A generalized method for Lagrangian modeling of power conversion circuit with integrated magnetic components

A generalized Lagrangian is proposed to enable systematic analysis of integrated magnetic components. Although a few conventional theories are known that handle magnetic circuit, they cause difficulties in modeling or analysis, especially when applied to a highly integrated core. These difficulties are avoided in the proposed theory, as its Lagrangian is configurable directly from the physical core structure. As an example, the Lagrangian of the trans-linked three-phase boost converter is presented. Along with the Lagrangian, two types of circuit analysis are also presented: one is to obtain the state-space model of the converter; the other is to translate the integrated magnetic component into an equivalent circuit of basic components such as transformers and inductors. The analyses show the usefulness of the proposed method in practical applications.