Fast evaluation of generalized Sommerfeld integral and the mutual impedance calculation between overhead conductors and underground conductors

An efficient approach to calculate the generalized Sommerfeld integral (GSI), which is based on the discrete complex image method, is presented. GSI is separated to the sum of two terms, one is the approximate value obtained from an analytical expression by means of Prony's method, the other is an emendatory integral acquired by an adaptive quadrature. The emendatory integral kernel is the difference between the original and the asymptotic integral kernel and converges very fast. The validity of the method herein in proved by the numerical solution of the mutual impedance between overhead power lines and underground telecommunication lines. It is shown, compared with the conventional integration method, that the method herein can increase the calculation efficiency more than 20 times.