From Surface Potential to Surface Charge: An Inversion Algorithm for Shift-Variant System Based on Hybrid LBD-Tikhonov Method

The surface charge accumulation at a gas-solid interface distorts the local electric field and in turn leads to surface flashover, which restricts the development and application of high-voltage direct current (HVDC) gas-insulated switchgear (GIS)/gas-insulated transmission line (GIL). Surface charge inversion is the premise of studying surface charge accumulation because it provides a tool to obtain surface charge distribution after measuring surface potential distribution. In this article, on the basis of an iterative regularization technique, a surface charge inversion algorithm based on hybrid Lanczos bi-diagonalization (LBD) and Tikhonov regularization was constructed for a shift-variant system. After constructing the least squares (LS) problem for charge inversion, the LS problem was projected to a Krylov subspace with a smaller dimension by the LBD method and Tikhonov regularization was applied to solve the projected problem at each iteration. Moreover, the adaptive weighted generalized cross-validation (A-WGCV) method was adopted to choose the regularization parameters automatically for the projected problem. The implementation progress and performance of the hybrid LBD-Tikhonov algorithm were discussed in detail with the simulated examples, and the efficiency and accuracy were compared with the charge simulation method and Wiener filter method. At last, the effectiveness and reliability of the algorithm were verified by the experiment and dust figure. This methodology improves the computational efficiency of surface charge inversion and the selection of regularization parameters, which is beneficial to the development of surface charge measurement technology.