Z-Parameter Estimation for Multiple-Input Multiple-Output Wireless Power Transfer Systems via a Phase Retrieval Method

Multiple-input multiple-output (MIMO) wireless power transfer (WPT) systems offer multiple benefits to users, such as improved power transfer efficiency, adjustable transmission power, and reduced magnetic field leakage. The estimation of the Z-parameters, which describe the behavior of the linear electrical network in the systems, is essential for the control of MIMO WPT systems. In this study, we propose a method that can estimate all the elements of the Z-parameters without requiring synchronization between the transmitters and receivers. The elements are estimated using the measured complex amplitudes of the voltage and current at the transmitters as well as the direct current (DC) at the output of the full-bridge rectifiers on the receivers, all of which can be measured at a low cost. Numerical simulations of the proposed method for MIMO WPT systems were performed for three configurations: two transmitters and two receivers $(2 \times 2)$, three transmitters and two receivers $(3 \times 2)$, and three transmitters and three receivers $(3 \times 3)$. The simulation results show that each element of the Z-parameters could be estimated within 1% of the true value after four measurements for the $2\times 2$ system, four measurements for the $3 \times 2$ system, and eight measurements for the $3 \times 3$ system.