ABSTRACT
This thesis aims to extract d-axis machine parameters of a 214 MVA high-speed turbogenerator
using well-established off-line techniques. MATLAB/SIMULINK tool has been
utilized to model the generator and perform sudden short-circuit (SSC) tests. Because
constant speed operation of the generator is vital consideration for the accuracy of SSC
tests for parameter extraction, this thesis has employed an arrangement of 2 DC motors
operating alongside a drive system, which is configured to couple the combined motor
to drive the shaft of the generator to maintain synchronous speed throughout the test.
Simulating the different drive configurations, the SSC oscillographs were captured and
transformed into symmetrical envelope waveforms which were then used to extract the
operational impedances and time constants of the generator. From the simulation tests,
the influence of speed departures on shaft torques and current waveforms were
presented and analysed. The results obtained for the variable-speed simulation using
the drive system were then validated with those calculated from standard equations, as
well as those of the constant-speed mode. The test results confirm that SSC tests can
be performed on synchronous machines under rated conditions if the couplings can be
appropriately designed to contain the dangerous values of electromagnetic torque that
are developed during such tests. In addition, an electronic switch was designed to
manage the abnormal field current which results from the introduction of SSC currents.
In the end, the switching contraption is seen to reduce the power losses in the
machine’s field winding during SSC.
TABLE OF CONTENTS
Certification Page ii
Title Page iii
Dedication iv
Acknowledgement v
Abstract vi
Table of Contents vii
List of Tables ix
List of Figures x
Key Abbreviations xi
Chapter One: Introduction 1
1.1 Background of the Study 1
1.2 Motivations 5
1.3 Objectives 7
1.4 Three-Phase Short-Circuit Fault in Synchronous Generators: An Overview 8
1.5 Study Limitations 10
1.6 Thesis Outline 11
Chapter Two: Review of Related Literature 13
2.1 Analysis and Modelling of Synchronous Generators 13
2.2 Methods of Solution to Short-Circuit Current Analysis 14
2.3 Importance of Balanced Short-Circuit Fault Analysis in Synchronous Generators 15
2.4 Objectives of Computer Modelling and Simulation to Synchronous Generator Studies 16
2.5 Identification of Synchronous Generator Parameters 17
2.6 Statement of Originality 18
Chapter Three: Dynamic Modelling of Synchronous Generators 20
3.1 Assumptions for Model Development 20
3.2 System Identification 20
3.3 Model Selection 21
3.4 Modelling of Synchronous Generators 23
3.5 Park’s Transformation and dq Modelling of Synchronous Generators 25
3.5.1 Park’s Transformation 25
3.5.2 Formulation of Voltage Equations 27
3.5.3 Per-Unit Notation of Voltage Equations 29
3.6 Open-circuit Operation 33
viii
3.7 Full-load Operation 34
3.8 DC Motor Model 35
3.9 Description of the Drive System 37
3.10 Design of an RL-load Model 40
3.11 Modelling and Dynamic Simulation in MATLAB 41
3.11.1 Simulation Tools 41
3.11.2 Simulation of Synchronous Generator and DC Motor Model 42
3.11.3 Design and Modelling of the Drive System 45
3.11.4 Model of RL-load and Current Controller 48
Chapter Four: Simulation Results 51
4.1 System Simulations 51
4.2 Constant-speed Simulation 55
4.3 Variable-speed Simulation 55
4.4 Analysis of Simulations 56
4.5 Parameter and Time Constant Extraction 62
4.5.1 Methodology 62
4.5.2 Results 67
4.5.3 Discussions based on Parameter Extraction 68
4.5.4 Simulation of RL-load and Implementation of SSC Current Controller 69
Chapter Five: Conclusion and Recommendations 72
References 77
Appendices 79
CHAPTER ONE
1.1 Background of Study
Synchronous machines exist both as a generator and as a motor depending
on how and/or which of the windings is energized to operate them as well as the
type of load it is designed to supply. Nearly all of the electric power used throughout
the world is generated by synchronous machines driven by hydro or steam turbines
or combustion engines [1]. It is the primary means by which mechanical energy is
converted into electrical energy. By further explanation, conventional synchronous
machine has the field-winding wound on the rotating member (the rotor), and the
armature wound on the stationary member (the stator). A dc current, creating a
magnetic field that must be rotated at synchronous speed induces a 3-phase set of
voltages within the stator windings of a synchronous generator. The excitation of the
rotating field-winding can be achieved through a set of slip rings and brushes
(external excitation), or from a diode-bridge mounted on the rotor (self-excited or
brushless excitation) [2].
Because of increased amount of maintenance and power losses associated
with slip rings and brushes, brushless exciters are preferred for large synchronous
machines. A brushless exciter is a small ac generator with its field mounted on the
stator and its armature circuit mounted on the rotor shaft. The 3-phase output of the
exciter generator is rectified to direct current by a 3-phase rectifier circuit also
mounted on the shaft of the generator, and is then fed to the main dc circuit. To
make the excitation of a generator completely independent of any external power
sources, a small pilot exciter can be used. A pilot exciter is a small ac generator with
permanent magnets mounted on the rotor shaft and a 3-phase winding on the stator.
It produces power for the field circuit of the exciter, which in turn controls the field
circuit of the main machine.
Elsewhere, it has been defined that a synchronous machine acting as a motor
is an ac rotating machine whose speed under steady state condition is proportional
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to the frequency of the current in its armature and this causes the magnetic field
created by the armature currents to rotate at the same speed as that created by the
field current on the rotor, which is rotating at synchronous speed, resulting to a
steady torque.
Synchronous generators have been variously described and classified and
more details will be provided much later in Chapter Three. However, it is good to
mention here that a general attempt has been made to describe them based on the
two types of their rotor structures – round or cylindrical rotor and salient pole rotor
types (see Fig. 1); the basic difference being that the later is magnetically
unsymmetrical.
Historically, the commercial birth of the synchronous generator, also called
alternator, dates back to August 24, 1891 when the first large-scale demonstration of
ac power generation was carried out during an international electrical exhibition in
Frankfurt, Germany. The success of its adoption since then is based on the
feasibility of transmitting ac power over long distances. In 1895, the same
technology was applied to the New York Niagara Falls power plant and this marked
the end of the great dc versus ac duel. Today, tremendous development in machine
ratings, insulation components, and design procedures have been recorded,
however, the basic constituents of the machine have remained practically
unchanged.
The largest and perhaps the most popular of synchronous machines are the
three-phase synchronous generators [2]. Though constructing them is relatively
more expensive, their higher efficiency is an advantage at very high power ratings.
The stator windings are identically distributed over pole-pairs, and the phase axes
are spaced 120° apart. The rotor on the other hand, can be salient or cylindrical.
Salient pole construction is mostly used in low-speed applications where the
diameter to length ratio on the rotor can be made larger to accommodate the high
pole number.
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Fig. 1. Illustration of Synchronous Machines of (a) salient rotor structures and (b)
round or cylindrical rotor
Generally, the round rotor structure is used for high speed synchronous
machines, such as steam turbine generators, while salient pole structure is used for
low speed applications, such as hydroelectric generators. In salient pole
synchronous generators, the short, pancake-like rotor has separate pole pieces
bolted onto the periphery of a spider-web-like hub and the “salient” simply refers to
the protruding poles; the alternating arrangement of the pole iron and the inter-polar
gap results in preferred directions of magnetic flux paths or magnetic saliency. Nonsalient-
pole (cylindrical) rotors are utilized in two-or-four-pole machines, and, very
rarely, in six-pole machines.
The rotor of a synchronous machine is equipped with a field winding and one
or more damper windings, which accounts for the different electrical characteristics
unique to rotor windings. In the basic two-pole representation of synchronous
generators, the axis of the North Pole is called the direct or d-axis. The quadrature,
or q-axis, is defined in the direction 90 electrical degrees ahead of the direct axis.
Under no-load operation with only field excitation, the field MMF will be along the daxis,
and the stator internal voltage, will be along the q-axis.
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From the structure of a synchronous generator, the rotor field is a physical
winding; while damping windings may just be electrically equivalent windings [1]-[2].
For example, the damping windings for a salient-pole generator represent the
damping effect of damping rods distributed on the rotor while for a round rotor
generator; the damping function produced is developed by the eddy current inside
the whole rotor. In other words, they are just equivalent windings and can be
represented by a single or multiple damping windings. These damping windings are
made of copper bars short-circuited at both ends and embedded in the head of the
pole, close to the face of the pole. The purpose of this winding is to start the motor
under its own power as an induction motor, and take it unloaded to almost
synchronous speed when the rotor is “pulled in” by the synchronous torque. The
winding also serves to damp the oscillations of the rotor around the synchronous
speed, and is therefore named damping-winding (also known as amortisseurs).
Synchronous machine can be adapted as motors where constant speed drive
is required because of the rotor speed which is proportional to the frequency of
excitation or as synchronous condensers in power systems for power factor
correction or for control of reactive KVA flow. The latter is made possible because
the reactive power generated by an unloaded synchronous machine can be adjusted
by controlling the magnitude of the rotor field current. With power electronic variable
voltage variable frequency (VVVF) power supplies, synchronous motors, especially
those with permanent magnet rotors, are widely used for variable speed drives; this
type of motors are known as brushless dc motors since they do not need brushes.
Since the synchronous machines have been generally accepted as a threephase
generator for power generation, there is a body of literature on their modeling
and the determination of parameters. A few of such studies are mentioned as
references [1]-[3]. Much later in this work, Chapter Three has been designed to
explain the mathematical model that is based on the equivalent idealised
synchronous machine with the rotor equipped with a field winding and three damper
windings.
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So far, the background information provided in this section for the generator
action of synchronous machines is sufficient to undertake this research work and it
is thus structured in the following sections.
1.2 Motivations
Off-line sudden short-circuit (SSC) tests in synchronous generators have
continued to generate growing amount of research interests because it offers an
advantage in determining some transient parameters in synchronous generators on
the basis that their transient behaviour can be accurately captured. Synchronous
generator sudden short-circuit tests are also necessary in power system studies to
provide protective equipment designed to isolate the faulted generator from the
remainder of the system in the appropriate time. The interrupting capacity of the
breakers should be designed to withstand the highest value of possible short-circuit
currents.
Of primary concern during sudden short-circuit tests is to maintain a constant
speed for both the driver and driven machine. To this end, short-circuit
measurements for very small synchronous generators do not pose a serious
challenge because a separately excited dc motor of about two times its rating can be
used to drive them without encountering speed departures. However, for very large
machines, this is not possible because the electromagnetic torque of the
synchronous generator will increase in the event of sudden short-circuit currents,
and in turn this will appear as a very large load torque to the driving motor.
Consequently, the speed of the motor suddenly drops with such an additional load.
On the other hand, an induction motor is not amenable to drive large
synchronous generators because of the difficulty in maintaining their speed constant
where possible.
Looking at synchronous motors they are hard to brake. Moreover, if an
attempt is made to employ synchronous motors to drive large synchronous
generators, the presence of short-circuit currents will result in values as high a three
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times it rated current value leading to higher torque values of up to six or more its
rated value and this poses greater mechanical threat to the connecting shaft which
can result in its breaking and/or either of the machine being destroyed.
In contemporary practice, linear mapping using the reduced field current
method which is an attempt to avoid the dangerous impact of very high short-circuit
currents and torque have been attempted. This method is impractical because it
assumes a linear operation of the generator by reducing the field current to a safe
value which operates to produce short-circuit current values below the machine
rated values. It is difficult to accurately predict, based on this assumption, what
happens at the non-linear saturation point on the B-H curve. Even if so many
interpolations are taken in the linear region, it is difficult to predict what happens in
the non-linear region using this method. Moreover, this kind of approximation can be
very inaccurate for extraction of parameters and time constants of large
synchronous generators in the transient and sub-transient regions. Hence, SSC
under rated conditions drive the machine fluxes into deep saturation.
Separately-excited dc motors that operate under constant speed are best
choice for driving synchronous generators, but when compared to large
synchronous generators – to be considered in this work – they come in relatively
small sizes with very low speed and efficiency. Turbo generators (of ratings of
several MVA) operate at very high speed otherwise they will not deliver the required
power. The biggest and practical sizes of dc motor are about 2MW. It has been
stated that dc motor sizes double or more than of 2MW exist, but this is highly
inefficient as they operate with enormous losses.
In some cases, designers prefer to transport large synchronous generators
after they have been manufactured to generating sites where they are then
randomly tested. But this approach is also not justifiable when the cost of
transportation and other logistics are brought into consideration.
In this work, the main motivation is to develop a drive system using a system
of coupled separately excited dc motors to drive a large synchronous generator
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under short-circuit conditions without altering the speed of both the motor and that of
the generator to guarantee the accurate extraction of the d-axis parameters of the
synchronous generator. In addition, this work will also consider how to design and
implement a switching system to turn off the generator at dangerous levels of shortcircuit
currents. In the first case, the system to be modeled is in three separate parts
and includes all realistic components of the drive system. This enables the accurate
extraction of all the vital information needed to estimate the machine d-axis
parameters under transient and steady conditions such as Xd, Xd′, Td, Td′, and Td′′. In
the second case, a full-load operation mode of the synchronous generator is
assumed so as to allow for the determination of the minimum safest field excitation
at which the generator can be operated without compromise of its safety.
1.3 Objectives
The objective of this work is to accurately extract the d-axis machine
parameter of a large synchronous generator using coupled DC motors to
appropriately set-up a drive system. Non-trivial equations for the coupling shaft will
also be derived. These efforts will seek to provide answers to the following research
questions:
1. How does one ensure a valid drive system for driving large synchronous
generators?
2. What type of motor can be used to conveniently drive large synchronous
generators to capture short-circuit oscillographs?
3. What practical measures are needed to ensure that the speed of large
synchronous generators remain constant during sudden short-circuit tests?
The target then is to ensure that the speed of the drive system must remain
constant at the instant when the short-circuit occurs to the point where sufficient
data for parameter extraction has been captured without altering the speed of the
drive system. This hypothesis is on the basis that the speed was constant before the
test and therefore must be maintained at a constant value as much as possible in
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the duration of the test. Altering the speed of the machines alters the frequency of
the current and by extension, everything about the short-circuit current from which
vital machine parameters will be extracted. Moreover, capturing the machine
parameters and time constants at rated speed values will offer opportunity to make
close comparison with known tests, thereby providing greater confidence for
accuracy.
Also, using the MATLAB/SIMULINK® toolbox is a deliberate effort to design a
flexible computer programme which can be amenable to various dynamic analyses
and is simple enough to permit fast, low-cost and safe testing of the machine model.
In this way, it will be possible to study short-circuit fault at various machine
conditions and models. Moreover, another advantage of using this method is that it
can be done at the factory of the manufacturer; it poses a reduced risk factor to the
machine being tested, and provides complete data in the direct axis.
Another objective for this research is to incorporate a control that can regulate
the generator field current at SSC current modes. Again, MATLAB®/Simulink will be
used to achieve this stage of the research after relevant deductions from the
machine have been made at full load operation. A number of research questions are
raised here:
1. What is the maximum safest (trip-off) field current at which the generator can
be excited?
2. How can one automatically switch off the field current if it exceeds a threshold
value?
3. How can one implement a switching system to automatically switch off the
field current at dangerous SSC rates?
1.4 Three-Phase Short-Circuit Fault in Synchronous Generators: An
Overview
A synchronous generator, connected to an infinite bus whose voltage is the
generator rated voltage, has its stable operating point defined by the following rated
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values: armature voltage, apparent power, speed, power factor and excitation
voltage. This set of values are maintained during normal operation, and in a situation
where they are not, the generator is said to be operating under fault or more
commonly, under transient condition. For this very reason, it is important that all the
generator ratings and nameplate parameters are always maintained within rated
machine values.
Synchronous generator failure is usually caused by external factors such as
lightning strikes, heavy rain, strong winds, or contamination of insulators. Most of the
faults that occur in synchronous generators are non-symmetric; long-term average
short-circuit statistics indicate that 70 percent of synchronous generator faults occur
during electrical storms [1], [4].
The procedure for symmetrical short-circuit test of an unloaded generator
using the reduced field current method is described in references [5]-[8] thus: The
terminals of the machine at no load, excited by a reduced field current and rotating
at rated speed are shorted while the currents in the armature windings and the field
windings are recorded.
Physically, short-circuit faults produce severe forces during the operation of
large alternators, and to calculate the magnitude of these forces will require the
magnitude of the short-circuit currents to be known as a first step [9], although the
process is extremely short (usually about 0.1~0.3s).
For this reason, the task is to provide protective equipment designed to
isolate a faulted generator from extreme impacts of short-circuit currents in the
appropriate time. The interrupting capacity of breakers should be designed to
accommodate the largest short-circuit currents and hence care must be taken not to
base the precision decision simply on the results of a balanced three-phase shortcircuit
[4]. The circuit protective mechanism should be capable of carrying for a short
time the specified short-circuit current. However, the possibility of catastrophic
failure exists if the short-circuit currents are not properly calculated and the
protection is subjected to fault values that exceed its rating. The stator phase and
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rotor field currents at short-circuit faults take dangerous values, thermally
overloading the machine. The critical value of electromagnetic torque, during short
circuit transient, equally has to be known by designers to appraise the mechanical
strength of the generator.
A look at the sudden short-circuit of a synchronous generator that has initially
been operating under open-circuit steady state condition, the machine undergoes a
transient in all the three phases and finally ends in a new steady-state condition.
Immediately upon short circuit, the dc off-set currents appear in all three phases;
each with different magnitude since the point at which the short circuit occurs is
different magnitude for each phase voltage, displaced 120° apart. The developed
symmetrical short-circuit current is limited initially only by the leakage reactance of
the machine, and because the air gap flux cannot change instantaneously to counter
the demagnetization of the armature short circuit current, currents appear in the field
winding as well as in the damper winding in a direction to help the main flux. These
currents then decay in accordance with the winding time constants.
1.5 Study Limitations
A major limitation was encountered in this research thesis during the
modelling of the drive system using stiffly-coupled DC motors. Because of the
novelty of the approach, very little literature evidence exists on its methodology. To
overcome this limitation, a number of assumptions were necessary and advanced.
In another instance, the process leading to the development of a switching
system was altogether challenging. The first attempt to externally model a current
controller for the field circuit using a system of Simulink blocks which comprise time
delays, logic gates and signal converters did not operate accordingly as the
controlled current appears not to account for the dynamics of the field circuit. A
cursory attempt to consider varying the field resistance was trailed as it is not
physically achievable given the enormously high occurrence of field current (up to 3
p.u.) during SSC. Similarly, developing and incorporating a MATLAB code inside the
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embedded Simulink block of the synchronous generator, using logical control
commands to operate the field current at SSC, did not suffice.
Again, a different approach which required that the integrator which was used
to perform the differential component of the voltage equation of the field windings be
bounded at some limits during SSC, yet abortive was initiated. It was initially
anticipated, and actually undertaken, that the boundary limits will be determined
from simulations of the generator based on normal operating conditions. This
attempt was mainly impractical because it was later observed that the Simulink
integrator block is not time-bound. Eventually, a single switch block from the
Simulink library was preferred and configured to realize the control of the high
currents appearing in the field windings during SSC.
During the extraction of parameters from SSC current oscilloscope using the
symmetrical envelope technique, the transient and subtransient time constants for
constant speed and rubber damping drive configurations did not follow after the
normal process of plotting ‘ ‘ ‘ I + I on semilog paper. This was because the current
envelopes did not amend exactly to the conventional MATLAB codes developed for
this purpose. In the end, ‘
d T and ”
d T were calculated using standard synchronous
machine equations from the values obtained for d x and ”
d x respectively.
1.6 Thesis Outline
The thesis is divided into five chapters. Chapter One has been discussed and
is being summarized here. Chapter Two presents a review of previous works on
parameter estimation in synchronous generator short-circuit tests which includes
analysis and modelling of synchronous generators, methods of solution to shortcircuit
current analysis of synchronous generators, importance of balanced short
circuit fault analysis in synchronous generators, objectives of simulation programs to
synchronous machine modeling, identification of synchronous generator parameters
and a direction to pattern the current research. Chapter Three highlights the detailed
modelling of synchronous generators and DC motors as well as the formulation of a
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suitable interconnecting drive system. It stresses on system identification, model
selection, formulation of voltage equation and flux-linkage equations in both ac
generator and dc motor, description of the drive system and the per-unitization
concept. Also, provision was made much later in Chapter Three to discuss the
configuration and determine the field excitation for assuming full-load operation of
the synchronous generator, design an RL-load model and model a switching
mechanism to control the generator field current at high values of SSC. In addition,
Chapter Three deals on the computer software implementation of the models earlier
developed. Chapter Four begins with a description of the methodology involved in
undertaking the simulation tests and also presents the simulation results. Chapter
Five is used to conclude and give relevant recommendations.
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