Analytical and Normalized Equations to Implement the Optimized Triple Phase-Shift Modulation Strategy for DAB Converters

A fully normalized algorithm to implement the optimal triple-phase-shift (TPS) modulation strategy of the dual active bridge (DAB) converter is proposed in this article. The algorithm evaluates three simple expressions that fit the optimal solutions obtained in recent works, which allows the algorithm to be implemented in real-time and valid for the whole operating range. As a result, the converter operates under zero voltage switching (ZVS) conditions and minimizes conduction losses. In addition, the algorithm considers the minimum current required to guarantee the ZVS condition that faces the undesired dead-band of switching devices effect. The proposal achieves a soft transition between any operation region and a fast closed-loop response with no stability concern, presenting robustness under leakage inductance deviation. Finally, the algorithm presented in this article is verified with a 4-kW experimental prototype. Experimental results show that the algorithm proposed can be evaluated with less than 2.8 $\mu \text{s}$ and allows soft transition between any operation region to be achieved. Besides, fast closed-loop changes of 750 $\mu \text{s}$ through all the operating ranges, keeping minimum rms current under ZVS, are shown.