The 19th International Symposium on High Voltage Engineering, Pilsen, Czech Republic, August, 23 – 28, 2015

COMPOSITE INSULATORS PROFILE OPTIMIZATION USING

PARTICLE SWARM ALGORITHM AND FINITE ELEMENT METHOD

E. M. El-Refaie, M. K. Abd Elrahman and M. Kh. Moha med Faculty of Engineering, Helwan University – Cairo, Egypt

Email: mustafa_ali03@h-eng.helwan.edu.eg Abstract : Insulators are very important element in electric power systems. Composite insulators such as silicone rubber provide an excellent alternative to porcelain and glass in the field of high voltage applications. It has been widely used by power utilities since 1980’s owing to their superior contaminant performances. Electric field stress along the insulators profile is one of the most important factors governing the electrical performance of composite insulator. The main objective of this paper is to improve the electric field distribution of composite insulators by reducing the value of maximum electric field strength, in order to enhance its long term performance. This will be done by modifying the dimensions of already exist practical insulators through an efficient optimization technique. This technique combined Particle Swarm Optimization (PSO) algorithm and Finite Element Method (FEM). PSO algorithm has been implemented using MATLAB program, on the other hand, the electric field strength was calculated by using commercial software package COMSOL Multiphysics that is able to calculate the electric field strength in two and three dimensional problems based on the finite element method. Four insulators of 11 kV with different profiles are used as samples for this study. Several parameters such as shed diameter, shed spacing, shed inclination angle, number of sheds, shed arrangement type and end fitting diameter can be used in order to optimize insulator profiles. Attention was paid to optimize some effective parameters in insulators design including shed diameter, shed spacing and metal end fitting diameter. The insulators profile parameters have been checked after optimization according to IEC/TS 60815-3. The obtained results indicated that the maximum value of the electric field strength can be reduced significantly by using the proposed technique. This work is able to provide theoretical support to design and select the profile of composite insulators in order to obtain a better performance.

1 INTRODUCTION Electrical insulators are essential components in the electric power systems. In the early days, insulators were made of ceramic and glass materials. But in 1963, composite insulators were developed. Spectacular Improvements in design and manufacturing in the recent years have made them attractive to utilities. Composite insulators have many advantages over the ceramic and glass insulators such as good performance in contaminated environments because of hydrophobic nature. Also, the lighter weight, considerably lower cost, easy handling and maintenance free make composite insulator more competitive [1]. The performance of composite insulator depends upon the operating conditions such as electrical, mechanical, thermal and environmental stresses. In this study, the focus was on the electrical stresses represented in the study by the distribution of the electric field strength on the surface of the insulator and which in turn depends on the geometry of the insulator and the materials used in its manufacture. The structure of composite insulators can be divided into the following four major parts: (i) Rod

of fiber reinforced polymer (FRP); (ii) polymer sheath on the rod; (iii) weather sheds of composite materials; (iv) metal end fittings. For most transmission line applications, the dominant direction of the electric field is along the axis of the insulator [2]. High electric field strength at the metallic end fitting will initiate corona and surface electrical discharge that can lead to early degradation, In order to prevent, minimize or at least reduce the discharge activity near the surface of the insulator, it is necessary to control the electric field. Literatures suggest some limits of electric field to avoid the corona discharges; these values were proposed for dry and clean composite insulators, according to [2] as follow:

• on the shed material and surrounding the end fittings: 4.5 kV/cm (rms), measured 0.5 mm above the surface of the sheath;

• internal to the fiberglass rod and the rubber shed material: 30 kV/cm (rms);

• at the surface of the metallic end fittings and corona rings: 21 kV/cm (rms).

In [3] the paper shows that by using two different configurations of end fittings, the electric field strength near the two ends of the composite insulator will decreases for the configuration of large end fitting radius with round edges.

In [4] the paper proposed a new compound mode composed of a composite insulator in series with several units of glass insulators at the conductor side to improve the electrical field distribution of composite insulators. The electrical field and potential distribution are calculated by using FEM for different numbers of glass insulator. Manufacturers can design and produce varied composite insulators with different leakage distances according to the requirement of users by altering the shed array mode or the shed spacing and the shed radius. If the design of insulator profile is unreasonable, it is easy to lead to bridge down between two sheds or even flashover of the whole insulator [5]. Thus from the above mentioned different design of insulators, it is necessary to research for the optimal design of composite insulator in order to guarantee the safety and the reliability of the power grid. 2 THE PROPOSED ALGORITHM In this paper electrical field distribution along composite insulator was calculated by using Finite Element Method (FEM) with the aid of commercial software package COMSOL Multiphysics [6]. The PSO algorithm has been implemented using MATLAB program. Finally, the FEM and PSO are combined to conduct optimization process for the insulator profile structure. The flowchart of the optimization process is shown in Figure 1. 2.1 Particle swarm optimization PSO, proposed by James Kennedy and Russ Eberhart in USA (1995), was basically developed through simulation of bird flocking in two-dimensional space [7]. The optimized variables are shed diameter, shed spacing and end fitting diameter, particle is a candidate solution i.e. each particle is considered to be a solution for the problem. Each particle has two components of xi

(current position) and vi (current velocity). The particle position is defined as the value of the variable in the solution space, while the particle velocity is defined as the change in this value every iteration. These variables are updated until the optimum value of electric field stress is obtained. To discover the optimal solution, each particle changes its searching direction according to two factors, its own best previous experience and the best experience of all other members. Thus, a new generation of community comes into being, which has moved closer towards the best solution, ultimately converging onto the optimal solution. Therefore, the new velocity was obtained as follows:

���� � 1� � � � ����� � � � � ������� ������� � � � �� � ������� � �������

� � ������ !����������

The new position of the particle is obtained by:

���� � 1� � ����� � ���� � 1� Where: "#$%&' = The best position that particle i has ever found (#$%&' = The group’s best position that the neighborhood particles of the ith particle have ever found k = The number of the optimized parameters ) = The constriction factor )+ and ), = Acceleration coefficients -+ and -, = Two random parameters chosen uniformly within interval [0, 1] . = The particle inertia coefficient '&$-= The current iteration '&$-/01= The maximum No. of iterations

Figure 1 : Flowchart of proposed technique for composite insulator profile design After several parameter setting attempts for this particular optimal problem, it has been found that the suitable value of) is set to be 1, )+to 0.6, ), to 0.6, '&$-/01 to 30 iterations, population size to 10. The main objective of PSO algorithm is obtaining the minimum value of the maximum

(1)

(2)

(3)

No

Yes

Stop

Check the stopping

criteria

Start

Initialize swarm optimization algorithm with random

particles

Evaluate the objective function (Emax) for the particles using FEM in

COMSOL Multiphysics

Calculate the velocity and update particle

positions and check the constraints in

MATLAB

Output the best value of (Emax) and the corresponding

optimized parameters

electric field strength on the surface of the insulator by changing the insulator parameters. 2.2 Electric field calculation Generally the electric field values are very high near to the energized and grounded ends of the composite insulators [3]. The electric field distribution of a composite insulator is more nonlinear when compared to ceramic insulators due to the absence of intermediate metal parts which provides a certain degree of stress grading [2,3]. The field distribution can be evaluated using numerical techniques, such as, Finite Difference Method (FDM), Finite Element Method (FEM), Boundary Element Method (BEM) and Charge Simulation Method (CSM) or combination of these methods [8]. In contrast to other methods, FEM takes into accounts for the no homogeneity of the solution region. Also, the systematic generality of the method makes it a versatile tool for a wide range of problems [9-11]. Input parameters for the COMSOL Multiphysics program are the dimensions of insulators, permittivity of the materials and the boundary conditions (potential of metal parts). In this study four different composite insulator profiles of 11 kV were selected to investigate the ability of the proposed technique. The relative permittivity of each domain is listed in Table 1. 2.3 Models parameters

Structural parameters of composite insulator profile are generally including three variables, namely shed diameter, shed spacing and end fitting diameter, and all of them can be defined as optimization variables. The structure of four models before and after optimization are shown in Figure 2, and the values of insulators structure parameters are indicated in Table 2.

The initial dimensions of insulator for model 1 have been taken from ref. [3], while the dimensions of model 2 have been taken from ref. [12]. The initial dimensions of models 3 and 4 have been taken from practical insulators used in the Egyptian electrical grid. The initial values of design parameters, the range of permissible variation of each parameter and the resultant optimum values, calculated by the proposed algorithm, are presented in Table 3. 3 CHECKING OF PROFILE PARAMETERS The insulators profile parameters should be checked after optimization to ensure a good performance of insulators such as avoiding the rain bridging, preventing local short circuiting between sheds, aiding self-cleaning, avoiding pollution traps and controlling local electric field strength. These parameters are checked according to IEC/TS 60815-3 [13].

Table 1: Relative permittivity of each domain for insulator modeling

Material Relative permittivity εr Air background Silicone Rubber FRP Core Forged steel

1 4.3 7.2 106

Figure 2 : Insulators profile (a) before optimization and (b) after optimization. Spacing versus shed overhang (s/p) is the ratio of the vertical distance between two similar points of sheds of the same diameter and the maximum shed overhang. This factor is important for the avoidance of “shorting out” creepage distance bridged by a shed-to-shed arc. Minimum distance between sheds (c) is the minimum distance between adjacent sheds of the same diameter, measured by drawing a perpendicular line from the lowest point of rim of the upper shed to the next shed below of the same diameter. It is very important characteristics for insulator profile evaluation for avoiding shed-to-shed arcing. Creepage distance versus clearance (l/d) where d is the straight air distance between two points on the insulating part or between a point on the insulating part and another on a metal part, and l is the part of the creepage distance measured between the above two points. (l/d) is the highest ratio found in any section. Creepage factor (CF) is the ratio of the total creepage distance to the arcing distance of the insulator. Creepage factor is a global check of the overall density of creepage distance. These design parameters have been calculated and checked as shown in Table 4.

Model 1 Model 2

Model 3 Model 4

(a) (a)

(a) (a)

(b) (b)

(b) (b)

Table 2: Structure parameters of four models of composite insulators

Structure parameters Model 1 Model 2 Model 3 Model 4

Creepage distance (mm) Arcing distance (mm) Sectional length (mm) Core thickness (mm) Shed type No. of sheds

430 180 360 18

Uniform 4

325 190 276 18

Uniform 3

525 188 318 16

Alternating 5

495 188 318 16

Alternating 5

Table 3: Optimization values of design parameters

Models

Optimization parameter s shed diameter (mm) Spacing (mm) End fitting diameter

(mm) Model 1 Model 2 Model 3 Model 4

Min. Max. Init. Optim. Min. Max. Init. Optim. Min. Max. Init. Optim. 80 80

80/50 80/50

110 130

160/130 160/130

85 90

134/105 134/105

94.4 110

106/76 105/75

26 25 35 70

55 60 50

100

43 58 50 100

26.7 37.5 36.5 70

34 34 40 40

60 60 60 60

40 40 46 46

58 58 54 54

Table 4: Calculation of factors of insulator profile design according to IEC/TS 60815-3

Factors

Recommended range

Model 1

Model 2

Model 3

Model 4

Uniform shed

Alternate shed

Init. Optim. Init. Optim. Init. Optim. Init. Optim.

Minimum distance between sheds (c) (mm) Difference of shed overhang (P1-P2) (mm) Spacing versus shed overhang (s/p) Creepage distance versus clearance (l/d) Creepage Factor (CF)

≥ 25

---

≥ 0.8 < 4.5

< 4.5

≥ 35

≥ 15 ≥ 0.8

< 4.5

< 4.5

42

---

1.56

2.21

2.39

26.1

---

0.83

3.56

1.88

56.5

---

1.9

1.98

1.7

36.5

---

0.95

3.07

1.72

46.8

15

0.93

3.67

2.79

35

15

0.96

3.7

2.84

93.6

15

1.87

3.67

2.63

65.5

15

1.83

3.19

2.38

4 RESULTS AND DISCUSSION The maximum value of electric field strength is reduced for all the models after optimization process and the percentage of reduction is approximately ranging from 10% to 17% as indicated in Table 5. Based on the results, in order to improve the electric field distribution on the insulator surface, the optimal shed diameter for models 1 and 2 are 94.4 mm and 110 mm respectively, while models 3 and 4 large per small shed diameter are 106/76 mm and 105/75 mm respectively, these results indicated that the shed diameter of uniform shed models has been increased after optimization process, while the alternating shed models larger and smaller diameters have been decreased after optimization. The optimal shed spacing for models 1, 2, 3 and 4 are 26.7 mm, 37.5 mm, 36.5 mm and 70 mm respectively. These results indicated that the shed spacing for all models has been decreased after optimization. The optimal end fitting diameter for models 1 and 2 is 58 mm and for models 3 and 4 is 54 mm. These results show that for all models

when the end fitting increased the maximum value of electric field is decreased; however the increasing of end fitting diameter is restricted by other considerations. Table 5: Values of maximum electric field strength

Model No.

Emax (kV/cm) Percentage reduction in E max Init. Optim.

Model 1 2.285 1.925 15.77 % Model 2 2.473 2.053 17 % Model 3 1.77 1.524 13.9 % Model 4 1.678 1.528 9.8 %

The distribution of electric field strength on the insulator surface for all models before and after optimization is shown in Figures 3, 4, 5 and 6 respectively, from these figures it is noted that the electric field magnitudes are larger close to the energized and grounded ends of a composite insulator. The electric field distributions along the creepage distance of insulator for all models before and after optimization are shown in Figures 7, 8, 9 and 10 respectively. The energized end is subjected to the highest field magnitudes. The maximum electric field strength is reduced after optimization for all models.

Figure 3 : Electric field distribution of model 1 (a) before optimization and (b) after optimization

Figure 4 : Electric field distribution of model 2 (a) before optimization and (b) after optimization

Figure 5 : Electric field distribution of model 3 (a) before optimization and (b) after optimization

Figure 6 : Electric field distribution of model 4 (a) before optimization and (b) after optimization

Figure 7 : E-field distribution along creepage distance of model 1 before and after optimization.

Figure 8 : E-field distribution along creepage distance of model 2 before and after optimization.

Figure 9 : E-field distribution along creepage distance of model 3 before and after optimization.

Figure 10 : E-field distribution along creepage distance of model 4 before and after optimization.

(a) (b)

(b) (a)

(b) (a)

(b) (a)

5 CONCLUSION In this paper, the optimal design of the insulator shed diameter, spacing and metal end fitting diameter has been studied, in order to reduce the maximum value of the electric field strength inside and outside the composite insulator. The values of the above mentioned optimized insulator parameters have been checked according to IEC/TS 60815-3 and their values are within the recommended ranges.

Four different models of composite insulator profiles of 11 kV were selected to be optimized by using FEM combined with PSO algorithm. The electric field distribution for all models has been improved and the maximum reduction percentage in the electric field strength was around 17%. The numerical results show that increasing of metal end fitting diameter and decreasing of the spacing between sheds can improve the electric field distribution. With respect to the shed diameter, increasing it for uniform shed models and decreasing it for alternating shed models leads to improving the electric field distribution. This contradiction may be due to the original dimensions of insulators before optimization. Generally the relation between shed diameter and electric field distribution depends on insulator structure and shed arrangement type. The electric field distribution of models 3 and 4 is better than that of models 1 and 2; this may be due to the shape of end fitting, the large value of creepage distance as well as the number and arrangement of alternating sheds. According to the research results, it has been found that combined method of FEM and PSO could be effective in optimization of insulator structure.

ACKNOWLEDGMENTS

Many thanks and appreciations are due to Dr. Mohamed Abdellah and UMR Industries staff (factory of composite insulators in Industrial zone Badr City, Cairo, Egypt) for the supporting and providing the details of practical composite insulators data.

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