A Thermal Black-Box Theory for Scaling Design of Planar Magnetic Coils in Wireless Charging Systems

Thermal management of magnetic coils is essential for the safe and stable operation of high-power wireless charging systems (WCS). Upon a deficiency of detailed thermal analysis, this article presents a thermal model under natural convection featuring both accuracy and simplicity. Analysis shows that the loss distribution between different parts of the coil has little effect on the resultant temperature. This in the context leads to a key conclusion that the maximum allowable power loss density decreases in an
m
^-1/8
relationship with the increasing area gain
m
, given the coil geometry and natural convective condition. It also indicates that the coil set can be thermally treated as a black-box to predict how the temperature would rise and determine the necessary coil area for heat dissipation. These conclusions provide guidelines for the material and structure choices of the coils as well as for flexible scaling design. The proposed model is verified by simulation and experiment studies on a 5 kW prototype. The maximum error of temperature estimation is shown to be 9.5%.