View of MODIFIED GREY WOLF OPTIMIZATION ALGORITHM APPLIED TO LOAD FREQUENCY CONTROL OF MULTI-AREA INTERCONNECTED SYSTEM

Vol.04, Issue 01, January 2019, Available Online: www.ajeee.co.in/index.php/AJEEE MODIFIED GREY WOLF OPTIMIZATION ALGORITHM APPLIED TO LOAD FREQUENCY

CONTROL OF MULTI-AREA INTERCONNECTED SYSTEM Pooja Sahu¹, Amit Goswami²

1,2Disha Institute Of Management & Technology, Raipur (C.G), India

1poojasahu80@yahoo.com, ²amit.goswami23feb@gmail.com

Abstract:- Controller design aspects play vital role in load frequency control (LFC) of power system networks. In this work, a PID controller with derivative term is tuned to control the frequency and tie-line power deviations of a two-area non-reheat thermal system using modified grey wolf optimization (MGWO). MGWO is a modified version of grey wolf optimization (GWO) algorithm which is based on the hunting behavior of grey wolves. For optimization purpose, the fitness function is formulated by considering integral errors of frequency and tie-line power deviations. Four different cases of load perturbation conditions in both areas are considered. A comparative assessment of the proposed controller is carried out with GWO and cuckoo search algorithm (CSA) based controllers and the obtained results are tabulated. Time-domain simulations are carried out to further establish the superior performance of the proposed controller.

Keywords:- Load frequency control; Modified grey wolf optimization; grey wolf optimization;

PID controller; multi-area interconnected system.

1. INTRODUCTION

The main objective of electric utilities is to supply of reliable power with acceptable quality of power, and the main challenge lies in maintaining the equilibrium between the generation and the supply [1]. Because if there is no equilibrium between generation and the supply the whole power system may collapse due the mismatch of frequency between the interconnected system. Load frequency control (LFC) involves the real and the reactive power control in it, reactive power control involves the Automatic Voltage Regulation (AVR) and the real power control involves LFC.

Multi-area power system is generally an interconnected system and in such interconnected systems maintaining the change in frequencies in permissible values in the interconnected areas due to the change in the load demand is done by the LFC system. LFC does this by changing the set-position of the generators for the corresponding change in the load and this change in the demand will go as the error input to the controller in the respective system called as the Area Control Error (ACE).

Every time the controller takes the corresponding control action and maintains the frequency and the tie-line power in equilibrium such that the ACE will become zero and hence, the change in the frequencies and the tie-line power becomes zero and the system will be stable [2]. The control mechanism of the

LFC is evolved as Integral Controller (I- Controller), Proportional Integral Controller (PI-Controller), Integral Differential Controller (ID-Controller) and Proportional Integral Differential Controller (PID-Controller) and so-on.

Many researchers are working on the many modern controllers such as Fuzzy Interface Controller, Neural Network Interface Controller, Reinforcement Control and ANFIS etc. As these new controllers evolve their control action which is better than the earlier controllers but, all these controllers have a complex structure compared to the conventional P, PI, ID and PID controllers.

Hence, for the sake of simplicity and user friendliness, the conventional controllers are more preferred than the modern controllers by the experts.

Here, in this thesis, the Proportional Integral Differential Controller with Derivative Filter (PIDN) is adopted. Even though the quality of the controller plays a prominent role in the effectiveness of the LFC, others aspects like the technique used for tuning the control parameters of the respective controller and also on the objective function opted for optimizing the controller parameters are also vital in the LFC [3]. Many optimization algorithms are used in the optimization of the control parameters for the LFC.

Vol.04, Issue 01, January 2019, Available Online: www.ajeee.co.in/index.php/AJEEE The effectiveness of these

algorithms depends on how fast these algorithms are tending to the optimal controller values. Many optimization algorithms such as Bacterial Forging Algorithm (BFA) [4], Particle Swarm optimization (PSO) [5], Fire-fly Algorithm (FA) [6], Cuckoo search Algorithm (CSA) [7] and Genetic Algorithm (GA) [8] etc.

Likewise, many algorithms have been used in the literatures till date and many new algorithms are being proposed. In this work, a PID controller with derivative term is tuned to control the frequency and tie-line power deviations of a two-area non-reheat thermal system using Modified grey wolf optimization (MGWO).

MGWO is an efficient optimization algorithm which is based on the hunting behavior of grey wolves [9]. For optimization purpose, the fitness function is formulated by considering integral errors of deviations in frequency and tie- line power deviations. Four different cases of load perturbation conditions in both areas are considered. A comparative assessment of the proposed controller is carried out with grey wolf optimization (GWO) and CSA based controllers and the obtained results are tabulated. Time- domain simulations are carried out to further establish the superior performance of the proposed controller.

1.1 System Modeling

The system adopted in this thesis is a two equal area interconnected system with two non-reheat thermal plant with individual area rating of 2000 MW with a nominal load of 1000MW in each area is shown in Fig. 1. In the system,

ACE

₁ and

ACE

2 are the area control errors of area- 1 and area-2 respectively;

B

₁ and

B

₂are the frequency bias of the area-1 and area- 2;

R

₁ and

R

₂are the speed regulations in (pu Hz);

u

₁ and

u

₂ are the error outputs of controllers;

T

_G1 and

T

_G2 are the governor time constants in (sec);

 P

_G1

and

 P

_G2 are the change in the governor power outputs in (p.u);

T

_T1 and

T

_T2 are the turbine time constants in sec;

 P

_T1

and

 P

are the change in the turbine

powers in (p.u);

 P

_D1 and

 P

_D2 are the changes in the demands in (p.u);

 P

_Tie is the changes in the tie-line power in (p.u);

1

K

P and

K

_P2are the power system gains ;

1

T

PS and

T

_PS2 are the power system time constants in (sec);

 F

₁ and

 F

₂ are the changes in the frequencies in area-1 and area-2.

1

1

1s TG 1

1

1s TT 1

1 1s TP S

2

1

1s TG 2

1

1s TT 2

1 1sTP S

PIDN Controller

PIDN Controller



 





P_D1

P_D2

a12

a12





1

1 R

2

1 R

B1

B2

 



 















 



ACE1

ACE2

controller

controller

Governer

Governer Turbine

Turbine

1

Pref



2

Pref



u1

u2

1

PG



2

PG



1

PT



2

PT



T1 2

s PTie

 Power system

Power system P12



P21



F1



F2





Fig 1. Block diagram for a two-area non- reheat thermal system

The two area system shown in the Fig. 1 consists of a governor, turbine, and a generator each, and each area has three inputs and two outputs, error output from the controller (denoted by

 u

₁,

 u

₂or

1

Pref

 ,P_ref2), change in the load (denoted by

 P

_D1,

 P

_D2), change in tie-line power (denoted by

 P

_Tie) are the inputs and the change in the frequencies in the two areas (denoted by

 F

₁,

 F

₂) and the area control error (denoted by

ACE

₁and

ACE

2) are the outputs of the system.

The model used in our work has a wide range of usage in the literature for the study of the two-area system. A PID controller with a derivative filter is used in this study. Fig. 2 shows the block diagram representation of controller structure. The input to the controller is

ACE

ant the output control signal is

u

. K ,

K

and

K

are the proportional,

Vol.04, Issue 01, January 2019, Available Online: www.ajeee.co.in/index.php/AJEEE integral and derivative gains.

n

is the

derivative gain term for the filter and is used A conventional to reduce the effect of the noise in the signal. The transfer function of the controller is given as

1 1

controller p i d

TF K K K n

s n

s

  

    

       

(1)

Proportional gain

Integral gain

Derivative gain Filter with derivative term

+

+ + +

-

Fig. 2. Controller structure

The input to the controller

ACE

for the two areas are given as

1 1 1 tie

ACE  B    f P

(2)

2 2 2 12 tie

ACE  B   f a  P

(3) 2. PROBLEM STATEMENT

The objectives considered in this work is minimization of the integral of time multiplied absolute error (ITAE) of the

 f

₁

,  f

₂

and  P

_Tie.

The corresponding ITAE is represented as

 

 

 

1 1

0

2 2

0

0

sim

sim

sim

t ITAE

t ITAE

t ITAE

Tie Tie

f f t dt

f f t dt

P P t dt

    

    

    







(4)

1 2

ITAE ITAE ITAE

J   f   f   P

Tie (5)

J

is considered as the objective function to be minimized throughout the study.

The constraints to the problem are the minimum and maximum value of the controller coefficients defined as

min max

min max

min max

min max

p p p

i i i

d d d

K K K

K K K

K K K

n n n

 

 

 

 

(6)

2.1 Modified Grey Wolf optimization (MGWO)

1. Grey Wolf Optimization

The GWO is firstly proposed by Mirjalili et al., [9]. The algorithm was inspired by the democratic behavior and the hunting mechanism of grey wolves in the wild. In a pack, the grey wolves have a very strict social dominant hierarchy. The leaders, which are a male and a female, are called alpha.

The second level of grey wolves, which are subordinate wolves that help the leaders, are called beta. The third level of grey wolves is delta, which has to submit to alphas and betas, but dominate the omega. The lowest rank of the grey wolf is omega, which have to submit to all the other dominant wolves. The GWO algorithm is provided in the mathematical models as follows:

2.1.1 Social Hierarchy: In the social hierarchy of wolves when designing GWO, the best solution is considered as the alpha (



), the second and third best solutions are considered as beta (



) and delta (



) respectively. The rest of the candidate solutions are assumed to be omega (



). The



wolves are guided by



,



, and



, and followed by these three wolves.

2.1.2 Encircling Prey: The grey wolves encircle prey during the hunt. The encircling behavior can be mathematically modelled as follows:

   

D   C X

p

t  X t

(7)

 ¹ 

p

 

X t   X t   A D

(8) Where,

t

is the current iteration, A and

C

are coefficient vectors,

X

_p is the position vector of the prey (global solution), and X is the position vector of a gray wolf.

Vol.04, Issue 01, January 2019, Available Online: www.ajeee.co.in/index.php/AJEEE The vectors A and

C

are calculated as

follows:

2

1

A  a r   a

(9)

2

2

C   r

(10) Where components of

a

are linearly decreased from 2 to 0 according to iterations and

r r

₁

,

₂ are random vectors in [0, 1].

2.1.3 Hunting: The hunt is usually guided by the alpha, beta and delta, which have better knowledge about the potential location of prey. The other search agents should update their positions according to the position of the best search agent. The update of their agent position can be formulated as follows:

D

_

 C X

1



_

 X

_ ;

D

_

 C

2

 X

_

 X

_ ;

D

_

 C

3

 X

_

 X

_ ; (11)

     

1 1

;

2 2

;

3 3

X    X

_

A D

_

X    X

_

A D

_

X    X

_

A D

_

(12)



¹



^{1 2 3}

3

X X X

X t   

(13) 2.1.4 Attacking Prey And Search For

Prey (Exploitation And Exploration):

The prey being attacked by the gray wolves is the ability of the gray wolves capturing the prey. In other words, the ability of the grey wolves can result in the global optima; that is the exploitation ability. Since the value of

a

is decreased from 2 to 0, A is also decreased by. In other words, A is a random value in the interval [-2a, 2a]. When

A  1

, the wolves are forced to attack the prey.

On the other hand, the search for prey by the gray wolves is the ability of the gray wolves in searching for various positions of the prey. In other words, the search for prey is the exploration ability.

The random values of A are utilized to oblige the search agent to diverge from the prey. When

A  1

, the gray wolves are forced to diverge from the prey.

2. Modified Grey Wolf Optimization Although the GWO has a helpful mechanism to smoothly balance the exploration and exploitation, i.e. the adaptive values of

a

andA, the GWO may trap in local optima. Since the GWO emphasizes the exploration ability which depends only on the

C

vector. According the parameterA, it is found that it can utilize the parameter A to select the strategy to compute the vector considering that the absolute parameter A is less than 1 or greater than 1. The aim of the use of modification is to increase the diversity of the agent.

The movement of agent in GWO depends greatly on the alpha, beta, and delta circumstances. Fig. 5.2 shows how a search agent updates its position. In contrast, in MGWO, the movement of the agent depends on the alpha, beta, delta, or those random chosen agents according to the random values of. In this thesis, a new strategy is added to calculate the vector which is helpful for a search agent to have more exploration ability and not trap in the local optima. The update position can be formulated as follows:

1 3 2 1 3 1

1 _{r r} ; 2 _{r r} ; 3 _{r r}

D_   C X X D_  C X X D_ C X X (14)

     

1 1 ; 2 2 ; 3 3

XX_ A D_ XX_ A D_ XX_ A D_ (15)



¹



^{1 2 3}

3

X X X

X t      (16)

Where the indexes

 

1

,

2

and

3

1, 2,...,

r r r  N

are randomly

chosen indexes and

r

₁

  r

₂

r

₃. 3. The Pseudo Code Of MGWO:

Initialize the grey wolf population



^{1, 2,...,}



Xi i N Initialize

a

,A, and

C

. Calculate the fitness of each search agent:-



X

_= the best search agent

 X_ = the second-best search agent



X

_ = the third best search agent While (t < Max number of iterations) for each search agent if _A1 Calculate

D

_,

D

_ and

D

_ by equation

Vol.04, Issue 01, January 2019, Available Online: www.ajeee.co.in/index.php/AJEEE (5.5) else Calculate

D

_



,

D

_



and

D

_



by

equation (5.8) end if Update the position of the current search agent by equation (5.7) or equation (5.10) depending upon selected strategy. End for Update a, and C by (5.4), and A is updated by using (5.3) Calculate the fitness of all search agents Update

X

_,X_, and

X

_. T = t+1 end while return

X

_.

3. SIMULATION RESULTS AND DISCUSSIONS

In this work, controller tuning for automatic generation control (AGC) of two-area interconnected thermal power system is carried out. The parameters of the studied system are listed in Appendix A. A classical PID controller with derivative filter is used. As it is already discussed any change of load in one area affects other area too as both areas are connected with each through tie-line.

Modified grey wolf optimization (MGWO) algorithm is used to tune the controller parameters.

To verify the controller performance, various sets of step load disturbances are created in both areas.

The proposed controller is compared to grey wolf optimization (GWO) and cuckoo search algorithm (CSA) based controller to validate its superiority. The time-domain simulations are carried out to further validate the superior performance of the proposed controller. A total of 50 iterations and 10 population size is considered for MGWO, GWO and CSA. All simulations are carried out in MATLAB environment.

The boundary conditions of the controller parameters used in this work are defined as follows:

0 2

0 2

0 2

100 500

p

i

d

K K K n

 

 

 

 

(17)

Following section discusses various case scenarios of the simulations.

Case 1: A step load increase of 0.05 pu in Area 1 at

t  0

s with no load change in Area 2

In Table 1, the system is studied under Case 1. The tuned controller parameters are listed in the table. From the table, it is found the minimum value of objective

function J, equal to 0.0276, is obtained from MGWO based controller which is better than GWO and CSA based controllers.

Additionally, the settling times of frequency deviations of area 1 and area 2 with tie-line power deviations are found to be 2.2490, 1.5170, and 1.9605, respectively with the proposed controller whose sum is minimum in comparison to GWO and CSA based controllers. The time-domain simulations of frequency and tie-line power deviations are shown in Fig.

3 (a) –(c). The figure illustration agrees with the tabulated results of Table 1.

The figures suggest that a load change in area 1 is affecting the frequency of area 2 and tie-line power which is as per our expectations. From the figure, it can easily be identified that proposed controller is better performer in terms of settling times than GWO and CSA based controllers. From the above discussion, it can be concluded that MGWO based controllers are outperforming GWO and CSA based controllers in solving AGC problem.

Table 1. Simulation results for Case 1

CSA GWO MGWO

Objective

function

J

^{0.0485 0.0394 0.0276}

Controller parameter s

K

P 1.8251 1.8301 2.0000

K

I 2.7716 3.0000 4.6812

K

D 0.4555 0.5629 0.6831

n

^333.763

0 327.773

5 103.107

1 Settling

times

f

1



2.2401 2.2781 2.2490

f

2



3.3944 3.0917 1.5170

P

tie



3.2595 3.0550 1.9605

Fig. 3 (a) Frequency deviation of Area 1 for Case 1

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Fig. 3 (b) Frequency deviation of Area 2 for Case 1

Fig. 3 (c) Tie-line power deviation for Case 1

Case 2: A step load increase of 0.05 pu in Area 2 at

t  0

s with no load change in Area 1.

In Table 2, the system is studied under Case 2. The tuned controller parameters are listed in the table. From the table, it is found the minimum value of objective function

J

, equal to 0.0277, is obtained from MGWO based controller which is better than both GWO and CSA based controllers.

Additionally, the settling times of frequency deviations of area 1 and area 2 with tie-line power deviations are found to be 1.5271, 2.2445, and 2.1102, respectively with the proposed controller which is minimum in comparison to GWO and CSA based controllers. The time- domain simulations of frequency and tie- line power deviations are shown in Fig. 4 (a) –(c). The figure illustration agrees with the tabulated results of Table 2.

The figures suggest that a load change in area 2 is affecting the frequency of area 1 and tie-line power which is as per our expectations. From the figure, it

can easily be identified that proposed controller is better performer in terms of settling times than GWO and CSA based controllers. From the above discussion, it can be concluded that MGWO based controller is outperforming GWO and CSA based controllers in solving AGC problem.

Table 2. Simulation results for Case 2

CSA GWO MGWO

Objective

function

J

^{0.0501 0.0395 0.0277}

Controller parameter s

K

P 1.7228 1.8384 2.0000

K

I 3.0000 3.0000 4.5523

K

D 0.8431 0.5750 0.6660

n

^174.373

0 145.062

8 128.198

1 Settling

times

f

1



2.4920 3.0598 1.5271

f

2



3.2586 2.2597 2.2445

P

tie



4.0488 3.0429 2.0102

Fig. 4 (a) Frequency deviation of Area 1 for Case 2

Fig. 4 (b) Frequency deviation of Area 2 for Case 2

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Fig. 4 (c) Tie-line power deviation for Case 2

Case 3: A step load decrease of 0.05 pu in Area 1 at

t  0

s with no load change in Area 2.

In Table 3, the system is studied under Case 3. The tuned controller parameters are listed in the table. From the table, it is found the minimum value of objective function

J

, equal to 0.0279, is obtained from MGWO based controller which is better than GWO and CSA based controller. Additionally, the settling times of frequency deviations of area 1 and area 2 with tie-line power deviations are found to be 2.2921, 1.3156, and 2.0270, respectively with the proposed controller whose sum is minimum in comparison to GWO and CSA based controllers.

The time-domain simulations of frequency and tie-line power deviations are shown in Fig. 5 (a) – (c). The figure illustration agrees with the tabulated results of Table 3. The figures suggest that a load change in area 1 is affecting the frequency of area 2 and tie-line power which is as per our expectations. From the figure, it can easily be identified that proposed controller is better performer in terms of settling times than GWO and CSA based controllers. From the above discussion, it can be concluded that MGWO based controllers are outperforming GWO and CSA based controllers in solving AGC problem.

Table 3. Simulation results for Case 3

CSA GWO MGWO

Objective

function

J

^{0.0480 0.0395 0.0279}

Controller parameter

K

P 2.0000 1.8976 2.0000

K

I 2.6295 3.0000 4.5142

s

K

D 0.6166 0.5719 0.6840

n

^100.000

0

199.030 5

186.412 5 Settling

times

f

1



1.5708 2.2117 2.2921

f

2



3.6203 3.1285 1.3156

P

tie



3.7640 3.1066 2.0270

Fig. 5 (a) Frequency deviation of Area 1 for Case 3

Fig. 5 (b) Frequency deviation of Area 2 for Case 3

Fig. 5 (c) Tie-line power deviation for Case 3

Case 4: A step load decrease of 0.05 pu in Area 2 at

t  0

s with no load change in Area 1.

Vol.04, Issue 01, January 2019, Available Online: www.ajeee.co.in/index.php/AJEEE In Table 4, the system is studied under

Case 4. The tuned controller parameters are listed in the table. From the table, it is found the minimum value of objective function

J

, equal to 0.0279, is obtained from MGWO based controller which is better than GWO and CSA based controllers. Additionally, the settling times of frequency deviations of area 1 and area 2 with tie-line power deviations are found to be 1.6218, 2.2267, and 1.9423, respectively with the proposed controller which is minimum in comparison to GWO and CSA based controllers.

The time-domain simulations of frequency and tie-line power deviations are shown in Fig. 6 (a) – (c). The figure illustration agrees with the tabulated results of Table 4. The figures suggest that a load change in area 2 is affecting the frequency of area 1 and tie-line power which is as per our expectations. From the figure, it can easily be identified that proposed controller is better performer in terms of settling times than GWO and CSA based controllers. From the above discussion, it can be concluded that MGWO based controllers are outperforming GWO and CSA based controllers in solving AGC problem.

Table 4. Simulation results for Case 4

CSA GWO MGWO

Objective

function

J

^{0.0524 0.0394 0.0279}

Controller parameter s

K

P 1.3651 1.8180 2.0000

K

I 2.6856 3.0000 4.7569

K

D 0.6285 0.5740 0.6805

n

^409.460

9 432.778

8 119.447

8 Settling

times

f

1



2.3035 3.0392 1.6218

f

2



3.0699 2.3096 2.2267

P

tie



2.6951 3.0331 1.9423

Fig. 6 (a) Frequency deviation of Area 1 for Case 4

Fig. 6 (b) Frequency deviation of Area 2 for Case 4

Fig. 6 (c) Tie-line power deviation for Case 4

4. CONCLUSION

In this work, an equal two-area interconnected power system widely used in the literature is taken for the simulation purpose for load frequency control (LFC). A conventional PID controller with derivative filter is used to be tuned. A single objective function is formulated with ITAE of frequency and tie-line power deviations. Modified grey wolf optimization (MGWO) algorithm is

Vol.04, Issue 01, January 2019, Available Online: www.ajeee.co.in/index.php/AJEEE applied to tune the controller parameters

for LFC.

Four different cases of step load disturbances are simulated to test the performance of the proposed controller.

The performance of the proposed controller is established by comparing it with grey wolf optimization (GWO) and cuckoo search algorithm (CSA) based controller. The simulation results are tabulated and the results suggest that MGWO based controller is outperforming GWO and PSO based controller for all cases.

To further validate the superiority of the proposed controller, time-domain simulations of frequency deviations of each areas and tie-line power deviations for all cases are illustrated. From the simulation, the superior performance of MGWO based controller is established.

APPENDIX A

The parameters of the equal two-area interconnected system are listed here.

Nominal parameters of the system investigated are:

 P_R = 2000MW (rating);

 P_L = 1000 MW (nominal loading);

 f = 60 Hz; B₁= B₂= 0.045 p.u.

MW/Hz;

 R₁ = R₂ = 2.4 Hz/p.u.;

 T_G1 = T_G2 = 0.08 sec;

 T_T1 = T_G2 = 0.3 sec;

 K_PS1 = K_PS2 = 120 Hz/p.u. MW;

 T_PS1 = T_PS2 = 20 sec;

 T12 = 0.545 p.u.; a₁₂= -1.

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