in Fig. 2 in moments 400 s and 1600 s.

Fig. 2. Temperature distributions obtained for the FK-NS model, at various moments in time

The main mass of air flowed alongside walls and heated the air located in close distance of the ceiling. Thus, the air located near the ceiling has slightly higher temperature than the air near the floor. This observation is illustrated in a more readable way in Fig. 4, where temperature distribution in height was presented. In


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next moments (5000 s and 6600) the flow of air created a several vortexes. They were directing the flow of air alongside the floor and to the wall, and then to the ceiling. It is a balanced flow, but unfortunately it cannot be achieved by using computations in steady-state mode, which should greatly reduced computation time.

Comparison of both of these approaches (FK and FK-NS) in a form of temperature change in time for the point on the surface of the floor was presented in Fig. 3. The functions marked by numbers 4 and 5 are a result of using the FK-NS model. Temperature change presented as a line without any shapes (4) is for the point located on the surface of the floor. Temperature change presented as a line with wheels (5) is for the point located 1,5 m above the floor. In case of the FK-NS model, average temperature of air does not need to be assumed, as it is in the FK model. Thus, significant differentials between solutions of these two approaches can be seen (1, 2 and 3 functions on Figure 3). Small modification of the FK model was also tried. The first was to assume that average temperature of air in the room is changing during simulation, and it is defined as a linear function of time, for 0 s temperature equals 280 K, and for 20000 s equals 290 K. In the result of this modification, temperature change marked by 1 (Fig. 3) was obtained. The second modification was to use exponential function as a description of change of average temperature of air in the room (graph number 2 and 3 in Fig. 3) for different functions.

Fig. 3. Temperature change of one of the point on floor surface, calculated using different methods


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Fig. 4. Temperature distribution with height of the model of the room, for different moment of time The temperature change in case of intermittently heated room was presented in

Fig. 5. Temperatures of three locations were presented for location of heating cables, for a point located on the floor surface and for a point located 1,5 m above the floor. After 10000 seconds, the generation of heat has been off. Thermal inertia of the floor is significant, thus causing temperature rising even then. Even one hour after the generation of heat has been off, temperature of air in a point 1,5 m above the floor does not change significantly. This could not be observed without the use of the FK-NS model for numerical simulation.

Fig. 5. Temperature change in different location of intermittently heated room


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4. Summary

Many interesting programs with very high computational capability can be found among commercially available engineering software. Unfortunately, their costs often exceed the financial capabilities of a small research team, which does not have enough money to buy any software needed for performing numerical simulations of physical phenomena. Elmer capabilities allow simulating many different phenomenon easily, even in case of coupled field problems.

In the paper, many of Elmer system capabilities were presented. We have been using this software for numerical simulation of underfloor heating system, which is a very interesting and popular building heating system in many countries. Heat equation and Navier-Stokes equation were used in those simulations, but Elmer provides more various mathematical models. Transient state analysis of underfloor heating system in an exemplary room was conducted. Unfortunately, such calculations are very time-consuming, they can last even a couple of days. It depends on the grid density and computer speed. Hence, it may seem that this approach better suits researchers' purposes than designers'. However, even designers can effectively use Elmer in their work. The big advantage of the system is the capability of using multi-core processors, which nowadays are standard. In this case, the mesh of the model was divided into several parts, which were run as separate Elmer problems on every core of the processor.

Two methods of numerical simulation of thermal properties of the room heated with underfloor heating system were compared. The solution of the FK model, based on the heat equation, was the distribution of temperature in the solid elements of the room. The solution of this model was based on knowledge or assumption of average temperature of air in the room. Thus, this model is more suitable to studies of temperature field of floors, walls and ceilings. Although these are very important issues, various others treat temperature field of air in the room as an unknown. Hence, the FK-NS model, should be used. The solution of this model is the temperature field in air and solid elements, but also the velocity and pressure distribution.

Presented software allows defining the value of the heat power dependent on the value of temperature of air in the room or on simulation time. It is possible to simulate the use of the temperature controller to control underfloor heating system. This allows examining the impact of the thermal dynamics on the control of the room’s temperature, which is an important in case of underfloor storage heating system.

To sum up, multiphysical simulation software Elmer is worth a closer look.


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References

[1] Bartosiak A., Petera J., Zastosowanie oprogramowania ANSYS do modelowania numerycznego wentylacji wyporowej pomieszczeń biurowych, Ciepłownictwo, Ogrzewnictwo, Wentylacja nr 12 (441) grudzień 2006.

[2] Elmer finite element software http://www.csc.fi/english/pages/elmer strona domowa programu Elmer, data uzyskania dostępu 31.01.2010.

[3] Geuzaine C., Remacle J.-F. Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, Volume 79, Issue 11, pages 1309-1331, 2009.

[4] Gołębiowski J., Kwiećkowski S., Analytical and numerical modelling of a stationary temperature field in a three dimensional electric heating system, Electrical Engineering, Vol 81, No 2 May 1998, p 69-76.

[5] Nadolna M., Ziembicki P., Malinowski P., Zastosowanie modelowania numerycznego do prognozowania pionowego rozkładu temperatury w obiekcie z ogrzewaniem podłogowym, Ciepłownictwo Ogrzewnictwo Wentylacja, nr 10 (415), październik 2004.

[6] Nielsen P. V., Computational fluid dynamics and room air movement, Indoor Air International Journal of Indoor Environment and Health, Vol. 14 Issue s7, 2004, pp. 134-143, Blackwell Munksgaard 2004.

[7] Overview of Elmer, CSC – IT Center for Science, http://www.csc.fi/english/pages/elmer/documentation dostęp 31.01.210.

[8] Savolainen V., Heikonen J., Ruokolainen J., Anttila O., Laakso M., Paloheimo J., Simulation of large-scale silicon melt flow in magnetic Czochralski growth, J. Crystal Growth 243 (2002), 243-260.


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Application of „Smart Metering” in load diagrams analysis

Bogumiła Wnukowska, Wiktoria Grycan, Marek Kott, Bartosz Brusiłowicz

Wrocław University of Technology 50-370 Wrocław, ul. Wybrzeże Wyspiańskiego 27,

e-mail: [email protected], [email protected], [email protected], [email protected]

1. Introduction

In connection with necessity of increasing of energy savings and energy efficiency, which are priorities of the energy policy of European Union, it is expected that polish industries will reduce energy intensity of production processes and maximize efficient rational management of demand for electric energy. Activities of particular entrepreneurs have significant influence on National Power System, because they are shaping the national load curves. Irregularity of power consumption cause that, during the time of the biggest power demand, it is necessary to start additional, usually less efficient, energy sources. That is connected with not only higher costs of energy but also with power safety. Activities of entrepreneur should help in correction of global load diagrams by reducing energy usage in pick hours and increase in off-pick hours. One method of improving energy efficient consumption is rational management of demand for electric energy for example by technical improvements like: modifying manufacturing process, machine park upgrade or usage of automatics improving efficiency production process efficiency and also shaping energy use among others by analysis of load diagrams. From the point of view of energy consumption in a group of small and medium firms, there are possible two solutions: calculation through standard load profiles and, alternatively, installation of meter with registration of hourly consumption with suitable memory.

2. Smart Metering

The idea of smart metering i.e. intelligent measurements is to enable the

communication between seller and energy recipient in a real time and enable recipient the current control of energy consumption based on information about actual price of energy. It is ensured by using new, smart equipment. According to indications of organization ESMA (European Smart Metering Alliance) smart meters should comprise following features: automatic transfer, automatic management and use of measuring data and bilateral communication (remote

B. Wnukowska, W. Grycan, M. Kott, B. Brusiłowicz / „Smart Metering” in …

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transfer of information from meter and transmission of information to meter, for example remote power disconnection) (Fig.1). Through use of those meters, the full information about energy consumption can be reached, presented in a clear way. Thus, the following effects can be achieved effects in a form of: reduction of cost of energy supply, tariff’s adaptation to individual needs of groups of clients, precision of calculations of consumed energy, reduction of energy consumption, technical simplification of seller’s change procedure and improvement of quality of delivery and energy parameters such as correct voltage and frequency values [2,3,5].

Fig. 1. Features of smart meters [5,13]

3. Smart Metering and customer

Every customer has installed meter in his house/building. Registered data is transferred through PLC (Power Line Communication), GSM (Global System for Mobile Communications), SDR (Software Defined Radio) etc to the data collection. They are also available for the customer. Then they are transferred to measuring’s database and from this place or from customer’s information system go to the client. Based on delivered information, customer can create and time modify in real his energy consumption. He can also analyze and choose right energy tariff, the most economical for him (Fig.2).This modification create shape of customer’s load curves and also have influence on form of load diagrams for area of the country [6].

This kind of system gives information not only to customer but also system managers who know actual load and energy consumption. For the distribution system operator information is especially important because of safety of the system, forecasting future load value based on accurate data and facilitation of steal detecting (Fig. 2, Fig. 3).


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Fig. 2 Smart metering – customer’s information system [6]

Fig. 3. Smart metering system [6]

4. Possibilities for entrepreneurs created by Smart Metering

Elementary and the most important advantage of implementation of smart

metering network for companies is the possibility of financial savings connected with energy payments. Management of manufacturing processes based on actual energy price unfortunately isn’t possible for every profile of production. However, savings obtained by load curve’s equation during the off-pick hours by some of companies, should cause a general decrease of prices. That would be beneficial for every energy consumer [10].

The consequence of individual energy consumption management would be energy tariff adjustment to individual needs of recipients. Also a change of energy seller would be highly facilitated and more available for larger group of interested customers.

Moreover, because of that kind of solution, the billing system based on forecasts can be eliminated, that repeatedly are different than real consumption. In this situation client would pay only for real energy consumption, found with a high precision.

Smart metering would be also source of information about earlier consumption. Those data could be helpful for entrepreneur for analysis of manufacturing process, work organization and estimating of single product’s cost.

A way of presentation of measurement is also important. Data presented graphically would be more legible and clear than numbers for larger group of


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clients. Therefore, monitoring of energy consumption wouldn’t be as complicated and laborious as it is now.

The smart metering network would be also a source of information about the risk of emergency breaks in power supply. This could be helpful for firms to reduce to reduce losses connected with deficiencies in energy supply.

Figure 4 shows benefits and applications of smart metering infrastructure. The information read from meter is used for calculation and invoicing is available for client through customer service. A customer has possibility of energy consumption management based on data received from customer service, retail sales and system technical support. System technical support is more efficient because it has access directly to the measurements read from meter.

Also management of energy quality and energy consumption and energy sales network work better because of easier information flow.

Fig. 4. Applications and benefits of smart metering infrastructure [6]

5. Functioning of Smart Metering in Europe

The European Union country where smart metering implementation is the most developed and where it started is Italy. In this country the process of implementation started in a year 2001. According to the regulations, until year 2011 all devices should be “smart”. The reason of investment in this system was age of previous meter devices and also problem with illegal power consumption and its detection ability. The smart meter implementation in Italy was undertaken by Enel, the dominant operator in this country, with over 27 million customers. Between


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2000 and 2005 Enel deployed smart meters to its all customer buildings. However, user’s interest of system is negligible. There are taken efforts on implementation of monitors and consumer displays, which could encourage customers to higher activity in individual energy consumption management. In Italy the initiation of smart metering is regulated by resolutions of Office of Energy and Gas (number 292/06 and 235/07) [1, 14, 17].

In Spain operator implementing smart metering is Endesa (ownership of firm Enel), that has 13 million of customers. By the end of 2010, Endesa should have 150,000 smart meters, which will mean a significant step towards smart grids. In June 2010 Endesa was the first company to introduce smart meters to the power grid in Spain in Malaga (project ‘Smartcity’ creating an energy efficient city with the support of Endesa). Endesa’s remote management plan assumes the installation of the new meters in homes of the company’s domestic customers in Spain in less than six years. The plan involves investment of over 1,600 million Euro and will create 2,000 jobs. According to the regulations of Ministry of Economy and Tourist all energy meters should by smart until the year 2018 [16].

There is a significant expansion of smart metering in Northern Europe. In 2003 Sweden declared to require a change of all electricity meters for monthly readings by 2009. Soon activities started in the other Nordic countries. Vattenfall, Fortum and E.ON decided to implement smart metering network in Finland, as well as in Sweden. Expansion in Denmark has started in 2004 with several ambitious projects. Norway was more cautious, but in June 2007 the Norwegian energy authority NVE decided that it would recommend a new legislation imposing smart meters to expanded in 2013. Since August 2007, almost all of the distribution system operators in Sweden have signed contracts for AMM (Automated Meter Management) solutions. According to regulations in Sweden, smart metering network should fully work in households. Unlike in Italy, there is a pretty interest in smart metering of users in Sweden but still there are no regulations about consumer’s information forms [1].

In France operator which has 96% of the market is implementing smart meters because of operation cost’s reduction, minimization of stealing of energy, load measurement in a real time and making the network management more effective. Until the year 2014 50% of installed meters will be changed to the new-smart meters, and until 2016 95% of all installed meters will be smart. Pilot installation includes 3x100 000 smart meters until September 2010 [1, 17].

In Holland it is planned to implement smart meters till 2018. Since 2011 smart meters will be obligatory in all new buildings. In years 2011-2013 pilot plants will be implicated. Since Year 2013 all changing meters should be replaced by smart meters. In this country there is a problem with operator’s concerns about profitability of the project [1, 14].


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Smart metering system will be also implicated in Germany (2020), England (2020), Greece (2018) and Portugal (2018) where regulations are developed. In Europe there are still countries like Poland or Slovak Republic which need a big step for smart metering implementation [14].

Fig. 5. Implementation of smart metering in Europe [6]

6. Regulations for Smart Metering in Poland Poland is obligated to smart metering implementation by European Union

directives [8]: Directive 2006/32/WE (obligation of implementation until 17.05.2008) tells that

obligation of Member State is to ensure final recipient of energy, gas or CO (carbonous oxide) the possibility of acquisition in competitive, individual prices meters precisely giving information about real energy consumption and informing about real time of energy use.

Directive 2009/32/WE (obligation of implementation until 03.09.2012) tell about conditional duty of implementation by the Member States of the intelligent meter’s system that allow for active participation of consumers in energy supply market.

“Energy Package” (2007/C 305/01) that obliges European Countries to increase to 20% the participation of Renewable Energy Sources, increasing by 20% the energy efficiency and reducing by 20% CO2 emission until the year 2020 [9]. There is also internal commitment in Poland: Declaration on implementation of

smart metering to the polish power system (signed by President of the federation of consumer, president of consumer associations, Chairman of the Forum for electricity and gas, President of KAPE (Krajowa Agencja Poszanowania Energii –


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The Polish National Energy Conservation Agency) and President of URE (Urząd Regulacji Energetyki – The Energy Regulatory Authority).

Still, there is need for creation of regulations describing smart metering implementation. Several issues has to be characterized such as dates of implementation, operator’s commitment, guidelines, description of meter’s features etc.

7. First steps in Poland

Despite no regulations of smart metering operators attempt with pilot programs.

In Poland actually work several of pilot installations of remote reading of individual customer’s meters operating from tens to almost 2 000 of meters. Those implementations are unfortunately only pilot projects. But still, the development is noticeable [13].

Energa Operator works actually on choosing application supplier, communication solutions and meters. They plan to install 100 000 meters until the first term of 2011. Energa’s project assumes covering 25% of country with system and installation of smart meters to more than 3 000 0000 customers. All projects will be realized until year 2017. Average cost per one measurment point will be under 400 zl that is about 100 €. Energa estimate that their client will save thanks to the project 2,7 billion zl what is 675 000 000 € during 20 years [4].

Energia Pro has started his own project in 2004. First actions were and still are based on centralization of informatics systems and standardization of rules of measurments of measured data canvassing. For Energia Pro the first need was unification of operator’s measures with OSP (power system operator), neighboring distribution system operators and TPA (third party access) clients. The next step will be the separation of measures data from billing, because the billing system cannot be used for measures management. There are also pilot projects with changing meters to smart by particular clients [12].

8. Potential problems connected with Smart Metering implication in Poland

The idea of smart metering seems to be promising and forward looking but it is

also connected with numbers of organization and technical problems. First of all it is necessary to create regulations specifying the requirements on

devices, readings, client’s information system and also methods of encouraging clients to effective energy use , for example by creating a system of new tariffs. Those tariffs should induce the consumer to buy energy in off-pick hours and, respectively, bonus for energy consumption in those hours. Information about new possibilities is also significant. It is very important that the information is passed easily, with simple and understandable language. Even elders and less educated customers should see benefits for themselves from smart metering system.


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Otherwise, the idea of smart metering system implementation can meet the barrier of reduced demand and only the increasing demand can create supply of technical devices [7,15,17].

Among the technical difficulties, security of system of consumer’s data is important and is to protect the whole system against unauthorized access. Not without significance are also costs of implementation of technology connected with smart metering. The costs are estimated on 339 zł/system with one-way data transmission and 467 zl/system with bidirectional transmission with possibility of realization of extra functions including meters management, connecting/disconnecting of power. There appears also a question about who would take the costs.

Also making decision about choosing the technology of data sending could be a problem. There can be used PLC, GSM, LAN (Local Area Network), Wi-Fi(Wireless Fidelity) and there can also be created a new network. PLC and LAN are cheaper solutions because of their capacity (LAN) or availability (PLC), GSM is also worth of being considered. Choosing right technology would be connected with area, conditions, costs, existing infrastructure.

Important is also the need of creation of database which will process, collect and share information from meters and other receivers of those data.

9. Summary

Poland is challenged with implication of the idea of smart metering connected

with whole technological infrastructure with the same name. Capabilities of smart networks seem to be impressive. They can give consumers numerous benefits; become a source of savings for firms.

It is obvious that there is a need of smart metering implementation. It can significantly reduce energy consumption inter alia by easier consumer’s access to his actual data about energy use. By accessibility to tariff’s plans and approachable consumer’s panel, client will be encouraged to increase of energy efficiency because he will see the real money in it without unnecessary formalities.

There is a long way to come, technological and formal, to implement smart network. It is good that operators develop and apply new technologies, making them available for their clients. We are in a good position, because we can observe other countries, more developed in implementation of smart metering, and learn on their mistakes. It is a huge chance for our country and entrepreneurs.

Entrepreneurs, as the consumers who will be forced to pay for new technology and new possibilities, have a good reason to get to know smart metering better to fully use new opportunities. The example of Italy shows that awareness of the client is almost as important as the new technological solutions.


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References

[1] Babś A.: Przegląd reprezentatywnych wdrożeń inteligentnych systemów pomiarowych w Europie, Instytut Energetyki Oddział Gdańsk, Warszawa 24.03.2010.

[2] Burgess J., Nye M.: Re-materialising energy use through transparent monitoring system. Energy Policy 36 (2008), pages 4454–4459.

[3] Butler D.: Energy efficiency: Super savers: Meters to manage the future. Nature 445, pages 586-588 (8 February 2007).

[4] Elektro systemy: Enera instaluje 100tys. Inteligentnych liczników, nr 8(127)/2010, page 18.

[5] ESMIG (European Smart Metering Group for Europe): Smart Metering for Europe A key technology to achieve the 20-20-20 targets, 21 January 2009.

[6] Grzejszczak Paweł dla PIPER: Wdrożenie inteligentnego opomiarowania - główne aspekty prawne, konferencja „Zaawansowane systemy pomiarowe smart metering w elektroenergetyce i gazownictwie”, Warszawa 23.03.2010.

[7] Malko J., Sieci inteligentne – zasady i technologie. Rynek Energii 2009, nr 3. [8] Majchrzak H.: Perspektywy rozwoju inteligentnego opomiarowania w Polsce,

konferencja „Perspektywy rozwoju inteligentnych sieci energetycznych- technologiczny przełom w polskiej energetyce i szansa na wypełnienie celów pakietu klimatycznego”, Warszawa, Sejm RP, 27.10.2009 r.

[9] Opinia Komitetu Regionów „Pakiet energetyczny”, Dziennik Urzędowy Unii Europejskiej (2007/C 305/01).

[10] Smith R.: Smart Meter, Dumb Idea? The Wall Street Journal Business April 27, 2009.

[11] Szkutnik J., Smart metering jako decydujące uwarunkowanie wdrożenia strategii DSM w Polsce, Rynek Energii, nr 1/2010.

[12] Zazina R.: Inteligentne pomiary, Wulkan nr 01(17)/2009, pages 4-8. [13] http://earth2tech.files.wordpress.com/2009/12/energy-usage.jpg, 30.08.2010. [14] http://www.guardian.co.uk/, 30.08.2010 [15] http://www.kape.gov.pl/, 30.08.2010 [16] http://www.sourcews.com/malaga-seville-barcelona-now-have , 30.08.2010 [17] http://www.ure.gov.pl/portal, 30.08.2010


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Anticipating energy intensity of industry using software

for creating econometric models

Marek Kott, Bogumiła Wnukowska, Wiktoria Grycan Wrocław University of Technology

50-370 Wrocław, ul. Wybrzeże Wyspiańskiego 27 e-mail: [email protected], [email protected],

[email protected]

The article presents the current problems of energetic and the current state of the mining

industry and electric industry, as well as indicators of energy intensity projections were compiled using the program GRETL to create econometric models.

1. Introduction

Due to the ever-increasing energy needs of a growing national economy and the

large capital- for fuel and energy investments, the primary element in energy policy is to ensure security of supply of cheap energy which has high performance parameters and is produced from green sources. One way to improve national energy security is to reduce the energy intensity of industry, which is the largest purchaser of electricity. Mining of coal and lignite brings energy supplies for the electricity industry, whose product is electricity. It can be concluded, therefore, that those industries are most important from an energy point of view. Prediction of energy consumption indicators in that branches allows for better planning of national development strategies of industry and improvement of energy security.

2. Mining industry

In Poland there are two coal basin: Upper Silesian Coal Basin and Lublin Coal Basin with one active mine. Lower Silesia Coal Basin is now closed. Proven reserves of coal are shown in Table 1.

Table 1. Proven reserves of coal [4]

Specification Geological resources, mln tones Industrial

resources balance off-balance Upper Silesian Coal Basin 36638 22679 7164 Lublin Coal Basin 9262 6918 338 Other resources (Coal Basins in liquidation) 66 3812 –

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The adequacy of the resources of this material occurs only for documented deposits in terms of balance. With high probability it can be assumed that the demand for coal in Poland is stable at 75 to 80 million tones per year. There are many papers talking about the adequacy of the resources of coal. Most of them determines that resources, which are documented in active mines, can satisfy the energy needs of the country for 45-50 years. Balance resources of unexploited deposits permitted to extend the mining operations to the next 35 years [5, 6, 8]. Taking into consideration current geological research, we should not expect new discoveries in the Polish coal-producing areas.

Second in terms of quantity used for energy extraction is lignite. Eight areas of reservoir can be named, in which is documented the occurrence of lignite. The richest areas are: Legnica, Wielkopolska, West of the Country and Bełchatów, where is the evidence of almost 1 million tones of lignite. Table 2 shows the proven reserves of lignite.

Table 2. Proven reserves of lignite [4]

Specification Geological resources, mln tones balance balance

West of the Country 2854 12602 North-West of the Country 300 952 Legnicki 3803 12726 Wielkopolski 3689 12834 Koniński 780 1036 Łódzki 551 550 Bełchatowski 1862 341 Radomski 92 –

Viability of existing lignite mines is estimated at 30-35 years. The largest

prospective reserves are located in the vicinity of Legnica, the real output is 4500 million tones. This quantity provides a mining rate of approximately 55 million tones per year for over 80 years.

World coal production continues to increase, mainly because Asian countries (China, India). However, the fate of coal mining in Western Europe may indicate that the material may be replaced by other energy carriers (renewable energy, nuclear energy). Extractive industry in Poland is the second largest coal producer in Europe and seventh in the world. The annual production of lignite in the country is at 60 million tones per year, which gives in fourth place on the Old Continent and seventh in the world in terms of production volume. However, despite such a high position in the world the export rate is only about 14% of the annual output of coal (11.9 million tones in 2007). Lignite is consumed in its entirety on the domestic production of electricity and heat. It would seem, therefore, that by analogy, the coal mining meets the needs of consumption in power stations as the


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fuel. However, in 2008 nearly 60% of burned raw material had domestic origin, the rest came from import (Fig. 1). From the significant manufacturer, Poland is becoming a country where others deposit their (export) their coal, and the effect of this is that the annual electricity from imported coal is at the 20% level, which reduces the level of national energy security [1, 4, 6].

Fig. 1. Consumption of coal and lignite in polish power plants [4]

Despite numerous operations, including employment restructuring, capacity reduction by closing of mines, mining debt reduction, organizational and legal changes to create new structures, the profitability of the mining remains consistently low, and the energy intensity of production sold in 2007 was 27 kWh per 100 PLN production sold. The main reasons for reducing the demand for coal is a relatively high price of Polish coal, resulting, inter alia, from difficult mining conditions, elimination of the capacity of old plants with high production costs and very high environmental installation costs and high costs of rail transport.

3. Electric industry

Electricity industry is highly dependent on coal as the main energy source. In

2008, nearly 92% of the electricity produced in the country was in power plants fired by coal or lignite. This structure does not change over the last decade, which has bad influence of the country's energy security in the absence of diversification of energy sources (Fig. 2).

Fig. 2. The Generation of electric energy from national sources [4]


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Limitation is increasing with age and technical parameters of power blocks in Poland. The installed capacity of domestic power is 35 000 MW, for comparison, in Spain more than 63 000 MW, although both countries are characterized by a similar number of inhabitants. Unavailability of generating units was in 2008 at around 15%. The reason for this high rate are failures, current repairs and upgrades. Over 80% of power plants in Poland were built before the year 1987 (Fig.3).

Fig. 3. Polish Power Plant [4]

The dynamics of investment expenditures in electric industryThe dynamics of investment expenditures in mining industryThe investment expenditures in electric industryThe investment expenditures in mining industry

Fig. 4. The investment expenditures and them dynamics in chosen branch of industry [4] In order to improve the energy security, investments in new electricity

generation capacity and modernization of power plants are therefore a necessity. The national electricity industry also faces the problem of insufficient quantity, quality and age of power transmission lines. Over 80% of the 400 kV transmission lines and 99% of the 220 kV lines was built over 20 years ago. Poland is a kind of "energy island". Trans-border merger does not allow for larger flows or on a larger scale of exchange. It is therefore necessary to investment in transmission networks and their modernization. Power losses are estimated at about 12-15% of power, which gives around 5 000 MW per year. Bad law, lack of funding, many protected areas, such as the European Nature 2000 sites and public protests effectively


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restrict the expansion and modernization of power system [3, 4]. Despite of the steadily increasing investment in developing the power network, the state of energy security does not improve at a satisfactory pace (Fig. 4).

4. Anticipating the energy intensity factors

Commonly used prognostic method is to build predictive models of causes and effects, which is based on relationships between the dependent variable (eg, energy intensity index) and explanatory variables (eg, coal consumption, gross domestic product, expenditure on investment, average employment). These models are called econometric or energometric models depending on the nature of the explanatory variables. Linear econometric model with many explanatory variables is:

( )∑=

++=K

kkk XaaY

10 ε (1)

where: Y – dependent variable, Xk – k -th explanatory variable for k = 1, 2 …K, a0, ak – struktural parameters of the model for k = 1, 2 …K,ε – random variable.

To determine the various parameters of the econometric model, the classical method of least squares should be used. The next steps in the econometric analysis are presented in Figure 5. To verify the econometric model, the number of statistical tests can be used, which can be done with GRETL software, developed at Wake Forest University in North Carolina. Diagnostics consisted: assessing the coefficient of variation, assessed the relevance of structural parameters (Student's t-test, F-Snedecora test), assessing the degree of fit of the model (R2 determining factor), an assessment of normal distribution (test Jarque'a-Bery), evaluating the linearity of the analytical form of model (White test) and assessing the collinearity of dependent variables [2, 7].

The analysis shows that the energy consumption (understood as the power consumption of 100 PLN production sold) are influenced by many factors. Among these factors are mainly technical and energy, financial, economic, social and ecological ones. The energy-technical factors includes, among others, energy balance of production and distribution of electricity or the balance of power from the perspective of the whole economy. In recent years, the impact of financial-economic factors is growing. Factors such as the price of electricity, investment rate or turnover profit margin have a decisive impact on the finances of enterprises. Econometric model, to truly reflect the reality, must also take into account social factors such as number of employees, salary or outlays on research and development activities. The European Union has paid increasing attention to the protection of the environment, which reinforces the importance of environmental factors (pollution reduction, investment in fixed assets for environmental protection).


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Fig. 5. The Diagram of Econometric analysis

In Tables 3 and 4 there are the structural parameters of models for the industries surveyed. Then, based on the model, indicators of energy intensity projections were developed (Fig. 6), assuming moderate growth in electricity demand. Analysis of statistical data during the period (1995-2007), expert opinions and guidelines laid down by EU directives provide for the designation of dependent variables trends in the coming years [1, 4, 7].

Table 3. The structure parameters of mining industry

Symbol Value Description Unit a0 86,7 Constant - a1 -0,8 Investment expenditure Year 1995=100% a2 0,14 Total employment Thousand of people a3 -0,45 Number of branch companies Unit a4 1,15 Electric energy consumption GWh


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Table 4. The structure parameters of electric industry

Symbol Value Description Unit a0 143,6 Constant - a1 -10,9 Production of electric energy TWh a2 0,58 Electric energy consumption

on 1 employer MWh/1 employer

a3 -1,67 Gross national product Year 1995=100% a4 1,15 Price of electric energy previous year =100% a5 0,46 Investment means

on environment protection mln zł count on

year1995

Fig. 6. The energy intensity factors of production sold on horizon 2015

5. Summary

Energy intensity index for mining and electricity during the 15 years declined 3

times. But in recent years, it can be seen a significant slowdown of the process. To maintain economic growth, we should pay special attention to the reported industries, so that they can be a powerhouse of the national economy, and not the main obstacle preventing its development. It is therefore necessary to extend and continue this type of research.

Poland is standing in front of a difficult and costly problem of modernization of the national electricity system (construction of new power plants and transmission lines). The development of ecologically clean energy is associated with reducing greenhouse gas emissions. It is possible that Poland, to meet international obligations related to the problem of warming, will have to make continually postponed decision to build several nuclear power plants. Restructuring and modernization of key industries will allow the realization of country energy policy in accordance with its objectives, mainly zero-energy growth.


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References

[1] Janasz W.: Zarys Strategii Rozwoju Przemysłu. Difin, Warszawa 2006. [2] Kufel T.: Ekonometria. Rozwiązywanie problemów z wykorzystaniem programu

GRETL. Wydawnictwo Naukowe PWN, Warszawa 2007. [3] Pyk J.: Szanse i zagrożenia rozwoju rynku energetycznego w Europie i Polsce.

Wydawnictwo Akademii Ekonomicznej w Katowicach, 2007. [4] Statistic YearsBook of Poland. GUS. Warszawa 1996-2008. [5] Stablik J.: Model ekologicznego i ekonomicznego prognozowania wydobycia i

użytkowania czystego węgla Tom 1. Główny Instytut Górniczy, Katowice 2004 [6] The Master Plan Study for Energy Conservation in the Republic of Poland, ECCJ,

Japan 1999. [7] Zeliaś A. Pawełek B. Wanat S.: Prognozowanie ekonomiczne - Teoria, Przykłady,

Zadania. PWN, Warszawa 2003. [8] Ziębik A. Szargut J.: Podstwy gospodarki energetycznej. Wydawnictwo Politechniki

Śląskiej, Gliwice 2004.


201

Suppression of impulse noise in Track-Before-Detect Algorithms

Przemysław Mazurek

West-Pomeranian University of Technology 71-126 Szczecin, ul. 26. Kwietnia 10, e-mail: [email protected]

Influence of the impulse noise in recurrent Track-Before-Detect Algorithms is considered in this paper. Impulse noise from the object should improve tracking performance but it is not true. This is the SNR paradox that could be explained using Markov matrix theorem. Suppression of the signal value using threshold techniques improves output SNR. Description of this effect is detailed shown in the paper using illustrative examples. Obtained results could be applied for numerous applications of TBD systems.

1. Introduction

Object tracking techniques are used in numerous applications and there are a lot of tracking algorithms currently available [4]. Tracking is the object state estimation using disturbed measurements. The state space could be defined in many domains, but the most typical is the position. Obtained trajectory could be used as output and also as a basis of calculation of next steps. Tracking algorithm uses prediction from previous measurements for estimation of the area where the object could be available. The new measurements descript position of the object. Difference between predicted and measured position is small if the correct motion model is assumed. A small maneuver may occurs because the object trajectory is driven by the numerous factors (intentional or noise) and the difference (an estimation error) is used for update of the predictor state.

There are many tracking algorithms investigated in literature and verified in the practice. The most important are the Benedict-Boerdner [4, 6], the Kalman [4, 6, 9], and the Bayes [4, 14] filters. High quality of the detection process is assumed in the conventional tracking systems. Raw measurements are processed using different signal processing algorithms but binary output is expected. The output value is 1 if the object is detected and corresponding position in the measurement space is available. The output value is 0 otherwise. Such formulation loose signal data what is a source of lower quality of such systems in comparison to the alternative approach where detection is not in the first processing stage. System based on TBD (Track-Before-Detect) approach accumulates signal value so much higher tracking quality could be obtained. The SNR (Signal-to-Noise Ratio) for the first approach must be high (SNR>>1). Signals hidden in the noise floor could be tracked by multiple measurements using the TBD approach [4].

P. Mazurek / Suppression of impulse noise in Track-Before-Detect Algorithms

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Possibilities of the TBD algorithms are used in the stealth object tracking, especially in the air, space, marine and underwater surveillance applications but non-military applications are available also [4, 5]. The most significant difference between both approaches is depicted in the Fig.1. Conventional approach uses detection first so only selected measurements are used for tracking (some of them could be a noise or true objects position). All possible trajectories are processed by TBD algorithms and signal values over every trajectory separately are accumulated. TBD algorithms process giant amount of trajectories independently on the real number of objects (multitarget tracking). Conventional tracking algorithms support only single object tracking but multitarget scenarios are supported if an additional assignment algorithm is used [3, 4]. Both systems should be selected carefully to the particular applications.

Tracking Detection Assignmentmeasurements tracks

Detection Tracking Assignmentmeasurements tracks

Fig. 1. Conventional and TBD processing schemes

2. Track-Before-Detect Algorithms

There are numerous types of TBD algorithms: recurrent and non-recurrent. Both of them are very important and they behave similarly to the linear IIR and FIR filters respectively. The recurrent algorithms are simpler in implementation with the lower computation and memory costs what is very important for real-time processing. State-space should be carefully designed to the recurrent algorithms for specific set of the possible trajectories. Much more convenient for the trajectory set selection are non-recurrent algorithms. Set of the trajectories define the motion model of the object.

TBD algorithm needs a lot of computations but TBD variants with a limited state-space search are available also. Such algorithms like Particle Filters [7, 13] are used for low reliability applications and they are not optimal. Typical recurrent TBD algorithm like Spatio-Temporal TBD (or Spatial-Temporal TBD) [1, 2, 10-12] uses only a previously computed state space and update it using a new observations what is very useful for the memory limited processing devices. The Spatio-Temporal TBD has following pseudoalgorithm:


203

Start 0),0( skP //initialization (1a)

For 1k

S

kkkk dsskPssqskP 111 ),1()|(),( //motion update: (1b)

),()1(),(),( skXskPskP //information update (1c) EndFor Stop where: k – iteration number, s – particular space, X – input data, )|( 1kk ssq −

state transition (Markov matrix), P – predicted TBD output, P – TBD output, – weight - smoothing coefficient. )1,0( .

The smoothing coefficient is responsible for the balance between dispersion (motion update) and new observations. High values (e.g. 0.9 and more) are used in TBD applications because only a high value gives possibilities of low SNR signal tracking. Simplified Likelihood Ratio TBD [14] has similar code structure so most results could be extended to this algorithm also. Recurrent algorithms like Spatio-Temporal or Likelihood Ratio TBD uses the Markov matrix for the motion model description. TBD algorithm uses the accumulative approach by multiple measurements. There are two sources of multiple measurements: from the multiple sensors or from the multiple scans. Both sources could be used together for maximal performance. The accumulative approach (calculating of a mean from multiple noised values) increases SNR and it is reason why TBD algorithms restores signals for a low SNR measurements. In this paper a single sensor is assumed for simplification of analyses.

TBD algorithms work very well for high SNR also. Reduction of the object signal reduces a performance of TBD. There is the special class of objects with constant or variable slowly signal level and an additive positive impulses (salt noise). Airplanes, satellites or asteroids have such signal signatures for example. Such positive impulses should improve greatly a tracking process because a high value will be accumulated and output SNR should be improved.

In a few papers [10-12] computer simulations for such cases are shown – the results are different from the expectations. Positive impulse should improve tracking process but an overall tracking performance is reduced. Reduction of measurement values (by the saturation function) improves tracking performance (this is paradox, because results should be opposite). In this paper paradox will be explained also using one-dimensional model of infinite grid. Simple Markov matrix is assumed: there is a dispersion of particular value over the three grid cells


204

(Fig.2) in every processing step k . The information update formula is based on the exponential filter.

t+1

t

a b a

xnxn-1 x n+1

xn

Fig. 2. Markov matrix based values evolution

The sum of the Markov matrix transitions should be equal to the unity (sum of row) because information can not be generated using the recurrent formula. Response of the Markov matrix after N -scans could be calculated [8] using following formula:

NPrNr 0 (2)

where: 00000 Cr - starting vector, with the single object and without a noise, C − pulse magnitude, e.g. 1C .

Symmetrical values of transitions are assumed in the Markov matrix what is typical in typical tracking scenarios and is assumed for simplification of the analysis:

1 aba (3) so the Markov matrix has following form:

abaaba

abaaba

aba

Q


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Following formula could be used for calculations of the real response of TBD for assumed existence of the impulse only in the input measurements:

NNN Prr

0)1()1( (4)

The first part of this formula )1( represent of the input measurement mixing with existing state space. The second part of formula )1( N represents a recurrent calculations and the exponential values reduction.

3. Evolution of Impulse Responses

Distortions generated by impulses are the Markov matrix values dependent. Two examples are shown because they depicts a possible results and lack of the impulse noise reduction (impulse has a magnitude 30, but the expected measurement values are from the range 1,0 . The smoothing coefficient is set to

the 9.0 value. Measured impulse is reduced to the 130 value by the information update formula in the first processing step.

The first one example assumes transitions with the three equal values 3/1,3/1,3/1 aba - uniform values of this kernel. After a few iterations a Gaussian shape is obtained what is the result of the central limit theorem (similar technique is used often for the recurrent approximation of the Gaussian filter).

Obtained results shown in Fig.3 and Fig.4 are unimodal with the single maximum. In the center of value set ( b -value position) is this maximum located. This impulse exists in next scans (with decaying values) due to recurrent calculations of Spatio-Temporal Recurrent TBD. Central elements ( b ) of Markov matrix has quite often a higher value in comparison to the surrounding ( a ) and the simulation result is shown in the next example.

Fig. 3. Time evolution of impulse - transition set 3/1,3/1,3/1 aba


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Fig. 4. Impulse response of TBD system - transition set 3/1,3/1,3/1 aba

In Fig.5 and Fig.6 single modal response are shows (they are less dispersed in

comparison to the previous example). The impulse in this example is long-time living and disturbs the proper trajectory of moving object. This disturbance occurs if the proper trajectory is different from direction of defined by the impulse response maxima. Multiple maxima (mods) are possible for special cases (if the central element has lower value than surrounding) and for example the set 45.0,1.0,45.0 aba has such property.

There is a special case of the Markov matrix where impulse noise behaves according to the expectation (improves SNR). Complete signal value is passed to the next scan and is reduced only by the information update formula for

1;0 ba (so Markov matrix has only ones and zeros). Such case is interesting for the applications with the fixed object motion. Measurements limiting by the saturation algorithm for this special case is not so good idea.

Fig. 5. Time evolution of impulse - transition set 1.0,8.0,1.0 aba


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Fig. 6. Impulse response of TBD system - transition set 1.0,8.0,1.0 aba

4. Single and Parallel Track-Before-Detect Analysis

Spatio-Temporal TBD is the linear signal processing algorithm so the linear

systems theorem could be used for the impulse response and the object signal analysis. The single Spatio-Temporal TBD block depicted in Fig.7 could be replaced by the two parallel TBD processing blocks with separated inputs. The TBD1 block processes the signal and noise. The TBD2 block process impulse noise only. Such separation is not possible in the real case but is very convenient for the explanation of paradox - observed results is the sum of responses of both TBD blocks.

OutputInput(taget signal + noise

+ impulse noise)

TBD

Output

Input

(taget signal + noise)

TBD

Input

(Impulse noise)

TBD

Fig. 7. Decomposition of the linear Track-Before-Detect systems


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The constant object signal and zero mean Gaussian noise are assumed. The TBD1 give response related to the object with a suppressed noise. The TBD2 block give the impulse response and the output of this block behaves according to the description from the previous section and create the long-time decaying response (with direction defined by the central value b ).

The output value of TBD1 does not exceed the 1.0 magnitude for noise-less case. The maximal response value for some time moment for TBD2 could be larger then 1.0. The maximal value is obtained from the impulse not from the real object so it is a source of tracking errors and the paradox is explained finally.

5. Suppression of impulse noise with fixed threshold

There are available different techniques for the reduction of this noise related to the object signal [10-12]. The first technique is based on the saturation of the upper value using fixed and arbitrary set threshold value T , incorporated into the information update formula:

)),,(()1(),(),( TskXSatskPskP (5) High value of threshold gives abilities of higher influence of the impulse noise

on final results. The second technique is based on the switching between two update formulas:

otherwiseskXskPTskXskP

skP:),()1(),(

),(:),(),(

(6)

Predicted value is used only if the input signal value exceeds threshold value. The input measurement is set to the zero for high value of the smoothing coefficient ( 0.1 ).This technique could be considered also from another point-of-view as a replacement of the input value by the predicted one. Values below threshold are used like in the original information update formula.

Recurrent behaviors of considered Spatio-Temporal TBD lock ability of the direct application of the median filter. Non-recurrent TBD algorithms are much better for incorporating median filtering together with an accumulation.

6. Examples of Suppression of Impulse Noise with Fixed Threshold

In the following test examples the smoothing coefficient is equal to the 0.95. There are 313 iterations for full circle of the target and threshold values: 2, 3 and 5 are tested. Signal strength is equal to the 1 and measurements are disturbed by an additive noise with uniform distribution and values from 0 to 0.5 range.


209

Fig. 8. Euclidean errors for threshold value 2 and algorithm (5), 5% impulse rate


Saturation algorithm according to (5) preserves additive pulse strength what is not recommended and occurs if threshold value is high. Alternative algorithm (6) remove pulse what is much more efficient and smaller error are obtained. Further lowering of the threshold level for the formula (5) will reduce errors and introduce some nonlinear effect to the overall signal if the level will be to near the upper boundary defined as a sum of constant signal strength and the positive noise values. In Fig. 8 and Fig.9 are shown example where the errors are comparable for low threshold value 2.

Formula (6) is preferred if the impulse rate is low and the threshold value is high, otherwise information update works as a data proxy between steps and integration process is not working well (Fig. 11).

For the high ratio pulses threshold basic threshold (5) work better what is shown in Fig. 10 and Fig. 11.


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7. Conclusions

Presented analysis of the SNR paradox in TBD systems shows reasons why the positive impulse (or impulses) reduces tracking performance. High-peak impulse value force the trajectory according to the maxima of impulse response. Reduction of peaks even by simple saturation functions improves tracking. Such assumption is correct for a non-trivial Markov matrix. A trivial case of Markov matrix where in every row is the single 1.0 value has not such behavior and the saturation function reduce a performance. Obtained results are correct for TBD systems based on Spatio-Temporal and Likelihood Ratio TBD. Analysis of this paradox is very important for the real systems. An improvement by saturation function is important for implementations based on the fixed-point arithmetic.


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Selection of the correct formula and the threshold value is non trivial task, because depending on the threshold level results are different. Large threshold value is not recommended for formula (5). High impulse ratio reduces possibility of application of formula (6). Selection between them will be considered in the further works.

Acknowledgements

This work is supported by the MNiSW grant N514 004 32/0434 (Poland). This work is supported by the UE EFRR ZPORR project Z/2.32/I/1.3.1/267/05

"Szczecin University of Technology - Research and Education Center of Modern Multimedia Technologies" (Poland).

References [1] Bar-Shalom Y.: Multitarget-Multisensor Tracking: Applications and Advances, vol.

II, Artech House 1992. [2] Barniv Y.: Dynamic Programming algorithms for Detecting Dim Moving Targets.

In: Bar-Sahlom, Y. (ed.): Multitarget-Multisensor Tracking. Artech House 1990. [3] Blackman S.: Multiple-Target Tracking with Radar Applications. Artech House

1986. [4] Blackman S., Popoli R.: Design and Analysis of Modern Tracking Systems. Artech

House 1999. [5] Boers Y., Ehlers F., Koch W., Luginbuhl T., Stone L.D., Streit R.L. (eds.): Track

Before Detect Algorithm, EURASIP Journal on Advances in Signal Processing, Hindawi 2008.

[6] Brookner E.: Tracking and Kalman Filtering Made Easy. Willey-Interscience 1998 [7] Doucet A., de Freitas N., Gordon N., Smith A. (eds.): Sequential Monte Carlo

Methods in Practice, Springer 2001. [8] Grinstead C.M., Snell J.L.: Introduction to Probability, AMS 1997. [9] Kalman R.E.: A New Approach to Linear Filtering and Prediction Problems.

Transactions of the ASME-Journal of Basic Engineering, Vol. 82, Series D 35-46 (1960).

[10] Mazurek P.: Improving response of recurrent Track-Before-Detect algorithms for small and point targets. 14. Konferencja Naukowo-Techniczna “Zastosowania Komputerów w Elektrotechnice” ZKwE’2009 Poznań, 351-352, 2009.

[11] Mazurek P.: Impulse noise of small and point targets in recurrent Track-Before-Detect algorithms, "Academic Journals: Electrical Engineering". no.61, 662-664, Poznań University of Technology 2010.

[12] Mazurek P.: Suppresion of impulse noise in Track-Before-Detect algorithms using saturation and pulse removal, 15. Konferencja Naukowo-Techniczna “Zastosowania Komputerów w Elektrotechnice” ZKwE’2010 Poznań, 301-302, 2010.

[13] Ristic B., Arulampalam S., Gordon N.: Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House 2004.

[14] Stone L.D., Barlow C.A., Corwin T.L.: Bayesian Multiple Target Tracking. Artech House 1999.


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BMJ2K – walking octaped robot with 24 servomechanisms

Bartłomiej Kuśnierz, Jan Marlewski, Andrzej Rybarczyk, Karol Gugała

Poznan University of Technology 60-965 Poznań, ul. Piotrowo 3a, e-mail: [email protected]

BMJ2K is a walking octaped robot designed for educational purposes. It uses walking algorithms based on biological observations. It’s master control unit, ATmega128, communicates with a PC and transfers data to 8 slave ATmega8 microcontrollers. These are responsible for generating PWM signals for 24 servomechanisms which make robot walk.

1. Introduction

Nowadays, when automation and computerization have significant influence on civilization development, scientists are attempting to fulfill human needs. Replacing people with more efficient and precise automated devices becomes more and more frequent (let’s take KUKA or FANUC manipulators for instance). Biorobotics can be mentioned as an example of strongly evolving discipline of automatic science. It’s aim is to create machines based on patterns observed in nature. The biggest challenge for scientists is to create a humanoid robot which could communicate with people and also act out emotions.

Walking robots can be classified into following groups: • one-legged robots, • two-legged robots, • four-legged robots, • multiple-legged robots.

Two and four legged robots are most dominant, but multi-legged solutions offers better stability and easiness in moving on rough surfaces. In this paper we present our proposition of design approach and construction details of octaped robot. Next section says about solutions chosen in design path. Mechanical calculations and parts design was described in section III, also used software was listed there. Section IV specifies electronics layer of robot: circuits, connections etc. OpenGL mechanic visualizations software made in this project is depicted in section V. Section VI says about robot firmware and PC software development. Finally in section VII short conclusion was made and future plans were presented

2. Brief for design

The first step was design of the mechanical parts of the robot (see section III). Robot assembly drawings were made using CATIA V5 Dassault Systems. In order

B. Kuśnierz, J. Marlewski, A. Rybarczyk, K. Gugała / BMJ2K – walking octaped robot…

213

to verify the correctness of the construction we used DMU Kinematics module for kinematic analysis.

By using laser cutting techniques all the elements were prepared in order to assemble them with servos and other additional elements of construction. The next stage of work was the design and execution of the electronics.

With the use of EAGLE software from CadSoft, a printed circuit board was made which is responsible for controlling a single leg (lower layer of electronics) and a printed circuit board placed on the body of the robot (top layer of electronics), in charge of sending commands to the bottom layer of electronics and communication with the PC.

Based on the analysed algorithms of how walking robots move and the analysis of biological patterns[1,2], firmware was made for ATmega8 and ATmega128 microcontrollers. As communication bus needed to exchange data between the upper and the lower layer of electronics TWI bus was used, ensuring the free exchange of data in both directions.

In order to simulate walk of a robot and optimization of the kinematics – software visualization were created with Visual C ++ using OpenGL.

The next step was to develop a system of battery powering, together with the charging system, allowing the independent movement of the robot without the external power source. To solve this problem the lithium-ion cells from notebook computers were used.

In addition, in order to allow observation of the robot's current operating mode (a leg, which is currently moving, walking algorithm, etc.) graphical display with dimensions of 128 to 64 pixels was mounted on the body. By using this type of display it is possible to present any graphics or even simple animations.

3. Mechanical design

The design of eight-leg walking robot requires consideration of many parameters, such as the shape of the legs, number of degrees of freedom, or the type of electric drives used to set feet in motion. Only after a careful consideration of those issues, design of the robot could begin. There are many different solutions for the construction of a walking robot, particularly its legs. After analyse of the available solutions proposed in literature [1,2] and other projects of such robots [3] the decision was made to build legs with three degrees of freedom (Fig. 1). Such a solution can reach every point in the workspace, and do not limit the possibility of the movement of legs. This construction imitates the structure of insects’ legs. The first segment of the leg is a hip (lat. coxa), second segment – a thigh (lat. femur), and the third segment – a shinbone (lat. tibia).


214

Fig. 1. Leg with three degrees of freedom

Another assumption taken into account during designing the shape of the robot’s leg

was the choice of driving elements. The best for such tasks were Hitec servos. Their big advantage is the fact that their construction allows simple mounting to

the leg structure. In the case of the shape of both body and legs there is quite a big flexibility of design, but it is necessary to take into account the above assumptions because it can have a significant influence on the range of motion of the leg.

Most servomechanisms are controlled with PWM signals. By modifying the duty cycle of a rectangular waveform, servo offset can be changed. The control signal must have the frequency of 50Hz (20ms period). Typically, servos position 0 is achieved with 1ms duty cycle set, the center position - 1.5ms and the maximum angle (of about 180deg) for 2ms. Servos used in the solution are: Hitec HS 422 • dimensions: 40.6 x 19.8 x 36.6[mm], • weight: 45.5[g], • torque (at 4.8/6[V]): 3.3 / 4.1 [kg/cm], • speed (at 4.8/6[V]): 0.21 / 0.16 [sec/60°]. Hitec HS 475HB • dimensions: 38.8 x 19.8 x 36 [mm], • weight: 40[g], • torque (at 4.8/6[V]): 4.4 / 5.5 [kg/cm], • speed (at 4.8/6[V]): 0.23 / 0.18 [sec/60°]. Hitec HS 635 • dimensions: 40.6 x 19.8 x 38.8[mm], • weight: 50[g], • torque (at 4.8/6[V]): 5.0 / 6.0 [kg/cm], • speed (at 4.8/6[V]): 0.18 / 0.15 [sec/60°].


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During the robot design, decision was made that elements of the body and legs would be made from plexiglas. The advantages of this material are: relatively high strength and low weight compared to aluminium components of the same thickness. In addition, those elements require no painting and give a wide range of colours and thickness of the material.

Plexiglas used in this project was 3 mm thick - black (hips, thighs and body) and 4 mm – clear (tibia). The elements were cut with laser technology to ensure high accuracy and performance of elements. Despite the fact that the system CATIA V5 supports CNC equipment, it was difficult to find a company that would enable the cut of these elements on the basis of drawings made in this system. It was therefore necessary to make drawings in Corel Draw 9 on the basis of pre-made designs. Other elements of the robot, such as spacers and servomotors clamping systems, were made individually to ensure the needed parameters.

Fig. 2. CATIA design (screenshot)

4. Electronics

Problem of control each of the servos was solved by use one main master processing unit, that was responsible for receiving commands from the PC (like “go forward”) and transmitting proper commands (like “move the leg backward”) to slave units. Every slave unit controlling each leg sends adequate PWM control signals to each of legs servos.

According to above assumptions, one main PCB holding the master unit with peripherals was created. Additionally eight slave boards, one for each leg, was constructed.

The chosen microcontrollers were Atmel ATmega128 as the master unit and ATmega8 as slave units. Main advantage of those devices are low price, easiness in firmware development and debugging and availability on market. The RS-232 communication interface was chosen for data transmission between PC and master controller. TWI interface was used to transmit data between master and slave units. It was also important to find microcontrollers that have at least 3 independent PWM channels. ATmega8 can provide this functionality.


216

Although all elements used in the project (microcontrollers, servos and LCD) work at 5V operating voltage, an unit converting signals from an RS-232 serial port to TTL compatible signals was needed. The MAX232 circuit was used to enable PC – ATmega128 communication.

The fragment of main PCB is shown on fig. 3. The following slots were placed on the board: • external power supply slot, • ISP slots:

o SPI, o JTAG,

• RS-232 port slot.

Fig. 3. Master unit schematic fragment

As for the slave board, the input signals are: • VCC – regulated 5V supply voltage, • GND – ground, • SCL – clock signal of TWI, • SDA – data signal of TWI.


217

Fig. 4. Slave unit schematic

Fig. 5. Slave unit PCB project

5. OpenGL visualisationV

The application for visualization of BMJ2K’s movement was developed using C++ programming language and OpenGL. Microsoft Visual Studio 2008 was used as an integrated development environment.

To create the visualization, both forward and inverse kinematics had to be computed for robot’s body and each of it’s legs.

Figure 6 shows the kinematic structure for a sample leg, described using modified Denavit-Hartenberg parameters, as shown in Table 1, a1, a2 and a3 are constant, while q1, q2 and q3 are the angles set by servos.


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Fig. 6. Kinematic chain of a leg

Table 1. Modified Denavit-Hartenberg parameters

i ai-1 αi-1 di θi 1 0 0 0 q1 2 a1 90º 0 q2 3 a2 0 0 q3 – 90º 4 a3 0 0 0

Fig. 7. Visualization of virtual surfaces


219

Application provides a visualization of robot motion, using different gait algorithms and allows user to change every servos angles for each leg. Information on each leg position (current angles, tip coordinates in both local and global systems) are displayed on the screen. Implementation of the inverse kinematics algorithm allows to move the tip along each of the three axes of the global system.

The latest modification of the program allows to define virtual surfaces (Fig. 7). Every leg tip can be bind to one surface. Robot movement is performed by changing the global position and orientation of chosen surfaces or robot’s body, rather than by moving each leg separately.

6. Firmware and software development

The aim of microcontroller communication was to let user send control signals to master unit, which takes proper decisions and communicates with every slave unit using Two Wire Interface, giving them instructions where to move the leg. Slave unit is interpreting signals received from the master unit, generate appropriate PWM signals and send them to servos.

The function responsible for moving a leg takes each servo expected offset as a parameter, and completes the algorithm: • find which servo has the biggest offset from current to expected position, • find out in which direction the movement for each servo should be done, • gradually change control signals from current position to the end, • save new servos positions to global variables.

To analyze gait algorithms it is necessary to define some basic terms used to describe them. Gait period is the time needed to make one full sequence of leg movement. Duty factor is the ratio of time when a leg has the contact with surface to gait period. The relative phase of gait specifies the time between putting certain leg on the ground and the beginning of gait (or time when other leg touched the surface).

During movement, leg may be in two phases: • leg touches the ground (retraction), • leg is located above ground (protraction).

Studies made on arachnids Neoscona Nautica [2], specifically on scorpions Hadrurus arizonensis [3] allowed to recognize basic walk sequence of those animals. Analyze of photographs made to those arachnids it was found that at least four legs to support . It uses two groups of legs in this process (Fig. 8): • first group: L1, R2, L3, R4, • second group: R1, L2, R3, L4.

Those groups are used interchangeably. In first step first group is in motion and second one is support. In second phase groups change their functions (first is support, second is moving).

Each cycle of robots gait consists of eight phases of protraction and eight phases of retraction. Duty factors available for BMJ2K are as follows:


220

• 1/2 (shown on Fig. 8), • 7/8, • 6/7.

Fig. 8. Gait with duty factor ½

BMJ2K was designed to be controlled with a PC. To communicate between a computer and robot’s master unit, RS-232 communication was used.

The user interface software for steering the robot was written in C++ using Microsoft Visual Studio 2008.

It allows user to choose between 3 duty factors (1/2, 7/8 and 6/7) and can make robot move in one of 8 directions. Properties of a serial port class can also be modified.

Fig. 9. User interface window


221

Program is working according to the algorithm: • gait information is sent to ATmega128 through RS-232, • microcontroller processes the information and begins to carry out the gait, • after completing, a callback information is sent to the PC, • if no errors occurred, next data packet is sent.

Pressing any button responsible for changing the direction of BMJ2K’s movement changes the data sent to robot. According to this, the change in robot’s movement is taking effect after another data packet is sent.

The robot can be supplied from a built-in battery system. The main restrictions when thinking of supplying BMJ2K were to obtain operating voltage between 7-9V (as an input for 5V voltage regulators) and be able to get the current value greater than 10A. 14.8V cells with capacity of 5200mAh, typically used to supply laptops, were used in this project.

In BMJ2K project the graphic LCD EA DIP128J-6N51W was used to display callback information from the robot. This device was chosen because of its many advantages: • compact size, • 128x64 pixels resolution, • easiness of use (the unit is controlled by KS0108 driver), • 5V operating voltage, compatible with project platform.

The main disadvantage of the LCD is that it doesn’t have any font generator implemented by default. In order to display text messages on the screen, a custom font table was made, with character resolution 5x8 pixels.

7. Conclusion

Our proposal of octal robot construction was described, whole design path has been depicted, also solutions for many problems occurred during robot building and testing was presented. Robot was built and tested laboratory (Fig. 10). The main problem now is the weight of cells needed to power servos, but as the batteries made nowadays are getting lighter and gains more capacitance in the near future this problem should be solved.

BMJ2K project was meant to be a platform for further development. The possible options of improvement are: • remote control via Wi-Fi, • installing cameras for terrain recon, • distance sensor for detecting obstacles, • pressure sensors at legs tip for passing through obstacles.


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Fig. 10. Built robot

References [1] Zielińska T., Maszyny kroczące. Podstawy, projektowanie, sterowanie i wzorce

biologiczne, Wydawnictwo Naukowe PWN, Warszawa, 2003. [2] Takeo Ohnishi, Toshiyuki Asakura, Spider-Robot 8-Leg Cooperative Walking Velocity

Control Strategy Based on Environmental Information JSME International Journal Series C, Vol. 47, No. 4, 2004.

[3] Bowerman R.M., The Control of Walking in the Scorpion, J. Comp. Physiol. Vol. 100, [4] Doliński J., Mikrokontrolery AVR w praktyce, Warszawa 2003.


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IRp-6 industrial robot control panel

Bogdan Fabianski

Poznan University of Technology 60-965 Poznan, ul. Piotrowo 3a, e-mail: [email protected]

In the article, an IRp-6 originally manufactured robot control panel adaptation was presented. Modernized robot programming panel was adjusted to the new control system which replaced factory made steering case. The main goal for the project was to increase overall system value as an industrial solution. Original mechanical construction was left untouched, so the default HMI. CPU (8081) was replaced with Cortex core based micro-controller provided hardware Ethernet interface (which was main interface of the new robot control system).

1. Introduction A. IRP-6 UNIT

Detailed information about factory-made construction of IRp-6 was included in its technical documentation [1]. There are several units in scope of robot system: control case, manipulator with 5th freedom degree (handling 6 kilos) and programming panel which is the main research target described in the article.

In the work [2] an historical overview first and single (until now) Polish robot unit was introduced. Market competition in face of lack of modernization, development backup bring production to close. However, thanks to the presence at polish technical universities, IRp-6 was became object research in field of electrical drives, visual or high-end, overriding movement trajectory generating systems in such as academic units as: AGH University of Science and Technology, Wroclaw University of Technology, Warsaw University of Technology and Poznan University of Technology.

B. FACTORY-MADE CONTROL PANEL

A standard, factory-made control (programing) panel system was well suited for its destination s a part of robotic stand. It have had a solid and ergonomic case for handling as presented on Fig. 1, below.

Panel HMI consist of [3]: − keyboard in configuration of matrix, divided in three segments, − analog joystick for manipulator movement, − kinematics switch (external, internal), − “not aus” push button, − security switch, − LEDs built in keyboard panel, − alphanumeric VFD: 2 rows/40 chars.

B. Fabiański / IRp-6 industrial robot control panel

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Fig. 1. IRp-6 programing panel

Keys form F group could take a function defined by the lower row display. A multifunction keys are very popular in modern HMIs (Human Machine Interfaces) – also the robotic ones.

Inside the panel could be divide into two PCBs (Printed Circuit Boards). The upper one includes VFD (Vacuum Fluorescent Display) and its driver board, when the second central processing unit (CPU) based on 8081 micro-processor.

2. A new concept

A. PROJECT GENESIS

Works [2] and [4] that were expended for main aspects of the IRp-6 new control system (NCS) weren't enclosed important part of the industrial robotic unit which is mobile programing panel.

Factory-made construction of the considered object couldn't be directly used in the NCS. The main barrier was low-tech communication interface based on serial RS-232 standard, where the main communication bus for worked out system (NCS) was Ethernet (functional describe [5]). According to the present, available technology, decision was made to remove panel main board and compile the new one served with Ethernet.

Fig. 2. IRp-6 programing panel place in NCS


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B. MAIN GOALS According to the factory-made panel analysis, that pointed on economical

justification panel case leaving untouched (original system meets safety requirements), the main goal was to change communication interface for new control system. On the functional level, mobile control panel (MCP) is alternative for numeric programing from remote PC application, the alternative that in industrial environment rapidly increasing comfort and flexibility programing process. MCP makes very popular “teaching by doing” trajectory generation method possible.

C. REQUIREMENTS

Before the exact phase of design, requirements identification in range of power supply and internal panel parts interfacing was done. The task was as difficult as the lack of original technical documentation. After hard stage of signal decrypting all was made clear. The keyboard keys were connected into matrix configuration of a-rows, b-columns where an interface was a+b wire tape cable. Joystick position x-y was obtained from two potentiometers powered from voltage source. Rest of switches was simple line shorting devices. It was important to pay attention on “not aus” button. Safety requirements defines, that this device must guarantee taking off supply from joints motor drives thus it mustn't be connected as an internal CPU signal, but traced out as control signal for power relay. As mentioned before, there was also an VFD as part of the programing panel. Because of PCB integrity (see Fig. 3), the factory-made display control board was used. The PCB had 40-pins interface connector and all of those pins were functionally recognized.

Fig. 3. VFD control board

As Fig. 3 shows, VFD control board consist of thirteen chips, were twelve of them were serial-to-parallel interface logic (STP) and one 8-bit buffer. The buffer was used for driving LEDs (lighting controls are visible from front of the MCP). When VFD considering as an dots matrix, one character field has 7(8)x5 points (one row for underlining). Eight STPs were used for control all dots in single column characters grid (one STP has 10 parallel output – five for upper character and five for other). All of those eight serial-to-parallel chips are connected to all of


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the grids in display, so there's need to have one signal to enable exactly one column which is valid for appropriate characters. This was done by rest four chips whose having summary 40 parallel outputs could provide “grid enable” signals for all display consist of forty columns (Fig. 4, below).

Fig. 4. Single character dot matrix control schema

Based on researches and theory of Vacuum Fluorescent Displays [6], construction of power supply section which isn't as simple as standard LCD was proposed. VFD driver require three levels of voltage: 3.3 for CPU, 5 for STP logic and 24 [V] anode supply. It's important to know that there are two ways to get electron from cathode to be emitted and so – the brighter displayed text, more clear for user: increasing cathode current or anode voltage. The first solution should be use very carefully. The higher cathode line current – the faster oxidizing process leading to cathode line breakdown. On the other hand we've anode voltage which is limited to power supply possibilities and serial-to-parallel chip maximum driving voltage.

D. CENTRAL PROCESSING UNIT

STM32 was selected for panel CPU. The reasons were as follow: high speed up to 72 [MHz], computing power up to 1.25 [MIPS/MHz]. As the follower of ARM7, Cortex M3 (which is STM32 core) was designed to increase computing power/energy consumption coefficient. As the main project requires, STM32 Connectivity Line includes hardware 100 [Mbps] Ethernet MAC ( Media Access Controller) process unit with dedicated DMA (Direct Memory Access) what has a key influence on communication system performance. STM32 require physical layer Ethernet controller in cooperation which gives enough power to drive Ethernet UTP (Universal Twisted Pair) cable wires. The MII (Media Independent Interface) provides data interface between units. Ethernet was described in [4].

Except of STM32 performance, it's the unit widely available in local market, relatively cheap and large, free to use with STM code libraries[7][8].


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E. VFD UNIT As mentioned, display was an array, an array of 3200 dots (8 rows x 5 columns

x 40 characters x 2 lines). To display a text, human eye abilities were used. Consequences of the VFD hardware construction, only one character can be displayed at same time. All screen must be refreshed in frequencies above 50 [Hz] (like TVs). An advantages of VFD are high contrast and lack of back-lightning (points of VFD array light itself). Control algorithm was presented above, at Fig. 5. All variables begins with “grid_” are signal for serial-to-parallel group chips generating signal “grid enable”, variables begins with “dots_” are signal for STP chips driving dots in single grid. TB means text buffer array 2 lines x 40 characters in line. It represents text to display. FM – is an byte two dimensional array where single character is encoded into five parts (as there are five columns in single character grid). FM was initialized in CPU memory. It defines characters font. To make font defining process easier, an computer application was created.

Fig. 5. VFD driving algorithm schematics


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Fig. 6. IRp-6 panel font creator PC application

The application consist of main field with 5x7 buttons matrix, where single dot can be light on or off by click on field. On the right there are 5 bytes describing font for single character, a preview, where correct character is show and control panel form where it's possible to save work result to memory and all defined font to file. The file is text formatted and provide easily copy to embedded system code. The application makes possible to read and modify font created before.

3. Summary

At the beginning of the article, an IRp-6 robot unit was focused so the new

control system was. Omitted before, factory-made programming panel was adapted to make it suitable in Ethernet network. New IRp-6 control system become more attractive and more applicable in industrial works. In the end, on Fig. 7, proposed VFD driving algorithm was presented as an real working panel photo.

Fig. 7. Example of VFD driving with proposed algorithm


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References

[1] Industrial Automation Division (ZAP): DTR RMM-01-00, Ostrow Wielkopolski, 1988. [2] Fabianski B.: Industrial robot drive, SENE conference, Lodz, 2009. [3] ZAP: IRp robot programing guide (RMMS-0466), 1988. [4] Fabianski B.: Communication interfaces in robot control system, SENE conference,

Lodz, 2009. [5] Microchip Corp.: Ethernet theory of operation (AN1120), 2008. [6] http://en.wikipedia.org/wiki/Vacuum_fluorescent_display, 2009. [7] Yiu J.: The definitive guide to the ARM Cortex-M3, Elsevier, 2007. [8] Paprocki K.: Micro-controllers STM32 in practice, BTC, 2009.


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Fuzzy models of the biological-chemical processes

in the west-water treatment plant

Krzysztof Szabat, Czesław T. Kowalski Wroclaw University of Technology

50-372 Wrocław, ul. Smoluchowskiego 19, e-mail: [email protected], [email protected]

In the work issues related to control of the electrical blowers installed in the waste water treatment plant (WWTP) are demonstrated. After a short introduction a description of a real treatment plant is presented. Then the main sewage drives are described. Next the commonly used control strategies for the biological-chemical process are presented. The model ASM1 of the biological chemical transformation used in the advanced MPC (model predictive control) strategy is introduced. Then the fuzzy system based on the TSK model is presented. The ability of the TSK fuzzy system to estimate the biological-chemical variables are demonstrated.

1. Introduction

Control processes in WWTP is a rapidly growing field of knowledge [1]-[4]. This follows the universality of using urban and industrial processes in wastewater treatment, striving for continuous reduction of maintenance costs as well as a complicated and non-linear model of the transformation of compounds in the treatment process. Optimal control strategy should be on one hand, easy to install on the other hand leads to a reduction of operating costs and prevent exceeding the limits on the outflow of sewage [1]-[5].

The electrical drives installed in the WWTP can be divided into a few group. To the first group a electrical blowers which are responsible for delivering the air (oxygen) to the bioreactor are included. Those drives are the main consumption elements in the WWTP [4]-[6]. In the typical WWTP they take approximately of 80%- 90% of the electrical consumed energy. The second group encompasses the pumps and mixers. The other drives are including in the third group (e.g. in the station of mechanical cleaning).

The design of the control strategy which saves the energy is quite a complicated process because it required knowledge from different fields (chemical, electrical and control engineering). Additionally, the process is nonlinear and depending on many hardly identified factors. Therefore, commonly-used strategies are not advanced and usually relying on keeping a constant dissolved oxygen level in bioreactor. The more advanced concepts such as MPC are still not used in practice but they are in intensive laboratory tests [6]-[7]. Its application can decrease the

K. Szabat, C. T. Kowalski / Fuzzy models of the biological-chemical processes…

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operational costs significantly. However, one of the main drawback of the MPC is a large computational burden which can be reduced by finding a faster model.

The main goal of the paper is to present the ability of the TSK fuzzy system to model the biological-chemical processes of a WWTP. The design model will be used in the advanced control structure (MPC) of the electrical blowers installed in a WWTP. The paper presents the a first part of the work connected to the research project: advanced monitoring and control of the electrical drives in the WWTP and its devoted to analysis of the ability of the different fuzzy system to model the biological-chemical transformation. Contrary to the papers [8]-[9] where the comparison of the properties between the Mamdani and TSK systems was presented, in the current work more deeply analysis concerned only TSK system is included.

The paper is organized as follows. After a short introduction a description of the plant used in the study is provided. Then the commonly-used strategies of the WWTP are briefly described. The advantages and drawbacks of the MPC are analyzed. Next the fuzzy models are introduced. The ability of the fuzzy system to model the biological-chemical transformation processes are presented. In conclusion some final remarks are given.

2. Description of the plant

In order to remove the nitrogen from the wastewater two biological processes

nitrification and denitrification are used. In the nitrification process ammonium is oxidized to nitrate and then in the denitrification process nitrate is transformed to gas nitrogen. In order to ensure an adequate nitrification level in the aerobic environment the following factor must be fulfilled: namely the sufficient concentration of dissolved oxygen level in aerobic zone. However, aeration causes high energy costs and may unfavorably influence the denitrification rate in the anoxic compartments [4]. Different configurations of the WWTP can be used in practice. A diagram of the test plant is shown in Fig.1.

Fig. 1. The general scheme of the WWTP


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It consists of the five zones. In the first zone (80 m3) the phosphorus is removed by special microorganisms. Then the plant has two series denitrification-nitrification (110 m3-210 m3) zones. The internal recycle circuits deliver nitrate to the denitrification zones. After those zones the waste water flows into secondary settlers (225 m3), in which sedimentation and clarification take place. Some of the waste water is clear after reaching the output of the plant. The sludge is turned back to the input of the plant or optimally to the waste-sludge tank. The daily inflow of the plant is approximately 850 m3, which means that the tested plant is relatively small (countryside with the population of approximately 8 thousands citizens). In Fig. 2a the bioreactor of the WWTP is shown. The inner partitions which divide the zones are hidden by the wastewater.

a) b)

Fig. 2. A view of the bioreactor (a) and blowers station (b)

The tested plant has the following drives: a pump from the primary settlers to bioreactor (4.7kW), recirculation pumps (3x1.3kW) and a blowers station (4x18kW). As can be concluded from the presented data, the main consumption elements are the electrical blowers. Therefore, the strategy which can save energy is look for. In Fig. 2b view of the blowers station is shown. In order to minimize the noise the blowers have special housing.

In the literature a number of control structures for control processes used in the sewage treatment plant are presented [1]-[5]. The simplest control strategies are based on maintaining constant air flow to the zones of nitrification in the biological reactor. An advantage of this approach is its simplicity. Disadvantages of this strategy steam from the constant flow of air from the electrical blowers. Under conditions of low water flow the bioreactor is overaerated. Even a slow increase in the flow of pollution can bring about exceeding the limits in the outflow. Despite these drawbacks, this strategy is still in use in practice [1].

A more advanced control strategy commonly used for small wastewater treatment plants in Poland relies on the controlling of the dissolved oxygen level in bioreactor. It requires installation of oxygen sensors in the selected parts of the bioreactor. Usually the PI (in the case of the variable speed drive) or hysteresis (in the case of the direct switched motors without converter) controllers are applied.


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Depending on the value of the control signal a number of the electrical blowers can be set on or off. This control strategy does not take into consideration the variation of the input of the bioreactor. The large values of the inflow can lead the dissolved oxygen level below the required value. On the contrary, smaller inflow of the ammonia can make the waste water overaerated which can disturb the denitrification process. This may result in unnecessary consumption of the energy by the blowers.

One of the most advanced control strategies for the WWTP is MPC. MPC is an optimization-based strategy requiring a solution to a mathematical optimization problem at each sampling time. The control objectives are directly expressed in a cost function. Despite the fact that optimization problems can be solved efficiently using off the- shelf solvers, the computational effort required for the implementation of the MPC algorithms on-line can be quite prohibitive for many real-time applications. This is particularly evident in systems with complicated nonlinear mathematical model. One of the ways which can ensure the real-time MPC application is the simplification of the mathematical model of the plant [7],[10].

3. Mathematical model of the bioreactor

ASM1 model describes the transformation of organic compounds and nitrogen in the sewage treatment plant. Its original form was proposed in 1987 in [11]. It consisted of eight equations that describe the kinematics of change by manipulating the 13 state variables. ASM1 model was based on mass balance equations and stoichiometric relationships of kinematics. The currently used form consists of ten equations which describe the transformation of the fourteen variables. ASM1 model operates on the following state variables: − SS easily degradable organic compounds considered as dissolved, − SI dissolved organic compounds biologically nondegradable, − SNH – ammonium nitrogen, expressed as the sum of ammonia (NH3) and

ammonium (NH4+),

− SNO nitrate nitrogen, expressed as an aggregate concentration of nitrates and nitrites,

− SND Dissolved organic nitrogen, − SO dissolved oxygen, − SALK alkalinity, − XS slowly biodegradable organic compounds, − XI organic compounds in a suspension of biologically non degradable, − XBH heterotrophic bacteria, microorganisms, which in carry out the

biodegradation in aerobic and anaerobic zones, as well as the hydrolysis and ammonification of XS,

− XBA autotrophic bacteria, microorganisms that carry out the process of nitrification - derive energy from oxidation of ammonia; this fraction express at the same time the microorganisms which oxidizing of nitrite and ammonia,


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− XP products of biomass death, − XND organic nitrogen in the suspension, Organic nitrogen which is connected with

the fraction XS. Together with XS hydrolyzes to dissolved organic nitrogen (SND), − XMIN – mineral slurry, a suspension, which is not included in the COD and do

not undergo any treatment. The transformations of the wastewater, taking into account the above-

mentioned fractions, are described by ten kinematics equations and the stoichiometric and number coefficients. Due to the length of the model, it is not presented. The exact description can be found in [2]-[5].

4. Takagi-Sugeno fuzzy model

The TSK model was proposed in 1985 by Takagi and Sugeno and later in 1988 by Sugeno and Kang. Nodaways it is one of the most frequently applied fuzzy systems. It consists of several rules in the following form [12]:

R1:IF x1=A11 AND…AND xj=A1j THEN y=f(x1, x2… xj,x0) Rn:IF x1=An1 AND … AND xj=Anj THEN y=f(x1, x2… xj,x0)

where x0 is a constant value. An illustration of the TSK system computational scheme is presented in Fig. 3.

After the fuzzyfication procedure of the two input values e1 and e2, the degree of the premises part of each rule is computed using the min operator as the t-norm. The consequent part of the rule is a function of the input variables. After its calculation the implication and aggregation methods are applied to the system. Then the output of the system is conducted by means of the singleton defuzzyfication strategy.

0y

10211 ,, axxfF

20212 ,, axxfF

Fig. 3. Illustration of the TSK system computation scheme

The TSK model has the following advantages. First of all, it allows reducing the computational complexity of the whole system. This steams from the fact that the integration of the non-linear surface is replaced by the sum and prod operations (in defuzzyfication methodology). Furthermore, by suitable selection of the input


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membership functions it is possible to obtain the sectors in the control surface depending only on one rule, which simplifies optimization of the fuzzy system. Due to this reason the TSK model is often called a quasi-linear fuzzy model. Fuzzy c-clustering method

Fuzzy clustering plays an important role in solving problems in the areas of fuzzy model identification. It have been widely applied in different engineering areas such as: information technology, electrical engineering, chemical engineering etc. A variety of fuzzy clustering methods have been proposed in the literature [13]-[16]. Most of them are based upon distance criteria. Contrary to the classical clustering method, in fuzzy clustering one sample can belong to more than one cluster. It means, that a specific certain datapoint that is located near to the center of a cluster has a bigger degree of belonging to that cluster than another datapoint located farther. One commonly used algorithm is the fuzzy c-means (FCM) algorithm. It uses reciprocal distance to compute fuzzy weights. Although more advanced methodologies have been proposed, fuzzy c-mean is still one of the most popular approaches.

The idea of FCM is using the weights that minimize sum of distances dik between the kth sample and the ith cluster center vi, i.e., the total mean-square error function defined as:

C

i

N

kik

mik duVUJ

1 1

2, (1)

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Tikikik vxvxvxd A22 (2)

N

k

mik

N

kk

miki uxuv

11 (3)

The A matrix (M × M) in (?) is set to the identity matrix I in most cases. The degree of membership of the kth datapoint to the ith cluster has a fuzzy value (in the range between 0 and 1). The bigger membership value means higher degree of membership to specific cluster. The sum of membership values of the kth datapoint for each of the clusters should satisfy the following equation:

10,,11

ik

C

iik uku (4)

m is a fuzziness coefficient which could has a range between 1 and infinity. Setting the coefficient m=1 means that the membership function of each datapoint could have only one of the two values: zero or one. It means that instead of fuzzy the hard clustering methodology is implemented. When m goes to infinity, the result of minimization leads to uik =1/C for all of the datapoints and cluster centers. That means all of the datapoints have equal membership values.


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To start of the algorithm the following parameters should be specify: cluster number C, fuzziness coefficient m and membership matrix U. The center of the cluster are determined with the help of the (3). Next membership values are calculated by:

12

1

1

mC

j jk

ikik d

du (5)

Iterative calculations based on above presented equation 2, 3, and 5 are performed.. The stop criterion usually is defined as the minimal value of the objective function J or the set number of the iteration.

5. Results

Training data have been generated in an analytical model separately in two

temperatures: 20 and 10 degrees Celsius (because behavior of the bioreactor depends on the temperature). The total duration of one simulation has been set to 40 days. To the learning procedure only every 50-th sample has been selected. During the learning the fuzzy c-means clustering method has been applied. In this work the results related to the transformation processes in a one nitrification zone are considered. They can be easy extended to the other zones.

The input vector of the fuzzy system consists of the following element: the state vector of the nitrification zone in the previous sample (k-1), the state vector of the inflow to the nitrification zone in the current sample (k), the volume of the inflow over the volume of the nitrification zone in the current sample (k). The output vector consist of the state vector of the nitrification zone in the current sample (k).

From the output vectors the state S0 has been eliminated. The dissolved oxygen is not used in the output vector due to the two reasons. First of all the level of the S0 can be easy regulated so it can be treated as a control variable. Secondly the regulation time of this variable is very short – in the range of a few minutes compared to the sampling time of the fuzzy model which is approximately one hour. Also XND has been eliminated form the input and output vector because in the nitrification zone its value is very close to zero.

In order to check the learning ability of the TSK fuzzy system the test data have been generated in different conditions. First of all they were obtained in the temperature of 15 degrees Celsius. Also the amplitude of the inflow and its component has been changed. The inflow of the bioreactor used in the testing data is shown in the Fig. 3. The variation of the input of the plant due to the different days (week days and weekend), part of the day (day and night) are clearly visible in its transient. Additionally some bigger disturbances connected with the raining period and two storms are evident in the picture. During the weekdays the inflow varies from the 550 to over 1500 m3. Contrary to the weekdays, at the weekend the maximal inflow is reduces to1200 m3. During the raining day the value of the


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wastewater delivered to the sewage treatment plant increased to 2500m3. The storm events add to the system short disturbances with the inflow on the boundary of 3000 m3.

100 200 300 400 500

1000

1500

2000

2500

3000

Inflow [number]

[m3 ]

Fig. 4. The inflow of the WWTP

First the TSK fuzzy system with two clusters has been investigated. After the learning procedure the fuzzy TSK model of the transformation processes has been obtained. Then the system has been examined using testing data. The transients of the real and estimated state variables as well as their estimation errors are presented in Fig. 5.

As can be concluded from the transients presented in Fig. 5 the fuzzy TSK model based on the two cluster has very good generalization ability. In the most of the state the estimation error are very small. Only in the transients of SNH and SND the estimation errors reach bigger value. Then the percentage estimation error for all variables has been calculated. There are presented in Table 1.

The generalization ability of the fuzzy system can be improved by increasing the number of clusters. Unfortunately, on the other hand this will also boost the computational complexity of the obtained model. In the presented study the number of the fuzzy clusters has been increased while the estimation error has been reduced. The optimal number of clusters has been set to 290. The estimation error of such system are presented in Table 2.

As can be concluded from the data presented in Tab. 1 and Tab. 2, the system with the much bigger number of clusters (290) has very similar performance as the simple one. The percentage errors are almost the some for those two system. It means that the TSK system with only two clusters can successfully represent the biological-chemical processes in the bioreactor (contrary to the Mamdani system [8]). The small number of clusters means also simplicity of the future of the real-time implementation of the obtained fuzzy system.


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Fig. 5. Real and modeled by fuzzy system transients as well as an modeled error of the state variables in the case TSK model with 2 clusters and testing data

Table 1. Estimation errors for the TSK system with number of the cluster 2

Number of the variable Number of the cluster 1 2 3 4 5 7 8 9 10 11 12 14

2 5,67 0,67 42,74 2,95 16,46 1,61 6,05 0,83 0,74 0,60 0,46 0,58

Table 2. Estimation errors for the TSK system with number of the cluster 290

Number of the variable Number of the cluster 1 2 3 4 5 7 8 9 10 11 12 14

290 5,66 0,63 42,10 2,95 16,43 1,59 5,95 0,82 0,74 0,59 0,46 0,56


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6. Conclusions

In the paper issues connected with fuzzy modeling of the chemical-biological processes for the MPC control strategy of the electrical blowers are presented. From the presented analyses and results the following remarks can be formulated: − In order to save the energy consumed by the electrical blowers an advanced strategy should be applied. The main drawback of the real time realization of the MPC is its computational complexity, which can be decreased by suitable selection of the applied model.

The TSK system has a very good generalization ability. The obtained model based on the TSK system has small modeling errors of all state variables. Due to its simplicity the TSK model can be successfully applied in the real-time MPC control structure of the WWTP.

The next investigation will concern the real time implementation of different control strategies (including MPC) in a real WWTP plant.

ACKNOWLEDGEMENTS

This research work is supported by the Ministry of Science and Higher Education (Poland) under Grant R01 014 03.

References

[1] M.A. Brdys, M. Grochowski, T. Gminski, K. Konarczak, M. Drewa. Hierarchical predictive control of integrated wastewater treatment systems, Control Engineering Practice, vol. 16, Issue 6, 2008, 751-767.

[2] A. Stare, D. Vrecko, N. Hvala, S. Strmcnik, Comparison of control strategies for nitrogen removal in an activated sludge process in terms of operating costs: simulation study, Water research, vol. 41, 2007, 2004-2014.

[3] M. Yong, P. Yongzhen, U. Jeppsson, Dynamic evaluation of integrated control strategies for enhanced nitrogen removal in activated sludge processes, Control Engineering Practice, vol. 14pp. 1269–1278, 2006.

[4] Olsson G., Newell B., Wastewater Treatment Systems, Modeling, Diagnosis and Control, IWA Publishing, 1999.

[5] http://www.ensic.inpl-nancy.fr/benchmarkWWTP/Bsm1/Benchmark1.htm [6] M. Ekman, B. Bjorlenius, M. Andersson, Control of the aeration volume in an

activated sludge process using supervisory control strategies, Water research, vol. 40, pp. 1668 – 1676, 2006.

[7] J. Maciejowski, Predictive control with constraints. Prentice Hall, 2002. [8] K. Szabat, C. T. Kowalski, Rozmyty model procesów biologiczno-chemicznych w

oczyszczalniach ścieków, XV Conference ZKwE '10, 2010, 321-322. [9] K. Szabat, C.T. Kowalski, Fuzzy models of the biological-chemical processes in the

sewage treatment plant for an advanced control of electrical blowers, accepted to IECON’10, 2010.


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[10] Borowa A., Brdys M. A., Mazur K., Modeling of wastewater treatment plant for monitoring and control purposes by state-space wavelet networks, International Journal of Communications & Control, vol. 2, 2007, 121-131.

[11] M. Henze, C. P. L. Jr Grady, G. V. R. Marais, T. Matsuo, Activated Sludge Model No. 1, IAWPRC Scientific and Technical Reports No 1., IAWPRC, London. IWA Task Group on Mathematical Modelling for Design and Operation of Biological Wastewater Treatment. London, IWA Publishing, 2000.

[12] A. Piegat. Fuzzy Modeling and Control. Springer-Heidelberg, New York, 2001. [13] X. Li, X. Lu, J. Tian, P. Gao, H. Kong, and G. Xu, Application of Fuzzy c-Means

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[14] W. Pedrycz, V. Loia, S. Senatore, Fuzzy Clustering With Viewpoints IEEE Transactions On Fuzzy Systems, Vol. 18, No. 2, 2010.

[15] R. K. Brouwer, A. Groenwold, Modified fuzzy c-means for ordinal valued attributes with particle swarm for optimization, Fuzzy Sets and Systems, vol. 161, (2010) 1774–1789.

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242

Electric Power System from the point of view

of model development

Jerzy Tchórzewski University of Podlasie

08 – 110 Siedlce, 3- Maja 54, e-mail: [email protected]

1. Introduction

In order to conduct the identification of the development of the Electrical Power System (EPS) appropriate numerical data were collected concerning fourteen input variables (u1-u14) and four output variables (y1-y4) for the period of 1946-2007, with the input variables structure presented in Table 1 and output in Table 2 [25-37]. Identification of electrical power system (EPS) for the 30 one-year-long periods for the years 1946-2007, with the step of one year was conducted in the MATLAB environment using System Identification Toolbox [1, 7, 41].

2. Some results of identification EPS system for the period of 1946-2007

The models obtained for the fourteen input variables and the first output

representing employment in 33 power stations (in total) were presented in table 3 (characteristics a(q) and in table 4 (characteristics B(q)). An example of arx133 characteristic of the EPS system for the period 1969-1998, with the accuracy of 99.14% is presented in Fig. 1.

It can be noticed that there are certain regularities in the EPS system models, mainly regularities as regards the structure of the model and as regards the values of their parameters. Arx131 model predominated in most periods. Its similarity to real data of EPS system is 99.03%. Moreover, the values of the parameters in these models were almost identical (there were slight parameter changes in the system). However, the identification conducted for the whole period of 61 years (1946-2007) generated arx133 model with the accuracy of 99.14%.

Moreover, attention should be paid to the fact that there are only six types of models, i.a. arx131, (for the periods: 1-4, 7-11, 14, 17-19, 23, 25-26, 28-32), arx135 (for the period 3-4), arx132 (for the periods: 12, 15, 27), arx134 (for the periods: 13, 22), arx133 (for the periods 16, 20, 24), arx619 (for the period 33), i.a. six structural changes that took place in EPS in the examined period of time the experiment covers.

J. Tchórzewski / Electric Power System from the point of view of model development

243

Table 1. Coefficients at q-i in terms A1(q)

0 Period q-1 q-2 q-3 q-4 q-5 q-6

1 46-75 -0.1342 0 0 0 0 0 2 47-76 -0.1342 0 0 0 0 0 3 48-77 -0.1342 0 0 0 0 0 4 49-78 -0.1342 0 0 0 0 0 5 50-79 -0.0935 0 0 0 0 0 6 51-80 -0.0935 0 0 0 0 0 7 52-81 -0.1342 0 0 0 0 0 8 53-82 -0.1342 0 0 0 0 0 9 54-83 -0.1342 0 0 0 0 0

10 55-84 -0.1342 0 0 0 0 0 11 56-85 -0.1342 0 0 0 0 0 12 57-86 0.1533 0 0 0 0 0 13 58-87 -0.0106 0 0 0 0 0 14 59-88 -0.1342 0 0 0 0 0 15 60-89 0.1533 0 0 0 0 0 16 61-90 -0.4884 0 0 0 0 0 17 62-91 -0.1342 0 0 0 0 0 18 63-92 -0.1342 0 0 0 0 0 19 64-93 -0.1342 0 0 0 0 0 20 65-94 -0.4884 0 0 0 0 0 21 66-95 -0.1342 0 0 0 0 0 22 67-96 -0.0106 0 0 0 0 0 23 68-97 -0.1342 0 0 0 0 0 24 69-98 -0.4884 0 0 0 0 0 25 70-99 -0.1342 0 0 0 0 0 26 71-00 -0.1342 0 0 0 0 0 27 72-01 0.1533 0 0 0 0 0 28 73-02 -0.1342 0 0 0 0 0 29 74-03 -0.1342 0 0 0 0 0 30 75-04 -0.1342 0 0 0 0 0 31 76-05 -0.1342 0 0 0 0 0 32 77-06 -0.1342 0 0 0 0 0 33 78-07 -0.7413 0.0791 0.0446 -17.04 1.427 -0.238

The example of the model of electrical power system development generated

for the whole period of 61 years using arx method is as follows: )()(),()(),( euqKByqKA (1)

where: ,1342.01)( 1 qqA

,1443.005387.01342.0)(1 321 qqqqB


244

,3264.07748.01965.0)(2 321 qqqqB ,52.293683.0191.5)(3 321 qqqqB

)2(,17.14715.95.14)(4 321 qqqqB,06803.005293.01554.0)(5 321 qqqqB ,006739.002755.001335.0)(6 321 qqqqB

,6104.02766.005234.0)(7 321 qqqqB ,02639.0007408.0002718.0)(8 321 qqqqB

,02883.01073.003015.0)(9 321 qqqqB ,1541.02976.008841.0)(10 321 qqqqB ,04736.006231.0131.0)(11 321 qqqqB

,009608.0009961.001546.0)(12 321 qqqqB ,2337.01287.002857.0)(13 321 qqqqB .02655.03019.002198.0)(14 321 qqqqB

0 10 20 30 40 50 60 70 80-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

4

Time

Measured and simulated model output

Fig. 1. EPS characteristic (conformity with the real system equal 99.14)

Therefore, the sought value of the obtainable power produced by the power

stations (in total) [MW] e.g. in the year θ = 2010 is influenced by the following quantities: the value of the obtainable power for the previous year (θ-1, i.e. 2009) and all fourteen input variables for the previous three years (θ-1, i.e. 2009, θ-2, i.e. 2008, θ-3, i.e. 2007).


245

Models for input variables and for individual output variables were obtained e.g. for the output representing employment in power stations (in total). In one of the experiments (the total number of experiments exceeds ten) 33 models of electrical power system development were obtained (characteristics A(q) and characteristics B(q)). The example of EPS characteristic obtained with the accuracy of 99.14% compared with the real data (optimum model) for the period of 1969-1988 is arx133 characteristic.

Table 2. Coefficients at q-i in terms B1(q)

θ Period q-1 q-2 q-3 q-4 q-5 q-6 q-7 q-8 q-9

1 46-75 0.343 -0.05387 -0.1443 0 0 0 0 0 0 2 47-76 0.343 -0.05387 -0.1443 0 0 0 0 0 0 3 48-77 0.343 -0.05387 -0.1443 0 0 0 0 0 0 4 49-78 0.343 -0.05387 -0.1443 0 0 0 0 0 0 5 50-79 0 0 0 0 -0.03472 0.2841 -0.175 0 0 6 51-80 0 0 0 0 -0.03472 0.2841 -0.175 0 0 7 52-81 0.343 -0.05387 -0.1443 0 0 0 0 0 0 8 53-82 0.343 -0.05387 -0.1443 0 0 0 0 0 0 9 54-83 0.343 -0.05387 -0.1443 0 0 0 0 0 0 10 55-84 0.343 -0.05387 -0.1443 0 0 0 0 0 0 11 56-85 0.343 -0.05387 -0.1443 0 0 0 0 0 0 12 57-86 0 0.634 -0.1422 -0.3217 0 0 0 0 0 13 58-87 0 0 0 -0.3397 0.05204 0.1923 0 0 0 14 59-88 0.343 -0.05387 -0.1443 0 0 0 0 0 0 15 60-89 0 0.6134 -0.1422 -0.3217 0 0 0 0 0 16 61-90 0 0 -0.0553 -0.0100 0.09545 0 0 0 0 17 62-91 0.343 -0.05387 -0.1443 0 0 0 0 0 0 18 63-92 0.343 -0.05387 -0.1443 0 0 0 0 0 0 19 64-93 0.343 -0.05387 -0.1443 0 0 0 0 0 0 20 65-94 0 0 -0.0553 -0.0100 0.09545 0 0 0 0 21 66-95 0.343 -0.05387 -0.1443 0 0 0 0 0 0 22 67-96 0 0 0 -0.3397 0.05204 0.1923 0 0 0 23 68-97 0.343 -0.05387 -0.1443 0 0 0 0 0 0 24 69-98 0 0 -0.0553 -0.0100 0.09545 0 0 0 0 25 70-99 0.343 -0.05387 -0.1443 0 0 0 0 0 0 26 71-00 0.343 -0.05387 -0.1443 0 0 0 0 0 0 27 72-01 0 0.6134 -0.1422 -0.3217 0 0 0 0 0 28 73-02 0.343 -0.05387 -0.1443 0 0 0 0 0 0 29 74-03 0.343 -0.05387 -0.1443 0 0 0 0 0 0 30 75-04 0.343 -0.05387 -0.1443 0 0 0 0 0 0 31 76-05 0.343 -0.05387 -0.1443 0 0 0 0 0 0 32 77-06 0.343 -0.05387 -0.1443 0 0 0 0 0 0 33 78-07 0 0 0 0 0 0 0 0 -20.12

Therefore, after the elimination of the time shift operator q-i the following

model of EPS system was obtained:


246

).()3(02655.0)2(3019.0)1(02198.0)3(2337.0)2(1287.0)1(02857.0)3(009608.0)2(009961.0)1(01546.0

)3(04736.0)2(06231.0)1(131.0)3(1541.0)2(2976.0)1(08841.0)3(02883.0)2(1073.0)1(03015.0)3(02639.0

)3()2(007408.0)1(002718.0)3(6104.0)2(2766.0)1(05234.0)3(006739.0)2(02755.0)1(01335.0)3(06803.0

)2(05293.0)1(1554.0)3(17.14)2(715.9)1(5.14)3(52.29)2(3683.0)1(191.5)3(3264.0)2(7748.0

)1(1965.0)3(1443.0)2(05387.0)1(1342.0)1(1342.0)(

14141413

1313121212

1111111010

109998

8877

76665

55444

33322

21111

euuuuuuuuu

uuuuuuuuuu

uuuuuuuuu

uuuuuuuuuu

uuuuyy

Therefore, the sought value of the obtainable power produced by the power stations (in total) [MW] e.g. in the year θ=2010 is influenced by the following quantities: the value of the obtainable power for the previous year (θ-1, i.e. 2009) and all fourteen input variables for the previous three years (θ-1, i.e. 2009, θ-2, i.e. 2008, θ-3, i.e. 2007).

Models for input variables and for individual output variables were obtained e.g. for the output representing employment in power stations (in total). In one of the experiments (the total number of experiments exceeds ten) 33 models of electrical power system development were obtained (characteristics A(q) and characteristics B(q)). The example of EPS characteristic obtained with the accuracy of 99.14% compared with the real data (optimum model) for the period of 1969-1988 is arx133 characteristic.

3. Genetic code as self-evolving model

Coding the Electrical Power System development is connected with obtaining

the model of development in the form of artificial genetic code (development code). In case of coefficient-based development code for the polish electrical power system the following artificial code of development is obtained, i.e.:

)4(],1,m395.0,mmm395.0;1[)a,V(K 22211122ws

which, in case of structural changes, is connected with the fact that a new gene appears in the artificial genetic code of the development, thus obtaining:

)5(],a,1,m395.0,mmm395.0;1[)a,V(K 322211122ws

The quantity a3 that occurrs in (5) may be determined analytically or experimentally, which was described, i.a. in papers [27-32].

For the models IEEE RST (results from Table 1 and Table 2 can be found in paper [26-27]) the following artificial genetic codes may be obtained, e.g. for A(q) – for the coefficient at the term q -1 according to the following dependence (6):


247

,7413.01342.01342.01342.01342.01342.0

1533.01342.01342.04884.01342.001066.0

)6(1342.04884.01342.01342.01342.04884.01533.0

1342.001066.01533.01342.01342.01342.01342.0

1342.009354.009354.01342.01342.01342.01342.0:chchanges

XXXIII1

XXXII1

XXXI1

XXX1

XIX1

XXVIII1

XXVII1

XXVI1

XXV1

XXIV1

XXIIII1

XXII1

XXI1

XX1

XIX1

XVII1

XVI1

XV1

XIV1

XIII1

XII1

XI1

X1

IX1

VIII1

VII1

VI1

V1

IV1

III1

II1

I11

and: ch1 – genetic code connected with parametric changes of the first coefficient (i=1) at the term A(q) at the time shift operator q-1, when the notation is coefficient-based - changes in the value of coefficient take place in individual periods of long time θ and can be noticed at transitions from one period to another [3,6,22], q-i – delay operator.

Structural changes may also be observed according to the dependence (5), e.g. for the artificial genetic code built using the coefficients in the polynomial A(q) and B1(q), i.e.:

)]1443.0,05387.0,343.0(),1342.0[( 3211IIII

)]1443.0,05387.0,343.0(),1342.0[( 3211IIIIIIII

)]1443.0,05387.0,343.0(),1342.0[( 3211IIIIIIIIIIII

)]1443.0,05387.0,343.0(),1342.0[( 3211IVIVIVIV

)]175.0,2841.0,03472.0,0,0,0,0(),09354.0[( 76543211VVVVVVVV

)]175.0,2841.0,03472.0,0,0,0,0(),09354.0[( 76543211VIVIIVIVIVIVIVIVI

)]1443.0,05387.0,343.0(),1342.0[( 3211VIIVIIVIIVII

)]1443.0,05387.0,343.0(),1342.0[( 3211VIIIVIIIVIIIVIII

)]1443.0,05387.0,343.0(),1342.0[( 3211IXIXIXIX

)7()]1443.0,05387.0,343.0(),1342.0[( X3

X2

X1

X1

)]1443.0,05387.0,343.0(),1342.0[( 3211XIXIXIXI


248

)]3217.0,1422.0,634.0,0(),1533.0[( 43211XIIXIIXIIXIIXII

)]1923.0,5204.0,3397.0,0,0,0(),01066.0[( 6543211XIIIXIIIXIIIXIIIXIIIXIIIXIII

)]1443.0,05387.0,343.0(),1342.0[( 3211XIVXIVXIVXIV

)]3217.0,1422.0,6134.0,0(),1533.0[( 43211XVXVXVXVXV

)]09545.0,01004.0,05535.0,0,0(),4884.0[( 543211XVIXVIXVIXVIXVIXVI

)]1443.0,05387.0,343.0(),1342.0[( 3211XVIIXVIIXVIIXVII

)]1443.0,05387.0,343.0(),1342.0[( 3211XVIIIXVIIIXVIIIXVIII

)]1443.0,05387.0,343.0(),1342.0[( 3211XIXXIXXIXXIX

)]09545.0,01004.0,05535.0,0,0(),4884.0[( 543211XXXXXXXXXXXX

)]1443.0,05387.0,343.0(),1342.0[( 3211XXIXXIXXIXXI

)]1923.0,05204.0,3397.0,0,0,0(),01066.0[( 6543211XXIIXXIIXXIIXIIIXXIIXXIIXXII

)]1443.0,05387.0,343.0(),1342.0[( 3211XXIIIXXIIIXXIIIXXIII

)]09545.0,01004.0,05535.0,0,0(),4884.0[( 543211XXIVXXIVXXIVXXIVXXIVXXIV

)]1443.0,05387.0,343.0(),1342.0[( 3211XXVXXVXXVXXV

)]1443.0,05387.0,343.0(),1342.0[( 3211XXVIXXVIXXVIXXVI

)]3217.0,1422.0,634.0,0(),1533.0[( 43211XXVIIXXVIIXXVIIXXVIIXXVII

)]1443.0,05387.0,343.0(),1342.0[( 3211XXVIIXXVIIXXVIIXXVII


249

)]1443.0,05387.0,343.0(),1342.0[( 3211XXIXXXIXXXIXXXIX

)]1443.0,05387.0,343.0(),1342.0[( 3211XXXXXXXXXXXX

)]1443.0,05387.0,343.0(),1342.0[( 3211XXXIXXXIXXXIXXXI

)]1443.0,05387.0,343.0(),1342.0[( 3211XXXIIXXXIIXXXIIXXXII

)].12.20,0,0,0

,0,0,0,0,0(),7413.0[(

7876

543211XXXIIIXXXIIIXXXIIIXXXIII

XXXIIIIXXXIIIIXXXIIIXXXIIIIXXXIIIIXXXIII

and in case of structural changes, the issue is the appearance or disappearance of si gene in the artificial coefficient-based genetic code, which may be, in particular, artificial genetic code of a subsystem, system, converter, element, e.g. in case of transition from the period IV to V, XII to XIII and XIII to XIV, or from the period XXXII to XXXIII. Artificial genetic codes obtained in this way, may be further used to generate the initial population for the System Evolutional Algorithm (SAE) that can be used to search for a stronger (more robust) population, i.e. for the conditions of the discussed problem of more robust electrical power system.

As a result of using SAE algorithm, a polynomial A(q) as well as polynomials Bi(q) may be obtained, as well as elements of matrices present in the equations in the state space [22,30].

Using the following arx development model defined using the polynomial A(q) and B2(q) [9] the following is obtained:

)()()3264.07748.01965.0()()1342.01( 3211 euqqqyq (8) which, after the elimination of time shift operator q-1 and appropriate transformations, allows us to obtain the following form expressing operational efficiency in time θ:

)()3(3264.0

)()2(7748.0

)()1(1965.0

)()1(1342.0

)()(

uu

uu

uu

uy

uy

D

(9)

with the first term expressing the operational efficiency of the results for the period θ-1 calculated into the outlay of the period θ; similarly the second term concerns analogous results for the period θ-2, and the third term – for period θ-3.

Due to the fact that the values of streams of power that may be generated in power stations y1(θ) and the power installed in power stations u2(θ) in individual periods are known, it is possible to determine the value of operational efficiency, which, for the discussed example, equals -0.56. Operational efficiency for the year 2007 is negative, and equals 56%. Therefore, in 2007, 1 MW of installed power translated into the need to decrease the obtainable power by 56%. The results that


250

were obtained confirm the usefulness of the method leading to searching for metamodels of electrical power system development.

4. Defining the problem of EPS development

The research on the regularities of the polish electrical power system (EPS) may

be brought down to examining structural changes and parametric changes in long time θ [22]. In order to achieve it, the problem of EPS development may be linked with the movement of roots on the complex variable plane s and use the method of Evans’ root lines [7, 22, 24-37].

Parametric changes are connected with movement of roots along the existing root lines, and structural changes are connected with the appearance of new lines or disappearance of the existing ones. In case of the examined EPS system e.g. for the output y1 concerning total achievable power, it turned out that the appearance of new values of coefficients (or roots) was characteristic of parametric changes while structural changes were connected with the appearance of a higher order polynomial or the reduction of the order of the polynomial, e.g. the appearance of new coefficients of polynomials or new roots. It is very imported when we want to obtain model of system EPS as unmanned manufactory [3, 16, 19, 24-30].

Due to the fact that the technique of programming the development not only looks for the model of development but also for the rules of development in long time θ, an attempt was made to generalize the phenomenon of structural changes and parametric changes in the development of EPS system characterizing individual 30-year long periods of development in the years 1946-2007, with the step equal 1 year. The results of the research were published in papers [25-37]. Appropriate th models, obtained as a result of identification, their counterparts in the form of state and output equations, or in the form of a transmittance matrix as well as characteristics of changes of the matrix elements, were presented in the papers. Then, the problem of the EPS system development was linked to the movement of roots on the complex variable plane s [39].

A number of characteristics of Evans' root lines was obtained. Selected results generated for the output y1, representing the total power achievable in power plants, were presented in Table 1. In the studied case, the model of development was e.g. a model of state variables described by the state equation and the output equation, with the parametric changes being connected with the changes in the values of the elements of matrices A, B, C, D present in state and output equations. Due to the fact that the elements of matrix A are responsible for the internal organization of the EPS system, the elements of matrix B are responsible for the connections between the EPS system and the external surroundings by means of inputs, the elements of matrix C are responsible for the connections between the EPS system with the external surroundings by means of outputs, it was convenient


251

to observe parametric and structural changes by observing the changes occurring in each state matrix [2, 6, 9-15, 22].

In case of structural changes both the quantities and their number change as well as the ranks of matrices A, B, C and D, which results from including in the model new state variables, new inputs or outputs of the system (or resignation from the existing ones) as a result e.g. technological, organizational, etc. changes. Therefore, the structural changes of the EPS system result both from the change in the number of elements and the change of the relations between the elements.

On the other hand, the analysis of the EPS system resulting from the changes of the elements of matrices A, B, C and D in the state variable equations indicates that the EPS system as a developing system is characterized by the changeable structure, depends on long time θ and is susceptible (sensitive) to changes of the parameters of development.

It turned out that parametric changes do not disturb the state of safe development of the EPS system and the development of the electric power system. However, structural changes introduce the unsafe state of development both with respect to the model as well as the electric power system, the occurrence of which may result in sudden change in quantity characteristics and the values of state variable quantities as well as inputs and outputs [2, 5, 6, 11, 16, 22-24].

Examining the stability of linear continuous or impulse-based systems may be brought down to studying the positions of the roots of characteristic equation by means of appropriate criteria of stability. It showed that some of the models, both arx models and the corresponding models in state space ss, obtained as a result of identification process, were unstable (some roots of characteristic equation were not located in the left semi-plane of the complex variable). Therefore, it is important to analyze the changes to avoid unstable development of the EPS system.

Due to the fact that in some models of development that were obtained, some real parts of the eigenvalues (characteristic values) the were positive, these models needed to be improved by introducing parametric and structural alterations. Stability of closed systems is examined most often. Therefore, the paper assesses the stability of the polish electrical power system as a closed system, with the denominator's roots being the poles and the numerator's roots being zeros.

Then, the problem of the EPS system development was linked to the movement of roots on the complex variable plane s using the Evans' root lines method, and making the amplification coefficient k changeable. Movement of roots along the existing root lines was observed as the system's parameters changed (k - as a cumulated amplification parameter) and the appearance or gradual disappearance of root lines in case of structural changes (disintegration or integration of the existing zeros and poles of the transmittance) [6, 16, 22, 25, 38, 40].

We may say, after Robert Staniszewski [22], that one-dimensional linear model of development of an electric power system is stable only when the values of parameters and the relations between them (structure) do not belong to the critical


252

state of values of elements and relations, which is directly connected with the concept of development safety. In other words, a system of development i.e. an electric power system as a one-dimensional, linear system is unstable when critical states may occur in the system that are defined by the physical nature of the processes undergoing in the electrical power system. The interpretation of this instability may be conducted by means of the analysis of the nature of the electric power system development [2, 7, 13, 21-24].

The causes of the unstable development may be the physical nature of the EPS system development itself (some physical processes in the system of development may have a tendency to unstable development, e.g. imposed emission restrictions), construction errors in the systems and elements of the EPS system as a technical system, technological errors, especially resulting from the cooperation of new technologies concerning renewable energy with the existing EPS system [19, 33].

Therefore, in order to eliminate the occurrence of unstable state of development of the polish electric power system, the causes of unstable development have to be identified [25, 35-37, 24]. It makes it possible to design the development of the EPS in such a way so as to eliminate potential states of unstable development in the future. Thus, when unstable systems of development and unstable models of development occur, the efficient method to eliminate them is to design the system in such a way that no unstable states occur. This additionally proves the usefulness of this paper as it is necessary to study the systems and their models prior to the introduction of the development solutions.

Also, it must be emphasized that parametric changes only in some cases allow for a change in the distribution of zeros and poles on the complex variable plane s so as they are all located in the left semi-plane of the complex variable. However, the efficient method involves controlled structural changes, which, by means of the introduction of new zeros and/or poles, result in a different distribution of the existing zeros and poles, thus resulting in a new distribution of Evans' root lines [39].

Thus, the elimination of the instability of the system of the polish electric power system is connected with the necessity to introduce parametric changes, and if this proves ineffective, with the need to introduce structural changes or even perform a system transformation, where it is especially important to eliminate the costs of the unstable work of the polish electric power system and similarly unstable development of the polish electric power system.

In the discussed experiment, the cause of the instability of the development were structural changes connected, i.a. with the technological changes, e.g. the introduction of new powers to the EPS system, the introduction of new power lines, as well as economic changes such as denomination of the Polish currency. It must be added that in the discussed case, we deal with the instability of the development of the EPS system and the instability of the model of development of the EPS system. Positive feedback (not negative one) is responsible for the


253

development. Therefore, a temporary instability of the development should only be treated as a warning for the designers of the development.

5. Analysis of the EPS system development

Analysis of the EPS development may be conducted from different points of

view. Due to extremely fast process of automation of the polish electric power system, EPS, it is significant to conduct the analysis of development from the point of view of the growth of the internal organization of the EPS system and in order to develop a higher level of control, including the control of development. Evans' root lines method proved very useful in this respect [39].

A model of a subsystem was used as an example, which has an input u1 - employment in power plants in total, and an output y1- total power achievable in power plants. It turned out that in the studied period three models were present, i.e. the following model occurring in the periods of development 1946-1975 and 1950-1979:

)10(,5109.0s)s(C1 which, as a result of structural changes and parametric changes transformed into the following model in the years 1955-1984:

)11(,s8934.1s)s(C 22

and, which, during the periods 1961-1990 and 1966-1995, 1971-2000, 1976-2005 changed back into the model described by the dependence (10), and then in the years 1978-2007 it assumed the following form, i.e.:

)12(.s2399.1s)s(C 452

Therefore, assuming that higher level of development is characterized by a higher level of complexity of the internal organization of the EPS system, we may talk about periods of faster and slower development of the EPS system, in the discussed case, especially from the point of view of the total achievable power (y1) and changes concerning employment (u1) [25-37]. Hence, in the discussed case, there is the following characteristic polynomial in the highest order:

)13(,asasasasasa)s(C 012

23

34

45

52 in which respective coefficients in individual periods of development assumed values equal zero. If we further write it down in the radical form, taking into account the possibility of making structural and parametric changes in the development, we obtain the following:

)14(),5109.0sm()s(M 11 which indicates that the only changes which might have taken place were connected with the coefficient m1, responsible for parametric changes in the period.

Taking into account the fact that, the growth (expansion) of the system is connected with the appearance of another root, the following form may be obtained:


254

)15(),ksm()5109.0sm()s(M 2211 and, after the transformation, the following is obtained:

)16(.k5109.0s)kmm5109.0(smm)s(M 22122

211 Comparing coefficients from (11) and (16), we obtain the following:

.0k5109.0)17(,8934.1kmm5109.0

,1mm

2

212

21

Thus, parametric and structural development was connected with the following parametric changes (k2=0):

.8934.15109.0

m1m

)18(5109.08934.1m

,0k

21

2

2

As a result of next structural changes, we obtain a polynomial which has the same form as the one before first changes took place, which means that the development is negative. The transition from (11) to (10) took place. Thus, the polynomial (10) might take the following form:

)19(),8934.1sm()ksm()s(M 2112 and, after the transformations, the following is obtained:

)20(,k8934.1s)kmm8934.1(smm)s(M 11212

212 As a result of appropriate comparisons of coefficients in equation (10) and in equation (11) we obtain:

.5109.08934.1

k1mor

8934.11m

)21(,8934.15109.0k

,0mor0m

121

1

12

Finally, as a result of next structural changes, the polynomial (14) was obtained, which was connected with other structural and parametric adjustments, i.e.:

)22()ksm()ksm()ksm()ksm()5109.0sm()s(M

5534

332213

which indicates that structural development took place (4 new roots appeared) and that parametric changes accompanying structural changes also took place. The results of development may also be analysed by studying the changes in positions of both the roots as well as Evans' root lines on the complex variable plane s (Table 3).


255

Table 3. An illustration of the relationship between the development and the course of Evans' root lines for the outpuy y1(K,θ) - total achievable power

(taking into account 14 inputs)

No. years Model Characteristic Evans' root lines 1946-1975 arx111 (83.7845%)

u1 y11

EPS development in the 50s was a result of growing demand for electric power, mainly caused by power-consuming heavy industry, which, in turn, resulted in increasing the installed power to 6316 MW in 1960. The length of power lines with the voltage 220V was 1660 kilometres, and the system network with voltage 110 V was 9140 km long. The first international connection with the voltage 220 kV was finished in 1960 and in 1964 the first line with the voltage 400kV was completed, It was 317 km long. At the same time, a system generating power was expanded by two new units: 120 MW and 200 MW. This changes is reflected by the appearance of a new Evans' root line, along which parametric changes take place in this period of time.

5109.01566.0

1

sCE

1950-1979 arx111 83.7845%

u5 y15

In the period of 1975-1979, there were no structural changes, and the existing lines did not undergo any changes as well. In this period, parametric changes along one Evans' root line took place. In the 1970s, EPS system developed very fast, which was connected with the expansion of transmission power network 400kV, system network 100kV, introduction of transformer-based connections 400 kV/220 kV, 400 kV/110 kV, 220 kV/110 kV, the installation of 200 MW units, the introduction of 500 MW units and completion of the pumped storage power plant, which was a continuation of so far adopted direction of development.

5109.01566.0

5

sCE

1955-1984 arx112 98.4917%

u10 y110

The economic crisis in the years 1979-1985 resulted in the decreased consumption of electric power. As a consequence, the decision not to expand the transmission network 220 kV was made. Instead it was decided to expand the transmission network 400 kV and build the line 750 kV (year 1985). A pumped storage power plant was built (1982), power plants in Połaniec, Bełchatów and Opole. Structural changes appeared, which is reflected in the appearance of new Evans' root lines.

)8934.1(1958.0

1

ssCE


256

1961-1990 arx111 83.9845%

u15 y115

In the years1984-1990 structural changes took place, the indication of which are the disappearance of Evans' root lines as well as the changes in the course of the only remaining line, along which parametric changes occur in this period of time. In the 80s, first indications of economic decline could be noticed. It was also the time when first PCs were produced, and decentralization of computing took place1. A new generation of remote control engineering together with optic fibre network with the throughput of 2.4 Gb/s were introduced.

5109.01566.0

1

sCE

1966-1995 arx111 83.7845%

u20 y120

In the years 1990-1995, parametric changes occur along one Evans' root line. Energy Law act comes into force, the market of electric power is created, the Electrical power Stock Exchange (GEE), distribution companies, turnover companies (PO), technical operators (OT), technical-trade operators (OT-H)2 , etc. are created. However, these changes do not result in the restructuring of employment and do not change the relation in terms of the degree of automation of the EPS system. According to the forecasts concerning the energy consumption in Poland, polish consumption is going to increase 80-93% by 20253.

5109.01566.0

20

sCE

1971-2000 arx111 83.7845%

u25 y125

In the years 1995-2000 further parametric changes occur along one Evans' root line, and there are still problems as regards privatization of electrical power engineering industry, which makes effective investment policy more difficult, as regards the development of EPS system.

5109.01566.0

25

sCE

1 In 1990, CDC 3170 system (used for making analyses off-line) was stopped being used, and CDC 1700 and 1774 systems were replaced by the DYSTER system (it started to be used in 1996). 2 According to the Energy Law, the target model of the electric power market is based on access of third parties to electric power networks (TPA). Moreover, the Polish model of the market allows to make bilateral deals, transactions on the stock exchange and the balance market, managed by the Transmission System Operator (OSP). PSE S.A. acts as the Transmission System Operator. This solution conforms to the European Union directive 96/92/EC.

3Announcement by the Minister of Economy and Labour of 1 July 2005 concerning polish energy policy by 2025 ( M.P. of 22 July 2005).


257

1976-2005 arx111 83.7845%

u30 y130

In the period of 2000-2005 there were no structural changes, which is indicated by the fact that the number of Evans' root lines did not change and the there were no changes in the course of the only existing Evans' root line. In this period, parametric changes occur along one Evans' root line.

5109.0s1566.0C 30E

1978-2007

arx115 97.5939%)

u33 y133

In the years 2005-2007, further structural changes occurred, which is indicated by the appearance of four new root lines and the changes in the course of the existing line. In this period parametric changes occur along five Evans' root lines.

Moreover, cogeneration technologies used so far, often have low index of association i.e. proportion of electrical power production to heat production. The cause of insufficient development of cogeneration technologies are economic (financial), legal, administrative and social barriers. Taking into account the level of development of technologies currently used in the field of electrical power engineering, technical barriers are of little importance.

)2399.1(0043.0

433

ss

CE

6. Summary and directions of further research

The paper presents selected results of research concerning the development of

the polish electric power system. The paper is one of a series of papers devoted to finding a model of the EPS system. Thus, the results of identification, obtained in previous papers, were used in this paper. They were in the form of appropriate models of development, which were then used to link the problem of development to the movement of roots on the complex variable semiplane s [25, 35-37].

Visualization of the development was obtained, and the analysis of development was conducted using as the example the output representing total achievable power. The research is continued as regards thorough analysis concerning internal organization of the EPS system as well as its higher level of development. It was noticed that it is also possible to conduct analytical research using characteristic polynomials obtained for each period of development. The change in the number of roots and their values indicated structural changes and parametric changes.


258

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Białystok 1989. [19] Paska J.: Niezawodność systemów elektroenergetycznych. OW PW, Warszawa 2005. [20] Rebizant W.: Metody inteligentne w automatyce zabezpieczeniowej. Monografie Nr

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260

Combined monitoring and time-frequency analysis for transients

in wind energy systems

Taduesz Łobos, Tomasz Sikorski Wroclaw University of Technology

50-370 Wrocław, Wybrzeże Wyspianskiego 27, e-mail: [email protected], [email protected].

Hortensia Amarís, Monica Alonso, Diana Florez

Carlos III University of Madrid e-mail: [email protected], [email protected], [email protected].

The aim of this paper is the application of selected time-varying power quality indices combined with detailed time-frequency analysis for assessment of transients in wind energy system. Presented proposition utilizes short-term harmonic distortion in voltage (STHDV) characteristic as an indicator for detail local time-frequency analysis of the transients. Introduced ideas can be treated as hybrid system absorbing both power quality indices and time-frequency representation.

1. Introduction Interaction between power system elements exhibits itself in many different

phenomena which requires different methods for assessment. In case of fault the most important is time response. Power quality monitoring introduce averaged parameters and statistical classification. Problem of harmonics is open area for different spectrum estimation methods. One of the phenomena which may consider a composition of different assessment method is the transient state in companion with harmonics. The idea presented in this paper proposes mixing the algorithms. Fast algorithm is dedicated to detection of the event and serves as a trigger for the time-consuming methods which can be performed for further precise investigation. As an example we present results of application of time-frequency analysis triggered by short-time harmonic distortion of voltage (STHDV) index in case of investigation of power quality disturbances caused by sequential compensation with capacitor banks in small wind power plant (SWP) using traditional induction generator.

In points of energy production SWP use usually asynchronous generators, squirrel cage or wound rotor, working in a fixed speed regimen. For greater power the

T. Łobos, T. Sikorski, H. Amaris, M. Alonso, D. Florez / Combined monitoring …

261

synchronous or double-fed asynchronous machines are dedicated. Asynchronous unit is characterized by reactive power consumption in process of active power generation. Thus in point of control system it requires soft-starter, shut-off automation control in case of supply decay from network side as well as fitting the electrical equipment by reactive power compensation, usually realized by regulated set of capacitor banks. Voltage generation level is usually low voltage. Integration of SWP using asynchronous generators with power system is realized by direct connection at low-voltage level or, much more often, via MV/LV transformer from low to medium voltage 0.

Small wind turbines became a part of wide family of distributed generation (DG). General discussion around integration of dispersed energy sources with power system has been developed for last decades including affection of power quality. It seems to be still opened issue especially in companion with increasing number of DG installations and introduced new technologies. Last works of Ackerman 0,0, Dugan et al 0,0,0,0, Baggini 0 or Bollen 0,0 underline crucial need of investigations and determine few selected issues concentrated on sustained interruptions, voltage regulation, harmonics, voltage events, operating conflicts as utility fault-clearing requirements, reclosing, interference with relaying, and finally islanding.

Additional motivation for this work is also permanent development in definition of new power quality indices dedicated to transient disturbances. First suggestion was introduced by Heydt et al. in 0,0 depicting application of windowed FFT algorithm (short-time Fourier transform) for definition of short-term harmonic distortion index (STHD). Further works reintroduced time-frequency analysis and provided unified or novel definitions of transient version of power quality indices. In works 0, 0 we can find unified definition of normalized instantaneous distortion energy ratio (NIDE) - which is a transient version of distortion index DIN, or instantaneous K-factor (IK). Works 0, 0, 0 represent wide overview of different signal processing methods dedicated to assessment of power quality disturbances. Application of parametric spectrum estimation methods and wavelet transform for disturbance detection in fixed speed wind farms was presented in 0. Selected non-parametric and parametric time-frequency representations were discussed in work 0, 0 with special consideration of to distributed generation in 0, 0.

It is worth emphasizing that represented in the paper aspects of composition of different assessment method follows by newest concepts in power systems related to remote measurement, smart grids and virtual power plant. All mentioned efforts are grouped around common trend associated with energy safety and smart grids. Following by this direction we can observe increasing requirements for range of information dedicated to remote measurement which goes beyond standard electricity meter.


262

Developed systems are intended to realize aggregation of complex data including power flows, state of substation connector and breakers, as well as monitoring of power quality indices of the particular customer and crucial network nodes. The newest concept dedicated directly to distributed generation is so called virtual power plant, understood as complex union of distributed resources coupled with control system, energy consumption forecast and energy market 0. Integration of these technologies may leads to the “smart” cluster which would react in global and local sense in case of regulation, intervention and reserves of power. Thus gives desirable flexible properties of the power production which can react on energy market fluctuation or critical event as blackout, islanding and system recovery.

The intention of this paper is to look at the problem of analysis of transient states from the angle of monitoring mode in full consciousness of time-consuming requirements characteristic for time-frequency analysis. In other word, we propose to track selected power quality index in time, characterized by light computation, and activate local time-frequency analysis only if the index exceed given threshold. Obtained characteristic of instantaneous values of the index can be treated as indicating criterion for performing full two-dimensional analysis.

2. Investigated case

The measurements were done in a wind power plant with 500kW induction

generator, connected to the grid by 11 kV/400 V Dyn11 transformer. Compensation of reactive power is realized by two step capacitor banks. Digital sampling rate is 6250 Hz that gives 125 samples per one-cycle of fundamental component. Fig. 1 presents an example of recorded phenomena in wind turbine system under transient condition caused by switching on two-step capacitor banks.

3. Specification of the prposed method

Proposed method is a composition of monitoring mode and high quality analysis of

the detected disturbances. First level of the algorithm is concentrated on continuous monitoring of voltages and current in 3-phase system. The aim of this level is detection of the disturbances and must be characterized by light computation. Presented application is dedicated to assessment of transients in companion with harmonics, thus our proposition is to calculate short-term total harmonic distortion index of voltage (STHDV), for every one-cycle of the signal. In presented example the sampling rate equals 6250 Hz. One cycle estimation of local THD means rough estimation on the


263

basis of 125 samples which gives 50Hz frequency resolution. For calculation is taken H=62 harmonics according to Nyquist frequency. Overlapping is not used, so every next value of STHDV is calculated using next one-cycle window. Local value of THDV, associated with particular position in time, is expressed by:

2

2

1

*100%

H

hh

h

VTHDV

V

(1)

Fig. 1. Fragment of voltages and currents in the LV system with small wind turbine under process

of reactive power compensation using two-steps capacitor banks Here must be mentioned that standard IEC Electromagnetic Compatibility Part 4,

Section 7 and Section 30 recommends calculation of harmonics and THD using 10-cycle series. Investigated records are based on sampling rate equals 6250 Hz that leads to 125


264

samples per cycle and 1250 samples per 10-cycle. According to the standards 10-cycle series would allow to obtain 5 Hz frequency resolution. However proposed method applies local THD calculation only for trigger mode and 10-cycle series would not fulfill the requirements for fast detection of the distortion. In other words in the presented idea we do not scope the attention on exact values of STHDV but use it only as indicator of transients. One-cycle series with poor frequency resolution of 50Hz is recommended and leads to possible fast detection time. Decision about storing selected fragment and its further time-frequency calculation is made when STHDV exceed threshold, here specified to 2%. The length of segments taken for investigation can be specified using constant value of pre and post recorded number of samples or can depend on time-constant of the transient. Monitoring of the STHDV is done parallel in three phase of voltage however for further investigation every three channels of voltage and every three channels of current are recorded parallel.

Triggered transient phenomena is then analyzed using selected method of time-frequency analysis. Family of time-frequency transformation contains many of representatives. Selected aspect of its application in electrical engineering has been investigated in 0, 0, 0 and indicated methods with special construction of the kernel which are dense functions like Gaussian or cone-shaped kernel. It is also recommended to apply additional smoothing window along the frequency axis h(τ) and among time axis g(t). It leads to so called smoothing pseudo time-frequency planes. Below equation represents smoothed version of Wigner-Ville transformation:

SPWVD ,

d d2 2

x

jA A

t h g t

x x e

(2)

Logical diagram of proposed method depicts Fig. 2, including also an example of one-phase voltage and current and calculated

trend of STHDV which serves as indicator of the transient for further detail analysis using time-frequency representations. The methodology of the method assumes that excitation of the STHDV threshold in any three-phase voltage system can trigger parallel multichannel recording of every voltage and current signals. Recording interval can be defined with specification of pre and post recording time. These multichannel records are dedicated for further multichannel time-frequency analysis. As STHDV is rough and fast characteristic, which leads to detection of the transient with harmonics, as time-frequency analysis represents high-quality analysis depending on parameterization of the applied transformation.


265

2

2

1

*100%

H

hh

h

VTHD

V

Fig. 2. Visualization of the proposed method of the investigation as combination of monitoring mode based on STHDV trend and high quality analysis uses time-frequency analysis

4. Results of the investigations

Application of monitoring mode using STHDV trend has indicated two transients

referred to activities of two-step capacitor banks. In order to evaluate contribution of frequency components in the transient state we propose to present time-frequency planes scaled in percentage of fundamental component before the event, obtained from pre-event recording interval. As an example we present multichannel time-frequency analysis of voltage and current of selected transient segments T1 and T2 on the basis of smoothed version of Wigner-Ville representation. It applies additional smoothing windows: h(τ) is multiplied with signal and brings smoothing effect along frequency axis, other one, g(t), is convoluted with obtained representation and exhibits itself in smoothing effect along. Presented calculation utilizes one-cycle Hamming windows. Frequency resolution for the time-frequency analysis is 5Hz. Results of the investigation for subsequence T1 and T2 are presented in Fig. 3 and Fig. 4.


266

Fig. 3. Details of the detected transient T1 and its multichannel time-frequency analysis using smoothed

version of Wigner-Ville distribution


267

Details of transient T2 and its multichannel time-frequency planes using smoothed version of Wigner-Ville representation

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2.04 2.06 2.08 2.1 2.12time (s)

2.142.04 2.06 2.08 2.1 2.12time (s)

2.142.04 2.06 2.08 2.1 2.12time (s)

2.14

2.14 2.14 2.14

2.142.142.14

%ub 50Hzpre-event

%uc 50Hzpre-event

%ia 50Hzpre-event

%ib 50Hzpre-event

%ic 50Hzpre-event

Fig. 4. Details of the detected transient T2 and its multichannel time-frequency analysis using smoothed

version of Wigner-Ville distribution


268

Obtained time-frequency planes indicate higher harmonics which appears during switching-on the capacitor banks. Prominent influence is visible in current. Details of subsequence T1 shows decaying components with maximum contribution of 590Hz in phase A (126.92% of pre-event current in phase A), 610Hz in phase B (51.53% of pre-event current in phase B) and 575Hz in phase C (88.25% of pre-event current in phase C). Second step of capacitor banks T2 has introduced time invariant spectrum components with maximum contributions of 510Hz in phase A (112.22% of pre-event current in phase A), 520Hz in phase B (92.63% of re-event current in phase B) and 515Hz in phase C (112.19% of pre-event current in phase C). Investigated operation of switching on two-step capacitor banks exhibits itself in voltages as fast transient event with slight contribution and fast decaying time.

5. Conclusions

Presented in the paper idea of combined monitoring mode with triggered time-

frequency analysis makes some efforts to propose solution for limitation of direct continuous analysis of long data. Heaviness associated with computational power and time consuming is reduced to fast selection of segments and relatively fast calculation of the selected transients. As a main method of the analysis two dimensional time-frequency algorithms are proposed, working in a triggering mode, activated by parameters of short-time harmonics distortion index. Cooperation of the algorithms serves as complex assessment of the event and makes some efforts to meet increasing expectation of monitoring systems. Possible application can be localized in dispersed measurements dedicated to assessment of disturbances distribution in power system.

References

[1] Ackerman T., Wind power in power systems, John Wiley & Sons, 2005. [2] Ackerman T., Embedded wind generation in weak grids economic optimisation and

power quality simulation, Renewable Energy, vol.18, pp. 205-221, 1999. [3] Dugan R. C. et al, “Electrical Power Systems Quality”, McGraw-Hill, 2004. [4] Dugan R.C. Mcdermontt E et al, “Distributed Generation”, IEEE Industry Application

Magazine, 2002. [5] Dugan R.C. Mcdermontt E et al, “PQ, Reliability and DG”, IEEE Industry Application

Magazine, 2003. [6] Dugan R.C.,Walling R.A. et al, “Summary of Distributed Resources Impact on Power

Delivery Systems”, IEEE Transactions on power delivery, vol.23, no 3, 2008. [7] Baggini A., “Handbook of Power Quality”, John Wiley & Sons, 2008.


269

[8] Bollen M., Gu I., “Signal processing of power quality disturbances”, John Wiley & Sons, IEEE, 2006.

[9] Bollen M., Renders B. et all, “Distributed Generation for Mitigating Voltage Dips in Low-Voltage Distribution Grids”, IEEE Transaction on Power Delivery vol. 23, no 3. 2008.

[10] Heydt G.T., Fjeld P.S.,Liu C.C., Pierce D., Tu L., Hensley G., Applications of the Windowed FFT to Electric Power Quality, IEEE Trans. Power Delivery, vol. 14, no. 4, pp. 1411-1416, 1999.

[11] Jaramillo S.H., Heydt G.T., O’Neill-Carrillo E., Power Quality Indices for Aperiodic Voltages and Currents, IEEE Trans. Power Delivery, vol. 15, no. 5, pp. 784-790, 2000.

[12] Shin Y.J., Power E.J., Grady M., Araposthasis A., Power quality indices for transient disturbances, IEEE Trans. Power Delivery, vol. 21, no. 1, pp. 253-261, 2006.

[13] Shin Y.J., Power E.J., Grady M., Araposthasis A., Signal Processing-Based Direction Finder for Transient Capacitor Switching Disturbances, IEEE Trans. Power Delivery, vol. 23, no. 4, p. 2555-2562, 2008.

[14] Yu-Hua Gu I., Bollen M.H.J: Time-Frequency and Time-Scale Domain Analysis of Voltage Disturbances, EEE Trans. Power Delivery, vol. 15, no. 4, p. 1279-1284, 2000.

[15] Yu-Hua Gu I., Bollen M.H.J: Estimating Interharmonics by Using Sliding-Window ESPRIT, EEE Trans. Power Delivery, vol. 23, no. 1, p. 13-23, 2008.

[16] Łobos T., Rezmer J, Janik P., Amaris H., Alvarez C., Florez D: Application of wavelets and Prony method for disturbance detection in fixed speed wind farms, Electrical Power and Energy Systems, vol. 31, pp. 429-436, 2009.

[17] Sikorski T., Ruczewski P., Lobos T., Time-Frequency Representation for Non-Stationary Phenomena in Electrical Engineering, Przeglad Elektrotechniczny, no. 2, 2005.

[18] Leonowicz Z., Lobos T., Sikorski T., Time-frequency Analysis of Complex Space Phasor in Power Electronics, IEEE Transactions on Instrumentation and Measurement, vol. 43, no. 4, pp. 971-980, 2007.

[19] Sikorski T., Ziaja E., “Advanced signal representation methods for analysis of transient states in embedded generation systems”, Systems – Journal of Transdisciplinary Systems Science, vol. 13, 2008.

[20] Sikorski T., Ziaja E., Herlender K., Bobrowicz W., Power quality disturbances in power system with distributed generation, 9th International Conference on Environment and Electrical Engineering, s. 553-556, 2010.

[21] Pudjianto D, Ramsay C, Strbac G., “Microgrids and virtual power plants: concepts to support the integration of distributed energy resources”, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Volume 222, Number 7 / 2008.


270

Calculator for Electricity Supply’s Unreliability Estimation

(OZZEE)

Andrzej Purczyński Higher Vocational State School in Kalisz

62-800 Kalisz, ul. Nowy Świat 4, e-mail: [email protected]

Ryszard Frąckowiak Poznań University of Technology

60-965 Poznań, ul. Piotrowo 3a, e-mail: [email protected]

In the paper, the OZZEE software developed by the authors to compute the unreliability indicators of the electrical energy delivery to the customers and to support the reliability analysis of electric power systems is described. Basing on a given reliability structure and on the integrated elements parameters, the program can found the mean annual downtime, mean annual failure rate as well as the power supply unreliability coefficient. In analysis of the complex structures, the computation model based on the mean failure cuts (MFC) method has been applied. The assumptions applied when constructing the algorithm of computations as well as examples of the program applications in analysis of the complex grid systems have been presented.

1. Introduction

Reliability characteristics of electric power systems describe the technical and economical properties of the energy generation, transmission, distribution and receiving systems. Regarding technical aspects, the characteristics have a high impact on the adequate designing of the structure as well as on the choice of its elements. Regarding technical aspect, they are used to estimate the consumers’ losses resulting from the electrical energy supply interruptions as well as the costs incurred by the energy supplier including the investments improving the energy supply’s reliability and the compensations to the consumers. On the generic plot in Fig. 1, the total cost (curve 3) is a sum of the consumer’s losses (curve 1) and supplier’s assets (curve 2). As we can see, the costs are always resulting from the compromise reached by both the supplier and the consumer.

There are plenty of reliability coefficients that can be used to assess the system’s technical conditions and to estimate costs [1]. Program of the electrical energy delivery unreliability (OZZEE) refers not but to three parameters: − unreliability coefficient denoted as q, − annual average failure rate ,d, in 1/a units, − annual average supply interruption duration , t, resulting from the failure [in

hours].

A. Purczyński, R. Frąckowiak / Calculator for Electricity Supply’s…

271

Fig. 1. Costs versus reliability -generic plot

These coefficients are mutually related by a relationship (1):

8760tdq

(1)

From the consumer’s point of view, the supply recovery time after failure is the key time and is different from the restoration time referred also in the literature as the failure duration time. The restoration time includes the period from the failure –caused loss of the power supply until the repair’s completion and recovery of the supply capability. The time of the energy interruption is counted from the moment the failure occurs until the supply is restored. Regarding the operation of the automatic protections and control devices, the supply interruption duration can be shorter than the restoration time.

The unreliability coefficient ,q, and the reliability coefficient, p, are strictly related to each other (p = 1 – q); therefore, they can be used alternatively.

Electric power system includes the electric power grid with the devices for electrical energy generation or consuming connected to each other. The system’s structure is determined by the system of connections between the system’s elements such as lines, transformers, connectors, bus sections etcs. In such a case, we use the integrated elements which can include some individual objects that form a functional entity.

The system’s structure should be meant as different from the configuration that reflects the actual state of the connectors’ switch-off and switch-over.

The reliability structure defines not only the way the systems elements are related to each other but also how the system’s failures depends on its elements’ failures. Thus, the reliability structure of the system depends not only on the system’s structure but also on the system’s tasks, and can differs strongly from the system’s structure.

The reliability structure is the base of the calculation of the system’s unreliability parameters.


272

In general, the reliability structure of the simple systems of energy transmission and distribution is a serial or serial parallel one [2]. In such cases, the calculations are relatively simple. However, the true systems are often more complex; there are some power supply sources as well as paths to the intake point under consideration. Therefore, the computer-aided calculation methods are applied.

2. Minimal Failure Cuts Method

The electric power system reliability computation methods can be splitted into

three groups: − analytical methods, − simulation methods, − combined methods.

Among analytical methods using divers mathematical tools, there are methods based on finding the minimum worthiness paths and minimum disability cuts [3]. In practice, the electrical power supply systems are of high reliability, i.e. the probability of the failure to them is low. In such cases, the more suitable method of the system’s unreliability estimation is the Minimal Failure Cuts method.

A minimal failure cut (or minimal unreliability cut), C, is defined as a set of elements of the system’s reliability structure for which: − the system is damaged if all lumped elements of this cut are damaged, − there is no subset of the C cut’s elements with property as mentioned above.

Each system of the coherent reliability structure has a finite number of MFC. Then, the probability of the system failure F(τ) in time τ is (2):

)()1()()( 11

1 ss

jijii

s

iCCPCCPCPF

(2)

where: Ci – ith MFC; s – total number of MFC; P(Ci) – probability of failure of the ith cut; P(CiCj) – probability of failure of the system consisted of two cuts and the cuts can have some common elements, and any element can be considered once only.

The set of all MFC determines explicitly the reliability structure of the system. Such a statement is very significant for convenient computations as, in general, not all lumped elements of the system occur in the MFC; therefore, it is sufficient to determine the reliability parameters for these elements only which enter into MFC.

Each system is disabled if and only if all elements of at least one MFC are damaged. It implies that the lumped elements of each MFC are forming the parallel structure whilst all MFC are connected in series.

Referring to relationship (2), it is possible to estimate the system’s failure probability at arbitrary preset accuracy, for instance (3):

i

iji

jii

i CPFCCPCP )()()()( (3)

An example of calculations using the relationship (3) for a bridge structure is presented in materials 0.


273

Often, a proper estimation of unreliability can be achieved by considering the one-, two- or no more than three-element cuts. The error resulting from the omission of the more-than-three-element cuts is of no importance for practical results of reliability analysis [2].

For a two-parameter estimation of the serial reliability structure consisting of n single-element cuts, m two-element cuts and l three-element cuts MFC, the d and t indices are found from relationship (4):

l

k

IIIk

m

j

IIj

n

i

Ii dddd

111

l

k

IIIk

m

j

IIj

n

i

Ii

l

k

IIIk

IIIk

IIj

m

j

IIj

Ii

n

i

Ii

ddd

tdtdtdt

111

111 (4)

Average interruption rate per year (średnia częstość przerw w roku) for a two-element MFC cut and an average interruption duration in the year are described by relationships (5):

8760)( 2121 ttddd II

21

21

ttttt II

(5)

The parameters corresponding to the three-element MFC cut are given by formulas (6):

2323121321

8760)( ttttttdddd III

323121

321

tttttttttt III

(6)

where: i, j, k – variables described on the single-element (I), two-element (II) and three-element (III) MFC cuts, respectively, and indices 1, 2, 3 define the integrated elements composing the actual cut.

Also, the system elements’ unreliability estimation depends significantly on the input data of the elements’ reliability parameters. Correctness of the data is grave for obtaining the authoritative results from computations.

Reliability indices of the system elements are the results of multiannual observations and tests of the electric power system elements. In Table 1, selected data concerning the electric power system elements is specified.

System unreliability analysis with MFC method is based on simplifying assumptions: − state of each of the system’s integrated elements is described by the stationary

random process, − random processes describing the elements’ states are independent processes, − during the interruption of operation, the system elements are not damaged and

are not subject to restoration. Relationships (4) i (5) have been derived on the assumption that the interruption

duration time distributions are exponential.


274

Table 1. Reliability indices of the electric power devices acc. to [2, 4, 5, 6]

Item Element Unit

j

Average annual failure rate , d

j100a

1

Average interruption duration, t

[ h ]

Unreliability coefficient

510q

1. GPZ 110/15 kV pcs 33,12 0,07 0,2647 2. 110 kV overhead line km 1,5 (3,6) 6 (2,4) 1 (0,98) 3. 110/15 kV transformer pcs 6 (8) 12 (6) 8,2 (5,5) 4. 110 kV circuit breaker pcs 3 (2,1) 6 (3) 2 (0,72) 5. 110 kV isolating switch pcs 0,8 (0,6) 4 (6) 0,4 (0,41) 6. 110 kV current transformer pcs 0,4 10 0,46 7. 110 kV voltage transformer pcs 0,3 (0,7) 10 (4) 0,34 (0,32)

8. 110 kV busbar (outdoor substation) bay 4 (2,6) 4 (2,5) 1,8 (0,74)

9. GIS circuit breaker pcs 0,26 72 2,28 10. GIS isolating switch pcs 0,06 72 0,5 11. GIS current transformer pcs 0,006 72 0,05 12. GIS voltage transformer pcs 0,08 72 0,66 13. GIS busbar bay 0,04 72 0,33 14. 30 kV overhead line km 6,5 13,2 9,8 15. 15 kV cable line km 22 12 30 16. 15 kVoverhead line km 2,5 13,7 4 17. 6 kV cable line km 24,4 (32) 59 (60) 164 (219) 18. MV-LV transformer pcs 4,8 29,2 16 19. MV circuit breaker pcs 13,2 (2,1) 5,5 (6) 8,3 (1,44) 20. MV isolating switch pcs 0,55 8,7 0,55 21. MV current transformer pcs 0,8 5 0,46 22. MV busbar bay 0,32 9,8 0,36 23. 0,4 kV overhead line km 15 4 6,8 24. 0,4 kV cable line km 6 12 8,2 25. 0,4 kV circuit breaker pcs 1,5 3 0,5 26. 0,4 kV isolating switch pcs 0,8 3 0,3 27. 0,4 kV open air substation pcs 1 3 0,34

For protections, two failure states are distinguished [2]:

− lack of required action resulting in the action of the higher level protections followed by the interruption of power supply to great number of consumers,

− unnecessary action resulting from an incorrect operation of the protection. Missing required action rate, db, per year is described by the missing actions

coefficient, kb , found as the quotient of the missing actions number in the year, Nb, and the number of all necessary actions in the year, N. Theses relationships are shown in formulas (7):


275

NNk b

b

1

1

n

xxbb dkd (7)

where: x – a variable described on the number of the outgoing feeders n, dx – average failure rate of the xth outgoing feeder.

Incorrect actions are described by the unecessary actions rate dn (8):

ZNd n

n (8)

where: Nn – number of unnecessary actions in the year, Z – number of all protections of one type installed.

Fig. 2 shows how the unreliability of protections in the substation’s reliability structure is considered.

Fig. 2. Protections in the substation’s reliability structure

In electric power systems, two basic types of integrated elements are

distinguished: − node including busbars with the selector switch disconnectors and current

transformers, − branch (arc) including the interrupting apparatus, lines, transformers etc.

Unreliability elements of protections are the components of both the node and the (Fig. 2). Along with other elements, they form a serial structure.

3. Basic functions of calculator

With OZZEE calculator, three parameters listed in section 1 can be estimated referring to the reliability structure scheme as well as to the data of its integrated elements. Computations can be carried out for simple structures (serial, parallel, bridge) as well as for more complex electric power distribution systems.

In Fig. 3, the initial screen of the application is shown. The first step of the work is either the selection of option in the field Struktura pod/systemu ( Subsystem structure) or read in of the prepared data file from menu Zestaw, option Otwórz... (Open...).


276

Fig. 3. Initial screen of OZZEE calculator Shortly, the basic properties of the application are:

− need for Windows 98/XP/Vista/7 operational system, − size 5 MB including description file, − very simple installation and removing of the application, − program can be started on external memories (pendrive etc.), − up to 100 integrated elements can be introduced in the complex structure, − simple structures ( serial or parallel) can hold up to 9 elements, − for bridge-type structure, parameters for 5 elements are to be defined, − simple rules of the structure’s construction based on the selection from the set

of the ready graphical blocks, − structural scheme area is 26 x 16 blocks (624 x 384 px), − built-in suggestions which simplify the choice of reliability parameters, − preliminary verification of the reliability structure is carried out automatically, − the reports with computation results can be saved as ASCII (txt) file and can be

easily transferred to many other applications, − the option of saving the structure scheme in bmp form is provided, − application is equipped with detailed description including examples of the

calculator applications to diverse electric power system configurations. In Fig. 4, a scheme of the data and results transfer in the OZZEE program is

presented. Parameters are denoted as d, t, q as described in section 1. Parameter s denotes the number of units. In the program, the results and data can be entered to the data set; thus, the preliminary calculations can be carried out, especially if the integrated elements consist of some elements of the simple structure.


277

Fig. 4. Data and results transfer scheme in OZZEE application

4. OZZEE calculator – examples of applications

In his book [2], Jerzy Sozański presents the MFC method and calculation

example concerning the complex electric power system. This example is solved using the OZZEE and shown in Fig. 5.

Fig. 5. Example according to [2]


278

In the case presented in [2], the single- and two-element cuts have been taken into account. By the OZZEE calculator, the three-element cuts (here: 30) for the analysed110 KV network system have been additionally considered. However, in fact, the final result does not differ from that reported by Sozański (d = 0,326 1/a; t=6,14 h). Thus, the correctness of the statement that the failure cuts with number of elements exceeding three affects insignificantly the accuracy of the found parameters of the power supply reliability has been proved.

In the complex substation systems with double bar system, sectionalized and with the bus ties, the application of graphical blocks considering the sharing of the integrated elements as well as the connectionless crossing of the lines is required to find the reliability structure. Examples of electric schemes accompanied by corresponding reliability structures compounded from the OZZEE calculator’s graphical blocks are shown in Fig. 6 a,b.

Power sources are denoted A1, A5 and A2, A7. The intake points are denoted H5 and J4, respectively. Integrated elements F1, F5, C4, H2 and H6 incorporate the entire bus sections with disconnectors connected to them; therefore, it was not shown separately on the electric schemes.

a)

b)

Fig. 6. Two-substation systems and corresponding reliability structures plotted by OZZEE program


279

In Fig. 6b, the dotted raster for the reliability structure has been saved. The raster can be removed by selecting a proper option from the application menu; however, it simplifies the layout of elements in the plotting area.

The calculator enters automatically the symbols of integrated elements on the structure’s drawing, and indicators corresponding to them can be either entered from the keyboard or selected from the list attached to the program. The case of elements denoted by symbols E3 and A4 is shown in Fig. 7. Using the keys, the recording of parameters can be attached (key “+”) or removed (key “-”) from the list of indicators.

After having entered data and having completed the calculations, one can analyze the results and browsing the report. In Fig.8, a report related to the example of the complex structure presented above is presented.

In the final part of report, all MFC cuts found in the actual structure are displayed. Such display is omitted when the option Minimalne Przekroje Zawodności ( Minimal Failure Cuts) within the menu Raport (Report) is not marked.

Fig. 7. Data selection / entering window

Fig. 8. Report window


280

5. Final remarks

The OZZEE calculator is a small application supporting the calculations of the basic reliability parameters for the transmission and distribution electric power systems. It gives opportunity to estimate the important parameters from the point of view of the reliability of electrical energy supply to consumers.

Parameters’ estimation accuracy depends mostly on the input indices determined for the reliability structure’s components referring to many years of observations of the elements failures and to statistical research.

Basic assumptions in the method are: − independence between the integrated elements failures, − constant intensity of the integrated elements failures, − separation of damages in the failure cuts.

The completed calculations indicate that, in practice, the impact of the multi-element MFC cuts on the reliability parameters estimation significantly decreases.

Due to the Minimal Failure Cuts method applied in the OZZEE calculator, the analysis of relatively complex reliability structures such as substation systems with the multi-circuit busbars as well as with the switchable and bypass busbars can be carried out.

References

[1] Paska J., Niezawodność systemów elektroenergetycznych (Electric power system

reliability), Oficyna Wydawnicza, Politechniki Warszawskiej, Warszawa 2005. [2] Sozański J., Niezawodność i jakość pracy systemu elektroenergetycznego (Electric

power system reliability and operation quality), WNT, Warszawa 1990. [3] Karpiński J., Firkowicz Sz., Zasady profilaktyki obiektów technicznych (Preventive

measures principles for technical objects), PWN Warszawa 1981. [4] Goc W., Mrowiec H., Urban J., Wskazówki obliczania niezawodności przemysłowych

sieci elektroenergetycznych (Indications for reliability calculations in industrial electric power systems), Elektroprojekt, Warszawa 1981.

[5] Marzecki J., Elektroenergetyczne sieci miejskie (Municipal electric power grid), Oficyna Wydawnicza Politechniki Warszawskiej 2006.

[6] Stępień J.C., Parametry niezawodnościowe głównych punktów zasilających 110/15 kV (110/15 kV Bulk power source reliability parameters), Mat. Konf. Aktualne Problemy w Elektroenergetyce, Jurata 2007.

[7] Purczyński A., Frąckowiak R., Zastosowanie metody minimalnych przekrojów do oceny zawodności zasilania (MFC method application to power supply unreliability estimation), Materiały ZKwE’2009, Poznań, s.109-110.


281

Models of individual consumers load versus standard profiles;

MS Excel – aided study

Ryszard Frąckowiak, Tomasz Gałan Poznań University of Technology

60-965 Poznań, ul. Piotrowo 3a, e-mail: [email protected]

In the paper, the results of comparative analysis for electrical energy consumption by the household group individual consumers settled according to the G (LV) tariff and the standard profiles elaborated PTPiREE are reported. In analysis, the special tailored IT tool using the MS Excel has been applied.

1. Introduction

Since the introduction of the TPA rule to the retail market (individual

consumers), the approach to the electrical energy market has significantly changed. The tracking of the yearly cycle of energy consumption by individual consumers became a figure of merit and the standard profile of electrical load has been constructed referring to the observations [1].

A new born (in July, 2007) electrical energy market in Poland at the level of the consumer fed on the LV side shows that the energy consumption measuring data for former years is missing [2]. Thanks to the works on the data acquisition, saving and processing conducted by PTPiREE (Polish Association for Electrical Energy Transmission and Dispatch - Polskie Towarzystwo Przesyłu i Rozdziału Energii Elektrycznej), a catalogue of the electric energy consumers’ characteristics has been developed and the standard profiles ( for consumers with defined features) have been constructed [3].

When constructing the standard profiles, a definition of the proper number/list of the consumer groups, i.e. the proper number of standard profiles for a specific consumer type (for example, the consumers included into the household group settled acc. to the G tariff) is an important task. To accomplish the task, a high number of the load profiles of individual consumers with various features has to be acquired and adequate analyses are to be carried out. The main goal of the research is to indicate the groups of consumers with strongly diverse graphs. For this task, the investigation and determination of the impact of the substantial factors on the load graphs in specific groups as well as on the difference between them are helpful.

In the paper, the chosen results from analysis of the load graphs for individual consumers settled according to the G tariff as well as those for two standard profiles developed by PTPiREE for such consumer type are reported. The research

R. Frąckowiak, T. Gałan / Models of individual consumers load…

282

aims to evaluate the mentioned profiles and to indicate the reasons of the would-be discrepancies between the standard profiles and the load graphs for consumers encountered by the specific profiles.

Regarding the great number of consumers and the wide scope of research, a specific tailored IT tool (Excel spreadsheet) has been developed to accomplish the task as described above [4].

2. Tested consumer’s characteristics

Division and the most important features of the individual consumers groups covered by the study are presented in Table 1 [5, 6].

Table 1. Characteristics of the consumer groups under consideration

Tariff group Consumer localization

Electric heating of rooms

Electric heating of running water Group name

G11 City G11 M1 G11 Rural No G11 W1 G11 City G11 M2 G11 Rural

No Yes G11 W2

G12 No No G12 M1 G12 No Yes G12 M2 G12

City Yes Yes G12 M4

In Table 2, the list of three load profiles for the household-type individual

consumers (settled acc. to G tariff) developed by PTPiREE, aggregated by the type of the used electric power tariff and by the type of heating applied in the household are presented.

Table 2. Standard profile acc. to PTPiREE

Profile name Tariff group Electric heating A Profile G11 No data B Profile G12 No C Profile G12 Yes

Among the presented standard consumers graphs, the A profile is the most

general. The only criterion of the consumer’s assignation to the A profile is Tariff group – G11 (single-zone consumers) which the actual consumer belongs to. The analysis has shown that there is neither splitting according to the consumer’s administrative localization (town, village) nor according to the water and room heating type (electric, non-electric). Other presented profiles (B, C) have been elaborated for two-zone consumers (G12), and the main criterion of the consumer’s assignation to the profile was the water and room heating type (electric, non-


283

electric). In Table 3, extreme and average values of daily power normalized per one consumer within specific profile groups developed referring to data from 2008 are presented.

Table 3. Extreme and average values of daily power for profiled consumers

Pd min

kW/consumer Pd śr

kW/ consumer Pd max

kW/ consumer

MAX 0,490 0,708 0,872

AVG 0,277 0,450 0,585 A Profile

MIN 0,210 0,322 0,396

MAX 0,611 0,770 0,986

AVG 0,378 0,533 0,714 B Profile

MIN 0,265 0,426 0,556

MAX 1,541 1,894 2,486

AVG 0,596 0,890 1,241 C Profile

MIN 0,213 0,452 0,616

The average values explicitly depend on the group type. The higher level of electric equipment in the group, the higher values of the power.

3. Analysis results – selected examples

3.1. A profile consumers

In Fig. 1 the yearly averaged daily load curves for the consumer groups under

consideration as well as their total daily curve (G11 graph) and the daily load curve for the A profile found for working days in 2007 are presented.

On these curves, two specific extreme values appearing between 5 A.M. and 6 A.M.(minimum – morning off-peak period) and 6 P.M. and 10 P.M. ( maximum – evening peak) can be perceived. The daily load variability analysis for successive month of the year have shown that in wintertime the evening peak is more evident than in summertime (the curve reaches higher values). Such a rise is related to intensive use of electricity for lighting purposes.

Further investigation of the consumer groups indicated that the morning off-peak appears nearly at the same hours, both in winter and in summer; however, it takes slightly different values for different groups. The times when the extreme daily loads occur are close to each other (Tdmin – 5A.M. till 6 A.M., Tdmax – 7 P.M. till 10 P.M.).


284

Fig. 1. Daily load variability averaged per year for tested consumer groups

Regarding the A profile construction, the choice of the individual consumers to the group seems to be important. In Fig.1, the total waveform which is the average waveform for the consumers under consideration (Group G11 graph) is shown. In the constructed group, the total waveform is mostly affected by the consumer living in rural area and using the electric water heating ( the average daily consumption is twice higher than that in the total waveform).

In Fig. 2, the PTPiREE yearly average of daily load for the A profile which was compulsory in the period 2007-2009 is presented. The curves has been plotted referring to the measuring data for individual customers from the overall area of Poland. The A profile for 2007 and 2008 have been constructed referring to the data acquired from about 600 consumers of electrical energy whilst the profile 2009 – for 700 recorded waveforms. The analysis has shown that the selection of the consumers for an actual profile is rather a random process and can result in the different shape of the curves. Total curve depends on the percentage of the consumers belonging to specific groups (Table1).

Basing on the authors’ expertise in the graphs analysis, the conclusion can be drawn that in the case of the G11 tariff group’s consumers, the shape of the graph is mostly affected by the sunset time (Tzach). Among the consumer groups under consideration, such influence is the most evident by the consumers using the non-electric sources for heating rooms and water [5].

In Fig. 3, the variability of the monthly average power consumption (Pm śr) versus the monthly averaged sunset hour for the , G11 M1 group and the A profile 2007 are compared.


285

Fig. 2. Yearly average of daily load for A profile worked for 2007-2009

Fig. 3. Variability of the monthly average power consumption versus the monthly

averaged sunset hour (2006)

The graph for consumers belonging to the G11 M1 group (Fig. 3) can be described by the linear function in the form:

śrmzachśrm TP 0,01-4,0 (1)

where )2015( 1642 śrmzachT . Matching coefficient is relatively high (R2 = 0,89).


286

For the A profile, the relation between the monthly averaged power consumption and the sunset hour is much more weak (R2 = 0,62) when comparing to the G11 M1 group.

Detailed investigation of the variability of the power load for A profile(2007 – 2009), have shown the light influence of the air temperature on the value of energy consumed during a daytime. The situation is changing during night time when the profiled consumer can use the completing electrical heating of rooms. The impact of temperature is more explicit when śr attains daily the values below 10ºC (Fig. 4).

a)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

1 31 61 91 121 151 181 211 241 271 301 331 361

Day of year

P dśr

kW/cos

tumer

-30

-20

-10

0

10

20

30

śr

d °C

Power

Temperature

b)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

1 43 85 127 169 211 253 295 337

Day of year

P d ś

r kW/cos

tumer

-10

-5

0

5

10

15

20

25

30

śr

d °C

Power

Temperature

Fig. 4. Annual variability of temperature and average powers for :(a) A profile 2008,

(b) A profile 2009

More detailed analysis of the curves shows that the impact of the sunset time and temperature on the A profile load in different years is different. Such conclusion is confirmed by the study of the correlation coefficient between the


287

hourly power consumptions for 24 hours and the external factors found for years 2007 and 2008 (Fig. 5). There is high correlation between the considered factors (Tzach, śr). The shape of curves for 2008 (Fig. 5a) indicates higher impact of the temperature, whilst in 2009 the explicit impact of the sunset hour can be observed (lighting loads). a)

b)

Fig. 5. Variability of correlation coefficient values :(a) A profile 2008, (b) A profile 2009

Impact of the sunset hour on the consumed power is perceptible in after dinner

and evening hours when the consumers use the electric lighting. In sum, the A profile consumers group includes the consumers of diverse

specific characteristics and with different external conditions which significantly affect the shape and values of the electric power consumption graphs.


288

3.2. Consumers included into C profile

The Consumers assigned to the C profile are those settled according to the G12 tariff using the electric heating of rooms and water, like the G12 M4 consumers. The significant impact of the temperature on the consumed power value should be expected

In Fig.6, a case of the annual variability of average load (Pdśr) and daily average temperature (dśr) found for working days, C profile 2007 (recording 2006) and the two-zone consumers living in town and using electrical heating of rooms and water (G12 M4) is presented (data for 2006). The characteristics of these groups are very close to each other.

Fig. 6. Annual variability of average load and temperature in 2006

Preliminary analysis of graphs in Fig.6 has shown small differences in the

consumed power values in the summertime. Perceptible differences in the waveforms occur in the wintertime when the electric heating is working.

In addition, the study on the impact of temperature () on the consumed electric power univocally shows that the influence of this factor is the most evident during the heating period (from October till March). In other months it is weaker but still significant. Moreover, in the summertime (June- August) in the P.M. zone with higher energy prices, a slight influence of the Tzach on the consumed energy value is observed [6].


289

In Fig.7, the annual variability of the power correlation coefficient in specific hours of the day at the average daily temperature for the G12 M4 type consumers and C profile 2007 are reported.

-1,0

-0,9

-0,8

-0,7

-0,6

-0,5

-0,4

-0,3

-0,2

-0,1

0,0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of day h

Cor

rela

tion

coef

ficie

nt P

dśr

with

Tem

p av

g

G12 M3 C Profile

Fig. 7. Annual variability of average load and temperature in 2008

Tracking of the correlation coefficient (Fig. 7) in tested groups confirms a

strong relation between the consumed power and the temperature. For the G12 M4 group, higher values of the correlation coefficient can result from the consumers character i.e. room and water heating by the electric energy. The directives concerning the selection of consumers for the C profile do not distinguish the consumer using the electrical heating either for room or for water from that heating the both at the same time. Like in the A profile, the straightforward criterions of the consumers’ selection for the profile become primordial.

On the base of the annual variability shown in Fig.6 and respective temperature variability for the heating period, the relationship can be established: − for G12 M4 consumers:

śrdśrdP 0,069-89,1 (3) (R2=0,88)

− for C profile: śrdśrdP 0,032-38,1 (4)

(R2=0,82) where: Cśrd )105,19( . Formulas (3) and (4) are similar for successive years of observations.


290

In Fig. 8, the power consumption average values in month in so called lower price zone of energy (zone II) are compared to the average temperature in month, for the consumer groups under consideration (C Profile 2007 and G12 M4 – 2006).

Fig. 8. Annual variability of average load and temperature in successive months, 2006

There is strong relation between the power consumed in the II zone (lower price

of energy) and temperature. The relation can be expressed by formulas: − for G12 M4:

śrmśrmIIP 8,27-1,21 (5) − for C profile:

śrmśrmIIP 10,6-14,20 (6)

where: Cśrm )65,19( .

3.3. Evaluation of profiles’ significant features

In our research, the impact of defined factors on the values appearing in the load graphs has been analyzed and the extraction of significant features in specific groups and standard profiles has been carried out.

In Table 4, the features of the energy consumers settled according to the G11 tariff and the A profile consumers are listed.

A profile has been constructed for consumers settled according to G11 tariff which are differently equipped with electrical devices and differently localized. Then, the total graph (A profile) depends on the percentage of the specific consumer groups classified for its construction.


291

Table 4. Impact of external factors on the shape and values of the G11 graphs

Group Tzach śr Pdśr [kW/consumer] G11 M1 strong no 0,218 G11 W1 strong no 0,224 G11 M2 weak no 0,568 G11 W2 weak weak 1,175 A profile strong * ?* 0,3940,579

* - depending on the year of observation

In Table 5, features of the consumers encountered to the G12 M4 group and the C profile consumers are specified.

Table 5. Impact of external factors on shape and values of G12 graphs

Group Tzach śr Pdśr [kW/consumer]

G12 M4 weak* strong 1,25 C Profile weak* strong 0,821,24

* - at certain times of the day (16-22)

In groups compared in Table 5, a significant impact of temperature on the daily consumption of energy is observed. However, the strongest relationship power – temperature has been observed in the hours of the lower price of energy.

Opposite to the G12 M4 consumer group, in the description of the C profile consumers the latter using the electric power for the water and rooms heating (generalized profile) are not distinguished.

4. Final remarks

To acquire a thorough knowledge on characteristic parameters and their properties in the electric load graphs for individual consumer groups, a series of analyses is required. Coexistence of some factors affecting the graphs significantly hampers the research. Construction of the specialized IT tools simplifies the investigations and becomes a precious source of information on the factors significantly affecting the electrical consumption curves by the consumers.

The carried out analysis has shown that precisely formulated criterions of selection of individual consumers to the profile group when constructing the standard profiles should be precise; too general criterions introduce a great spread of the energy consumption by specific consumers from the average value for the group. A standard profile should be constructed from the consumers of similar or very close features. However, it should be kept in mind that too detailed criterions of selection of the consumer to the profile can complicate the construction and application of profiles in true practice.


292

References

[1] M. Sołtysik, J. Bogacz, Proceedings of XII Konferencja Naukowo-Techniczna, Using the energy consumption profiles as supporting mechanism for consumers in the balancing market (in Polish), Kazimierz Dolny, 2006.

[2] M. Wrocławski, Wokół Energetyki, Standard profiles of loads or the energy counters’ replacement? A way to open the market ( in Polish, June 2006, pp.47-48.

[3] Energy Management and Conservation Agency S.A., Tracking the loads and construction of the electrical energy consumer characteristics catalogue (in Polish) Warszawa 2000.

[4] Frąckowiak R., Gałan T., Computer aid for analysis of the load variability at the LV system - fed consumers, Academic Journals PUT, Electrical Engineering, 59 (Poznan 2009), 111-122.

[5] Frąckowiak R., Gałan T., Impact of chosen factors describing the consumer and external features on load curves of G11 tariff consumer groups (in Polish), published in Proceedings of XII Międzynarodowej Konferencji Naukowej – Current Problems in electric Power Engineering, Jurata 2007.

[6] R. Frąckowiak, T. Gałan, Electrical load curves for household-type consumers settled according to G12 tariff. (in Polish), Przegląd Elektrotechniczny, June 2009.


293

Wind power stations

Tomasz Wawrzyniak

Poznan University of Technology 60 - 965 Poznan, Piotrowo St 3A, e-mail: [email protected]

The article describes the subject of renewable energy produced in Poland against the background of European Union. Special attention was devoted to utilization of the energy of the wind, representing a range of the types of wind turbines used in the construction of wind power stations. While presenting individual types both defects and the advantages of solutions were listed with the reference to the production of electric energy.

1. Introduction

The EU directive orders the limitation of emission of carbon dioxide by 20% and the increase of the production of renewable energy by 20% in the countries of European Union by 2020. For Poland this means 15% of renewable sources in the production of energy. Considering the preparations of Poland, it is easy to notice that the largest growth falls on use of the energy of the wind and the co-burning of biomass (Fig. 1) [1].

Fig. 1. The production of renewable energy in Poland [1]

T. Wawrzyniak / Wind power stations

294

In 2008, the total share of renewable energy was 4,27% [2], 0,51% of which [1] was from wind power stations. The comparison of power of installed wind power stations in Poland relative to the member countries of UE in 2007 is presented by Fig. 2. It is worth adding that in 2009 the power installed was 666 MW worth, while in 2010 it amounted to 1005 MW [1]. This corresponds to the aims imposed on Poland in the endeavor of realizing guidelines contained in the EU directive.

Fig. 2. The power installed of wind power stations in 2007 in UE on the basis of the data from EWEA [5]

2. The typed of wind power stations

Due to their construction, one can distinguish two types of wind power stations: those working in the horizontal axis, where the plane described through propellers is perpendicular to the direction of the strength of the influence of the wind, and those working in the perpendicular axis, working propellers of which create the cylinder, and the strength of the influence of the wind is directed to its side surface.

The wind power stations of the horizontal axis, appearing most frequently are three blade propellers (Fig. 3), making up the compromise between the large rotatory speed one and two blade propeller (Fig. 4), and the large rotatory moment low-speed multi blade propeller. They are characterized by the largest efficiency of processing the energy of the wind into electric energy.

The common features of the wind power stations of the horizontal axis: − the necessity of placing them against the wind, realized through turning of the

head, mostly by using the electric engines, − the large durability of the tower which has to hold out the mass of wind turbine,

transmission gear, and generator, and transfer the resistance force of all wind power station during the work near with the strong wind,


295

− the spades of the propeller with changing profile in relation to length with keeping the great precision of the realization and balancing of the whole propeller [4].

Fig. 3. Three blade propeller wind power stations of the horizontal axis installed on the bank of the backwater Jeziorsko, province łódzkie

Fig. 4. Wind power stations one and two blade propeller [9, 10]

Another way of usage of the wind turbine of the horizontal axis are the wind power stations with Magnus rotors, where the whirling cylinder was applied instead of the propeller. This solution allows to obtain considerably larger rotary moments of the propeller connected with considerably larger aerodynamic strength appearing on whirling rotors in comparison to traditional propellers. Unfortunately, electric engines were used to drive rolls, which, as a result, complicates constructions considerably and reduces the total efficiency of wind power station.


296

An example of such a wind power station together with the patern of the formation of aerodynamic strength, was presented below (Fig. 5).

Fig. 5. Wind power station of horizontal axis with Magnus rotors, Acowind And-63 [6]

There are also types of wind power stations which are made with the rotors of Magnus which use other smaller wind turbines to drive rotors. These solutions did not bring positive effects, because the resistances of the rotation of the whole propeller grew. The Japanese firm Mecaro solved this problem, by applying a borer surface for the rotor together with with system of suitable transmissions on the main shaft of the wind power station (Fig. 6).

Fig. 6. Wind power station with Magnus rotors of the firm Mecaro [7]

Rotors begin to turn over simultaneously, producing buoyancy and the rotatory movement of the whole propeller as a result of the pressure of the wind. It is worth adding that the especially designed borer surface also causes enlargement of the circuit rotors which is directly connected with the larger circumferential speed and larger buoyancy produced.


297

The wind power stations of the perpendicular axis are divide into two groups differing in the way of the influence of the wind on the propeller wind turbine. Savonius rotor (Fig. 8) uses the front pressure of the wind.

Fig. 8. The Savonius wind turbine [11]

The rotary speed, approximately the speed of the wind, and low efficiency was the reason why it was not used in the production of electric energy. However, it is frequently used for the wind speed measurement because of its rotary speed.

Fig. 9. The Darrieus wind turbine [11, 12]


298

Darrieus - rotor (Fig. 9) uses the side pressure of the wind thanks to which the buoyancy coming into being on its propellers allows to achieve larger rotary speeds. Low start-up torque is its characteristic feature as well as the necessity of using of the starter. The development of this type of wind turbine is H-Darrieus (Fig. 10), simplified construction which does not exact crooked spades of the propeller [3].

Fig. 10. The H-Darrieus wind turbine [13]

The general comparison of wind turbines was presented on Fig. 11. The horizontal axis defines the relation of the circumferential speed of the wind turbine, to the speed of wind V. The perpendicular axis defines the coefficient of use of the energy of the wind Cp, being the reference of the real mechanical power on the shafts of the given wind turbine in relation to the theoretical energy of the wind, operating on the same surface itself of the wind turbine of the horizontal axis.

One can conclude from the above mentioned figure, that developmental tendencies are, and will be, directed to the wind power stations of the horizontal axis in the three blade propeller version mainly - going towards the highest efficiency, with large reliability and technologically simple construction.

The incessant search for better solutions, being man’s natural feature, leads to the formation of new conceptions of wind power stations. The example of one unclassified construction, with respect to the axis of the wind power station, is firm Magenn’s conception presented on Fig. 12. Its working is based on using the pressure of the wind, like in the Savinouswind turbine. The turning of the roller, crosswise to the wind causes formation of buoyancy known as Magnus effect. Wind power station rises in the air thanks to this strength stretching the lines which are the point of the support for installed after sides generators simultaneously [8].


299

Fig. 11. The comparison of wind turbines [3]

Fig. 12. The wind power station of the firm Magenn [8]


300

3. Summary Weather and field conditions in Poland (Fig. 14) allow the installation even up

to 23000 MW [1] power from a wind power station. At present, there are installed circa 1005 MW [1] wind power stations and next investments are planned in order to achieve the minimum imposed on Poland by UE. The prognosis of the development of the Polish energetics OZE on the basis of “Politics of Energy for Poland till 2030” [1] was presented on Fig. 13.

The difficulties with the quick development of wind energetics in Poland are connected first of all with the novelty of the subject having just several years. Investors willing to build the wind farm are exposed to heavy temporary financial tests. It takes not only the gathering of the huge quantity of working plan which can last up to two years, but also the annexation to often distant grid (Fig. 14) after building the wind farm.

The lack of concrete information about the windiness of a given area is the next factor discouraging potential investors. In order to plan the investment well, they have to put the special measuring station themselves working for at least a year. Despite huge advantages arising from the installation of the cleanest energy power stations, the ecologists look for negative sides, often using accidental situations e.g. the perishing the birds or damage of the scenery. The question arises, how the landscape will look like in next 2000 years if the production of the electricity and warmth will only be obtained through burning carbon and biomass.

Fig. 13. The plans of the development of the economy of energetics in Poland till 2030 [1]


301

Fig. 14. The map of Poland - windy conditions, the arrangement of industrial nets enabling connecting wind power station [1]

References

[1] PSEW: "Ocena możliwości rozwoju i potencjału energetyki wiatrowej w Polsce do

2020r.", „Energetyka wiatrowa w Polsce” www.psew.pl 29.11.09. [2] Biuletyn Urzędu Regulacji Energetyki nr 6(68) 02.11.09 str. 22. [3] Erich Hau "Wind Turbines Fundamentals, Technologies, Application, Economics"

2nd Edition 2006r. [4] W. Jagodziński „Silniki wiatrowe” 1959r. [5] European Wind Energy Association, Raport: “Wind Energy - The Facts”

www.ewea.org 10.12.09. [6] www.darmowa-energia.eko.org.pl/pliki/wiatr/magnus.html 02.11.09 [7] MECARO www.mecaro.jp 25.08.10. [8] Magenn www.magenn.com [9] Nordic WindPower www.nordicwindpower.com [10] NASA MOD-0, Photo by NASA Glenn Research Center www.en.wikipedia.org [11] “Technology solutions for wind power generated electricity”

www.thegreentechnologyblog.com [12] “Technical introduction on Darrieus wind turbine” www.windturbine-

analysis.netfirms.com [13] “Horizontal Axis Wind Turbine” www.winddose.com

302

AUTHORS INDEX Monica Alonso 260 Hortensia Amaris 260 Edward Anderson 46 Szymon Banaszak 132 Karol Bańczyk 9 Michał Borysiak 38 B. Brusiłowicz 184 Mirosław Dąbrowski 61 Ivo Dolezel 141 Mateusz Dybkowski 120 Bogdan Fabiański 223 Stefan F. Filipowicz 26 Diana Florez 260 Ryszard Frąckowiak 270, 281 Tomasz Gałan 281 Konstanty M. Gawrylczyk 132 Wiktoria Grycan 184, 193 Karol Gugała 212 Jacek Hauser 174 Aleksander Jastriebow 150 Marcin Kamiński 105 Janusz Karolak 46 Łukasz Knypiński 93 Janusz Kołodziej 72 Vaclav Kotlan 141 Marek Kott 184, 193 Czesław T. Kowalski 230 Marcin Kowol 72 Henryk Krawczyk 9 Zuzanna Krawczyk 38 Daniel Kucharski 174 Dariusz Kusiak 53 Bartłomiej Kuśnierz 212 Yvonnick Le Menach 93 Tadeusz Łobos 260 Marian Łukaniszyn 72 Marek Malinowski 161 Jan Marlewski 212 Wojciech Mazurek 161

Przemysław Mazurek 201 Ryszard Niedbała 174 Lech Nowak 93 Teresa Orłowska-

Kowalska 81, 105

Zygmunt Piątek 53 Jerzy Proficz 9 Jan Purczyński 1 Andrzej Purczyński 270 Kazimierz Radziuk 93 Andrzej Rudeński 61 Andrzej Rybarczyk 212 Tomasz Rymarczyk 26 Piotr J. Serkies 120 Jan Sikora 26 Tomasz Sikorski 260 Grzegorz Słoń 150 Jacek Starzyński 38 Krzysztof Szabat 105,

120, 230

Tomasz Szczegielniak 53 Tymoteusz Świeboda 161 Grzegorz Tarchała 81 Jerzy Tchórzewski 242 Bohus Ulrych 141 Tomasz Wawrzyniak 293 Marcin Wesołowski 174 Józef Wiśniewski 46 Bogumiła Wnukowska 184,

193

computer applications in electrical engineering

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