CHAPTER 5 ANALYSIS OF ELECTRIC FIELD AND VOLTAGE DISTRIBUTION

Transcription

1 96 CHAPTER 5 ANALYSIS OF ELECTRIC FIELD AND VOLTAGE DISTRIBUTION 5.1 INTRODUCTION The electric field distribution of polymeric insulator is different when compared to porcelain and glass insulators. Generally the electric field distribution of a polymeric insulator is more nonlinear than that of a porcelain and glass insulator. The reason is that there are no intermediate metal parts in polymeric insulators. Two categories of methods have been used to investigate the electric field distribution along polymeric insulators. These methods can be divided into experimental methods and numerical analysis methods. In experimental methods, capacitive probes, flux meters, dipole antennas and electro-optical quartz sensors can be used as Electric field (Efield) measuring devices to study the electric field distribution along polymeric insulators. The numerical analysis methods can be used to calculate the E-field and voltage distribution (EFVD) along polymeric insulators. etic field problems can be expressed by partial differential equations, which are subject to the associated boundary conditions. There are two different kinds of numerical analysis methods, using either differential equations or integral equations. The first one one is known as the source distribution technique or boundary method. The domain methods include the finite difference method (FDM) and finite

2 97 element method (FEM). The boundary method includes the charge simulation method (CSM), and the boundary element method (BEM).The BEM has disadvantages when compared with FEM. Since the formulation of integral in the case of inhomogeneous and non-linier problems because fully populated system of equations will often occur in BEM thus making the storage requirement and computational time to increase significantly. Since the research task is related to inhomogeneous, non-linear and open boundary problems, the self adaptive FEM is adopted for the study in this dissertation. This chapter discusses the development of FEM model of polymeric insulators that can be used to investigate the E-field and voltage distribution over the clean and polluted insulators with different fog conditions, to investigate the degree of uniformity and heat generated in uniform pollution layer and dry band region. 5.2 FEM MODEL FOR POLYMERIC INSULATOR UNDER DIFFERENT CONDITIONS Polymeric insulators have four major components: fiber reinforced polymer (FRP) rod, polymer sheath on the rod, (c) polymer weather sheds and (d) metal end fittings. In the present work, insulator made with silicone rubber polymeric material is considered for simulation. Dimensions and geometry of the 11 kv and 22 kv polymeric insulators used in the simulation study are shown in Table 5.1 and Figure 5.1. A commercially available software (2D-ELECTRO of Integrated Engineering Software) based on the FEM is employed for the modelling. The 2D triangle element mesh is used and its number varies from to Figure 5.1&5.2 shows the FEM model of polymeric insulators used in the study. This research is to investigate the E-field and voltage distribution (EFVD) of the11kv and 22 kv polymeric insulators at four different surface conditions such as,

3 98 Case 1 : Case 2 : Case 3: Case 4 : Dry and clean insulator Uniform medium pollution layer covered in the insulator surface Dry band of 1 cm introduced in the sheath of the uniformly polluted insulator Insulator under fog condition (i) Case (Fog Hydrophobic classes) FHC1,(ii) case FHC2,(ii) case FHC3 Table 5.1 Geometrical Parameters of Polymeric Insulators 11kV 22kV Total length 276mm 476mm Disc diameter 90mm 90mm No.of Disc 3 6 Creepage distances 323mm 600mm 11kV Polymeric Insulator 22kV Polymeric Insulator: Unit in mm Figure 5.1 Geometry and Dimensions of Polymeric Insulators

4 99 Table 5.2 shows the properties of the materials such as relative permittivity, conductivity of pollution layer and thickness/height of pollution layer, dry band and water droplets used for the FEM modelling of the insulators. The insulator is equipped with metal fittings at both line and ground ends. Table 5.2 Material Properties of FEM Model Properties SIR FRP core Pollution Layer Dry band Air Water droplet Relative Permittivity, ( r ) Thickness/Height - - 1mm/- 1mm/1cm - -/1-5mm Figure.5.2 FEM Model of 11kV & 22kV Insulator Clean and Dry Model, Uniformly Polluted Model

5 100 FHC1 FHC2 FHC3 FHC1 FHC2 FHC3 (i) (ii) Figure 5.3 FEM Model of 11kv Polymeric Insulator (i) Clean Insulator Under Different FHC (ii) Polluted Insulator Under Different FHC 5.3 SOLVING FINITE ELEMENT METHOD An easy way to evaluate the electric field distribution is to calculate electric potential distribution initially and then to calculate field distribution by minus gradient of electric potential distribution. This can be written as follows; E V (5.1)

6 101 E (5.2) ( 0 r ), 0 is air or space permittivity (8.854x ) and permittivity of dielectric material. r is relative The Pois (5.1) in equation (5.2) 2 V (5.3) 2 V 0 (5.4) The two dimensional functional F(v) in the Cartesian system of coordinates can be written as follows; where dv dv F( v) x y dxdy dx dy (5.5) 2 x and y are the x- and y- components of the permittivity in the Cartesian system of coordinates and v is the electric potential. In the case of isotropic permittivity distribution ( = y = y ), the above equation can be rewritten as, 2 1 F( v) v ds 2 (5.6) If the effect of pollution layer conductivity on the electric field distribution is considered, the complex functional and F(v) should be taken as

7 102 2 * 1 * F( v) ( j ) v ds (5.7) 2 * v F ( ) complex potential function. Inside each sub domain a linear dependency of v on x and y is assumed, which gives rise to the first order approximation, v e( e1 e2 e3 m x, y) a a x a y ;( e 1,2,3... ) (5.8) where v e ( x, y) is the electric potential of any arbitrary point inside each subdomain, a e1, a e2, ae3 are the computational coefficients for a triangle element e and m is the total number of triangle elements. The calculation of the electric potential at every node in the total network composed of many triangle elements is carried out by minimizing the function F(v), that is F( vi ) 0 v i ; i 1,2,3,... k (5.9) where k is the total number of nodes in the network. The final matrix expression is where e e e H v Q i, j 1,2 k ij (5.10) ij i j,... H is the stiffness matrix, j v is the unknown potentials vector matrix and Q is the free terms matrix vector. The above matrix equation is solved by iterative methods. i

8 103 The usual finite element analysis would proceed from the selection of a mesh and then to the generation of a solution to an accuracy assessment and analysis. Adaptive procedures try to automatically refine, or relocate a mesh to achieve a solution having a definite accuracy in an optimal way. The computation typically begins with a trial solution generated on a coarse mesh with a low order basis. The error of this solution is evaluated. If it fails to satisfy the prescribed accuracy, adjustments are made with the goal of obtaining the desired solution with minimal error The computer simulation flow chart of this method is shown in Figure 5.4. Input data Geometry, Source, material & Boundary Condition Coarse Mesh (h,p) Solve Coarse Mesh (v c ) New optimal Coarse Mesh Fine Mesh (h/2,p+1) Solve Fine Mesh (v f ) Compute error e v f v c e<0.001 Calculate E and display Figure 5.4 Flow Chart for Simulating Self Adaptive FEM

9 SIMULATION RESULTS Dry and Clean Insulator Figures 5.5 a & b show the equi-potential contours and E-Field contours of 11 kv silicone rubber insulator under clean and dry surface conditions respectively. Similarly Figures 5.6a&b show the equi-potential contours and E-Field contours of 22 kv silicone rubber insulator under clean and dry surface conditions respectively. From the figures, as expected, it is noticed that the potential contours and E-field contours of the clean and dry insulator seem to be without any distortions from high voltage end to the ground end. It is also noticed that the maximum electric field stress is occurring at the triple junction point( high voltage end fitting, SiR and air region). Figure 5.5 Equi-Potential Contours E-Field Contours of 11 kv Silicone Rubber Insulator under Clean Dry Surface Condition

10 105 Figure 5.6 Equi-Potential Contours E-Field Contours of 22 kv Silicone Rubber Insulator under Clean Dry Surface Condition Polluted Insulator Figures 5.7 a&b show the equi-potential contours and E-field contours respectively of 11 kv silicone rubber insulator under uniformly, lightly polluted surface condition. Similarly Figures 5.8a&b show the equipotential contours and E-Field contours respectively of 22 kv silicone rubber insulator under uniformly, lightly polluted surface condition. In general, it can be observed that the potential and E-field contours of the polluted insulators are significantly distorted over the insulator surface from line end to ground end due to the presence of the pollution layer. It is observed that electric field strength is much higher at the junction region between the sheath and the shed than at the middle part of the sheath region. In addition, the E-field contour lines are also concentrated at the tip of the weather sheds to some extent and maximum electrical stress is noticed at the tip of the first shed nearer to high voltage end, when compared with other sheds.

11 106 Figure 5.7 Equi-Potential Contours E-Field Contours of 11 kv Silicone Rubber Insulator under Uniformly, Lightly Polluted Condition Figure 5.8 Equi-Potential Contours E-Field Contours of 22 kv Silicone Rubber Insulator under Uniformly, Lightly Polluted Condition

12 Polluted Insulator with Dry Band Formation Figures 5.9a& b show the equi-potential contours and E-field contours of 11 kv silicone rubber insulator under uniformly, lightly polluted surface condition with dry band formation respectively. Similarly Figures 5.10a&b show the equi-potential contours and E-Field contours of 22 kv silicone rubber insulator under uniformly, lightly polluted surface condition with dry band formation respectively. Dry band for the 11 kv insulator is simulated nearer to high voltage end, whereas for 22 kv insulator it occurs in the middle of the insulator. From the figures, it is observed that the high voltage is shifted to the edge of the dry band located towards the line end and similarly the earth potential is transferred from the ground end fitting to the other edge of dry band. Thus a very high potential is noticed across the dry band. From the E-field contours, it is noticed that the electric field lines are concentrated towards the dry band region and the maximum electric field strength is observed in the dry band region. Since the electric field stress across the dry band exceeds the breakdown stress of air, it leads to the formation of partial arc across the dry band. This partial arc is the root cause for the increase in surface temperature, surface degradation due to thermal stress and finally flashover of the polymeric insulator. In real time situations, the dry band may appear at any place on the surface of the insulator due to the non-uniform leakage current density. Considering this, in the present work, simulation work was carried out with dry band at different locations on the surface of the insulator such as nearer to high voltage end, nearer to ground end and at the middle of the insulator. From the above reported simulation results, maximum electric field strength is calculated for both 11 kv and 22 kv insulators at different surface conditions and it is presented in Table 5.3 From the tabulated results, it is observed that the electric field stress is very much enhanced when the dry band is located nearer to the high voltage end for both 11 kv and 22 kv insulators.

13 108 Figure 5.9 Equi-Potential Contours E-Field Contours of 11 kv Silicone Rubber Insulator under lightly Polluted Condition with Dry Band Formation Figure 5.10 Equi-Potential Contours E-Field Contours of 22 kv Silicone Rubber Insulator under lightly Polluted Condition with Dry Band Formation

14 109 Table: 5.3 The Maximum E-field Strength [MEFS] Condition of insulators MEFS (kv/cm) 11kV 22kV Dry and clean Uniform pollution Uniform pollution with dry band at middle Uniform pollution with dry band at near H.V end Uniform pollution with dry band at near to L.V end Insulator under Fog Condition Under fog conditions in the fog chamber, the water droplets stay on the top surface of the weather sheds and also attach to the undersides of the weather sheds. Occasionally, there are some small and medium water droplets on the sheath surface of the insulators. Three typical cases of the polymeric insulator under different wetting conditions without pollution and with pollution in the fog chamber are illustrated by the photographs shown in Figure Based on the Hydrophobicity classes (HC), they are named as FHC1, FHC2 and FHC3. In this condition only 11kV insulator with half

15 110 FHC1 FHC2 (c)fhc3 (i)clean insulator (ii) Polluted insualtor Figure 5.11 Water Droplet Distributions on the Surface of Polymeric Insulator in the Fog Chamber

16 111 Side has been modelled due to high calculation time and complex design structure. Case FHC1 represents a SiR insulator under early wetting condition in the fog chamber as shown in Figure There are small and medium water droplets on both the top and underside of the shed. There are only one or two droplets on the sheath region of insulator. Case FHC2 represents a SiR insulator under high humidity wetting status, as shown in Figure There are medium size water droplets on top of each shed, on the underside of each shed, and small and medium water droplets on sheath region of the insulator as well. Case FHC3 represents a SiR insulator under high humidity wetting status, which is shown in Figure 5.11(c). There are large size water droplets on top of each shed, small size on the underside of each shed, and small and medium water droplets on sheath region of the insulator as well. The model used for the calculation is shown in Figure 5.3. The equipotential contours and E-field contours along clean and polluted polymeric insulator are calculated and then compared with those of the insulators under fog conditions. The voltage contours are shown in Figure 5.12 for all conditions. The water droplets present in the clean insulator surface make the voltage distribution more linear along the surface when compared to the dry case. The water droplets present in the polluted insulator surface make the voltage redistribution more linear when compared to clean insulators.

17 112 FHC1 FHC2 (c) FHC3 FHC1 FHC2 (c) FHC3 (i) Clean insulator (ii) Polluted insualtor Figure 5.12 Equi-Potential Contours of Polymeric Insulator in Different Fog Conditions The E-field contours are shown in Figure 5.13 for all conditions. The water droplets present in the clean insulator surface makes the E-field distribution nonlinear along the surface compared to the dry case. The water droplets present in the polluted insulator surface make the E-field distribution more non-linear than that of clean insulator. In clean insulator, the maximum E-field occurs in the triple junction point on electrode, air and polymer but in the polluted insulator maximum E-field occurs in the junction region of shed and sheath and also the water droplet present in the surface makes the E-field concentration more on the sheds surface, both on the top and at the under region.

18 113 FHC1 FHC2 (i) FHC1 Clean insulators FHC2 (ii) (c) FHC3 (c) FHC3 Clean insulators Figure 5.13 E-Field Contours of Polymeric Insulator in Different Fog Conditions The typical electric field strength threshold value for water droplet triggered corona is in the range of 5-7 kvrms/cm (weiguo 2001). The calculated maximum E-field is in the range of 4.9 to 5.19 for clean insulators and 5.1 to 6 kvrms/cm for polluted insulators under fog conditions. So it leads to water corona on the surface of polymeric insulators.

19 RESULTS AND DISCUSSION Analysis of E-Field along the Sheath and Tip of Sheds of Insulator The real and imaginary components of E-field strength along the sheath surface of the insulator were also calculated for three different surface conditions (refer case1, 2 and 3). The calculation path (the line A-B shown in Figure.5.6 is 4mm away from the surface of the sheath and starts from the point 0.2 mm above the line end metal fitting. Figures 5.14 and show the real and imaginary parts of e-field distribution along the sheath surface of 11 kv insulator respectively. Corresponding results for 22 kv insulator are shown in Figure 5.15 and. It is observed that the EFVD along the insulator under uniform pollution condition is completely different from the dry and clean insulator. Under polluted conditions, E-field strength in the shed section is larger than middle of the sheath section. In the case of dry band formation conditions, E-field is much higher in the dry band region than other regions. It is also noticed that the imaginary part of EFVD is absent under clean dry surface conditions, whereas it is present under polluted conditions and it may be attributed to the flow of leakage current under polluted conditions. It is important to understand the E-field at the tip of the weather sheds under polluted conditions, because E-field stress enhancement also occurs at the small curvature of the shed under polluted conditions. Figure 5.16 shows the E-field evaluated at the tip of the weather sheds of 11 kv and 22 kv insulators under polluted conditions. It can be seen that the shed very near to the H.V end is subjected to maximum stress under polluted conditions. It is also observed that the electric field stress at the shed tips is higher than the stress at the middle part of sheath region.

20 115 Figure 5.14 E-Field Distribution of the 11 kv Polymeric Insulator Real part, Imaginary part Figure 5.15 E-Field Distribution of the 22 kv Polymeric Insulator Real part, Imaginary part Figure 5.16 E-Field Distribution of the Polymeric Insulator at the Tip of the Shed 11 kv 22 kv

21 Analysis of Voltage Distribution along the Sheath of Insulator The potential distribution along the sheath surface is shown in Figures 5.17& 5.18 Real part of potential in dry and clean conditions is linear between two ends, and there is no imaginary part. In the other two cases the potential distribution curves were different from the case of clean and dry conditions. In uniformly polluted case, the real part of the potential is getting non linear and distribution curve is away from the case obtained for clean and dry condition and imaginary part is presented in the negative side. In the dry band conditions, the real part of the potential is divided into two parts, one is maximum value and (11kV and 22kV) the other one is the minimum value (0kV). Positive and negative imaginary parts are also presented. Figure 5.17 Voltage Distribution in 11 kv Polymeric Insulator Real Part, Imaginary Part Figure 5.18 Voltage Distribution in 22 kv Polymeric Insulator Real Part, Imaginary Part

22 Evaluation of the Degree of Uniformity field and it is defined as (Looms 1997), V (5.11) d * E max where E max = Maximum electric field strength and V= Applied voltage les one to make a comparison of the uniformity of fields formed between two electrodes. The degree of uniformity of the electric field is evaluated at different surface conditions of polymeric insulators and it is reported in Table 5.4. As expected, it is observed that under polluted conditions the uniformity is very less when compared with clean and dry conditions. This confirms that the E-field and voltage distribution (EFVD) in polymeric insulator is highly non-linear at wet and polluted conditions. Table 5.4 The Degree of Uniformity Condition of insulators The degree of 11 kv 22 kv Dry and clean Uniform pollution Uniform pollution with dry band at middle Uniform pollution with dry band near H.V end Uniform pollution with dry band near to L.V end

23 Evaluation of the Heat Generated in the Surface of Insulator As seen from the experimental results given in chapter 2, the magnitude of the leakage current flow during clean and dry surface condition is negligible and therefore the possibility for surface heat generation is very less. Whereas, under polluted conditions, significant amount of leakage current is flowing and it can generate considerable amount of heat on the surface of the insulator. This heat plays a major role in the formation of dry bands over the insulator surface and therefore will lead to partial arcing and surface degradation of the polymeric insulator. When the arcing continues and elongates, it will result in flashover. Therefore it becomes necessary to understand the amount of heat generated in polymeric insulators in order to improve its thermal resistance during manufacturing process. The heat generated by the A.C is given by (Looms 1997), r 2 E f tan Wac (5.12) *10 where E = E max above formula, the heat generated in the surface of the insulator was evaluated and presented in Table5.5. It is observed that more heat is generated when the dry band formation is nearer to high voltage end and therefore the possibility of surface degradation of polymeric insulator nearer to high voltage end is more when compared with other portions.

24 119 Table 5.5 Heat Generated in Polymeric Insulator Condition of insulators Heat Generated W ac (mw/cm 3 ) 11 kv 22 kv Dry and clean Uniform pollution Uniform pollution with dry band at middle Uniform pollution with dry band near H.V end Uniform pollution with dry band near to L.V end Analysis of E-Field and Enhancement Factor under Fog Condition The magnitude of E-field strength along the sheath, top of first shed and under region surface of the insulator was also calculated for three different fog conditions. The calculation path in the sheath region (the dotted line shown in Figure.5.12(i) ) is 1 mm away from the surface of the sheath and starts from the point 0.2 mm above the line end metal fitting. The calculation path in the shed region is 10 mm away from the surface of the sheath and starts from the point 0.2 mm above the top of shed and bottom surface. The calculated E-field for both clean and polluted insulators in the sheath surface with different fog conditions is shown in Figure 5.19.

25 120 Clean insulator Polluted insulator Figure 5.19 Electric Field along the Sheath of the Insulator under Different Fog Conditions The E- field distribution along the sheath surface of the insulator is pretty close for case clean and FHC1. The water droplet present in the sheath makes the E-field non linear than clean and FHC1 between two sheds. In polluted insulator, the pollution layer reduces the non- linearity created by the water droplet and increases field strength at the junction between sheath and shed region, for all the three cases.

26 121 The calculated E-field, for both clean and polluted insulators with different fog conditions at first shed on top region is shown in Figure 5.20 and for under region is shown in Figure 5.21 The E-field distribution along the surface is highly non- linear due to water droplet than clean case. The E-field value in the trip junction point shed surface, in air and water droplet contact point, will increase depending on the size and diameter of the water droplet. In the polluted insulator the E-field value is maximum at the end region of the shed surface, both at the top region and at the under region. In the middle surface region, E-field is pretty close to dry and clean case. Clean insulator Polluted insulator Figure 5.20 Electric Field on the Top of the First Shed under Different Fog Conditions

27 122 Clean insulator Polluted insulator Figure 5.21 Electric Field on the Bottom of the First Shed under Different Fog Conditions Finally the influence of the water droplet in the E-field strength is studied by the field enhancements factor (E.F) value. The E.F values are calculated for all the fog conditions in different regions of the clean and polluted insulators. The values are shown in Figure The E.F values are calculated as follows: E-field strength (0.71kV rms /cm) at the middle surface of the sheath region in clean insulator for case FHC1 is higher than clean case(0.69 kv rms /cm). So the E.F value is 0.71/0.69=1.03. As per the above

28 123 method, the E.F values are calculated for shed joint, top of the first shed middle, top of the first shed end, under the first shed middle and under the first shed end. Clean insulator Polluted insulator Figure 5.22 Electric Field Enhancements Factor on Different Regions of the Insulator under Different Fog Conditions

29 124 From the Figure 5.22, it was observed that E-field values at the middle of the shed, both on top region and under region of cases FHC1,FHC2 and FHC3 are much enhanced than clean insulator due to presence of fog on the surface. But in polluted insulator the E-field values are more enhanced at the end region of the shed surface, than with dry conditions. 5.6 CONCLUSION E-field and voltage distribution (EFPD) along polluted composite insulators have been analyzed in this chapter. This analysis showed that the presence of pollution layer on the surface of polymeric insulator significantly altered the E-field and potential distribution along the length of the insulator. Maximum E-field stress is observed when the dry band formation is nearer to high voltage end of the insulator. Under uniformly polluted conditions without any dry band formation, the electric field stress is concentrated at the junction between the shed and sheath and also at the small radius of curvature of the weather sheds. Reported results also confirm that the electric field enhancement in the dry band region is sufficient to initiate partial arc along the insulator surface. The heat generated on the insulator surface is evaluated and it indicates that the possibility of surface degradation of the polymeric material nearer to high voltage end is high when compared with other sections of the insulator. The water droplets present in the insulator surface will lead to water droplet corona more rapidly in the polluted insulator than the clean insulator. The model developed for the calcualation is based on photographs of insulators undergoing pollution test in a fog chamber.