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

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.