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.

中文翻译：

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基于积分方程法的表面电荷反演算法

准确的表面电荷反演可以指导GIS/GIL中绝缘子表面改性的研究。目前的反演算法存在计算成本高、精度低的缺点。在此基础上，提出积分方程法（IEM）来计算变换矩阵。与传统的解析法（AM）相比，IEM计算过程简单。IEM的计算速度比AM快很多。为了抑制IEM中的数值发散，引入了Tikhonov正则化方法，提出了Tikhonov-IEM。对于方形绝缘子，与 IEM 相比，峰值均方误差 (PMSE) 降低了约 40%。然而，Tikhonov-IEM 不适用于盆式绝缘子。因此，引入最小二乘法（LSM）并提出LSM-IEM。对于盆式绝缘子，与 IEM 相比，PMSE 降低了约 30%。最后通过物理测试验证了算法的准确性。