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Bilinear Discrete-Time Modeling and Stability Analysis of the Digitally Controlled Dual Active Bridge Converter

Dual active bridge (DAB) converters have been widely used in distributed power systems and energy storage equipment. However, the inherent nonlinearity of the DAB converters can cause stability problem, such as output voltage oscillation. In this paper, the dynamic behavior and stability of a digitally controlled DAB converter with a closed-loop controller are studied. First, to accurately study the nonlinear dynamics and stability in a DAB converter, a bilinear discrete-time model considering the output capacitor equivalent series resistance (ESR) and the digital control delay in circuit is established. Based on the model, the nonlinear dynamic characteristic and stability of the DAB converter versus the control parameter are studied. Furthermore, extensive analyses are performed to study the effect of the transformer leakage inductance and the output capacitor ESR on the stability boundaries of the control parameter. The accuracy of the model and the theoretical analyses are validated by simulation and experimental results. The proposed model of the digitally controlled DAB converter can accurately predict the stability boundaries, which can be effectively applied to the design of the system parameters and guarantee stable operation of the converter.