Transient Simulation of Magnetic Circuits Using the Permeance-Capacitance Analogy Jost Allmeling Wolfgang Hammer John Schonberger¨ Plexim GmbH Plexim GmbH TridonicAtco Schweiz AG Technoparkstrasse 1 Technoparkstrasse 1 Obere Allmeind 2 8005 Zurich, Switzerland 8005 Zurich, Switzerland 8755 Ennenda, Switzerland Email:
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[email protected] Abstract—When modeling magnetic components, the R1 Lσ1 Lσ2 R2 permeance-capacitance analogy avoids the drawbacks of traditional equivalent circuits models. The magnetic circuit structure is easily derived from the core geometry, and the Ideal Transformer Lm Rfe energy relationship between electrical and magnetic domain N1:N2 is preserved. Non-linear core materials can be modeled with variable permeances, enabling the implementation of arbitrary saturation and hysteresis functions. Frequency-dependent losses can be realized with resistors in the magnetic circuit. Fig. 1. Transformer implementation with coupled inductors The magnetic domain has been implemented in the simulation software PLECS. To avoid numerical integration errors, Kirch- hoff’s current law must be applied to both the magnetic flux and circuit, in which inductances represent magnetic flux paths the flux-rate when solving the circuit equations. and losses incur at resistors. Magnetic coupling between I. INTRODUCTION windings is realized either with mutual inductances or with ideal transformers. Inductors and transformers are key components in modern power electronic circuits. Compared to other passive com- Using coupled inductors, magnetic components can be ponents they are difficult to model due to the non-linear implemented in any circuit simulator since only electrical behavior of magnetic core materials and the complex structure components are required.