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

Abstract

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.

Calculation of Leakage Inductance of Integrated Magnetic Transformer with Separated Secondary Winding Used in ZVS PSFB Converter

“…According to the analysis of the magnetic field intensity, the inner leakage energy becomes: (6) where l w is the core width along z axis, h w is the height of the core window.…”

“…By designing the magnetic circuit rationally, the resonant inductor can be integrated into transformer, named integrated magnetic (IM) transformer. It means that the power density of DC-DC converter can be successfully improved [5][6][7][8][9].…”

A Magnetic Structure Integrating Differential-Mode and Common-Mode Inductors with Improved Tolerance to DC Saturation

“…As a result, we also need to expand the cross-section of the center leg by α, according to similar discussion to obtain (13). In addition, we need to expand the cross-section of the top and bottom beams by α because the (a) (b) Fig.…”

“…Below, we show the reason utilizing the Lagrangian modeling (13) (14) . As discussed previously (13) (14) , the Lagrangian modeling offers a systematic method to transform an integrated magnetic component into an equivalent circuit of basic transformers and inductors, each of which consists of a single closed magnetic path. In this method, we first translate the physical magnetic structure into Lagrangian, which can be directly configured from their electric and magnetic networks.…”

Lagrangian-Based Derivation of a Novel Sliding-Mode Control for Synchronous Buck Converters

“…We utilized Lagrangian modeling (3) to derive this control method because it can convert complicated energy conserving systems into simple dynamically equivalent systems (3) (4) . In fact, this paper converts the synchronous buck converter into two independent systems, which enables decoupling between the output voltage and the load current.…”