Fast Numerical Model of Power Busbar Conductors Through the FFT and the Convolution Theorem

Skin and proximity effects can cause a non-uniform current distribution in the electrical conductors used in alternating current (ac) busbar systems, which increases resistance, decreases internal inductance, and causes asymmetries in the electromagnetic fields and forces. As no explicit solution fo...

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Bibliographic Details
Published inIEEE transactions on power delivery Vol. 37; no. 4; pp. 3291 - 3301
Main Authors Martinez-Roman, Javier, Puche-Panadero, Ruben, Sapena-Bano, Angel, Burriel-Valencia, Jordi, Terron-Santiago, Carla, Pineda-Sanchez, Manuel, Riera-Guasp, Martin
Format Journal Article
LanguageEnglish
Published New York IEEE 01.08.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Bars
Busbars
Conductivity
Conductors
Convolution
Current density
Current distribution
Electric conductors
Electromagnetic fields
Fast Fourier transformations
Fourier transforms
Inductance
Mathematical analysis
Mathematical models
Matrices (mathematics)
Multiplication
Numerical methods
Numerical models
Skin
skin effect
spectral analysis
Theorems
Transmission line matrix methods
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Summary:Skin and proximity effects can cause a non-uniform current distribution in the electrical conductors used in alternating current (ac) busbar systems, which increases resistance, decreases internal inductance, and causes asymmetries in the electromagnetic fields and forces. As no explicit solution for the ac resistance or the ac internal inductance of a rectangular conductor has been found, numerical methods are needed to obtain the distribution of the currents inside the busbars. In this paper, a novel numerical approach, based on the fast Fourier transform (FFT) and the convolution theorem, is proposed to model the rectangular conductors of the busbar system, based on the subdivision of the conductor in filamentary subconductors. This technique is know to lead to a dense, huge inductance matrix, that must be multiplied by the current vector, which limits its practical application. The proposed method replaces this matrix-vector multiplication with a simple element-wise vector product in the spatial frequency domain. The FFT speed makes the proposed method very fast and easy to apply. This approach is theoretically explained and applied to an industrial busbar system.
ISSN:0885-8977
1937-4208
DOI:10.1109/TPWRD.2021.3126265