Analytical design of Archimedean spiral coils used in inductive power transfer for electric vehicles application

The inductive power transfer (IPT) systems have been drawing much attention in the wide variety of industrial and automotive electric power applications such as battery chargers in automated guided vehicles and electric vehicles (EVs) these days. At the heart of this IPT system are two mutually coupled coils also known as charging pad. Among different existing charging pads, circular charging pad is the most widely adopted charging pad for stationary charging of EV. This is mainly due to ease of manufacturing, symmetric coupling profile, ease of experimental characterization and its non-directional characteristics which ensure simplicity of use by a driver. Circular charging pads consist of coils in the form of Archimedean spirals. For the design of Archimedean spiral, i.e., calculation of number of turns, outer and inner diameter, air gap between primary and secondary coil is often done using finite element analysis software (FEA). However, FEA simulations are complicated and may require a significant number of iterations before achieving the final design goals and therefore are time-consuming. Therefore, the aim of this paper is to formulate simple analytical expressions to design Archimedean spiral from given electrical parameters. An analytical expression for self-inductance as well mutual inductance has been presented. Analytical expressions have been validated using five different coil-pairs fabricated for the same electrical parameters. Usefulness and limitations of the analytical expressions have been discussed.