Surface charge inversion algorithms based on integral equation method

Accurate surface charge inversion can guide the research on surface modification of insulators in GIS/GIL. The current inversion algorithms have disadvantages of high computational cost and low accuracy. Based on that, the integral equation method (IEM) is proposed to calculate the transformation matrix. Compared with the traditional analytical method (AM), IEM has a simple calculation process. The calculation speed of IEM is much faster than that of AM. To suppress the numerical divergence in IEM, the Tikhonov regularisation method is introduced and Tikhonov-IEM is proposed. For square insulators, compared to IEM, the peak-mean square error (PMSE) is reduced by about 40 percent. However, Tikhonov-IEM is not suitable for basin insulators. Therefore, the least square method (LSM) is introduced and the LSM-IEM is proposed. For basin insulators, compared to IEM, the PMSE is reduced by about 30 percent. Finally, the accuracy of the algorithms is verified by physical tests.