Traditional WPTSs generally ignore the importance of smoothness and continuity of coil windings and replace continuous windings with segmented lines and corners which can reduce performances of WPTSs. In this paper, a novel unified and precise mathematical model for combining circular and square coils is proposed which proves their consistency in physical structures. With the model, continuous coils can be obtained. FEM simulations are conducted to calculate mutual inductances and coupling coefficients of coils with different transfer distances and misalignments. It is verified that proper selections of corners will improve power transfer efficiencies of WPTSs. When the transfer distance and misalignments are large, smaller coil corners are prone to achieve high transfer efficiency. Finally, three case studies are conducted with three prototype coils. The measured mutual inductances and coupling coefficients are in good agreement with simulated results which support the of FEM simulation. A 1.5kW experimental platform is built for experimental verification with a transfer distance of 150mm. The transfer efficiency reaches 96.40%, 96.64% and 96.58% with k=0.258, 0.263 and 0.270.
