pso based fractional order automatic generation controller for two area power system

8/10/2019 Pso Based Fractional Order Automatic Generation Controller for Two Area Power System

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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6545(Print),

ISSN 0976 6553(Online) Volume 5, Issue 9, September (2014), pp. 17-28 IAEME

17

PSO BASED FRACTIONAL ORDER AUTOMATIC GENERATION

CONTROLLER FOR TWO AREA POWER SYSTEM

CH. Ravi Kumar Dr. P.V.Ramana Rao

Assistant Professor/E.E.E, Professor & H.O.D/E.E.E,

University College of Engg & Tech. University College of Engg & Tech.

Acharya Nagarjuna University Acharya Nagarjuna University

ABSTRACT

This paper presents the development and application of Fractional order PID controllers

based on particle swarm optimization (PSO) for load frequency control of two-area inter connected

system. The dynamic response of the system has been studied for 1% and 10% step loadperturbations in area2. The performance of the proposed FOPID controller is compared against the

traditional PID controllers based on PSO and ANFIS based intelligent controller. Comparative

analysis demonstrates that proposed FOPID controllers based on PSO reduces the settling time and

overshoot effectively, against small step load disturbances. Simulations have been performed using

MATLAB / Simulink.

Keywords:Adaptive Neuro Fuzzy Inference System (ANFIS), Fractional PID Controller, Particle

Swarm Optimization (PSO), Automatic Generation Control (AGC).

I. INTRODUCTION

In an interconnected power system Automatic Generation control or Load frequency controlis important in Electrical Power System design and operation. Large scale power system comprises

of interconnected subsystems (control areas) forming coherent groups of generators, where as

connection between the areas is made using tie-lines [1-2]. Each control area has its own generation

and is responsible for its own load and scheduled interchanges with neighbouring areas. The load in

a given power system is continuously changing and consequently system frequency deviates from

the desired normal values. Therefore to ensure the quality of power supply, a load frequency

INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &

TECHNOLOGY (IJEET)

ISSN 0976 6545(Print)

ISSN 0976 6553(Online)

Volume 5, Issue 9, September (2014), pp. 17-28

IAEME: www.iaeme.com/IJEET.asp

Journal Impact Factor (2014): 6.8310 (Calculated by GISI)

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IJEET

I A E M E


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Fig.1:Block diagram of AGC for Two area system with secondary loop

ii

j

i fBACE +P=n

1=

ijtie, (1)

Where ACEi is area control error of the ith

area

if = Frequency error of itharea

ijtie,P = Tie-line power flow error between ithand jtharea

Bi = frequency bias coefficient of ith

area

III. INTEGER ORDER PID CONTROLLER

The PID control is a widely used approach for designing a simple feedback control system

where in three constants are used to weigh the effect of the error (the P term), the integral of the error

(I term) and the derivative of the error(the D term). A typical structure of classical IOPID controlled

system [15] is shown in Fig.2.

Fig.2:Structure of PID control

P

+

sG2+1

1

2

1R

sT2+1

1

2D+s22

1

H

B2

w

ACE2

+

+

+

ACE1

+

+sG1+1

1

1D+s12

1

H

sT1+1

1

1

1

R

B1

S

T12

2

w

+

+

+

+

System

KP

Kd

Ki

d/dt

+

r(t)e(t) u(t) y(t)


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To implement a PID controller that meets the design specifications of the system under

control, the parameters [Kp, Ki, Kd, B1, B2] must be determined for the given system. An IOPID

controller is designed for frequency control in power system in this paper, whose parameters were

optimized using Particle swarm optimization.

IV. FRACTIONAL CALCULUS

Fractional calculus can have different definitions in different perspectives [15]. There are two

commonly used definitions for fractional calculus so far, that is Grunwald-Letnikov definition,

Reiman-Liouville definition.

]/)[(

0=0h

)()1+(

)+(

)h(

1=)( lim

hat

K

ta KhtfK

KtfD

(2)

t

nn

n

ta dt

f

dt

dtfD

)(1)(

)(

)-(n

1=)( (3)

Grunwald-Letnikov definition is perhaps the best known one due to its most suitability for the

realization of discrete control algorithms. The m order fractional derivative of continuous function

f(t) is given by [10]

( ) [ ]

( )

( )

dtm

tfdm

jhtfj

mx

j

jh

mLt

htfD

m

=

=

=

0)1(

0 (4)

Where [x] is a truncation andh

mtx )(= ;

jm is binomial coefficients

,!

)1+()1(=

j

jmmm

j

m

K0),=(1,= j

j

m

it can be Replaced by Gamma function,

1)+(j!

1)+(=

jm

m

j

m

. The general calculus operator including fractional order and integer order

is defined as [10]

t

a

ta

Rd

R

Rdtd

D

0)(/

>=

(5)

Where a and t are the limits related to operation of fractional differentiation, is the calculus order.


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The Laplace transform of the fractional derivative off(t)is given by

0=

1 )]([)(=)}({t

tfDsFstfDL

(6)

Where F(S)is the Laplace transform off(t). The Laplace transform of the fractional integral off(t)is

given as follows.

)(=)}({ sFstfDL (7)

V. FRACTIONAL PID (PID) CONTROLLER

The FOPID (or PID) controller involves an integrator of fractional order and a

differentiator of order , which has the following fractional order transfer function.

SK

S

KKsG

d

i

pc++=)( (8)

Where is the fractional order of the integrator and is the fractional order of the

differentiator, which both can take any value of complex numbers. The classical

controllers are particular cases of the FOPID controller. If ==1, the classical IOPID

controller is obtained. For ==0, the P controller is obtained, for =0, =1 the PD controller is

obtained. Illustration of different types of integer and fractional order controllers as and vary as

shown [15] in Fig3.

Fig.3:Illustration of IO and FO controllers

As the FOPID has two more extra tuning knobs than the classical integer-order PID

controller, the use of fractional controller (and are non-integers) gives more flexibility for the

design of a control system and gives better opportunity to adjust system dynamics if the originalsystem to be controlled is fractional system. In time domain input to the system to be controlled takes

the following form.

)(+)(+)(=)( teDKteDKteKtu dip (9)

Where is the integral order, is the differential orderKp, Ki, Kdare the parameters of PID

controller.


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A. Optimization of PID

Controllers parameters

Fractional controller has five parameters and currently there are no practical engineering

applications in frequency control of power system. Determine its parameters based on experience

like traditional controllers are not possible and so a fast and efficient way to optimize its parameters

must be found.

Particle swam optimization (PSO) is a kind of swarm intelligence algorithm, simulatingbiological predation phenomenon in nature. PSO employs swarm intelligence, which comes from

cooperation and competition between particles of a group, to guide the optimization search, with

strong convergence, global optimization and computation-efficiency [10, 15].

B. Calculation of fitness functionThe design of PI

D

controller is actually a multi dimensional function optimization problem.

The objective of controller parameters optimization is to make the control error tend to zero and

there is smaller over shoot and faster response. In order to obtain satisfactory transition of the

dynamic characteristic, the paper has used Integral squared error (ISE) performance index for the

parameters minimum objective function. ISE can be expressed as follows [15].

t

dtteISE0

2)(= (10)

C. Particle swarm optimization

Particle swarm optimization is a new population based evolutionary computation. The PSO

algorithm attempts to mimic the natural process of group communication of individual knowledge,

which occurs when such swarms flock, migrate; forage etc in order to achieve some optimum

property such as configuration or location.

In PSO the swarm is initialized with a population of random solutions. Each particle in the

swarm is a different possible set of the unknown parameters to be optimized. Representing a point in

the solution space, each particle adjusts its flying experience and shares social information among

particles. The goal is to efficiently search the solution space by swarming the particle towards thebest fitting solution encountered in previous iterations with the intent of encountering better solutions

through the course of process and eventually converging on a single minimum error solution [10].

In PSO, a swarm consists of N particles moving around in a D-dimensional search space. The

random velocity is assigned to each particle. Each particle modifies its flying based on its own and

companions experience at every iteration.

The formulas (11) and (12) are the particles velocity and position update formulas [11].

)(c+)(c+= 112211

11

1

t

id

t

gd

t

id

t

id

t

id

t

idxprxprvv (11)

+= 1tidt

id xxt

idv (12)

The ith

particle is denoted as ),(= 2,1 idiii xxxX K whose best previous solution Pbest is

represented as is ),(= 2,1 idiii pppP K current velocity (position change rate) is described

by ),(= 2,1 idiii vvvV K . Finally, the best solution achieved so far by the whole swarm is represented

as ),(= 2,1 gdiig pppP K .


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At each time step, each particle moves towards Pbestand gbestlocations. The fitness function

evaluates the performance of particle to determine whether the best fitting solution is achieved. is

the inertia weight factor, c1and c2are acceleration constant. 1rand 2r are random numbers between

zero and one. can be adjusted by the following formula (13),

tT

.=max

minmaxmax

(13)

max and min are maximum and minimum values of inertial weight coefficient, Tmaxis the maximum

of iterations, t is the current number of iterations.

D. Design of fractional order PID controller using psoWhen PI

D

controllers parameters are optimized using particle swarm optimization, the

five parameters of the fractional controller and B1,B2frequency bias coefficients of area1 and area2

can be viewed as a particle, that is K= [Kp, Ki, Kd,, , B1,B2].The seven members are assignedas real values. If there are n individual in a population, then the dimension of that population is n*7.

In this paper n is set as 10. In order to limit the evaluation value of each individual of the population,

feasible range must be set for each parameter as follows

Kp1max= Kp2max=1.5; Kp1min= Kp2min= 0; Ki1max= Ki2max= 1.5; Ki1min= Ki2min= 1;

Kd1max= Kd2max=1.5; Kd1min= Kd2min=0;

Kp1vmax=Kp1max/10; Ki1vmax=Ki1max/10; Kd1vmax=Kd1max/10;

Kp1vmin=Kp1min; Ki1vmin=Ki1min; Kd1vmin=Kd1min;

1max= 2max=2; 1min= 2min=0; 1max= 2max=2; 1min= 2min=0;

1vmax= 1max/10; 1vmin= 1min; 1vmax= 1max/10; 1vmin= 1min;

Kp2vmax=Kp2max/10; Ki2vmax=Ki2max/10; Kd2vmax=Kd2max/10;

Kp2vmin=Kp2min; Ki2vmin=Ki2min; Kd2vmin=Kd2min;

B1max= B2max=35; B1min= B2min=15; B1vmax=B1max/35; B1vmin=B1min;

B2vmax=B2max/25; B2vmin=B2min; C1=2, C2=2.Now the design steps are as follows [11-14]:

1. Randomly initialize the individuals of the population including position and velocities in the

feasible range.

2. For each individual of the population, calculate the values of the performance criterion in

(10).

3. Compare each individuals evaluation value with its personal best P id. The best evaluation

value among all Pidis denoted as Pg.

4. Modify the member velocity of each individual according to (11) where the value of is setby equation (13).

5. Modify the member position of each individual according to (12).

6.

If the number of iterations reaches the maximum, then go to step 7 otherwise go to step2.7. The latest Pg is the optimal controllers parameters.

In this study optimal parameters of fractional controller for 1% and 10% step load perturbations are:

B1=17.4191,B2=25, Kp1=0.2819, Ki1=1.5, Kd1=1.2618,1=1.1869,1=0.5524.

Kp2=1.3213, Ki2=1.5, Kd2=1.1813,2=0.8336,2=1.0770.


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VI. RESULTS AND DISCUSSIONS

In the present work Automatic Generation Control of two area interconnected power system

has been developed using PSO based IOPID Control, ANFIS controller and PSO based FOPID

controller using Matlab/Simulink package. Figs 4 to 9 respectively represent the plots of change in

system frequency for 1% and 10% step load variations in area1. The results obtained are also givenin Tables 3 and 4.

Case I: For 1% Step load Perturbation

0 2 4 6 8 10 12 14 16 18 20-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-4

Time in Seconds

Deviationinfrequency(p.u.)

Change in frequency w ith PSO based IOPID control for 1% step load perturbation

Del f1

Del f2

Fig 4: Frequency deviations f1, f2withPSObased IOPID control

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1x 10

-3 Change in frequency with ANFIS Control for 1% step load perturbation

Time in Seconds

Dev

iationinfrequency(p.u.)

Del f1

Del f2

Fig 5:Frequency deviations f1, f2withANFIScontrol

0 2 4 6 8 10 12 14 16 18 20-5

-4

-3

-2

-1

0

1

2x 10

-4 Change in f requency w ith PSO based FOPID Controller f or 1% s tep load perturbation

Time in seconds


Del f1

Del f2

Fig 6:Frequency deviations f1, f2withPSObased FOPID controller


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Case II: For 10% Step load Perturbation

0 2 4 6 8 10 12 14 16 18 20-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-3

Time in Seconds

Deviaioninfrequency(p.u.)

Change in f requency w ith PSO based IOPID Controller for 10% step load per turbation

Del f1

Del f2

Fig 7: Frequency deviations f1, f2withPSObased IOPID Control

0 2 4 6 8 10 12 14 16 18 20-7

-6

-5

-4

-3

-2

-1

0

1x 10

-3 Change in frequency with ANFIS Controller for 10% step load perturbation

Time in Seconds


Del f1

Del f2

Fig 8:Frequency deviations f1, f2withANFIScontrol

0 2 4 6 8 10 12 14 16 18 20-5

-4

-3

-2

-1

0

1x 10

-3

Time in Seconds


Change in f requency w ith PSO based FOPID controller for 10% step load perturbation

Del f1

Del f2

Fig 9:Frequency deviations f1, f2withPSObased FOPID controller


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than the classical IOPID controller, gives more flexibility for the design of a control system and

gives better opportunity to adjust system dynamics. Simulation results shows that the proposed

Fractional controller has better dynamic performance than the Integer order controller and ANFIS

controller with faster response and smaller overshoot.

REFERENCES

[1] O.I.Elgerd, Electric Energy Systems Theory: An Introduction. Newyork: McGraw-Hill, 1982.

[2] Kundur. P, Power system stability and control, McGraw-Hill, Inc., 1994.

[3] Ibraheem, Prabhat Kumar, and Dwaraka P.Kothari, Recent philosophies of automatic

generation control strategies in power systems, IEEE Transactions on Power Systems, 20,

no.1, pp. 346-57, February 2005.

[4] J. Talaq and F. Al-Basri,Adaptive fuzzy gain scheduling for load frequency control,

IEEE Trans.Power Syst., vol.14, no.1, pp.145-150, Feb.1999.

[5] Y.L. Karnavas and D.P.Papadopoulos, AGC for autonomous Power System using combined

intelligent techniques, Elect. Power Syst.Res. vol.62, no.3,pp. 225-239, Jul.2002.

[6] Sathans and A.Swarup Intelligent Automatic Generation Control of Two area

Interconnected Power System using Hybrid Neuro Fuzzy Controller, World academy ofScience, Engineering and Technology 60 2011.

[7] Gayadhara Panda, Siddhartha Panda and C.Ardil, Hybrid Neuro Fuzzy Approach for

Automatic Generation Control of Two Area Interconnected Power System, International

Journal of Computational Intelligence 5:1 2009.

[8] Jifeng Wang. Control Performance analysis for Fractional order systems. Bei Jing: Publishing

House of Electronics Industry, 2010.

[9] Jiliu Zhou, Yifei Pu, Ke Liao. The Theory of Fractional calculus and its application in

modern signal analysis and processing. Bei Jing: Science Press, 2010.

[10] Jun-Yi Cao and Bing-Gang Cao. Design of Fractional Order Controller Based on Particle

Swarm Optimization. IJCAS, vol.4, no.6, pp.775-781, Dec 2006.

[11] Xiuye Wei, Hongxia Pan. Particle Swarm Optimization and Intelligent Fault Diagnosis. Bei

Jing: National Defence Industry Press, 2010.

[12] Ling Wang, Bo Liu. Particle Swarm Optimization and Scheduling Algorithm. Bei Jing:

Tsinghua University Press, 2008.

[13] Yishu Zhao, Zhijian Hu, Yang Gao, etc. Study of Fractional Order PID Conrollers for

STATCOM. Southern Power System Technology, 2009, 3(4): 26-30.

[14] Shuncai Yao, Hongxia Pan. Fractional order PID Controller for Synchronous Machine

Excitation using Particle Swarm Optimizaion. Proceedings of the CSEE, 2010, 30(21): 91-97.

[15] Muwaffaq Irsheid Alomoush. Load frequency control and automatic generation control using

Fractional order controllers. Electr Eng (2010) 91:357-368.

[16] Guishu Liang, Zhilan Wang. Design of fractional load frequency controller. International

Conference on Control Engineering and Communication Technology, 2012.

[17]

Ch.Ravi Kumar, Dr.P.V.Ramana Rao, Application of Hybrid Neuro Fuzzy Controller forAutomatic Generation Control of Three Area Power System Considering Parametric

Uncertainties, International Journal of Electrical Engineering Technology (IJEET),

Volume 4, Issue 5, pp. 104-114, 2013. ISSN Print: 0976-6545, ISSN Online: 0976-6553.

[18] P. Sobha Rani and Dr. A. Lakshmi Devi, Performance Improvement of Distribution System

with Multi Distributed Generation using Particle Swarm Optimization, International Journal

of Electrical Engineering Technology (IJEET) volume 5, issue 2, pp. 44 - 50, 2014.

ISSN Print: 0976-6545, ISSN Online: 0976-6553.


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BIOGRAPHY

Ch.Ravi Kumar was born in India in 1981; He received the B.Tech degree in

Electrical and Electronics Engineering from A.S.R.College of Engineering and

Technology, Tanuku in 2003 and M.Tech degree from JNTU Anantapur, A.P.-India

in 2005. Currently he is pursuing Ph.D in Electrical Engineering and working asAsst.Professor in University college of Engineering and Technology, Acharya

Nagarjuna University, Andhra Pradesh India. His areas of Interest are Power system

operation and control, Application of Intelligent control techniques to Power systems.

P.V.Ramana Rao was born in India in 1946; He received the B.Tech degree in

Electrical and Electronics Engineering from IIT Madras, India in 1967 and M.Tech

degree from IIT Kharagpur, India in 1969. He received Ph.D from R.E.C Warangal

in 1980. Total teaching experience 41 years at NIT Warangal out of which 12 years

as Professor of Electrical Department. Currently Professor of Electrical Department

in University college of Engineering and Technology, Acharya Nagarjuna

University, Andhra Pradesh, India. His fields of interests are Power system operationand control, Power System Stability, HVDC and FACTS, Power System Protection, Application of

DSP techniques and Application of Intelligent control techniques to Power systems.

pso based fractional order automatic generation controller for two area power system

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