Batch 22 Final Documentation
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Transcript of Batch 22 Final Documentation
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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
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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.
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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)
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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
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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
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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
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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
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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
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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
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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.
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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
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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.
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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
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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.
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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.
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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
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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.
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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
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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.
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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.
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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
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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.
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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
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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
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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.
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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
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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
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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
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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
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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
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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.
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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)
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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
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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.
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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
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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:
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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
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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.
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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.
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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.
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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
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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.
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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
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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
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Fig 4.6.2 Membership functions for acceleration
Fig 4.6.3 Membership functions for OUTPUT voltage
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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.
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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.
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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.
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MA
GN
ITU
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OF
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MET
ERS*
* I
N p
.u.
MA
GN
ITU
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OF
PA
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MET
ERS*
* I
N p
.u.
TIME IN SECONDS
TIME IN SECONDS
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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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MET
ERS*
* I
N p
.u.
MA
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ITU
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OF
PA
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MET
ERS*
* I
N p
.u.
TIME IN SECONDS
TIME IN SECONDS
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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
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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
Improvement in a Large Electric Power System, PowerCon 2002, Vol. 2, Oct 2002, pp. 1223-
1227,International Journal of Engineering Research & Technology (IJERT) Vol. 1 Issue 9, November
- 2012ISSN: 2278-018.
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