Mathematical Approach for an Accurate Solution of the Circuit Model of Resonator Arrays for Inductive Power Transfer

In this thesis, a mathematical approach is used to solve the equivalent circuit of a resonator array for inductive power transfer (IPT). With this approach the equivalent impedance of the array of resonators is obtained in closed form, and the impedance matrix that represents the array circuit is inverted thus allowing the current in each resonator to be found analytically. In this way, a better and deeper understanding of the power transfer in IPT systems that use arrays of resonators is achieved, since this study can be applied to different types of configurations (arrays connected to a load, or with one or two receivers over it), different system parameters or operating conditions. It was found that the equivalent impedance remains constant if the array is terminated with the equivalent impedance of an infinite array of resonators. By computing the currents in each resonator, it is possible to determine the efficiency of the system, the power delivered to a load, to one or two receivers and the conditions for maximum efficiency or maximum power transfer. The power transferred and the efficiency depend not only on the system electrical parameters, but also on the number of resonators of the array and on the position of the receiver. Additionally, the magnetic near field generated by an array of resonators was analysed. It was concluded that when the array is perfectly terminated, the variation of the magnetic flux density is smoother. All the theoretical results were validated with numerical simulations and using an experimental setup composed of an H-bridge inverter operating in the hundred kHz range, supplying a resonator array and delivering up to about 90W to a load or receiver. This validation shows the practical applicability of the closed-form expressions obtained, which can be used as a design tool.