The Effect of Cross-Coupling on the Dynamic Performance of a Dual Phase Shift Controlled BiWPT System

In a bidirectional wireless power transfer (BiWPT) system, dual phase shift (DPS) control is used to maintain the optimal efficiency at constant output power over varying misalignment. The presence of multiple control and output variables in DPS control creates cross-coupling between the transmitter and receiver sides, making BiWPT a multi-input–multi-output (MIMO) system. Due to cross coupling, any change in control variable in one side of the BiWPT system will affect the output of the same side as well as the output and control input in the other side. This results in an uncertain dynamic behavior of the output response. The cross-coupling effect has not been adequately researched in the literature. Hence, this article presents an accurate dynamic model using a generalized state-space averaging approach (GSSA) and an extended describing function (EDF) method for a multivariable control of the S-S compensated BiWPT system. This model is used to derive the system’s relative gain array (RGA), which is used to study the effect of cross-coupling terms on the output variables. A 1-kW S-S compensated BiWPT experimental setup is used to validate the effect of cross-coupling on the dynamic behavior of the system by comparing DPS and single phase shift (SPS) controlled experimental waveforms. The steady-state and transient behavior of the BiWPT system has also been investigated with the simulation and experimental results.