The inductive power transfer (IPT) technology is drawing increasing attention. Variations in the height of the secondary coil are inevitable due to the fluctuations in the height of the electrical equipment or the pressure of the tires, which leads to variations in the coils’ parameters (self-inductances and mutual inductance). The coils’ parameters and load variations can dramatically affect the performance of the IPT system. In this article, a unified mathematical model, which can describe multiple compensation topologies, is established. A design method is proposed to obtain suitable topology and component parameters based on the unified mathematical model and the nondominated sorting genetic algorithm II (NSGA-II). In addition, not only the stable output voltage/current is achieved, but the efficiency and cost are also improved. Finally, two experimental prototypes were built to verify the effectiveness, which has the output characteristics of constant current (CC) (3.5 A/600 W) and constant voltage (CV) (72 V/100 W). The results show that the output fluctuations are less than 5.63%, and the maximum efficiency is above 94.69% when the coils’ parameters (the primary self-inductance changes from 85.76 to

$102.2 \mu \text{H}$

, the secondary self-inductance changes from 86.26 to

$102.35 \mu \text{H}$

, and the mutual inductance changes from 38.2 to

$72.1 \mu \text{H}$

) and load (double change) vary.

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