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.
Highlights
Received: 20 November 2021Power transformers are valuable assets in a power system which require accurate modeling for their design, monitoring, diagnosis, and maintenance
In the case of circular conductors and very thin rectangular conductors with constant electric field on their surfaces, the ac resistance is defined as the ratio of surface electric field to the current flowing in the conductor [23]
Different analytical approximation of ac resistance of single rectangular conductors were considered from literature, and their results were compared with those obtained by Finite Element Method (FEM) simulation
Summary
Power transformers are valuable assets in a power system which require accurate modeling for their design, monitoring, diagnosis, and maintenance. While it is not easy to define an accurate boundary condition for nonmagnetic rectangular conductors, two different boundary condition definitions are found in the literature [22,23] for two-dimensional analytical calculations of thick rectangular conductors. This paper proposes an accurate quasi-analytical approximation for the ac resistance of a single rectangular conductor using FEM simulation and a modified two-dimensional analytical calculation. It takes into account the skin effect, the edge effect, and the thickness of rectangular conductors. As the two-dimensional analytical approach is not accurate for nonmagnetic conductors [23], this paper combines it with FEM simulation results using a least-square approach to calculate the ac resistance of rectangular conductors accurately.
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