Lagrangian derivation and analysis of a simple equivalent circuit model of wireless power transfer system with dual transmitting resonators

This paper proposes a novel analysis method for the dual transmitting resonators wireless power transfer (DTR-WPT) system. The DTR-WPT is attractive for its higher efficiency and greater power transfer capability compared with the conventional single transmitting resonator wireless power transfer (STR-WPT) system. However, analytical understanding of the DTR-WPT is difficult due to its complicated operating principle caused by two transmitting resonators and a receiving resonator, which are all magnetically coupled each other. Therefore, practical applications of the DTR-WPT may be hindered by difficulty in establishing a design optimization method and a control scheme. This difficulty is addressed in this paper by proposing a novel simple equivalent circuit model of the DTR-WPT. Lagrangian dynamics is employed to derive this model. Brief analysis of this model showed improvement in the efficiency and the power transfer capability by the DTR-WPT compared with the conventional STR-WPT. In addition, the power transfer of the DTR-WPT system was found to be expressed by the same equivalent circuit model as the STR-WPT system. Therefore, similar design optimization methods and similar control schemes as for the STR-WPT are applicable to the DTR-WPT. Along with the theory, this paper presents experiments that verified appropriateness of the proposed model as well as the analysis results based on this model.