Lagrangian dynamics model and practical implementation of an integrated transformer in multi-phase LLC resonant converter

Mostafa Noah, Kazuhiro Umetani, Jun Imaoka, Masayoshi Yamamoto

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


In conventional arrangements of three-phase LLC converters, there are at least three magnetic components that occupy a considerable volume and mass of the power converter. Although, the three-phase LLC topology has many advantages over the single-phase one, circuit designers tend to select the single-phase topology because it has the minimal number of magnetic components. The purpose of this study is to reduce the number of the magnetic components of the three-phase topology, by integrating the three-discrete transformers into a single magnetic core, based on a theoretical framework. Lagrangian dynamics is applied to theoretically prove that it is possible to replace the three-discrete transformers by a single integrated transformer. The Lagrangian dynamics theory allowed us to derive a physically motivated model for the integrated transformer, in which each component of the integrated transformer has its own Lagrangian parameter. The Lagrangian model reveals that in a symmetrical design, there is no interphase coupling, and as a result the magnetic components can be downsized owing to the ac flux cancellation. Along with the theoretical discussion, the practical merits of implementing the integrated transformer is reported. Furthermore, the experimental tests are conducted utilizing a 500 W-390 V/12 V-200 kHz prototype.

Original languageEnglish
Pages (from-to)339-347
Number of pages9
JournalIET Power Electronics
Issue number2
Publication statusPublished - 2018 Feb 20
Externally publishedYes

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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