System Identification and Tuning of Wireless Power Transfer Systems with Multiple Magnetically Coupled Resonators

We present a procedure for system identification and tuning of a wireless power transfer (WPT) system with four magnetically coupled resonators, where each resonator consists of a coil and a capacitor bank. The system-identification procedure involves three main steps: 1) individual measurement of the capacitor banks in the system; 2) measurement of the frequency-dependent two-port impedance matrix of the magnetically coupled resonators; and 3) determining the inductance of all coils and their corresponding coupling coefficients using a Bayesian approach. The Bayesian approach involves solving an optimization problem where we minimize the mismatch between the measured and simulated impedance matrix together with a penalization term that incorporates information from a direct measurement procedure of the inductance and losses of the coils. This identification procedure yields an accurate system model which we use to tune the four capacitance values to recover high system-performance and account for, e.g., manufacturing tolerances and coil displacement. For a prototype WPT system, we achieve 3.3~kW power transfer with 91\% system efficiency over an air-gap distance of approximately 20~cm.