A Lagrangian dynamics model of integrated transformer incorporated in a 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 a minimal number of magnetic components. In this paper, with the purpose of promoting the industrial applications of the three-phase topology, 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 remarkable result to emerge from the Lagrangian model is that in a symmetrical design, there is no interphase coupling; this is regardless of the value of the coupling coefficient between the phases. This means that there is no return path for the three ac fluxes, and as a result the magnetic components can be downsized. Therefore, the major advantages of using integrated magnetics in the LLC converter can be concluded as: cost-reduction, reduced weight, and realizing higher power density. Along with the theoretical discussion, experimental validation is provided utilizing a 500W-390V/12V-200kHz prototype.