Multi-resolution complex image method of horizontal multilayer earth

In order to improve numerical performance of grounding computation of horizontal multilayer earths, a new type of complex image method has been presented. A closed form expression of Green's function with arbitrary soil parameters, source/observation position has been derived. The infinite value of coefficients A/B in Green's function has been obtained by derived closed form expression. Though numerical value of A/B can be obtained by symbolic algorithms, GNU multiple precision algorithms provides a more simple and reliable way to solve the linear equations of A/B. Then, multi-resolution complex image (MRCIM) method was presented for improvement on both stability and accuracy in numerical grounding computation of horizontal multilayer soils. MRCIM consists of adaptive sampling, decomposition of sampling space, and automations of complex image method approximation. The formula of numerical error by MRCIM has been derived. The validity of MRCIM has been proved by comparative cases. Numerical results show that, during the earth surface potential (ESP) calculation for HVDC transmission earth-return current, DC grounding electrodes can be treated as a current point when observation point is away from over 10 times of dimension of electrodes.