Using fourier series to derive optimal soft-switching modulation schemes for dual active bridge converters

A generic, Fourier-based method for the derivation of optimal, full-operating-range zero voltage switching (ZVS) modulation schemes for dual active bridge (DAB) converters is presented. Thereby, the AC-link voltages and currents, and the DAB´s input current and power flow, are described using trigonometric Fourier series. Furthermore, the amount of charge that is available in the bridge currents to charge the nonlinear parasitic output capacitances of the switches during commutation is deduced from the respective Fourier current coefficients. This yields ZVS constraints that are more accurate than the energy-based ZVS constraints proposed in literature. Subsequently, it is shown that by combing the equation for the DAB´s input current with the ZVS constraints in a numerical optimization algorithm, an optimal, ZVS modulation scheme can easily be derived with higher flexibility, lower calculation time, and lower implementation effort compared to the traditional piecewise-linear modeling approach. Although applicable to any DAB implementation, the procedure is demonstrated for a full-bridge full-bridge DAB as core part of a single-phase, single-stage, bidirectional, isolated AC-DC converter. The modulation scheme outputted by the presented Fourier-based method is compared with the modulation scheme calculated using a previously published piecewise-linear modeling approach, showing a negligible deviation.