Improved Reverse Algorithm of Surface Charge Density Distribution and Electric Field Distribution Based on Electrostatic Probe

Surface charge accumulation on insulating materials is a major factor that distorts the electrical field and thus reduces the insulation level. Therefore, the phenomenon of surface charge accumulation has drawn more and more attention. In this paper, the relationship between the surface charge density distribution and the output voltage of electrostatic probe was discussed, and an improved algorithm was built to calculate the charge density and electrical field distribution from the output voltage. Two-dimensional Discrete Fourier Transformation (2D-DFT) was used to reduce the amount of calculation by transferring the convolution in spatial domain to multiplication in spatial frequency domain. The algorithm considered the influence of electrostatic probe, and the Wiener filter was employed to reduce the noise. The influence of the meshed size on noise suppression and algorithm's accuracy was studied, and the spatial resolution of this measurement system including the reverse calculation process and the accuracy of algorithm was investigated. The charge density distribution as well as the field distribution was calculated by this improved algorithm, when a lightning impulse voltage was applied to a PMMA plate. The results show that the surface charge density and electric field distribution calculated by this algorithm have a good resolution. The spatial resolution of this measurement system with 1mm gap between the electrostatic probe and the surface of the insulation is 0.3341mm, and the peak-mean square error is only 0.23%. Reduce the size of the meshed unit can effectively suppress the noise and increase the algorithm's accuracy. The improved reverse algorithm has great resolution and accuracy, and can exactly calculate the surface accumulating charge density and electrical field distribution of insulating materials.