Quasi-Analytical Calculation of Frequency-Dependent Resistance of Rectangular Conductors Considering the Edge Effect

Barzan Tabei, Akihiro Ametani, Aniruddha M. Gole and Behzad Kordi
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Barzan Tabei: Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB R3T5V6, Canada
Akihiro Ametani: Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB R3T5V6, Canada
Aniruddha M. Gole: Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB R3T5V6, Canada
Behzad Kordi: Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB R3T5V6, Canada

Energies, 2022, vol. 15, issue 2, 1-21

Abstract: This paper presents an accurate quasi-analytical approximation of frequency-dependent ac resistance of single rectangular conductors. In this work, first, a two-dimensional analytical ac resistance of rectangular conductors is derived. Unlike circular conductors, where current density distributes evenly in each layer of the conductor’s cross-section, the edge effect is involved for rectangular conductors. Due to the edge effect, one cannot define an accurate boundary condition for solving the two-dimensional partial differential equation of magnetic field or current density of rectangular conductors. Hence, the calculated two-dimensional analytical current density result is not accurate and is modified and fitted on FEM simulation, taking the conductor’s thickness into account using the least-square problem to improve its accuracy. Unlike numerical approaches, the proposed method yields an easy-to-use formula applicable to industrial applications in different fields. Contrary to the one-dimensional approach, which is only valid for very thin rectangular conductors, this method takes edge effect into account and can be used for any thickness (from square to very thin rectangular conductors). The proposed method can be used in applications where an accurate ac resistance of rectangular conductors over a wide frequency range is required, such as white-box modeling of power transformers and interpreting its frequency response analysis (FRA), and calculating the resistance of electric machine winding, busbars, and printed circuit board traces.

Keywords: skin effect; edge effect; ac resistance; ac loss; rectangular conductors; white-box modeling; finite element method (FEM) (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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