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ADAPTIVE AND NON-LINEAR EXCITATION CONTROL OF
SYNCHRONOUS GENERATOR‟S STABILITY THROUGH NEURAL
NETWORK
B.E. (EE) PROJECT REPORT
Batch 2005-06
Prepared By:
SYED MUSTAFA ALI ZAIDI (EE- 050)
HASSAN AHMED (EE- 305)
SYED FAIZAN TAHIR (EE- 051)
MIRZA OVAIS BAIG (EE- 047)
Project Advisors:
MR. ABDUL GHANI ABRO
ASST.PROF. ELECTRICAL ENGINEERING DEPARTMENT
N.E.D UNIVERSITY OF ENGINEERING AND TECHNOLOGY
MR. AQEEL AHMED
DEPUTY GENERAL MANAGER, ABB, PAKISTAN
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ABSTRACT
Adaptive and non linear Excitation control of synchronous generator‟s stability through Neural
Network
Control equipment of synchronous generators such as automatic voltage regulators, speed governors
and power system stabilizers have been developed to maintain stability and to improve damping of the
power systems. When an operating condition changes greatly, however, such controllers may become
less effective because of nonlinearity of the power system. And hence these drastic changes in the
power system caused by faults and circuit switching may cause control performance to become
unsatisfactory. In this project, a nonlinear adaptive generator control system using neural networks is
proposed. In this controller we have integrated a voltage regulator and a power system stabilizer. The
proposed neural network based controller generates appropriate control signals enhancing transient
stability and damping of the power system.
The proposed system is demonstrated by computer simulation in MATLAB by first modeling a power
system with conventional controller (AVR & PSS) and then these controllers are used to TRAIN the
neural network controller. After training the neural network based controller is used to control the same
power system and it is proved through simulation that the neural network controller performs better
than the conventional controller, improving the transient and dynamic stability.
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We take this opportunity to acknowledge, with gratitude, those persons whose valued suggestions and
constructive criticism helped achieve our learning targets in this project. Firstly, we owe our deepest
acknowledgments to our project internal, Mr. Abdul Ghani Abro without whom this learning curve of
our life was never possible. He was instrumental throughout the course, from the point of project
selection to project report submission. His valuable discussions and guidance proved critical for the
success of this project.
It is also an honour for us to thank our project external. Mr. Aqeel Ahmed, who proved to be
inspirational for our work and added a new dimension to our project, his mentoring made our project to
progress in a professional and organized manner. We would also take the honour by thanking the Dean,
Chairman and Co-Chairman of our department for providing us the infrastructure in the university
throughout our academic career.
And above all we would thank Allah Almighty, who is able to do immeasurably more than we ask or
imagine, according to His power that is at work within us.
ACKNOWLEDGMENTS
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This project proved to be challenging for us from the point of its selection. We had no idea as to how
and what we will be doing to complete this project when we submitted the project proposal last year,
because this project was unlike the conventional projects of the past years in our department. Yet, we
selected this project because its title fascinated us and also that we had believe in ourselves and faith in
people guiding us.
The first shock we had in this project was when we started to collect and read the research papers in
this field and it became evident to us that we have a huge mountain to climb. And in order to
understand one research paper we had to refer several books which was a hard task but then proved to
be instrumental in giving us the complete idea of the project.
Our next task was to understand as to how a neural network works. This was completely a different
subject in which we had no prior knowledge. We had no idea of Artificial Intelligence before and we
went through some difficult times those days. One thing that proved to be very good in creating the
understanding of neural network for us was some lectures we saw on you-tube, conducted by an Indian
professor.
Throughout the year, defeating one difficulty unwinded another but believe and hardwork was the key
for us. And now we are very satisfied that we have achieved what we were aiming for in the start of the
year.
PREFACE
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PROJECT MANAGEMENT-GANTT CHART
A Gantt chat is a type if Bar Chart that illustrates a project schedule. Gantt chart illustrates the
start and end date of the elements of a project. It also shows the Work Breakdown Structure of
the project and also work dependency.
TITLES STARTING DATES DURATION(DAYS) ENDING DATES
PROJECT SELECTION 1/20/2009 15 2/4/2009
DECIDING PROJECT INTERNAL 1/23/2009 3 1/26/2009
COLLECTING LITERATURE 1/21/2009 24 2/14/2009
STUDYING NEURAL NETWORK 2/15/2009 21 3/8/2009
STUDYING POWER SYSTEM 2/17/2009 15 3/4/2009
COLLECTING IEEE PAPERS 3/7/2009 25 4/1/2009
LEARNING MATLAB SKILLS 3/15/2009 10 3/25/2009
MEETING WITH EXTERNAL 3/30/2009 1 3/31/2009
STUDYING MATLAB TUTORIAL 4/2/2009 12 4/14/2009
STUDYING IEEE PAPERS 4/2/2009 20 4/22/2009
MEETING WITH EXTERNAL 5/13/2009 1 5/14/2009
POWER SYSTEM MODELING 5/18/2009 15 6/2/2009
NN MODELING 6/3/2009 20 6/23/2009
NN TRAINING 6/28/2009 4 7/2/2009
NN IN PS 7/2/2009 2 7/4/2009
COMPARING 7/4/2009 4 7/8/2009
IMPROVING MODEL 7/6/2009 30 8/5/2009
PROJCT REPORT 1/21/2009 190 7/30/2009
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GRAPHICAL REPRESENTATION OF GANTT CHART
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EXECUTIVE SUMMARY ___________________________________________________ 1
BACKGROUND _____________________________________________________ 1
PROPOSED SCHEME _________________________________________________ 3
CHAPTER # 01
POWER SYSTEM STABILITY ANALYSIS ____________________________ 5
1.1 POWER SYSTEM ANALYSIS __________________________________________ 6
1.2 POWER SYSTEM STABILITY ___________________________________________ 7
1.3 DEFINITION OF POWER SYSTEM STABILITY ____________________________ 7
1.4 CLASSIFICATION OF STABILITY _______________________________________ 8
1.5 TRANSIENT STABILITY _______________________________________________ 10
1.6 SWING EQUATION ____________________________________________________11
1.7 EQUAL AREA CRITERION _____________________________________________ 12
1.8 EXCITATION SYSTEM ________________________________________________ 13
1.9 AUTOMATIC VOLTAGE REGULATOR (AVR) ____________________________ 15
1.10 PURPOSE OF AVR FOR STABILITY ____________________________________ 17
1.11 POWER SYSTEM STABILIZER ________________________________________ 17
Table Of Contents
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CHAPTER # 02
ARTIFICIAL NEURAL NETWORK ___________________________________ 22
2.1 ARTIFICIAL INTELLIGENCE & NEURAL NETWORK _____________________ 23
2.2 HISTORICAL MOTIVATION __________________________________________ 23
2.3 DEFINITION _________________________________________________________ 26
2.4 BENEFITS OF NEURAL NETWORK _____________________________________ 27
2.5 RESEMBLENCE WITH THE HUMAN BRAIN _____________________________ 28
2.6 MODELS OF A NEURON _______________________________________________ 30
2.7 TYPES OF ACTIVATION FUNCTION ____________________________________ 33
2.8 NETWORK ARCHITECTURES __________________________________________34
2.9 NEURAL NETWORK‟S ARCHITECTURE _________________________________ 36
2.10 TRAINING ALGORITHM ______________________________________________ 37
2.11 THE BACK PROPAGATION ALGORITHM _______________________________ 39
2.12 POSSIBILITIES OF CONVERGENCE ____________________________________ 41
2.13 GAUSS–NEWTON ALGORITHM _______________________________________ 43
2.14 BACK PROPAGATION WITH LEVENBERG-MARQUARDT ALGORITHM ____ 44
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CHAPTER # 03
MATLAB SIMULATION ______________________________________________ 46
3.1 MODEL DESCRIPTION ________________________________________________ 46
3.2 SYNCHRONOUS MACHINE ____________________________________________ 47
3.3 EXCITATION SYSTEM _______________________________________________ 52
3.4 THREE-PHASE PARALLEL RLC LOAD __________________________________53
3.5 THREE PHASE FAULT _______________________________________________ 56
3.6 BUS SELECTOR - SELECT SIGNALS FROM INCOMING BUS _______________ 60
3.7 SCOPE AND FLOATING SCOPE ________________________________________ 62
3.8 THREE-PHASE TRANSFORMER _______________________________________ 64
3.9 RMS VALUE CALCULATOR ___________________________________________ 66
3.10 GAIN - MULTIPLY INPUT BY CONSTANT ______________________________ 70
3.11 NEURAL NETWORK MODELLING ___________________________________ 72
CHAPTER # 04
RESULTS________________________________________________________________ 77
4.1 COMPARISON OF TERMINAL VOLTAGE _________________________________ 79
4.2 COMPARISON OF ROTOR SPEED DEVIATION ____________________________ 81
4.3 GRAPHS COMPAIRING TRAINING THROUGH 6 AND 7 NEURON ___________ 83
CONCLUSION __________________________________________________________ 84
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FUTURE IMPROVEMENTS ______________________________________________ 85
BIBLIOGRAPHY _________________________________________________________ 86
APPENDIX A _____________________________________________________________88
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HYPOTHESIS:
Adaptive and non linear Excitation control of synchronous generator‟s stability through
Neural Network
BACKGROUND:
Both the historical and the present-day civilization of mankind are closely interwoven with energy,
and there is no reason to doubt but that in the future our existence will be more and more dependent
upon the energy. Electrical energy occupies the top position in the energy hierarchy. Therefore, it is
more favorable to make the generation and transmission of electrical energy more economical and
reliable.
Keeping in mind this economic condition 3φ synchronous generators (known as alternators) are used
for large scale power generation. Here the armature winding is placed on the stator while the field
winding is placed on the rotor. The field winding is responsible for excitation control of the
generator which maintains generator voltage and controls the reactive power flow [01].
Most synchronous generators are connected to large interconnected power system and hence work on
an infinite bus. The control of active and reactive power keeps the system in steady state. Changes in
real power affect mainly the system frequency while the reactive power is mainly dependent on
voltage magnitude. In synchronous machine this real power is controlled by governor action i.e. by
controlling the input mechanical power. The reactive power and hence the terminal voltage is
controlled by Voltage Regulator i.e. by controlling the excitation voltage. Hence the controller for
voltage regulator holds an important position in determining the power system stability.
Today‟s automatic control theory is all based on the concept of feedback. The essence of feedback
theory consists of three components, measurement, comparison and correction. In order for the
controller to perform its best under all operating conditions it must be capable of having good
learning and adaptation capabilities to cope with changes and uncertainties in the system.
EXECUTVE SUMMARY
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A basic approach to controller design for synchronous machines is an implementation of state
feedback optimal control. It is typically designed for a linear model about a specific operating point,
which does not necessarily guarantee sufficient robustness to handle changes in system power loads
and variations due to system parameter uncertainties. Due to its limitations, this approach has lost its
original popularity. Subsequently, adaptive control was developed over the past decade. Most
algorithms are still based on a linear model. However, the synchronous machine is a nonlinear, fast-
acting multivariable system and interconnected in a power system. The machine operates over a wide
range of operating conditions, and is subject to different types of disturbance. The conditions change,
but the outputs have to be coordinated so as to satisfy the requirements of power system operation.
For this type of system it is recognized that classical control theory and mathematical model-based
control algorithms can not be successfully employed. [02]
To overcome the above problems, a new approach to controller design which uses new technologies
such as artificial neural networks is needed. And therefore there has been some research on using the
neural network approach for nonlinear systems control.
This project presents an application of artificial neural network as a controller for a synchronous
machine excitation system. A hierarchical architecture of an ANN is adopted for controller design,
which is used for data mapping and control respectively, based on the Back Propagation Algorithm
(BPA).
An artificial neural network (ANN), usually called "neural network" (NN), are applied in this work
because they are remarkable on several counts. First, they are adaptive: they can take data and learn
from it. Thus they infer solution from the data presented to them, often carrying quiet subtle
relationship. This ability differs radically from standard software techniques because it doesn‟t
depend on the programmer prior knowledge of rules. Second, NN can generalize: they can correctly
process data that only broadly resembles the data they were trained on originally. They can also
solve problems that lack existing solutions. Third NN are non linear, in that they can capture
complex interaction among an input variable in a system. These are some reasons why NN is used in
this project.
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PROPOSED SCHEME:
This thesis provides a means of determining the application of neural network in the excitation
systems of synchronous generator. The responses of synchronous machine in a power system are
observed by computerized simulation.
In fig.1.1 the block diagram representation of the power system model is shown, which is a simple
representation of a general power system model. It is highlighted here that in the proposed scheme
the conventional based controller of AVR and PSS are replaced by neural network based controller.
Fig. 1.1: Block diagram representation of the power system model
Before the neural network based controller can be employed in the system they must be trained
[chapter 04]. For the training of network we need the training data i.e. telling the neural network the
inputs and the desired outputs so that it can adjust itself in such a way that the next time when it is
provided with such input data it generates the desired output. Before training the
network we have to decide two important things: firstly its architecture and then the training
Algorithm [chapter 02].
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CHAPTER #
01
POWER SYSTEM STABILITY
ANALYSIS
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1 POWER SYSTEM STABILITY
ANALYSIS
ABOUT THE CHAPTER:
Successful operation of a power system depends on the engineer‟s ability to provide reliable and
uninterrupted service to the loads. The reliability of the power supply implies much more than
merely being available. Ideally, the voltage and frequency at every bus must remain constant at all
times to keep system intact. In practical terms this means that both voltage and frequency must be
held within close tolerances so that the customer‟s equipment may operate satisfactorily. For
example a drop in voltage of 10-15% at any system bus or a reduction of the system frequency of
only a few hertz may lead to synchronism lost stalling of the motor loads on the system.[03] Thus it
can be accurately stated that the power system operator must maintain a very standard of continuous
electrical service.
The first requirement of reliable services is to keep the synchronous generators running in parallel
and with adequate capacity to meet the load demand. If at any time a generator loses synchronism
with the rest of the system, significant voltage and current fluctuations may occur and transmission,
line may be automatically tripped by their relays at undesired locations. If a generator is separated
from the system, it must be resynchronized and then loaded, assuming it has not been damaged and
its prime mover has not been shut down due to the disturbance that caused the loss of synchronism.
This thing forces us to have a power system of greater reliability which work with perfection and
decrease the probability of loss of synchronism and let the generator work normally even in case of
severe faults. Therefore realizing the importance of having a good understanding of a power system,
in this chapter we will discuss about the power system stability and the excitation system consisting
of AVR (Automatic Voltage Regulator) and PSS (Power System Stabilizer).
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1.1 POWER SYSTEM ANALYSIS
Having the economic condition and reliability under consideration, 3φ synchronous generators
(known as alternators) are used for large scale power generation which is driven either by steam
turbines, hydro turbines or gas turbines. An alternator operates on the same fundamental principle of
electromagnetic induction, has 3-phase winding on the stator and a dc field winding on the rotor. The
3-phase windings, called the armature winding are placed on the stationary part called stator. The
field is placed on the rotating part of alternator, called rotor and is driven by a prime mover at
constant speed. The field requires an excitation system for its excitation; the field requires power 0.2
- 3 percent of the machine rating. The rotor may be of two types
1.Salient (or projecting) pole type
2.Non-salient (or cylindrical) pole type
Low and medium speed alternator (120-400 rpm) such as those driven by diesel engines or water
turbines have salient pole type rotors because salient field poles causes an excessive windage loss if
driven at high speed and would tend to produce noise and it cannot bear mechanical stress.
High speed alternators (1500 or 3000 rpm) are driven by steam turbines and use non-salient poles
because of mechanical robustness and gives noiseless operation at high speed and have better flux
distribution. Since steam turbines run at high speed and a frequency of 50 Hz is required, we need a
small no. of poles on the rotor of high-speed alternators. We cannot use less than 2poles and this
fixes the highest possible speed. For a frequency of 50 Hz, it is 3000 rpm. The next lower speed is
1500 rpm for a 4poles machine. Consequently, turbo alternators possess 2 or 4 poles and have small
diameter and very long axial lengths while the salient type of rotor has concentrated windings on the
poles and non-uniform air gaps. It has a relatively large no. of poles, short axial length and large
diameter. [04]
1.2 POWER SYSTEM STABILITY
Synchronous machines do not easily fall out of step under normal conditions. If a machine tends to
speed up or slow down, synchronizing forces tend to keep it in step. For more machines however
there is more possibility of losing synchronism. A major shock to the system may also lead to a loss
of synchronism for one or more machines.
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It is frequently convenient to talk about the power system in the “steady state”, such a state never
exists in the true sense. Random changes in load are taking place at all times, e.g. a fault on the
network, failure in a piece of equipment, sudden application of a major load such as a steel mill, or
loss of a line or generating unit. We may look at any of these as a change from one equilibrium state
to another. It might be tempting to say that successful operation requires only that the new state be a
“stable” state. For example, if a generator is lost, the remaining connected generators must be
capable of meeting the load demand; or if a line lost, the power it was carrying must be obtainable
from another source. Unfortunately, this view is erroneous in one important aspect; it neglects the
dynamics of the transition from one equilibrium state to another. Synchronism frequently may be lost
in that transition period, or growing oscillations may occur over a transmission line, eventually
leading to its tripping.
The stability problem is concerned with the behavior of the synchronous machines after they have
been perturbed. If the perturbation does not involve any net change in power, the machines should
return to their original state. If an unbalance between the supply and demand is created by a change
in load, in generation, or in network conditions, a new operating state is necessary. In any case all
interconnected synchronous machines should remain in synchronism if the system is stable; i.e., they
should all remain operating in parallel and at the same speed.
1.3 DEFINITION OF POWER SYSTEM STABILITY
“Power system stability is the ability of an electric power system, for a given initial operating
condition, to regain a state of operating equilibrium after being subjected to a physical disturbance,
with most system variables bounded so that practically the entire system remains intact.”
[IEEE/CIGRE Joint Task Force on Stability Terms and Definitions]
The power system is a highly nonlinear system that operates in a constantly changing environment;
loads, generator outputs and key operating parameters change continually. When subjected to a
disturbance, the stability of the system depends on the initial operating condition as well as the
nature of the disturbance.
Stability of an electric power system is thus a property of the system motion around an equilibrium
set, i.e., the initial operating condition. In an equilibrium set, the various opposing forces that exist in
the system are equal instantaneously (as in the case of equilibrium points) or over a cycle.
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Power systems are subjected to a wide range of disturbances, small and large. Small disturbances in
the form of load changes occur continually; the system must be able to adjust to the changing
conditions and operate satisfactorily. It must also be able to survive numerous disturbances of a
severe nature, such as a short circuit on a transmission line or loss of a large generator. A large
disturbance may lead to structural changes due to the isolation of the faulted elements. [5]
At an equilibrium set, a power system may be stable for a given (large) physical disturbance, and
unstable for another. It is impractical and uneconomical to design power systems to be stable for
every possible disturbance. The design contingencies are selected on the basis they have a reasonably
high probability of occurrence. Hence, large-disturbance stability always refers to a specified
disturbance scenario. A stable equilibrium set thus has a finite region of attraction; the larger the
region, the more robust the system with respect to large disturbances. The region of attraction
changes with the operating condition of the power system. The generator power can be expressed as:
1.4 CLASSIFICATION OF STABILITY
1.4.1 Voltage Stability
Voltage stability is concerned with the ability of a power system to maintain steady voltages at all
buses in the system after being subjected to a disturbance from a given initial operating condition.
Instability that may result occurs in the form of a progressive fall or rise of voltages of some buses. A
possible outcome of voltage instability is loss of load in an area, or tripping of transmission lines and
other elements by their protection equipment leading to cascading outages.
1.4.2 Frequency Stability
Frequency stability is concerned with the ability of a power system to maintain steady frequency
within a nominal range following a severe system upset resulting in a significant imbalance between
generation and load. It depends on the ability to restore balance between system generation and load,
with minimum loss of load. Instability that may result occurs in the form of sustained frequency
swings leading to tripping of generating units and/or loads.
1.4.3 Rotor Angle Stability
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Rotor angle stability is concerned with the ability of interconnected synchronous machines of a
power system to remain in synchronism after being subjected to a disturbance from a given initial
operating condition. It depends on the ability to maintain/restore equilibrium between
electromagnetic torque and mechanical torque of each synchronous machine in the system.
Instability that may result occurs in the form of increasing angular swings of some generators leading
to their loss of synchronism with other generators
Fig 1.1: Classification Of Power System Stability
1.5 TRANSIENT
STABILITY
Transient stability analysis is
primarily concerned with the
immediate effects of transmission
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line disturbances on generator synchronism. Fig.1.2 illustrates the typical behavior of a generator in
response to a fault condition. Starting from the initial operating condition (point 1), a close-in
transmission line fault causes the generator electrical output power PE to be drastically reduced. The
resultant difference between electrical power and mechanical turbine power causes the generator
rotor to accelerate with respect to the system, increasing the power angle (point 2). When the fault is
cleared, the electrical power is restored to a level corresponding to the appropriate point on the
power-angle curve (point 3). Clearing the fault necessarily removes one or more transmission
elements from service and at least temporarily weakens the transmission system. For simplicity, this
effect is not shown in Fig.1.2.
After clearing the fault, the electrical power output of the generator becomes greater than the turbine
power. This causes the unit to decelerate (point 4), reducing the momentum the rotor gained during
the fault. If there is enough retarding torque after fault clearing to make up for
the acceleration during the fault, the generator will be transiently stable on the first swing and will
move back toward its operating point in approximately 0.5 second from the inception of the fault. If
the retarding, torque is insufficient, the power angle will continue to increase until
Synchronism with the power system is lost. [IEEE TUTORIAL COURSE POWER SYSTEM STABILIZATION
VIA EXCITATION CONTROL] [06].
Excitation system forcing during and following the fault attempts to increase the electrical power
output by raising the generator internal voltage Eq, thus increasing PMax. Fast and powerful excitation
systems can improve transient stability, although the effect is limited due mainly to the large field
inductance of the generator which prevents a sudden change in E‟q for a sudden increase in exciter
output voltage. The steady-state stability refers to the ability of a power system to maintain
synchronism at all points for incremental slow-moving changes in power output of units or power
transmission facilities. Steady-state stability a small signal phenomenon is governed by the
synchronizing coefficient. Transient stability a large signal phenomenon is also governed by the
synchronizing coefficient. A fast acting, high gain AVR in general increases the synchronizing
coefficient but may decrease the damping coefficient. Thus a high gain AVR helps the steady state
and transient stabilities but may reduce the oscillatory stability. In order to damp out the oscillations
of rotor PSS (Power System Stabilizer) is used.
1.6 SWING EQUATION
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Let angular displacement = θ
Angular velocity, ω = dθ/dt radians/second
Angular acceleration, α = dω/dt = d2θ/dt
2 radians/second
2
Power developed, P = Tω watts where T is torque in N-m
Angular momentum, M = IωJ J-s/radian
Where I is moment of inertia in kg-m2
or J-s2/radian
2
Under normal working, the relative position of the rotor axis and the stator magnetic field axis is
fixed. The angle between the two is called load angle(or torque angle)δ, which upon the loading of
the machine. Larger the loading, larger the load angle(δ). In case load is added or removed from the
shaft of the synchronous machine, the rotor will decelerates or accelerates accordingly with respect
to the synchronously rotating stator field. The equation giving the relative motion of the rotor (load
angle δ) with respect to the stator field as a function of time is called the sing equation.
It is obvious that any difference between the input and output torques will cause the acceleration or
retardation of the rotor depending whether the input torque is greater than output torque or otherwise.
Accordingly for a generator
TAG = TS - TE
Where TAG is the net torque causing acceleration of the rotor and will be positive if TS > TE .
A similar relation holds good when expressed in terms of power, i.e. ,
PAG = PS - PE
Where PAG is the accelerating power
PAG = TAG ω = Iαω = Mα
Since the angular position θ of the rotor is continually varying with time, it is more convenient to
measure the angular position and velocity with respect to a synchronously rotating axis.
Angular displacement θ with respect to time, t can be expressed as
Θ = ωs t + δ
Differentiating with respect to time t, we have
dθ/dt = ωs + dδ/dt
d2θ/dt
2 = d
2δ/dt
2
since, M α = PAG
by substituting α = d2θ/dt
2 = d
2δ/dt
2 and PAG = PS - PE in above equation
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M d2δ/dt
2 = PS - PE
The above equation is called the swing equation. The angle δ is the difference between the internal
angle of the machine and the angle of the synchronously rotating axis which in this case corresponds
to the infinite bus.
1.7 EQUAL AREA CRITERION
Starting with swing equation
M d2δ/dt
2 = PS - PE = PA
Multiplying both sides dδ/dt, we have
M d2δ/dt
2 dδ/dt = PS dδ/dt - PE dδ/dt = dδ/dt (PS - PE)
½ M d/dt(dδ/dt)2
= (PS - PE) dδ/dt
Re-arranging multiplying by dt and integrating, we have
(dδ/dt)2
= δo∫δ 2(PS - PE)/M dδ
dδ/dt = [ δo∫
δ 2(PS - PE)/M dδ]
1/2
where δo is the torque angle at which the machine is operating while running at synchronous speed
under normal consitions. Under the above conditions the torque angle was not changing.
i.e. before the disturbance dδ/dt = 0. Also if the system has transient stability the machine will again
operate at synchronous speed after the disturbance. i.e. dδ/dt = 0.
Now let us consider a generator connected to
the infinite bus through a single line. Let PS
be the power supplied by generator to the
infinite bus in normal conditions and let δo
be the corresponding load angle. Now say
there occur a 3-phase fault on the line
temporarily. The power angle curve will
correspond to horizontal axis because
output power becomes zero. If the breaker
recloses after some time corresponding to
clearing angle δc when the fault vanishes, the
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output will be more than the input and therefore the rotor decelerates. Finally, if the clearing angle δc
is such that A1 = A2. The system becomes stable.
1.8 EXCITATION SYSTEM
An excitation system is required to provide the necessary field current to the rotor winding of a
synchronous machine. The availability of excitation at all times is of paramount importance. Loss of
excitation of a unit on the bus results in a more serious disturbance than that resulting from dropping
of alternator from the bus, as the remaining units must not only pick up the load dropped but supply
the large reactive current drawn by the unexcited alternator. In the view of this an excitation system
with better reliability is preferable, even if the initial cost is more.
The main requirements of an excitation system are reliability under all conditions of service,
simplicity of control, ease of maintenance, stability and high transient response.
The amount of excitation required depends on the load current, load power factor, and speed of the
machine. Larger the load currents, lower the speed and lagging power factors, more the excitation
required.
The excitation system can be broadly classified as
1. DC excitation system
2. AC excitation system
3. Static excitation system
1.8.1 DC excitation system
In dc excitation system the system has two exciters-the main exciter (a separately excited dc
generator providing the field current to the alternator) and a pilot exciter (a compound wound self
excited dc generator providing the field current to the main exciter). The main and pilot exciters can
be either driven by the main shaft (directly or through gearing) or separately driven by a motor.
Direct driven exciters are usually preferred as these preserve the unit system of operation and the
excitation is not affected by external disturbances. The voltage rating of main exciter is around 400V
and its capacity is about 0.5% of the capacity of the alternator. [07]
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1.8.1. AC excitation system
An ac excitation system consists of an ac generator and thyristor rectifier bridge directly connected to
the main alternator shaft. It eliminates the commutator, the main alternator field collector rings and
some other connections. The main exciter may be either self excited or separately excited. A rotating
thyristor excitation system employs self excited main exciter whereas the brushless excitation system
employs a separately excited main exciter.
1.8.1.1 Rotating thyristor excitation system
The rotating thyristor excitation system consists of an ac exciter having a rotating armature and a
stationary field. The output of the exciter is rectified by a full-wave thyristor bridge rectifier circuit
and supplied to the field winding of the main alternator. The field winding of the exciter is also
supplied from its output through another rectifier circuit.
1.8.1.2 Brushless excitation system
The brushless excitation system consists of an alternator, rectifier, main exciter and a permanent
magnet generator pilot exciter. Both the main and pilot exciters are driven directly from the main
shaft. The main exciter has a stationary field and a rotating armature directly connected, through
silicon rectifiers, to the field of the main alternator. The pilot exciter is shaft driven permanent
magnet generator having rotating permanent magnets attached to the shaft and a 3-phase full-wave
phase controlled thyristor bridges. This system eliminates the use of commutator, collectors and
brushes and has a short time constant and a response time of less than 0.1 second.
1.8.2 Static excitation system
In static excitation system the excitation supply is taken from the alternator itself through a 3-phase
star/delta connected, oil immersed, forced air cooled, indoor type step down transfer and a rectifier
system employing mercury-arc rectifiers or silicon controlled rectifiers. The star-connected primary
is connected to the alternator bus, the delta-connected secondary supplies power to the rectifier
system and the delta-connected tertiary feeds power to grid control circuits and other auxiliary
equipment. The rectifiers are connected in parallel to provide sufficient current carrying capacity.
This system has a very response time (about 20 milliseconds) and provides excellent dynamic
performance SCRs are ideally suited for a static excitation system because they have high speed of
response, high power gain and can be easily paralleled. The advantage of the static excitation system
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is elimination of exciter windage loss and commutator bearing and winding maintenance resulting in
reduced operating cross and electronic speed response. The face that in static excitation the voltage is
proportional to the speed, affords a major advantage in load rejection.
1.9 Automatic Voltage Regulator (AVR)
Automatic voltage regulators consist of two units: the measuring unit and the regulating Unit. The
function of the measuring unit is that of the detecting a change in the input or output voltage of
the automatic voltage regulator and producing a signal to operate the Regulating unit. The
purpose of the regulating unit is that of acting, under the measuring unit, in such manner as
to correct the output voltage of the regulator to, as near as possible, a constant or predetermined
value. In some cases, a unit is required to control the regulating unit. This additional unit needed is
known as the controlling unit. It is some times necessary to introduce another unit in order to
prevent hunting. Hunting is a continual fluctuation or oscillation of the voltage regulator. This
unit is known as anti-hunting unit [08].
1.9.1Types of Measuring Unit
In all measuring units used in automatic voltage regulators, there must always be some
reference, which the voltage is compared with. The difference will be translated into the output
signal of the measuring unit. The accuracy of the measuring unit is directly dependent on the
accuracy of the reference. Therefore, accuracy is the most important criteria for choosing a
reference. Measuring units may be divided basically into two types: Discontinuous-control type
of measuring unit and Continuous-control type of measuring unit. The measuring unit can be
any one of three classes: Electro-mechanical, Electrical and a combination of electrical and
electro-mechanical.[19]
1.9.1.1 Discontinuous-control Type of measuring Unit
The function of this type of measuring unit is to produce a constant variation in the signal if
the voltage goes outside certain limits but to not produce any signals so long as the voltage is within
these limits.
1.9.1.2 Continuous-control Type of Measuring Unit
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In this type of measuring unit, the output must be approximately proportional to the change
of voltage from its correct value. In order for the regulating unit to produce an output other than
normal, a continuous signal must be provided by the measuring unit
1.9.2 Types of Regulating Unit
Devices, which may be operated as regulating units, can usually be used as controlling or
sub-controlling units. Similarly to the measuring unit, the regulating unit may be divided
basically into two types: Discontinuous-control type of regulating unit and Continuous-control
type of regulating unit. Each type of measuring unit consists of two classes: Electro-mechanical
and Electrical.
1.9.2.1 Discontinuous-control Type of Regulating Unit
In this type, the rate of change of voltage is often constant during the whole of the change. When
the signal from the measuring unit ceases, the regulating unit remains at its new setting independent
of any signal.
1.9.2.2 Continuous-control Type of Regulating Unit
In this type, the change of voltage produced by the regulating unit must be approximately
proportional to the signal from the measuring unit. In order for the output of the regulating unit to be
other than normal, a continuous signal must be provided by the measuring unit.
1.10 Purpose of AVR for stability
Excitation system (AVR) forcing during and following the fault attempts to increase the electrical
power output by raising the generator internal voltage Eq, thus increasing PMax. Fast and powerful
excitation systems can improve transient stability, although the effect is limited due mainly to the
large field inductance of the generator which prevents a sudden change in E‟q for a sudden increase
in exciter output voltage. The steady-state stability refers to the ability of a power system to maintain
synchronism at all points for incremental slow-moving changes in power output of units or power
transmission facilities. Steady-state stability a small signal phenomenon is governed by the
synchronizing coefficient. Transient stability a large signal phenomenon is also governed by the
synchronizing coefficient. A fast acting, high gain AVR in general increases the synchronizing
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coefficient but may decrease the damping coefficient. Thus a high gain AVR helps the steady state
and transient stabilities but may reduce the oscillatory stability.
1.11 POWER SYSTEM STABILIZER
In present-day systems, a machine being transiently stable on the first swing does not guarantee that
it will return to its steady-state operating point in a well-damped manner and thus be stable in an
oscillatory mode. Significant improvement in transient stability has been achieved through very
rapid fault detection and circuit breaker operation. System effects such as sudden changes in load,
short circuits, and transmission line switching not only introduce transient disturbances on machines,
but also may give rise to less stable operating conditions. For example, if a transmission line must be
tripped due to a fault, the resulting system may be much weaker than that existing prior to the fault
and oscillatory instability may result.
One solution to improve the dynamic performance of this system and large scale systems in general
could be to add more parallel transmission lines in order to lower the reactance between the
generator and the load center. Such a solution may be quite costly as well as unfeasible to
implement. In the presence of a weak transmission system, control means, such as a power system
stabilizer (PSS), acting through the voltage regulator, can provide significant stabilization of such
oscillations if properly implemented.
Since a fast acting, high gain AVR in general increases the transient stability but may decrease the
damping, it seems reasonable that a supplementary signal to the voltage regulator can increase
damping by sensing some additional measurable quantity. In doing so, not only can the undamping
effect of voltage regulator control be cancelled, but damping can be increased so as to allow
operation even beyond the steady state stability limit. This is the basic idea behind the power system
stabilizer (PSS). The supplementary signal of a PSS may be derived from such quantities as changes
in shaft speed (Δω), generator electrical frequency (Δf)), or electrical power (ΔPE). There are a
number of considerations in selecting the right input quantity.
The speed and frequency inputs have been widely used. The trend is more towards PSS design based
on integral of accelerating power. This type of PSS provides satisfactory damping
Despite their relative simplicity, power system stabilizers may be one of the most misunderstood and
misused pieces of generator control equipment. The ability to control synchronous machine angular
stability through the excitation system was identified with the advent of high speed exciters and
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continuously acting voltage regulators. By the mid-1960‟s several authors had reported successful
experience with the addition of supplementary feedback to enhance damping of rotor oscillations.
The function of a PSS is to add damping to the unit‟s characteristic electromechanical oscillations.
This is achieved by modulating the generator excitation so as to develop components of electrical
torque in phase with rotor speed deviations. The PSS thus contributes to the enhancement of small-
signal stability of power systems
Early PSS installations were based on a variety of methods to derive an input signal that was
proportional to the small speed deviations characteristic of electromechanical oscillations. After
years of experimentation the first practical integral-of accelerating-power based PSS units were
placed in service. This design provided numerous advantages over earlier speed-based units and
forms the basis for the PSS implementation that is used in most units installed in North America.
This design is now a requirement in many Reliability Regions within North America and has been
modeled in the IEEE standards as the PSS2A and PSS2B structures.[20]
1.11.1OVERVIEW OF PSS STRUCTURES
Shaft speed, electrical power and terminal frequency are among the commonly used input signals to
the PSS. Alternative forms of PSS have been developed using these signals. Here we describe the
practical considerations that have influenced the development of each type of PSS as well as its
advantages and limitations.
1.11.1.1 Speed-Based (Dw) Stabilizer
Stabilizers employing a direct measurement of shaft speed have been used successfully on hydraulic
units since the mid-1960s.
In early designs on vertical units, the stabilizer‟s input signal was obtained using a transducer
consisting of a toothed-wheel and magnetic speed probe supplying a frequency-to-voltage converter.
Among the important considerations in the design of equipment for the measurement of speed
deviation is the minimization of noise caused by shaft run-out (lateral movement) and other causes
Conventional filters could not remove such low-frequency noise without affecting the
electromechanical components that were being measured. Run-out compensation must be inherent
to the method of measuring the speed signal. In some early applications, this was achieved by
summing the outputs from several pick-ups around the shaft, a technique that was expensive and
lacking in long-term reliability.
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The original application of speed-based stabilizers to horizontal shaft units (e.g. multi-stage 1800
RPM and 3600 RPM turbo-generators) required a careful consideration of the impact on torsional
oscillations. The stabilizer, while damping the rotor oscillations, could reduce the damping of the
lower-frequency torsional modes if adequate filtering measures were not taken. In addition to careful
pickup placement at a location along the shaft where low-frequency shaft torsionals were at a
minimum, electronic filters were also required in the early applications.
While stabilizers based on direct measurement of shaft speed have been used on many thermal units,
this type of stabilizer has several limitations. The primary disadvantage is the need to use a torsional
filter. In attenuating the torsional components of the stabilizing signal, the filter also introduces a
phase lag at lower frequencies. This has a destabilizing effect on the “exciter mode,” thus imposing a
maximum limit on the allowable stabilizer gain. In many cases, this is too restrictive and limits the
overall effectiveness of the stabilizer in damping system oscillations. In addition, the stabilizer has to
be custom-designed for each type of generating unit depending on its torsional characteristics. The
integral-of accelerating power-based stabilizer, referred to as the Delta-P-Omega (ΔPω) stabilizer
throughout this section, was developed to overcome these limitations.
1.11.1.2 Frequency-Based (Δf) Stabilizer
Historically terminal frequency was used as the input signal for PSS applications at many locations.
Normally, the terminal frequency signal was used directly. In some cases, terminal voltage and
current inputs were combined to generate a signal that approximates the machine‟s rotor speed.
One of the advantages of the frequency signal is that it is more sensitive to modes of oscillation
between large areas than to modes involving only individual units, including those between units
within a power plant. Thus it seems possible to obtain greater damping contributions to these
“interarea” modes of oscillation than would be obtainable with the speed input signal. Frequency
signals measured at the terminals of thermal units contain torsional components. Hence, it is
necessary to filter torsional modes when used with steam turbine units. In this respect frequency-
based stabilizers have the same limitations as the speed-based units. Phase shifts in the ac voltage,
resulting from changes in power system configuration, produce large frequency transients that are
then transferred to the generator‟s field voltage and output quantities. In addition, the frequency
signal often contains power system noise caused by large industrial loads such as arc furnaces.
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1.11.1.3 Power-Based (ΔP) Stabilizer
Due to the simplicity of measuring electrical power and its relationship to shaft speed, it was
considered to be a natural candidate as an input signal to early stabilizers. The equation of motion
for the rotor can be written as follows:
1.11.1.4 Integral-of-Accelerating Power (ΔPω) Stabilizer
The limitations inherent in the other stabilizer designs led to the development of stabilizers that
measure the accelerating power of the generator .
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CHAPTER # 02
Literature Review
ARTIFICIAL NEURAL NETWORK
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2 ARTIFICIAL NEURAL NETWORK
ABOUT THE CHAPTER:
One of the leading researches in the field of NN describes them with the property they don‟t possess.
“They don’t apply the principle of digital or logic circuit. Neither the neurons nor the synapses are
bi stable memory elements. No machine instruction nor is control codes occur in NN, their working
is not algorithmic. And on the highest level the nature of information processing is different from
that of digital computer.”
ANN provides a powerful approach towards dealing with chaos and randomness. It has the inherent
feature of dealing with incomplete random and disordered information. They have the ability to
learn, to adapt them to the changing environment. Further NN have the remarkable ability to forecast
and predict future value and may thus be very efficiently used here to predict future disorders.
Realizing the importance of neural network, in this chapter we will have an insight about what
exactly are NN, how they work. And also we will discuss about the architecture and learning
algorithm of the NN used in this project.
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2.1 ARTIFICIAL INTELLIGENCE & NEURAL NETWORK
Artificial is the intelligence of machines and the branch of computer science which aims to create it.
Major AI textbooks define the field as "the study and design of intelligent agents, where an
intelligent agent is a system that perceives its environment and takes actions which maximize its
chances of success. John McCarthy, who coined the term in 1956, defines it as "the science and
engineering of making intelligent machines.
The field was founded on the claim Intelligence (AI) that a central property of human beings,
intelligence can be so precisely described that it can be simulated by a machine. This raises
philosophical issues about the nature of the mind and limits of scientific hubris, issues which have
been addressed by myth, fiction and philosophy since antiquity. Artificial intelligence has been the
subject of breathtaking optimism, has suffered stunning setbacks and today, has become an essential
part of the technology industry, providing the heavy lifting for many of the most difficult problems
in computer science.
Neural Network is a branch of Artificial Intelligence and it can be defined as a system based on the
operation of biological neural networks, in other words, is an emulation of biological neural system.
The utility of artificial neural network models lies in the fact that they can be used to infer a function
from observations. This is particularly useful in applications where the complexity of the data or task
makes the design of such a function by hand impractical.
2.2 HISTORICAL MOTIVATION
The history of ANNs begins with the pioneering work of McCulloch and Pitts who designed very
simple artificial neurons in 1943. The neurons were binary, summing their unweighted inputs and
performing a threshold operation. ANNs sprang into exercise around the same time as the first
computers, and it is widely known that John Von Neumann, instrumental in the construction of the
modern serial computer we heavily influenced by the work of McCulloch and Pitts.
In 1949 Donald Hebb's famous book The Organization of Behavior was published. In this book,
Hebb postulated a plausible qualitative mechanism for learning at cellular level in brains. In 1951,
Minsky constructed the first neurocomputer, the Snark [09]. The neurocomputer did operate
successfully from a technical standpoint (it adjusted its weights automatically), but never actually
carried out any particular interesting information-processing function. Nonetheless, it provided
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design ideas that were used later by other-investigators
In 1958 Rosenblatt developed his neurocomputer, the perceptron. He proposed learning rule, the
perceptron convergence theorem.
In 1960, Window and Hoff [Window and Hoff, (1960), Window and Lehr, (1990)] introduced the
least square (LMS) algorithm and used it to formulate the ADALINE (adaptive linear element). The
LMS algorithm is still in widespread use, particularly in the field of adaptive signal processing.
About the same time Minsky and Papert began promoting the field of artificial intelligence (Al) at
the expenses of ANN research. In this book they mathematically proved that perceptrons were not
able to compute certain essential computer predictions like the exclusive OR Boolean function.
From the late 1960s to the early 1980s, research on ANN was almost non-existent,
The introduction of self organizing maps by Kohonen in 1982, simulated annealing by Kirkpatrick et
al. in 1983 and Boltzmann learning by Ackley et al in 1985 further popularized the field of ANNs.
The real breakthrough in ANN research came with the discovery of the back-propagation algorithm,
Although it was discovered in 1974 [Werbos,(1974)[, it was not until the mid 1980s that the back
propagation technique became widely publicized([Rumelhart and McClelland , (1986a,1986b)]. This
algorithm still dominates the neural dominates the neural network literature and thousands of
academic , industrial and government researchers report the results of back probation stimulations
and application at technical conference and in journal ever year In 1987, the first conference on
neural networks, The IEEE International Conference on Neural Networks (1700 participants) was
held in San Diego USA and the International Neural Network Society (INNS) was formed. In 1988
the INNS journal Neural Networks was formed, followed by neural computation in 1989, the IEEE
transaction on Neural Networks in 1990 and subsequently many others
In 1988 Broom head and Lowe introduced radial basis function (RBF) networks to the neural
network community. The theory of these networks was further enriched by Pogio and girosi in 1990.
A generalization of RBF networks, known as the Local Model Networks (LMNs) was introduced by
Johansen and Foss in 1992-93 [Johansen and Foss, (1992a,1992b,1992c,1993)]and was further
popularized by Murray-Smith(1994)
The history of NNs can be divided into it) First attempts when there were some initial simulations
using formal logic and then using computer simulations [Hagan and Beal‟s(1966)], ii) Promising and
emerging technology this is the time when psychologists and engineers also contributed to the
progress of NN simulation[Kasabov(1966)]. iii) Period of frustration and disrepute when Minsky
and Papert wrote a book in which they generalized and limitations of single layer perceptron systems
due to this discouraging remarks, funding of NN research was eliminated [Hertz, Krogh and
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Palmer(1977)]. iv) Innovation here due to some public interest research work takes boost and new
era starts. During this period several paradigms were generated [Rumehart (1997), Hinton (1998) and
Haykin Simon(1999)]. Reemerging late 1970 to 1980 was important for this research field
comprehensive books, conference and industry based group pf people came forwarded [Searle
(2000)]. vi) Today neurally based chips are emerging and applications to complex problem
developing. Clearly, today is a period of transition of NN technology, [ Reed and Mark (2001),
Zurada (2002)]
Indeed the above developments have made very important contribution to the success of ANNs.
However, there are also other reasons for the recent interest in ANNs,
One is the desire to build a new breed of pIowerful computers that can solve problems that are
proving to be extremely difficult for current digital computers, and yet are easily done by human in
everyday life. Cognitive tasks like understanding spoken and written languages, image processing ,
retrieving contextually appropriate information from memory are examples of such task.
Another is the benefit that neuroscience can obtain from ANN research. New network architecture
are constantly being developed and new concepts and theories being proposed to explain the
operations of these architectures. Many of these developments can be used by neuroscientists are
new paradigms for building functional concepts and model of elements of the brain.
Many ANN architectures have been proposed. These can be roughly divided into three large
categories: feed forward ( multilayer) neural networks, feedback neural networks and cellular neural
networks. This thesis is solely concerned with the feed forward neural networks. Therefore , other
types of ANNs will not be described in this chapter.
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2.3 DEFINITION
Work on artificial neural networks, commonly referred to as "neural networks," has been motivated
right from its inception by the recognition that the human brain computes in an entirely different way
from the conventional digital computer. The brain is a highly complex, nonlinear, and parallel
computer (information-processing system). It has the capability to organize its structural
constituents, known as neurons, so as to perform certain computations (e.g., pattern recognition,
perception, and motor control) many times faster than the fastest digital computer in existence today.
Consider, for example, human vision, which is an information-processing task (Marr, 1982; Levine,
1985; Churchland and Sejnowski, 1992). It is the function of the visual system to provide a
representation of the environment around us and, more important, to supply the information we need
to interact with the environment. To be specific, the brain routinely accomplishes perceptual
recognition tasks (e.g., recognizing a familiar face embedded in an unfamiliar scene) in
approximately 100-200 ms, whereas tasks of much lesser complexity may take days on a
conventional computer.
For another example, consider the sonar of a bat. Sonar is an active echo-location system. In addition
to providing information, about how far away a target (e.g., a flying insect) is, a bat sonar conveys
information about the relative velocity of the target, the size of the target, the size of various features
of the target, and the azimuth and elevation of the target. The complex neural computations needed
to extract all this information from the target echo occur within a brain the size of a plum. Indeed, an
echo-locating bat can pursue and capture its target with a facility and success rate that would be the
envy of a radar or sonar engineer.
Neural network may be defined as
A neural network is a massively parallel distributed processor made up of simple processing units,
which has a natural propensity for storing experiential knowledge and making it available for use. It
resembles the brain in two respects:
1. Knowledge is acquired by the network from its environment through a learning process.
2. Interneuron connection strengths, known as synaptic weights, are used to store the acquired
knowledge.[10]
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2.4 BENEFITS OF NEURAL NETWORK
It is apparent that a neural network derives its computing power through, first, its massively parallel
distributed structure and, second, its ability to learn and therefore generalize. Generalization refers to
the neural network producing reasonable outputs for inputs not encountered during training (learning).
These two information-processing capabilities make it possible for neural networks to solve complex
(large-scale) problems that are currently intractable. In practice, however, neural networks cannot
provide the solution by working individually. Rather, they need to be integrated into a consistent
system engineering approach. Specifically, a complex problem of interest is decomposed into a number
of relatively simple tasks, and neural networks are assigned a subset of the tasks that match their
inherent capabilities. It is important to recognize, however, that we have a long way to go (if ever)
before we can build a computer architecture that mimics a human brain.
The use of neural networks offers the following useful properties and capabilities:
2.4.1 Nonlinearity.
An artificial neuron can be linear or nonlinear. A neural network, made up of an interconnection
of nonlinear neurons, is itself nonlinear. Moreover, the nonlinearity is of a special kind in the sense
that it is distributed throughout the network. Nonlinearity is a highly important property, particularly
if the underlying physical mechanism responsible for generation of the input signal (e.g., speech
signal) is inherently nonlinear.
2.4.2 Input—Output Mapping.
A popular paradigm of learning called learning with a teacher or supervised learning involves
modification of the synaptic weights of a neural network by applying a set of labeled training
samples or task examples. Each example consists of a unique input signal and a corresponding
desired response. The network is presented with an example picked at random from the set, and the
synaptic weights (free parameters) of the network are modified to minimize the difference between
the desired response and the actual response of the network produced by the input signal in
accordance with an appropriate statistical criterion.
2.4.3 Adaptivity.
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Neural networks have a built-in capability to adapt their synaptic weights to changes in the
surrounding environment. In particular, a neural network trained to operate in a specific
environment can be easily retrained to deal with minor changes in the operating environmental
conditions.
2.4.4 Fault Tolerance.
.A neural network, implemented in hardware form, has the potential to be inherently fault tolerant,
or capable of robust computation, in the sense that its performance degrades gracefully under
adverse operating conditions. For example, if a neuron or its connecting links are damaged, recall of
a stored pattern is impaired in quality. However, due to the distributed nature of information stored
in the network, the damage has to be extensive before the overall response of the network is
degraded seriously.
2.5 RESEMBLENCE WITH THE HUMAN BRAIN
Artificial neural networks emerged after the introduction of simplified neurons by McCulloch and
Pitts in 1943 [11]. These neurons were presented as models of biological neurons and as conceptual
components for circuits that could perform computational tasks. The basic model of the neuron is
founded upon the functionality of a biological neuron. "Neurons are the basic signaling units of the
nervous system" and "each neuron is a discrete cell whose several processes arise from its cell
body".
Fig. 2.1: Block diagram representation of nervous system
The neuron has four main regions to its structure. The cell body, or soma, has two offshoots from it,
the dendrites, and the axon, which end in presynaptic terminals. The cell body is the heart of the
cell, containing the nucleus and maintaining protein synthesis. A neuron may have many dendrites,
which branch out in a treelike structure, and receive signals from other neurons. A neuron usually
only has one axon which grows out from a part of the cell body called the axon hillock. The axon
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conducts electric signals generated at the axon hillock down its length. These electric signals are
called action potentials. The other end of the axon may split into several branches, which end in a
presynaptic terminal. Action potentials are the electric signals that neurons use to convey
information to the brain. All these signals are identical. Therefore, the brain determines what type of
information is being received based on the path that the signal took. The brain analyzes the patterns
of signals being sent and from that information it can interpret the type of information being
received. Myelin is the fatty tissue that surrounds and insulates the axon. Often short axons do not
need this insulation. There are uninsulated parts of the axon. These areas are called Nodes of
Ranvier. At these nodes, the signal traveling down the axon is regenerated. This ensures that the
signal traveling down the axon travels fast and remains constant (i.e. very short propagation delay
and no weakening of the signal). The synapse is the area of contact between two neurons. The
neurons do not actually physically touch.
Fig. 2.2: The pyramidal cell
The neuron sending the signal is called the presynaptic cell and the neuron receiving the signal is
called the postsynaptic cell. The signals are generated by the membrane potential, which is based on
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the differences in concentration of sodium and potassium ions inside and outside the cell membrane.
Neurons can be classified by their number of processes (or appendages), or by their function. If they
are classified by the number of processes, they fall into three categories. Unipolar neurons have a
single process (dendrites and axon are located on the same stem), and are most common in
invertebrates. In bipolar neurons, the dendrite and axon are the neuron's two separate processes.
Bipolar neurons have a subclass called pseudo-bipolar neurons, which are used to send sensory
information to the spinal cord. Finally, multipolar neurons are most common in mammals.
Examples of these neurons are spinal motor neurons, pyramidal cells and Purkinje cells (in the
cerebellum). If classified by function, neurons again fall into three separate categories. The first
group is sensory, or afferent, neurons, which provide information for perception and motor
coordination. The second group provides information (or instructions) to muscles and glands and is
therefore called motor neurons. The last group, interneuronal, contains all other neurons and has two
subclasses. One group called relay or projection interneurons have long axons and connect different
parts of the brain. The other group called local interneurons are only used in local circuits.
2.6 MODELS OF A NEURON
A neuron is an information-processing unit that is fundamental to the operation of a neural network.
The block diagram below shows the model of a neuron, which forms the basis for designing
(artificial) neural networks. Here we identify three basic elements of the neuronal model:
1. A set of synapses or connecting links, each of which is characterized by a weight or strength
of its own. Specifically, a signal xj at the input of synapse j connected to neuron k is multiplied
by the synaptic weight wkj. It is important to make a note of the manner in which the
subscripts of the synaptic weight wkj are written. The first subscript refers to the neuron in
question and the second subscript refers to the input end of the synapse to which the weight
refers. Unlike a synapse in the brain, the synaptic weight of an artificial neuron may lie in a
range that includes negative as well as positive values.
2. An adder for summing the input signals, weighted by the respective synapses of the
neuron; the operations described here constitutes a linear combiner.
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3. An activation function for limiting the amplitude of the output of a neuron. The activation
function is also referred to as a squashing function in that it squashes (limits) the permissible
amplitude range of the output signal to some finite value.
Typically, the normalized amplitude range of the output of a neuron is written as the closed unit
interval [0, 1] or alternatively [-1, 1].
The neuronal model here also includes an externally applied bias, denoted by bk. The bias bk has the
effect of increasing or lowering the net input of the activation function, depending on whether it is
positive or negative, respectively.
In mathematical terms, we may describe a neuron k by writing the following pair of equations:
and
yk = φ (uk + bk)
Where xl, x2... xm, are the input signals; wk1, wk2… Wkm are the synaptic weights of neuron k; uk is
the linear combiner output due to the input signals; bk is the bias; φ (•) is the activation function;
and yk is the output signal of the neuron. The use of bias bk has the effect of applying an affine
transformation to the output uk of the linear combiner in the model, as shown by
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v k = uk + bk
In particular, depending on whether the bias bk is positive or negative, the relationship between the
induced local field or activation potential vk of neuron k and the linear combiner output uk is
modified.
The bias bk is an external parameter of artificial neuron k. We may account for its presence as
follows:
and
yk = φ (vk)
In Eq. (1.4) we have added a new synapse. Its input is
xo = + 1
And its weight is
Wk0 = bk
We may therefore reformulate the model of
neuron k as in figure below. In this figure, the
effect of the bias is accounted for by doing
two things: (1) adding a new input signal
fixed at +1, and (2) adding a new synaptic weight equal to the bias bk .
2.7 Types of Activation Function
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The main types of
Activation Function are
a. Threshold Function.
b. Piecewise-linear Function
c. Sigmoid Function a. Threshold Function b. Piecewise-linear Function c. Sigmoid Function
Fig. 2.3: a. Threshold Function
b. Piecewise-linear Function
c. Piecewise-linear Function
2.8 NETWORK ARCHITECTURES
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The manner in which the neurons of a neural network are structured is intimately linked with the
learning algorithm used to train the network. We may therefore speak of learning algorithms (rules)
used in the design of neural networks as being structured. In general, we may identify three
fundamentally different classes of network architectures:
2.8.1 Single-Layer Feed forward Networks
In a layered neural network the neurons are organized in the
form of layers. In the simplest form of a layered
network, we have an input layer of source nodes that
projects onto an output layer of neurons (computation
nodes), but not vice versa. In other words, this network is
strictly a feed forward or acyclic type. It is illustrated in Fig.
2.4 for the case of four nodes in both the input and
output layers. Such a network is called a single-layer
network, with the designation "single-layer" referring to the
output layer of computation nodes (neurons). We do not count
the input layer of source nodes because no computation is
performed there.
Fig.
2.4: Single Feed forward NN
2.8.2 Multilayer Feed forward Networks
The second class of a feed forward neural network distinguishes itself by the presence of one or
more hidden layers, whose computation nodes are correspondingly called hidden neurons or hidden
units. The function of hidden neurons is to intervene between the external input and the network
output in some useful manner. By adding one or more hidden layers, the network is enabled to
extract higher-order statistics. In a rather loose sense the network acquires a global perspective
despite its local connectivity due to the extra set of synaptic connections and the extra dimension of
neural interactions [12]. The ability of hidden neurons to extract higher-order statistics is
particularly valuable when the size of the input layer is large.
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The source nodes in the input layer of the network supply respective elements of the activation
pattern (input vector), which constitute the input signals applied to the neurons (computation nodes)
in the second layer (i.e., the first hidden layer). The output signals of the second layer are used as
inputs to the third layer, and so on for the rest of the network. Typically the neurons in each layer of
the network have as their inputs the output signals of the preceding layer only. The set of output
signals of the neurons in the output (final) layer of the network constitutes the overall response of the
network to the activation pattern supplied
by the source nodes in the input (first)
layer. The architectural graph in Fig. 3.5
illustrates the layout of a multilayer feed
forward neural network for the case of a
single hidden layer
The neural network in Fig. 2.5 is said to
be fully connected in the sense that every
node in each layer of the network is
connected to every other node in the adja-
cent forward layer. If, however, some of
the communication links (synaptic
connections) are missing from the
network, we say that the network is
partially connected.
Fig. 2.5: Multilayer Feed forward NN
2.8.3 Recurrent Networks
A recurrent neural network distinguishes itself from a feed forward neural network in that it has at
least one feedback loop. For example, a recurrent network may consist of a single layer of neurons
with each neuron feeding its output signal back to the inputs of all the other neurons.
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2.9 NEURAL NETWORK‟S ARCHITECTURE
The selection of a appropriate network is crucial for successful operation. The first thing to select is
whether to go for single layer or for multi layer neural network. We are using multilayer neural
network instead of single layer because single layer ANN cannot approximate all kind of functions
like XOR, whereas multilayer neural network is a Universal approximator. This is the reason of
having three layers in our architecture as shown in the figure. The first layer is the input layer,
second is the Hidden Layer and third is the output layer.
Fig 2.6: Architecture of the Neural Network
The next problem was regarding the number of elements to be used in these layers. The number of
inputs and output are same as of the trainer. Therefore we have three inputs namely direct voltage,
quardrature voltage and rotor speed deviation. These were the inputs required by the conventional
controller (Teacher) and hence are the inputs to the neural network. Also, since the output of the
conventional controller (Teacher) was only one i.e. the excitation voltage and hence it is the output
of the neural network. The next thing is to select the number of hidden neurons. There is no such
formula to find the exact number of hidden neurons required for a particular application. We
therefore selected an intermediate number of 7 which gave us satisfactory results. Going for a very
small number decreases the learning capability of the network and going for a very large number
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makes the neural network learn unimportant things from the sample or training data (Appendix A).
And it also increases the complexity which justifies our architecture.
The activation function used for the hidden layer is the sigmoid function; the reason for this is
1. The BPA requires the function to be differential at all points.
2. It limits the output of the hidden neurons between -1 to +1.
The activation function used for the output neuron is the linear transfer function (chapter 3) mainly
because the output had no numerical boundaries.
2.10 TRAINING ALGORITHM
Following are the main learning algorithms for the neural network 1. Error
correction Learning 2.
Memory based Learning 3.
Hebbian Learning 4.
Competitive Learning
Here Error correction learning (for single layer) is the one preferred for control systems and for
multilayer neural network its modified form is BACK PROPAGATION LEARNING, which is the
learning algorithm used in this project.
The main theme of this algorithm is to first calculate the error and then using Gradient Decent
method to calculate the change in weight of the neurons. And then propagating that error to the
hidden layer. For fast convergence we are using improved version of this algorithm known as
Levenberg-marquardt algorithm. Also, we are incorporating an important property of momentum
which helps us not to be stuck in local minima.
2.10.1 WORKING OF BACK PROPAGATION
During back-propagation training, a network passes each input pattern through the hidden layer to
generate a result at each output node. It then subtracts the actual result from the target result to find
the output-layer errors. Next the network passes the derivatives of the output errors back to the
hidden layer using the original weighted connections. This backward propagation of errors gives the
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algorithm its name. Each hidden node then calculates the weighted sum of the back-propagated
errors to find its indirect contribution to the known output errors.
After each output and hidden node finds its error value, the node adjusts its weights to reduce its
error. The equation that changes the weights is designed to minimize the sum of the network‟s
squared errors. This minimization has an intuitive geometric meaning. To see it, all possible sets of
weights must be plotted against the corresponding sum-of-squares errors. The result in an error sum
of shaped like a bowl, whose bottom marks the set of weights with the smallest sum-of-squared
error. Finding the bottom of the bowl- that is the best set of weights is the goal during training.
Back-propagation achieves this goal by calculating the instantaneous slope of the error surface with
respect to the current weights. It then incrementally changes the weights in the direction of the
locally steepest path toward the bottom of the bowl. This process resembles rolling a ball down a hill
and is called gradient descent or steepest descent method. Steepest descent method improves the
network‟s overall accuracy as a result of the aggregate corrections during training. The relationship
of sum-of-squared errors and weights are shown inn fig. Back –propagation is in effect a procedure
for finding the weights that minimize sum-of-squares error.
Real error surfaces can have complex ravine-like features and many dent-like local minima. Since
gradient descent always follows the locally steepest path, the back-propagation algorithm can train a
network into a local minimum that it cannot escape. This effect depends on the exact path down the
gradient, which in turn depends on the initial values of the weights and other factors.
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2.11 THE BACK PROPAGATION ALGORITHM
STEP 1 Initialize Weights and Threshold:
I = no. of input nodes,
J = no. of hidden nodes,
K = no. of output nodes,
I,j,k = Loop variables
Set Wokj (0) (0 <= j <= j - 1),(0 <= k <= k - 1) and θ
ok to small random values. Here W
okj (t) is the
weight on the connection from the jth hidden unit at time t = 0 to kth output node, and θok is the
threshold value in the kth output node.
Set Wh
ji (0) (0 <= i <= I - 1),(0 <= j <= J - 1) and θhj to small random values hidden node, and θ
hj is
the threshold value in the jth hidden node.
The „h‟ & “o” superscripts refer to quantities on the hidden layer & output layer respectively.
STEP 2 Present New Input and Desired Output:
Present a continuous valued input vector xpo , xp1 , xp2 , …. , xP J-1 and specify the desired outputs yp1 ,
yp2 , …. , yP K-1 where “p” is the number of patterns in the training set. If the net used as a classifier
then all desired.
Outputs are typically set to zero except for that corresponding to the class the input is from. That
desired output is 1. The input could be new on each trial or samples from a training set could be
presented cyclically until weights stabilize.
STEP 3 Calculate the net-input values to the hidden layer units:
neth
pj = ∑ Wh
ji xpi + θh
j
STEP 4 Calculate the outputs from the hidden layer:
ipj = fh
j (neth
pj)
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This is obtained through sigmoidal function shown below:
fh
j(nethpj) = 1/[1+exp(-net
hpj)]
STEP 5 Move to the output layer. Calculate the net-input values to the output layer
units:
netopk = ∑ W
okj ipj + θ
OK
STEP 6 Calculate the output:
Opk= fok(net
opk)
This is obtained through sigmoidal function shown below:
fok(net
opk) = 1/[1+exp(-net
opk)]
STEP 7 Calculate the error terms for the output units:
δopk = (ypk - Opk) Opk (1 - Opk)
where Ypk is the desired output node of node k and Opk is the actual output of node k
STEP 8 Calculate the error terms for the hidden units:
δ h
pj = ipj (1 - ipj) ∑ δopk w
okj
STEP 9 Update the weights on the output layer:
wokj (t+1) = w
okj (t) + η δ
opk ipj + α[w
okj (t) - w
okj (t-1)]
STEP 10 Update the weights on the hidden layer:
Whji (t+1) = w
hji (t) + η δ
hpj xi + α[w
hji (t) – w
hji (t-1)]
STEP 11 Calculate the total error for each input pattern:
Ep = ∑δ2
pk
Since this quantity is the measure of how well the network is learning. When the error
is acceptably small for each of the training pattern, training can be discontinued.
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2.12 Possibilities of Convergence
Weights:
Weights should be initialized to small, random values – say between ±0.5 weights should be
initialized to small, random values- say between ±0.5 as the bias terms, θL, that appear in the
equations for the net input to a unit common practice to treat this bias value as another weight, which
is connected to a fictitious unit that always has an output of 1. Bias value sometimes helps in the
convergence of the problem to the solution. But its use is optional.
Fig 2.7: Graph showing relation between weight and error
2.12.1 Learning Rate Parameter:
Selection of a value for the learning rate parameter, η, has a significant effect on the network
performance. Usually, η must be a small number- on the order of 0.05 to 0.25- to ensure that the
network will settle to a solution. A small value of η means that the network will have to make a large
number of iterations, but that is the price to be paid. It is often possible to increase the size of η as
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learning proceeds. Increasing η as the network error reaches a minimum, but the network may
bounce around too far from the actual minimum value if η gets too large.
2.12.2 Momentum „α‟:
Another way to increase the speed of convergence is to use a technique called momentum. When
calculating the weight-change value, Δpw, we add a fraction of the previous change. This additional
term tends to keep the weight changes going in the same direction-hence the term momentum. The
weight-change equation on the output layer then becomes.
Wokj (t+1) = W
okj (t) + ηδ
opk ipj + α [W
okj (t) – W
okj (t-1)]
With a similar equation on the hidden layer. In the above equation, α, is the momentum parameter,
and it usually set to a positive value less than 1. The use of the momentum term is also optional.
2.12.2 Local Minimum:
A final topic the possibility of converging to a local minimum in weight space. Figure illustrates the
idea. Once a network settles on a minimum, whether local or global, learning ceases. If a local
minimum is reached, the error at the network outputs may still be unacceptably high. Fortunately,
sometimes, this problem does not appear to cause much difficulty in practice. If a network stops
learning before reaching an acceptable solution, a change in the number of hidden nodes or in the
learning parameters will often fix the problem; or we can simply start over a different set of initial
weights. When a network reaches an
acceptable solution, there is no guarantee that it
has reached the global minimum rather than a
local one. If the solution is acceptable from an
error standpoint, it does not matter whether the
minimum is global or local, or even whether the
training was halted at some point before a true
minimum was reached. [14]
Fig 3.7: Local minima
2.13 Gauss–Newton algorithm
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The Gauss–Newton algorithm is a method used to solve non-linear least squares problems. It can be
seen as a modification of Newton's method for finding a minimum of a function. Unlike Newton's
method, the Gauss–Newton algorithm can only be used to minimize a sum of squared function
values, but it has the advantage that second derivatives, which can be challenging to compute, are not
required.
Non-linear least squares problems arise for instance in non-linear regression, where parameters in a
model are sought such that the model is in good agreement with available observations.
The method is named after the mathematicians Carl Friedrich Gauss and Isaac Newton.
DISCRIPTION
Given m functions r1, …, rm of n variables β = (β1, …, βn), with m ≥ n, the Gauss–Newton algorithm
finds the minimum of the sum of squares
Starting with an initial guess for the minimum, the method proceeds by the iterations
where the increment Δ is the solution to the normal equations:
Here, r is the vector of functions ri, and Jr is the m×n Jacobian matrix of r with respect to β, both
evaluated at βs. The superscript T denotes the matrix transpose.
In data fitting, where the goal is to find the parameters β such that a given model function y = f(x, β)
fits best some data points (xi, yi), the functions ri are the residuals
Then, the increment Δ can be expressed in terms of the Jacobian of the function f, as
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2.14 Back propagation with Levenberg-marquardt algorithm
It has been found that the back propagating algorithm is very slow in many applications even with
adaptive learning rate and momentum. Several attempts have been made to improve the training
speed of standard back propagating algorithm in addition to adaptive learning rate and momentum.
Recently Hagan and Minhaj have shows that the training time can significantly be be improved if we
incorporate the Levenberg-marquardt (L-M) algorithm. According to Zhou and Si the L-M
incorporation into the back propagation not only improve the training time but also provide the
superior performance in term of training accuracy and convergence properties. However a
disadvantage of the algorithm is that it computationally expensive and hence can be unsuitable for
large network. This disadvantage can be overcome by using a reasonably small data set for training.
This algorithm updates the network parameters as follows
∆w = (JTJ +µI)
-1 J
Te
Where J is the Jacobean matrix of derivatives to each weight, µ is the scalar and e ai the error vector.
The µ determines whether the learning progress according to Gauss-Newton method or gradient
decent. If µ is large the JTJ term becomes negligible and the learning progress according to µ
-1 J
Te
which approximate to gradient decent. When the step is taken and error increases, µ is increased
until a step can be taken without increasing errors .However if µ becomes too large no learning take
place (i.e. µ-1
JTe →0).this occurs when an error minimum has been found and is why learning stops
when µ reaches its max value [12].
has been found and is why learning stops when µ reaches its max value [12].
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CHAPTER #
03
MATLAB SIMULATION
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3 MATLAB SIMULATION
ABOUT THE CHAPTER:
In this chapter we will be discussing the simulation done to prove our hypothesis. For the simulation
we have used MATLAB software.
MATLAB (meaning "matrix laboratory") was invented in the late 1970s by Cleve Moler. MATLAB is a
numerical computing environment and fourth generation programming language. Developed by The
MathWorks, MATLAB allows matrix manipulation, plotting of functions and data, implementation
of algorithms, creation of user interfaces, and interfacing with programs in other languages.
Although it is numeric only, an optional toolbox uses the MuPAD symbolic engine, allowing access
to computer algebra capabilities. An additional package, Simulink, adds graphical multidomain
simulation and Model-Based Design for dynamic and embedded systems.[21]
Firstly, we have modeled synchronous generator in the power system and then the neural network
controller. These are further explained in this chapter.
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3.1 Model Description:
In this model a three-phase generator rated 200 MVA, 13.8 kV, 1800 rpm is connected to a
230 kV, 10,000 MVA network through a Delta-Wye 210 MVA transformer. A load of 5MW is
connected to a 13.8 KV bus which shows the auxiliary load in the generating station. Further 10MW
load shows the load on the system. To connect system an infine bus bar we use 10,000MVA ,230
KV source. At t = 30.0 s, a three-phase to ground fault occurs on the 230 kV bus. The fault is
cleared after 150ms (t = 30.15 s). Through this model we have proved that neural network controller
(AVR and PSS) work more better than conventional controller. NN controller injects excitation
power and damped out oscillation more faster than conventional controller.
3.2 Synchronous Machine
Model of the dynamics of a three-phase round-rotor or salient-pole synchronous machine [15].
Description
The Synchronous Machine block operates in generator or motor modes. The operating mode is
dictated by the sign of the mechanical power (positive for generator mode, negative for motor mode).
The electrical part of the machine is represented by a sixth-order state-space model and the
mechanical part is the same as in the Simplified Synchronous Machine block.
The model takes into account the dynamics of the stator, field, and damper windings. The equivalent
circuit of the model is represented in the rotor reference frame (qd frame).[16] All rotor parameters
and electrical quantities are viewed from the stator. They are identified by primed variables. The
subscripts used are defined as follows:
d,q: d and q axis quantity
R,s: Rotor and stator quantity
l,m: Leakage and magnetizing inductance
f,k: Field and damper winding quantity
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The electrical model of the machine is
with the following equations.
Note that this model assumes currents flowing into the stator windings. The measured stator currents
returned by the Synchronous Machine block (Ia, Ib, Ic, Id, Iq) are the currents flowing out of the
machine.
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3.2.1 Dialog Box and Parameters
Standard Parameters in p.u
3.2.2 Rotor type; Nominal power, L-L voltage, and frequency
Specifies rotor type: Salient-pole or Round (cylindrical).
3.2.3 Reactances
The d-axis synchronous reactance Xd, transient reactance Xd', and subtransient reactance Xd'', the q-
axis synchronous reactance Xq, transient reactance Xq' (only if round rotor), and subtransient
reactance Xq'', and finally the leakage reactance Xl (all in p.u.).
3.2.4 d-axis time constants; q-axis time constant(s)
Specify the time constants you supply for each axis: either open-circuit or short-circuit.
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3.2.5 Time constants
The d-axis and q-axis time constants (all in s). These values must be consistent with choices made on
the two previous lines: d-axis transient open-circuit (Tdo') or short-circuit (Td') time constant, d-axis
subtransient open-circuit (Tdo'') or short-circuit (Td'') time constant, q-axis transient open-circuit
(Tqo') or short-circuit (Tq') time constant (only if round rotor), q-axis subtransient open-circuit
(Tqo'') or short-circuit (Tq'') time constant.
3.2.6 Stator resistance
The stator resistance Rs (p.u.).
3.2.7 Coefficient of inertia, friction factor, and pole pairs; Initial conditions; Simulate
saturation; Saturation parameters
The inertia constant H (s), where H is the ratio of energy stored in the rotor at nominal speed over the
nominal power of the machine, the damping coefficient D (p.u. torque/p.u. speed deviation), and the
number of pole pairs p.
3.2.8 Inputs and Outputs
The units of inputs and outputs vary according to which dialog box was used to enter the block
parameters. For the non electrical connections, there are two possibilities. If Standard Parameters in
p.u is used, the inputs and outputs are in p.u. (angle , which is always in rad).
The first input is the mechanical power at the machine's shaft. In generating mode, this input can be a
positive constant or function or the output of a prime mover block. In motoring mode, this input is
usually a negative constant or function.
The second input of the block is the field voltage. This voltage can be supplied by a voltage regulator
in generator mode. It is usually a constant in motor mode.
.If we use the model in p.u., Vf should be entered in p.u. (1 p.u. of field voltage producing 1 p.u. of
terminal voltage at no load).
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The first three outputs are the electrical terminals of the stator. The last output of the block is a vector
containing 21 signals. They are, in order:
Signal Definition
1 - 3 Stator currents (flowing out of machine) isa, isb, and isc
4 - 5 q- and d-axis stator currents (flowing out of machine) iq, id
6 - 8 Field and damper winding currents (flowing into machine) ifd, ikq, and ikd
9 - 10 q- and d-axis magnetizing fluxes mq, md
11 - 12 q- and d-axis stator voltages vq, vd
13 Rotor angle deviation with respect to a synchronous rotating frame
14 Rotor speed r
15 Total electrical power Pe, including losses in stator, field, and damper windings
16 Rotor speed deviation d
17 Rotor mechanical angle (degrees)
18 Electromagnetic torque Te
19 Load angle (electrical degrees)
20 Output active power Peo
21 Output reactive power Qeo
We can demultiplex these signals by using the Machine Measurement Demux block provided in the
Machines library.
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3.3 Excitation System
Provide excitation system for synchronous machine and regulate its terminal voltage in generating
mode
Description
The Excitation System block is a Simulink system implementing a DC exciter described in [17],
without the exciter's saturation function. The basic elements that form the Excitation System block
are the voltage regulator and the exciter.
3.3.1 Inputs and Outputs
Vref- The desired value, in pu, of the stator terminal voltage.
Vd- vd component, in pu, of the terminal voltage.
Vq- vq component, in pu, of the terminal voltage.
Vstab- Connect this input to a power system stabilizer to provide additional stabilization of power
system oscillations.
Vf- The field voltage, in pu, for the Synchronous Machine block.
3.3.2 Generic Power System Stabilizer -
Description
The Generic Power System Stabilizer (PSS) block can be used to add damping to the rotor
oscillations of the synchronous machine by controlling its excitation. The disturbances occurring in a
power system induce electromechanical oscillations of the electrical generators. These oscillations,
also called power swings, must be effectively damped to maintain the system stability. The output
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signal of the PSS is used as an additional input (vstab) to the Excitation System block. The PSS input
signal can be either the machine speed deviation, dw, or its acceleration power, Pa = Pm - Peo
(difference between the mechanical power and the electrical power).
3.3.3 Inputs and Outputs
In:
Two types of signals can be used at the input In:
The synchronous machine speed deviation dw signal (in pu)
The synchronous machine acceleration power Pa = Pm - Peo (difference between the
machine mechanical power and output electrical power (in pu))
Vstab:
The output is the stabilization voltage (in pu) to connect to the Vstab input of the Excitation
System block used to control the terminal voltage of the synchronous machine.
3.4 Three-Phase Parallel RLC Load
Description
The Three-Phase Parallel RLC Load block implements a three-phase balanced load as a parallel
combination of RLC elements. At the specified frequency, the load exhibits a constant impedance.
The active and reactive powers absorbed by the load are proportional to the square of the applied
voltage.
3.4.1 Dialog Box and Parameters
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3.4.2 Configuration
The connection of the three phases. We can select one of the following four connections:
Y(grounded) Neutral is grounded.
Y(floating) Neutral is not accessible.
Y(neutral) Neutral is made accessible through a fourth connector.
Delta Three phases connected in delta
The block icon is updated according to the load connection.
3.4.3 Nominal phase-to-phase voltage Vn
The nominal phase-to-phase voltage of the load, in volts RMS (Vrms).
3.4.4 Nominal frequency fn
The nominal frequency, in hertz (Hz).
3.4.5 Active power P
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The three-phase active power of the load, in watts (W).
3.4.6 Inductive reactive power QL
The three-phase inductive reactive power QL, in vars. Specify a positive value, or 0.
3.4.7 Capacitive reactive power QC
The three-phase capacitive reactive power QC, in vars. Specify a positive value, or 0.
3.4.8 Measurements
We Selected Branch voltages to measure the three voltages across each phase of the Three-Phase
Parallel RLC Load block terminals. For a Y connection, these voltages are the phase-to-ground or
phase-to-neutral voltages. For a delta connection, these voltages are the phase-to-phase voltages.
Also that, we selected Branch currents to measure the three total currents (sum of R, L, C currents)
flowing through each phase of the Three-Phase Parallel RLC Load block. For a delta connection,
these currents are the currents flowing in each branch of the delta.
Then we selected Branch voltages and currents to measure the three voltages and the three currents
of the Three-Phase Parallel RLC Load block.
By Placing a Multimeter block in our model we displayed the selected measurements during the
simulation. In the Available Measurements list box of the Multimeter block, the measurements are
identified by a label followed by the block name.
Measurement Label
Branch voltages Y(grounded): Uag, Ubg, Ucg Uag: , Ubg: , Ucg:
Y(floating): Uan, Ubn, Ucn Uan: , Ubn: , Ucn:
Y(neutral): Uan, Ubn, Ucn Uan: , Ubn: , Ucn:
Delta: Uab, Ubc, Uca Uab: , Ubc: , Uca:
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Measurement Label
Branch currents Y(grounded): Ia, Ib, Ic Iag: , Ibg: , Icg:
Y(floating): Ia, Ib, Ic Ian: , Ibn: , Icn:
Y(neutral): Ia, Ib, Ic Ian: , Ibn: , Icn:
Delta: Iab, Ibc, Ica Iab: , Ibc: , Ica:
3.5 THREE PHASE FAULT
Implement programmable phase-to-phase and phase-to-ground fault breaker system
Description
The Three-Phase Fault block implements a three-phase circuit breaker where the opening and closing
times can be controlled either from an external Simulink signal (external control mode), or from an
internal control timer (internal control mode).
The Three-Phase Fault block uses three Breaker blocks that can be individually switched on and off
to program phase-to-phase faults, phase-to-ground faults, or a combination of phase-to-phase and
ground faults.
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The ground resistance Rg is automatically set to 106 ohms when the ground fault option is not
programmed. For example, to program a fault between the phases A and B you need to select the
Phase A Fault and Phase B Fault block parameters only. To program a fault between the phase A and
the ground, you need to select the Phase A Fault and Ground Fault parameters and specify a small
value for the ground resistance.
If the Three-Phase Fault block is set in external control mode, a control input appears in the block
icon. The control signal connected to the fourth input must be either 0 or 1, 0 to open the breakers, 1
to close them. If the Three-Phase Fault block is set in internal control mode, the switching times and
status are specified in the dialog box of the block.
Series Rp-Cp snubber circuits are included in the model. They can be optionally connected to the
fault breakers. If the Three-Phase Fault block is in series with an inductive circuit, you must use the
snubbers.
3.5.1 Dialog Box and Parameters
3.5.2 Phase A Fault
If selected, the fault switching of phase A is activated. If not selected, the breaker of phase A stays in
its initial status. The initial status of the phase A breaker corresponds to the complement of the first
value specified in the vector of Transition status. The initial status of the fault breaker is usually 0
(open). However, it is possible to start a simulation in steady state with the fault initially applied on
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the system. For example, if the first value in the Transition status vector is 0, the phase A breaker is
initially closed. It opens at the first time specified in the Transition time(s) vector.
3.5.3 Phase B Fault
If selected, the fault switching of phase B is activated. If not selected, the breaker of phase B stays in
its initial status. The initial status of the phase B breaker corresponds to the complement of the first
value specified in the vector of Transition status.
3.5.4 Phase C Fault
If selected, the fault switching of phase C is activated. If not selected, the breaker of phase C stays in
its initial status. The initial status of the phase C breaker corresponds to the complement of the first
value specified in the vector of Transition status.
3.5.6 Fault resistances Ron
The internal resistance, in ohms (Ω), of the phase fault breakers. The Fault resistances Ron parameter
cannot be set to 0.
3.5.7 Ground Fault
If selected, the fault switching to the ground is activated. A fault to the ground can be programed for
the activated phases. For example, if the Phase C Fault and Ground Fault parameters are selected, a
fault to the ground is applied to the phase C. The ground resistance is set internally to 1e6 ohms
when the Ground Fault parameter is not selected.
3.5.8 Ground resistance Rg
Ground resistance Rg (ohms) parameter is not visible if the Ground Fault parameter is not
selected. The ground resistance, in ohms (Ω). The Ground resistance Rg (ohms) parameter
cannot be set to 0.
3.5.9 External control of fault timing
If selected, adds a fourth input port to the Three-Phase Fault block for an external control of the
switching times of the fault breakers. The switching times are defined by a Simulink signal (0 or 1)
connected to the fourth input port of the block.
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3.5.10 Transition status
We have to specify the vector of switching status when using the Three-Phase Breaker block in
internal control mode. The selected fault breakers open (0) or close (1) at each transition time
according to the Transition status parameter values.
The initial status of the breakers corresponds to the complement of the first value specified in the
vector of switching status.
3.5.11 Transition times(s)
Also we have to specify the vector of switching times when using the Three-Phase Breaker block in
internal control mode. At each transition time the selected fault breakers opens or closes depending
to the initial state. The Transition times (s) parameter is not visible in the dialog box if the External
control of switching times parameter is selected.
3.5.12 Snubbers resistance Rp
The snubber resistances, in ohms (Ω). Set the Snubbers resistance Rp parameter to inf to eliminate
the snubbers from the model.
3.5.13 Snubbers capacitance Cp
The snubber capacitances, in farads (F). Set the Snubbers capacitance Cp parameter to 0 to eliminate
the snubbers, or to inf to get resistive snubbers.
3.5.14 Measurements
First we selected Fault voltages to measure the voltage across the three internal fault breaker
terminals.
Then we selected Fault currents to measure the current flowing through the three internal breakers. If
the snubber devices are connected, the measured currents are the ones flowing through the breakers
contacts only.
Then we selected Fault voltages and currents to measure the breaker voltages and the breaker
currents.
By Placing a Multimeter block in your model to display the selected measurements during the
simulation. In the Available Measurements list box of the Multimeter block, the measurements are
identified by a label followed by the block name and the phase:
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Measurement Label
Fault voltages Ub <block name> /Fault A: Ub <block name> /Fault B: Ub <block name> /Fault C.
Fault currents Ib <block name> /Fault A: Ib <block name> /Fault B: Ib <block name> /Fault C.
3.5.15 Inputs and Outputs
The three fault breakers are connected in wye between terminals A, B and C and the internal ground
resistor. If the Three-Phase Fault block is set to external control mode, a Simulink input is added to
the block to control the opening and closing of the three internal breakers.
3.6 Bus Selector - Select signals from incoming bus
Description
The Bus Selector block outputs a specified subset of the elements of the bus at its input. The block
can output the specified elements as separate signals or as a new bus. When the block outputs
separate elements, it outputs each element from a separate port from top to bottom of the block.
3.6.1 Data Type Support
A Bus Selector block accepts and outputs real or complex values of any data type supported by
Simulink software, including fixed-point and enumerated data types.
3.6.2 Parameters and Dialog Box
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3.6.3 Signals in the bus
The Signals in the bus list shows the signals in the input bus.
3.6.4 Selected signals
The Selected signals list box shows the output signals. We can order the signals by using the Up,
Down, and Remove buttons. Port connectivity is maintained when the signal order is changed.
If an output signal listed in the Selected signals list box is not an input to the Bus Selector block, the
signal name is preceded by three question marks (???).
3.6.5 Output as bus
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If selected, this option causes the block to output the selected elements as a bus. Otherwise, the
block outputs the elements as standalone signals, each from its own output port and labeled with the
corresponding element's name.
3.7 Scope and Floating Scope
It display signals generated during simulation.
Description
The Scope block displays its input with respect to simulation time.
The Scope block can have multiple axes (one per port) and all axes have a common time range with
independent y-axes. The Scope block allows you to adjust the amount of time and the range of input
values displayed. We can move and resize the Scope window and you can modify the Scope's
parameter values during the simulation.
When we start a simulation the Scope windows are not opened, but data is written to connected
Scopes. As a result, if you open a Scope after a simulation, the Scope's input signal or signals will be
displayed.
If the signal is continuous, the Scope produces a point-to-point plot. If the signal is discrete, the
Scope produces a stair-step plot.
The Scope provides toolbar buttons that enable us to zoom in on displayed data, display all the data
input to the Scope, preserve axis settings from one simulation to the next, limit data displayed, and
save data to the workspace. The toolbar buttons are labeled in this figure, which shows the Scope
window as it appears when you open a Scope block.
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3.7.1 Color Coding Used When Displaying Multiple Signals
The scope block can display one signal per axes. When displaying a vector or matrix signal on the
same axis, the Scope block assigns colors to each signal element, in this order:
1. Yellow
2. Magenta
3. Cyan
4. Red
5. Green
6. Dark Blue
The Scope block cycles through the colors if a signal has more than six elements.
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3.8 Three-Phase Transformer
Description
The standard Three-Phase Transformer (Two Windings) block uses three single-phase transformers
to implement a three-phase model. When a three-phase transformer is built with a three-limb core or
a five-limb core this model does not represent the couplings between windings of different phases.
A three-phase transformer using a three-limb core and two windings per phase is shown on the figure
below. Windings are numbered as follows: 1, 2 for phase A, 3, 4 for phase B and 5, 6 for phase C.
This core geometry implies that winding 1 is coupled to all other windings (2 to 6), whereas in a
three-phase transformer using three independent cores (as in the Three-Phase Transformer (Two
Windings) block) winding 1 is coupled only with winding 2.
3.8.1 Winding Connections
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The two windings of the transformer can be connected in the following manner:
Y
Y with accessible neutral
Grounded Y
Delta (D1), delta lagging Y by 30 degrees
Delta (D11), delta leading Y by 30 degrees
3.8.2 Dialog Box and Parameters
Configuration Tab
3.8.3 Limitations
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This transformer model does not include saturation. If you need modeling saturation connect the
primary winding of a saturable Three-Phase Transformer (Two Windings) in parallel with the
primary winding of your model. Use same connection (Yg, D1 or D11) and same winding resistance
for the two windings connected in parallel. Specify Y or Yg connection for the secondary winding
and leave it open. Specify appropriate voltage, power ratings and desired saturation characteristics.
The saturation characteristic is the characteristic obtained when then transformer is excited by a
positive-sequence voltage.
If you are modeling a transformer with three single-phase cores or a five-limb core, this model will
produce acceptable saturation currents because flux stays trapped inside the iron core.
For a three-limb core, it is less evident that this saturation model also gives acceptable results
because zero-sequence flux circulates outside of the core and returns through the air and the
transformer tank surrounding the iron core. However, as the zero-sequence flux circulates in the air,
the magnetic circuit is mainly linear and its reluctance is high (high magnetizing currents). These
high zero-sequence currents (100% and more of nominal current) required to magnetize the air path
are already taken into account in the linear model. Connecting a saturable transformer outside the
three-limb linear model with a flux-current characteristic obtained in positive sequence will produce
currents required for magnetization the iron core. This model will give acceptable results whether the
three-limb transformer has a delta or not.
The following example shows how to model saturation in an inductance matrix type two-winding
transformer.
3.9 RMS VALUE CALCULATOR:
Measure root mean square (RMS) value of signal
Description:
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This block measures the root mean square value of an instantaneous current or voltage signal
connected to the input of the block. The RMS value of the input signal is calculated over a running
average window of one cycle of the specified fundamental frequency.
as this block uses a running average window, one cycle of simulation has to be completed before the
output gives the correct value. For the first cycle of simulation the output is held to the RMS value of
the specified initial input.
3.9.1 Dialog Box and Parameters
Fundamental frequency
The fundamental frequency, in hertz, of the input signal.
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3.10 Three-Phase Source
Implement three-phase source with internal R-L impedance
Description
The Three-Phase Source block implements a balanced three-phase voltage source with an internal R-
L impedance. The three voltage sources are connected in Y with a neutral connection that can be
internally grounded or made accessible. We can specify the source internal resistance and inductance
either directly by entering R and L values or indirectly by specifying the source inductive short-
circuit level and X/R ratio.
3.10.1 Dialog Box and Parameters
3.10.2 Phase-to-phase rms voltage
The internal phase-to-phase voltage in volts RMS (Vrms)
3.10.3 Phase angle of phase A
The phase angle of the internal voltage generated by phase A, in degrees. The three voltages are
generated in positive sequence. Thus, phase B and phase C internal voltages are lagging phase A
respectively by 120 degrees and 240 degrees.
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3.10.4 Frequency
The source frequency in hertz (Hz).
3.10.5 Internal connection
The internal connection of the three internal voltage sources. The block icon is updated according to
the source connection.
We have to select one of the following three connections:
Y The three voltage sources are connected in Y to an internal floating neutral.
Yn The three voltage sources are connected in Y to a neutral connection which is made
accessible through a fourth terminal.
Yg The three voltage sources are connected in Y to an internally grounded neutral.
3.10.6 Specify impedance using short-circuit level
We have Select to specify internal impedance using the inductive short-circuit level and X/R ratio.
3.10.7 3-phase short-circuit level at base voltage
The three-phase inductive short-circuit power, in volts-amperes (VA), at specified base voltage, used
to compute the internal inductance L. This parameter is available only if Specify impedance using
short-circuit level is selected.
The internal inductance L (in H) is computed from the inductive three-phase short-circuit power Psc
(in VA), base voltage Vbase (in Vrms phase-to-phase), and source frequency f (in Hz) as follows:
3.10.8 Base voltage
The phase-to-phase base voltage, in volts RMS, used to specify the three-phase short-circuit level.
The base voltage is usually the nominal source voltage. This parameter is available only if Specify
impedance using short-circuit level is selected.
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3.10.9 X/R ratio
The X/R ratio at nominal source frequency or quality factor of the internal source impedance. This
parameter is available only if Specify impedance using short-circuit level is selected.
The internal resistance R (in Ω) is computed from the source reactance X (in Ω) at specified
frequency, and X/R ratio as follows:
3.10.10 Source resistance
This parameter is available only if Specify impedance using short-circuit level is not selected.
The source internal resistance in ohms (Ω).
3.10.11 Source inductance
This parameter is available only if Specify impedance using short-circuit level is not selected.
The source internal inductance in henries (H).
3.10 Gain - Multiply input by constant
Description
The Gain block multiplies the input by a constant value (gain). The input and the gain can each be a
scalar, vector, or matrix.
We specify the value of the gain in the Gain parameter. The Multiplication parameter lets us specify
element-wise or matrix multiplication. For matrix multiplication, this parameter also lets us indicate
the order of the multiplicands.
The gain is converted from doubles to the data specified in the block mask offline using round-to-
nearest and saturation. The input and gain are then multiplied, and the result is converted to the
output data type using the specified rounding and overflow modes.
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3.10.1 Data Type Support
The Gain block accepts a real or complex scalar, vector, or matrix of any numeric data type
supported by Simulink software. The Gain block supports fixed-point data types. If the input of the
Gain block is real and the gain is complex, the output is complex.
3.10.2 Parameters and Dialog Box
The Main pane of the Gain block dialog box appears as follows: [18]
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3.12 NEURAL NETWORK MODELLING
This section presents the architecture of the network that is most commonly used with the
backpropagation algorithm - the multilayer feedforward network.
The following diagram explains how the neural network is trained from its Teacher.
The architecture of the network has been previously explained [3.8], now we are aiming to model it
in MALAB. This can be done by either modeling the mathematical equation of the network or
simply by using some commands.Remembering that our network has one hidden and one output
layer both employing different transfer functions which are mentioned below:
The transfer function used for the hidden layer is Log-sigmoidal transfer function
The transfer function used for the hidden layer is Log-sigmoidal transfer function
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3.11.1 Creating a Network (newff)
The first step in training a feedforward network is to create the network object. The function newff
creates a feedforward network. It requires four inputs and returns the network object. The first input
is an R by 2 matrix of minimum and maximum values for each of the R elements of the input vector.
The second input is an array containing the sizes of each layer. The third input is a cell array
containing the names of the transfer functions to be used in each layer. The final input contains the
name of the training
function to be used.
For example, the following command creates a two-layer network. There is one input vector with
two elements. The values for the first element of the input vector range between -1 and 2, the values
of the second element of the input vector range between 0 and 5. There are three neurons in the first
layer and one neuron in the second (output) layer. The transfer function in the first layer is tan-
sigmoid, and the output layer transfer function is linear. The training
function is traingd
net=newff([-1 2; 0 5],[3,1],{'tansig','purelin'},'traingd');
this network is trained by gradient desent(gd).
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3.11.2 PROGRAM CODING
uvft=transpose(vf);
uvd=vd.signals.values;
uvq=vq.signals.values;
uspd=spd.signals.values;
uvdt=transpose(uvd);
uspdt=transpose(uspd);
uvqt=transpose(uvq);
input=[uvdt;uvqt;uspdt];
net=newff(minmax(input),[7,1],{'logsig','purelin'},'trainlm');
net = init(net);
net.trainParam.show = 500;
net.trainParam.lr = 0.05;
net.trainParam.epochs = 1500;
net.trainParam.goal = 1e-7;
[net,tr]=train(net,input,uvft);
DISCRIPTION:
uvft=transpose(vf);
uvd=vd.signals.values;
uvq=vq.signals.values;
uspd=spd.signals.values;
uvdt=transpose(uvd);
uspdt=transpose(uspd);
uvqt=transpose(uvq);
input=[uvdt;uvqt;uspdt];
The above commands were used to create the input and output training vector. These
values(uvft,uvd,uvq,uspd) were first collected from the power system model using conventional
controller. And then converted into the required form and then the inputs were combined to form the
input vector named „input‟.
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net=newff(minmax(input),[7,1],{'logsig','purelin'},'trainlm');
net = init(net);
The above commands created the network of 2 layer having transfer functions 'logsig' and 'purelin'
respectively and having the training algorithm as Back propagation with Levenberg-marquardt
algorithm ('trainlm'). The next command initializes the values of the weight to a random value. If
the network
net.trainParam.show = 500;
net.trainParam.lr = 0.05;
net.trainParam.epochs = 1500;
net.trainParam.goal = 1e-7;
[net,tr]=train(net,input,uvft);
The above commands are used to set the training parameters and then train the network.
The function “net.trainParam.show = 500” is used so that the training results are displayed after
every 500 iterations.
The function “net.trainParam.lr = 0.05”, sets the learning rate to 0.05.
The function “net.trainParam.epochs = 1500”, sets the total number number of epochs i.e. how many
times MATLAB should iterate the training data to reduce the error.
The function “net.trainParam.goal = 1e-7”, tells the software to stop the training when the error is
reduced to 1e-7.
The following graph shows the training of the network:
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POWER SYSTEM MODEL
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CHAPTER # O4
RESULTS
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4 RESULTS
ABOUT THE CHAPTER:
In this chapter we are comparing the results of Conventional Controller‟s AVR and PSS with the
Neural Network‟s AVR and PSS. We have proved through the graphs of rotor speed deviation and
terminal voltage for three phase and two phase fault condition have better results with the ANN
controller. And also to justify the use of 7 neurons in the hidden layer we have changed it to 6 and
then 8 neurons. The results justify the use of 7 neurons.
It should be remembered that the differences in the graph of conventional and NN controller should
be viewed by keeping in mind that the axis have been scaled down such that one small box is of
200V. Hence, even a small difference which looks insignificant from naked eye is also critical.
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4.1 Comparison of terminal voltage:
Fig 4.1 and 4.2 shows the graph between terminal voltage and time. Time axis starts from 28
sec and ends at 45 sec when the system regains its steady state position. At 30 sec three phase fault
occur on 230 KV bus bar so terminal voltage suddenly drops, but after 150ms when fault become
clear it return to its initial value. Better AVR action and hence better transient stability can be
observed by noticing that the blue line (ANN Controller) comes quickly to the original voltage
(8000V) than the red line (conventional controller) after the injection of fault. Fig 4.1 also shows that
neural network (NN) controller reaches its initial condition in well damped manner than
conventional controller which shows a good PSS action. We observed from the graph that NN
controller reached steady state value within 35sec while Conventional controller reached in 43 ms.
Further graph also shows that after fault happening terminal voltage drop less in NN controller than
conventional controller and first swing of voltage of NN controller is early than conventional
controller.
Fig 4.1: Graph between terminal voltage and time for three phase fault
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In fig.4.2 the same thing can be seen as observed in the previous graph. As the fault is of smaller
magnitude the difference is not that significant from naked eye because the controllers are not
pushed to their limits.
Fig 4.2: Graph between terminal voltage and time for two phase fault
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4.2 Comparison of rotor speed deviation:
Fig 4.3 shows the graph between rotor speed deviation and time. Time axis starts from 28 sec and
end at 45 sec when the system regains its steady state position. At 30 sec three phase fault occur on
230 KV bus bar so electrical power suddenly drops so rotor going to accelerate. After 150 ms fault
become clear and faulted part is separated from the system so system returns to its initial operating
condition. Blue line shows NN graph and Red line shows Conventional controller. It is very clear
from graph that NN controller‟s stabilize the system within 38sec while conventional controller‟s is
still not able to stabilize in 45sec.
Fig 4.3 : Graph between rotor speed deviation and time for three phase fault
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The same thing is evident in this different condition when system is subjected to 2 phase fault. And it is
clearly evident that the conventional controller (Red) is not being damped out while the neural network
controller (blue) has damped out the oscillations.
Fig 4.4 : Graph between rotor speed deviation and time for two phase fault
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4.3 Graphs compairing training through 6 and 7 neuron:
Fig 4.5 and 4.6 shows graph of terminal voltage of ANN and the conventional controller, when
ANN is employing 6 and then 8 neurons in the hidden layer respectively. Although the result is
better than the conventional controller but there is no significant change when compared with the 7
neuron proposed scheme from naked eye. But, close examination showed that the 7 neuron structure
performed better than the 6 and 8 neuron structure
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45
In this project we aimed to first model the synchronous generator in a power system along with its
conventional controllers i.e. AVR and PSS. Then we collected the training data for the ANN from
this system of AVR and PSS. And then after training the ANN controller was applied to this same
network and was shown that its performance was better than its teacher. (That is conventional AVR
and PSS).
Therefore we conclude that
“Artificial neural network controller is employed in electrical alternator or synchronous generator
excitation system have been successful”
Hence when employed ANN will improve the transient stability by performing as a fast and high
gain AVR without compromising on dynamic stability because it also damps out the oscillation
faster than the conventional PSS, thus performing a better PSS action.
Conclusion
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The thesis has reported successful development of artificial neural networks for the control of
excitation systems of synchronous generator. However, there are many aspects, which need further
attention. There are some areas in simulation model that can be improved further on. The ultimate
goal of any power system is to simulate, as closely as possible, the actual behavior of the controllers
and the machine in the system.
Furthermore, the model can be extended to a multi machine system instead of a single synchronous
machine. Also, the analysis can be extended to the voltage on the transmission line whereas in this
project the voltage on the generator terminal was considered.
This project becomes further improved if the training is done online i.e. during the time when
conventional controllers are applied in the power system and performing their task the data is
collected and ANN is trained, all in the real time.
Another interesting proposition could be to train the neural network by PID controller and then
compare the results.
Hopefully in the future these points can be implemented foe more complete and accurate model and
results.
Future Improvements
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[01] Schlief et al (1962)
[02] Excitation Control in Synchronous machine via an ANN (IEEE paper)
by Weiming Zhang & M.E.El-Hawary
[03] Anderson,fouad (1977)
[04] V.K.Mehta
[05] IEEE/CIGRE Joint Task Force on Stability Terms and Definitions
[06] IEEE tutorial course power system stabilization via excitation control
[07] J.B.Gupta (2005)
[08] AVR Design (Queen‟sland University)
[09] Minsky, (1954)
[10] Neural Network A Comprehensive Foundation by Simon Haykin
[11] McCulloch & Pitts, (1943)
[12] Church land and Sejnowski , (1992)
[13] Hagan and Minhaj, (1994)
[14] ANN Applications in Electrical Alternator Excitation Systemby Aslam Pervez Memon
[15] Krause, P.C., Analysis of Electric Machinery, McGraw-Hill, 1986, Section 12.5.
[16] Kamwa, I., et al., "Experience with Computer-Aided Graphical Analysis of Sudden-
Short-Circuit Oscillograms of Large Synchronous Machines," IEEE Transactions on Energy
Conversion, Vol. 10, No. 3, September 1995.
Bibliography
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[17] Kundur, P., Power System Stability and Control, McGraw-Hill, 1994, Section 12.5.
[18] MATLAB help files
[19] G.N. Patchett, Automatic Voltage Regulators and Stabilizers“, Sir Isaac Pitman& Sons,
LTD., London
[20] IEEE tutorial course power system stabilization via excitation control
[21] Wikipedia Encyclopedia
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APPENDIX“A”
The data which is used for training of the neural network is shown below. This data is from the Excitation
System block in a Simulink system of MATLAB (Recommended Practice for Excitation System Models
for Power System Stability Studies,"IEEE Standard 421.5-1992, August, 1992) and Generic Power System
Stabilizer block also in MATLAB (Kundur, P., Power System Stability and Control, McGraw-Hill, 1994,
Section12.5).
Time Vq Vd Spd Vf Time Vq Vd Spd Vf
28.1 0.9052 0.42086 3.33E-06 1.504 29.65 0.90587 0.4214 2.20E-05 1.5283
28.15 0.9055 0.42138 1.21E-05 1.5133 29.7 0.90537 0.42133 1.69E-05 1.5284
28.2 0.9052 0.42109 1.66E-05 1.5211 29.75 0.90512 0.42147 4.53E-06 1.5142
28.25 0.9059 0.4217 1.36E-05 1.5219 29.8 0.90265 0.41882 -1.01E-05 1.4926
28.3 0.9054 0.42168 7.27E-06 1.5117 29.85 0.90526 0.42153 -2.06E-05 1.4749
28.35 0.9052 0.42134 -5.64E-06 1.4975 29.9 0.90523 0.42105 -2.48E-05 1.4667
28.4 0.9035 0.41993 -1.30E-05 1.4831 29.95 0.90608 0.42192 -1.01E-05 1.4758
28.45 0.9086 0.42477 -1.85E-05 1.4746 30 0.90633 0.42225 4.73E-07 1.4912
28.5 0.9057 0.42143 -1.29E-05 1.4754 30.05 0.39751 0.038694 0.006856 11.5
28.55 0.9056 0.42132 -7.43E-06 1.4841 30.1 0.41763 0.022531 0.013821 11.5
28.6 0.9052 0.42075 1.02E-06 1.4993 30.15 0.44274 0.016312 0.02076 11.5
28.65 0.9045 0.42015 1.25E-05 1.5152 30.2 0.5825 0.67113 0.008496 11.5
28.7 0.9052 0.42125 1.66E-05 1.5242 30.25 0.59542 0.7088 -0.00736 9.5704
28.75 0.9086 0.42511 1.59E-05 1.5239 30.3 0.75395 0.67528 -0.02238 0
28.8 0.9051 0.42162 8.51E-06 1.5149 30.35 0.99186 0.48584 -0.03069 0
28.85 0.9052 0.42145 -5.43E-06 1.4977 30.4 1.1142 0.14372 -0.02735 0
28.9 0.9051 0.42146 -1.52E-05 1.484 30.45 1.0943 -0.14757 -0.01402 0
28.95 0.9052 0.42123 -1.54E-05 1.4758 30.5 1.0706 -0.24829 0.002901 0
29 0.9052 0.42102 -1.73E-05 1.477 30.55 1.1136 -0.15385 0.017171 4.1555
29.05 0.9044 0.42015 -1.30E-05 1.4818 30.6 1.1293 0.098362 0.024028 3.2998
29.1 0.9035 0.41915 5.08E-06 1.4974 30.65 1.0282 0.37843 0.021811 5.339
29.15 0.9057 0.42126 1.19E-05 1.5158 30.7 0.89561 0.56299 0.012704 9.7453
www.final-yearproject.com | www.finalyearthesis.com
89
29.2 0.9052 0.42129 1.70E-05 1.5248 30.75 0.83104 0.6279 0.00015 0.916
29.25 0.9055 0.42188 1.54E-05 1.5232 30.8 0.87041 0.60655 -0.0116 0
29.3 0.9062 0.42289 1.44E-06 1.511 30.85 0.98617 0.48113 -0.01874 0
29.35 0.9027 0.41955 -1.34E-05 1.4915 30.9 1.0863 0.271 -0.01858 0
29.4 0.9052 0.42129 -2.22E-05 1.4734 30.95 1.1144 0.06975 -0.01152 0
29.45 0.9057 0.42154 -2.34E-05 1.4712 33.35 0.90386 0.44427 0.000861 2.5811
29.55 0.9029 0.419 3.99E-06 1.4983 33.4 0.90287 0.44834 -0.00049 0.8668
29.6 0.9056 0.42096 1.71E-05 1.5168 33.45 0.90645 0.44106 -0.00154 0
32 1.0084 0.27776 -0.00349 0 33.5 0.91034 0.42114 -0.00194 0
32.05 1.0126 0.24817 -0.00012 0 33.55 0.91844 0.40296 -0.00163 0
32.1 1.0067 0.2657 0.003032 0 33.6 0.92349 0.38961 -0.00078 0
32.15 0.9856 0.30878 0.005084 2.6146 33.65 0.91855 0.3834 0.000336 1.0314
32.2 0.9655 0.37513 0.005465 4.0779 33.7 0.91454 0.39096 0.001309 2.4804
32.25 0.9376 0.42544 0.004125 3.6321 33.75 0.91044 0.40821 0.001792 3.4482
32.3 0.9186 0.46024 0.001603 1.4702 33.8 0.90608 0.42673 0.001598 3.5456
32.35 0.9102 0.46751 -0.00112 0 33.85 0.90552 0.44337 0.000811 2.7478
32.4 0.919 0.45182 -0.0031 0 33.9 0.90348 0.44586 -0.00025 1.374
32.45 0.935 0.41462 -0.00386 0 33.95 0.90524 0.43958 -0.00116 0
34.05 0.9128 0.40935 -0.00136 0 35.75 0.90299 0.42516 0.00093 2.931
34.1 0.9124 0.39592 -0.00067 0.0428 35.8 0.90291 0.43393 0.000523 2.5131
34.15 0.9124 0.39277 0.000253 1.2146 35.85 0.90662 0.4404 -9.37E-05 1.6881
34.2 0.9079 0.39743 0.001064 2.4636 35.9 0.90384 0.43305 -0.00066 0.7933
34.25 0.9049 0.41182 0.00146 3.2703 35.95 0.90649 0.42572 -0.00095 0.2005
34.3 0.9042 0.4282 0.001286 3.3212 36 0.90525 0.41344 -0.00084 0.1517
34.35 0.9022 0.43867 0.000617 2.606 36.05 0.90514 0.40651 -0.0004 0.6536
34.4 0.9033 0.44267 -0.00027 1.4138 36.1 0.90707 0.40585 0.00019 1.4828
34.45 0.9051 0.43662 -0.00102 0.2323 36.15 0.90534 0.41039 0.00069 2.2929
34.5 0.9107 0.42849 -0.00133 0 36.2 0.90217 0.41706 0.000904 2.7675
34.55 0.9079 0.40844 -0.00111 0 36.25 0.90188 0.42711 0.000751 2.7291
34.6 0.9107 0.40116 -0.00047 0.3975 36.3 0.90334 0.43529 0.000294 2.1946
34.65 0.9091 0.39866 0.000331 1.499 36.35 0.90369 0.43522 -0.00028 1.3852
34.7 0.9075 0.40604 0.000992 2.5665 36.4 0.90528 0.43042 -0.00073 0.6305
34.75 0.9029 0.41486 0.001258 3.1708 36.45 0.90511 0.42027 -0.00087 0.2432
34.8 0.9011 0.42841 0.001019 3.0814 36.5 0.90742 0.41337 -0.00066 0.3808
34.85 0.9026 0.43871 0.00038 2.3442 36.55 0.90715 0.40802 -0.00019 0.9667
34.9 0.9036 0.44004 -0.0004 1.2539 36.6 0.90613 0.40808 0.00035 1.7532
34.95 0.9085 0.43696 -0.00099 0.2621 36.65 0.9025 0.41118 0.000733 2.4178
35 0.9074 0.42168 -0.00117 0 36.7 0.90096 0.41973 0.000813 2.6983
35.05 0.9087 0.40974 -0.00087 0.0082 36.75 0.9052 0.43219 0.000568 2.4949
35.1 0.9067 0.40149 -0.00025 0.7733 36.8 0.90337 0.43445 9.13E-05 1.8943
35.15 0.9069 0.40274 0.000465 1.8099 36.85 0.9043 0.43307 -0.00041 1.1388
35.2 0.9089 0.41395 0.00098 2.6933 36.9 0.90515 0.42662 -0.00074 0.5389
www.final-yearproject.com | www.finalyearthesis.com
90
35.25 0.9017 0.42026 0.001096 3.0761 36.95 0.90625 0.41833 -0.00076 0.3408
35.3 0.9028 0.43243 0.00077 2.8174 37 0.90731 0.41199 -0.00047 0.6201
35.35 0.9031 0.43865 0.000138 2.0269 37.05 0.90664 0.40827 1.71E-07 1.2511
35.4 0.9041 0.43732 -0.00054 1.0246 37.1 0.90759 0.41159 0.000465 1.9662
35.45 0.9081 0.43141 -0.00098 0.2229 37.15 0.90473 0.4168 0.000732 2.4734
35.5 0.9079 0.41921 -0.00101 0 37.2 0.90353 0.42472 0.000699 2.5818
35.55 0.9084 0.40951 -0.00063 0.3235 37.25 0.90242 0.43017 0.000385 2.2539
35.6 0.905 0.40325 -1.05E-05 1.1525 37.3 0.90366 0.43319 -8.25E-05 1.6254
35.65 0.9057 0.40649 0.000602 2.097 37.35 0.90788 0.43146 -0.00051 0.952
35.7 0.9041 0.41469 0.000963 2.7777 37.4 0.91043 0.42868 -0.00072 0.5113
42.15 0.905 0.42609 -0.00011 1.4369 44.5 0.90487 0.42399 8.42E-05 1.6716
42.2 0.9048 0.42336 -0.00025 1.1998 44.55 0.9052 0.42474 -3.25E-05 1.5111
42.25 0.9057 0.42118 -0.00028 1.0853 44.6 0.90514 0.42342 -0.00014 1.3479
42.3 0.9059 0.41834 -0.00021 1.1424 44.65 0.90552 0.42191 -0.00018 1.2467
42.35 0.904 0.41505 -4.94E-05 1.3414 44.7 0.90446 0.41882 -0.00015 1.251
42.4 0.906 0.41682 0.000128 1.6033 44.75 0.90499 0.41782 -6.05E-05 1.3569
42.45 0.9052 0.41908 0.000247 1.8148 44.8 0.90569 0.41846 5.07E-05 1.5186
42.5 0.9025 0.41924 0.000265 1.8975 44.85 0.90515 0.41922 0.000139 1.6676
42.55 0.9023 0.42148 0.000174 1.8167 44.9 0.9056 0.4213 0.000168 1.7413
42.6 0.9025 0.4239 1.34E-05 1.6078 44.95 0.90508 0.42301 0.000129 1.72
42.65 0.9055 0.42505 -0.00015 1.3581 45 0.90562 0.42394 3.79E-05 1.6086
42.7 0.9055 0.4229 -0.00025 1.1703
42.75 0.904 0.41885 -0.00025 1.1201
42.8 0.9063 0.41824 -0.00014 1.2252
42.85 0.9059 0.41695 1.54E-05 1.4386
42.9 0.9058 0.41841 0.000163 1.6699
42.95 0.903 0.418 0.000242 1.8284
43 0.9046 0.42252 0.000226 1.853
43.05 0.9022 0.42272 0.000114 1.7338
43.1 0.9052 0.42537 -4.15E-05 1.5196
43.15 0.9036 0.42252 -0.00018 1.3005
43.2 0.9059 0.42243 -0.00024 1.1689
43.25 0.9058 0.4194 -0.0002 1.1712
43.3 0.9032 0.4156 -8.77E-05 1.3056
43.35 0.904 0.41613 6.02E-05 1.5126
43.4 0.9078 0.42101 0.000181 1.7117
43.45 0.9051 0.42115 0.000225 1.8202
43.5 0.9032 0.42159 0.000179 1.7975
43.55 0.9087 0.43 6.34E-05 1.6571
43.6 0.9049 0.42462 -8.11E-05 1.4527
43.65 0.9056 0.42388 -0.00019 1.2682
43.7 0.9043 0.41997 -0.00022 1.1835
43.75 0.9047 0.41807 -0.00016 1.2285
www.final-yearproject.com | www.finalyearthesis.com
91
43.8 0.9057 0.41789 -3.43E-05 1.3815
43.85 0.9057 0.41825 0.0001 1.5812
43.9 0.9055 0.42004 0.000189 1.7406
43.95 0.9051 0.42213 0.000198 1.7983
44 0.908 0.42675 0.000128 1.7344
44.05 0.9048 0.42455 5.56E-06 1.5752
44.1 0.9077 0.42635 -0.00012 1.3876
44.15 0.904 0.42101 -0.00019 1.2496
44.2 0.9034 0.41754 -0.00018 1.2173
44.25 0.9057 0.41858 -0.00011 1.2982
44.3 0.906 0.41847 1.22E-05 1.4563
44.35 0.906 0.41926 0.000123 1.6287
44.4 0.9057 0.42077 0.000186 1.7481
44.45 0.9054 0.42281 0.000168 1.7648
www.final-yearproject.com | www.finalyearthesis.com