Study of Skin and Proximity Effects of Conductors for MTL-Based Modeling of Power Transformers Using FEM

Tabei, Barzan; Ametani, Akihiro; Gole, Aniruddha M.; Kordi, Behzad

doi:10.1109/pesgm41954.2020.9281776

Cited by 3 publications

(6 citation statements)

References 11 publications

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“…Hence, it covers the edges very well. The magnetic vector potential A(x, y) = A z (x, y) ẑ and, consequently, the current density distribution is calculated by solving the diffusion equation [29] ∇ 2 A z (x, y)−jωσ(x, y)µ(x, y)A z (x, y)+µ(x, y)J ez (x, y) = 0. ( 16)…”

Section: Skin Effectmentioning

confidence: 99%

“…A z (x, y) goes to zero at infinity. To solve (16), the Dirichlet boundary condition (i.e., A z (x, y) = 0) at a far enough boundary is employed (i.e., truncating the outer boundary at a distance much larger than a conductor size) [20,29,44]. In this section, ( 16) is solved at each frequency using the PGD approach and approximated as…”

Section: Skin Effectmentioning

confidence: 99%

“…The PUL ac resistance calculated using PGD is R ac = 9.81344 × 10 −5 Ω/m, which matches well with FEM R FEM = 9.7293 × 10 −5 Ω/m with an error of 0.86%. (See [29] for details of the resistance calculation.) Selecting a smaller threshold may lead to a more accurate result as more terms are used (see Figure 4).…”

Section: Case 1: Single Rectangular Conductormentioning

confidence: 99%

“…When there is more than one current-carrying conductor, in addition to the skin effect of the conductor itself, current density distribution also gets affected by the magnetic field of the nearby conductors. This phenomenon is known as the proximity effect [19,29]. Due to the proximity effect, there is more resistive loss because of the change in the distribution of current, resulting in a higher ac resistance.…”

Section: Proximity Effectmentioning

confidence: 99%

“…There are traditional two-dimensional (2D) numerical methods such as finite difference time domain (FDTD) [19] and finite element methods (FEM) [29] to calculate the per-unit length (PUL) resistance of rectangular conductors. The 2D FEM has been used for PUL parameter or eddy current loss calculations of ac machines while heavy computation is the main drawback of the approach [30,31].…”

Section: Introductionmentioning

confidence: 99%

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Skin and Proximity Effect Calculation of a System of Rectangular Conductors Using the Proper Generalized Decomposition Technique

Tabei,

Gole,

Kordi

2024

Energies

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This paper presents the application of a numerical approach known as proper generalized decomposition (PGD) to calculate the per-unit length (PUL) ac resistance of rectangular conductors. PGD has been successfully used in areas such as fluid mechanics and biomedical applications. It solves a partial differential equation (PDE) by decomposing the answer into a set of unknown one-dimensional (1D) functions in an iterative approach until it reaches a predetermined convergence. In this paper, a frequency-dependent meshing scheme is employed in the PGD technique at each frequency to properly take skin and proximity effects into account. One of the main advantages of PGD over traditional numerical approaches such as finite element or finite difference methods is that it confines the answers within a set of one-dimensional functions, which require fewer computational resources. Different examples of single and multiple rectangular conductors are considered to study skin and proximity effects. The PGD results are compared with those obtained using a commercial finite element method (FEM) software to verify the accuracy of the model. This approach can be used in applications such as white box modeling of transformers, EMC analysis, hairpin winding design used in electric vehicles, and busbar simulation.

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Section: Skin Effectmentioning

confidence: 99%

Section: Skin Effectmentioning

confidence: 99%

Section: Case 1: Single Rectangular Conductormentioning

confidence: 99%

Section: Proximity Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Skin and Proximity Effect Calculation of a System of Rectangular Conductors Using the Proper Generalized Decomposition Technique

Tabei,

Gole,

Kordi

2024

Energies

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A Study on AC Resistance Calculation of Single Rectangular Conductors

Tabei

Ametani

Gole

et al. 2021

2021 IEEE Electrical Power and Energy Conference (EPEC)

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

et al. 2022

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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.

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Study of Skin and Proximity Effects of Conductors for MTL-Based Modeling of Power Transformers Using FEM

Cited by 3 publications

References 11 publications

Skin and Proximity Effect Calculation of a System of Rectangular Conductors Using the Proper Generalized Decomposition Technique

Skin and Proximity Effect Calculation of a System of Rectangular Conductors Using the Proper Generalized Decomposition Technique

A Study on AC Resistance Calculation of Single Rectangular Conductors

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

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