Coordination of PID Based Power System Stabilizer and AVR Using Combination Bacterial Foraging Techique – Particle Swarm Optimization

IBG Manuaba1,2, M Abdillah1, A Soeprijanto1, Mauridhi Hery P1

1Department of Electrical Engineering Institut Teknologi Sepuluh Nopember Surabaya 6011, Indonesia

2Department of Electrical Engineering Universitas Udayana Denpasar, Bali, Indonesia

Abstract The damping of oscillation in power system

commonly use known controller such as power system stabilizer (PSS). Proportional integral derivative (PID) controller tuning based on power system stabilizer and AVR is presented in this paper. The parameters of PID controller such as proportional gain, integral factor, differential coefficient and gain AVR are selected and optimized by BF-PSOTVAC. The proposed method is applied to PID controller tuning and is compared to another method. The integral time absolut error standards of optimization design as objective function. The results of simulations show that the proposed method has the capability to damn optimally and suppresses error to minimum

Keywords-PSS, AVR, PID controller, Bacterial foraging, Particle swarm optimization, time varying acceleration coefficient

1. Introduction

Modern power system control requires a continuous balance between electrical generation and a varying load demand. One of the most important aspects in electric system operation is the stability of power systems. The power system must maintain the frequency and voltage level, under any disturbances. On the impact of interconnection of large electric power systems, there has been spontaneous system oscillation at very low frequencies in order of 0.2 to 3.0 Hz. Low-frequency oscillations present limitations on the power-transfer capability. Moreover, to enhance system damping, the generators are equipped with power system stabilizers (PSS)[1].

PSS contributes in maintaining power system stability and improve dynamic performance by providing a supplementary signal to the excitation system. A PSS provides a supplementary control signal to the automatic voltage regulator (AVR) loop for excitation control. The PSS is a control device used to damp out low frequency oscillations and to provide supplementary feedback that stabilizing signals in the excitation systems[2]

This paper proposed a method applied to optimize the proportional-integral-derivative (PID) based PSS

and AVR gain to damp the oscillation on power system. The bacterial foraging – particle swarm optimization – time varying acceleration coefficient (BF-PSOTVAC) is a method to optimize PID based PSS and AVR gain used in this research on optimization problem. The comparison result of the methods to other methods i.e. open loop system, conventional PSS, conventional PID based PSS, AVR-PID based PSS optimized by PSO, AVR-PID based PSS optimized by BF, AVR-PID based PSS optimized by BF-PSO and AVR-PID based PSS optimized by BF-PSOTVAC carried out to find the difference of result of damping oscillation simulation. The rest of this paper is organized as follows. In section 2, we describe the model of single machine infinite bus (SMIB) for simulation and analysis, followed by particle swarm optimization and bacterial foraging optimization in section 3. In section 4, we explain an overview of the proposed method which used on this paper. In section 4, we explain the proposed method which used on this paper. In section 5, the illustrative simulation results are presented.

2. Power system modeling

2.1 Single machine infinite bus The system considered for small-signal performance

study is shown in Fig. 1. The linearized model of studied power system consisted of synchronous machine connected to infinite bus bar through transmission line is represented in a block diagram as shown in Fig. 2.

Figure 1. Single machine-infinite bus (SMIB)

978-1-4577-0005-7/11/$26.00 ©2011 IEEE

DsM +.1

. 1A

A

KT s + 103

3

+sdKK

s0ω δΔ

FDEΔEΔ

4K 5K2K

1K

ωΔ

1U

2U

6K

K

K

K K

K

Figure 2. Block diagram the linearized model of studied power system [4]

State space formulation of block diagram power system modeling can be expressed as follow [4]

∆δ ω ∆ω (1) ∆ω M K ∆δ D∆ω K ∆E′ (2)

∆E′ T′ K ∆δ ∆E′K EFD (3) ∆EFD T KAK ∆δ KAK ∆E′ ∆EFD KAu (4) We transform equation (1) – (4) into state space formula as below X t AX t Bu t (5) Y t CX t Du t Where XT ∆δ ∆ω ∆E′ ∆EFD The matrix of A, B, C and D as follows:

A 0 ω 0 0 KM D M KM 0 KT′ 0 1K T′d 1T′d K KTA 0 KAKTA 1TA

000 1 0 0 00 1 0 00 0 1 00 0 0 1 0

2.2 Power system stabilizer The operational function of a Power System

Stabilizer (PSS) is to produce a proper torque on the rotor of the machine involved in such a way that the

phase lag between the exciter input and the machine electrical torque is compensated. Supplementary stabilizing signal considered is one proportional to speed. The transfer function of the ith PSS is given by[1]:

U K TT T TT T ∆ω s (6)

Where Δωi is the deviation in speed from the synchronous speed. This type of stabilizer consists of a washout filter, a dynamic compensator. The output signal, Ui to the regulator of the excitation system. The washout filter, which essentially is a high pass filter, is used to reset the steady-state offset in the output of the PSS. The value of the time constant Tw is usually not critical and it can range from 0.5 to 20 s 2.3 PID based power system stabilizer

The PID control algorithm remains the most popular approach for industrial process control despite continual advances in control theory. The transfer function of a PID controller is described as follows[3]:

G s k k s (7)

Where kp, ki, and kd are the proportional, integral and derivative gains, respectively.

3. Particle swarm optimization and bacterial foraging optimization

3.1 Particle swarm optimization Particle swarm optimization (PSO) is a stochastic

global optimization method which is based on simulation of social behavior. PSO consists of a population refining its knowledge of the given search space. PSO is inspired by particles moving around in the search space. The individuals in a PSO thus have their own positions and velocities. These individuals are denoted as particles. Each particle adjusts its trajectory towards its own previous best position, and towards the best previous position. This position is called the personal best and is denoted by Ppb. Among these Pi, there is only one particle that has the best fitness, called the global best, which is denoted by Pgb. The velocity update equations of PSO are given by [3] [9]:

V ωV c r P X c r P X (8)

The position update equations of PSO are:

(9) where

i = 1, 2,….N N = the size of the population

= a constriction factor that constrict velocities

ω = the inertia weight c1,c2 = are cognitive and social parameter

respectively

ri1 and ri2 are random numbers uniformly distributed within the range [0, 1] Xi

k = position of particle i at iteration k Ppb

k = best position of particle i at iteration k Pgb

k = best position of the group at iteration k 3.2 Time varying particle swarm optimization

The time varying accelerator coefficient (TVAC) changing the acceleration coefficients c1 and c2 with time in such a manner that the cognitive component is reduced while the social component is increased as the search proceeds. This would lead to enhance the global search in the early part of the optimization and to encourage the particles to converge towards the global optima at the end of the search. With a large cognitive component and small social component at the beginning, particles are allowed to move around the search space instead of moving toward the population best during early stages. The PSO technique with time varying inertia weight can locate good solution at a significantly fast rate, its ability to fine tune the optimum solution is weak, mainly due to the lack of diversity at the end of the search. In population-based optimization methods, the policy is to encourage individuals to roam through the entire search space during the initial part of the search, without clustering around local optima. During the latter stages, convergence towards the global optima is encouraged, to find the optimal solution efficiently. On the other hand, a small cognitive component and a large social component allow the particles to converge to the global optima in the latter part of the optimization process. The acceleration coefficients are expressed as [5]:

(10)

Where C1i, C1f, C2i and C2f are initial and final values of cognitive and social acceleration factors respectively. The concept of time varying inertial weight was introduced as per which w is given by[5, 6] (11)

Where iter is the current iteration number while itermax is the maximum number of iterations. Usually the value of w is varied between 0.9 and 0.4. Constant c1 pulls the particles towards local best position whereas c2 pulls it towards the global best position. 3.3 Bacterial foraging optimization

Natural selection tends to eliminate animals with poor foraging strategies and favor those having successful foraging strategies is the base idea of BFA. After many generations, poor foraging strategies are either eliminated or reshaped into good ones. The E. coli bacteria have a foraging strategy governed by four processes namely chemotaxis, swarming, reproduction, elimination and dispersal[7][9]. Chemotaxis is achieved

through swimming and tumbling. Depending upon the rotation of the flagella in each bacterium, it can move in two different ways. Swimming decides whether it should move in a predefined direction or tumbling for different direction, in the entire lifetime of the bacterium. To represent a tumble, a unit length random direction, say φ(j), is generated; this will be used to define the direction of movement after a tumble. We use equation as below:

θ j 1, k, l θ j, k, l C i j (12)

Where θ1(j, k, 1) represents the ith bacterium at jth chemotactic kth reproductive and Ith elimination and dispersal step. C(i ) is the size of the step taken in the random direction specified by the tumble/run length unit Swarming –Swarming makes the bacteria congregate in to groups, since they their desired place more rapidly. Reproduction –To make the population of the bacteria constant, the healthiest bacteria split into two, while the poor health bacteria die. Elimination and Dispersal-The life of population of bacteria changes overtime influences and kill or disperse all bacteria in a region. This can possibly destroy the chemotactic progress, but in contrast they also assist it, since dispersal may place bacteria in a location of good food sources. Elimination and dispersal helps in reducing the behavior of stagnation,( i.e. being trapped in a premature solution point or local optima).

4. Proposed method The BF-PSOTVAC algorithm is a new algorithm

that combine bacterial foraging - particle swarm optimization with time varying. It makes full use of the ability of bacterial foraging algorithm not only to acquire new solution in the dispersed and eliminated, but also to exchange social information. The main steps of BF-PSOTVAC are given below:

1. Initialize parameters n, S, Nc, Ns, Nre, Ned, Ped, c(i) (i=1,2,…S), Δ, C1, C2, R1, R2

Where: n = dimension of the search space S = the number of bacteria in the population Sr = half the total number of bacteria Ns = maximum number of swim length Nc = chemotactic steps Nre = the number of reproduction steps Ncd = elimination and dispersal events Ped = elimination and dispersal with probability C(i) = the step size taken in the random direction C1, C2 = PSO random parameter R1, R2 = PSO random parameter

2. Elimination-dispersal loop: l = l + 1 3. Reproduction loop: k = k + 1 4. Chemotaxis loop: j = j + 1

• For i = 1,2, ..., S, calculate cost function value for each bacterium i as follows

J(i,j,k,l) = Func (θ i (i,j,k,l)) J i, j, k, l J i, j, k, l J θ j, k, l , P j, k, l - Compute value of cost function in

Jlast(i,j,k,l) - Let Jlast = Jsw(i,j,k,l) to save this value since

we may find a better cost via a run. The best cost for each bacterium will be selected to be the local best Jlocal Jlocal (i,j,k,l) = Jlast (i,j,k,l)

- End of For loop • For i = 1,2, ..., S take the tumbling/swimming

decision - Tumble : Generate a random vector Δ(i)

∈ℜP with each element Δm (i) m = 1,2, ...p, a random number on [-1,1]

- Move: let update position and cost function delta

θ j 1, k, l θ i, j, k, l C i ∆ i J(i,j + 1,k,l) = Func (θ i (i,j+1))

J i, j, k, l J i, j, k, l J θ j, k, l , P j, k, l - Swim :

i) Let m = 0; (counter for swim length) ii) While m < Ns (have not climbed down

too long) a. Let m = m + 1 b. If J (i,j+1,k,l) < Jlast then Jlast =

Jsw(i,j+1,k,l) Update position and cost function θ j 1, k, l θ i, j, k, l C i ∆ i

J(i,j + 1,k,l) = Func ( θ i(i,j+1))

J i, j, k, l J i, j, k, l J θ j, k, l , P j, k, l

And use this Pcurrent (i,j+1,k,l) = θ i (j+1,k,l) to compute the new Jlocal(i,j+1,k,l)=Jlast(i,j+1,k,l)

c. Else, Pcurrent(i,j+1,k,l) = θ i (j+1,k,l)

Jlocal(i,j+1,k,l)=Jlast(i,j+1,k,l) let m = Ns. This is the end of the while statement

• Go to next bacterium (i+1) if i ≠ S [i.e go to b] to process the next bacterium

• If min (J) {minimum value of “J” among all the bacteria} is less then the tolerance limit then break all the loops

Evaluate the new direction for each bacterium C C C JN C1

V w V C R P P CR P P ∆ V 5. If j < Nc, go to 4). In case , continue chemotaxis

since the life of the bacteria is not over 6. Reproduction

• For the given k and l, and for each i = 1,2, ... S, let ∑ , , , be the health of the bacterium i (a measure of how many nutrients it got over its life time and how successful it was at avoiding noxious substance). Sort bacteria in order of ascending cost Jhealth (higher cost means lower health).

• The Sr = S/2 bacteria with highest Jhealth values die and other Sr bacteria with the best value split (and the copies that are made are placed at the same location as their parent)

7. If k < Nre go to 3), in case, we have not reached the number of specified reproduction steps, so we start the next generation in the chemotactic loop.

8. Elimination-dispersal: For i = 1,2, ..., S, with probability Ped, eliminate and disperse each bacterium (this keeps the number of bacteria in the population constant).To do this, if you eliminate a bacterium, simply disperse one to a random location on the optimization domain.

The cost function value for each bacterium came from time-domain simulation of power system. Using each set of controllers’ parameters, the time domain simulation is performed and the cost function value for each bacterium is determined. The cost function of each bacterium uses performance index of integral time absolute error standard as below:

|∆ |

Where J is the integral time absolute error (ITAE) Based on this performance index J optimization (minimization) problem can be stated as:

Perfomance Index (PI) = min (J)

Subjected to

Figure 3. Proposed Method flowchart

5. Simulation and results

In this section, the simulations carried out using MATLAB and SIMULINK® . In this paper, a step signal 0.05 p.u as load change applied to provide the output performance of power system in order to investigate the stable performance of the system. The modeling of SMIB which used in this paper consists of a single synchronous generator with PID based PSS and AVR gain, connected through one transmission by an infinite bus. The linear model of block diagram SMIB is shown in Figure 4.

DsM +.1

. 1A

A

KT s + 103

3

+sdKK

s0ω δΔ

FDEΔEΔ

4K 5K2K

1K

ωΔ

1U

2U

6K

K

K

K K

K

Figure 4. Block diagram of SMIB with Optimal PID based PSS

RsT+11

W

W

sTsT+1 01

20

asasa

++ sK

maxsV

minsV

sVωΔ

Figure5. PID-PSS block diagram

Figure 6. Performance of rotor angle deviation

Figure 7. Performance of speed rotor angle deviation

Figure 6. and Figure 7. are comparison result of our method to other methods. Comparison in performance of rotor angle deviation is shown in Figure 6, while comparison in speed rotor angle deviation is shown in Figure 7.

Tabel 1. Overshoots (pu)

ωΔ δΔ

Open Loop -0.001208 -0.06069

Conventional PSS -0.001103 -0.05581

Conventional PIDPSS -0.001029 -0.05275

Coordination PSO -0.0009248 -0.04709

Coordination BFO -0.0009063 -0.04724

Coordination BFPSO -0.0008777 -0.04604

Coordination BF-PSOTVAC

-0.000844 -0.04417

Tabel 2. Settling times (second)

ωΔ δΔ

Open Loop >10 >10

Conventional PSS 8.01 6.01

Conventional PIDPSS 3.27 3.75

Coordination PSO 2.64 2.8

Coordination BFO 2.45 2.69

Coordination BFPSO 2.18 2.61

Coordination BF-PSOTVAC 2.01 2.56

TABEL 3. Optimization value of parameters value of Kp,Ki, Kd, and Ka

KA Kp Ki Kd Conventional

PID 10 0.01 0.02 0.2

BFO 9.9218 0.1264 0.0301 0.3909PSO 9.9875 0.1871 0.1716 0.3542

BFPSO 9.7975 0.1779 0.0301 0.4412BF-PSOTVAC 9.9900 0.2891 0.1570 0.4892

Tabel 4. Performance index of the system

IP

Conventional PIDPSS 0.0238

Coordination PSO 0.0166

Coordination BFO 0.0155

Coordination BFPSO 0.0141

Coordination BF-PSOTVAC 0.0128

From Table 1, we know that BF-PSOTVAC has

lower overshoot value, which means that it has better damn ability compare to other methods. Table 2 shows that BF-PSOTVAC achieves steady state faster than the other, indicates better stability

From Table 4, we know that proposed method has the capability to minimize error.

6. Conclusion In this paper, proportional-integral-derivative power

system stabilizer (PID-PSS) has been proposed for enhancement of dynamic stability. Gain setting of PID-PSS has been optimized using BF-PSOTVAC. The

0 1 2 3 4 5 6 7 8 9 10-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

Time (second)

Rot

or a

ngle

dev

iatio

n (p

u)

Performance of rotor angle deviation (pu)

OpenloopConventional PSSConventional-PIDPSS

Coordination By PSO

Coordination By BFO

Coordination By BFPSOCoordination By BFPSOTVAC

0 1 2 3 4 5 6 7 8 9 10-1.5

-1

-0.5

0

0.5

1x 10

-3

Time (second)

Spe

ed r

otor

ang

le d

evia

tion

(pu)

Performance of speed rotor angle deviation (pu)

Openloop

Conventional PSS

Conventional-PIDPSSCoordination By PSO

Coordination By BFO

Coordination By BFPSO

Coordination By BFPSOTVAC

proposed method has the capability to damping optimally and suppresses error to minimum

Appendix

Conventional PSS K1 = 2, Tw = 2, T1 = 0.22, T2 = 0.121, T3 = 0.22, T4 = 0.121 Conventional PID-PSS TR = 0.05, Tw = 5, a0 = 0.5, a1 = 0.001, a2 = 0.00001, Ks = 10 BFA Parameters P=4,S=20, Ne=50,Ns=4,Nre=4, Sr=s/2, Ned=2, Ped=0.25, C=0.1, d_attaract=0.1, w_attaract=0.2, h_repellant=0.1, w_repellant=10 PSO Parameters P=20,S=50,Ne=50,Ns=4,Nre=4,Sr=s/2,Ned=2,Ped=0,C1=1.5,c2=2 BFA PSO Parameters P=4,S=20, Ne=50, Ns=4, Nre=4, Sr=s/2, Ned=2,P ed=0.25, C=0.1, d_attaract=0.1, w_attaract=0.2, h_repellant=0.1, w_repellant=10 BFA PSO TVAC Parameters P=4,S=20,Ne=50,Ns=4,Nre=4,Sr=s/2,Ned=2,Ped=0.25,C=0.1,d_attaract=0.1,w_attaract=0.2,h_repellant=0.1,w_repellant=10,wmax=0.9,wmin=0.4,c1i=2.5,c2i=0.5,c1f=0.5,c2f=2.5 Machine parameters f=50 hz H=4 K1=1.755, K4=1.7125, D=0.3072; K2=1.2578, K6=0.4971, K5=-0.0409, K3=1.9767

Td0=1.6573

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