This study proposes a comprehensive mathematical model that includes coil-system circuit and loss models for power converters in wireless power transfer (WPT) systems. The proposed model helps in understanding the performance of WPT systems in terms of coil-to-coil efficiency, overall efficiency, and output power capacity and facilitates system performance optimization. Three methods to achieve constant output power for variable-load systems are presented based on system performance analysis. An optimal method can be selected for a specific WPT system by comparing the efficiencies of the three methods calculated with the proposed model. A two-coil 1 kW WPT system is built to verify the proposed mathematical model and constant output power control methods. Experimental results show that when the load resistance varies between 5 and 25 Ω, the system output power can be maintained at 1 kW with a maximum error of 6.75% and an average error of 4%. Coil-to-coil and overall efficiencies can be maintained at above 90% and 85%, respectively, with the selected optimal control method.