journal paper 3

8/3/2019 Journal Paper 3

http://slidepdf.com/reader/full/journal-paper-3 1/12

1

OPTIMAL TUNING OF POWER SYSTEMS STABILIZERS (PSS) AND AUTOMATIC

VOLTAGE REGULATOR (AVR) GAINS USING PARTICLE SWARM

OPTIMIZATION TECHNIQUE1U. Jafaru,

2G. A. Bakare,

1B. U. Musa and

1M. Abdulkadir

1Department of Electrical and Electronics Engineering, University of Maiduguri,

Borno State.e-mails: [email protected], [email protected], [email protected]

Electrical and Electronics Engineering Programme, Abubakar Tafawa Balewa

University, Bauchi, Bauchi State.

e-mail: [email protected]

AbstractPower System Stabilizers (PSS) resolves the instability problem which results from the use of

static excitation and long distance transmission line in the power industry. Simultaneous and

coordinated tuning of stabilizer parameters and automatic voltage regulator (AVR) gains in

Single machine infinite bus (SMIB) power systems is considered. This problem is formulated as

an optimization problem. This research focuses on the optimal tuning of the Power SystemStabilizer (PSS) parameters and Automatic Voltage Regulator (AVR) gains using particle swarm

optimization (PSO) technique. It is aimed at minimizing the damping ratio of the power systemby optimally determining the values of the control parameters of the PSS/AVR. The

effectiveness of the PSO technique for tuning PSS/AVR in a large scale power system was tested

by applying it to a SMIB. MATLAB version 7.0 was used as a simulation platform to determinethe effect of the PSS/AVR. The simulation results obtained are the speed deviation, rotor angle

deviation and the terminal voltage with PSO based PSS/AVR, with conventional PSS/AVR and

without PSS/AVR response in per unit value. Simulation results on SMIB revealed that the PSO

based tuning of PSS/AVR damped faster and has less overshoot and settling time (2 sec) ascompared with the conventional PSS/AVR (5 sec) and without PSS/AVR (9 sec). The results

obtained has significantly shown the effectiveness and robustness of the particle swarm

optimization algorithm in solving power system stability problems.

Keywords: Power system stabilizers, Automatic Voltage Regulator, Particle swarm

optimization Single Machine Infinite Bus System.

1. IntroductionThe need for improved power availability and power system quality has been increasing over the

years. This has made a lot of generators to operate continuously and to maintain the electricitysupply within statutory limits of voltage and frequency. Large transmission distances and highly

complex distribution system in Nigeria may lead to dynamic instability, (this instability can lead

to disturbance and frequency oscillation. Power systems experiences low frequency oscillations

due to disturbances, an increase in damping of the system response is desirable, not only becauseit reduces the fluctuations in the controlled variables and hence improving the quality of power

supply, but mainly because damping is translated into an increase in the power transmission

stability limits. Higher stability limits brings significant economic savings as the need for theexpansion of the transmission system can be ignored (Kundur, 1994). The fundamental idea of

Power System Stabilizer is to provide an additional positive damping to the system by

introducing a stabilizing signal of proper phase through the excitation system.



2

Over the past four decades, many researches have been published on the design of power

system stabilizers (PSS); to resolve the dynamic instability problem which results from thewidespread use of static excitation systems and long-distance transmission lines in multimachine

power systems. Most of these works are concerned with the tuning of suitable stabilizer

parameters to achieve satisfactory damping characteristics of the system (Gibbard, et-al, 2001).

Low frequency oscillations if sustained may grow to cause system collapse if adequate dampingis not provided. To enhance system damping, the generators are equipped with power system

stabilizers (PSSs) that provide supplementary feedback stabilizing signals in the excitation

system (Feliachi et-al 1988). This is an easy, economical and flexible way to improve powersystem stability in interconnected AC power systems.

The concept of synchronous machine stability as affected by the excitation control is

presented in Do-Bomfim, et-al (2000). Gibbard et-al (2001) used the sensitivity of mechanicalmode damping with respect to stabilizer gain to pick out the generator that is most effective for

stability enhancement using power system stabilizers. Do-Bomfin et-al (2000) proposed a

method that simultaneously optimizes both phase compensation and gain settings for the

stabilizers using Genetic Algorithms (GA). Although GA is sufficient enough in finding global

or near global optimal solution of the problem, it requires a very long run time that may beseveral minutes or even several hours depending on the size of the system under study. That is

why this kind of application could not be applied on-line. The concept of induced torquecoefficients is introduced for the systematic coordination of stabilizers (Gibbard et-al 2001) with

linear programming of a multi-machine system. Techniques for the coordination of stabilizers

based on the calculation of eigenvalue shifts from the residues are developed in Martins andLima (1990). Both techniques, using residues or induced torques are mathematically equivalent

in regard to eigenvalue shifting estimation (Pagola et-al, 1989). Later, El-Zonkoly (2006)

presented an approach using a concept of coherent groups, being a technique which is extremely

useful in transient stability studies.

2.1 Linearized model of a single-machine infinite-bus system for small-signal stability

A single machine-infinite bus (SMIB) system is considered for the present investigations

(Kundur, 1994). A machine connected to a large system through a transmission line may be

reduced to a SMIB system, by using Thevenin’s equivalent of the transmission network external

to the machine. Because of the relative size of the system to which the machine is supplying

power, the dynamics associated with machine will cause virtually no change in the voltage and

frequency of the Thevenin’s voltage (infinite bus voltage). In this section we will study the small

signal performance of a single machine connected to a large system through transmission lines.

A general system configuration is shown in Fig 1. Analysis of system having such simpleconfigurations is extremely useful in understanding basic effects and concepts. After we develop

an appreciation for the physical aspects of the phenomena and gain experience with the

analytical techniques, using simple low-order systems, we will be in a better position to deal with

large complex systems. A block diagram of the system with AVR and PSS is shown in Fig. 2 andthe thyristor excitation system with AVR and PSS is shown in Fig. 3. This study system is

described by the following state space representation:

(1)where

(2)



3

The matrices A, B, C and D are as follows:

[

]

(3)

(4)

(5)

(6)

where,

,

, , ,

,

,

Fig.1: Single machine connected to a large power system through transmission lines.

G pss(s)

Fig.2 Block diagram representation SMIB with AVR and PSS

V ref

∆ω

∆T m

∆T e ∆ψ fd ∆δ

Field circuit

-

-+

+

+

+

K 4

K 2

K 1

∑ ∑ ∑

K 6

K 5

∑

∆v1

∆vs

∑ Gex(s) ∆E fd

Exciter-

-

+

++

∆ωr

∆δ

Voltage transducer

∆E 1

Local load

Infinite BusG

E t E B

Z eq=R E + jX E



4

2.2 Mathematical Modeling

The synchronous machine is represented by a third-order model comprising the

electromechanical swing equation and the machine’s internal voltage equation. The machineequations are described in Kundur, 1994, Sa’adat, 2002, Panda and Padhy, 2007.

Electrical Equations:Stator winding equations are given by:

qd d ad d I x I R E V '' (7)

d d qaqq I x I R E V '' (8)

Rotor winding equations are given by:

qqd d

d

qoI x x E

dt

dE T )'('

'' (9)

fd d d d q

q

do E I x x E

dt

dE T )'('

''

2'2

'

)()(

)'()()'()(

d eea

oqd eod ea

d x x R R

CosV E x xSinV E R R I

(10)

2'2

'

)()(

)'()()'()(

d eea

oqd eoqea

q x x R R

SinV E x xCosV E R R I

(11)

The torque or electrical power equation is given by;

qqd d e I E I E P'' (12)

The IEEE type-ST1 exciter is used, modeled as:

fd

fe

f

t tr

e

e

fd E sT

sK V V

sT

K E

11(13)

Mechanical Equations:

Rotor swing equation is given by:

dampem T PPdt

d M

(14)

Fi 3: Th ristor excitation s stems with AVR and PSS

∑

transducer Exciter

Com ensationWashoutPhase

V

Gain

(3

(4

(5

(1

(2

-

Power S stem Stabilizer



5

Where;

H M 2 DT damp

)(1

em PP D Ms

(15)

so

(16)

The detailed derivations of the equations given above and the notations used are given in

Kundur, 1994.

2.3 Simulink Modelling The derived equations representing the system under study were modeled in the Simulink

environment. The complete model is shown in Fig 4. It contains the subsystem block,

conventional PSS block, differential evolution PSS block and the scopes to indicate the desiredoutputs.

Fig. 4: Complete generator model including DEPSS and CPSS

3.1 Overview of particle swarm optimizationPSO is one of the optimization techniques and belongs to evolutionary computation techniques

(Fukuyama, 1999; Kennedy & Eberhart, 1995; Naka, Genji, Yura, & Fukuyama, 2001). The

method has been developed through a simulation of simplified social models. The features of themethod are as follows:

(1) The method is based on researches on swarms such as fish schooling and bird flocking.

(2) It is based on a simple concept. Therefore, the computation time is short and it requires few

memories.According to the research results for bird flocking, birds are finding food by flocking (not

by each individual). It leaded the assumption that information is owned jointly in flocking.

According to observation of behavior of human groups, behavior pattern on each individual is

based on several behavior patterns authorized by the groups such as customs and the experiencesby each individual (agent). The assumptions are basic concepts of PSO. PSO is basically

developed through simulation of bird flocking in two-dimension space. The position of each

individual (agent) is represented by XY axis position and the velocity is expressed by vx (the

delta

To Workspace3

dw

To Workspace2

t

To Workspace1

Switch

Vpss

Vref

dw

delta

Subsystem

Scope1

Scope

In1Out1

DEPSS

1

Constant

Clock1

In1Out1

CPSS



6

velocity of X axis) and vy (the velocity of Y axis). Modification of the agent position is realized

by the position and velocity information. An optimization technique based on the above concept

can be described as follows: namely, bird flocking optimizes a certain objective function. Each

agent knows its best value so far (pbest) and its XY position. Moreover, each agent knows the

best value so far in the group (gbest) among pbests. Each agent tries to modify its position using

the following information:1 the current positions (x,y),

2 the current velocities (vx,vy),3 the distance between the current position, pbest and gbest.

This modification can be represented by the concept of velocity. Velocity of each agent can be

modified by the following equation:

( ) (17)

Using the above equation, a certain velocity, which gradually gets close to pbest and gbest can be

calculated. The current position (searching point in the solution space) can be modified by thefollowing equation:

(18)

Fig. 4 shows a concept of modification of a searching point by PSO and Fig. 5 shows a searchingconcept with agents in a solution space.

For the linearized system model presented in Section 2, the eigenvalues of the total system can

be evaluated. The proposed method is aiming to search for the optimal parameters set of theexciter and the power system stabilizers so that a comprehensive damping index (CDI) ( Cai &

Erlich, 2005) can be minimized:

∑ (19)

where is the damping ratio and n is the total number of the dominant eigenvalues. Theobjective of the optimization is to maximize the damping ratio as much as possible. The control

parameters to be tuned through the optimization algorithm are exciter gain (KA), KSTAB, Tw, T1

and T2 of single machine infinite bus system.

Table 1: Upper and lower limits of the control parameters

Parameter KA KSTAB TW T1 T2

Upper limit 400 50 10 0.5 0.05

Lower limit 50 20 1 0.05 0.005

3.2 Realization of PSO based Optimal Tuning of PSS/AVRStep I: Input system data: the following data are inputted,

Y

X

Vk

Vk+1

Vgbest

Vpbest

Sk+1

Sk X1

X2

X3

X4

Xn

Fig 4. Concept of modification of

a searching point by PSO.

Fig 5. Searching Concept with agents

in a solution space by PSO.



7

The network configuration during the operating conditions under study.

The load values at each bus during the same operating conditions.

The generator data and parameters.

The upper and lower limits of the parameters to be optimized.Step II: Initialize the swarm with random position and velocities.

Step III: Evaluate the fitness of each particle (objective value) as described by Eq. (19).Step IV: Determine the personal and global best positions.

Step V: Update the velocity of agents using Eq. (17).

StepVI: Update the position of agents using Eq. (18).

Step VII: Perform the position check (the boundaries of each parameter). If violated then repair

the algorithm then go to step 8. If not violated go to step 8.Step VIII: Check the stopping criterion. If met go to step 9 and if not met go back to step 3.

Step IX: Output the optimal solution, which is the optimal values of the control parameters of the

single machine infinite bus system.

4 Simulation results and discussions

The simulation is carried out using MATLAB version 7.0. Fig 5 shows the characteristics of theDE based system, it can be seen that the algorithm converges in 75 generations. In order toguarantee that the control parameters selected were optimal, the system response under

disturbance conditions, such as increasing or reducing the mechanical torque of the machine was

studied and the system response is given in Fig 6. The Optimal DE values of PSS and AVRParameter Settings for DE Based Tool are as seen in Table 1 below and the DifferentialEvolution Simulation Results are presented in Table 2.

Table 2: Optimal values of PSS/AVR Parameter Settings for PSO Based Tool

Control Parameters Particle Swarm Optimization

Maximum generation, genmax

Number of control devices, DPopulation size, np

Scaling factor for mutation, F

Crossover constant, CR

Objective function scaling constant, a

190

5200.8

0.5

2.0

Fig 5: Convergence characteristics of PSO based system.



8

(a) (b) (c)

Figure 14: Speed deviation at different conditions

Figure 14 (a), (b), and (c) are the Speed Deviation at different conditions. The speed deviation’s

amplitude of oscillation in DEPSS/AVR based system is 11 x 10-3

rad/sec which is much morelower than that of CPSS/AVR (15 x 10-3) rad/sec and comes to damp within 3 sec, while

CPSS/AVR converges at about 5 sec. and its amplitude of oscillation is much lower as compared

to the one without PSS/AVR (30 x 10-2

). The response without PSS/AVR converges inapproximately 7 sec. which is lately than even the CPSS/AVR.

(a) (b) (c)

Figure 15: Rotor angle deviation at different conditions

Similarly, in figure 15, the rotor angle deviation’s amplitude of oscillation in DEPSS/AVR basedsystem is 0.6 rad. which is much more lower than that of CPSS/AVR (0.75 rad.) and comes to

converge within 3 sec, while CPSS/AVR converges at about 5 sec. and its amplitude of

oscillation is much lower as compared to the one without PSS/AVR (1.5 rad.) The response

without PSS/AVR converges in approximately 7 sec. which is lately than even the CPSS/AVR.

0 1 2 4 5 6 7 8 9 10 -0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

t(sec)

Rotor Angle

with DEPSS & AVR

0 1 2 3 4 5 6 7 8 9 10 -0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2 -0.1

0

0.1

t(sec)

Rotor Angle

With CPSS & AVR

0 1 2 3 4 5 6 7 8 9 10 -1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

t(sec)

Rotor Angle

Without PSS & AVR

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

-8

-6

-4

-2

0

2

4 x 10 -

t(sec)

Speed Deviation

With DEPSS & AVR

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

-6

-4

-2

0

2

4

6 x 10 -3 Speed Deviation

t(sec)

With CPSS & AVR

0 1 2 3 4 5 6 7 8 9 10 -0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

t (sec)

Speed Deviation

Without PSS & AVR

dw(rad/sec)

delta(rad) delta(rad) delta(rad)

dw(rad/sec) dw()rad/sec



9

The response before the introduction of fault has less overshoot than that of when fault wasintroduced. Both did not settle until after 10 seconds or more. The disturbance is from altering

the mechanical torque of the subsystem/generator.

Fig 6(b) is the DEPSS/AVR based response of the generator. At this point DEPSS/AVR

was installed. It can be observed from the figure that rotor speed’s overshoots have reduceddrastically and the settling time of the response without disturbance reduced to 3 seconds, while

that with disturbance has reached 5 seconds before it came to settled. This response revealed that

the DE based tuning of PSS and AVR converges faster and have less overshoot and settling timeas compared with the conventional PSS/AVR and without PSS/AVR.

Figure 17: Terminal voltage response

Figure 17 is the terminal voltage response, it represent the voltage at the terminal of the

generator/machine. The DEPSS/AVR based terminal voltage has less overshoot and converges in

lesser time than CPSS/AVR and that without PSS/AVR which makes it convenient fortransmission due to reduction in fluctuation.

(b)

Fig 7 (a) compares the speed deviations of DEPSS/AVR with CPSS/AVR and withoutPSS/AVR at all. It can be seen clearly that the DEPSS/AVR based system has less overshoot and

converges in lesser time than CPSS/AVR and that without PSS/AVR. Fig 7 (b) also compares

the Rotor angle of DEPSS/AVR with CPSS/AVR and without PSS/AVR at all. It can be seen

clearly also that the DEPSS/AVR based system has less overshoot and converges in lesser time

than CPSS/AVR and that without PSS/AVR.

Table 2: DE Simulation Results

Control Parameters Particle Swarm Optimization

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

0.2

0.4

0.6

0.8

1

1.2

1.4

t(sec)

Without AVR & PSS With CPSS & AVR With DEPSS & AVR

Fig 7: (a) Speed and (b) Rotor angle deviation

Vt(pu)



10

Exciter Gain, K A

Stabilizer Gain,K STAB

Washout Time,T W

Compensation Time, T 1 Compensation Time, T2

64.3600

48.5155

1.1811

0.1836

0.0230

In Fig 6(a) the response before the introduction of disturbance has less overshoot than that of when disturbance was introduced. Both did not settle until after 10 seconds or more. The

disturbance is from altering the mechanical torque of the subsystem/generator. In Fig 6(b) the

overshoots have reduced drastically and the settling time of the response without disturbance

reduced to 2 seconds, while that with disturbance has reached 7 seconds before it come to rest.

5. Conclusion

This paper presents an effective technique to maximize the damping ratios of the system byoptimally determining the values of the control parameters of the system generators. The

optimization problem was solved using the particle swarm optimization technique. The proposedtechnique proved to be efficient in determining the optimal values of the control parameters suchthat the system response is satisfactory under different operating conditions. Besides being

effective, the particle swarm optimization technique proved to be fast compared with other

artificial intelligent optimization techniques such as genetic algorithms and compared tomathematical programming optimization approaches such as linear programming and quadratic

programming methods.

References

Byerley, R. T., & Sherman D. E. (1978). Frequency domain analysis of low frequencyoscillations in large electrical power systems. EPRI, Palo Alto, CA, Rep. EL-726, Project 744-1.

Cai, L. J., & Erlich, I. (2005). Simultaneous coordinated tuning of PSS and FACTS damping

controllers in large power systems. IEEE Transactions on Power Systems, 20(1).Do-Bomfim, A. L. B., Taranto, G. N., & Flacao, D. M. (2000). Simultaneous tuning of power

system damping controllers using genetic algorithms. IEEE Transactions on Power Systems,

15(1).

Feliachi, A., Zhang, X., & Sims, C. S. (1988). Power system stabilizers design using optimalreduced order models part II: Design. IEEE Transactions on Power Systems, 3(4).

Fukuyama, Y. (1999). A particle swarm optimization for reactive power and voltage control

considering voltage stability. Proceedings of IEEE international conference on intelligent systemapplications to power systems (ISAP), Rio de Janeiro.

Gibbard, M. J., Martins, N., Sanchez-Gasca, J. J., Uchida, N., Vittal, V., & Wng, L. (2001).

Recent applications of linear analysis techniques. IEEE Transactions on Power Systems, 16(1).

Gibbard, M. J., Vowles, D. J., & Pourbeik, P. (2000). Interactions between, and effectiveness of,power system stabilizers and FACTS devices stabilizers in multimachine systems. IEEE

Transactions on Power Systems, 15(2).

Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. Proceedings of IEEEinternational conference on neural networks (ICNN), IV, Perth, Australia.

Kundur, P. (1994). Power system stability and control. New York, NY: McGraw-Hill. 556 A.M.

El-Zonkoly / Expert Systems with Applications 31 (2006) 551 – 557



11

Martins, N., & Lima, L. T. G. (1990). Determination of suitable locations for power system

stabilizers and static VAR compensators for damping electromechanical oscillations in largepower systems. IEEE Transactions on Power Systems, 5(4).

Naka, S., Genji, T., Yura, T., & Fukuyama, Y. (2001). Practical distribution state estimation

using hybrid particle swarm optimization. Proceedings of IEEE power engineering socity winter

meeting, Columbus, Ohio, USA.Pagola, F. L., Perez, I. J., & Verghese, G. C. (1989). On sensitivities, residues

and participations — Applications to oscillatory stability analysis and

control. IEEE Transactions on Power Systems, 4(1).Pourbeik, P., & Gibbard, M. J. (1996). Damping and synchronizing torques

induced on generators by FACTS stabilizers in multimachine power

systems. IEEE Transactions on Power Systems, 11(4).Pourbeik, P., & Gibbard, M. J. (1998). Simultaneous coordination of power

system stabilizers and FACTS device stabilizers in a multimachine power

system for enhancing dynamic performance. IEEE Transactions on Power

Systems, 13(2).

Pourbeik, P., & Gibbard, M. J. (2002). Proof of the equivalence of residues andinduced torque coefficients for use in the calculation of eigenvalue shifts.

IEEE Power Engineering Review.Urdaneta, A. J., Bacalao, N. J., Feijoo, B., Flores, L., & Diaz, R. (1991). Tuning

of power system stabilizers using optimization techniques. IEEE

Transactions on Power Systems, 6(1).Zanetta, L. C., & Da Cruz, J. J. (2005). An incremental approach to the

coordinated tuning of power systems stabilizers using mathematical

programming. IEEE Transactions on Power Systems, 20(2).

REFERENCES

Babu, B. V. and Gaurav Chaturvedi, (2000), Evolutionary Computation strategy for

Optimization of an Alkylation Reaction., Proceedings of 53rd Annual Session of IIChE

(CHEMCON-2000), Calcutta.

B. V. Babu, and Rakesh Angira, (2001), Optimization of Nonlinear functions usingEvolutionary Computation., Proceedings of 12th ISME Conference, Chennai, India. Bakare G. A., Venayagamoorthy G. K. and Aliyu U. O. (2007) , Reactive Power and Voltage

Control of the Nigerian Grid System Using Micro-Genetic Algorithm, Proceeding of IEEE

Power Engineering Society General Meeting, San Francisco, California USA.

Do-Bomfim, A. L. B., Taranto, G. N., & Flacao, D. M. (2000), Simultaneous Tuning of Power

System Damping Controllers Using Genetic Algorithms. IEEE Transactions on Power Systems,

15(1).

El-Sayeed MAH, (1998), Ruled Based Approach for Real Time Reactive Power Control in

Interconnected Power System,” Expert System with applications, Vol. 14, pp. 335-360.

El-Zonkoly A.M. (2006), Optimal Tuning of Power Systems Stabilizers and AVR Gains UsingParticle Swarm Optimization.

Feliachi, A., Zhang, X., & Sims, C. S. (1988), Power System Stabilizers Design Using Optimal

Gibbard, M. J., Martins, N., Sanchez-Gasca, J. J., Uchida, N., Vittal, V., and Wng, L.

(2001), Recent Applications of Linear Analysis Techniques. IEEE Transactions on Power

Systems, 16(1).



12

Gibbard, M. J., Vowles, D. J., & Pourbeik, P. (2001), Interactions between, and Effectiveness

of, Power System Stabilizers and FACTS Devices Stabilizers in Multimachine Systems. IEEE

Transactions on Power Systems, 15(2).

Kit Po Wong and Zhao Yang Dong (2005), Differential Evolution, an Alternative Approach to

Evolutionary Algorithm.

IEE Proc., Pt. C, Gen., Trans.and Distrib.Kundur, P. (1994), Power System Stability and Control. New York, NY: McGraw-Hill.

Pagola, F. L., Perez, I. J., & Verghese, G. C. (1989), On Sensitivities, Residues and

Participations — Applications to Oscillatory Stability Analysis and Control. IEEE Transactions

on Power Systems, 4(1).

Price, K. and Storn, R. (1995), Differential Evolution – A Simple and Efficient Adaptive

Scheme for Global Optimization over Continuous Spaces, Technical Report TR-95-012.

Price, K. and Storn, R. (1997), Differential Evolution - A simple evolution strategy for fast

optimization., Dr. Dobb's Journal, 22 (4).

Price, K. and Storn, R. (2002), Web site of DE, http://www.ICSI.Berkeley.edu/~storn/code.html

http://www.icsi.berkeley.edu/~storn/code.html




journal paper 3

Documents