dynamic stability enhancement of power system using intelligent power system stabilizer

Dynamic Stability Enhancement of PowerSystem Using Intelligent Power SystemStabilizer

Swati Paliwal, Piyush Sharma and Ajit Kumar Sharma

Abstract The destabilizing effect of high gain in voltage regulators persists inpower system. The power oscillations of small magnitude and high frequency,which often persisted in power system, present the limitation to the amount ofpower transmitted within the system. In this paper, a linearized Heffron–Phillipsmodel of a single machine infinite bus (SMIB) is developed using different con-trollers like fuzzy logic power system stabilizer (FPSS), PID controller, particleswarm optimization (PSO)-based PID controller for analyzing the stabilityenhancement in power system. For FPSS, speed deviation and acceleration devi-ation are taken as inputs. Comparison of the effectiveness (steady-state error, ess,overshoot (Mp), and settling time (ts) for a different controller has been done. Theperformance of the SMIB system using FPSS has been analyzed when comparingwith conventional controllers used in SMIB. Similarly the PSO is done usingdifferent iterations on conventional PID controller. The results of the simulationshow that for low frequency oscillations, FPSS is more effective in dampingcompared to conventional controllers, and similarly PSO-based PID controller ismore effective than a conventional PID controller.

S. Paliwal (&)Electrical and Electronics Engineering Department, Amity University,Noida, Indiae-mail: [email protected]

P. SharmaElectrical Engineering Department, SS College of Engineering, Udaipur,Rajasthan, India

A.K. SharmaElectrical and Electronics Engineering Department,Northern India Engineering College, Delhi, Indiae-mail: [email protected]

A.K. Sharmae-mail: [email protected]

© Springer India 2015K.N. Das et al. (eds.), Proceedings of Fourth International Conference on SoftComputing for Problem Solving, Advances in Intelligent Systems and Computing 335,DOI 10.1007/978-81-322-2217-0_46

571

Keywords Heffron–Phillips model � Power system stabilizer � Fuzzy logic powersystem stabilizer � Reduced rule fuzzy logic power system stabilizer � Controller �Membership functions � PID controller and particle swarm optimization

1 Introduction

Stability of electric power system is one of the most significant concerns in anyelectric power system network. This can be traced from the fact that in steady state,the average electrical speed of the generators must be in synchronism. The powersystem may be broadly defined as that property of power system that enables it toremain in a state of operating equilibrium under normal operating condition and toregain an acceptable state of equilibrium after being subjected to a disturbance.

Power system stability [1] can be classified into: Transient stability and Smallsignal stability. Transient stability of a system was conventionally suppressed usingautomatic voltage regulator (AVR), has the electric system, and has been seen withoscillations of frequencies ranging from 0.1 to 2 Hz. These regulators have highgain leading to destabilizing effect on power system and also these are designed forspecific operating condition hence limiting to specific level of performance [2]. Thesolution to this problem is provided by using different controllers like fuzzy logiccontroller, PID controller. This paper also investigates the optimization in PIDcontroller through particle swarm optimization (PSO) technique using differentiterations. Under PSO technique, the best probabilities are considered for PIDcontrollers. Fuzzy logic [3–5] has the features of simple concept, easy implemen-tation, and computational efficiency. This provides an easy method to draw thedefinite conclusion from hazy, uncertain, or inexact information. Also, the PIDcontroller has the ability to reduce both peak overshoot as well as the settling timeof a system. So in this paper, the fuzzy logic-based power system stabilizer modeland PID controller are evaluated on a single machine infinite bus (SIMB) powersystem, and then, the performance of conventional power system stabilizer (CPSS),fuzzy logic-based power system stabilizer (FPSS) is compared, also there will be acomparison between the PID controller together with PSO-based PID controller.

2 Modeling of Power System

Synchronous generators from the principle source of electric energy in powersystem. SMIB system consists of a synchronous machine connected to an infinitebus through a transmission line (Fig. 1).

Figure 2 shows the block diagram of SMIB power system model. This diagramwas developed by Heffron and Phillips so to represent a single synchronousgenerator connected to the grid through a transmission line. Heffron–Phillips model

572 S. Paliwal et al.

[6] is a linear model. It is quite accurate for studying LFOs and stability of powersystems. It has also been successfully used for designing classical power systemcontrollers, which are still active in most power utilities.

3 Controllers

Controller is a gadget fabricated in a chip form, analogue electronics, or computerthat supervise and actually alters the working conditions after checking the errors ofa considered dynamical system. This paper deals with different types of powersystem controllers discuss below.

Fig. 1 Single machine infinite bus system (SMIB)

Delta Eq'

Delta Efd

Pe

Wb

sWb / s

1

M.s+D

Transfer Fcn

Power Angle Deviation

Speed Deviation

Pm

KA

Ta.s+1KA

K5

1K5

K4

1K4K3

K3*Tdo'.s+1

K3

K2

1K2

K1

1

K1

K6

1

K 6

Fig. 2 MATLAB/SIMULINK model of Heffron and Phillips without controller

Dynamic Stability Enhancement of Power System … 573

3.1 Conventional Power System Stabilizer (CPSS)

The power system stabilizer (PSS) is used to provide a sufficient damping toelectromechanical oscillations in SMIB energy system. So CPSS [7–11] is used toachieve desired transient behavior and low steady-state error. The input to con-troller is speed deviation Dxð Þ. The PSS as represented in Fig. 3 has three com-ponents. They are phase compensation block, signal washout block, and gain block.

The controller gain Ks is an important factor as the damping provided by thePSS increases in proportion to an increase in the gain up to a certain critical gainvalue, after which the damping begins to decrease. The phase compensator block isused to make the system “settle down” quickly. The outcome value of the controllerhas to be gradually drawn toward zero in steady-state condition. Therefore, awashout transfer function [Tw.S/(Tw.S+1)], which has a steady-state gain zero isused. The value of washout time constant Tw, may be in the range of 1–20 s.

3.2 Fuzzy Logic Controlled Power System Stabilizer (FPSS)

The fuzzy power system stabilizer is a two-input component which have singleoutput. These inputs are angular speed deviation and angular acceleration whileoutput of fuzzy logic controller is a voltage signal.

3.2.1 Fuzzy Logic Control System

Concept of fuzzy logic has been given by Lotfi Zadeh in 1965. This logic is used inmany applications in the industry because of some advantages: simple and fastertactic, reduce a propose enlargement cycle, simple to execute, reduce hardware cost,improve the control performance, simplify design convolution. So it is used as acontroller in a power system as a fuzzy power system stabilizer [12–20]. Thedesigning process is carried out with the help of MATLAB 2009a. A fuzzy con-troller comprises of three stages: fuzzification, fuzzy rule, and defuzzification(Table 1).

KsTw.S

Tw.S+1

T1.S+1

T2.S+1

Gain Wash out Lead-Lag

InputOutput

Fig. 3 Structure of conventional lead-lag controller


Membership functions are used to adapt the fuzzy standards between 0 and 1 forboth input and output values (Figs. 4 and 5).

3.3 PID Controller

The PID control algorithm is a robust and simple algorithm that is widely used inthe industry. The algorithm has sufficient flexibility to yield excellent results in awide variety of applications and has been one of the main reasons for the continueduse over the years. As the name suggests, PID algorithm consists of three basiccoefficients; proportional, integral, and derivative which are varied to get optimalresponse (Fig. 6).

Table 1 49 Rule base offuzzy logic controller Acceleration

NH NM NS ZR PS PM PH

NH NH NH NH NH NM NM NS

NM NH NM NM NM NS NS ZR

NS NM NM NS NS ZR ZR PS

ZR NM NS NS ZR PS PS PM

PS NS ZR ZR PS PS PM PM

PM ZR PS PS PM PM PM PH

PH PS PM PM PH PH PH PH

Fig. 4 Membership functionsfor fuzzy controller for inputand output variables


3.4 Particle Swarm Optimization

PSO concept is attributed to Kennedy (social-psychologist) and Russell Eberhart(electrical engineer) in 1995. PSO is an artificial intelligence technique for findingapproximate solutions toward extremely difficult or impossible numeric maximi-zation and minimization problems. This candidate-based Stochastic optimizationtechnique is motivated by social behavior of Fish Schooling and swarming theory.It uses a number of agents (particles) that constitute a swarm moving around in thesearch space looking for the best solution. In this paper, PSO technique is appliedso that using different iterations, we analyzed the stability enhancement conditionsat each particular interval with accuracy. The PSO technique gives more accurateresults than a conventional PID controller.

Figure 7 shows the flow chart of PSO technique which shows how the selectionof different parameters is done and generates the best initial fitness parameters(Fig. 8).

Delta Eq' Delta Efd

Pe

Wb

s

Wb / s

1

M.s+D

Transfer Fcn

Speed Deviation

Power Angle Deviation

Pm

Output

1Output

KA

Ta.s+1KA

K5

1K5

K4

1K4

K3

K3*Tdo'.s+1

K3

K2

1K2

K1

1

K1

K6

1

K 6

Input2

1Input2

Input1

1

Input1 Fuzzy Logic Controller

du/dt

Derivative

Fig. 5 Shows the Heffron–Phillips MATLAB/SIMULINK model of single machine infinite bus(SMIB) equipped with FLC


Fig. 6 MATLAB/SIMULINK model plant controlled by small perturbed PID controller

Fig. 7 Flowchart of particle swarm optimization


4 Simulation Results

Figures 9, 10, 11, 12 and 13 show the speed deviation (Δω), power angle deviation(Δδ) of the SMIB system without controller, controlled by conventional controller,FLC, PID-based controller, and PSO-based PID, respectively. The system param-eters (a) Speed deviation (Δω) (b) Power angle deviation (Δδ) of generator obtainedwith the proposed controllers are given in Table 2. The outputs of SMIB systemwithout PSS (a) Speed deviation (Δω) (b) Power angle deviation (Δδ) of generatorare shown in Fig. 9. The responses clearly show that system has large overshoot(Mp) and large settling time (ts), and error steady state 0 and 2 for speed deviationand power angle, respectively.

Fig. 8 MATLAB/SIMULINK model plant controlled by PSO-based PID controller

Fig. 9 Output of SMIB system without PSS a speed deviation (Δω) b power angle deviation (Δδ)of generator


Fig. 10 Output of SMIB system conventional lead-lag PSS a speed deviation (Δω) b power angledeviation (Δδ) of generator

Fig. 11 Output of SMIB system fuzzy PSS for triangular membership function a speed deviation(Δω) b power angle deviation (Δδ) of generator

0 1 2 3 4 5 6 7 8 9 10-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Time in second

Spee

d de

viat

ion

Angular speed deviation

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time in seccond

Pow

er a

ngle

dev

iati

on

Power angle deviation for PID controller

(a)

(b)

Fig. 12 Output of SMIB system with PID controller a speed deviation (Δω) b power angledeviation (Δδ) of generator


The outputs of SMIB systems with conventional PSS (a) speed deviation (Δω)(b) power angle deviation (Δδ) of generator are shown in Fig. 10. The responsesshow that system has still larger overshoot (Mp) and larger settling time (ts), anderror steady state 0 and 2 for speed deviation and power angle, respectively. Thiscan be further improved by fine tuning of controller parameters.

The outputs of SMIB system with Fuzzy PSS for a triangular membershipfunction (a) speed deviation (Δω) (b) power angle deviation (Δδ) of generator areshown in Fig. 11. The responses show that system has smaller overshoot (Mp) andsmaller settling time (ts), and error steady state 0 and 2 for speed deviation andpower angle, respectively. So performance improved by using Fuzzy PSS. This canbe further improved by fine tuning of controller parameters.

The outputs of SMIB system with PID controller (a) speed deviation (Δω) (b)power angle deviation (Δδ) of generator are shown in Fig. 12. The responses clearlyshow that system has small overshoot (Mp), small settling time (ts), and errorsteady state for speed deviation is zero and 2 for Power angle. This can be furtherimproved by fine tuning of controller parameters.

0 1 2 3 4 5 6 7 8 9 10-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Time in second

Spee

d D

evia

tion

Angular speed deviation

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time in second

Pow

er A

ngle

Dev

iati

on

Power angle Deviation

(a)

(b)

Fig. 13 Output of SMIB system with PID PSO a speed deviation (Δω) b power angle deviation(Δδ) of generator


Tab

le2

System

parameterswith

differentcontroller

S. no.

System

parameter

With

conv

entio

nalPS

Scontroller

FuzzyPS

Sfortriang

ular

mem

bershipfunctio

nPID

controller

PID

PSO

controller

1Sp

eed

deviation

(Dω)

Large

overshoo

t(M

p),peak

value=0.04

9pu

,largeset-

tling

time(ts),ess=0

Smallerov

ershoo

t(M

p),peak

value=0.03

7pu

,sm

allerset-

tling

time(ts),ess=0

Smallerov

ershoo

t(M

p),peak

value=0.02

76pu

,sm

aller

settlingtim

e(ts),ess=0

SmallerMax.ov

ershoo

t,Mp=0.02

0pu

,sm

aller

settlingtim

e(ts),ess=0

2Po

wer

angle

deviation

(Dδ)

Large

overshoo

t(M

p),peak

value=4.5pu

,largesettling

time(ts),ess=

2

Smallerov

ershoo

t(M

p),peak

value=3.9pu

,smallersettling

time(ts),ess=2.01

Smallerov

ershoo

t(M

p),peak

value=3.5pu

,smallersettling

time(ts),ess=2.02

SmallerMax.ov

ershoo

t.Mp=3.37

pusm

allsettling

time(ts),ess=2.01


The outputs of SMIB system with PSO-based PID controller (a) speed deviation(Δω) (b) Power angle deviation (Δδ) of generator are shown in Fig. 13. Theresponses clearly show that system has smaller overshoot (Mp), smaller settlingtime (ts) as compare to PID controller, and error steady state for speed deviation iszero and 2 for Power angle.

5 Conclusion

In this paper, initially the effectiveness of power system stabilizer is reviewed. Theproposed method has been simulated on a SMIB energy system with FLC, PIDcontroller, and conventional controller using complete state space model. TheMATLAB/SIMULINK simulation results showed that in the presence of smalldisturbances in the system, fuzzy controller is more effective as compared to theconventional controller, and also, PSO-based PID controller is also more effectivethan PID controller. The fuzzy logic power system stabilizer (FPSS) gives zerosteady-state error, smaller overshoot, and settling time as compared to conventionalpower system stabilizer.

Appendix

Parameter ValuesGenerator: M = 7.0 s, D = 0, Xd = 1.8, Xq = 1.76, X 0

d ¼ 0:3, T 0do ¼ 7:2940,

ωb = 314Exciter: (IEEE Type ST1): KA = 200, TA = 0.02 s, T1 = 0.154, T2 = 0.033,

KS = 9.5, TW = 1.4, K1 = 0.7636, K2 = 0.8644, K3 = 0.3231, K4 = 1.4189,K5 = 0.1463, K6 = 0.4167, Kp = 278.65, Ki = 271.41, Kd = 18.14.

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dynamic stability enhancement of power system using intelligent power system stabilizer

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