enhancement of dynamic performance of automatic generation … · 2018. 3. 15. · enhancement of...

Enhancement of Dynamic Performance of

Automatic Generation Control of a

Deregulated Hybrid Power System

1Dillip Kumar Mishra,

2Subhranshu Sekhar Pati,

3Tapas Kumar Panigrahi,

4Asit Mohanty and

5Prakash Kumar Ray

1,2,3,5Department of Electrical Engineering , IIIT, Bhubaneswar, India

[email protected]

4Department of Electrical Engineering, CET, Bhubaneswar, India

Abstract In recent days Fractional order control has been widely established as an

effective and alternative control approach. In order to increase the

performance of dynamic systems factional order controllers has been used.

The widely used traditional Proportional Integral and Proportional Integral

Derivative (PID) controllers are commonly implemented in the automatic

generation control (AGC) to enhance the dynamic performance and to

decrease or eliminate steady state error. This study develops Fractional

order (FO) PID controller based AGC system to enhance the system

stability and performance. The study uses the PI/PID/optimized FOPID

having ITAE is the objective function. The paper explores AGC for

interconnected power system with diverse source and demonstrates that

TLBO optimized based FOPID performs better than traditional PI and PID

controllers. Furthermore, robustness analysis is carried out with their

performance index.

Key Words:Automatic generation control (AGC), fractional order, PID

controller, teaching learning based optimisation (TLBO).

International Journal of Pure and Applied MathematicsVolume 118 No. 5 2018, 303-319ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

303

1. Introduction

In recent years, power are consists of several large interconnected multi source

area to meet the load demand. For smoothing operation of power system the

cycles per second should have constant. Hence generation speed should have a

fixed value and also relative power angle in an individual area.in general load

demand and losses must match with power generated. Due to the sudden

variation of load by the user may mismatch the power balance. And it enter into

the system affecting the speed variation of rotor and hence frequency of the

overall system. This mismatch problem is commonly solved by solved by

abstraction of kinetic energy from the system. Hence rotor speed decreases and

also frequency. As the frequency slowly declines, the old load consumption also

decreases. To avoid these deviations automatic generation control (AGC) is

included in the system which regulates the set point speed of multiple

generation sources in each area. Hence it becomes our primary objective of

AGC to control the power from different plant so that the overall frequency kept

within given limits in the power system [1].

Several areas are interrelated via tie lines. These tie lines have mainly two

functions. Firstly for mutually power exchange between different area and

secondly inter area support in case of anomalous operating condition. To

overcome this problem high voltage direct current (HVDC) is adopted for

transmitting power from one area to another. HVDC owns eye-catching

features such as fast controllability of power in HVDC links by the help of

convertor control, facility to reduce transient stability difficulties linked with

AC tie lines and other economic benefits [2].

Electrical power is generated by different types of units such as gas, thermal,

hydro, nuclear power plant. As the efficiency of nuclear power plant is

maximum. Hence it is operated at base load so it does not take part in AGC

control as the output is always be at maximum. Nuclear power plant are suitable

for fluctuating loads so for peak load condition Nuclear power plants are one of

the suitable choices for meeting the varying load demand. For our study of AGC

process, grouping of multiple units in a control area with taking their

participation factor and nonlinear characteristics using time delay (TD) are

genuine investigation [3].

To realize these objectives, an enormous number of studies have been conceded

out for an robust design of AGC controller [4], with the revolutionary works by

Elgerd and Fosha [5].The control methods such as conventional [6] and optimal

control [7] have been proposed for AGC. R K. Cavin et al [8] has

demonstrated fault of AGC in the interrelated power system from the optimal

stochastictics concept.Thus steadying of frequency oscillations becomes

challenging and greatly expected in the view competitive market analysis .As a

result control design should be sophisticated in AGC in order to balancing the

frequency oscillation.

International Journal of Pure and Applied Mathematics Special Issue

304

Now days, engineering and science uses fractional order controller in design

and simulation purpose. With advancement of fractional calculus Podlubny[9]

given a more adaptable structure PIλD

μ by extended in traditional notion of PID

controllers [9] by including two degree of freedom in the controller design.

Hence the traditional controller performance improved. As a result more

accurate system performance can be identified and analyzed.

By discussing the above feature of FOPID controller, a maiden approach has

been taken out to apply the ABC optimisation algorithm to tune the FOPID, PID

and output feedback controller for hybrid source multi area with AC-DC link.

To make the system more actual, nonlinear parameter such as time delay (TD)

is added in the system modelling. It is observe by comparing the result that,

FOPID controller gives better performance with respect to conventional PID

and optimal controller. The effectiveness and healthiness of suggested controller

is also checked by changing the system and load constraints. Finally overall

response is investigated by the use of AGC for same interconnected control area

with AC-DC link.

2. Nomenclature

B1, B2 are the frequency bias parameters in area-I, II resp..

1u & 2u stand for control outputs of the area-I,II resp.

1GP & 2GP stand for change in governor power of area- I,II resp.

1TP & 2TP stand for change in turbine output power in area- I,II resp.

TieP is the tie line power deviation (p.u) in area- I,II resp.

1PST & 2PST stand for power system time constant in area-I,II resp.

1ACE & 2ACE are the area control errors in area- I,II resp.

1R & 2R stand for governor regulation parameter of area- I,II resp.

1VP & 2VP are the change in governor valve positions (pu) area- I,II resp.

1GT , &GH GNT T

stand for governor time constants thermal, gas & nuclear resp.

1TT & ,&W RST T

stand for of turbine time constant thermal, gas & nuclear resp.

1 &r RHT T Stands for of turbine time constant thermal & nuclear resp


305

1PSK & 2PSK are the power system gains in area- I,II resp.

12T is the synchronizing coefficient and

1f & 2f are the frequency deviations in Hz in area- I,II resp;

&DC DCK TStands for HVDC parameters

3. System Modeling

Proposed Power System Model

The system under examination comprises of two interconnected area with AC-

DC link as shown in fig. 1. The area consists of reheat thermal, gas and nuclear

power generation unit. The impact to the nominal loading is decided by own

regulation parameter and participation factor of each control area. Sum of the

entire participation factor in each control area should equal to one. The

proposed investigation model can be represented by its transfer function which

is shown in fig.2 [2]. Each area have size of 2000 MW and nominal loading as

1000 MW. Contribution of loading in each area is 600 MW in thermal, 250 MW

gas and 150 MW in nuclear as power generation. Time delay of 50 ms has been

taken in each controller for each area. Power rating of area -1 and area-2 is

represented by Pr1 and Pr2 in MW respectively. Let it be assuming for area-1 the

constants are represented as Kt1, Kh1 and Kn1 for the portions of power generated

from thermal, gas, and nuclear source.PGt1, PGh1 and PGg1 are power generations

in MW with thermal, gas and nuclear units in area-1.

1 1 1 1 1 1 1 1 1; ;Gt t Gt Gg h G Gn n GnP K P P K P P K P (1)

The power generated under nominal operating conditions, PG1 for area 1 is

given by:

1 1 1 1G Gt Gg GnP P P P (2)

1 1 1 1t g nK K K (3)

The power flowing between area-1 and area-2 is given by:

12max 1 2sin( )TieACP P (4)

For small load variation Eq. (4) can be written as:

12max 1 2( )TieACP T (5)

T12is called as synchronizing coefficient and expressed as:


306

12 12max 1 2cos( )T P (6)

When incremental power flow at rectifier end in DC link is modelled, it can

adjust the incremental change in frequency .

For small load perturbation AC tie-line flow, TieACP is given by

121 2

2( )TieAC

TP F F

s

(7)

The nonconformity of power flow,∆Ptie12 Ptie12=∆PtieAC

For small perturbation the DC tie-line flow, TieDCP can be given as:

1 2( )1

DCTieDC

DC

KP F F

sT

(8)

power ,Ptie12 can be written as:

12Tie TieAC TieDCP P P (9)

Conv-1 Tie - LineAREA-I AREA-II

Conv-II

Figure 1: Multi-Area Power system

For small load variation, eq (9) can be written as:

12Tie TieAC TieDCP P P (10)

The area control errors ACE1 and ACE2 by considering AC-DC tie line are

given by:

1 1 1 TieAC TieDCACE F P P (11)

2 2 2 12 ( )TieAC TieDCACE F P P (12)

Where β1 and β2 are frequency influenced parameter.


307

α12 is called as area size ratio:

12 1 2/ 1r rP P (13)

The transfer function model of thermal, gas and nuclear plant is shown in fig 2.1

(a,b & c)

Ts G11

1

T rs

T rK rs

11

111

Ts t11

1

Figure 2.1.a: Thermal with Reheat Plant Transfer Function

1

1 GNsT

2

1 1 2

1

(1 )(1 )(1 )RH T RH

sA S B

sT sT sT

Figure 2.1.b: Nuclear Power Plant Transfer Function

2

2

X

Y

2

2

2

1

1

X

Y

sT

2

1

b cs

2

2

CR

F

T

T

2

2

2

1

1

CR

F

T

T

sF

2

1

1 CDsT

Figure 2.1.c: Gas Power Plant transfer function

Fractional Order PID Controller(FOPID)

In recent year, FOPID controller is used in system design and PIλD

μ controller is

the generalised form. It have extra features such as design controller gains

(KP,KI,KD) and design commands of integral and derivative. The order of

integral and derivative controller should have any real number. It simplifies the

conventional integral order PID controller and provide more elasticity in PID

control design. The transfer function of the controller is given by

sK

s

KKsG D

IP )(

(17)

If λ and μ value are taken as 1 then it will become classical PID controller.

Above all these classical controllers are special type of PIλDμ controller is

depicted in fig.3


308

PK 1

Proportional

IK -λs

μsDK

Fractional Integral

Fractional Derivative

Figure 3: Block Diagram of FOPID Controller and FOPID

Controller Characteristics

In the design section of controller, the objective function should be predefined

first based upon the selective specification and constraints using teaching

learning optimization technique. Although, it is observed that Integral of Time

multiplied Absolute Error (ITAE) has been chosen as an objective function in

AGC problems. Thus in this study, TLBO technique is employed to optimize

the PID and FOPID parameter with ITAE criterion.

The ITAE objective function can be written as. (18).

simt

1 2 Tie

0

J=ITAE= ΔF + ΔF + ΔP ×t×dt (18)

∆F1and ∆F2 are called as system frequency deviation and Ptie is power

deviation in the tie line and tsim is the duration of simulation.

Teaching Learning Based Optimization (TLBO)

Teaching Learning Based Optimization (TLBO) optimization technique was

first developed by [11] Rao et al (2011, 2012a, b) and Rao & Savsani (2012).

This method is now very popular and most effective technique and employed in


309

many fields of application. This technique has numerous advantage like lesser

time is required for the best solution and give more stable performance with

multiple frequency constraint. TLBO is mainly divided into two phases

First phase (Teacher phase)

Second phase (learner phase)

During the first phase students learn from the teacher and in the second phase

students learn by communicating with other students. The above two phases of

TLBO algorithm can be described as follows:

Initialization

Initially generate the random number of population and number of dimension

variable parameters. i:e Np and D. The mark secured by each number of

students in different subject can be written in matrix form i:e ith column with ith

subject. Here initial population taken as X.

P

11 12 1D

2,1 2,2 D

NP 1 NP 2 NP-D (N ×D)

x x .... x

x x .... x

X= . . .

. . .

x x .... x

First phase (Teacher phase)

In the first phase, the influence of teacher of the students in a class. The

Teacher has to play a major role in this phase and he must have very strong

knowledge in their assigned subject and to teach the students to get the best

score and performance. The best score shows the shine of a best teacher as

compared to another teacher, i:e Xbest

The mean value of result of each student in each subject can be estimated as:

d 1 2 DM = m ,m ,.....,m (3)

The results can be compared with mean value of same subject & results of

assigned teachers is given by

diff best F dM = rand(0,1) X - T M (4)


310

-a12

+

+

-

+

+

-

-

+

a12

DP

K H

KT

+

+

+

+-

+-

-

NK

DP

K H

K T

+

+

+

+

+

+

+

1ACE

2ACE

B1

2B

1

1

R2

1

R3

1

R

1

1

R2

1

R3

1

R

Thermal with Reheat

Plant

Gas Plant

Nuclear Power Plant

Power

System

Power

System

Thermal with Reheat

Plant

Gas Plant

Nuclear Power Plant

Tie-

Line

NK

TL

BO

Op

tim

ized

FO

PID

Co

ntr

oll

er

TL

BO

Op

tim

ized

FO

PID

Co

ntr

oll

er 1u

1u

1u

2u

2u

2u

HVDC

HVDC

Figure 2.2: Proposed model of Two-Area diverse source power system

Where FT can be represented as teaching factor with )1,0(rand has been

considered as random number among 0 &1. Value of TF can be either 1 or 2 &

is chosen randomly from the equation (5)

FT =round[1+rand(0,1)] (5)

The old population is now calculated by equation (6)

new diffX =X+M (6)

New value of population is accepted (New) o if newf X <f X

else X old are

accepted.

Second phase (Learner phase)

In the second phase, the learner can improve their knowledge into two ways.

One can go through more discussion with the teacher and other can

communicate with other learner themselves. A learner takes advantages from

other learner with random selection of learner and interacts with him or her. So

the learner can get a more knowledge. The process of this phase can be

expressed as:

Choose two learners randomly, iX and jXwhere ji .


311

new i i jX =X +rand(0,1)(X -X ), if i jf(X )<f(X )

(7)

Else

new i j iX =X +rand(0,1)(X -X ). Accept newX

if it is best solution

Choice of objective function

The main objective of the AGC is to reduce the Area Control Error (ACE) with

a very short period of time. In order to get low value of ACE, the cost function

can be defined as

t

1 2

0

f= Δw -Δw .tdt (8)

Where, dt is change in time , 1Δwand 2Δw

are the frequency deviation in area-I

and area-II respectively. Present study, a step load disturbance of 1% is changed

in area-I and start simulation with TLBO optimization technique for 50 times to

get the optimal values of gain of the PID controller.

4. Simulation Results and Discussion

The Matlab/Simulink based model is designed here to analyze the system

performance with Teaching Learning based optimization having ITAE is the

objective function. Primarily, a Proportional Integral (PI) controller is employed

for each area and the performances are shown on fig.4.Then the PID controller

is utilized in the same model and responses are shown in fig.4. Meanwhile, in

order to reduce the steady state error, settling time, overshoot, undershoot and

ITAE TLBO optimisation being used to tune the FOPID parameter. This shows

the better performance as compared to other two controllers. The TLBO

algorithm was repeated 100 times and best value is selected from 100 runs to

minimize the objective function.

To study the transient response of the system a step load perturbation (SLP)

10% is applied at time t=0 sec in area-I and the response are shown in fig.4 (a-

c). Then, 10% SLP in area-I and 5% in area-II are applied and shown in fig.4 (d-

f). To show the dynamic response of proposed system, frequency deviation in

area-I, frequency deviation in area-II and tie line power deviation characteristics

are shown in fig.4 (a-f) and also measured the performance indices (settling

time, overshoot % ITAE) are shown in table-II. Robustness analysis is done to

show the vigor of the system with ±25% loading and parameter variation. The

parameters are TSG, TGN, TT, TGH varied from their nominal values. The

measured value (settling time, overshoot, & ITAE) of proposed system is

represents as performance indices. It is clear that, there is negligible effect in the

system with parameter variation and loading. Accordingly, proposed system


312

gives robust control during the change in system parameter and loading.

Table 1: Tuned Controller Parameters

Controller

gains PID FOPID

KP1 -1.448 -1.644

KP2 -1.5369 -0.311

KI1 -0.8430 -0.5035

KI2 -1.170 1.015

KD1 -1.872 -0.3163

KD2 0.692 -0.9662

λ1 --- 0.8031

λ2 --- 0.4051

μ1 --- 0.8451

μ2 --- 0.6294

Table 2: Settling Time, Overshoot and Error

Controller

Settling time (sec) Peak Overshoot

ITAE ∆F1 ∆F2 ∆Ptie ∆F1 ∆F2 ∆Ptie

PI 24.08 21.52 17.17 0.1369 0.1693 0.0128 8.901

PID 20.32 19.04 13.13 0.069 0.0398 0.0006 7.8106

TLBO- FOPID 5.14 4.09 7.05 0.035 0.0286 0.0023 4.562

Figure 4.A

Figure 4.B


313

Figure 4.C

Figure 4.D

Figure 4.E

Figure 4.F


314

Figure 4.G: Settling Time

Figure 4.H: Overshoot

Figure 5.A

Figure 5.B


315

Figure 5.C

Figure 5.D

Fig.4 (a-c) Dynamic responses for 1% step load change in area I

(a) Frequency deviations of area 1 (b) Frequency deviations of area II (c) Tie

line power deviations

Fig.4 (d-f) Dynamic responses for 1% step load change in area I and 0.5% step

load change in area II (a) Frequency deviations of area 1 (b) Frequency

deviations of area 2 (c) Tie line power deviations

Fig.5 (a-d) Robustness analysis figure

Table 3: Robustness Analysis (Settling Time)

Parameters variations

Per

cen

tage

chan

ge

Settling Time in (Sec)

Overshoot ITAE

∆ F1 ∆ F2 ∆ PTie ∆ F1 ∆ F2 ∆ PTie

Nominal 0 4.19 3.82 6.45 0.0454 0.0502 0.0043 4.5771

Loading conditions

+25 4.20 3.87 6.54 0.0589 0.0671 0.0024 4.5957

-25 4.18 3.80 6.47 0.0512 0.0408 0.0053 4.5694

TT -25 4.17 3.75 6.59 0.0662 0.0623 0.0070 4.5899

+25 4.21 3.87 6.41 0.0466 0.0471 0.0072 4.5784

TSG -25 4.24 3.6 6.55 0.0497 0.0612 0.0012 4.5948

+25 4.128 3.79 6.47 0.0432 0.0575 0.0045 4.5784

TRH -25 4.08 4.60 6.63 0.0564 0.0661 0.0036 4.5848

+25 4.54 4.01 5.93 4.19 3.82 6.45 4.5801

TCN -25 4.18 4.59 6.43 4.20 3.87 6.54 4.5921

+25 4.58 4.15 5.89. 4.18 3.80 6.47 4.5730


316

5. Conclusion

The study was conducted on a two area interconnected power system, where

dynamic performance of FOPID, PID and optimal controller have been shown

for parallel AC-DC links. To establish the power system more realistic, the non-

linearity parameter such as time delay is included in the system model. Gains of

the optimal/PID/FOPID controllers have been optimized with TLBO

techniques. To establish the superiority of the FOPID controller, results have

been compared with conventional PID controller. The proposed controllers are

found to be robust and ensures satisfactory system performance in system

operating load conditions.

Appendix: Power System Parameters

Area-1 Area-2

Thermal: Tg=0.08s, Kr1=0.3 ,

Tr1=5s, Tt1=0.3s

Thermal: Tg=0.08s, Kr1=0.3 ,

Tr1=5s, Tt1=0.3s

Gas:X1=0.6s,T1=1s,b1=0.05s,

c1=1s,TCR=0.3s,TF=0.25s,TCD=0.2s

Gas:X1=0.6s,T1=1s,b1=0.05s,

c1=1s,TCR=0.3s,TF=0.25s,TCD=0.2s

Nuclear:TRH1=7s,TRH2=9s,TT1=0.5s,

TGN=0.08s

Nuclear:TRH1=7s,TRH2=9s,TT1=0.5s,

TGN=0.08s

Power system: Kp=120, TP=20s,

HVDC: KDC=1, TDC=0.2s,

Tie Line: T12=0.045.

β=0.425 puMW/Hz, R=2.4Hz/pu

References

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[3] Bevrani, Robust Power System Frequency Control, Springer (2009).

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