Computation methods in simulation of the dielectric behavior of non uniformly polluted insulators

This chapter deals with the dielectric behavior of non-uniformly polluted insulators by means of a mathematical procedure based upon well known models, a model developed by the authors of the chapter and using available own experimental data. The surface of the insulator is considered to be non-uniformly contaminated, since the pollution layer is treated to follow different functions of distribution. The distribution of the pollution layer is determined according to two methods : i) the insulator is divided into two major parts, each one considered to be uniformly contaminated and ii) the pollution layer of the insulator is considered to be distributed across the creepage distance according to a mathematical function. Thereafter, the critical voltage of the insulator is defined under the specified distribution of the pollution, by means of the above mentioned procedure and using only the geometric dimensions of the insulator, the arc constants and the pollution severity. In this chapter is presented the dependence of the critical voltage upon the distribution of the pollution layer and the total deposit on the insulator. Furthermore a curve fitting procedure is developed in order to determi ne a simple analytical correlation between the critical voltage and the distribution of the pollution layer as well as the total deposit of the insulator. Diagrams show the variation of the coefficients of the curve fitting formula upon basic insulator characteristics. Introduction A major problem of the insulation systems is the accumulation of airborne pollutants due to natural, industrial, or even mixed pollution, during the dry weather period and their subsequent wetting, mainly by high humidity. This problem was the motivation for the installation of a test station in order to perform laboratory tests on artificially polluted insulators. The experiments carried out, using either the salt fog method or the solid layer cool fog method, provided us with numerous experimental data (maximum withstand voltage versus pollution, ratio between creepage distance and minimum flashover voltage versus pollution, maximum withstand salinity at a given applied voltage, leakage current, etc.) for several insulator types. The above experimental results permitted the evaluation of the arc constants A, n and of the surface conductivity Xs of the insulator with a quite high accuracy, by means of a mathematical procedure. It has been proved that, the computed values of A, n and Xs are independent of the insulator type and the kind of pollution. In this chapter, the dielectric behavior of stab type insulators is investigated, by means of a computer model described below and using the calculated values of A, n and Xs. Generalised Model of the Polluted Insulator The most simple model for explanation and evaluation of the flashover process of a polluted insulator consists of a partial arc spanning over a dry zone and the resistance of the pollution layer in series (Fig. 1). Fig. 1: Equivalent circuit of polluted insulator. The applied voltage U should satisfy the following equation : ( ) ( ) U I r x r L x a 0 = ⋅ ⋅ + ⋅ − where x is the length of the arc, L is the creepage distance of the insulator and I is the leakage current. ra is the resistance per unit length of the arc: r A I a (n 1) = ⋅ − + where A and n, are the arc constants, which has been determined with a quite high accuracy. The values of A, n were found to be : A = 131.5, n = 0.374 independently of the type of insulator and the kind of pollution. r0 is the resistance per unit length of the pollution layer defined by the formula: r 1 D X 0 d s = ⋅ ⋅ π where Xs is the surface conductivity and Dd is the equivalent diameter of the polluted insulator. Xs is given versus the equivalent salt deposit density C (ESDD), by the formula: ( ) X 369.05 C 0.42 10 s 6 = ⋅ + ⋅ − Xs is obtained in Ù and r0 in Ù / cm, for C expressed in mg / cm and Dd in cm. The equivalent diameter Dd of the insulator is defined as follows: D L K d s = ⋅ π where Ks is the coefficient of the insulator shape : ( ) K dl D l s 0 L = ⋅ ∫ π D(l) is the diameter of the insulator, varying across its creepage distance L. At the critical condition, when the partial arc is developed into a complete flashover, current I obtains its critical value Ic which is given by the formula: