Batch 22 Final Documentation

ENHANCEMENT OF POWER SYSTEM DYNAMIC STABILITY

USING FUZZY LOGIC BASED PSS

Project report submitted in Partial fulfilment of the requirement for the award of the

Bachelors Degree by

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY-Kakinada

In the Department of

Electrical and Electronics Engineering

SUBMITTED BY

P.T.R. PRAMODH V.VINOD KUMAR

(Reg.No.11341A0278) (Reg.No.12345A0204)

K.YERNAMMA V.V. KALYAN VARMA

(Reg.No.12345A0215) (Reg.No.11341A02A7)

Under the esteemed guidance of

Mrs. S. LALITHA KUMARI

Assistant Professor

Dept. of EEE

GMRIT

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

GMR INSTITUTE OF TECHNOLOGY

Accredited by NBA, NAAC with A Grade & ISO 9001:2008 certified institution (Approved by AICTE, New Delhi & Autonomous institute Affiliated to JNTUK, Kakinada)

G.M.R. Nagar, Rajam-532 127, A.P

APRIL-2015

Department of Electrical and Electronics Engineering

G.M.R. INSTITUTE of TECHNOLOGY

G.M.R.NAGAR, RAJAM

CERTIFICATE

This is to certify that the project report entitled ENHANCEMENT OF POWER

SYSTEM DYNAMIC STABILITY USING FUZZY LOGIC BASED PSS that is being

submitted by P.T.R. PRAMODH, V.VINOD KUMAR, K.YERNAMMA, V.V. KALYAN VARMA in

partial fulfilment for the award of B.Tech degree in Electrical and Electronics Engineering to

the Jawaharlal Nehru Technological University is a record of bonafide work carried out

under our guidance and supervision.

The results embodied in this report have not been submitted to any other University or Institute

for the award of any degree or diploma.

PROJECT GUIDE HEAD OF THE DEPARTMENT

Mrs. S. LALITHA KUMARI Dr.T.SURESH KUMAR

Assistant Professor Professor, HOD

Dept. of EEE Dept. of EEE

GMRIT, GMRIT,

Rajam. Rajam.

ACKNOWLEDGEMENT

We are very much grateful to our Project Guide Smt. S.LALITHA KUMARI, Assistant

professor in Department of Electrical and Electronics Engineering, GMRIT, Rajam for her

help, guidance and patience she rendered to us in the completion of our project successfully.

We are glad to express our sincere thanks and respect to our beloved Head of the

Department Dr. T. SURESH KUMAR, for supporting us in our project.

We extend our sincere gratitude to our Principal, Dr. C.L.V.R.S.V PRASAD who has made

the atmosphere so easy to work.

Last but not the least; we thank the lab authorities and staff members of Electrical and

Electronics Department and everyone else who extended their help and guidance in the completion of

our project.

Sincerely,

PROJECT ASSOCIATES

P.T.R. PRAMODH (11341A0278)

V.VINOD KUMAR (12345A0204)

K.YERNAMMA (12345A0215)

V.V. KALYAN VARMA (11341A02A7)

CONTENTS

Page no.

List of figures i

List of symbols iii

Abstract v

Chapter 1: POWER SYSTEM STABILITY

1.1 Introduction 1

1.2 Power System and its problem statement 3

1.3 Classification of power system stability 4

1.3.1 Transient stability 4

1.3.2 Small signal stability 5

1.4 Damping of power system oscillations 5

1.5 Power system constraints 5

1.6 Stability constraints 6

Chapter 2: POWER SYSTEM STABILIZER

2.1 Introduction 7

2.2 Control action and controller design 7

2.3 Input signals 8

2.4 Control and tuning 9

2.5 Power system modelling 9

2.6 SMIB Power System Block 11 Diagram Model including PSS

2.7 Automatic voltage regulators and power conditioners 12

2.8 The need for automatic voltage regulation 14

2.8.1 Utility voltage levels 14

2.8.2 Voltage drop in a facility 15

2.8.3 Sensitivity to voltage levels and fluctuation 15

2.8.4 Changing voltage levels 16

2.8.5 Voltage too high, too low 16

2.8.6 The cost of voltage problems 17

Chapter 3: FUZZY INFERENCE SYSTEM

3.1 Introduction 19

3.2 What are inference systems? 19

3.3 Difference between fuzzy logic and conventional control methods 20

3.4 Design of fuzzy logic controller 20

3.5 Membership functions in fuzzy logic 21

3.6 Elements of fuzzy logic controller 23

3.6.1 Fuzzification 23

3.6.2 Rule base and inference engine 23

3.6.3 De-fuzzification 25

3.7 Features of fuzzy logic 26

Chapter 4: PROBLEM FORMULATION

4.1 Classical system model 28

4.2 Power system stabilizer 30

4.3 Fuzzy controller 32

4.4 Controller design procedure 33

4.5 Fuzzy logic based PSS 34

4.6 Selection of input and output variable 34

4.7 Membership functions 34

4.8 Fuzzy rule base 35

4.9 Defuzzification 36

4.10 Fuzzy inference system 36

Chapter 5: SIMULATION MODELS AND RESULTS

5.1 Performance with conventional PSS lead-lag 40

5.2 Results of AVR with PSS 41

5.3 Performance with fuzzy logic based PSS 42

5.4 Results of fuzzy logic based PSS 43

5.5 Comparison of results 44

5.6 Conclusion 45

Future scope 55

References 56

LIST OF FIGURES

Fig.no. Page.no.

2.1 Control system block diagram of PSS 7

2.2 Block diagram of PSS 10

2.3 Block diagram of the static 11

3.1 Block Diagram of fuzzy logic 21

3.2 Types of membership functions 22

4.1 Classical model of generator 28

4.2 Block diagram of single machine infinite bus system with classical model 29

4.3 Block diagram of representation with AVR and PSS 30

4.4 Thyristor excitation system with AVR and PSS 31

4.5 Equivalent diagram of fuzzy logic 33

4.6 Fuzzy interference system 37

4.6.1 Membership functions of speed deviation 37

4.6.2 Membership functions of acceleration 38

4.6.3 Membership functions of output voltage 38

4.7 Rule viewer of fuzzy controller 39

4.8 Surface viewer of fuzzy controller 39

5.1 The Simulink model of lead-lag power system stabilizer 40

5.2 Output for AVR with PSS with K5 positive 41

5.3 Output for AVR with PSS with K5 negative 41

i

5.4 Simulink Model of fuzzy logic based PSS 42

5.4.1 Fuzzy logic based PSS 42

5.5 Output of fuzzy logic based PSS with K5 negative 43

5.6 Output of fuzzy logic based PSS with K5 positive 43

ii

LIST OF SYMBOLS

Rotor Angle of Synchronous Generator in rad

f Frequency Oscillations in Hz

Damping Ratio

n Natural (Undamped) Frequency

D Damping Coefficient

Efd Excitation System Voltage in p.u.

GPSS(s) Transfer Function of the Power System Stabilizer

H Inertia Constant

K1 the change in electrical torque for a change in rotor angle

K2 the change in the electrical torque for a change in the flux linkages

K3 the impedance factor

K4 the demagnetizing effect of a change in rotor angle

K5 the change in the terminal voltage for change in the rotor angle

K6 the change in the terminal voltage for change in flux linkages

KA Exciter Gain

KD Damping Torque Coefficient

KPSS Power System Stabilizer Gain

KS Synchronizing Torque Coefficient

KS (AVR) Synchronizing Torque Coefficient of AVR

P Real Power Output

Q Reactive Power Output

Ra Armature Resistance

Re Transmission Line Resistance

T Sampling Period

TA Exciter Time Constant

Te Electrical Power Output in p.u.

Te (AVR) Electrical Power Output of AVR in p.u.

Tm Mechanical Power Input in p.u.

TPSS(z) Power System Stabilizer Transfer Function in z-domain

iii

TR Time constant of transducer

TW Washout Time Constant

T1 Lead Time Constant

T2 Lag Time Constant

T'do Open Circuit d-axis Time Constant in sec

Vb Rated Voltage

Vref Exciter Reference Input

Vs Power System Stabilizer Output Voltage

Vt Terminal Voltage

Vw Power System Stabilizer Washout Voltage

iv

ABSTRACT

The power system is a dynamic system and it is constantly being subjected to

disturbances. It is important that these disturbances do not drive the system to unstable conditions.

For this purpose, additional signal derived from speed deviation, excitation deviation and

accelerating power are injected into voltage regulators. The device to provide these signals is

referred as power system stabilizer.

The use of power system stabilizer has become very common in operation of large

electric power systems. The conventional PSS (AVR) which uses lead-lag compensation, where

gain setting designed for specific operating conditions, is giving poor performance under different

loading conditions. So, in this project it is discussed about the fuzzy logic based power system

stabilizer that stated the rise in settling time when compared to conventional PSS (AVR). The

comparison between both the types of power system stabilizers is done for both positive and

negative gains.

v

1. POWER SYSTEM STABILITY

1.1 INTRODUCTION : Power systems have developed from the original central generating station concept to a

modern interconnected system with improved technologies affecting each part of the system

separately. Successful operation of a power system depends largely on providing reliable and

uninterrupted service to the loads by the power utility. Ideally, constant voltage and frequency

should be supplied to the load at all times. In practical terms this means that both voltage and

frequency must be held within close tolerances so that the consumer loads run without interruption.

For example, the motor loads on the system may stop by a drop in voltage of l0-15% or a drop of

the system frequency of only a few hertz. Thus it can be accurately stated that the power system

operator must maintain a very high standard of continuous and reliable electrical service.

Small-signal stability, or the dynamic stability, can be defined as the behaviour of the

power system when subjected to small disturbances. It is usually concerned as a problem of

insufficient or poorly damping of system oscillations. These oscillations are undesirable even at

low-frequencies, because they reduce the power transfer in the transmission line and sometimes

introduce stress in the system.

An important requirement of reliable service is to keep the synchronous generators

running in parallel and with appropriate capacity to meet the load demand. If a generator loses

synchronism with the rest of the system, significant voltage and current fluctuations may occur and

transmission lines may be automatically tripped by their relays disconnecting important loads from

service.

Subsequent adjustments of generation due to random changes in load are taking place at

all times which makes steady state operation of power system not actually true state. Furthermore,

major changes do take place at times, e.g., a fault on the network, failure in a piece of equipment,

sudden application of a major load, or loss of a line or generating unit. So 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 is lost, the power it

was carrying must be obtainable from another source, but this view is wrong in

1

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.

Extensive emphasis on the economic design of generators, especially those of large

ratings was placed in the middle of the 20th century. This leads to the development of machines

with very large values for steady-state synchronous reactance, and that resulted in poor load-

voltage characteristics, especially when connected through long transmission lines.

On load, significant drop in the overall synchronizing torque caused by reduction of field

flux which is due to the armature reaction. Therefore, the transient stability related problems for

synchronous operation became the major concern. The problem was resolved by using high gain,

fast acting excitation control systems that provide sufficient synchronizing torque by virtually

eliminating the effect of armature reaction on reduction in synchronizing torque. However, voltage

regulator action was found to introduce negative damping torque at high power output and weak

external network conditions represented by long overhead transmission lines, a very common

operating situation in power systems around the world. Negative damping gave rise to an

oscillatory instability problem. The contradicting performance of the excitation control loop was

resolved by adjusting the voltage regulator reference input through an additional stabilizing signal,

which was meant to produce positive damping torque. The control circuitry producing this signal

was termed a power system stabilizer (PSS).

Power system operating conditions are subjected to changes due to many reasons. One of

these reasons is the load changes in the system. These operating conditions affect the stability of

the synchronous machine. Therefore, in order to provide an estimate of the stability of the system

which is based on operating conditions of the system that is obtained by either computer

simulations or measurements, a small-signal stability analysis should be conducted.

Small-signal stability (also called dynamic stability) analysis studies the behavior of

power systems under small perturbations. Its main objective is to evaluate the low-frequency

oscillations (LFO) resulting from poorly damped rotor oscillations.

2

Traditionally, small-signal stability analyses are carried out in frequency domain using

modal analysis method. This method implies estimation of the characteristic modes of a linearized

model of the system. It requires first load flow analysis, linearization of the power system around

the operating point, developing a state-space model of the power system, then computing the

eigenvalues, eigenvectors, and participation factors. Although eigenvalue analysis is powerful,

however, it is not suitable for online application in power system operation, as it requires

significantly large computational efforts. Alternative method based on electromagnetic torque

deviation has been developed. Torque deviation can be decomposed into synchronizing and

damping torques. The synchronizing and damping torques are usually expressed in terms of the

torque coefficients Ks and Kd. These coefficients can be calculated repeatedly and this makes it

suitable for online stability assessment.

1.2 Power System and its problem statement

Power system stability may be generally defined as the characteristic of a power system

that enables it to remain in a state of operating equilibrium under normal operating conditions and

to regain an acceptable state of equilibrium after being subjected to a disturbance. The stability of

the power system is concerned with the behaviour of the synchronous machines after they have

been disturbed. If the disturbance 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.

In the evaluation of stability, the concern is the behaviour of the power system when

subjected to disturbance. The disturbance may be small or large. Small disturbances in the form of

load changes take place continually, and the system adjusts itself to the changing conditions. The

system must be able to operate satisfactory under these conditions and successfully supply the

maximum amount of load. It must also be capable of surviving numerous disturbance of a severe

nature, such as short-circuit of a transmission line, loss of large generator or load, or loss of a tie

between two subsystems. Much of the equipments are involved & affected during the system

response to a disturbance. For example, a short-circuit on a critical element followed by its

isolation by protective relays will cause variations in power transfers, machine rotor speeds, and

3

bus voltages; the voltage variations will actuate both generator and transmission system voltage

regulators; the speed variations will actuate prime mover governors; the change in tie line loadings

may actuate generation controls; the changes in voltage and frequency will affect loads on the

system in varying degrees depending on their individual characteristics.

Interconnected AC generators produce torques that depend on the relative angular

displacement of their rotors. These torques act to keep the generators in synchronism. Thus, if

angular difference between generators increases, an electrical torque is produced that tries to reduce

the angular displacement. The angular displacements should settle to values that maintain the

required power flows through the transmission network and supply the system load.

If the disturbance is large on the transmission system, the nonlinear nature of the

synchronizing torque may not be able to return the generator angles to a steady state. Some or all

generators then loose synchronism and the system exhibits transient instability. On the other hand,

if the disturbance is small, the synchronizing torques keep the generators nominally in

synchronism, but the generators relative angles oscillate. In a correctly designed and operated

system, these oscillations decay.

In an overstressed system, small disturbances may result in oscillations that increase in

amplitude exponentially and lead the power system to instability. Moreover, the transient following

a system perturbation is oscillatory in nature; but if the system is stable, these oscillations will be

damped toward a new non-oscillatory operating condition. These oscillations, however, are

reflected as fluctuations in the power flow over the transmission lines. If a certain line connecting

two groups of machines undergoes excessive power fluctuations, it may be tripped out by its

protective equipment thereby disconnecting the two groups of machines.

1.3 Classification of Power System Stability

1.3.1 Transient stability

Transient stability is the ability to maintain synchronism when the system is subjected to a

large disturbance. In the resulting system response, the changes in the dynamic variables are large

and the nonlinear behaviour of the system is important.

4

Small Signal Stability (dynamic stability)

Small Signal Stability is the ability of the system to maintain stability under small

disturbance. Such disturbances occur continuously in the normal operation of a power system due

to small variations in load and generation. The disturbances are considered sufficiently small to

permit the use of linearized system model in the analysis of the small signal stability.

1.4 Damping of Power System Oscillations

Early investigations considered attention in the literature of the excitation system and its

ability in enhancing stability of the power system. Researchers have found that the negative

damping of large interconnected coupled system introduced by voltage regulators with high gain

was the main reason to experience oscillations. A solution to improve the damping in the system

was achieved by introducing a stabilizing signal into the excitation system. This signal should be

taken from power system stabilizer

1.5 Power System Constraints

The Power System should meet some constraints in which it does not exceed the limits

of the generation.

These constraints are summarized as follows:

The system should have the ability to supply the total generation (demand and losses).

Each bus in the system should not exceed its voltage magnitude beyond 5% of the nominal bus voltage.

Each generator should not exceed the real and reactive power capability constraints.

All the transmission lines and the transformers should not be overloaded.

5

1.6 Stability Constraints

The system stability depends on the electric torque of a synchronous machine, which in

turns depends on the synchronizing and damping torque. If the synchronizing torque increased

above or decreased beyond a certain limit, this will lead the system to instability through a non-

periodic drift in the rotor angle. Whereas, if this happened in the damping torque, it will lead the

system to oscillatory instability.

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2. POWER SYSTEM STABILIZER

2.1 Introduction

Power System Stabilizer (PSS) is a device which provides additional supplementary

control loops to the automatic voltage regulators system (AVR). Power system stabilizers (PSS) are

often used as an effective means to add damping to the generator rotor oscillations. Adding

supplementary control loops to the generator AVR is one of the most common ways of enhancing

both dynamic and transient stability. To provide damping for the generator rotor oscillations, PSS

must produce a component of electrical torque in phase with rotor speed deviations.

The basic functions of the PSS is to add a stabilizing signal that compensates the

oscillations of the voltage error of the excitation system during the dynamic/transient state, and to

provide a damping component when its on phase with rotor speed deviation of machine.

SMIB Power System Model Including PSS.

2.2 Control Action and Controller Design

The action of a PSS is to extend the angular stability limits of a power system by providing

supplemental damping to the oscillation of synchronous machine rotors through the generator

excitation. This damping is provided by a electric torque applied to the rotor that is in phase with

the speed variation. Once the oscillations are damped, the thermal limit of the tie-lines in the

system may then be approached. This supplementary control is very beneficial during line outages

and large power transfers. However, power system instabilities can arise in certain circumstances

due to negative damping effects of the PSS on the rotor. The reason for this is that PSSs are tuned

around a steady-state operating point; their damping effect is only valid for small excursions around

this operating point. During severe disturbances, a PSS may actually cause the generator under its

control to lose synchronism in an attempt to control its excitation field.

Fig 2.1 Control system block diagram of PSS

The output signal of any PSS is a voltage signal, noted here as VPSS(s), and added as an input

signal to the AVR/exciter. For the structure shown in Figure, this is given by

7

This particular controller structure contains a washout block, sTW/(1+sTW), used to reduce the over-

response of the damping during severe events. Since the PSS must produce a component of

electrical torque in phase with the speed deviation, phase lead blocks circuits are used to

compensate for the lag (hence, lead-lag) between the PSS output and the control action, the

electrical torque. The number of lead-lag blocks needed depends on the particular system and the

tuning of the PSS. The PSS gain KS is an important factor as the damping provided by the PSS

increases in proportion to an increase in the gain up to a certain critical gain value, after which the

damping begins to decrease. All of the variables of the PSS must be determined for each type of

generator separately because of the dependence on the machine parameters. The power system

dynamics also influence the PSS values. The determination of these values is performed by many

different types of tuning methodologies.

2.3Input Signals

The input signal for the PSSs in the system is also a point of debate. The signals that

have been identified as valuable include deviations in the rotor speed (= mach - o), the

frequency (f) the electrical power (Pe) and the accelerating power (Pa). Since the main action of

the PSS is to control the rotor oscillations, the input signal of rotor speed has been the most

frequently advocated in the literature. Controllers based on speed deviation would ideally use a

differential-type of regulation and a high gain. Since this is impractical in reality, the previously

mentioned lead-lag structure is commonly used. However, one of the limitations of the speedinput

PSS is that it may excite torsional oscillatory modes.

A power/speed (Pe-, or delta-P-omega) PSS design was proposed as a solution to the

torsional interaction problem suffered by the speed-input PSS. The power signal used is the

generator electrical power, which has high torsional attenuation. Due to this, the gain of the PSS

may be increased without the resultant loss of stability, which leads to greater oscillation damping.

8

A frequency-input controller has been investigated as well. However, it has been found

that frequency is highly sensitive to the strength of the transmission system - that is, more sensitive

when the system is weaker - which may offset the controller action on the electrical torque of the

machine. Other limitations include the presence of sudden phase shifts following rapid transients

and large signal noise induced by industrial loads . On the other hand, the frequency signal is more

sensitive to inter-area oscillations than the speed signal, and may contribute to better oscillation

attenuation .

The use of a power signal as input, either the electrical power (Pe) or the accelerating

power (Pa = Pmech - Pelec), has also been considered due to its low level of torsional interaction. The

Pa signal is one of the two involved in the 4-loop AVR/PSS controller from, even though the

tuning method related to this design approach is valid for other input signals.

2.4 Control and Tuning

The conflicting requirements of local and inter-area mode damping and stability under

both small signal and transient conditions have led to many different approaches for the control and

tuning of PSSs. Methods investigated for the control and tuning include state-space/frequency

domain techniques , residue compensation, phase compensation/root locus of a lead-lag controller ,

desensitization of a robust controller, pole-placement for a PID-type controller , scarcity techniques

for a lead-lag controller and a strict linearization technique for a linear quadratic controller. The

diversity of the approaches can be accounted for by the difficulty of satisfying the conflicting

design goals, and each method having its own advantages and disadvantages. This is the crux of the

problem of low frequency oscillation damping by the application of power system stabilizers.

2.5 Power system modelling

The purpose of a PSS is to introduce a damping torque component in phase with the

speed deviation . PSS input signals can be derived from machine speed or power. Where PSS

output is connected to the input of the exciter.

A direct feedback of would result in a damping torque component if the exciter

transfer function Ka and the generator transfer function between Efd and Te were pure gains as

9

shown in Figure. However, in practice both the generator and the exciter exhibit frequency

dependent gain and phase characteristic. Therefore, the GPSS(S) transfer function, as shown in

Figure should have appropriate phase compensation circuits to compensate for the phase lag

between the exciter input and the electrical torque. In the ideal case, with phase characteristic of

PSS being an exact inverse of the exciter (AVR) and generator phase characteristic to be

compensated, the GPSS(S) would result in a pure damping torque at all oscillation frequencies.

If the phase-lead network provides more compensation than the phase lag between Te

and Vs, the PSS introduces, in addition to a damping component of torque, a negative

synchronizing torque component. Conversely, with under-compensation a positive synchronizing

torque component is introduced. Usually, the PSS is required to contribute to the damping of the

rotor oscillations over a range of frequencies, rather than a single frequency.

The Lead Lag PSS transfer function is given as,

As shown in Figure, the PSS block diagram representation is composed of three blocks:

a gain block, a signal washout block and phase compensation block.

Fig 2.2 Block diagram of PSS

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2.6 SMIB Power System Block Diagram Model including PSS

The theoretical basis for a PSS may be illustrated with the aid of the block diagram shown in

Figure

Fig 2.3 Block diagram of static excitation system

For small-signal stability study, stabilizer output limits and exciter output limits are not

considered so they are omitted in Figure.

The stabilizer gain (KPSS) function is to determine the amount of damping introduced by

the PSS. The basic function of the washout block is to serve as a high-pass filter, also it allows the

PSS to respond only to changes in speed and it prevent the steady changes in speed to modify the

terminal voltage. From the viewpoint of the washout function, the value of Tw is not critical and

may be in the range of 1 to 20 seconds. The main consideration is that it is long enough to pass

stabilizing signals at the frequencies of interest unchanged.

11

The function of the phase compensation block is to provide the appropriate phase-lead

characteristic to compensate for the phase lag between the exciter input and the generator electrical

(air-gap) torque.

In a single first-order phase compensation block were used to represent the phase

compensation circuit. However, in practice two or more first-order blocks may be used to achieve

the desired phase compensation. In some cases, second-order blocks with complex roots have been

used. Normally, the frequency range is 0.1 to 2 Hz, and the phase-lead network should provide

compensation over this entire frequency range. The phase characteristic to be compensated changes

with system conditions; therefore, a compromise is made and a characteristic acceptable for

different conditions is selected. Generally some under-compensation is desirable so that the PSS, in

addition to significantly increasing the damping torque, results in slight increase of the

synchronizing torque.

2.7 Automatic voltage regulators and power conditioners

An AVR is the heart of devices often called power conditioners or power stabilizers. The

typical power conditioner is an automatic voltage regulator combined with one or more other

power-quality capabilities such as:

Surge suppression

Short circuit protection (circuit breaker)

Line noise reduction

Phase-to-phase voltage balancing

Harmonic filtering, etc.

Power conditioners are typically used in low voltage (< 600V) applications and sizes

below 2,000 kVA. Since there is no official definition of a power conditioner, there are some

devices marketed as power conditioners that do not provide automatic voltage regulation. This fact

and the wide variation in capability between products make it imperative the buyer does his or her

homework to match product functionality and application needs.

The automatic voltage regulator (AVR) is a device designed to regulate voltage

automatically that is, to take a fluctuating voltage level and turn it into a constant voltage level.

12

There are many types of automatic voltage regulators.

Automatic voltage regulators not only vary in size and design, but also in name and

description. Common names for AVRs include:

Auto-boost regulator

Constant voltage regulator

Constant voltage transformer

CVT

Double conversion electronic voltage regulator

Electromechanical voltage regulator

Electromechanical voltage stabilizer

Electronic tap-switching voltage regulator

Electronic voltage regulator

EVR

Ferro resonant transformer

Ferro resonant voltage regulator

LDC

Line voltage regulator

Line drop compensator

Magnetic induction voltage regulator

Magnetic induction voltage stabilizer

Mechanical tap-changing regulator

Motor-driven variable autotransformer

Motorized variac

Motorized variable transformer

OLTC

On load tap changer

Servo voltage regulator

Servo voltage stabilizer

Step voltage regulator

Tap changer

Tap-switching voltage regulator

13

Variable autotransformer

In the sections describing the different types of voltage regulators, common names for

each type will be identified and used interchangeably along with generic names, such as AVR and

automatic voltage regulator. Please note that the descriptions, operational explanations and other

commentary provided about the different types of AVRs is for informational purposes only and is

intended to provide an overview of variations among a class of products generically called

automatic voltage regulators.

2.8 The need for automatic voltage regulation

Many factors contribute to the need for automatic voltage regulation. However, the

ultimate reason for using voltage regulation is financial to avoid the costs associated with

equipment damage and downtime caused by poor voltage levels.

This section discusses why voltage levels fluctuate, what can be expected, what type of

problems may be encountered and more

Utility Voltage Levels

Voltage Drop in a Facility

Sensitivity to Voltage Levels & Fluctuation

Changing Voltage Levels

Voltage Too High, Too Low

The Cost of Voltage Problems

2.8.1 Utility voltage levels

Anyone receiving power from an electric utility will see the nominal incoming voltage

level (e.g. 120V) change over the course of a day to a small or large degree. There are many factors

contributing to the amount of voltage level fluctuation observed including: 1) location on the local

distribution line, 2) proximity to large electricity consumers, 3) proximity to utility voltage

regulating equipment, 4) seasonal variations in overall system voltage levels, 5) load factor on local

transmission and distribution system, etc.

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Voltage levels are often highest during the night time hours and weekends when the

electrical demand is minimal and are lowest weekday afternoons when the demand for electricity

peaks. On the nominal 480V system, this would translate to incoming voltage ranging from 509V

(480V +6%) to 420V (480V-13%). Larger deviations from nominal voltage are also permissible on

a momentary basis or may simply be unavoidable.

2.8.2 Voltage drop in a facility

It is expected and accepted that there will be a voltage drop of 3 to 5% from the point

where the electric utility delivers power to the end user (usually at the meter) to the point within a

facility where the electricity is finally consumed in an electrical device (the load). Unlike utility

voltage levels which may be high or low, the voltage drop due to wiring impedance within a

building will always drive voltage levels lower. For example, if the incoming utility voltage is 5%

low, the voltage at the point of usage might be 8 to 10% (5%+3% to 5%+5%) below nominal due

to the voltage drop within a building.

AC motors are commonly rated at 460V (480V-4%) rather than 480V to address the

voltage drop in a facility and to optimize motor performance.

2.8.3 Sensitivity to voltage levels and voltage fluctuation

Every piece of electrical equipment will operate within a range of voltage levels,

however not necessarily with optimal performance. When the voltage level falls outside of its

operational range, a device may be unable to start or operate, it may malfunction or the device may

be damaged. The width of the voltage level range within which a device will operate is a measure

of its sensitivity to voltage level.

A device that will operate fairly well within a range of +/-10% of nominal voltage

would be considered to have a relatively low sensitivity to voltage level or voltage fluctuations. A

device that operates properly only when the voltage level is within +/-5% (or less) of nominal

voltage would be considered to be sensitive to voltage level or fluctuations. Three phase motors are

very tolerant of voltage level fluctuations while the electronic controls for the same motor might be

quite sensitive.

15

2.8.4 Changing voltage levels

One must realize that utility voltage levels are very dynamic and will most assuredly

change over time for better or for worse; instantly or over a long period. The problem is often that

there is no advance warning about when, how much or in which direction they will change.

An electric utility is required to provide electricity to all customers who demand it, and

the utility attempts to provide the best voltage levels possible to the greatest number of customers.

However, the utility usually has little control over the amount of electricity demanded by any

customer at any given time. Add to this the fact that increasing use of relatively sensitive

electronics in nearly all facets of business and industry and the growing need for voltage regulation

becomes clearer.

Worldwide, sales of voltage regulation products of all types are growing at nearly 10%

per year. Some of the factors that account for this are:

Growing use of sensitive electronics in industrial and commercial settings

Increasing demand for electric power

Electric generation and distribution infrastructure limitations

2.8.5 Voltage too high, too low

Voltage that is too high can cause premature failure of electrical and electronic

components (e.g. circuit boards) due to overheating. The damage caused by overheating is

cumulative and irreversible. Frequent episodes of mild overheating can result in the same amount

of component damage as a few episodes of severe overheating. Like slicing a loaf of bread you

can have many thin slices or a few really thick slices but when you get to the end, youre done.

Motors can, on the other hand, often benefit from voltages that tend to be a little bit high. The

reason is fairly simple. As the voltage level goes up, the current is reduced and lower current

usually equates to less heat generation within the motor windings.

There is a point where the voltage level supplied can be so high as to damage a motor

but this level is far higher than that for electronics. Keeping electrical and electronic components

cool tends to insure their longevity. Slight reductions in voltage levels may permit many electronics

to perform perfectly well while minimizing their temperature. Of course, the same is not true of

16

motors. Just as higher voltages can help reduce motor operating temperatures, low voltage is a

major cause of motor overheating and premature failure. A low voltage forces a motor to draw

extra current to deliver the power expected of it thus overheating the motor windings. The rule of

thumb for motors is for every 10 degrees C (50 degrees F) a motor is operated above its rated

temperature, motor life will be decreased by 50%.More than motors and circuit boards are at risk

for damage when voltage levels are bad, but chronic problems with either is often an indication of a

voltage problem.

2.8.6 The cost of voltage problems

Few homeowners can justify the cost of an automatic voltage regulator for whole-house

application. Except for those living in remote or isolated areas, the voltage supplied by the local

utility is usually entirely adequate for common household appliances and electronics. Even if the

voltage levels is off by as much as 5% or more, most household devices will operate satisfactorily

and have a reasonable service life. Those living in isolated areas will usually find the utility willing

to do all they reasonably can to deliver a proper voltage, but the homeowner may find themselves

having to make some accommodations to be able to operate large, power-consuming equipment

such as welders, woodworking equipment, etc.

There appears to be a growing number of very small automatic voltage regulators for

use with home theatre and audio equipment. These devices are quite inexpensive compared to their

commercial/industrial counterparts and do provide adequate performance and capability for home

electronics. Application of these home-type AVRs in applications with commercial and industrial

types of equipment has been reported to be quite unsatisfactory with the AVR failing very quickly.

Downtime in medium to large industrial operations can cost tens of thousands to millions of dollars

each hour. In smaller commercial and industrial companies, the dollars amounts may not be nearly

so dramatic but the impact of voltage-related problems can be equally devastating:

Lost production and revenue

Increased scrap and rework cost

Increased raw material cost

Increased labour or overtime

Increased quality problems and paperwork

17

Late or missed deliveries

Reduced customer satisfaction

Increased safety or environmental issues

What all of this really means is that voltage problems ultimately impact the bottom line of a

business through increased costs and reduced productivity. Each business has to evaluate its own

situation (proactively or reactively) and decide how much they can save by applying voltage

regulation.

18

3. FUZZY INFERENCE SYSTEM

3.1 Introduction

An objective of fuzzy logic has been to make computers think like people. Fuzzy logic

deal with the vagueness intrinsic to human thinking and natural language and recognizes that its

nature is different from randomness. Using fuzzy logic algorithms could enable machines to

understand and respond to vague human concepts such as hot, cold, large, small, etc. It also

could provide a relatively simple approach to reach definite conclusions from imprecise

information.

3.2 Fuzzy Interference Systems

Fuzzy inference is the process of formulating the mapping from a given input to an

output using fuzzy logic. The mapping then provides a basis from which decisions can be made,

or patterns discerned. The process of fuzzy inference involves all of the pieces that are described

in the previous sections: Membership Functions, Logical Operations, and If-Then Rules. There

are two types of fuzzy inference systems that can be implemented in Fuzzy Logic Toolbox:

Mamdani-type and Sugeno-type.

These two types of inference systems vary somewhat in the way outputs are

determined. Fuzzy inference systems have been successfully applied in fields such as automatic

control, data classification, decision analysis, expert systems, and computer vision. Because of

its multidisciplinary nature, fuzzy inference systems are associated with a number of names, such

as fuzzy-rule-based systems, fuzzy expert systems, fuzzy modeling, fuzzy associative memory,

fuzzy logic controllers, and simply (and ambiguously) fuzzy systems. Mamdani's fuzzy inference

method is the most commonly seen fuzzy methodology. Mamdani's method was among the first

control systems built using fuzzy set theory. It was proposed in 1975 by Ebrahim Mamdani as an

attempt to control a steam engine and boiler combination by synthesizing a set of linguistic

control rules obtained from experienced human operators. Mamdani's effort was based on Lotfi

Zadeh's 1973 paper on fuzzy algorithms for complex systems and decision processes. Although

the inference process described in the next few sections differs somewhat from the methods

described in the original paper, the basic idea is much the same.Mamdani-type inference, as

defined for Fuzzy Logic Toolbox, expects the output membership functions to be fuzzy sets.

After the aggregation process, there is a fuzzy set for each output variable that needs

19

defuzzification. it is possible, and in many cases much more efficient, to use a single spike as the

output membership function rather than a distributed fuzzy set. This type of output is sometimes

known as a singleton output membership function, and it can be thought of as a pre-defuzzified

fuzzy set. It enhances the efficiency of the defuzzification process because it greatly simplifies

the computation required by the more general Mamdani method, which finds the centroid of a

two-dimensional function. Rather than integrating across the two-dimensional function to find

the centroid, you use the weighted average of a few data points. Sugeno-type systems support

this type of model. In general, Sugeno-type systems can be used to model any inference system

in which the output membership functions are either linear or constant.

3.3 Difference between fuzzy logic and conventional control methods

Fuzzy Logic incorporates a simple, rule-based IF X AND Y THEN Z approach to a

solving control problem rather than attempting to model a system mathematically. The FL

model is empirically - based, relying on an operators experience rather than their technical

understanding of the system. For example , rather than dealing with temperature control in

terms such as SP=500F, T

Figure 3.1 Block Diagram of Fuzzy Logic

The fuzzy logic control has tried to handle the robustness, reliability and

nonlinearities associated with power system controls. Therefore a fuzzy logic controller (FLC)

becomes nonlinear and adaptive in nature having a robust performance under parameter

variations with the ability to get desired control actions for complex uncertain , and

nonlinear systems without their mathematical models and parameter estimation.

3.5 Membership Functions in Fuzzy Logic

The only condition a membership function must really satisfy is that it must vary

between 0 and 1. The function itself can be an arbitrary curve whose shape we can define as a

function that suits us from the point of view of simplicity, convenience, speed, and efficiency.

A classical set might be expressed as A = {x | x > 6}.A fuzzy set is an extension of a classical set.

If X is the universe of discourse and its elements are denoted by x, then a fuzzy set A in X is

defined as a set of ordered pairs. A = {x, A(x) | x ? X} A(x) is called the membership function

(or MF) of x in A.

The membership function maps each element of X to a membership value between 0 and 1.Fuzzy

Logic includes 11 built-in membership function types. These 11 functions are, in turn, built from

21

several basic functions: piecewise linear functions the Gaussian distribution function the sigmoid

curve quadratic and cubic polynomial curves

By convention, all membership functions have the letters mf at the end of their names. The

simplest membership functions are formed using straight lines. Of these, the simplest is the

triangular membership function, and it has the function name trimf. This function is nothing more

than a collection of three points forming a triangle. The trapezoidal membership function, trapmf,

has a flat top and really is just a truncated triangle curve. These straight line membership

functions have the advantage of simplicity.

Two membership functions are built on the Gaussian distribution curve: a simple Gaussian

curve and a two-sided composite of two different Gaussian curves. The two functions are gaussmf

and gauss2mf.

The generalized bell membership function is specified by three parameters and has the

function name gbellmf. The bell membership function has one more parameter than the Gaussian

membership function, so it can approach a non-fuzzy set if the free parameter is tuned. Because of

their smoothness and concise notation, Gaussian and bell membership functions are popular

methods for specifying fuzzy sets Although the Gaussian membership functions and bell

membership functions achieve smoothness, they are unable to specify asymmetric membership

functions, which are important in certain applications. Next, you define the sigmoidal membership

function, which is either open left or right. Asymmetric and closed (i.e.not open to the left or

right) membership functions can be synthesized using two sigmoidal functions, so in addition to

the basic sigmf, you also have the difference between two sigmoidal functions, dsigmf, and the

product of two sigmoidal functions psigmf.

Polynomial based curves account for several of the membership functions. Three related

membership functions are the Z, S, and Pi curves, all named because of their shape. The function

zmf is the asymmetrical polynomial curve open to the left, smf is the mirror-image function that

opens to the right, and pimf is zero on both extremes with a rise in the middle.

Fig 3.2 Types of Membership functions

22

There is a very wide selection to choose from when you're selecting your favorite

membership function. Fuzzy Logic Toolbox also allows you to create your own membership

functions if you find the list too restrictive.

However, if a list based on expanded membership functions seems too complicated, just

remember that you could probably get along very well with just one or two types of membership

functions, for example the triangle and trapezoid functions. The selection is wide for those who

want to explore the possibilities, but expansive membership functions are not necessary for good

fuzzy inference systems. Finally, remember that more details are available on all these functions

in the reference section.

Fuzzy sets describe vague concepts (e.g., fast runner, hot weather, and weekend days).A

fuzzy set admits the possibility of partial membership in it. (e.g., Friday is sort of a weekend day,

the weather is rather hot).The degree an object belongs to a fuzzy set is denoted by a membership

value between 0 and 1. (e.g., Friday is a weekend day to the degree 0.8).A membership function

associated with a given fuzzy set maps an input value to its appropriate membership value.

3.6 Elements of fuzzy logic controller

There are three principal elements to a fuzzy logic controller:

1) Fuzzification module (Fuzzifer)

2) Rule base and Inference engine

3) De-fuzzification module (Defuzzifier)

3.6.1 Fuzzification

Fuzzification is the process of transforming real-valued variable into a fuzzy set

variable. Fuzzy variables depend on nature of the system where it is implemented. The

triangular membership function with seven linguistic variable is used in this study. The natural

language representation of a variable is called as linguistic variable.

3.6.2 Rule base and inference engine:

The heart of the fuzzy system is a knowledge base consisting of fuzzy IF-THEN rules.

The rule base consists of a set of fuzzy rules. The data base contains the membership function of

23

fuzzy subsets. A fuzzy rule may contain fuzzy variables and fuzzy subsets characterized by

membership function. Fuzzy mathematical tools and the calculus of fuzzy IF-THEN rules

provide a most useful paradigm for the automation and implementation of an extensive body of

human knowledge heretofore not embodied in the quantitative modeling process. Fuzzy rule

base is formed using the decision table, the number of rules, is based on the number of

variables selected for each input membership function. The process of determining the exact

value and shape of membership is by experience and by trial & error method. These rules

relate input signals to the output control signal.

The core section of a fuzzy system is that part, which combines the facts obtained from

the fuzzification with the rule base and conducts the fuzzy reasoning process. This is called

a fuzzy inference machine.

In the following, for simplicity it is assumed that there is only one input x1=x and the

rule base is described with max/min operators,

then,

The operations can be reordered such that only the relevant operands are on the right-

hand side. Then,

This equation is obtained for the reasoning process. The inner term Hr, which combines

the fact with the premise, is a constant and is called degree of relevance of the ruler. It

characterizes the relevance of the fired rule and can be treated as a de-normalized universal

fuzzy set.

The control signal in the fuzzy form is obtained by applying mamdani product

implication inference because of its computational simplicity. The heuristic rules of the

knowledge base are used to determine the fuzzy controller action.

24

3.6.3 De-fuzzification

The purpose of de-fuzzification is to convert the output fuzzy variable to a crisp value, So

that it can be used for control purpose. It is employed because crisp control action is required in

practical applications. Since the fuzzy logic controller action corresponds to an increment Pc,

this type of controller will give zero steady-state error for an input step change in the reference to

any step disturbance. The centroid method of de-fuzzification is employed here. The membership

functions, knowledge base and method of de-fuzzification essentially determine the controller

performance.

A common and useful defuzzification technique is center of gravity. First, the results of

the rules must be added together in some way. The most typical fuzzy set membership function

has the graph of a triangle. Now, if this triangle were to be cut in a straight horizontal line

somewhere between the top and the bottom, and the top portion were to be removed, the

remaining portion forms a trapezoid. The first step of defuzzification typically "chops off" parts of

the graphs to form trapezoids (or other shapes if the initial shapes were not triangles). For

example, if the output has "Decrease Pressure (15%)", then this triangle will be cut 15% the way

up from the bottom. In the most common technique, all of these trapezoids are then superimposed

one upon another, forming a single geometric shape. Then, the centroid of this shape, called

the fuzzy centroid, is calculated. The x-coordinate of the centroid is the defuzzified value.

There are many different methods of defuzzification available, including the following:

AI (adaptive integration)

BADD (basic defuzzification distributions)

BOA (bisector of area)

CDD (constraint decision defuzzification)

COA (center of area)

COG (center of gravity)

ECOA (extended center of area)

EQM (extended quality method)

FCD (fuzzy clustering defuzzification)

FM (fuzzy mean)

25

FOM (first of maximum)

GLSD (generalized level set defuzzification)

ICOG (indexed center of gravity)

IV (influence value)

LOM (last of maximum)

MeOM (mean of maxima)

MOM (middle of maximum)

QM (quality method)

RCOM (random choice of maximum)

SLIDE (semi-linear defuzzification)

WFM (weighted fuzzy mean)

The maxima methods are good candidates for fuzzy reasoning systems. The distribution

methods and the area methods exhibit the property of continuity that makes them suitable for

fuzzy controllers.

3.7 Features of fuzzy logic

Fuzzy Logic offers several unique features that make it a particularly good choice for

many control problems.

1) It is inherently robust since it does not require precise, noise-free inputs and can be

programmed to fail safely if a feedback sensor quits or is destroyed. The output control is

a smooth control function despite a wide range of input variations.

2) Since the Fuzzy Logic controller processes user-defined rules governing the target control

system, it can be modified and tweaked easily to improve or drastically alter system

performance. New sensors can easily be incorporated into the system simply by generating

appropriate governing rules.

3) Fuzzy Logic is not limited to a few feedback inputs and one or two control outputs, nor is it

necessary to measure or compute rate-of-change parameters in order for it to be

implemented. Any sensor data that provides some indication of a system's actions and

26

reactions is sufficient. This allows the sensors to be inexpensive and imprecise thus

keeping the overall system cost and complexity low.

4) Because of the rule-based operation, any reasonable number of inputs can be processed

(1-8 or more) and numerous outputs (1-4 or more) generated, although defining the rule

base quickly becomes complex if too many inputs and outputs are chosen for a single

implementation since rules defining their interrelations must also be defined. It would be

better to break the control system into smaller chunks and use several smaller FL

controllers distributed on the system, each with more limited responsibilities.

5) Fuzzy Logic can control nonlinear systems that would be difficult or impossible to

model mathematically. This opens doors for control systems that would normally be deemed

unfeasible for automation.

27

4. PROBLEM FORMULATION

The best method for the analysis and maintaining the power system dynamic stability should be

formulated by analyzing all the results from different types of power system stabilizers at different gain

conditions.The Mathematical Models needed for small signal analysis of Synchronous Machines, lead-lag

power system stabilizer are briefly reviewed. The Guidelines for the selection of Power System Stabilizer

parameters are also presented. A Synchronous Machine Model The synchronous machine is vital for power

system operation. The general system configuration of synchronous machine connected to infinite bus through

transmission network can be represented as the mathematical models needed for small signal analysis of

synchronous machine; excitation system and the lead-lag power system stabilizer are briefly reviewed. The

guidelines for the selection of power system stabilizer parameters are also presented.

4.1 Classical System Model

The generator is represented as the voltage E' behind Xd' as The magnitude of E' is assumed to

remain constant at the pre-disturbance value. Let d be the angle by which E' leads the infinite bus voltage EB.

The d changes with rotor oscillation. The line current is expressed as

Fig 4.1 Classical model of generator

28

With stator resistance neglected, the air-gap power is equal to the terminal power. In per unit,

the air-gap torque is equal to the air gap power.

component

Fig 4.2 Block diagram of single machine infinite bus system with classical model

From the block diagram we have:

29

Solving the block diagram we get the characteristics equation:

Comparing it with general form, the undamped natural frequency n and damping ratio are expressed as

4.2 Power system stabiliser

The basic function of power system stabilizer is to add damping to the generator rotor oscillations

by controlling its excitation using auxiliary stabilizing signals. For provide damping signal the stabilizer must

produce a component of electrical torque in phase with rotor speed deviation. The Power System Stabilizer

with the aid of block diagram as shown,

VOLTAGE TRANSDUCER

Fig 4.3 Block diagram representation with AVR and PSS

30

Since the purpose of PSS is to introduce a damping torque component. A logical signal is use for

controlling generator excitation is the speed deviation r. The PSS transfer function GPSS(S), should have

appropriate Gain, Washout signals and Phase Compensation circuits to compensate for the phase lag between

exciter input and electrical torque. The following is a brief description of the basis for the PSS configuration ,

Fig 4.4 Thyristor excitation system with AVR and PSS

The phase compensation block provides the appropriate phase lead characteristics to compensate

for the phase lag between exciter input and generator electrical torque. The phase compensation may be a single

first order block as shown in Figure above or having two or more first order blocks or second order blocks with

complex roots. The signal washout block serves as high pass filter, with time constant Tw high enough to allow

signals associated with oscillations in r to pass unchanged, which removes D.C. signals. Without it, steady

changes in speed would modify the terminal voltage. It allows PSS to respond only to changes in speed.

The stabilizer gain KSTAB determines the amount of damping introduced by PSS. Ideally, the

gain should be set at a value corresponding to maximum damping; however, it is limited by other consideration.

The PSS parameters should be such that the control system results into the following

Enhance system transient stability.

Maximize the damping of local plant mode as well as inter-area mode oscillations without compromising

stability of other modes.

31

Not adversely affect system performance during major system upsets which cause large frequency

excursions; and

Minimize the consequences of excitation system malfunction due to component failure.

4.3 Fuzzy controller

Fuzzy logic is a derivative from classical Boolean logic and implements soft linguistic variables

on a continuous range of truth values to be defined between conventional binary i.e. [0, 1]. It can often be

considered a subset of conventional set theory. The fuzzy logic is capable to handle approximate information in

a systematic way and therefore it is suited for controlling non-linear systems and for modeling complex systems

where an inexact model exists or systems where ambiguity or vagueness is common. It is advantageous to use

fuzzy logic in controller design due to the following reasons

A Simpler and faster Methodology.

It reduces the design development cycle.

It simplifies design complexity.

An alternative solution to non-linear control.

Improves the control performance.

Simple to implement.

Reduces hardware cost

In classical set theory, a subset U of asset S can be defined as a mapping from the elements of S

to the elements the subset {0, 1},

U: S {0.1}

The mapping may be represented as a set of ordered pairs, with exactly one ordered pair present

for each element of S. The first element of the ordered pair is an element of the set S, and second element is an

element of the set (0, l). The value zero is used to represent non membership, and the value one is used to

represent complete membership. The truth or falsity of the statement 'X is in U' is determined by finding the

ordered pair whose first element is X. The statement is true if the second element of the ordered pair is 1, and

the statement is false if it is 0.

32

The fuzzy control systems are rule-based systems in which a set of fuzzy rules represent a control

decision mechanism to adjust the effects of certain system stimuli. With the help of effective rule base, fuzzy

control systems can replace a skilled human operator. The fuzzy logic controller provides an algorithm which

can convert the linguistic control strategy based on expert knowledge into an automatic control strategy. The

Figure illustrates the schematic design of a fuzzy logic controller which consists of a fuzzification interface, a

knowledge base, control system (process), decision making logic, and a defuzzification interface.

Fig 4.5 Equivalent diagram of fuzzy logic

4.4 Controller Design Procedure-

The fuzzy logic controller (FLC) design consists of the following steps.

1) Identification of input and output variables.

2) Construction of control rules.

3) Establishing the approach for describing system state in terms of fuzzy sets, i.e. establishing fuzzification

method and fuzzy membership functions.

4) Selection of the compositional rule of inference.

5) Defuzzification method, i.e., transformation of the fuzzy control statement into specific control actions.

The above steps are explained with reference to fuzzy logic based power system stabilizer in the following

section. Thus helps understand these steps more objectively.

33

4.5 Fuzzy Logic Based PSS

The power system stabilizer is used to improve the performance of synchronous generator.

However, it results into poor performance under various loading conditions when implemented with

conventional PSS. Therefore, the need for fuzzy logic PSS arises. The fuzzy controller used in power system

stabilizer is normally a two-input and a single-output component. It is usually a MIS0 system. The two

inputs are change in angular speed and rate of change of angular speed whereas output of fuzzy logic

controller is a voltage signal. A modification of feedback voltage to excitation system as a function of

accelerating power on a unit is used to enhance the stability of the system.

4.6 Selection of input and output Variable

Define input and control variables, that is, determine which states of the process should be

observed and which control actions arc to be considered. For FLPSS design, generator speed deviation and

acceleration can be observed and have been chosen as the input signal of the fuzzy PSS. The dynamic

performance of the system could be evaluated by examining the response curve of these two variables. The

voltage is taken as the output from the fuzzy logic controller. In Practice, only shaft speed is readily

available. The acceleration signal can be derived from the speed signals measure at two successive instants

using the following equations:

4.7 Membership Function

The variables chosen for this controller are speed deviation, acceleration and voltage. In this, the

speed deviation and acceleration are the input variables and voltage is the output variable. The number of

linguistic variables describing the fuzzy subsets of a variable varies according to the application. Usually an

odd number is used. A reasonable number is seven. However, increasing the number of fuzzy subsets results

in a corresponding increase in the number of rules. Each linguistic variable has its fuzzy membership

function. The membership function maps the crisp values into fuzzy variables. The triangular membership

functions are used to define the degree of membership. It is important to note that the degree of membership

plays an important role in designing a fuzzy controller. Each of the input and output fuzzy variables is

assigned seven linguistic fuzzy subsets varying from negative big (NB) to positive big (PB). Each subset is

associated with a triangular membership function to form a set of seven membership functions for each

34

fuzzy variable. The variables are normalized by multiplying with respective gains Kin1, Kin2, Kout so that

their value lies between -1 and 1. The membership functions of the input output variables have 50% overlap

between adjacent fuzzy subsets. The membership function for acceleration, speed and voltage are shown in

Figure

Membership functions for fuzzy variables

4.8 Fuzzy Rule Base:

A set of rules which define the relation between the input and output of fuzzy controller can be

found using the available knowledge in the area of designing PSS. These rules are defined using the

linguistic variables. The two inputs, speed and acceleration, result in 49 rules for each machine. The typical

rules are having the following structure:

Rule 1: If speed deviation is NM (negative medium) AND acceleration is PS (positive small) then voltage

(output of fuzzy PSS) is NS (negative small).

Rule 2: If speed deviation is NB (negative big) AND acceleration is NB (negative big) then voltage (output

of fuzzy PSS) is NB (negative big).

Rule 3: If speed deviation is PS (positive small) AND acceleration is PS (positive small) then voltage

(output of fuzzy PSS) is PS (positive small) and so on.

All the 49 rules governing the mechanism are explained in following Table where all the symbols

are defined in the basic fuzzy logic terminology.

35

4.9 Defuzzication

The input for the defuzzification process is a fuzzy set (the aggregate output fuzzy set) and the

output is a single crisp number. As much as fuzziness helps the rule evaluation during the intermediate steps,

the final desired output for each variable is generally a single number. However, the aggregate of a fuzzy set

encompasses a range of output values, and so must be defuzzified in order to resolve a single output value

from the set. The most popular defuzzification method is the centroid calculation, which returns the center of

area under the curve and therefore is considered for defuzzification. For a discretised output universe of

discourse,

Which gives the discrete fuzzy centroid, the output of the controller is given by following expression:

4.10 Fuzzy Inference System

Fuzzy logic block is prepared using FIS file in Matlab software and the basic structure of this file is as

shown in Figure. This is implemented using following FIS (fuzzy Inference System) properties:

And Method: Min

Or Method: Max

Implication: Min

Aggregation: Max

Defuzzification: Centroid

36

Fig 4.6 Fuzzy interference system

For the above FIS system Mamdani type of rule-base model is used. This produces output in

fuzzified form. Normal system need to produce precise output which uses a defuzzification process to

convert the inferred possibility distribution of an output variable to a representative precise value. In the

given fuzzy inference system this work is done using centroid defuzzification principle. In this min

implication together with the max aggregation operator is used. Given FIS is having seven input member

function for both input variables leading to 7*7 i.e. 49 rules.

Fig 4.6.1 Membership functions for speed deviation

37

Fig 4.6.2 Membership functions for acceleration

Fig 4.6.3 Membership functions for OUTPUT voltage

38

Fig 4.7 Rule Viewer of Fuzzy Controller

Fig 4.8 Surface Viewer of Fuzzy Controller

For the above FIS system Mamdani type of rule-base model is used result of which we get the

output in fuzzified form. Precise output is produced by the Normal System which uses a defuzzification

process to convert the inferred possibility distribution of an output variable to a representative Precise Value.

In the above given Fuzzy Inference System this work is done using centroid Defuzzification Principle

Method. In this system minimum implication together with the maximum aggregation operator is used.

39

5. SIMULATION MODELS AND RESULTS

5.1 Performance with Conventional PSS lead-lag

Fig 5.1 Simulink model of lead lag power system stabilizer

The variation of angular position and angular speed with time for 0.05 pu increase in torque for

negative and positive value of K5 are shown in the figures above. The system is coming out to be stable in both

the cases; however, the transients are more with negative K5 whereas the higher angular position is attained

with positive K5.

40

5.2 Results of AVR with PSS:

Fig 5.2 Variation of angular speed and angular position and torque when PSS (lead-lag) is applied

with K5 positive

[**parameters included are changes in angular speed,angular postion and torque]

Fig 5.3 Variation of angular speed, angular position and torque when PSS (lead-lag) is applied

with K5 negative.

41

MA

GN

ITU

DE

OF

PA

RA

MET

ERS*

* I

N p

.u.

MA

GN

ITU

DE

OF

PA

RA

MET

ERS*

* I

N p

.u.

TIME IN SECONDS

TIME IN SECONDS

5.3 Performance with Fuzzy Logic Based PSS

The Model used in Simulink/Matlab to analyze the effect of fuzzy logic controller in damping

small signal oscillations when implemented on single machine infinite bus system is shown below in Figure

and the details of the fuzzy controller are shown in Figure. As shown in Figure, the fuzzy logic controller

block consists of fuzzy logic Block and scaling factors. Scaling factors inputs are two & one for each input

and one scaling factor for output which determine the extent to which controlling effect is produced by the

Fuzzy Logic controller. Performance of Fuzzy Logic controller is studied for the scaling factors having the

values as Kin1=1.62, Kin2=29.58, K out=1.08.

Fig 5.4 Simulink model with fuzzy logic based PSS

Fig 5.4.1Fuzzy logic based PSS

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5.4 Results of fuzzy logic based PSS

Fig 5.5 Output of fuzzy logic based PSS with K5 negative.

Fig 5.6 Output of fuzzy logic based PSS with K5 positive.

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MA

GN

ITU

DE

OF

PA

RA

MET

ERS*

* I

N p

.u.

MA

GN

ITU

DE

OF

PA

RA

MET

ERS*

* I

N p

.u.

TIME IN SECONDS

TIME IN SECONDS

5.5 Comparison of results

The results from both the simulation outputs were compared and tabulated as below,

TYPES OF PSS

SETTLING TIME(sec)

WITH POSITIVE GAIN WITH NEGATIVE GAIN

AVR 4 to 5 6 to 7

FUZZYLOGIC BASED 1 to 2 2 to 3

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5.6 Conclusion

These results are for 5% change in mechanical torque. From figures it can be perceived that

with the application of fuzzy logic the rise time and the settling time of the system decreases. The system

reaches its steady state value much earlier with fuzzy logic power system stabilizer compared to

conventional power system stabilizer for negative K5. For the positive value of K5, the sluggish response

(over damped response) characteristic is resulted and the settling time remains largely unchanged. The step

response characteristics for angular position for both lead-lag PSS and fuzzy logic based PSS are compared

in Fig.5.1 and Fig.5.4 for negative and positive values of K5. From relative plots it can be retrieved that

oscillations in angular speed reduces much faster with fuzzy logic power system stabilizer than with

conventional power system stabilizer for both the cases i.e. when K5 positive and negative. As shown in Fig.

with fuzzy logic the variation in angular speed reduces to zero in about 2 seconds but with conventional

power system stabilizer it takes about 6 seconds to reach to final steady state value and also the oscillations

are less pronounced in fuzzy logic based PSS. Similar is the case with K5 positive.

Therefore, it can inferred that the fuzzy controller does not require any complex mathematical

support and the response is much improved than with conventional PSS.

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FUTURE SCOPE

As this project states that, Fuzzy Logic based PSS (FLPSS) is better method of stability control

compared to other techniques, it can be easily used for the future development.

Considered power system accompanying proposed FLPSS contributes optimal stabilizing

performance over wide range of operating conditions displaying its robust and adaptive feature.

Design of FLPSS by other algorithms and comparison of their performance with the proposed

method are topics of further research. The algorithms that can be used are as follows

1. Genetic algorithm

2. Artificial neural networks

REFERENCES:

[1] Mr. Manish Kushwaha & Mrs. Ranjeeta Khare,Dynamic Stability Enhancement of Power System using

Fuzzy Logic Based Power System Stabilizer,International Conference on Power, Energy and Control

(ICPEC),Feb 2013.

[2] Samer Said and Osama Bashir Kahlout, Design of Power System Stabilizer Based on Microcontroller for

Power System Stability Enhancement , June 2011.

[3] P V Etingov and N I Voropai, Application of Fuzzy Based PSS to Enhance Transient Stability in Large

Power Systems, IEEE PEDES 06, pp. 1-9, Dec 2006.

[4] P Bera, D Das and T K Basu, Design of P-I-D Power System Stabilizer for Multimachine System,

IEEE INDICON, pp. 446-450, Dec.2004.

[5] T Hussein, A L Elshafei, A Bahgat, Design of Hierarchical Fuzzy Logic PSS for a Multi-Machine Power

System, IEEE conf. on control and automation, Athens, Greece, July 2007.

[6] R Gupta, D K Sambariya and Reena Gunjan, Fuzzy Logic Based Robust Power System Stabilizer for a

Multi-machine Power System, IEEE ICIT, pp. 1037-1042, Dec 2006.

[7] Y J Lin Systematic Approach for the Design of Fuzzy Power System Stabilizer EEE- POWERCON 2004,

Singapore, pp.747-752, Nov 2004.

[8] N S D Arrifano, V A Oliveira, R A Ramos, Design and Application Fuzzy PSS for Power Systems Subject

to Random Abrupt Variations in Load, IEEE American Control conference 2004, vol. 2, pp. 1085-1090,

Jun 2004.

[9] A Singh and I Sen, A Novel Fuzzy Logic Based Power System Stabilizer for Multimachine System,

IEEE TENCON 03, vol.3, pp. 1002-1006, Oct 2003.

[10] N I Voropai and P V Etingov, Application of Fuzzy Logic Power System Stabilizers to Transient Stability

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