adaptive and non-linear excitation control of …

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

www.final-yearproject.com | www.finalyearthesis.com

ii

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.


iii

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


iv

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


v

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


vi

GRAPHICAL REPRESENTATION OF GANTT CHART


vii

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


viii

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


ix

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


x

FUTURE IMPROVEMENTS ______________________________________________ 85

BIBLIOGRAPHY _________________________________________________________ 86

APPENDIX A _____________________________________________________________88


1

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


2

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.


3

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].


4

CHAPTER #

01

POWER SYSTEM STABILITY

ANALYSIS


5

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).


6

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.


7

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.


8

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


9

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


10

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


11

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


12

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


13

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]


14

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


15

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


16

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


17

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


18

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.


19

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.


20

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 .


21

CHAPTER # 02

Literature Review

ARTIFICIAL NEURAL NETWORK


22

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.


23

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


24

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


25

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.


26

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]


27

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.


28

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


29

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


30

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.


31

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


32

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


33

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


34

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.


35

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.


36

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


37

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


38

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.


39

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)


40

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.


41

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


42

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


43

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


44

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].


45

CHAPTER #

03

MATLAB SIMULATION


46

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.


47

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


48

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.


49

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.


50

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).


51

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.


52

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.


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


53

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).


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.



54

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


55

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:


56

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.


57

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.


3.5.2 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


58

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.


59

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:


60

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.


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


61

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


62

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.


63

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.


64

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


http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/powersys/ref/threephasetransformertwowindings.html

65

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


Configuration Tab

3.8.3 Limitations


66

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:


67

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.


Fundamental frequency

The fundamental frequency, in hertz, of the input signal.


68

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.


3.10.2 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.


69

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.


70

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.


71

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]


72

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


73

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).


74

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‟.


75

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:


76

POWER SYSTEM MODEL


77

CHAPTER # O4

RESULTS


78

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.


79

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


80

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


81

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


82

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


83

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


84

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


85

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


86

[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


87

[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


88

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


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


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


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


adaptive and non-linear excitation control of …

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