High-order fast integration for earth-return impedance between underground and overhead conductors in Matlab

Abstract

Purpose – The earth-return mutual impedances between underground and overhead conductors can be expressed by Pollaczek integrals. Many efforts have been exerted to calculating this kind of integrals. However, most of numerical methods turn out to be time-consuming as integrands become highly oscillatory and strongly singular. Therefore, efficient algorithms should be devised. The paper aims to discuss these issues. Design/methodology/approach – The paper separates the singularity from the whole integral and couple with the singularity and oscillation, respectively. A sinh transformation is applied for the finite part and complex integration method is used to calculate the tail. Findings – Numerical experiments show that the given method shares the property that the stronger the singularity and the higher the oscillation, the better the accuracy of the calculation. Originality/value – The sinh transformation is first proposed to calculate Pollaczek integrals. This efficient algorithm can be used to evaluate mutual impedances between conductors. Also, it provides a new aspect of the research on fast calculation of Pollaczek integrals and Sommerfeld integrals.