Continuous Reduced-Order Dynamic Model Based on Energy Balancing for Inductive Power Transfer Systems

Resonant circuits are commonly used in inductive power transfer (IPT) systems for the charging of electric vehicles because of the high power efficiency. Transient behaviors of the resonant circuits, which play a significant role in the design and analysis of IPT systems, are cumbersome to model analytically because of the high-order. This article develops a reduced-order continuous dynamic model based on the energy interactions among the resonant tanks. By applying the proposed energy balancing method (EBM), the order of the dynamic model is reduced to half of the number of the passive components in the resonant circuits. To show the accuracy of the EBM, the dynamics of a series-series (SS) compensated IPT system are modeled using Laplace phasor transformation (LPT) and EBM separately and the results are compared. The order of the EBM is found to be one-fourth of that of the LPT method. The sensitivity of the EBM to the switching frequency is discussed when the zero voltage switching turn-on operation is attained. Besides, to prove the advantage of reducing the order of the dynamic model, model predictive controls (MPCs) based on EBM and LPT are developed. The transient performances of the MPC controllers are simulated and the control inputs are applied to an experimental setup. Finally, experiments are conducted to verify the accuracy of the proposed EBM under zero and nonzero conditions and the effectiveness of the developed MPC controller.