Determination of controller gains for frequency control

INTERNATIONAL JOURNAL and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN &
International Journal of Electrical Engineering OF ELECTRICAL ENGINEERING
0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME
TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 3, Issue 3, October - December (2012), pp. 52-62 IJEET
© IAEME: www.iaeme.com/ijeet.asp
Journal Impact Factor (2012): 3.2031 (Calculated by GISI) ©IAEME
www.jifactor.com

DETERMINATION OF CONTROLLER GAINS FOR FREQUENCY
CONTROL BASED ON MODIFIED BIG BANG-BIG CRUNCH
TECHNIQUE ACCOUNTING THE EFFECT OF AVR
Miss Cheshta Jain
Department of electrical and electronics engg., MITM, Indore
email:cheshta_jain194@yahoo.co.in

Dr. H.K. Verma
Department of electrical engg., S.G.S.I.T.S., Indore
email:vermaharishgs@gmail.com

Dr. L.D. Arya
Department of electrical engg., S.G.S.I.T.S., Indore
email:ldarya@rediffmail.com

ABSTRACT

This paper presents a methodology for determining optimized controllers gains for frequency control
of two area system. The optimized gains have been obtained using a fitness function which depends
on peak overshoot, steady state error, settling time and undershoot. The AVR loop has been included
in optimization and its effect on optimized PID controller has been investigated. The optimization has
been achieved using Big Bang-Big Crunch (BB-BC) optimization. The performance of controllers as
obtained by BB-BC technique have been compared on two area system with that obtained using
modified particle swarm optimization (PSO) and differential evaluation (DE) technique.
Keywords: AGC, AVR, Big Bang-Big Crunch, Differential evolution algorithm, Particle swarm
optimization.

NOMENCLATURE

∆f : frequency deviation.
i : subscript referring to area (i = 1, 2,……).
∆Ptie (i,j) : change in tie line power.
∆PL : load change.
D : ∆PL / ∆f
R : governor Speed regulation parameter.
Th : speed governor time constant.
Tt : speed turbine time constant
TP : power system time constant.

52

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

Te : exciter time constant.
TG : generator field time constant.
Ts : sensor time constant.
KP : power system gain.
H : inertia constant.
Us : undershoot
Mp : overshoot
ts : settling time.
tr : rise time.
ess : steady state error.

1. INTRODUCTION

AN interconnected power system is made up of several control areas with respect to megawatt-
frequency control. In each area, an AGC observes the system frequency, tie-lines flow and computes
the net change in the generation required to control error and set position of generation within each
area to keep the error (area control error) at a low value. Over the past decades, many researchers
have applied different control strategies, such as classical control, variable structure control, optimal
feedback control and robust control to AGC problem in order to achieve better performance [1]. Yu et
al. [2] have praised a linear quadratic regulation (LQR) method to tune PID gain, but it requires
mathematical calculation and solving equations. Sinha et al. [3] introduced genetic algorithm (GA)
based PID controller for AGC of two areas reheat thermal system. Ghoshal et al. [4] proposed PSO
based PID controller for AGC. Some deficiencies in performance of GA method are identified by
above paper. To stabilize the system for load disturbance comparative transient performance of
thyristor controlled phase shifter (TCPS) and superconducting magnetic energy system (SMES) are
proposed by Praghnesh Bhatt et.al with optimized gains by improved Particle swarm optimization
(craziness based PSO) [1]. The controller of AGC and AVR are set for a particular operating
condition. Many investigations in the area of AGC of isolated and interconnected power system have
been reported in the past but they do not consider the effect of AVR. Dabur et al. [5] proposed AGC-
AVR for multi-area power system with demand side management. The paper is mainly focused on
reduction of total load demand during period on peak demand to maintain security of system but not
explained the selection of optimum gain of controller.
The Big Bang- Big Crunch (BB-BC) a new optimization method relied on one of the theories
of the evaluation of the universe namely Big Bang theory and Big Crunch theory which is introduced
by Erol and Eskin [6]. This method has a low computational time and high convergence speed. The
proposed method is similar to the Genetic Algorithm in respect to creating an initial population. The
BB-BC method eliminates the possibility of Medicare scalability; one of the disadvantages of GA
based learning method.
In this paper a BB-BC based controllers is proposed as the supplementary controllers, which
show better dynamic response compared with DE and PSO based optimized controllers.
In view of the above, the following are the main objectives of the proposed work to:
1. Obtain the optimize gain of integral controller of AGC and PID controller of AVR by Big
Bang- Big Crunch algorithm for AGC-AVR of two area interconnected system.
2. Compare dynamic response of AGC system with and without AVR using MATLAB.
3. Compare the performance of the Big Bang- Big Crunch based controller to the DE and PSO
based controller.
The rest of the paper is organized as follows: In section 2 the two area system model and
scheduled loading availability model are developed. Section 3 describes BB-BC algorithm and the
implementation of BB-BC based controller is presented in section 4. Section 5 shows the result with
detailed discussion and conclusion is drawn in section 6.

2. AGC-AVR SYSTEM MODEL
The system investigated consists of two control areas with reheat type thermal unit connected
by tie-lines that allows power exchange between areas. If the load on the system is increased the

53


speed of turbine reduces before the governor can adjust the input of steam correspond to the new load.
As the change in output of system become smaller, the position of governor move to set point to
maintain a constant speed in automatic generation control (AGC). On the other hand the generator
excitation system control generator voltage and reactive power flow using automatic voltage regulator
(AVR) [19]. The proposed work investigates the effect of coupling between AGC and AVR.
2.1 AGC System:
The AGC have two control actions (i) primary control which makes the initial readjustment of
frequency to nominal value, (ii) supplementary control to provide precise control strategy for fine
adjustment of the frequency. The main function of supplementary control is to maintain system
frequency at predetermined set point after a load perturbation. The input to the supplementary
controller of the ith area is the area control error (ACEi) which is given by:
௡

‫ܧܥܣ‬௜ = ෍(∆ܲ௧௜௘(௜,௝ሻ + ‫ܤ‬௜ ∆݂௜ ሻ
௝ୀଵ
(1)
Where, Bi is frequency bias coefficient of ith area, ∆fi is frequency error, ∆Ptie is tie-line power
flow error and ‘n’ is number of interconnected areas [18]. The area bias Bi determines the amount of
interaction during load perturbation in neighboring area. To obtain better performance, bias Bi is
selected as:

(2)
2.2 AVR System:
This paper studied on coupling effect by extending the linear AGC to include the excitation
system. The real power transfer over the line is:
|‫ܧ‬ଵ ||‫ܧ‬ଶ |
ܲ= ‫ߜ݊݅ݏ‬
ܺ
(3)

This is the product of the synchronizing power coefficient (Ps) and the change in the power
angle (∆δ). Now include small effect of voltage on real power as:
∆ܲ௥௘௔௟ = ܲ ∆ߜ + ‫ܸ1ܭ‬
௦ ௙
(4)
Where, K1 is the change in electrical power for a small change in stator emf and Vf is output
of generator field. Also, including the small effect of rotor angle on generator terminal voltage as:
∆ܸ௧ = ‫ܸ3ܭ + ߜ∆2ܭ‬ ௙
(5)
Where, K2 is the change in the terminal voltage for a small change in the rotor angle at
constant stator emf, and K3 is the change in the terminal voltage for a small change in stator emf at a
constant rotor angle. Now finally modified generator field output is:
௄ಸ
ܸ௙ = (ଵା௦் ሻ (ܸ − ‫ߜ∆4ܭ‬ሻ
௘
ಸ
(6)
Where, Ve is exciter output voltage, KG is a generator gain constant, and TG is generator time constant.
The value of all the gains, time constants and constants are given in appendix.
The complete transfer function model of AGC-AVR is shown in fig 1.

54


Fig.1: Linear model of two area AGC-AVR system
.1:

3. OVERVIEW OF BIG BANG
BANG-BIG CRUNCH ALGORITHM
The Big Bang-Big Crunch algorithm has been introduced by Erol and Eskin. This algorithm is
Big
based on the formation of universe stated by Big Bang theory. According to this theory the universe
was once a sphere with infinite radius and density. Due to several internal forces, the existed mass is
exploded massively called Big-Ban and billions of particles moved outwards. Once particles start
Bang
spreading, a gravitational force arises which depends on masses of two bodies considered and distance
between them. As expansion takes place the gravitational force on each particle decreases and kinetic
energy of expansion dissipated rapidly [6 [6].
Because of expansion gravitational energy between particles overcomes the kinetic energy
resulting particles start shrinking. At this stage all particles collapse in to a single particle called Big-
Big
Crunch. This algorithm work through a simple cycle of stages as:
runch.

Stage 1 (Big Bang phase): The initialization in this phase is similar to other evolutionary method. An
initial population of candidate is generated randomly over the entire search space as:

(௞ሻ (௞ሻ
‫ݔ‬௜ (௞ = ‫ݔ‬௜(௠௜௡ሻ (௞ሻ + ‫ݔ( .݀݊ܽݎ‬௜(୫ୟ୶ሻ − ‫ݔ‬௜(୫୧୬ሻ ሻ
௞ሻ

(7)

Where,
k=1, 2, 3…….. no of paramete and i=1, 2,…..pop.
parameters
xi(min) and xi(max)are upper and lower limit of ith candidate.
The working of Big Bang phase is explained as energy dissipation. Randomness in the
ng
initialization is same as the energy dissipation in nature but this dissipation creates disordered from
ordered particles and use this randomness to create new solution candidate (disorder or chaos). The
(disorder
number of individuals in the population must be big enough in order not to miss the global point.
Stage 2 (Big Crunch phase): Big Crunch phase come as a convergence operator. This phase have only
:
one output named as center of mass. The center of mass is the weighted average of candidate solution
T rage
as [9]:

55


(ೖሻ
೛೚೛ ೣ
∑೔సభ ೔
ܺ௖௢௠ =
೑೔
೛೚೛ భ
∑೔సభ
೑೔
(8)

Where,
Xcom is position of the center of mass.
xik is position of ith candidate in N dimensional search space.
fi is fitness function value of ith candidate.
Pop is size of population.

Stage 3 (Generate new population): Big Bang phase is normally distributed around center of mass.
The new candidate around the center of mass is calculated by adding or subtracting a normal random

‫ݔ(ߙ .݀݊ܽݎ‬௜(୫ୟ୶ሻ − ‫ݔ‬௜(୫୧୬ሻ ሻ
number as:
‫ݔ‬௜௡௘௪ = ߚ. ܺ௖௢௠ + (1 − ߚሻ‫ݔ‬௕௘௦௧ +
݅‫݌݁ݐݏ ݊݋݅ݐܽݎ݁ݐ‬
(9)
Where,
α is parameter limiting the size of search space.
β is parameter controlling the influence of the global best solution xbest on the location of new
candidate solution. The best solution xbest influences the direction of search [9].
Stage 4 (Selection or recombination): Now apply selection criterion. Selection determines that,
whether the new candidate is suitable for next iteration or not. The value of fitness function of current
generation (f (xinew)) is compared with the previous fitness function (f (xi)) of corresponding
individual. If the fitness functions to newly generated candidate have lower value than previous one
then former candidate replaced by new generated candidate as:

୮୰୧୴୧୭୳ୱ ୮୰୧୴୧୭୳ୱ
x if f(x୧ ሻ ≤ f(x୧ ሻ
୬ୣ୵
x୧
୬ୣ୶୲ ୧୲ୣ୰ୟ୲୧୭୬
= ൝ ୧ ୬ୣ୵ ୮୰୧୴୧୭୳ୱ
ൡ
x୧ if f(x୧ ሻ < ݂(x୧
୬ୣ୵
ሻ

(10)
As the search space is contracted with new iteration, the algorithm arrives at the optimum
point very fast.

4. BB-BC BASED OPTIMIZATION OF CONTROLLER GAINS
This paper uses a fitness function based on overshoot, undershoot, steady state error and
settling time proposed by Ghoshal et.al [4] as:
ଶ
‫ = ݊݋݅ݐܿ݉ݑ݂ ݏݏ݁݊ݐ݅ܨ‬ቀ൫‫ܯ‬௣ + ݁‫ݏݏ‬൯. 1000ቁ + (ܷ௦ . 100ሻଶ + (‫ݐ‬௦ ሻଶ
(11)
Multiplying factor associated with overshoot (1000) and undershoot (100) are minimized its value to a
greater extent. The optimum selection of these factors depends on the designer’s requirement and
characteristics of the system. High settling time does not require any amplification.
4.1 Implementation of algorithm:
step1 Set system data (given in appendix), select value of α, β and number of population, number of
maximum iteration.
step2 Set iteration count c=1 and randomly initialize candidate solution (xi = x1, x1, ….xN) for gains
of controller within limits using eq.7.
step3 Run AGC-AVR model as given in fig.1 and calculate performance parameter such as Mp, Us,
ess, ts, for ith candidate solution.
step4 Calculate fitness function using eq. 11 for all candidate solution and also find best fitness
value.
step5 Find the center of mass using eq. 8 (Big Bang phase).

56


step6 Calculate new candidate around center of mass (eq. 9).
step7 Apply selection criterion (eq. 10) and set c=c+1.
step8 If maximum number of iteration reached then stop otherwise go to step 3.

5. RESULT AND DISCUSSION
This section presents simulation results of Big Bang-Big Crunch optimized gains for two area
automatic generation control with and without automatic voltage regulator. Figs 2-6 shown
comparative performance of BB-BC algorithm of the frequency, area control error and tie-line power
deviation in each area following a 0.01 pu load perturbation with particle swarm optimization and
differential evaluation algorithm. These results illustrate the effectiveness of the presented BB-BC
method over other evolutionary methods. Fig8 gives the better optimal performance using BB-BC
based gains for terminal voltage of generator field.
Table-1 and Table2 show that frequency response settling time is lower with BB-BC based
controller compared to those of the other methods. It also depicts that the computational time with
minimum fitness function is lowest.
As seen from Figs 8-11, the responses of BB-BC optimized AGC system with AVR exhibits
long-lasting oscillations with large overshoot and large steady state error compare to AGC without
AVR. It shows the effect of coupling between AGC and AVR loop.

Table-1 Optimal controller gains and best fitness function.

Algorithm PID Controller Gains of AVR Integral Fitness Execution
Gain of function time
AGC
KP KI KD KI
PSO 1.1090 0.6737 0.9198 0.2649 114.8966 58.848052
DE 0.6291 1.512 0.9466 0.2736 113.9013 140.608386
BB-BC 0.2904 0.2709 0.2594 0.3971 102.7837 51.005986

Table-2 Comparison of performance parameters

Algorithm System performance parameters
Settling Overshoot Undershoot Steady state error
time(Sec.)
PSO 9.619 6.466*10-5 -0.0473 2.4437*10-6
DE 9.427 5.675*10-4 -0.0497 2.2691*10-6
BB-BC 8.9245 1.82*10-4 -0.0382 9.459*10-7

0.005
f1PSO
f1DE
0
f1BBBC

-0.005

-0.01

-0.015

-0.02

-0.025

-0.03
0 5 10 15 20 25 30 35 40 45 50

Fig2 Comparative response of frequency deviation in area 1

57


0.01
f2PSO
0.005 f2DE
f2BBBC
0

-0.005

-0.01

-0.015

-0.02

-0.025

-0.03

-0.035
0 5 10 15 20 25 30 35 40 45 50

Fig3 Comparative response of frequency deviation in area 2

0.1
ACE1PSO
ACE1DE
0
ACE1BBBC

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6
0 5 10 15 20 25 30 35 40 45 50

Fig4 Comparative response of area control error of area 1.

0.05
ACE2PSO
ACE2DE
ACE2BBBC
0

-0.05

-0.1

-0.15

-0.2
0 5 10 15 20 25 30 35 40 45 50

Fig5 Comparative response of area control error of area 2.

58


-3
x 10
3
PtiePSO
PtieDE
2.5 PtieBBBC

2

1.5

1

0.5

0
0 50 100 150 200 250 300 350 400 450 500

Fig6 dynamic response of tie-line power deviation
1.4
vtPSO
vtDE
1.2
vtBBBC

1

0.8

0.6

0.4

0.2

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

Fig7 response of terminal voltage of generator field
0.05

0

-0.05 ACE1 of without AVR
ACE1 with AVR
-0.1

-0.15

-0.2

-0.25

-0.3

-0.35

-0.4

-0.45
0 5 10 15 20 25 30 35 40 45 50

Fig8 Dynamic response of area control error of AGC with AVR and without AVR of area1

59


0.05
ACE2 without AVR
ACE2 with AVR

0

-0.05

-0.1

-0.15

-0.2
0 5 10 15 20 25 30 35 40 45 50

Fig9 Dynamic response of area control error of AGC with AVR and without AVR of area2

-3
x 10
5
delta f1 without AVR
delta f1 with AVR

0

-5

-10

-15

-20
0 5 10 15 20 25 30 35 40 45 50

Fig10 effect of AVR on AGC system frequency deviation on area 1
0.01
delta f2 without AVR
0.005 delta f2 with AVR

0

-0.005

-0.01

-0.015

-0.02

-0.025

-0.03
0 5 10 15 20 25 30 35 40 45 50

Fig11 Comparative response of frequency deviation on area 2 with and without AVR

6. CONCLUSION
In this paper a new but effective global optimization algorithm named Big Bang- Big Crunch (BB-
BC) is used for optimizing gains of AGC-AVR system. Simulation results show the convergence
speed of the BB-BC is better than the PSO and DE with the same design parameter. This paper also
demonstrated that BB-BC algorithm has ability to search global optimum accurately compared to DE
and PSO methods.

60


Appendix
Nominal parameters of two area test system [5]:
H1=5, H2= 4 seconds
D1=0.62, D2= 0.91 P.U. MW/Hz
R1= 0.051, R2=0.065 Hz/P.U. MW
Th1=0.2, Th2=0.3 sec.
Tt1=0.5, Tt2=0.6 seconds
Kp1= Kp2=159 Hz P.U. MW
Ps=0.145P.U. MW/Radian
KH=KT=Ke= 1.
KA=10, TA=0.1.
Te=0.4.
KG=0.8, TG=1.4.
Ks=1, Ts=0.05.
K1=1, K2=-0.1, K3=0.5, K4=1.4.
Parameters for BB-BC algorithm:
Initial population= 20
Maximum iteration= 100
β=0.5, α=0.1.
Parameters for DE algorithm:
Scaling factor F= 0.5
Crossover probability (CR) = 0.98
Parameters for PSO algorithm:
Wmax= 0.6, Wmin= 0.1
C1= C2= 1.5

REFERENCES
[1] Praghnesh Bhatt, S.P.Ghoshal “Comparative performance evaluation of SMES-SMES, TCPS-
SMES and SSSC-SMES controller in automatic generation control for a two area hydro-
hydro system”,International journal of electrical power and energy, vol33 issue 10
DEC2011.
[2] G. Yu, and R. Hwang, (2004) “Optimal PID speed control of brush less DC motors using
LQR approach,” in Proc. IEEE Int. Conf. Systems, Maand Cybernetics, pp. 473-478.
[3] Nindul Sinha, Loi Lei Lai, Venu Gopal Rao, (April 2008) ” GA optimized PID controllers for
automatic generation control of two area reheat thermal system under deregulated
environment”, proc. IEEE international conference on electric utilizes deregulation and
restructuring and power technologies,6-9, pp. 1186-1191.
[4] S.P.Ghoshal ,N.K.Roy, (Sept. 2004) ” A novel approach for optimization of proportional
integral derivative gains in automatic generation control”, Australasian universities power
engineering conference (AUPEC 2004), 26-29.
[5] Praveen Dabur, Naresh kumar Yadav, Vijay Kumar Tayel, ”MATLAB Design and
Simulation of AGC and AVR Multi Area Power System and Demand Side Management”,
International journal of Computer Electrical Engg., vol. 3, no. 2, April 2011.
[6] K. Erol Osman, Ibrahim Eksin, “New optimization method: Big Bang- Big Crunch”, Elsevier,
Advances in Engineering Software 37 (2006), pp. 106-111.
[7] Nasser Jaleeli, Donald N. Ewart, Lester H. Fink; “Understanding automatic generation
control”, IEEE Transaction on power system, Vol. 7, No. 3, August 1992. Pages: 1106-1122.

61


[8] Vaibhav Donde, M.A.Pai, and Ian A.Hiskens; ”Simulation and Optimization in an AGC
system after Deregulation”, IEEE transactions on power systems, Vol.16, No -3, August
2001.
[9] Potuganti Prudhvi, “A complete copper optimization technique using BB-BC in a smart home
for a smarter grid and a comparision with GA”, IEEE conferenceCCECE, 2011.
[10] Engin Yesil, Leon Urbas, “Big Bang- Big Crunch Learning Method for Fuzzy Cognitive
Maps”, world Academy of Science, Engg and Technology, 71, 2010.
[11] Dr. L.D. Arya, Dr. H. K. Verma and Cheshta Jain, (April 2011) “Differential evolution for
optimization of PID gains in automatic generation control”, international journal of
computer science and application.
[12] A. Kaveh and H. Abbasgholiha, “Optimization Design of Steel Sway Frames using Big Bang-
Big Crunch Algorithm”, Asia jornal of Civil Engg. Vol. 12, no. 3, 2011, pp. 293-317.
[13] Moacir Kripka and Rosana Maria Luvezute Kripka, “Big Crunch Optimization Method”,
International Conference on Engg. Optimization 01-05 June 2008.
[14] Nindul Sinha, Loi Lei Lai, Venu Gopal Rao, (April 2008) ” GA optimized PID controllers
for automatic generation control of two area reheat thermal system under deregulated
environment”, proc. IEEE international conference on electric utilizes deregulation and
restructuring and power technologies,6-9, pp. 1186-1191.
[15] Swagatam Das and Ponnuthurai N.Suganhan (Feb. 2011) “ Diffrential evolution: A survey of
the state of the art”, IEEE trans. On evolutionary computation, Vol. 15, No. 1.
[16] R, Storn , K. Price, (1995) ” Differential evolution –A simple and efficient adaptive scheme
for globel optimization over continuous spaces”, Technical report TR-95-012, March
1995,ftp.ICSI.Berkeley.edu/pub/techreports, tr-95-012.
[17] Z.-L. Gaing, (June 2004) “A particle swarm optimization approach for optimum design of
PID controller in AVR system,” IEEE Trans. Energy Conversion, vol. 19, pp. 384-391.
[18] O.I. Elgerd, (2001) “Electric energy system theory an introduction”, McGraw Hill Co., 2001.
[19] Hadi Saadat; “Power System Analysis”, Mc Graw- Hill, New Delhi, 2002.

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