Extremum co-energy principle for analyzing AC current distribution in parallel-Connected wires of high-Frequency power inductors

Tomohide Shirakawa, Genki Yamasaki, Kazuhiro Umetani, Eiji Hiraki

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Inductor winding is often comprised of parallel-connected wires to suppress copper loss. However, in high-frequency inductors, the proximity effect can cause concentrated AC current distribution, hindering the suppression of the copper loss. Therefore, optimization of the physical inductor structure requires predicting the AC current distribution caused by the proximity effect. Certainly, simulators have been commonly employed for predicting the AC current distribution. However, simple analytical methods are also required for efficient design or invention of inductor structures that have more uniform AC current distribution among the parallel-connected wires. The paper proposes a novel simple analysis method for AC current distribution in parallel-connected wires of high-frequency inductors. The proposed method is based on a novel insight that AC current is distributed to give an extremum of the magnetic co-energy contributed by the AC flux under the given total AC current. Analysis of basic inductor structures revealed that the proposed method can derive the AC current distribution by straightforward calculation. In addition, experiments supported the analysis results. Consequently, the proposed method is suggested to be promising for developing inductor structures with less copper loss.

Original languageEnglish
Pages (from-to)35-42
Number of pages8
JournalIEEJ Journal of Industry Applications
Issue number1
Publication statusPublished - 2018
Externally publishedYes


  • AC current distribution
  • Inductor
  • Magnetic circuit
  • Magnetic co-energy

ASJC Scopus subject areas

  • Automotive Engineering
  • Energy Engineering and Power Technology
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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