Inversion Algorithm of Insulator Surface Charge Density Based on Hybrid LSMR Algorithm for Shift-Variant System

The surface charge accumulation of solid insulating materials can easily cause flashover along the surface, which is an important factor that must be considered in the design of the insulation system of ultrahigh-voltage direct current (UHVDC) power equipment. Therefore, it is very important to accurately obtain the surface charge distribution of solid insulating materials. In this article, a surface charge inversion method based on a hybrid least squares minimal residual (LSMR) algorithm is proposed, which is suitable for shift-variant systems. The algorithm projects the original potential-charge relationship matrix into the Krylov subspace with increasing dimensions through the Golub–Kahan (GK) bidiagonal process. Tikhonov regularization method is used to solve the LSMR subproblem, which greatly simplifies the computational complexity. The regularization parameters are selected by a modified adaptive weighted generalized cross-validation (MA-WGCV) method. The computational accuracy of the algorithm is discussed in detail through a simulation example and compared with the hybrid LSQR A-WGCV method and the Wiener filter method. Finally, the reliability and effectiveness of the algorithm are verified by electrostatic probe measurement and dust map method.