Abstract

Hybrid Electrical Vehicles-HEV!?s are the importnt ways to improve vehicle performance. The transformer isolated
bi-directional DC-DC converters are the key components of the traction system in HEV!?s. This paper presents adetail
mathematic model of isolated bi-directional DC-DC converter for HEV!?s. Approximate models are important
mathematic methods especially for analysis and closed-loop control design converter circuits.  These differential
equations, which govern the converter operation, change periodically among a set of linear differential equations
because of the switch effect. Basing on the time-scale the state variables was separate as fast-scale and slow-scale
variables. The fast changing variable of the leakage inductor was eliminated by substitute the fast-scale variable into
slow-scale variable equations, resulting in reduced order differential equations. From this set of  reduced order
differential equations the completely averaged model of the isolated DC/DC converter was derived. The simulated
results reveal that the circuit and mathematical model are consistent very well. The averaged state variables can be
treated as a small component plus a DC component, so the averaged model can be separated a dynamic small signal part and a DC part. This linearized small signal model is suit for control design and analysis at a steady point that is decided by the DC component. As an example a PI controller was design basing on the linear model.

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