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An Innovative Bio Inspired PSO Algorithm to Enhance Power System Oscillations Damping
R.Shivakumar
Assistant Professor / EEE, Sona College of Technology Salem, India mukil2005@gmail.com
Dr.R.Lakshmipathi
Professor / EEE, St Peters Engineering College Chennai, India drrlakshmipathi@yahoo.com
Abstract
—
In Modern Interconnected Power systems, Power System Stabilizers(PSS) are widely used to damp the Low Frequency Inertial Oscillations experienced in the System .In this paper, an innovative Particle Swarm Optimization (PSO) Algorithm is applied to compute the Optimal value of PSS parameters to enhance Power System Stability. The design problem is formulated as an Eigen value based Optimization problem and the PSS parameters are optimized to shift the system electromechanical modes of oscillations at different loading conditions to the left in the complex s- plane for stability. To show the robustness of the proposed controller, Non linear simulations have been carried out under various operating conditions of the system operation. The Novel feature of this paper is the Computation of Eigen values, its analysis and comparative study of the system model between Conventional Lead lag stabilizer and the PSO based PSS.
Keywords-LowFrequency Oscillations,Eigen values, Particle Swarm Optimization,Robust Control,Power System Stability.
I.
I
NTRODUCTION
Power Systems are in general nonlinear and the operating conditions can vary over a wide range. Low frequency oscillations of the order of 0.2 to 3 Hz are observed when large power systems are interconnected by weak tie lines [1].These low frequency oscillations once started would continue for a long period of time causing system separation if no adequate damping is available. To enhance system damping, the generators are equipped with Power System Stabilizers, whose basic function is to add damping to the generator rotor oscillations by controlling its excitation using supplementary stabilizing signals [2]. The problem of PSS parameter tuning is a complex exercise. The Conventional Power System Stabilizer (Conv. PSS), a fixed parameter lead lag compensator, is widely used by Power system utilities [3].The gain settings of these stabilizers are determined based on the linearized model of the power system around a nominal operating point. Since Power systems are highly nonlinear and the operating conditions can vary over a wide range, CPSS performance is degraded when the operating point changes from one to another because of fixed parameters of the stabilizer. Unfortunately, the conventional techniques are time consuming as they are iterative and require heavy computation burden and slow convergence. Recently Bio inspired global optimization technique like Genetic Algorithms, Evolutionary programming, Tabu search, Simulated annealing, Rule based Bacteria Foraging, Particle Swarm optimization [4] have been applied for PSS parameter optimization. In this paper, PSO algorithm has been implemented to calculate the optimum value of PSS Parameters. PSO is a population based stochastic optimization technique inspired by social behavior of bird flocking or fish schooling. The main objective of this work is to find the optimum value of PSS parameters for a Single Machine Infinite Bus Power system to damp the low frequency inertial oscillations, thus enhancing system stability. To show the Effectiveness and Robust Control of the proposed PSO based controller, the controller has been applied and tested on a weakly connected Power system under wide range of operating conditions. Also the Eigen value analysis and simulation results are compared between the Conventional Lead lag stabilizer and the PSO based PSS (PSOPSS). II.
TEST
SYSTEM
MODEL
Fig(1).Single Machine Infinite Bus Power System Model
Fig.(1) represents a Synchronous generator connected to an infinite bus through a Transmission line having an impedance Ze. All the relevant system parameters used for the simulation are given in Appendix. III.
THE
PROPOSED
TECHNIQUE
A.
Power System Stabilizer Model
The Power System Stabilizer model consists of the Gain block, Washout block and the Phase compensation block. The input to the PSS is the rotor speed deviation and the output is the supplementary excitation signal given to the Generator Excitation system. Here, Ks, T
1
, T
2
are the
2009 International Conference on Advances in Recent Technologies in Communication and Computing
978-0-7695-3845-7/09 $25.00 © 2009 IEEEDOI 10.1109/ARTCom.2009.213260
2009 International Conference on Advances in Recent Technologies in Communication and Computing
978-0-7695-3845-7/09 $26.00 © 2009 IEEEDOI 10.1109/ARTCom.2009.213260
2009 International Conference on Advances in Recent Technologies in Communication and Computing
978-0-7695-3845-7/09 $26.00 © 2009 IEEEDOI 10.1109/ARTCom.2009.213260
PSS parameters which should be computed using the Conventional Lead lag method and PSO based Stabilizer design. Here Ks represent Gain of PSS, T
1
and T
2
represent the Time constants of the PSS phase compensation Block.
B.
Proposed Problem Formulation
In order to calculate the Optimum value of the PSS parameters for system oscillations damping, the following Eigen value based objective function is taken as in equation (1). [J] =Max{Real (
λ
i) }, (
λ
i)
Є
(
λ
g) (1) where (
λ
i) belongs to the list of Electromechanical mode Eigen values(
λ
g). Real (
λ
i) represents the Real part of the ith electromechanical mode Eigen value. The Main aim is to Minimize this objective function J in order to shift the poorly damped Eigen values to the left hand side of the s- plane for System Stability. The Design problem including the constraints imposed on the various PSS parameters is given as follows
Optimize J
Subject to Ks
min
≤
Ks
≤
Ks
max
(2) T
1min
≤
T
1
≤
T
1max
(3) T
2min
≤
T
2
≤
T
2
max
(4) Typical ranges selected for Ks, T
1
and T
2
are as follows: For Ks [5 to 50], for T
1
[0.1 to 1] and for T
2
[0.1 to 1].This Minimization criterion has been implemented in this work to compute the optimum value of the parameters Ks, T
1
and T
2.
IV.
PARTICLE
SWARM
OPTIMIZATION PSO is an innovative Evolutionary Computation technique developed by Eberhart and Kennedy in 1995, which was inspired by the social behavior of bird flocking and fish schooling [5]. It utilizes a population of particles that fly through the problem hyperspace with given velocities. The position corresponding to the best fitness is called as
Pbest
and the overall best out of all the particles in the population is called
gbest.
At each iteration, the velocities of the individual particles are updated according to the best position for the particle itself and the neighborhood best position[6,7]. The velocity of each agent can be modified by the following equation
+⎟ ⎠ ⎞⎜⎝ ⎛ −+=
+
S Pbest rand C V V
iiW i
k ik k
*.
.
111
⎟ ⎠ ⎞⎜⎝ ⎛ −
S g rand C
i
k best
*.
22
(5) where Vi
k
= Velocity of agent i at iteration k. W = Weighting Function. Cj = Weighting factor. rand = random number between 0 and 1. Si
k
= Current position of agent i at iteration k. Pbest = Pbest of agent i. gbest = gbest of the group. The Current position can be modified by the following equation
V S S
iii
k k k
11
++
+=
(6) V.
SIMULATION
RESULTS The State Space model of Single machine infinite bus system Fig (1) was formulated and the open loop Eigen values was computed for various operating conditions, listed in Table II. The open loop Eigen values reveal that the system is unstable, having poorly damped electromechanical modes of oscillations located in right half of complex s- plane. Also Fig (2) shows the Speed deviation oscillations having large overshoots and huge settling time.
Fig(2). Speed Deviation Response for (0.6, 0.1) Condition without PSS.
The following Parameters are selected for PSO Algorithm implementation. (a). C
1
, C
2
= 1,1 (b) W
max
, W
min
= 1 , 0.5. (c) Swarm Size = 20 (d) Number of Generations = 10 Non linear Simulation based on minimizing the Integral Squared error (ISE) was carried out to show the effectiveness of the PSOPSS in damping the Low frequency Oscillations.
TABLE I OPTIMUM PSS PARAMETERS COMPUTED
S. No [P,Q] Conventional PSS [Ks, T
1
, T
2
] PSO based PSS [Ks, T
1
, T
2
]
1 [0.6, 0.1] [3.5927, 0.6441, 0.1] [26.3319, 0.1, 0.1481] 2 [0.55, 0.1] [3.8544, 0.6412, 0.1] [21.9009, 0.1, 0.1536]
The Optimized PSS parameters play a predominant role in shifting the poorly damped electromechanical modes of oscillations to left half of complex s-plane. Table II shows that the Conventional PSS aid in shifting the poorly damped modes to left plane, also it is clear that the PSO based PSS is best suited in shifting the poorly damped modes to left half of s- plane better than the Conventional method, thus enhancing system stability.
261
261
261
TABLE
II.
EIGEN
VALUES
COMPARITIVE
LIST
S.No Operating Point[P,Q] Open Loop Eigen Values Closed Loop Eigen Values
Conventional PSS PSO based PSS
1 [0.6 , 0.1] 0.0408 ± j 4.8282 -10.1392 ± j 3.7078 -14.7041 ; -0.0497 -0.0011 ± j 3.9086 -7.7453 ± j 6.0887 -14.5042 ; -0.0501 -5.6587 ± j 4.8627 -0.5636 ± j 5.0335 2 [0.55, 0.1] 0.0243 ± j 4.8199 - 10.1227 ± j 3.7399 -14.7041 ; -0.0497 -7.7377 ± j 6.1142 -0.0149± j 3.8938 -13.7322 ; -0.0501 -0.4249 ± j 5.0131 -6.0626 ± j 4.4325 Fig(3) Speed Deviation Response for (0.6,0.1) condition with Conv PSS and PSOPSS.
Fig (3), Fig(4) shows that the Speed deviation and Power angle deviation oscillations are damped in a better manner by PSO based PSS in comparison with the Conventional PSS. The Overshoots and settling time are reduced to a greater extent compared to the open loop response without PSS.
Fig(4) Power Angle Deviation Response for (0.6,0.1)
condition with Conv PSS and PSOPSS.
VI.
CONCLUSION In this paper, the implementation of innovative PSO algorithm provided a better solution to damp the low frequency inertial oscillations observed in the Single Machine Infinite Bus Power System model. The Optimum value of PSS parameters was computed by the PSO algorithm to shift the poorly damped electromechanical modes of oscillations to better positions in left half of s-plane compared to the conventional PSS, thus enhancing system stability. The Non linear simulation results under various operating conditions shows that the Rotor speed and Power angle deviation oscillations are damped out with reduced overshoots and quick settling time.
APPENDIX
Generator : M=9.26, Tdo’ = 7.76 Secs, D=0
x
d = 0.973,
x
d’=0.190, xq=0.550 Excitation : K
A
= 50, T
A
=0.05. Line and Load : R=0.034 , X = 0.997, G= 0.249 B= 0.262,V
t0
= 1.05, P=0.6, Q=0.1 All parameters are in p.u. unless specified otherwise. R
EFERENCES
[1]
C.Y.Chung,K.W.Wang,C.T.Tse,X.Y.Bian and A.K.David “Probabilistic Eigen Value Sensitivity analysis and PSS design in Multimachine Systems,IEEE Transactions on Power Systems,Vol 18,No.4,2008,pp.1439-1445. [2]
H,Ping,Y.W.Kewen,T.Chitong,B.Xiaoyan, “Studies of the improvement of Probabilistic PSSs using Single Neuron model”, Electrical Power and Energy Systems,Vol. 29,2007,pp.217-221. [3]
M.A.Abido , “Pole Placement Technique for PSS and TCSC based Stabilizer design using Simulated Annealing,”, Electrical Power and Energy Systems,Vol.22,2000,pp.543-554. [4]
M.A.Abido,“Robust Design of Multimachine Power System Stabilizers using Simulated Annealing,” IEEE Transactions on Energy Conversion,Vol.15,No.3,2003,pp.297-304. [5]
R.Eberhart and J.Kennedy, “A New optimizer using Particle Swarm theory” in Proc,6
th
International Symposium,Micromachine and Human Science(MHS),Oct 1995,pp.39-43. [6]
B.Zhao,Y.Cao, “A Multiagent based Particle Swarm Optimization approach for Optimal Reactive Power dispatch”,IEEE Transactions on Power Systems,Vol.20,No.2, 2005,pp.1070-1078. [7]
Jong Bae Park,Ki Song Lee,Joong in Shin and Kwang Y.Lee,“A Particle Swarm Optimization for Economic Dispatch with Non Smooth Cost functions”,IEEE Transactions on Power Systems,Vol.20,No.1,Feb 2005,pp.34-42.
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