Optimization of Insulator Shape Using GA and HGAPSO Methods

 Abstract—The flashover voltage of insulator is relative to the distribution of the electric field. The distribution of the electric field on the insulator is contributed to the shape of insulator. For this, we must optimize the shape of insulator. In this paper, we use FEM, GA and HGAPSO for optimizing the shape of insulator. The tangential electric field and the area of insulator are optimized by GA and HGAPSO. Then, the results obtained from GA and HGAPSO are compared with each other.


I. INTRODUCTION
HE flashover voltage is an important parameter of insulator.The low flashover voltage may be caused to electric discharge.The flashover voltage of insulator can be increased by optimizing the shape of insulator.Numerical methods for optimizing the shape of insulator are presented in [1][2][3].These methods are complex and may find local optimum.
CSM [4][5][6][7] and DAGA [8][9] are used in [10] for optimizing the shape of Taiwan power insulator.CSM which is used for computing the tangential electric field is not accurate.DAGA which is used for optimizing is relative to initial population.For this, the final shape of insulator is similar to the initial shape.In this paper, the average and variance of tangential electric field and the area of insulator are optimized by GA and HGAPSO.Finite element method (FEM) [11] is used for computing the tangential electric field of insulator.At the end, the optimal design obtained from GA and HGAPSO are compared with each other and with original Taiwan power company insulator.

II. OBJECTIVE FUNCTION
In this paper, the shape of Taiwan power company insulator which is shown in Fig 1 has been optimized.41 control points are considered for optimizing the shape of insulator.Search space of optimization is between ±1cm of the initial state of control points.Cubic spline function is used for smoothing the M. R. SALIMAN is with the Department of Electrical Engineering, Faculty of Shahid Abbaspour, Shahid Beheshti University, Tehran, Iran (email: bmsalimian@gmail.com).
H. JAVADI is with the Department of Electrical Engineering, Faculty of Shahid Abbaspour, Shahid Beheshti University, Tehran, Iran (e-mail: javadih@yahoo.com).shape of insulator.Tangential electric field and the area of insulator are optimized.The objective function is presented in [1]. (1) is the area of insulator shown in Fig 1 .shows the altitude of the jth control points on the upper surface of insulator.
shows the altitude of the jth control point on the lower surface of insulator.
shows the number of extremes on the lower surface of insulator.
is the tangential electric field of the control point i.
Optimization of Insulator Shape Using GA and HGAPSO Methods M. R. Salimian, and H. Javadi T Fig. 1 the original shape of Taiwan power insulator [10] III.HYBRID GA AND PSO (HGAPSO) This method is compound of GA and PSO.PSO is replaced by mutation in GA and change the position of population members by ( 8). ( is the inertia of the nth generation which is changed from 0.9 to 0.4. is a random vector.
is the best member of population. is the position of the jth member in the nth generation. is a constant which is considered as 2.
IV. SIMULATION RESULT MATLAB PDE toolbox [12] is used for computing the tangential electric field of insulator by FEM method.HGAPSO and GA which are coding by MATLAB are used for minimizing objective function.The population size, crossover fraction and the maximum number of generation are considered as 61, 0.8, and 30, respectively.The permittivity of dielectric and the voltage of electrode are considered as 2.5 and 1 p.u, respectively.
The results obtained from HGAPSO and GA for cm and are presented in

V. CONCLUSION
The minimum of objective function obtained from HGAPSO is smaller than GA.This shows the total coefficients of average and variance of electric field and the area of insulator obtained from HGAPSO is smaller than the result of GA.

Fig 2 and 3
, respectively.The optimal design of of insulator obtained from GA and HGAPSO which are shown in Fig4-5are compared with original insulator in Fig 6-7, respectively.The minimum of objective function obtained from HGAPSO is equal to 14.3268 which is smaller than the results obtained from GA that is equal to 14.6213.The average and variance of tangential electric field and the area of insulator are compared for different cases in Table1 .

Fig. 2
Fig.2 the minimum values of objective function obtained from HGAPSO

Fig. 8
Fig.8 the minimum values of objective function obtained from HGAPSO

TABLE II .
COMPARISON OF THE RESULTS OBTAINED FROM GA and HGAPSO WITH THE VALUES OF ORGINAL INSULATOR