Inverse calculation of surface charge based on surface potential measurement

Distribution of surface charge can not be directly measured with current techniques but only be determined by complicate inverse calculations based on the results from indirect measurements. Therefore, we studied methods for the inverse calculation, and presented an improved method on the basis of the method proposed by Ootera and his colleagues. In the improved method, the original twice inverses of the incidence matrix were simplified to a once inverse. The surface charge accumulated on cone-type insulator in the air or the SF₆ gas under DC voltage was calculated using the improved method. The results show that the distribution of the surface free charge obtained with the improved method is the same as that with the unimproved method. Compared with the original algorithm, the improved method can further obtain the density distributions of surface apparent charge and polarization charge. Moreover, it is found that, in the same gas environment, there is a significant difference in the amplitude of surface density between free charge and apparent charge, which is 370 and 530 pC/cm² in the air and SF₆ gas, respectively.