Fast and high-precision calculation of earth return mutual impedance between conductors over a multilayered soil. Issue 3 (8th May 2018)

• Record Type: Journal Article
• Authors: Ma, Junjie
• Is Part Of: Compel. Volume 37:Issue 3(2018)
• Page Start: 1214
• Page End: 1227
• Publication Date: 2018-05-08
• Subjects: Pollaczek integral -- Complex integration method -- Highly oscillatory integral -- Levin's method -- Transformed Clenshaw–Curtis quadrature; Electrical engineering -- Data Processing -- Periodicals; Electrical engineering -- Mathematics -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Data Processing -- Periodicals; Electronics -- Mathematics -- Periodicals; 621.3
• DOI: 10.1108/COMPEL-09-2017-0408
• Languages: English
• ISSNs: 0332-1649

Abstract

Abstract : Purpose: Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications. Design/methodology/approach: According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differential matrix. By transforming the integration path, the tail integral is calculated with help of a transformed Clenshaw–Curtis quadrature rule. Findings: Numerical tests show that this new method is robust to high oscillation and nearly singularities. Thus, it is suitable for evaluating Pollaczek integrals. Furthermore, compared with existing method, the presented algorithm gives high-order approaches for the earth return mutual impedance between conductors over a multilayered soil with wide ranges of parameters. Originality/value: An efficient truncation strategy is proposed to accelerate numerical calculation of Pollaczek integral. Compared with existing algorithms, this method is easier to be applied to computation of similar improper integrals, such as Sommerfeld integral.