Int. J. Data Mining, Modelling and Management, Vol. 5, No. 4, 2013 351

Copyright © 2013 Inderscience Enterprises Ltd.

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM-based controller parameters

Sidhartha Panda* Department of Electrical and Electronics Engineering, National Institute of Science and Technology, Palur Hills, Berhampur – 761008, Orissa, India E-mail: panda_sidhartha@rediffmail.com *Corresponding author

P.K. Mohanty and B.K. Sahu Department Electrical Engineering, Institute of Technical Education and Research (ITER), SOA University, Bhubaneswar – 751030, Orissa, India E-mail: pkmohanty68@rediffmail.com E-mail: binoda@rediffmail.com

Abstract: The coordinated design of power system stabiliser (PSS) and a static synchronous compensator (STATCOM)-based controller for power system stability improvement is presented in this paper. The design problem is formulated as a parameter constrained, simulation-based, non-linear optimisation problem and bacteria foraging optimisation algorithm (BFOA) is employed to determine the optimal controller parameters. The performance of the proposed controllers is evaluated and compared with a conventional power system stabiliser (CPSS) in a single-machine infinite-bus power system subjected to various transient disturbances. The non-linear simulation results show that the proposed coordinately designed STATCOM-based controller and PSSs improve greatly the system damping and are robust to variation in operating conditions and fault clearing sequence. Finally, the coordinated design problem is extended to a four-machine two-area system and the results show that the inter-area and local modes of oscillations are well damped with the proposed BFOA-optimised controllers.

Keywords: bacteria foraging optimisation algorithm; BFOA; power system stabiliser; PSS; static synchronous compensator; STATCOM; coordinated design; power system stability.

Reference to this paper should be made as follows: Panda, S., Mohanty, P.K. and Sahu, B.K. (2013) ‘Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM-based controller parameters’, Int. J. Data Mining, Modelling and Management, Vol. 5, No. 4, pp.351–369.

Biographical notes: Sidhartha Panda is a Professor at the National Institute of Science and Technology (NIST), Berhampur, Orissa, India. He received his PhD from Indian Institute of Technology, Roorkee, India in 2008, ME in Power Systems Engineering in 2001 and BE in Electrical Engineering in 1991. Earlier, he worked as an Associate Professor at KIIT University, Bhubaneswar, India and VITAM College of Engineering, Andhra Pradesh, India and Lecturer at the

352 S. Panda et al.

Department of Electrical Engineering, SMIT, Orissa, India. His areas of research include power system transient stability, power system dynamic stability, FACTS, optimisation techniques, distributed generation and wind energy.

P.K. Mohanty received his BE degree from the College of Engineering and Technology (CET), OUAT, Bhubaneswar, Odisha, India in 1991, MTech degree from Bengal Engineering College Calcutta University, (WB) India in 1993. He worked as a Lecturer at the Electrical Engineering Department, Orissa Engineering Collage, Bhubaneswar (Odisha), India from 1993 to 1998 and then worked as an Assistant Manager (Electrical) at Odisha Hydro Power Corporation, Bhubaneswar, Odisha, India form 1998 to 2008. Currently, he is working as an Assistant Professor at the Electrical Engineering Department, Institute of Technical Education and Research (ITER), SOA University, Bhubaneswar, Odisha, India since 2008.

B.K. Sahu received his engineering degree from the Institution of Engineer (India) in 2001, MTech degree from National Institute of Technology, Warangal (AP), India in 2003. He worked as a Lecturer and Sr. Lecturer at the Electrical Engineering Department, C.V. Raman College Engineering, Bhubaneswar (Odisha), India from 2003 to 2008. Currently, he is working as an Assistant Professor at the Electrical Engineering Department, Institute of Technical Education and Research (ITER), SOA University, Bhubaneswar, Odisha, India since 2008.

1 Introduction

Low frequency oscillations are observed when large power systems are interconnected by relatively weak tie lines. These oscillations may sustain and grow to cause system separation if no adequate damping is available (Kundur, 1994; Padiyar, 1996). Power system stabilisers (PSS) are now routinely used in the industry to damp out power system oscillations. However, during some operating conditions, this device may not produce adequate damping, and other effective alternatives are needed in addition to PSS. Recent development of power electronics introduces the use of flexible AC transmission system (FACTS) controllers in power systems. FACTS controllers are capable of controlling the network condition in a very fast manner and this unique feature of FACTS can be exploited to improve the stability of a power system.

Static synchronous compensator (STATCOM) is member of FACTS family that is connected in shunt with the system. Even though the primary purpose of STATCOM is to support bus voltage by injecting (or absorbing) reactive power, it is also capable of improving the power system stability (Hingorani and Gyugyi, 2000). When a STATCOM is present in a power system to support the bus voltage, a supplementary damping controller could be designed to modulate the STATCOM bus voltage in order to improve damping of system oscillations (Wang, 1999). The interaction among PSSs and STATCOM-based controller may enhance or degrade the damping of certain modes of rotor’s oscillating modes. To improve overall system performance, many researches were made on the coordination between PSSs and FACTS power oscillation damping controllers (Ramirez and Castillo, 2004, Panda, 2011). Most of proposals presented are based on small disturbance analysis that required linearisation of the system involved.

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 353

However, linear methods cannot properly capture complex dynamics of the system, especially during major disturbances. This presents difficulties for tuning the FACTS controllers in that the controllers tuned to provide desired performance at small signal condition do not guarantee acceptable performance in the event of major disturbances. Further, the controllers should provide some degree of robustness to the variations loading conditions, and configurations as the machine parameters change with operating conditions. A set of controller parameters which stabilise the system under a certain operating condition may no longer yield satisfactory results when there is a drastic change in power system operating conditions and configurations (Panda and Padhy, 2008).

The problem of PSS and FACTS controllers parameter tuning is a complex exercise as uncoordinated local control of FACTS devices and PSS may cause destabilising interactions. A number of conventional techniques have been reported in the literature pertaining to design problems of conventional PSS namely: the eigenvalue assignment, mathematical programming, gradient procedure for optimisation and also the modern control theory. Unfortunately, the conventional techniques are time consuming as they are iterative and require heavy computation burden and slow convergence. In addition, the search process is susceptible to be trapped in local minima and the solution obtained may not be optimal. The evolutionary methods constitute an approach to search for the optimum solutions via some form of directed random search process. A relevant characteristic of the evolutionary methods is that they search for solutions without previous problem knowledge. Bacteria Foraging Optimisation Algorithm (BFOA), proposed by Passino (2002), is a new comer to the family of nature-inspired optimisation algorithms. Natural selection of bacterial foraging tends to eliminate animals with poor foraging strategies for locating, handling, and ingesting food, optimisation models can be provided for social foraging where groups of parameters communicate to cooperatively forage in engineering. In view of the above, this paper proposes to use BFOA optimisation technique for the coordinated design of PSS and STATCOM-based controller. To improve the interactions between PSSs and STATCOM-based controller, BFOA-based optimal tuning approach is employed to simultaneous and coordinately design the proposed damping controllers.

The reminder of the paper is organised in five major sections. An overview of STATCOM and its control system is presented in Section 2. The structures of the PSS and STATCOM-based controller and the objective function are described in Section 3. In Section 4 a brief introduction about Bacteria Foraging Optimisation Algorithm is provided. Results are given and discussed in Section 5 and conclusions are presented in the Section 6.

2 Overview of STATCOM and its control system

A STATCOM is a controlled reactive-power source. It provides voltage support by generating or absorbing reactive power at the point of common coupling without the need of large external reactors or capacitor banks (Hingorani and Gyugyi, 2000). The functional block diagram model of the STATCOM is shown in Figure 1. The basic electronic block of a STATCOM is the voltage sourced converter (VSC), which in general converts an input dc voltage into a three-phase output voltage at fundamental

354 S. Panda et al.

frequency, with rapidly controllable amplitude and phase angle. In addition to this, the controller has a coupling transformer and a dc capacitor. References QReƒ and PReƒ define the magnitude and phase angle of the converter voltage Vcnv necessary to exchange the desired reactive and active power between the solid state voltage sourced converter and the ac system. If the device is operated strictly for reactive power exchange, PReƒ is set to zero and the external energy source is not required. The converter voltage Vcnv is in phase with the ac terminal voltage Vac and there is practically no real power flow from or to VSC (without energy storage). The STATCOM supplies reactive power to the ac system if Vcnv is greater than Vac and consumes reactive power if Vcnv is lower than Vac. The device can be designed to maintain the magnitude of the bus voltage constant by controlling the magnitude and/or phase shift of the VSC output voltage.

Figure 1 Functional block diagram model of STATCOM

Couplingtransformer

ControlVoltagesourced

converter

Energy Source(optinal)

fReP

fReQ

+ _

acV

dcVDC terminal

AC system

o AC terminalacI

dcI

cnvV

Figure 2 shows a single-line diagram of the STATCOM and a simplified block diagram of its control system. The control system consists of:

• A phase-locked loop (PLL) to synchronise on the positive-sequence component of the three-phase primary voltage V1. The direct-axis and quadrature-axis components of the AC three-phase voltage and currents (labelled as Vd, Vq and Id, Iq on the diagram) are computed using the output of the PLL.

• The measurement systems measuring the d-axis and q-axis components of AC positive-sequence voltage and currents to be controlled as well as the DC voltage VDC.

• The regulation loops, namely the AC voltage regulator and a DC voltage regulator. The output of the AC voltage regulator and DC voltage regulator are the reference current Iqref and Idref, for the current regulator.

(Optional)

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 355

• An inner current regulation loop consisting of a current regulator, which controls the magnitude and phase of the voltage generated by the PWM converter.

Figure 2 Single-line diagram of a STATCOM and its control system

AC VoltageMeasurement

AC VoltageRegulator∑

PLLCurrent

Measurement

acV

refV

1V

I

tωθ =

dq1V

qI

dI

DC VoltageMeasurement

DC VoltageRegulator∑

VoltageSourcedConvt.(VSC)

1V 2V

I

DCV

dcV

refdcV

PWMModulator

CurrentRegulator

∑

∑

θ

d2V

q2V

qI

dI

refqI

refdI

dq1V

+

−+

−

+−

+−

3 Problem formulation

3.1 Structures of STATCOM-based controller and PSS

The commonly used lead-lag structure is chosen in this study as STATCOM-based controller as shown in Figure 3. The structure consists of: a gain block; a signal washout block and two-stage phase compensation block. The phase compensation block provides the appropriate phase-lead characteristics to compensate for the phase lag between input and the output signals. The signal washout block serves as a high-pass filter which allows signals associated with oscillations in input signal to pass unchanged. Without it steady changes in input would modify the output. From the viewpoint of the washout function the value of washout time constant is not critical and may be in the range 1 to 20 seconds (Kundur, 1994). In this structure, the washout time constants TWS and the time constants T2S, T4S are usually prespecified (Panda and Padhy, 2008). In the present study, TWS = 10s and T2S = T4S = 0.3s are used. The controller gain KS and the time constants T1S and T3S are to be determined.

356 S. Panda et al.

Figure 3 Structure of the STATCOM-based controller

WSWSsT1

sT+ S2

S1sT1sT1

++

S4S3

sT1sT1

++

SK STVΔ

Gainblock Washout

blockTwo-stage

lead-lag block

∑++Input Output

fSTV Re_

STV

max

STVΔ

min

STVΔ

Figure 4 Structure of the generic power system stabiliser

Gainblock Washout

blockLead-lag block

InputPK

WPWPsT1

sT+ P2

P1sT1sT1

++

OutputSV

maxSV

minSV

Sensor

The generic PSS block of the SimPowerSystem toolbox is used to add damping to the rotor oscillations of the synchronous machine by controlling its excitation. The output signal of the PSS is used as an additional input to the excitation system block. The PSS input signal can be either the machine speed deviation, or acceleration power. The PSS model consists of a sensor, a general gain, a washout high-pass filter, a phase-compensation system, and an output limiter as shown in Figure 4. The general gain KP determines the amount of damping produced by the stabiliser. The washout high-pass filter eliminates low frequencies that are present in the input signal and allows the PSS to respond only to changes in the input. The phase-compensation system is used to compensate the phase lag between the excitation voltage and the electrical torque of the synchronous machine. In this structure, a wash out time constant TWP = 3s is used. The time constants T1P and T2P are to be determined.

3.2 Optimisation problem

It is worth mentioning that the PSS and STATCOM-based controllers are designed to minimise the power system oscillations after a large disturbance so as to improve the power system stability. In the present study, an integral time absolute error of the speed deviations is taken as the objective function for single machine infinite bus power system. For the case of multi-machine power system, an integral time absolute error of the speed signals corresponding to the local and inter-area modes of oscillations is taken as the objective function. The objective functions are expressed as:

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 357

For single-machine infinite bus (SMIB) power system:

0

| |simt t

t

J t dtω=

=

= Δ ⋅ ⋅∫ (1)

For multi-machine power system:

( )0

| | |simt t

L It

J t dtω ω=

=

= Δ + Δ ⋅ ⋅∑ ∑∫ (2)

where, Δω is the speed deviation in single-machine infinite bus system; ΔωL and ΔωI are the speed deviations of inter-area and local modes of oscillations respectively and tsim is the time range of the simulation.

For objective function calculation, the time-domain simulation of the power system model is carried out for the simulation period. It is aimed to minimise this objective function in order to improve the system response in terms of the settling time and overshoots.

4 Overview of bacteria foraging optimisation algorithm (BFOA)

Bacteria foraging optimisation algorithm (BFOA), proposed by Passino, is a new comer to the family of nature-inspired optimisation algorithms. BFOA is based on social and cooperative behaviours found in nature. Application of group foraging strategy of a swarm of E. coli bacteria in multi-optimal function optimisation is the idea behind BFOA. The foraging behaviour of E. coli bacteria present in our intestines, which includes the methods of locating, handling and ingesting food, has been successfully mimicked in BFOA. Each bacteria tries to maximise its obtained energy per each unit of time expended on the foraging process and avoiding noxious substances. Further, individual bacterium communicates with other individuals by sending signals.

The optimisation technique consists of determining the minimum of a function J(α) where the variables under consideration constitute the high-dimensional vector α ∈ ℜp and it is very difficult or almost impossible to determine δJ(α). Here α determines the position of a bacterium in high dimensional space. A negative value of J(α) indicates that the bacterium is in nutrient-rich environment, a zero value indicates a neutral environment and a positive value indicates a noxious environment. The objective will be to try and implement a biased random walk for each bacterium where it will try to climb up the nutrient concentration and try and avoid noxious substances and will attempt to leave a neutral environment as soon as possible.

This optimisation procedure comprises of four basic steps (Mishra, 2005):

a swarming and tumbeling

b chemotaxis

c reproduction

d elimination and dispersal.

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4.1 Swarming and tumbling via flagella (Ns)

During foraging of the bacteria, locomotion is realised by a set of tensile flagella. An E. coli bacterium can move in two different ways; it can swim for a period of time or it can tumble. When they rotate the flagella in the clockwise direction, each flagellum pulls on the cell, which results in the moving of flagella independently and finally the bacterium tumbles with lesser number of tumbling. In a harmful place it tumbles frequently to find a nutrient gradient. Moving the flagella in the counter clockwise direction helps the bacterium to swim at a very fast rate. The bacterium alternates between these two modes of operation its entire lifetime. The cell-to-cell signalling in E. coli swarm may be represented by:

( ) ( )1

, ( , , ) , ( , , )N

iC C

i

J P j k l J j k lα α α=

=∑

( ) ( )2 2

1 1 1 1

exp expN P N P

i iat at m m re re m m

i m i m

d w h wα α α α= = = =

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞= − − − + − −⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦∑ ∑ ∑ ∑ (3)

In the above equation, Jc(a,P(j,k,l)) is the objective function value which is to be added to the actual objective function to get a time varying objective function, N is the total number of bacteria, P is the number of variables to be optimised, a = [a1,a2,…aP]T is a point in the P-dimensional search domain and dat, wat, hre, wre are different attractant and repellant coefficients.

4.2 Chemotaxis (Nc)

Chemotaxis process simulates the movement of an E. coli cell through swimming and tumbling via flagella. Suppose ai(j,k,l) represents ith bacterium at jth chemotactic, kth reproductive and lth elimination-dispersal step. S(i) is the size of the step taken in the random direction specified by the tumble (run length unit). Then in computational chemotaxis the movement of the bacterium may be represented by:

( )( 1, , ) ( , , ) ( )( ) ( )

i iT

ij k l j k l S ii i

δα αδ δ

+ = +

where δ indicates a vector in the random direction in the range (–1, 1).

4.3 Reproduction (Nre)

In this process, the least healthy bacteria eventually die while each of the healthier bacteria giving better objective function values asexually split into two bacteria. These new bacteria are placed in the same location to keep the swarm size constant.

For reproduction, the population is sorted in order of ascending accumulated cost and the least healthy bacteria die while the other healthiest bacteria each split into two bacteria which are placed at the same location.

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 359

4.4 Elimination and dispersal (Ned)

Gradual or sudden changes in the local environment where a bacterium population lives may occur due to various reasons. When local significant increase in heat kills a population of bacteria that are currently in a region with a high concentration of nutrient gradients is called the elimination process. A sudden flow of water can disperse bacteria from one place to another. Elimination and dispersal events may destroy chemotactic progress, but they also have the effect of assisting in Chemotaxis, since dispersal may place bacteria near good food sources. To simulate this phenomenon in BFOA some bacteria are liquidated at random with a very small probability while the new replacements are randomly initialised over the search space.

5 Results and discussion

The SimPowerSystems toolbox is used for all simulations and damping controller design. In power system stability study, the fast oscillation modes resulting from the interaction of linear R, L, C elements and distributed parameter lines are of no interest. These oscillation modes, which are usually located above the fundamental frequency of 50 Hz or 60 Hz, do not interfere with the slow machine modes and regulator time constants. The phasor solution method is used here where these fast modes are ignored by replacing the network’s differential equations by a set of algebraic equations. The state-space model of the network is replaced by a transfer function evaluated at the fundamental frequency and relating inputs (current injected by machines into the network) and outputs (voltages at machine terminals). The phasor solution method uses a reduced state-space model consisting of slow states of machines, turbines, and regulators, thus dramatically reducing the required simulation time. In view of the above, the phasor model of STATCOM is used in the present study.

5.1 Single-machine infinite bus power system

In order to coordinately design PSS and STATCOM-based controller, as well as to assess their performance, a single-machine infinite-bus power system with STATCOM depicted in Figure 5 is considered at the first instance. The model of example power system shown in Figure 5 is developed using SimPowerSystems block set. The system consists of a of 500 MVA, 13.8 kV, 60 Hz hydraulic generating unit, connected to an infinite bus through a 300km long double-circuit transmission, three-phase 13.8/500 kV step-up transformer and a 100 MVA STATCOM. The generator is equipped with hydraulic turbine and governor (HTG), excitation system and a PSS. The HTG represents a non-linear hydraulic turbine model, a PID governor system, and a servomotor. The excitation system consists of a voltage regulator and DC exciter, without the exciter’s saturation function (see Appendix for details).

360 S. Panda et al.

Figure 5 Single-machine infinite-bus power system with STATCOM

Load

VSC

DCV

STV

GeneratorInfinite-bus

TV BV

bus-1 bus-2Tr. lineTrf.

For the purpose of optimisation of Equations (1) and (2), BFOA is employed. For the implementation of BFOA, several parameters are required to be specified like N (number of bacteria), NC (number of chemotactic steps), NS (length of a swim), Nre (number of reproduction steps), Ned (number of elimination-dispersal events), Pb (the probability that each bacteria will be eliminated/dispersed) etc. For the efficient performance of BFOA, these parameters should be selected carefully. In the present study, based on the previous experience N = 10, NC = 5, NS = 4, Nre = 4, Ned = 2, Pb = 0.25 are chosen.

The BFOA algorithm employed in the present study is described as follows (Mishra, 2005; Das et al., 2009):

Step 1 Initialise the following parameters:

( ) ( ) ( ) , , , , , , , , ,. , , , , , and ic s re ed ed at at re rep S N N N N P C i i P i j d w h wθ Δ

where

p = number of parameters to be optimised

S = number of bacteria used for searching

Nc = maximum number of iterations in a chemotaxis loop

Ns= swimming length after which tumbling of bacteria is performed

Nre = the maximum number of reproduction to be performed

Ned = the maximum number of elimination and dispersal events

Ped = the probability of elimination and dispersal

C(i) = size of the step taken in the random direction by the tumble

Δ (i) = direction of bacterium

P (i, j) = position of bacterium.

dat, wat, hre, wre = attractant and repellant coefficients.

In the above notations, j is the index for the chemotactic step, k is the index for the reproduction step and l is the index of the elimination-dispersal event.

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 361

Step 2 Elimination and dispersal loop: l = l + 1

Step 3 Reproduction loop: k = k + 1

Step 4 Chemotaxis loop: j = j + 1

Substep a for i = 1,2…S take a chemotactic step for bacterium i as follows

• Compute fitness function, J (i, j, k, l)

Let J (i, j, k, l) = J (i, j, k, l) + Jc ( θi ( j, k, l), P( j, k, l))

• Let J_last = J (i, j, k, l)

Substep b for i = 1,2…S take a take the tumbling/swimming decision

• For the first iteration, generate a random vector Δ (i) ∈ RP where each element Δm (i), m = 1, 2,… p a random number on [–1, 1]. For subsequent iterations, update the direction and position of bacteria using PSO.

• Move bacteria by letting ( )( 1, , ) ( , , ) ( )( ) ( )

i iT

ij k l j k l C ii i

θ θ Δ+ = +

Δ Δ

This results in a step of size C(i) in the direction of the tumble for bacterium i

• Compute J(i, j + 1, k, l) = J(i, j, k, l) + Jc(θi ( j+1, k, l), P( j+1, k, l))

• Swim 1 Let m = 0 (where m = counter for swim length) 2 While m < Ns (bacteria have not climbed down excessively

long) Let m = m + 1 If the bacteria is doing better i.e., if J(i,j + 1,k,l) < J_last, Let J_last = J(i,j + 1,k,l),

And let ( )( 1, , ) ( , , ) ( )( ) ( )

i iT

ij k l j k l C ii i

θ θ Δ+ = +

Δ Δ

Use this new θi(j + 1,k,l) to compute latest J(i,j + 1,k,l), 3 Else, let m = Ns .This is the end of the while statement for

swim. Substep c If i ≠ S, go to next bacterium (i + 1) (i.e., go to substep b to process

the next bacterium.

Step 5 If j < Nc , go to step 4 and continue chemotaxis until life of the bacteria is over.

Step 6 Reproduction:

362 S. Panda et al.

Substep a For the given k and l, and for each i = 1,2,..., S , find health of

bacterium i , iHLJ as:

1

1

( , , , ).CN

iHL

j

J J i j k l+

=

= ∑ iHLJ gives a measure

of how many nutrients it got over its lifetime and how successful it was at avoiding noxious substances. Sort bacteria and chemotactic parameters C(i) in order of ascending JHL value (higher JHL value means lower health).

Substep b The bacteria with the highest JHL values are removed and the remaining bacteria split i.e. Sr = S/2. New bacteria that are made are placed at the same location as their parent.

Step 7 If the number of reproduction steps has not been reached i.e., if k < Nre, go to Step 3 and start the next generation in the start the next generation of the chemotactic loop.

Step 8 Elimination and dispersal: For i = 1,2..., S with probability Ped, eliminate and disperse each bacterium to keep the number of bacteria in the population constant. If a bacterium is eliminated, disperse another one to a random location on the optimisation domain.

Step 9 If l < Ned go to Step 2 and repeat the process; otherwise end the algorithm.

Figure 6 Flowchart of BFOA optimisation process to optimally tune the controller parameters

Initialize all variables. Set all loopcounter and bacterium index i to 0

edNl >EndYes

No

Increase elimination and disperal loopcounter l = l + 1

Increase reproduction loop counterk = k + 1

reNk >Perform elimination

and disperal forall bacteria

No

Yes

Increase chemotaxis loop counterj= j + 1

sNj >

No

YesPerform reproduction

Increase bacterium indexi = i + 1

Si > Yes

No

Compute the cost function value for i-th bacterium as J ( i, j, k, l ) and set

J_last = J ( i, j, k, l )

Tumble: the i-th bacterium takes asetp of height C (i) along a randomly

generated tumble vector

Compute the cost function valueJ ( i, j+1, k, l )

Set swim counter m = 0

SNm >Yes

No

m = m + 1

Start

J ( i, j+1, k, l ) < J_last

Yes

Set J_last = J ( i, j, k, l )

SwimA

A

No

B

B

Set SNm=

)(iΔ

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 363

The flowchart of the BFOA algorithm is shown in Figure 6. One more important point that affects the optimal solution more or less is the range for unknowns. For the very first execution of the program, wider solution space can be given and after getting the solution one can shorten the solution space nearer to the values obtained in the previous iterations. Table 1 BFOA optimised parameters for single-machine infinite-bus power system

STATCOM-base controller PSS parameters

KS T1S T3S KP T1P T2P 43.564 0.4087 0.3187 2.652 0.7568 0.2208

The objective function is evaluated for each individual by simulating the example power system model, considering a severe disturbance. For objective function calculation, a three-phase short-circuit fault in one of the parallel transmission lines is considered. The optimisation process is repeated 20 times and the best solution among 20 runs are given in Table 1. The typical convergence of objective function is shown in Figure 7.

Figure 7 Convergence of fitness function for SMIB power system

0 20 40 60 80 100 120 140 160 180 2000.0139

0.014

0.0141

0.0142

0.0143

0.0144

0.0145

0.0146

Generations

Con

verg

ence

of J

To assess the effectiveness and robustness of the proposed controller, simulation studies are carried out under different fault disturbances and fault clearing sequences. The response without controller is shown with dotted line with legend ‘NC’; response with conventional PSS (Kundur, 1994) is shown with dashed line with the legend ‘CPSS’ and the response with the proposed coordinated PSS and STATCOM-based controller is shown with solid line with legend ‘Coordinated’.

The behaviour of the proposed controller is verified at nominal loading condition (Pe = 0.8 pu) under severe disturbance. A five-cycle three-phase fault is applied at the middle of one transmission line connecting at t = 1 sec. The fault is cleared by opening of the faulty line and the line is reclosed after five-cycles. The original system is restored upon the fault clearance. The system response under this severe disturbance is shown in Figures 8(a)–8(e). The plots in 8(a), 8(b), 8(c), 8(d) and 8(e) are, power angle (δ) in degrees, speed deviation (Δω) in pu, real power flow in the transmission line PL in MW, stabilising signal of PSS (VS) in pu and STATCOM reference voltage signal (VST) in pu respectively.

It can be observed from these figures that, with out control the system is highly oscillatory for the above contingency. It is also clear that, coordinately designed PSS and

364 S. Panda et al.

STATCOM-based controller outperform the CPSS. The responses with coordinated design are much faster, with less overshoot and settling time compared to CPSS.

Figure 8(a) Power angle response for five-cycle three-phase fault disturbance at middle of transmission line

0 1 2 3 4 5 6 7 8

15

20

25

30

35

40

45

Time (sec)

δ (d

eg)

NCCPSSCoordinated

Figure 8(b) Speed deviation response for five-cycle three-phase fault disturbance at middle of transmission line

0 1 2 3 4 5 6 7 8-8

-6

-4

-2

0

2

4

6x 10-3

Time (sec)

Δ ω

(pu)

NCCPSSCoordinated

Figure 8(c) Tie-line power flow response for five-cycle three-phase fault disturbance at middle of transmission line

0 1 2 3 4 5 6 7 8

100

200

300

400

500

600

Time (sec)

PL (M

W)

NCCPSSCoordinated

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 365

Figure 8(d) Stabilising signal of pss for five-cycle three-phase fault disturbance at middle of transmission line (continued)

0 1 2 3 4 5 6 7 8-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Time (sec)

VS (p

u)NCCPSSCoordinated

Figure 8(e) Variation of statcom reference voltage signal for five-cycle three-phase fault disturbance at middle of transmission line

0 1 2 3 4 5 6 7 8

0.9

0.95

1

1.05

1.1

Time (sec)

VST

(pu)

NCCoordinated

To test the robustness of the controller to loading conditions and fault clearing sequence, a five-cycle three-phase fault is applied near bus2 at heavy loading condition (Pe = 1.0 pu). The fault is cleared by opening of both the transmission lines and the lines are reclosed after five-cycles. The system speed deviation response for the above contingency is shown in Figure 9 which clearly illustrates the robustness of the proposed approach to operating condition and fault clearing sequence.

Figure 9 Speed deviation response at heavy loading for five-cycle fault at bus2

0 1 2 3 4 5 6 7 8

-0.02

-0.01

0

0.01

0.02

Time (sec)

Δ ω

(pu)

NCCPSSCoordinated

366 S. Panda et al.

5.2 Multi-machine power system

The design problem is further extended to Kundur’s four-machine, two area-system shown in Figure 10. The system consists of four generators divided in to two subsystems and are connected via an intertie. Following a disturbance, the two subsystems swing against each other resulting in instability. To improve the stability, a STATCOM is assumed at bus 8. The relevant data for the system can be found in reference (Kundur, 1994).

Figure 10 Four-machine two-area system with statcom

STATCOM

1

2

3

4

G1

G2

G3

G4

Area 1 Area 2

25 km 10 km110 km

25 km10 km5 6

7 8 910 11

L-1 L-2

110 km

Local control signals, though easy to get, may not contain the inter-area oscillation modes. So, compared to wide area signals, these are not as highly controllable and observable for the inter-area oscillation modes. Owing to the recent advances in optical fibre communication and global positioning system, wide area measurement system can realise phasor measurement synchronously and deliver it to the control centre even in real time, which makes the wide area signal a good alternative for control input. In view of the above, the speed deviation of generators G1 and G4 is chosen as the control input of STATCOM-based damping controller in this paper. Accelerating powers of the individual generators are chosen as the input signal for all four PSSs. The same approach as explained in Section 5.1, for single-machine infinite-bus case is followed to coordinately design the PSS and STATCOM-based controllers. The obtained parameters of STATCOM-based controller and PSS are shown in Table 2. Figure 11 shows the convergence of fitness function for coordinated design of PSS and STATCOM-based controller for multi-machine power system. Table 2 BFOA optimised parameters of STATCOM-based controller and PSSs for

four-machine two-area system

Controller/ Parameters STATCOM PSS1 PSS2 PSS3 PSS4

Gain 188.3307 2.959 3.7204 3.9941 4.6948 0.4021 0.0917 0.0615 0.0507 0.091 Time constant 0.1307 1.6602 1.2051 1.0586 1.3818

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 367

Figure 11 Convergence of fitness function for multi-machine power system

0 20 40 60 80 100 120 140 160 180 2000.01

0.011

0.012

0.013

0.014

0.015

0.016

Generations

Con

verg

ence

of J

To show the effectiveness of the proposed BFOA optimised controllers based on wide area signal under extreme conditions, time domain simulation is performed on the system with a three-phase fault applied at the sending-end of the circuit between buses 7 and 8 (near bus 7) that is cleared 100 ms later. Figures 12 and 13 show the variations of the inter-area and local mode of oscillation against time. The system is unstable without control for the above contingency and not shown in figures. From these figures it can be seen that, inter-area modes of oscillations are highly oscillatory with CPSS.

With the application of coordinately designed PSSs and STATCOM-based controllers, the inter-area oscillations are quickly damped out. Further, the proposed optimised controllers are also effective in suppressing the local mode of oscillations.

Figure 12 Variation of inter-area mode of oscillation

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

-4

-2

0

2

4

x 10-3

Time (sec)

ω1 -

ω4 (p

u)

CPSSCoordinated

368 S. Panda et al.

Figure 13 Variation of local mode of oscillation

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

-6

-4

-2

0

2

4

6x 10-4

Time (sec)

ω3 -

ω4 (p

u)CPSSCoordinated

6 Conclusions

In this study, bacteria foraging optimisation algorithm is employed for the coordinated design of PSS and STATCOM-based controller. For the proposed controller design problem, a non-liner, simulation-based objective function, to increase the power system stability is used and genetic algorithm optimisation technique is employed to optimally tune the parameters of the controller. The effectiveness of the proposed coordinated design approach in improving the power system stability is demonstrated for both single-machine infinite-bus and multi-machine power systems. It is observed that the proposed coordinately designed PSS and STATCOM-based controller adapt itself to generate suitable variation of the control signals and provide efficient damping to power system oscillations following a disturbance. Further, the proposed controllers are found to be robust to fault location and change in operating condition. Also, the inter-area and local modes of power system oscillations are effectively damped by the proposed controllers.

References Das, S. et al. (2009) ‘Bacterial foraging optimization algorithm: theoretical foundations, analysis,

and applications’, Foundations of Computational Intelligence, Vol. 3: Global Optimization Theoretical Foundations and Applications, Studies in Computational Intelligence, Springer Verlag, Germany.

Hingorani, N.G. and Gyugyi, L. (2000) ‘Understanding FACTS: concepts and technology of flexible AC transmission system’, IEEE Press, Piscataway, NJ, USA.

Kundur, P. (1994) Power System Stability and Control, McGraw-Hill, New Delhi. Mishra, S. (2005) ‘A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation’,

IEEE Transactions on Evolutionary Computation, Vol. 9, No. 1, pp.61–73. Padiyar, K.R. (1996) Power System Dynamics: Stability and Control, BS Publications, Hyderabad,

India.

Bacteria foraging optimisation algorithm for tuning of PSS and STATCOM 369

Panda, S. (2011) ‘Robust coordinated design of multiple and multi-type damping controller using differential evolution algorithm’, Int. J. Electrical Power and Energy Systs., Vol. 33, No. 4, pp.1018–1030.

Panda, S. and Padhy, N.P. (2008) ‘Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design’, Appl Soft Comput, Vol. 8, No. 4, pp.1418–1427.

Passino, K.M. (2002) ‘Biomimicry of bacterial foraging for distributed optimization and control’, IEEE Control Systems Magazine, Vol. 22, No. 3, pp.52–67.

Ramirez, J.M. and Castillo, I. (2004) ‘PSS and FDS simultaneous tuning’, Electric Power System Research, Vol. 68, pp.33–40.

Wang, H.F. (1999) ‘Phillips-Heffron model of power systems installed with STATCOM and applications’, IEE Proc. Gen. Trans. Distrib., Vol. 146, No. 5, pp.521–527.

Appendix

A complete list of parameters used appears in the default options of SimPowerSystems in the user’s manual. All data are in pu unless specified otherwise.

• Generator: SB = 500 MVA, H =3.7 s, VB = 13.8 kV, f = 60 Hz, RS = 2.8544 e -3, Xd = 1.305, Xd′ = 0.296, Xd″ = 0.252, Xq = 0.474, Xq′ = 0.243, Xq″ = 0.18, Td = 1.01 s, Td′ = 0.053 s, Tqo″ = 0.1 s., Pe=0.8 pu, δ0=48.480

• Load at Bus2: 100 MW

• Transformer: 500 MVA, 13.8/500 kV, 60 Hz, R1 = R2 = 0.002, L1 = 0, L2 = 0.12, D1/Yg connection, Rm = 500, Lm = 500

• Transmission line: 3-Ph, 60 Hz, Length = 300 km each, R1 = 0.02546 Ω/km, R0 = 0.3864 Ω/km, L1 = 0.9337e-3 H/km, L0 = 4.1264e-3 H/km, C1 = 12.74e-9 F/km, C0 = 7.751e-9 F/km

• Hydraulic turbine and governor: Ka = 3.33, Ta = 0.07, Gmin = 0.01, Gmax = 0.97518, Vgmin = –0.1 pu/s, Vgmax = 0.1 pu/s, Rp = 0.05, Kp = 1.163, Ki = 0.105, Kd = 0, Td = 0.01 s, β = 0, Tw = 2.67 s

• Excitation system: TLP = 0.02 s, Ka =200, Ta = 0.001 s, Ke =1, Te =0, Tb = 0, Tc = 0, Kf = 0.001, Tf = 0.1 s, Efmin = 0, Efmax = 7, Kp = 0

• PSSs: Sensor time constant = 0.015 s, VSmax = 0.15 pu, VS

min = –0.15 pu

• STATCOM parameters: 500 KV, ± 100 MVAR, R = 0.071, L = 0.22, Vdc = 40 KV, Cdc = 375 ± μF, Vref = 1.0, Kp = 50, Ki = 1,000

• STATCOM controller: Δ VSTmax = 1.1 pu, ΔVST

min = 0.9 pu, T2S = T4S = 0.2 s, TWS = 10 s.