A New Approach to Steady-State Modeling, Analysis, and Design of Power Converters

Steady-state models of power converters that provide accurate closed-form expressions for converter waveforms are extremely valuable for converter analysis and design, and enable comparative evaluation of different converter topologies. An obstacle in the development of such models is the inherent nonlinearity of switching power converters. This article presents a systematic procedure to model a broad class of power converters using ordinary differential equations (ODEs) with periodic and discontinuous inputs, and provides an approach to determine closed-form expressions for their steady-state waveforms. The formal mathematical proof of the proposed approach to finding closed-form expressions for the steady-state solution of ODEs with periodic and discontinuous inputs, Laplace-based theorem (LBT), is also presented. The presented modeling procedure and LBT, collectively called Laplace-based steady-state modeling (LBSM), serves as an effective analysis and design tool for power converters. The value of LBSM is demonstrated by using it to obtain closed-form expressions for the steady-state waveforms of different types of converters. In particular, two commonly used topologies-the series resonant converter and the phase-shift converter-are analyzed and compared using LBSM and their optimum operating conditions and applications are discussed. The converter waveforms, soft switching ranges and other characteristics obtained using LBSM are also validated through simulations and experiments.

Automated summary

This article presents a systematic procedure to model a broad class of power converters using ordinary differential equations with periodic and discontinuous inputs, and provides an approach to determine closed-form expressions for their steady-state waveforms. The value of this Laplace-based steady-state modeling (LBSM) method is demonstrated by obtaining closed-form expressions for the steady-state waveforms of different types of converters, and their characteristics are validated through simulations and experiments.