An Explicit Discrete-Time Large- and Small-Signal Modeling of the Dual Active Bridge DC-DC Converter Based on the Time Scale Methodology

The conventional method to model a dc-dc converter is by averaging its state variable over a switching period. However, due to the dc-ac-dc structure of the dual active bridge converter (DABC), the average value of the inductor current over a switching cycle is zero. Therefore, the conventional methodology cannot be applied to the DABC. The time-scale discrete-time modeling of the DABC is proposed to mitigate the zero average state variable problem. The time-scale methodology simplifies the analysis of the DABC by segregating the fast state variable inductor current and slow state variable output voltage. The proposed model has the advantage of the explicit large signal in terms of the circuit parameter, like the average value model. The explicit steady-state circuit expression from the large-signal model helps in the study of the soft-switching range of the DABC. Moreover, the small-signal model from the proposed method results in an explicit small-signal model. The model incorporates semiconductor ON-resistance, inductor equivalent series resistance, transformer resistance, and leakage inductance. The effect of the converter net equivalent resistance on the small-signal model is thoroughly studied. Finally, the model accuracy in the steady-state, open-loop, and the small-signal are verified in both the switching simulation model and experimental setup.