Accurate Small–Signal Discrete–Time Model of Dual Active Bridge using Saltation Matrices

The nonlinear nature of dual active bridge (DAB) converters arises from switching between linear dynamics at controlled intervals. In this paper, we model DAB as a hybrid dynamical system consisting of a finite number of modes with linear dynamics and switching surfaces specifying the transition between the modes. In the conventional phase shift modulation (PSM) strategy, the phase shift φ governs the mode transitions and can be used to control DAB output voltage and power. We incorporate φ as a system state and calculate a linearization about a nominal trajectory with so-called saltation matrices that capture the first-order effects of perturbing the states between mode transitions. We demonstrate this linearization provides an accurate discrete-time small-signal model of the DAB.