A Detailed Full-Order Discrete-Time Modeling and Stability Prediction of the Single-Phase Dual Active Bridge DC-DC Converter

The standard methodology to obtain the model of a power electronic converter is achieved by averaging the state-space dynamics of the converter’s state variables. But the average of the transformer current is null over a switching cycle in the resonant dc-dc converter. Therefore, the conventional method is not suitable for resonant converters, including the phase-shifted bidirectional dual active bridge (PSBDAB) converter. The two-time scale discrete-type models can resolve the problem associated with the standard state-space averaging methodology. The time-scale segregates the dynamics of the PSBDAB converter into fast and slow state variables, which can be modeled separately and eases the analysis of the PSBDAB converter. The effect of the core-loss of the inductor, dead-time of the semiconductor devices, output filter capacitor’s equivalent series resistance, semiconductor on-resistance, and the transformer copper loss components are included in the model to improve its steady-state and dynamics characteristics. Moreover, the stability analysis using a bifurcation diagram is carried out for the digitally controlled closed-loop of the system. Furthermore, the critical gain for the stable region with variations in the circuit parameters like load resistance, circuit equivalent inductance, and voltage demand is extensively studied. The modeling and stability analysis is validated in the simulation and experimental setup. The results verify that the proposed method accurately predicts the stable region with variations in the system circuit parameters. Thus this study provides a guide to select and tune the controller parameter to ensure the converter operates within the boundaries of the stable region.