Inversion algorithm to calculate charge density on solid dielectric surface based on surface potential measurement

Charge accumulation on a solid dielectric surface is one of the critical concerns for the design and optimization of the insulation system in a high-voltage power equipment, since it will lead to the overstress of electrical insulation. Therefore, it is important to obtain the charge density distribution on a solid dielectric surface with high accuracy. The acquisition of surface charge for insulators requires multipoint potential measurements to establish the inverse calculation for the determination of an unknown charge distribution. Up to now, extensive studies have been conducted on this subject; nevertheless, the methods are either too complicated and time consuming, or only applicable for specific arrangements, or with poor accuracy. In this paper, the problem is divided into two categories, i.e., shift-variant system and shift-invariant system, and the basic principle of an improved inversion algorithm is interpreted to solve the problem. The 2-D Fourier transform and Wiener filter techniques are employed in the algorithm for shift-invariant system thus the relationship between potential and charge density can be processed in spatial frequency domain, which tremendously simplifies the conventional procedure. The accuracy and resolution of the algorithm are discussed in detail with the aid of numerical examples. In the end, experiments are conducted and the effectiveness of the algorithm is verified.