Magnetic Beamforming Algorithm for Hybrid Relay and MIMO Wireless Power Transfer

Using magnetic beamforming, the power transmission efficiency can be highly increased for realizing the practical near-field magnetic resonant coupling (MRC) wireless power transfer (WPT). The usage of relay coils is also of great benefit for power transmission in the WPT system containing multiple transmitters (TXs) each with a coil. In this paper, we study the influence of relay coils and the magnetic beamforming for a MRC-WPT system with multiple TXs, relay coils and a single receiver (Rx), called multi-relay WPT (MWPT) system. The optimization problem is formulated to design the currents flowing through TXs in different places so as to maximize the power delivered to the RX load, subject to a given constraint of summational power consumed by all resistances in the MWPT system. In general, the problem is a non-convex quadratically constrained quadratic programming (QCQP) problem, which can be solved with relaxation of the Lagrange multiplier. Numerical results show that by comparing with equal-current and magnetic beamforming mode, relay coils significantly enhances the power transmission efficiency over the longer distances, and magnetic beamforming with passive relay coils significantly improve the transmission power, efficiency and distance.