Comparison of Electrostatic Field Calculation in Rod-plane Electrode Using Analytical and Finite Element Methods

In order to understand the behavior of arc inception and its transient propagation till complete breakdown across an insulator it is necessary to find out the maximum electric field " E_max ", at the arc tip in an air gap. The most widely used model is the rod-plane electrode configuration. Due to the strong non-uniformity of the electrostatic field distribution in this electrode configuration, it is impossible to derive an equation by using conventional electromagnetic methods such as Laplace's equation to find E_max. In fact, there is only one well-known analytic method, Roy's equation, which is commonly used for a rod-plane system to calculate E_max, i.e. by solving Laplace's equation based on a parabolic approximation. In this paper, the validity of the results obtained by Roy's equation is discussed and its results are compared with those obtained by finite element methods. It will also allow obtaining a better spectrum of the rod electrode system field distribution.