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CHAPTER 1

INTRODUCTION

1.1 PREAMBLE

Magnetic characteristics during saturation of synchronous machine

are the main consideration for improving the design and modeling of the

machines. In stability analysis of synchronous machines, magnetic saturation

characteristics are taken into account, as they determine the initial conditions

of the generator such as rotor angle, field current, rotor circuit flux linkages,

etc. Two magnetic characteristics are present in a synchronous machine, one

in direct axis (d-axis) and another in quadrature axis (q-axis). There are either

no direct measurement methods available to simultaneously estimate both the

d-axis and q- axis magnetic characteristics of a synchronous machine by

simple experiments or to model the q-axis magnetic characteristics by

uncomplicated methods. This thesis focuses on the measurement of d- and q-

axis flux and modeling of q-axis flux of projected pole synchronous

machines.

1.2 THE GENESIS OF THE THESIS

The d-axis magnetic characteristics of synchronous machine can be

determined easily from a conventional open-circuit test with machines excited

from their field winding. On the other hand, the q-axis magnetic

characteristics cannot be determined by any conventional method. Some

experimental methods, such as maximum lagging current method, steady-state

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on-load measurements method and back-to-back method for measuring the q-

axis saturation characteristics may give the result and however the degree of

complexity of test procedures, need of special, complex controllable

excitation system and loading limitation of the machine are serious issues.

Consequently, extensive research work is being carried out in order to

measure and model the d-q axes flux characteristics of synchronous machines

by simple, reliable and accurate heterogeneous techniques.

1.3 LITERATURE SURVEY

A survey of existing literature reveals that various methodologies

have been employed to determine and model the d-q axes magnetic

characteristics of synchronous machines. The different methods of

determination being dynamic and complex in nature, the literature survey of

this problem are classified into the following sections:

determination of q-axis saturation characteristics by

analytical and experimental methods

determination of intermediate axis saturation characteristics

development of saturation models

analysis of magnetic coupling between d-q axes

estimation of synchronous machine parameters

Neuro-Fuzzy techniques for control of machines and

analysis of various flux measurement techniques.

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1.3.1 Determination of q-axis saturation characteristics by analytical

and experimental methods

Kar et al (2000) discussed a new method to calculate q-axis

saturation characteristics of cylindrical-rotor synchronous generator from the

existing d-axis saturation characteristics. The saturated values of the d- and q-

axis self magnetizing reactances and mutual cross-magnetizing reactances

between the two orthogonal axes under the steady-state operation have been

calculated by them. The effect of q-axis saturation, on the power system

transient stability has also been presented.

Four different analytical methods for calculating the q-axis

saturation characteristics of the salient pole synchronous machines from the

measured d-axis saturation characteristics were explored by Ahmed El-Serafi

and Kar (2003). The q-axis saturation characteristics have been calculated

from the measured d-axis saturation characteristics and the d- and q-axis

unsaturated magnetizing reactances. A comparison made between the above

four methods reveal that two methods out of the four produce accurate results.

The saturation characteristics in both the direct and quadrature axis

are needed for the accurate prediction of the performance of saturated

synchronous machines. Three possible experimental methods for determining

the q-axis saturation characteristics of both cylindrical-rotor and salient pole

synchronous machines were presented by Kar and Ahmed El-Serafi

(2004 and 2006). The measured q-axis saturation characteristics obtained by

these experimental methods were compared and the various sources of errors

which affect the accuracy of characteristics determination investigated. The

maximum lagging current proposed is limited by human error. This method

requires a complex positive and negative excitation system. The on-load

measurement method can be conducted only upto certain values of load

angles because of the stability limits. The back-to-back test requires a special

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experimental set-up. In all the three methods, the stator resistance and the

variation in the armature leakage reactance due to saturation were neglected

which introduces some error.

1.3.2 Determination of intermediate axis saturation characteristics

An innovated model for the saturated synchronous machines using

the intermediate axis saturation characteristics has been proposed Narayan

Kar and Ahmed El-Serafi (2002). Two sets of parameters represent the

saturation characteristics in the various intermediate axes. The first set gave

the information about the saturation levels in the intermediate axes while the

second set, the corresponding phase angles between the resultant magnetic

flux and the resultant ampere-turns. This approach has been applied to three

laboratory synchronous machines of various designs. The accuracy and the

universality of the new model have been demonstrated.

Ahmed El-Serafi and Kar (2005) presented four analytical methods

for determining the intermediate axis saturation characteristics of salient pole

synchronous machines from the measured d-axis saturation characteristics.

The accuracies of these four methods have been verified by comparing the

measured field currents and load angles of two laboratory salient pole

synchronous machines of different designs with those calculated values. In

this context, the field currents and load angles have been calculated using an

innovated approach which uses the intermediate axis saturation characteristics

directly in the modeling of the saturated synchronous machines.

A synchronous machine model was proposed which applies the intermediate-

axis saturation characteristics directly in machine modeling.

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1.3.3 Development of saturation models

Shackshaft and Henser (1979) have used parameters obtained from

both no-load and on-load measurements to obtain a saturation model, of

adequate simplicity for use in multi machine studies. Both no-load and on-

load methods have been used to obtain the saturation characteristic of the

quadrature axis. The methods have produced good results but on-load method

has been recommended for its advantages over no-load method.

An efficient numerical algorithm for including the effects of

magnetic saturation in a model of a synchronous generator has been proposed

by Brandwajn (1980). It has been reported that one axis saturation model is

not totally adequate in the simulation of magnetic saturation effects.

Harley et al (1980) presented the results of an investigation into the

effect of different saturation models on the transient performance of a

synchronous machine. Various methods of calculating and using saturation

factors in the equations of synchronous machines in order to represent

saturation in both the direct and quadrature axes during three-phase fault

studies have been proposed.

The capability and suitability of a couple of simple saturation

model structures to reproduce steady state operating characteristics of

synchronous machines were explored by De Mello and Hannett (1986). The

results of sensitivity to variations in parameters and model structures have

been presented.

Joseph Ojo and Thomas Lipo (1989) have presented an improved

model for the transient analysis of saturated salient pole synchronous motors.

The modeling approach proposed, combines the advantages of the finite

element method for parameter determination and the simplicity of the

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equivalent circuit approach. The importance of this work is the derivation of

the d-q equations of the synchronous machine in the rotor reference frame

accounting for the instantaneous spatial saturation effects.

Chuanli Shi and Ming Li (1990) have developed a general model

for the analysis of salient pole machine as well as non-salient pole machine

under steady- state conditions. This method provides refinements over the

classical model on the basis of „two-reaction theory‟. It has been concluded

that the resolution of armature mmf is not necessary for the analysis of

synchronous machines under steady-state conditions and the real saturation

condition of machines can be taken into account in measuring magnetization

curves in d- and q- axis.

A new method to express the main flux saturation in synchronous

machines by using auxiliary currents and unsaturated magnetizing

inductances instead of the saturated inductances was presented by Tamura and

Takeda (1994). The new model has only constant coefficients defined in

terms of unsaturated values of the magnetizing inductances and other constant

parameters.

A consistent method for including magnetic saturation in the

general two-axis model of the salient pole synchronous machine was explored

by Tahan and Kamwa (1995). The general model covers both the main path

magnetic saturation and frequency effects in the dynamic equations.

Implementation of the model requires the easily available no-load saturation

curve and the two unsaturated reactances together with the saturated saliency

ratio.

Tsai et al (1995) presented a comprehensive procedure to develop

an artificial neural network (ANN) based saturation model for synchronous

generator stability assessment. A feed-forward network with multi

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dimensional mapping of the synchronous machine saturation and an error

back-propagation learning scheme was used. This developed scheme was

implemented in the generator dynamic transient stability study requiring only

small computational alteration in saturation model representation.

Levi (1997) has presented a general procedure for main flux

saturation modeling in smooth air-gap synchronous machines. The method

relies on the concept of „generalized flux‟ and „generalized inductance‟. A

number of models that result from the application of the method for different

selections of state-space variables were presented. The accuracy of saturation

representation in all the novel models was the same and these models find

application in synchronous machine simulation and control. The concept has

been extended to salient pole synchronous machines by Levi (1999), where

the saturation accounted for by means of single saturation factor approach.

An improved technique for incorporating saturation into the q-d

axis model of a synchronous machine was proposed by Corzine et al (1998).

The model has been verified for steady-state and transient conditions using a

laboratory synchronous machine-rectifier system similar to those commonly

used for Naval and aerospace power generation. The saturation function was

applicable for an infinite range of flux. The model has been shown to be

adequate in predicting the performance of a synchronous machine / rectifier

system.

A general, six winding salient pole saturated machine was

discussed by Levi (1998). It was shown that numerous alternative models,

with different sets of state-space variables may be derived. The major

advantage of numerous novel models was considered to be the simpler

structure of the system matrix, together with relatively small number of

saturation dependent coefficients, while stator d-q axis current components

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were retained as state-space variables. These models found application in

synchronous machine simulation.

Nhut-Quang Dinh and Jos Arrillaga (2001) described a salient-pole

generator harmonic model in sequence components that takes into account the

effects of rotor angle, saliency and saturation. Generator harmonic

impedances at the characteristic harmonics were obtained from the measured

generator terminal harmonic voltages and currents. The values were compared

with those calculated using the derived formulation. This analytical model

was found to be a powerful tool for a fast and accurate prediction of the

harmonic levels on the generator terminals in the presence of saliency and

distortion.

An enhanced saturation model for wound-rotor salient pole

synchronous machines based on experimental evaluation and analysis has

been proposed by Wang (2003). This new model used three nonlinear

lumped-parameter impedances to fully characterize the magnetic saturation

phenomenon in wide frequency and load range. They characterize

respectively, the d-axis saturation, the q-axis saturation and the nonlinear

coupling between the field and the stator windings due to the saturation. This

model considered to be convenient for implementation and tuning in drive

controllers based on the field-oriented algorithm. Improved drive control

accuracy and dynamic performance have been shown by simulation and

experimental results. Adequacy of the modeling approach was confirmed by

Finite element analysis.

A new flux-correction method to represent magnetic saturation in

classical q-d machine model was presented by Liwei Wang et al (2007). This

proposed method is simple and does not require calculation of the derivatives

of the saturated mutual inductances. It seemed to be very fast and accurate as

compared to other more complex models.

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A linearized model of synchronous reluctance generator has been

developed using a new saturation model to perform the steady-state stability

analysis by Souvik Guha and Kar (2008). The effect of the saturation both in

the direct and quadrature axes on the determination of the steady-state and

transient stability performances of synchronous reluctance machine has also

been investigated using the proposed linearized machine model.

The magnetic saturation phenomena were characterized by static

saturation inductances, based on which the saturated salient pole synchronous

motor model was established by Wei Jing and Guojun Tan (2010). The

changing discipline of the inductances in d-q reference frame align with

current was analyzed in detail under the magnetic saturation condition.

Simulation results indicate that main physical variables act in accordance with

the operating principles in nonlinear magnetic saturation situation and the

validity of the model was verified.

A new approach for identification and modeling of the saturated

synchronous reactances of synchronous machines was proposed by Martin

Jadric et al (2010). The saturated synchronous reactances were estimated and

modeled using fitting surfaces from steady-state operating data at a wide

range of operating conditions. Simulation studies have been conducted to

verify the developed steady-state saturation model.

Stiebler and Campeanu (2010) proposed a model which makes use

of an approximation with a single non-linear characteristic. The main field

saturation curve was approximated by a trigonometric function which reflects

the machine‟s no-load saturation curve. The result supported the common

practice to use the conventional Park‟s equations for modeling transient

behavior.

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1.3.4 Analysis of magnetic coupling between d-q axes

Cross-magnetizing effect (magnetic coupling between d- and q-

axis) in the d- and q- axis has been described by simple equations which show

that the change in flux in any axis of the synchronous machine due to the

cross-magnetizing effect is directly proportional to the ampere-turns in this

axis as well as the saturation degree in the other axis. A modified power/load

angle relationship including the effect of the cross-magnetizing has been

derived by El-Serafi et al (1988).

El-Serafi and Abdallah (1991) presented a model of a synchronous

machine which includes the effect of both the machine saturated reactances as

well as the cross-magnetizing phenomenon. This model was used to study the

steady-state stability of a synchronous machine connected to an infinite bus

system. These studies show that the effect of saturation has been noticeably

large and depends mainly upon cross-magnetizing effect.

A model for the d- and q- axis synchronous reactances was

developed by El-Serafi and Abdallah (1992) in which the effects of both the

d- and q- axis saturation factors and the cross-magnetizing phenomenon have

been included. The effect of saturation was found to reduce the values of both

d- and q- axis mutual reactances. The magnitude of this reduction was found

to be appreciable. Moreover, the reduction in the q-axis mutual reactance was

found to be larger than that in the case of the d-axis mutual reactance.

El-Serafi and Wu (1993) introduced the concept of the cross-

magnetizing phenomenon in saturated synchronous machines. Techniques for

determining the parameters, which represent the cross-magnetizing effect,

were proposed. The inclusion of the cross- magnetizing effect in the two-axis

frame model of a saturated synchronous machine depends on the methods of

defining the saturated d- and q- axis fluxes in the model. When the two

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saturation factors concept was applied to define these saturated fluxes, the

cross-magnetizing effect has been shown to exist in both the non-salient and

salient pole machines and demagnetizing in both the d- and q- axis.

Emil Levi and Viktor Levi (2000) discussed the impact of dynamic

cross-saturation on simulation accuracy of various saturated synchronous

machine models. Dynamic cross-saturation appear in all the saturated

machine models, which was the existence of non-zero elements in the system

matrix that describe cross-coupling between d- and q- axes. It has been found

that for one particular class of models, omission of dynamic cross-saturation

has practically no impact on accuracy.

An analytical method for determining the parameters that represent

the effect of the magnetic coupling between the d-axis and q-axis of saturated

cylindrical rotor synchronous machines has been proposed by El-Serafi and

Demeter (2000). Experimental investigations were carried out to verify the

accuracy of the proposed method.

1.3.5 Estimation of synchronous machine parameters

A test procedure for derivation of synchronous machine d-axis and

q-axis parameters has been described by De-Mello and Rebeiro (1977). This

involves simple procedures which can be implemented in the course of

normal operation of the machine as it is synchronized or taken off line.

De Mello and Hannett (1981) presented the results of transient

response tests on synchronous generators along with derivations of generator

model parameters from data. The adequacy of d- and q- axis generator model

structures was investigated through comparisons of model simulations against

tests. Transient response tests include load rejections from zero power factor,

under excited and over excited conditions for identification of d-axis

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characteristics. Rejection test from load conditions was used for identifying q-

axis characteristics. A simple modification of model to account for low

frequency shielding effect, without changing the order of the model has been

proposed.

Junya Matsuki et al (1993) have presented a new approach to

determine the saturated values of synchronous reactances, based on

permeance distributions in the air-gap inside a synchronous generator. Effect

of saturation was reflected in the air-gap flux distributions, hence the

permeance distributions in the air-gap, directly. In order to evaluate the

saturation level in the air-gap, the permeance distributions have been used in

this method. When the on-load permeance distributions are determined,

saturation effect can be estimated by them and easily related to the saturated

values of synchronous reactances. This method was found to be useful to the

analysis of saturation effect on machine constants, using a single search coil

placed on the stator.

An improved method for calculating the steady- and transient-state

leakage flux distributions in salient pole synchronous machines through the

leakage inductances has been reported by Shima et al (2003). The method

provides information on leakage flux distributions that cannot be obtained by

terminal quantities. The leakage inductances of a synchronous motor were

calculated under various loads and saturation of the inductances analyzed.

1.3.6 Neuro-Fuzzy techniques for control of machines

Mohanasundaram et al (2009) presented the design and simulation

of a fuzzy logic controller for speed regulation of voltage controlled induction

motor drive. The fuzzy algorithms in the proposed controller have been

systematically obtained from the intuition and experience about the motor

drive dynamics.

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Abul R. Hasan et al (1994) presented the design and application of

fuzzy control to the problem of Automatic Voltage Regulation of a

synchronous generator. The method explored deals with the use of binary

input-output fuzzy associative memories for control.

Radwan and Gouda (2005) have proposed speed control system for

permanent magnet synchronous motor (PMSM) drive, which newly

incorporates adaptive neuro-fuzzy with two input variables and one control

output variable. This control methodology solves the problem of non-linearity

and parameter variations of PMSM drive.

These references are related to Neuro-Fuzzy approach for speed

control and automatic voltage regulation in various electrical machines.

1.3.7 Analysis of flux measurement techniques

The V-I characteristics of a large variety of commercial diodes of

different types of germanium and silicon have been studied both at room

temperature and at liquid air temperature to investigate the effect of magnetic

field on the diode current by Parshad and Mehta (1967). Germanium diodes

show a large decrease in the forward current and a small decrease in the

reverse current on the application of the magnetic field, while the effect of

magnetic field on silicon diodes was found to be negligible.

The effect of a magnetic field in decreasing the forward current of a

germanium diode has been observed by Bansal and Parshad (1969). A bridge

set up using two diodes, to one of which the magnetic field is applied, and the

other used for temperature compensation, gave the unbalance voltage as a

function of magnetic field. To operate a bridge, it was first balanced by

adjusting the resistance arms without the application of the magnetic field. As

the magnetic field applied, the unbalanced voltage was measured. The relation

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observed between the magnetic field and the resulting unbalance voltage

could yield a practical method of measuring the magnetic field. The

observations show that by proper change of bridge input voltage, the overall

bridge sensitivity could be kept constant for all working temperatures. In

practice, for any set of particular diodes used in the bridge, the proper

working voltages for the bridge should be experimentally calibrated as a

function of working temperatures.

Measurement of magnetic field strengths has been one of the most

important measurement techniques in Electrical engineering. Such

measurements always involve inherent inaccuracies to a considerable

magnitude. Difficulties arise from the fact that the magnetic materials were

not homogenous and also suffer from the lack of uniformity in magnetic

properties between different batches of material. Hence a review of magnetic

flux measurement techniques has been discussed along with their applications

to various engineering fields by Karambelkar and Banerji (1973).

It is essential to understand the effect of magnetic field on circuit

parameters of semiconductor devices so as to apply them to various control

systems and equipment. Karambelkar (1979) has studied the effect of

magnetic field on bipolar and unipolar transistors. New applications for the

measurement of AC and DC voltage, current and power were also proposed.

Traditionally the magnetic field distribution throughout the

electrical machine core was obtained by positioning miniature enameled

copper wire search coils on test laminations stacked in an experimental core.

However their physical presence, when inserted in core, changes the flux and

field distribution, creates localized stress and an air gap between two adjacent

laminations. Basak et al (1995) proposed a method to overcome this drawback

by depositing sensors comprising a thin film structure, on the surface of

several laminations by vacuum evaporation of metals.

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Reininger and Hanisch (1997) have described possible tools for the

successful and competitive realization of a proper working magnetic sensor

for a certain field of application. The boundary conditions and interfaces to be

matched during the development of a magnetic switch towards a final product

for the industrial automation industry have been sketched. The difficulties

which go beyond the study of parameters influencing the working of a

physical sensor were mentioned.

A direction sensitive micro-magnetic field sensor was developed

using the giant magneto impedance effect by Steindl et al (2000). A quick-

response micro-sized magnetic sensor was investigated for high reliability

measurements of the stray fields of magnetic bar codes.

Chiriac and Chiriac (2003) have presented a new sensor for

magnetic field detection and mechanical displacement. A magnetic

amorphous wire was used as the active element. The magnetic field and the

displacement range can be modified by using different wire lengths.

A new method was proposed by George Loisos and Anthony

Moses (2003) for magnetic flux measurement in localized regions inside a

magnetic material using a novel surface probe sensor. It found to be more

accurate than the conventional probe sensor. It was proved to have an induced

voltage proportional to the flux density rate of change in a triangular cross-

sectional area instead of traditional orthogonal cross-sectional areas.

Precise magnetic sensors were used by Michal Vopalensky et al

(2003) for geophysical and space research magnetometers, for position

trackers and bio-magnetic measurements. Anisotropic magneto resistors and

Giant magneto resistors were the competitors for small size fluxgate sensors.

Their stability could be improved by ac techniques but the electronics

becomes complex and consumes more power. These offered higher sensitivity

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but unfortunately they could not be used for precise applications due to their

high non-linearity and hysteresis.

Nikitin et al (2003) have deposited thin film multi-layer structures

and optimized for various low noise magnetic field sensors. The developed

double-layer magneto resistive sensors revealed much less pronounced

hysteresis, lower noise when compared to single-layer sensors and have high

frequency band.

Marius Volmer and Jenica Neamtu (2007) have presented a method

to improve the quality of the Planar Hall effect used for micro compass

application. A linear isolator, which was able to measure the electrical

currents relatively with a high sensitivity, has been built. The behavior of the

magnetic sensors was simulated using a micro magnetic simulator.

Wheatstone bridge configuration was used to minimize the thermal drift and

to increase the magnetic sensitivity.

Yabukami et al (2009) have developed a thin film magnetic sensor

for magneto cardiogram measurement using the phase detection technique.

The technique was also applied for measurement of the low frequency field,

which resulted in achievement of a high magnetic resolution.

The literature survey shows that the measurement methods

presented by many researchers for the estimation of d-q axes flux are highly

complicated. Sensors for measuring flux in both the axes of synchronous

machines which give best results are required. No magnetic sensor is used by

the researchers for flux measurement in d- and q-axes of synchronous

machines.

The literature survey on modeling of flux reveals that the

estimation of flux in synchronous machines using Adaptive Network Fuzzy

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Inference System (ANFIS) based soft computing technique and mathematical

regression techniques are also not yet attempted by any researcher.

1.4 AIM AND CONTENT OF THE THESIS

From the review of literature, it has been inferred that various

researchers have proposed the estimation of d- axis, q- axis and intermediate

axis characteristics and made their analysis on the different aspects of degree

of complexity and accuracy. Further, these analyses were carried out using

few experimental techniques and certain analytical methods which use

machine models, derived in terms of machine parameters and have not

considered the measurement of flux using flux sensors and modeling by soft

computing methods.

Hence, specific approach is undertaken in this research work, to

propose new methodologies to alleviate estimation of d-q axes flux in

projected pole synchronous machines and to enhance the accuracy.

A methodology has been developed and presented for measurement

of d- axis and q- axis flux in synchronous machines using germanium diode

flux sensors. The laboratory machine that has been taken up for experimental

investigation is the projected pole (stationary field type) synchronous machine

of 415 V, 3000 VA. Flux in d- and q- axes in the machine were obtained by

measurements, which uses Germanium diode flux sensors.

The change in the property of Germanium diodes due to the effect

of application of magnetic field is used for the magnetic flux measurement. If

a forward biased diode is placed in the magnetic field, its forward current

decreases. The decrease in the forward current is directly proportional to the

strength of the magnetic field. The measurement of variation in this forward

current, leads to the measurement of magnetic flux.

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Mathematical models have also been developed employing

Multivariate linear regression and Multivariate polynomial regression for the

estimation of q- axis flux.

Soft computing models have been developed which uses ANFIS for

the estimation of q- axis flux. Various ANFIS models use different

membership functions for the two inputs viz., field excitation and d- axis flux.

Along with the experimental test results measured using

Germanium diode flux sensors, available q-axis magnetic flux data calculated

from the measured d-axis flux by Ahmed El-Serafi and Kar (2003), for

various Salient pole synchronous machines namely, a) Microalternator, b)

Machine No. 1 and c) Machine No. 2 form the basis of all the modeling

schemes reported in this thesis.

The proposed measurement method which uses germanium diode

flux sensor has to be a simplest instrumentation kit for the measurement of

d-q axis flux in projected pole synchronous machines. The models developed

have to be provided with simple known inputs to output an accurate value of

q- axis flux. The graphical representations of measured and modeled values of

flux have to be provided and comparisons of these are to be made available

with the reference values of flux to further enhance the analysis.

The objective of the thesis is structured as a block diagram in

Figure 1.1.

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Figure 1.1 Aim and Content of the Thesis

1.5 ORGANIZATION OF THE THESIS

The research work carried out are presented in six chapters and

structured in a top down approach as shown in Figure 1.2. The first chapter

briefly reports the review of literature, which necessitates the scope of the

present work.

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Figure 1.2 Organization of the Thesis

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The second chapter introduces d-q axes flux measurement in

projected pole synchronous machines.

Regression models, which estimate the q- axis flux from the d- axis

flux and field excitation, aim to make a comparison between the two

regression models are presented in the third chapter.

Chapter 4 reports the q- axis flux modeling using adaptive network

fuzzy inference system. The design, development and comparison of q- axis

flux obtained by three ANFIS models are discussed in this chapter.

In chapter 5 all the proposed models are compared with the actual

reference values. It also presents the estimation of residual for the models.

A comprehensive summary of conclusions obtained from this

research work and scope for future work are presented in the sixth chapter.