 Open Access
 Total Downloads : 320
 Authors : Le Anh , Nguyen Minh Tam , Le Trong Nghia , Quyen Huy Anh
 Paper ID : IJERTV6IS110021
 Volume & Issue : Volume 06, Issue 11 (November 2017)
 Published (First Online): 03112017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Optimal Power System Stabilizer Parameters Tuned by Cuckoo Search Algorithm
Le Anp, Nguyen Minh Tam1, Le Trong Nghia1, Quyen Huy Anp
1Faculty of Electrical and Electronics Engineering, HCMC University of Technology and Education Hochiminh city, Vietnam
AbstractThis paper presents the application of the Cuckoo Search algorithm (CS) to optimize the PSS parameters. PSS input is the speed deviation, the output signal to supply the automatic voltage regulators (AVR). The data to train is implemented in all the different operating conditions of the analysis model. The simulations are performed using the tool Simulink/Matlab. The results were compared with the PSS optimum algorithm (PSO), which showed that the performance of the proposed PSS was better than the PSSPSO [10].
Keywords Power system stabilizer; Automatic voltage regulators; Simulink/Matlab;Cuckoo Search algorithm.

INTRODUCTION
Power System Oscillations deals with the analysis and control of low frequency oscillations in the 0.23 Hz range which are a characteristic of interconnected power systems. These oscillations tend to die out automatically, but some of these may persist for a longer time causing power transfer impossible over the weak transmission lines.[1]
In early phase of 1960s, the fast acting, highgain automatic voltage regulators (AVR) were applied to the generator excitation system which inturn invites the problem of low frequency electromechanical oscillations in the power system. The device connected to generator excitation to control the oscillations were termed as power system stabilizer. It adds a stabilizing signal to AVR for modulating the generator excitation such as to create an electric torque component in phase with rotor speed deviation, which increases the generator damping [2]. Conventional PSS are designed using the theory of phase compensation in frequency domain and it can provide effective damping performance only for a particular operating condition and system parameters. [3].
Recently, optimization algorithms have been applied to PSS design such as Genetic Algorithm(GA)[6],Simulated Annealing (SA) [7], Tabu Search (TS) [8] and Particle Swarm Optimization (PSO) [9].The applications of these methods provide some degree of robustness to variation in system parameters, configurations and wide range of loading
In this paper, CS algorithm is proposed for optimal designing of PSSs parameters. A single machine power system is considered as case study and embedded with PSS. The parameters of the proposed PSS are tuned by using the proposed algorithms. Simulation results and performance indices demonstrate the robustness and relative stability of the CSPSS, which is promising with NoPSS and PSOPSS over a different operating condition to reduce low frequency oscillations.
The structure of the article: In Section 2, the modeling of power system under study, which is a SMIB power system with a PSS, is presented. The Cuckoo search algorithm which is used to optimize the PSS controller parameters is introduced in section 3. Part 4 presents the research results and conclusions are given in Section 5.

POWER SYSTEM UNDER STUDY
The SMIB power system shown in Fig. 1 is considered in this study. The synchronous generator is delivering power to the infinitebus through a transmission line . In Fig. 1, Vt and Eb are the generator terminal and infinite bus voltage respectively.
Fig. 1. Singlemachine infinitebus power system
Modelling the Synchronous Generator Infinitebus Power System.
The synchronous generator is represented by model 1.1,
i.e. with field circuit and one equivalent damper on qaxis. The machine equations are [10]:
d (S S )
conditions. These methods have problem of premature convergence, slow convergence and to be trapped in local optima to obtain the optimum solution.
CS is a metaheuristic search algorithm which is recently developed by Yang and Deb in 2009 [11, 12]. This novel algorithm has been shown to be very effective in solving
dt B m mo
dSm 1 D(S dt 2H
m Smo ) Tm Te
(1)
(2)
continuous optimization problems.
dE'
1 E'

(x
x' )i E
q
do
dt T'
q d d d fd
(3)
dE'
d
1 E' (x x' )i
above parameters need to be finetuned, which is a time consuming job. To compare the proposed PSO controller
d q q q
qo
dt T'
(4)
design with the best possible performance of CPSS, inspired by [10], Cuckoo search (CS) is used in this paper to find a good
The electrical torque Te is expressed in terms of variables
E' d , E' q , id and iq as:
CPSS design.
T E' i E' i (x' x' )i i
e d d q q d q d q
(5)
For a lossless network, the stator algebraic equations and the network equations are expressed as:
E' x' i v
Fig. 2. Structure of CPSS suggested by IEEE Std. 421.5

Objective Function
q d d q
(6)
The system electromechanical oscillations are reflected in
E' x' i v
terms of rotor speed deviations.
d q q d
(7)
v x i E cos
Fitness e2 (t)dt
q e d b
(8) 0
(12)
vd xeiq Eb sin
(9)
Here, e (t) represents the error deviations in generator speed (). The objective is to minimize, so that the integral of the
Solving the above equations, the variables id and iq can be obtained as:

x
x
i
b q
E cos E'
d '
e d (10)
b q
E sin E'

x
x
iq '
e q (11)
NOMENCLATURE
Rotor angle of synchronous generator in radians Sm Generator slip in p.u.
Smo Initial operating slip in p.u.
B Rotor speed deviation in rad/sec Tm Mechanical power input in p.u. Te Electrical power output in p.u. Efd Excitation system voltage in p.u. Vt Generator terminal voltage
i i
Eb Infinitebus voltage
squared error deviations are minimized for better stability of the system.


Proposed Metaheuristic CS algorithm
Cuckoo search (CS) is a Bio inspired optimization algorithm proposed by (Yang and Deb, 2009). It is inspired by the obligate brood parasitism nature of cuckoo species along with the Levy flight behavior of birds and flies in nature. Levy flight represents the flight behavior of animals and birds for food search . The cuckoo species lay their eggs in the nests of other host birds. If a host bird discovers the eggs are not its own, it will throw away these eggs or build a new nest elsewhere.
The following rules will describe the CS algorithm effectively.

Each cuckoo lays one egg at a time, and will put its egg in the nests, chosen randomly.

The best nests with good quality of eggs (potential solutions) will be carried over to next generations.

The number of host nests is fixed, and a host bird will discover an egg with a probability Pa (between 0 and 1).

When generating new solutions x(t+1) ,a Levy flight is performed based on the equation(14).
H Inertia constant
D Damping coefficient
xt 1 xt
Levy
(13)
Tdo Open circuit daxis time constant in sec Tqo Open circuit qaxis time constant in sec xd daxis synchronous reactance i p.u.
where a > 0 is the step size which should be proportional to the scales of the optimization problem. The product means entry wise walk during multiplications. LÃ©vy flights essentially provide a random walk while their random steps are drawn from a LÃ©vy distribution for large steps.


OPTIMIZATION OF CPSS PARAMETERS USING
Levy :
u t1 , (1 3)
(14)
CUCKOO SEARCH
Figure. 2 shows the typical block diagram of CPSS recommended by IEEE [3]. Usually the parameters of the two lead lag compensator blocks are the same (T1= T3, T2=T4), thus the tunable parameters of CPSS are T1, T2, T5, T6, and Kpss. To design a CPSS with good damping performance, the
This has an infinite variance with an infinite mean. Here the steps essentially form a random walk process with a power law steplength distribution with a heavy tail. Some of the new solutions should be generated by LÃ©vy walk around the best solution obtained so far, this will speed up the local search.
However, a substantial fraction of the new solutions should be generated by far field randomization and the locations should be far enough from the current best solution, this will make sure the system will not be trapped in a local optimum.
The proposed CS algorithm implemented in this paper to obtain the optimal damping controller parameters is given as follows:
Step 1: Specify the various parameters involved for CS algorithm implementation (i.e.) number of nests, minimum and maximum limits for PSS parameters (Ks,T1 and T2), number of generations, worst nests probability, termination criteria etc.
Step 2: Initialize a population of n host nests in the problem space.
Step 3: Evaluate the fitness function (Pi) for the randomly selected cuckoo (i) by Levy flights.
Step 4: Choose a nest j among available nests randomly and replace j by new solution, if the fitness (Pi) is greater than fitness (Pj).
Step 5: If the termination condition is reached, then optimal value of PSS parameters is equal to those obtained in current generation, otherwise go to step 6.
Step 6: Abandon a fraction of worse nests with probability
Fig. 3. SIMULINK model of SMIB with PSS
Pa.
Step 7: Repeat steps 36, until the termination criterion is
met.
The cuckoo search algorithm is easier to implement
and it provides the global solution required for parameter optimization in complex engineering problems. In this paper, the cuckoo search algorithm provides an optimal solution for the damping controller parameters, so that the system stability is enhanced to a greater extent possible.
TABLE I. OPTIMIZED PARAMETERS CS PSS AND PSO PSS [10]
Structure
Kpss
T1
T2
T5
T6
CSPSS
4.705
4.174
0.259
1.336
4.259
PSOPSS[10]
0.812
2.022
0.231
0.458
0.411

RESULTS AND SIMULATIONS
In order to simultaneously tune the parameters of the PSS, as well as to assess their performance and robustness under wide range of various fault disturbances, the MATLAB/SIMULINK model of the example power system shown in Fig. 1 is developed using equations (1)(11). The developed MATLAB/SIMULINK model of synchronous generator with PSS is shown in Fig. 3. The SIMULINK model for calculation of id , iq , E' d , E' q and Pe is shown in Fig. 4.
Fig. 4. SIMULINK model for calculation of id , iq , E' d , E' q , E fd and P
TABLE II. PSO AND CSO PARAMETERS IMPLEMENTED FOR CONTROLLER DESIGN
No
PSO Parameters
CS Parameter
1
Swarm Size (n)
70
Number of nests (n)
30
2
No of
Generations
10
No of Generations
10
3
No of variables
(nd)
5
No of variables (nd)
5
4
rand1 and rand2
rand(nd,n)
Worst nests
probability
0.5
5
Weighting function Wmax and
Wmin
0.2
Step size
Variation
6
Weighting factor
C1,C2
0.1, 0.1
Levy flight(,)
1.5, 0.01
7
Termination
Method
Maximum
Generations
Termination
Method
Maximum
Generations
In the following section, the CSoptimized CPSS is compared with optimized PSS with PSO and CPSS under two kinds of operating conditions, which are
Case 1, A three phase fault is applied at the generator terminal busbar at t = 1 sec and cleared after 5 cycles the impedance of the transmission line between the generator and infinite buses changes from Xep=0.6 to Xep=0at 1s.
Case 2, the operating point changes from Pg=0.6p.u.to Pg=0.3p.u.at 1s and Pg=0.3p.u. to Pg=0.5p.u. at 10s.
The comparisons of simulation results for the two cases are shown in Figs 5 – 10. In these figure, the redline represents the simulation results without stabilizing control No PSS, the black line represents the simulation results for PSO based power system stabilizer PSOPSS, and blue line for the proposed CS based power system stabilizer CSPSS.
System data: All data are in pu unless specified otherwise. Generator: H = 3.542, D = 0, Xd=1.7572, Xq=1.5845,Xd
=0.4245, Xq =1.04, Tdo = 6.66, Tqo=0.44, Ra=0, Pe=0.6,Qe=0.02224, 0=44.370.
Exciter: KA=25, TA=0.025 s Transmission line: Xe=0.6, G=0, B=0;

Comparison of system response for Case 1
Fig. 5. Variation of electrical power Pe : Case1
Fig. 6. Variation of speed deviation : Case1
Fig. 7. Variationof power angle :Case1

Comparison of system response for Case 2
Fig. 8. Variation of electrical power Pe : Case2
Fig. 9. Variation of speed deviation : Case2
Fig. 10. Variationof power angle : Case2


CONCLUSION
In this paper, CS algorithm is proposed for optimal designing of PSSs parameters. The PSSs parameters tuning problem is formulated as an optimization problem and CS algorithm is used to seek for optimal parameters. Simulation results confirm the robustness and superiority of the proposed controller in providing good damping characteristic to system oscillations over a wide range of loading conditions and short circuits. Moreover, the proposed CSPSS demonstrates its effectiveness than others via different performance indices.
ACKNOWLEDGMENT
This research was supported by Ho Chi Minh City University of Technology and Education under a research at the Power System and Renewable Lab.
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