Abstract：With the improvement of the level of DC transmission and the expansion of the application range, the surface charge accumulation of insulators in DC transmission system has been widely concerned by scholars. In order to suppress the charge accumulation on insulator surface under DC electric field and improve the insulation performance of DC GIS/GIL, accurate measurement of the charge density distribution is a very important step. The inverse calculation of surface charge on insulators is an important step for surface charge density distribution measurement, too. In this paper, based on hybrid Lanczos-Tikhonov method, an inversion algorithm is proposed for “shift-invariant system”. Firstly, the iterative regularization method is introduced, and in each iteration, after projecting the potential-charge transfer matrix to a low-dimensional subspace through Lanczos bidiagonalization, Tikhonov regularization is applied to solve the least squares problem of projection in subspace. At the same time, an adaptive weighted generalized cross validation (A-WGCV) method is introduced to adaptively select the optimal regularization parameter in each iteration. After the iterative calculation is finished according to the iterative stopping condition, the solution of the last iteration is transformed to obtain the complete result of the surface charge density distribution of the insulator. In order to analyze the calculation accuracy of hybrid Lanczos-Tikhonov algorithm, a simulation example is used to simulate the complete calculation process in real measurement. Firstly, the charge density was preset by COMSOL, and the corresponding surface potential distribution was calculated. After the data with different degrees of Gaussian noise are superimposed on the potential distribution data, Lanczos-Tikhonov hybrid algorithm, Wiener filtering method and apparent charge method are used to carry out inversion calculation for this example respectively. The calculation time and inversion image of the three methods are compared in this paper. In addition, the SNR and $\sqrt{\text{PMSE}}$ of the data results obtained by the first two algorithms are analyzed. Analysis shows that the accuracy and computational efficiency of the proposed algorithm in this paper are outstanding. Finally, in order to further verify the correctness of the inversion algorithm, the Lichtenberg figures is used to characterize the real charge distribution on the insulator surface. After negative polarity voltage was applied to the insulator surface by needle electrode, the surface potential of the insulator was measured and inverted by hybrid Lanczos-Tikhonov algorithm, Wiener filtering method and apparent charge method to obtain the charge distribution, which was compared with the Lichtenberg figures. It is proved that the hybrid Lanczos-Tikhonov algorithm can well restore the surface charge distribution of the insulator, and the image contour obtained by the hybrid Lanczos-Tikhonov algorithm is basically consistent with the Lichtenberg image. On this basis, the needle electrode is further used to apply different negative polarity voltage to the insulator surface, and the inversion results of hybrid Lanczos-Tikhonov algorithm are compared with the Lichtenberg image to verify the effectiveness of the algorithm. The experimental results also show that, with the increase of the applied voltage, the polarity of the accumulated charge in the insulator area aligned with the needle electrode will be reversed, and original negative polarity "round spot" charge will become "crescent shape" surrounding the positive polarity charge spot.
毛诗壹, 潘成, 罗毅, 邱宇杰, 唐炬. 基于混合Lanczos-Tikhonov算法的绝缘子表面电荷反演计算[J]. 电工技术学报, 2023, 38(7): 1921-1934.
Mao Shiyi, Pan Cheng, Luo Yi, Qiu Yujie, Tang Ju. Inversion Algorithm for Surface Charge on Insulator Based on Hybrid Lanczos-Tikhonov Algorithm. Transactions of China Electrotechnical Society, 2023, 38(7): 1921-1934.
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2023, Vol. 38 
