Nonlinear State-Space Mathematical Model for Dynamic Performance Evaluation of Bidirectional Dual Active Bridge Converters

Abstract

Bidirectional Dual Active Bridge (DAB) converters find numerous applications in battery energy storage systems, electric vehicle charging infrastructure, renewable energy conversion, and DC microgrids because of their bidirectional power transfer capability, galvanic isolation, and high-power density. To predict transient behavior and optimize the dynamic performance at different operating conditions, the mathematical modelling of these converters is necessary to be done accurately. Nonlinear and averaged state-space models, however, do not take into account the natural nonlinear nature of converter activity, resulting in a lower prediction accuracy in the transient case. This paper is a nonlinear mathematical state space model of dynamic performance of a Bidirectional Dual Active Bridge converter. Formulation is a mathematical formulation derived using nonlinear differential equations based on a converter electrical dynamics, with the leakage inductor current and output capacitor voltage as the major state variables. This model is numerically solved with an adaptive Runge-Kutta integration algorithm in MATLAB. To explore the transient response nature, the proposed framework is tested in startup, load variation and phase-shift control conditions. Settling Time (Ts) is used to measure the dynamic performance along with Rise Time, Peak Overshoot, Steady-State Error, Output Voltage Ripple, and Power Transfer Efficiency. The numerical findings show that the proposed nonlinear model has the lowest settling time of 2.84 ms which is 24.6% better than the standard averaged state-space model, and low voltage ripple, negligible steady-state error and maximum power transfer efficiency of 97.8. The mathematical framework proposed provides a computationally efficient algorithm to analyse dynamically, optimise converters, and create advanced control design in modern bidirectional power electronic systems using energy conversion.