The control and optimization of wireless power transfer (WPT) systems require the continuous monitoring of their performance or, similarly, some output parameters. The solution presented in this manuscript is based on the relationship between some figures of merit representative of the WPT systems and allows to control automatically (in a simple way, without any direct measurement at the load circuit) the performance of a three-coil WPT system under variations on the load and/or mutual inductance between the intermediate and load coils. The qualities and limitations of the proposed method are discussed in detail. Conventional circuit analysis and practical results are included to validate the presented theory and its applicability in an automatic control scheme.efficiency, figures of merit, inductive power transfer, power transfer capability, wireless power transfer
| INTRODUCTIONWireless power transfer (WPT) systems via inductive coupling have become a key technology in several fields, for example, electric vehicles' battery recharging systems and implantable medical devices, due to their intrinsic characteristics, such as flexibility, safety, reliability, and convenience. [1][2][3][4][5] Starting with the pioneer work of Tesla 6 using WPT systems with only two coils, several other arrangements using three or more coils have been recently researched. [3][4][5][7][8][9][10][11] For instance, typical three-coil WPT systems are composed of three circuits (usually tuned at the same resonance frequency to reduce the losses due to reactive effects), one containing the source, the other containing the load, and one intermediary (relay circuit), where all are coupled to the adjacent ones by their respective mutual inductances.Independently of the number of coils used, a typical WPT system is usually designed aiming optimal efficiency (η), which can be defined as the power delivered to the load circuit divided by the total power supplied by the source. Alternatively, the WPT systems can be designed optimizing their power transfer capability (P Ã ), which can be defined as the power delivered to the load circuit divided by the maximum ideal amount of power which can be delivered to the same load circuit.However, in some applications, the mutual inductance between the coils may vary because the relative position of the coils is not fixed. 12,13 In the same way, the load characteristics may vary with time or may be dependent on the employed remote device. Implantable medical devices 2,14 and electric vehicles charging 1,12,13,15,16 schemes, which