We present an optimization procedure for wireless power transfer (WPT) applications and test it numerically for a WPT system design with four resonant circuits that are magnetically coupled by coaxial coils in air, where the magnetic field problem is represented by a fully populated inductance matrix that includes all magnetic interactions that occur between the coils. The magnetically coupled resonators are fed by a square wave voltage generator and loaded by a rectifier followed by a smoothing filter and a battery. We compute Pareto fronts associated with a multi-objective optimization problem that contrasts: 1) the system efficiency; and 2) the power delivered to the battery. The optimization problem is constrained in terms of: 1) the physical construction of the system and its components; 2) the root-mean-square values of the currents and voltages in the circuit; and 3) bounds on the overtones of the currents in the coils in order assure that the WPT system mainly generates magnetic fields at the operating frequency. We present optimized results for transfer distances from 0.8 to 1.6 times the largest coil radius with a maximum power transfer from 4 kW to 9 kW at 85 kHz, which is achieved at an efficiency larger than 90%.
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