CHAPTER-1

INTRODUCTION

1

1.1BACKGROUND

An interconnected power system can generate, transport and distribute the

electric energy with the main objective of these power systems is to supply

electric energy with its system nominal frequency and terminal voltage.

According to the power system control theory the nominal frequency depends

upon the balance between the generated power and the consumed real powers [1].

If the amount of the generated power is less than the amount of demand power,

then the speed and frequency of generator units is going to decreased, and vice

versa. So for that reason the frequency deviation occurred in the power system.

For this purpose, a megawatt frequency controller or automatic generation control

(AGC) concept is used. Automatic generation control plays a vital role in power

system by maintaining scheduled frequency and tie line power flow during

normal operating condition and also during the presence of small perturbations.

The analysis and design of automatic generation control system of individual

generator eventually controlling large interconnected power system between

different control areas plays a vital role in automation of power system. The

purpose of AGC is to maintain system frequency very close to specified nominal

value to maintain the generation of individual units at the most economical values

and to keep the nominal value of the line power between different control areas.

AGC approaches may be classified into two categories as follows:

a) Energy storage system: Examples are pumped storage system,

superconducting magnetic energy storage system, battery energy storage

system etc.

b) Control strategy: This category focuses on the design of an automatic

generation controller to achieve better dynamic performance.

Automatic generation control (AGC) plays a vital role in power system in

maintaining the system frequency and power flow through tie-line at their

scheduled values both under normal operating condition and under a small step

load perturbations. Nuclear units are normally used to supply base load because

of their high efficiency and they do not take part in system automatic

generation control. Gas power generation is a small percentage of the total

2

power generation and is suitable to supply the varying power demand.

Therefore the nuclear units do not play any significant role in AGC of large

power system. However the role of AGC cannot be avoided in thermal power

systems.

1.2 OBJECTIVES

The main aim of this work is the application of evolutionary algorithm to

tune the control parameters of a Proportional, Integral and Derivative (PID)

controller. In view of the above, the present work investigates the following

aspects:

i) To optimize the parameters of the conventional PID controllers by

the use of evolutionary computational techniques for AGC of a 2

area hydro - thermal system.

ii) To analyse the dynamic responses of the controllers obtained in this

work using PSO

iii) To examine the effects of system parameter variations, load changes

and tie-line outages for the test system.

.

1.3 SCOPE OF THE THESIS

The thesis report is organized in six chapters. The following gives a brief

description of the broad contents of each of the chapters in the thesis:

Chapter 1

Chapter-1 presents a brief introduction to the need of limiting the frequency and

tie-line power deviation of an interconnected hydro thermal network and the role

of evolutionary computation to meet those challenges.

Chapter 2

Chapter-2 presents the status of available techniques as well as their limitations

are discussed. The objectives and contributions of the work are highlighted.

Chapter 3

Chapter-3 is concerned with the overview of the interconnected system. It deals

with transfer function model of the interconnected Automatic Generation

3

Control system and the parameters used in this work and the comparisons with

the previous similar work Here a Proportional Integral Derivative controller is

used along with AGC in order to get the desired response.

Chapter 4

Chapter-4 describes one evolutionary computational technique used to tune the

parameters of PID controller parameters. The features and methodology of

implementation of the evolutionary algorithm is discussed. The algorithm

considered is described and the pseudo code for the algorithm is given.

Chapter 5

Chapter-5 is concerned with the simulation result for the case; such as PID

controlled AGC; of a two area interconnected hydro-thermal tuned by

evolutionary algorithm.

Chapter 6

Chapter-6 presents the conclusion of the study done and the future scope it

holds.

4

CHAPTER-2

LITERATURE SURVEY

5

2.1 LITERATURE SURVEY

Literature survey shows that, early works on AGC was initiated by Cohn

[2]. After that a modern optimal control concept for interconnected systems of

AGC design is introduced by Elgerd and Fosha for the first time [3]. They

suggested a proportional controller and different feedback form to develop the

optimal controller. The first gain scheduling control method for AGC of

interconnected power system was proposed by Lee and co-workers in 1991 [4].

Their controller provided better control performance for a wide range of operating

conditions than the performances obtained so far. Later on, Rubaai and Udo

presented a multi-variable gain scheduling controller by defining a cost function

with a term representing the constraints on the control effort and then minimizing

that with respect to the control vector [5]. Talaq suggested an adaptive fuzzy gain

scheduling method for conventional PI controller in 1999 [6]. After then, Pingkang

optimized the gains of PI and PID controllers through real coded genetic algorithm

in a two area power system [7]. In 2003 from Pinkang‘s study, Abdel-Magid and

Abido proposed a usage of PSO for the same purpose [8]. In 2004, Yesil suggested

the self-tuning fuzzy PID type controller for AGC [9]. In 2011, Gozde and

Taplamacioglu proposed the usage of craziness based PSO algorithm for AGC

system for an interconnected thermal power plants [10]. Nanda, Mishra and Saikia

[11] have proposed a more elaborate and comprehensive approach for finding

optimum value of R for a multi-area system considering conventional integral

controller. Also some recent published works have been carried out related to inter

connected hydro thermal AGC. Abraham et al. [12] have presented the analysis of

AGC of a hydrothermal interconnected system with generation rate constraint

(GRC). Abraham et al. [13] have analysed AGC of two area interconnected

hydrothermal power system by taking a thyrister controlled phase shifter (TCPS) in

series with the tie line.

Ali and Abd-Elazim [14] have used bacteria foraging optimization

technique to obtain the optimum gains of a PI controller. Rout et al. [15] have

applied differential evolution algorithm to determine the gains of a PI controller for

AGC of a two area interconnected system. In the 2nd group researchers have

adopted self-tuning techniques with the help of neural network and fuzzy logic.

6

Hemeida [16] have applied wavelet neural network approach to damp the

frequency oscillation of a two-area interconnected power system. In 2010, Gozde et

al. designed the PSO based PI-controller with the new cost function and compared

their results with the results of Abdel-Magid and Abido‘s study [17]. In 2011,

Gozde and Taplamacioglu proposed the usage of craziness based PSO algorithm

for AGC system for an interconnected thermal power plants [18].

Over the past decades, many control strategies have been proposed for AGC

viz. Proportional and integral (PI), Proportional, Integral and Derivative (PID) [19-

20] and Optimal controllers, optimal control [21]. In the design of load frequency

controllers in order to achieve better dynamic performance among the various types

of load frequency controllers, the most widely employed in the design is the

conventional PID controller [22-23]. M. Farahani, S. Ganjefar, M. Alizadeh

suggested a method of using PID controllers for a two area thermal system tuned

by Lozi map based Chaotic Optimization Algorithm [24] which serves as a basis of

comparison in this work. For the better performance of PID control optimized

constraints have to be adopted. To getting the optimized value we are having

different optimization techniques such as classical, optimal, genetic algorithm,

fuzzy logic, artificial neural network, etc. for the design of supplementary

controller have been reported in literature.

The main aim of this study which is different from the above literature is

that a novel gain scheduling PID-control strategy is proposed for automatic

generation control (AGC) of a two area hydro thermal power system . In this

strategy, the control is evaluated as an optimization problem, The optimization is to

determine the best suitable solution to a problem under a given set of constraints. In

mid-1990‘s Kennedy and Eberhart enunciate an alternate solution to the complex

nonlinear optimization problem by emulating the collective behaviour of birds and

called particle swarm optimization (PSO) [25]. Based on this many applications

based on PSO are reported [26-29].

7

CHAPTER-3

MODEL DEVELOPMENT

8

3.1 INTRODUCTION

An ideal electric power system should always meet the fluctuating demands

of its loads at scheduled frequency and voltage without any interruption. The

system generators run synchronously and generate the power that is being drawn by

all the loads in addition to the transmission losses. The perturbations in generated

power ∆PG and ∆QG must match the load perturbations ∆PG and ∆QG, if exact

nominal state is to be maintained.

Unfortunately, the system load fluctuations are so random that it is

impossible to achieve a perfect instant–to-instant deviation the generation (∆PG and

∆QG) and the demand (PD and QD). The ever-present discrepancy causes frequency

fluctuations. The idea of load frequency control is to provide an automatic control

strategy to bring the frequency of power system back to its nominal value. The

tendency to interconnect neighbouring electric power systems through tie lines for

purposes of increased reliability and security of supply, has added a new dimension

to the problem of Load Frequency Control (LFC). These tie lines have scheduled

and emergency powers flowing in them. When an imbalance of generation and load

occurs in any part of an interconnected power system, all areas act to reduce the

frequency deviation. This in turn leads to changes in scheduled inter-area

exchanges of power. Normally, these schedules are to be maintained as a matter of

policy so that each area meets its own load variations in the steady state. As

frequency is returned to scheduled values, due to the co-operative action of all the

areas, the area in which the disturbance originally occurred is expected to effect a

change in its generation to match the new load. All other areas may then revert to

the pre-disturbed conditions. Thus summarizing all the above, the main objectives

of AGC are:

1. Each area regulates its own load fluctuations.

2. Each area assists the other areas, which cannot control their own load

fluctuations. 3. Each area contributes to the control of the system frequency, so that

the operating costs are minimized.

4. The deviations in frequency and tie line power flow error to zero in the steady

state. 5. When load changes are small, the system must be permitted to come back

9

to the steady state (by natural damping) so that the mechanical power does not

chase small disturbances for economic reasons.

3.2 LOAD FREQUENCY CONTROL

The load frequency control (LFC) is to control the frequency deviation by

maintaining the real power balance in the system. The main functions of the LFC

are;

i) To maintain the steady frequency,

ii) Control the tie-line flows, and

iii) Distribute the load among the participating generating units.

The control (input) signals are the tie-line deviation ΔPtie (measured from

the tie-line flows), and the frequency deviation Δf (obtained by measuring the angle

deviation). These error signals Δf and ΔPtie are amplified, mixed and transformed

to a real power signal, which is then controls the valve position. Depending on the

valve position, the turbine (prime mover) changes its output power to establish the

real power balance.

The first step in the analysis and design of a control system is mathematical

modelling of the system. The most common method is the transfer function

method. In order to use the transfer function and linear state equations, the system

must first to be linearized. Proper assumptions and approximations are made to

linearize the mathematical equations describing the system, and a transfer function

model is obtained for the following components.

The complete control schematic is shown in Fig.3. 1

10

Fig. 3.1 The Schematic representation of LFC and AVR of a synchronous

generator

3.2.1 Generator Model

The generator and the electrical load constitute the power system. The valve

and the hydraulic amplifier represent the speed governing system. Using the swing

equation, the generator can be modelled by;

Expressing the speed deviation in per unit (p.u.);

This relation can be represented as shown in Fig. 3.2.

11

3.2.2 Load Model

The load on the system is composite consisting of a frequency independent

component and a frequency dependent component. The load can be written as;

Where, ΔPe is the change in the load; Δ𝑃0 is the frequency independent load

component; ΔPf is the frequency dependent load component. ΔPf = DΔω. where, D

is called frequency characteristic of the load (also called as damping constant)

expressed as a percent change in load for 1% change in frequency. A value of

D=1.5, means that a 1% change in frequency causes 1.5% change in load.

12

3.2.3 Turbine Model

The turbine transfer function can be given as;

Where, ΔPv(s) is the change in valve output (due to action), ΔPm(s) is the

change in the turbine output. The turbine can be modelled as a first order lag as

shown in the Fig. 3.4

3.2.4 Governor Model

The real power in a power system is being controlled by controlling the

driving torques of the individual turbines of system. Fig. 3.5 shows a schematic

speed governing system.

13

Fig. 3.5 Speed governing system

3.2.4.1 Method of control:

By controlling the position measured by the coordinate XE , of the control

valve, the flow of steam or water through the turbine is controlled. A downward

small movement of the linkage point E increases the steam or water flow by a small

amount which represents megawatt increment ΔPv. This increase in steam or water

flow will be translated to turbine power increment. Hydraulic amplifiers are used to

change the position of the main valve against the high steam or water pressure. The

position of pilot valve can be affected via the linkage system in one of the three

ways:

1. Directly using speed changer.

2. Indirectly, via feedback; due to position change in main piston.

3. Indirectly, via feedback; due to position changes of linkage point B resulting

from speed changes.

The governor has two inputs; one ΔPref (reference power setting) and the second

Δf (changes in speed or frequency). Thus we can write for small increments

14

Where, R is referred to as regulation. Laplace transforms of equation 2.1 yields

The command ΔPg is transformed though the hydraulic amplifier to the steam

valve position command ΔPv. Assuming a linear relationship and considering

simple time constant Tg, we have the following s-domain relation;

3.2.4.2 Assumptions:

1. The system is originally running in its normal state with complete power

balance.

2. By connecting additional load ΔPD, the generation immediately increases its

output ΔPG to match new load, i.e. ΔPD = ΔPG.

3. The change is assumed uniform throughout the area, when a power imbalance

occurs in the area.

4. The old area load has a frequency dependency

15

Considering the above assumptions and solving, finally we get

Further simplifying,

Where,

All the individual blocks can now be connected to represent the complete LFC loop

as shown in Fig. 3.7.

3.2.5 Need of Supplementary Loop

The LFC loop shown in Fig. 3.7 is called the primary LFC loop. It achieves

the primary goal of real power balance by adjusting the turbine output ΔPm to

16

match the change in load demand ΔPD. All the participating generating units

contribute to the change in generation. But a change in load results in a steady state

frequency deviation Δf. The restoration of the frequency to the nominal value

requires an additional control loop called the supplementary loop. This objective is

met by using integral controller which makes the frequency deviation zero. The

LFC with the supplementary loop is generally called the AGC. The block diagram

of an AGC is shown in Fig. 3.8. The main objectives of AGC are;

i) To regulate the frequency (using both primary and supplementary controls),

ii) And to maintain the scheduled tie-line flows. A secondary objective of the AGC

is to distribute the required change in generation among the connected generating

units economically (to obtain least operating costs).

3.3 SINGLE AREA SYSTEM

In a single area system, there is no tie-line schedule to be maintained. Thus the

function of the AGC is only to bring the frequency to the nominal value. This will

be achieved using the supplementary loop (as shown in Fig. 3.8) which uses the

integral controller to change the reference power setting so as to change the speed

set point. The integral controller gain KI needs to be adjusted for satisfactory

response (in terms of overshoot, undershoot, and settling time) of the system.

Although each generator will be having a separate speed governor, turbine and all

the generators in the control area are replaced by a single equivalent generator.

17

3.4 TWO AREA INTERCONNECTED SYSTEM

An extended power system can be divided into a number of load frequency

control areas interconnected by means of tie lines. We shall consider a two area

case connected by a single line called tie line as illustrated in Fig. 3.9.

The control objective is to regulate the frequency of each area and

simultaneously regulate the tie line power as printer area power contracts. It is

conveniently assumed that each control area represented by an equivalent turbine,

generator and governor system. Symbols used with suffix 1 refer to area 1 and

those with suffix 2 refer to area 2 Power transported out of area 1 is given by;

Where δ 1° δ2

°=¿ power angles equivalent machines of two areas in electrical

degrees. For incremental changes in δ 1° and δ 2

°, the incremental tie line power can

be expressed as;

18

Where T 12=¿¿) = synchronizing coefficient. Since incremental power

angles are integrals of incremental frequencies, we can write eqn.(3.14) as ;

Where f1 and f2 are incremental frequency changes of area 1 and 2,

respectively. Similarly incremental tie line power out of area 2 is given by;

Where; T 21=¿¿ ( 3.17)

Let the step changes in loads PD1(s) and PD2(s) be simultaneously applied

to control areas 1 and 2 respectively. Area control error (ACE) in two area

interconnected power systems is defined as a linear combination of incremental

frequency and tie line power. Thus, for control area 1;

Where the constant B1 is called area frequency bias. Equation (3.18) can be

expressed in the Laplace transform as;

Similarly for the control area 2;

19

3.5 SYSTEM INVESTIGATED

The Automatic Generation Control system investigated in this work as shown

in Fig. 3.10 consists of two generating areas, i.e.; Area 1 comprising of thermal

system and Area 2 consists of hydro system. In this model, a reheat turbine is also

added to thermal control area. The use of both the systems in the interconnected

system can be considered as a simple model for general power system around the

world which basically consists of thermal as a primary means for the generation of

power to cater the demands of the ever-growing consumption. In order to

understand the control actions at the power plants for Load Frequency Control,

taking the boiler–turbine–generator combination into consideration of a normal

thermal generating unit. Most steam turbo generators (STG) now in service are

equipped with turbine speed governors. Moreover, to make the approach more

realistic both the areas taken into consideration have different time constants of

different control parameters.

20

Fig. 3.10 The control diagram of an interconnected two hydro thermal

system

21

The duty of the speed governor is to monitor continuously the turbine–

generator speed and to control the valves which in turn adjust steam flow into the

turbine in response to changes in frequency. Since all the movements are small the

frequency–power relation for turbine–governor control can be studied by a

liberalized block diagram . The imbalances between power generation and power

demand, the rotational kinetic energy of the generating units are generally affected

to an extent. The change in frequency due to the variation of load randomly

throughout the 24 hours which makes it impossible to forecast the real power

demand. Imbalances between real power generation and load demand (plus losses)

throughout the daily load cycle causes kinetic energy of rotation to be either added

to or taken from the on-line generating units, and frequency throughout the

interconnected system varying greatly. Each control area has a central facility

called the energy control centre, which monitors the system frequency and the

actual power flows on its tie lines to neighbouring areas.

In order to represent the basic layout of an interconnected power system, two

area hydrothermal systems are considered in this work for optimal automatic

generation control. For depicting a disturbance a step load perturbation of 1% is

applied in thermal Area 1, to study the transient response of change in the system’s

frequency of both the areas and power deviation of the interconnecting tie line.

In order to satisfy the above requirements, gains of Proportional-Integral-

Derivative (PID) Controller and Integral controller in AGC loop parameter are to

be optimized to have minimum undershoot (US), overshoot (OS) and settling time

(ts) in area frequencies and power exchange over the tie-line. The main aim of all

works of past literatures till today is to minimize the Area Control Error to a zero

value, i.e., if the load varies, the system attains the frequency and tie line power

deviation to the desired nominal value.

22

3.6 NEED OF CONTROLLER

A controller is a device which monitors and modifies the operational conditions

of a given dynamical system. The operational conditions are typically referred to as

output variables of the system which can be modified by adjusting certain input

variables. There are various types of classical controllers namely proportional (P),

proportional-derivative (PD), Proportional Integrator (PI) and Proportional Integral

and Derivative (PID) are present. Among all controllers PID controller is the most

important controller. The controllers are used to be optimized to have the minimum

undershoot (Ush), overshoot (Osh) and settling time (ts) in area frequencies and

power exchange over the tie-line.

So in order to overcome these problems regarding instability and to improve the

performance of the system and to settle the system at 0 p.u. (a steady value), the

need for a controller comes into account. The proportional-integral-derivative

(PID) controllers are the most important control devices employed in indus-trial

process control.

3.7 PROPORTIONAL INTEGRAL AND DERIVATIVE (PID)

CONTROLLER

Basically, different process industries use Proportional Integral and

Derivative controller as the most popular feedback control mechanism. Till date

23

from half of this century, it is the most popular feedback controller which is being

used in the process industries. This can be considered as an excellent controller that

can help in providing excellent performance of the process plant. It is due to their

easy and simple implementation in various control applications. Due to its

simplicity and excellent if not optimal performance in many applications, PID

controllers are used in more than 95% of closed-loop industrial processes.

The PID as given in fig. 3.11 controller consists of three basic modes:

proportional, integral, derivative modes respectively.

Fig. 3.11 Simulink representation of PID controller

A proportional controller gain (𝐾𝑝) reduces the rise time but does not

eliminate the steady-state error, integral gain (𝐾𝑖)eliminates the steady state

error but resulting a worse transient response, derivative gain (𝐾𝑑) increases

the stability of the system and improves the transient response and reduces

overshoot and undershoots [23]. These values of above gains are obtained by

hit and trial method based on the plant behaviour and experiences.

The equation below represents the transfer function of PID (Laplace Domain) is

given by:

24

In time domain, the output of PID controller is given by;

Where e(t) is error signal and u(t) is control signal. In the design of PID controller

(two in number) for this work the six gains are selected in such a way that the

desired response obtained of the closed loop system which refers that the system

should have a minimum settling time and a very less value of overshoot as well as

undershoots with less oscillations due to a 20% Step Load Perturbation.

In Fig.3.11, for the PID controllers the control inputs are 𝐴𝐶𝐸𝐼and 𝐴𝐶𝐸2whereas 𝑢1 and 𝑢2 are the outputs respectively. On relating the inputs and

outputs of the system 𝑢1 and 𝑢2are given as;

The value of Area Control Error (ACE) is the sum of Bias Factor and Tie line

power deviation. The Area Control Error in both the areas consists of Tie line

power error of the intermediate area and the Frequency error, given by;

In this work, the constraint of setting the gains of PID controller is a major

problem. Therefore, the PID gains should be in limits; i.e.

25

Where i is the number of controller gain (here𝑖=2, due to two controllers).

K pmin,K imin

,K dmin are the minimum values of controller parameters and

K pmax, K imax

, Kdmaxare the maximum allowable values for the controller parameters.

Henceforth, in this work the PID parameters are constrained within [0, 2].

3.7.1 Proper Tuning of PID Parameters

Tuning is adjustment of control parameters to the optimum values for the

desired control response. Stability is a basic requirement. However, different

systems have different behaviour, different applications have different

requirements, and requirements may conflict with one another. The gain tuning of a

PID controller for optimal control of a process depends on the plant‘s behaviour

and the type and characteristic of objective function. To design the PID controller,

the engineer must choose the tuning way of design gains to improve the transient

response as well as the steady-state error[30]. In the design of a PID controller, the

three gains of PID must be selected in such a way that the closed loop system has

to give the desired response. The desired response should have minimal settling

time with a small or no overshoot and undershoot in the applied step response of

the closed loop system.

Various conventional tuning rules just need trial and error on the

experiment or the simulation in order to adjust to the expected value. This

procedure is basically depended on the user‘s know-how. For the solution of such

problems, the PID optimal tuning method based on evolutionary computation is

developed.

Hence, in order to have a proper and better design; the parameters of the

PID controller must adopt a suitable tuning algorithm which would improve the

transient response by minimising the steady-state error. In the design of a PID

controller, the three gains of PID for each area i.e. 𝐾𝑝,𝐾𝑖and𝐾𝑑must be chosen

in such a manner that the closed loop system has to give the desired as well as the

26

best response. The proposed method computes the PID parameter that realizes

expected value without the user know-how. The concept of the proposed method is

shown in Fig. 3.12.

Fig. 3.12 Difference between conventional and optimal tuning of PID

controller

Here proper tuning is done by using Particle swarm optimization technique,

which has been explained in the next chapter.

27

CHAPTER-4

MODEL DESIGN

28

4.1 INTRODUCTION

The bulk of difficulties associated with the use of mathematical optimization on

large-scale engineering problems have contributed to the development of different

types of new and improved alternative solutions. Linear programming techniques

often fail to reach optimal solution rather fall in the local optima while solving

harder constrained problems either with large number of variables or a large search

space and non-linear objective functions. To overcome such type of serious

undesirable problems, literatures surveys have advent the use of evolutionary

algorithms (EAs) for searching near-optimum solutions to problems. Different

varieties of bio-inspired or surrounding-inspired evolutionary algorithms are the

probabilistic search methods that are able to simulate different varieties of natural

biological evolution or the behaviour of various biological entities (animals, birds,

etc.). The behaviour of biological entities is guided by learning, adaptation, and

evolution. For example, bird flocking, fish schooling, etc.

In an attempt to reduce processing time and improve the quality of solutions,

particularly to avoid being trapped in local optima, many other recent emerging

techniques inspired by different natural and different social patterns & behaviour

have been introduced: particle swarm optimization (PSO) algorithm, differential

evolution (DE) algorithm and also the combined of both the algorithms known as

hybrid DE-PSO algorithm. In general, EA shares common approach for their

application to such a given problem.

In this project the following computational technique have been used to address

the optimization of PID controller parameters for AGC problems mentioned above:

4.2 PARTICLE SWARM OPTIMIZATION ALGORITHM

Particle Swarm Optimization (PSO) method is originally developed by

Kennedy, Eberhart, and Shi. PSO is a stochastic global optimization method which

29

is based on simulation of social behaviour. PSO consists of a population refining its

knowledge of the given search space. Different types of behavioural patterns as

bird flocking and fish schooling inspired them with effect of grouping of species to

achieve their goals. The dynamics of bird flocking resulted in the basic of this

heuristic algorithm and thus into a powerful optimization algorithm which has

directly and indirectly helped in to solve a number of modern day power problems.

It is one of the optimization techniques and a kind of evolutionary computation

technique. The method has been found to be robust in solving problems featuring

nonlinearity and non differentiability, multiple optima, and high dimensionality

through adaptation, which is derived from the social-psychological theory. The

features of the method are as follows;

• The method is developed from research on swarm such as fish schooling and bird

flocking.

• It can be easily implemented, and has stable convergence characteristic with good

computational efficiency.

Instead of using evolutionary operators to manipulate the particle

(individual), like in other evolutionary computational algorithms, each particle in

PSO flies in the search space with velocity which is dynamically adjusted

according to its own flying experience and its companions‘ flying experience.

4.2.1 What Is PSO Algorithm?

PSO is a population based optimization technique which processes over a

population known as ‗swarm‘ and ‗particle‘ which is defined as the solution

candidate which moves around the search-space in the search of optimal solution

by getting adjust to ‗experience‘ of neighbouring particles. Eventually, it adjusts

itself to position with respect to time as well as its own experience based on

experiences of neighbouring particles. In the whole process, if the particle comes

across a satisfying solution then the whole swarm will move near it explore

thoroughly through the search space.

The PSO algorithm works by simultaneously maintaining several candidate

solutions in the search space. In each iteration of the algorithm, each candidate

solution that can be thought of as a particle flies through the search space to find

the maximum or minimum of the cost function (fitness value). Initially, the PSO

30

algorithm chooses candidate solutions randomly within the search space. Each

particle maintains its position, composed of the candidate solution and its evaluated

cost function, and its velocity. Additionally, it remembers the best fitness value it

has achieved thus far during the operation of the algorithm, referred to as the

individual best fitness, and the candidate solution that achieved this fitness, referred

to as the individual best position. Finally, the PSO algorithm maintains the best

fitness value achieved among all particles in the swarm, called the global best

fitness, and the candidate solution that achieved this fitness, called the global best

position.

4.2.2 Velocity And Position Update of The Particle

The best previous position of the 𝑖𝑡𝑕 particle is recorded and represented as

pbest. The index of the best particle among all the particles in the group is

represented by the gbest. The updated velocity and position of each particle can be

calculated as per following formulas:

Here ‘w’ is the inertia weight parameter which controls the global and local

exploration capabilities of the particle. ‘C1’ and ‘C2’ are acceleration constants

and, ‘rand’ and ‘rand2’ are random numbers between 0 and 1. In this work the

values of C1 and C2 are taken as 2.05. At the end of the iterations, the best position

of the swarm will be the solution of the problem. The basic steps of PSO algorithm

are represented below and the flow chart is depicted in fig. 4.1.

31

32

CHAPTER-5

RESULT ANALYSIS

33

5.1. CHOICE OF OBJECTIVE FUNCTION

Different stated algorithms are used to tune and optimize the PID parameters

and Integral parameters of the interconnected power system. As stated earlier in

this work, the main and foremost aim of tuning the system is minimizing the value

of Area Control Error (ACE). In order to achieve this, the cost function J is taken

as:

J=a1× ITSE+a2 (10)

Where ITSE=∫0

t

[ ACEi2 ] . t dt

Where, ′𝑑𝑡′ is a small time interval, 𝐴𝐶𝐸𝑖 is area control error of 𝑖𝑡𝑕 area (here,

i=2) and 𝑡 is time of simulation.𝑂𝑠𝑕is the maximum peak overshoot of the

response of frequency deviations of Area 1, Area 2 and of the tie line power

deviation.𝑎1 and 𝑎2 are various weight factors. This type of objective or fitness or

cost function has the main aim of minimization. The optimum values of PID

controller parameters are obtained by running the simulations for 500 times for

different combinations of 𝑎1 and 𝑎2 respectively. In this work, the optimum values

of 𝑎1 and 𝑎2 used are 0.65 and 0.35 respectively. This is carried out by the use of

the Evolutionary Algorithm which help in getting the optimal PID parameters so

that the value of cost function is as minimum as far as possible.

5.2 RESULTS ANALYSIS

As per the literature and many other past works it has been observed that many

researchers have considered to give the disturbance or to provide a small step load

perturbation (SLP) only in one area to optimize the gains of the controller. In this

34

work a step disturbance of 1% or 0.01 p.u. is provided in Area 1 and thus the

parameters of PID controllers are tuned in accordance to it. The PID controller is

tuned with one heuristic algorithms, i.e., Particle Swarm Optimization.

Fig. 5.1, Fig. 5.2 and Fig. 5.3 shows the curves of variations of frequency deviation

in Area 1(∆ f 1), frequency deviation in Area 2(∆ f 2) and the tie line power deviation

(∆ Ptie) respectively with SLP provided at Area-1.

0 5 10 15 20 25 30-10

-8

-6

-4

-2

0

2

4x 10

-3

Time in second

Cha

nge

in f

requ

ency

in A

rea

1

PSO

Fig. 5.1 Frequency deviation in area-1

35

0 5 10 15 20 25 30-12

-10

-8

-6

-4

-2

0

2

4x 10

-3

Chan

ge in

freq

uenc

y in

Are

a 2

Time in Second

PSO

Fig. 5.2 Frequency deviation in area-2

36

0 5 10 15 20 25 30-2

-1.5

-1

-0.5

0

0.5

1x 10

-3

Time in Second

Tie

line

Pow

er

PSO

Fig. 5.3 Tie line power deviation

The settling time (T s), maximum peak overshoot (Os h), minimum values of

undershoot (U s h) of ∆ f 1,∆ f 2 and∆ Ptie are depicted in Table 2.

37

Table 2

Settling time, peak overshoot and undershoot of Δ𝑓1, Δ𝑓2 and Δ𝑃𝑡𝑖𝑒Dynamic Response

Δ𝒇𝟏 Δ𝒇𝟐 Δ𝑷𝒕𝒊𝒆Ts in

sec

Ush in

p.u.

Osh in

p.u.

Ts in

sec

Ush in

p.u.

Osh in

p.u.

Ts in

sec

Ush in

p.u.

Osh in

p.u.

14.945

0

-0.009 0.003 14.7720 -0.010 0.0038 12.1240 -0.0018 0.0005

Table 3

Optimum gains of PID controller of area1 and integral controller of area 2 tuned by PSO algorithm

38

PID Controller gains of area 1 Integral gain of area 2

Parameters KP1 KI1 KD1 KI2

Using PSO 2.5000 2.4881 1.2971 0.00345

CHAPTER-6

CONCLUSION

39

6.1 CONCLUSION

The work presented here has attempted to cover the application of

evolutionary computational techniques on Automatic Generation Control class

of problems. Various cases have been handled and studied. In this work, one

heuristic evolutionary search techniques have been adopted for independent

determination of off-line nominal optimal PID Gains suitable for optimal

transient responses in automatic generation control.

To investigate LFC operation, one test system (i.e., AGC) have been taken

into consideration. This study presents the usage of PSO algorithm as the new

artificial intelligence based optimization technique in order to optimize the

AGC system and the comprehensive analysis of its tuning performance and its

contribution to robustness. Then transient response analysis is used to verify the

superiority of PSO algorithm.

The simulation results show transient performance for AGC tuned for PID

controller.

6.2 FUTURE SCOPE

This work, like any other project remains imperfect. A lot more can be done

in this regard.There are a variety of interconnected power-system networks on

which the nature inspired algorithms can beapplied to get the optimum values

of controller parameters. Even in AGC class of problems, there can be a variety

of models and systems. There are problems to be solved like hydro thermal

equal and unequal system, gas and diesel systems, multi-area multi- generation

system, etc. To make the optimization better, different types of cost functions

can be analysed based on various other constraints. Moreover, on the side of

evolutionary computation, new algorithms such as mine blast, improved

varieties of Particle Swarm Optimization (PSO), Differential Evolution (DE)

40

and many optimization algorithms etc. And also can be used along with the

option of hybridizing the old algorithms such as Hybrid DE-PSO.

The application of evolutionary computing can be done to other areas of

electrical engineering also, like optimal power flow, solving the Economic

Load Dispatch related problems, transmission expansion planning, power

quality classification and filter design.

41

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APPENDIX

System Data:

f= 60Hz ; Kr1=Kr2= 0.5 ; Tr1=Tr2= 10sec ; Th1=Th2= 0.08sec ; Tg1=Tg2= 0.2sec

Tt1=Tt2= 0.3sec ; Tp1=Tp2= 20sec ; T12=0.0707 ; D1=D2= 0.0083

Kp1=Kp2= 120Hz/p.u. MW ; R1=R2= 2.4𝐻𝑧/𝑝.𝑢 ; Pr1=Pr2= 1000MW

B1=B2= (B=1/R+D) 0.425𝑝.𝑢.𝑀𝑊/𝐻𝑧

45