A Unified and Precise Mathematical Model for Combining Circular and Square Coils in Wireless Power Transfer Systems

Many traditional wireless power transfer systems (WPTSs) often use resonant coil windings with segmented straight lines and sharp corners, which not only break the continuity of resonant coil but also reduce the transfer efficiencies and misalignment tolerance of WPTSs. In this paper, a novel and precise unified parametric coil structure model is proposed which combines the circular and rounded square coils together, proving and highlighting the inner consistency of their winding structures. Based on the proposed unified model, a series of resonant coils with different rounded corners are designed, whose mutual inductances and coupling coefficients (k) are analyzed with FEM simulations to determine the optimized corner design with high transfer efficiencies under different misalignments. Apparently, a proper selection of rounded corners will improve the power transfer efficiencies of WPTSs. When the transfer distance and misalignments are relatively large, smaller coil corners are prone to achieve high transfer efficiencies. Subsequently, three case studies are conducted with three prototype coils. The former perspectives are strongly supported by the good agreement between the measured results and simulated results of mutual inductances and coupling coefficients. A 1.5-kW experimental platform is built to verify prototype coils at the transfer distance of 150mm. The transfer efficiency reaches 96.40%, 96.64% and 96.58% when k = 0.258, 0.263 and 0.270.