1
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 qaxis 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
2
on-load measurements method and back-to-back method for measuring the qaxis 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 qaxis 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
4
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 intermediateaxis 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 onload 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 crossmagnetizing 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
12
characteristics. Rejection test from load conditions was used for identifying qaxis 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
14
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.
15
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 quickresponse 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 crosssectional 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
16
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
17
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.
18
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.
20
Figure 1.2 Organization of the Thesis
21
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.