Bi-directional wireless power transfer technology is one of the important research branches of wireless power transfer. The bi-directional wireless power transfer system with k+1 loop units is studied and its mathematic model is established. Moreover

the control scheme for both power flow direction regulation and power allocation via the relationships among converter voltages' amplitude and their phase difference is proposed. Then

the theoretical analysis and simulation are carried out for bi-directional wireless power transfer with three loop units and the constrain conditions of power flow direction and power allocation are also presented. Finally

the viability and feasibility of theoretical analysis are verified by simulation and experiments. This work is supported by National Key Research and Development Program of China(No. 2016YFB0101800)

National Natural Science Youth Foundation of China(No. 51507032)and Natural Science Youth Foundation of Jiangsu Province(No. BK20150617).