Optimal Design Of Coupling Coils Of WPT Systems Based On Modified Calculation Of AC Resistance

Wireless power transfer(WPT)technology has been applied in many areas as it developing.Such as mobile phones,electric toothbrushes,pacemakers and electric vehicles.Safety and flexibility promote the application of WPT technology,however,the energy transfer efficiency(ETE)of it is relatively lower than traditional wired charging.Coupling coils are core components of a WPT system,which greatly determine the ETE of a system.Therefore coupling coils design is an important work for WPT system design.Based on series-series compensation topology,the design constraints have been classified into four categories in this study according to load resistance and working frequency: 1)the load and the working frequency are allowed to be chosen in a wide range;2)the load can be chosen freely while the working frequency is given ahead,such as 85 kHz or 6.78 MHz;3)the load is given ahead while the working frequency can be chosen freely;4)the load and the working frequency are given ahead.This paper analyzes the relationship between the coil-coil efficiency and design parameters for four constraints type,and solves the optimization function.Design parameters in this paper include the geometric parameters of coils(number of turns,turn-spacing and the radius of the outermost turn)and system parameters(load resistance and working frequency).Once the optimization function has been solved,particle swarm optimization(PSO)algorithm has been applied to obtain the optimum design parameters.The design algorithm has been programmed with MATLAB to form an automatic design program.Designers just need to input the design constraints and then waiting for the output of optimum parameters corresponding to maximum coil-coil efficiency.One of the novelty of this paper is the modified analytical calculation method of AC resistance of litz-wire coils,in which conductive resistance is calculated with a frequency-dependent formula and proximity-effect resistance is calculated with a modified analytical method.The experimental results show that the modified calculation method is precise for coils winded closely or sparsely.Finally,three practical examples based on constraints type 3)are given,and three WPT systems are built with the PSO-based method.The differences between the coilcoil efficiencies of experimental results and theoretical results are lower than 1.3%,which validates the accuracy of the design method.In addition,a conventional method is applied for comparison,and the coil-coil efficiencies of the conventional method are lower than that of the PSO-based method from 1.0% to 2.0%.