Mutual Inductance and Output Voltage Estimation From Transmitter Side of Wireless Power Transfer by Utilizing Reflected Third-Order Harmonics

This article presents a real-time transmitter (Tx) side output voltage estimation method of a series-series compensated wireless power transfer (WPT) system by utilizing the reflected third-order harmonics generated by the receiver (Rx). The phase-shifted angle of the Tx inverter is set at 60° to eliminate the third-order harmonic voltage generated by the Tx. A thorough theoretical analysis is carried out, and a closed-form equation is derived to show the relationship between mutual inductance, fundamental and third-order harmonics, and other circuit parameters. The output voltage is further derived. The mutual inductance and output voltage are calculated using a digital signal processor after the magnitudes of the fundamental and third-order harmonic voltages of the Tx tuning capacitor are measured. A practical prototype is built, and the experimental results show the estimation errors of less than 3.1% for mutual inductance and output voltage under the wide variations of the coupling coefficient from 0.2 to 0.6 and the load resistance from 10 to 80 Ω, with an estimation delay of less than 1 ms.