Analytical Modelling and Optimization of DAB Converters Considering the Steady-State Behavior and All Degrees of Freedom

Bidirectional isolated DC-DC converters are attracting more and more attention because of their versatile application areas. The Dual Active Bridge (DAB) is one of the most promising topologies of this kind, especially in interfaces to batteries. Investigation with different abstraction levels is often needed in these power converters design process, e.g. ideal behavior (steady-state, dynamics), losses analysis, optimization of parameters and control. In this paper, the theoretical steady-state model for Dual Active Bridge DC-DC converters is studied, considering all the possible modulation techniques, i.e. phase-shifts between all legs (all "degrees of freedom"). The analytical developments presented, based on the superposition principle, allow to obtain the waveforms of inductor and output current using a simple and fast closed-form procedure. This analytical approach can replace dynamical simulations when only steady-state behavior is to be analyzed, with much faster execution. This allows to apply optimization methods for the selection of the operating point or during the design stage (e.g. for selecting inductance and frequency values). Moreover, the novel fully analytical model describes the output current vs. phase-shifts relationship, which can be exploited for control design or characterization of the converter behavior. Simulations in PLECS Blockset validate the theoretical results.