Proof and Derivation of Explicit Rational Polynomial Solution to the Voltage Distribution Problem along the Suspension Insulator String

This paper deals with the analytical solution to the problem of determining the voltage distribution along the suspension insulator string composed of contaminated uniform disks and having uniform grading ring or line capacitance. Recurrence relations describing the voltage distribution were formulated based on the equivalent lumped circuit of the insulator string and explicit solutions in rational functions were derived. Formulae for calculating the voltage distribution and the string efficiency, which take simpler forms in the absence of contamination and guard ring, were obtained and proved by induction. The numerator and denominator of the rational functions were shown to be special polynomials with binomial coefficients. Furthermore, generating functions for these polynomials were also derived.