###### Abstract  
The paper is focused on the optimization of the compensation network of a wireless power transfer system (WPTS) intended to operate in dynamic conditions. A laboratory prototype of a WPTS has been taken as a reference in this work, allowing for the experimental data and all the numerical models here presented to reproduce the configuration of the existing device. The numerical model has been used to perform FEM analysis with variable relative positions of the emitting and receiving coil to simulate the movement in a'recharge while driving' condition. Inductive lumped parameters, i.e., self and mutual inductances computed from FEM results, have been used for the optimal design of the compensation network necessary for the WPTS operation. The optimal design of the resonance circuits has been developed by defining objective functions, aiming to achieve these goals: transmitted power must be as constant as possible when the vehicle is in movement and the electrical efficiency must be satisfactory high in most of the coupling conditions. The performances of the optimized network are finally compared and discussed. dynamic wireless power transfer; finite element analysis; circuital analysis; compensation network; optimization +
Footnote †: journal:  
0000-0001-5000-0001-5000]M.M.B.J. 0000-0001-5000-0001-5000]M.  
subsequently fully aligned, partially aligned, or misaligned with respect to the transmitting coil, and also the airgap may vary in a random way. In previous works, the authors investigated the self- and mutual-inductance at different conditions, starting from the fully alignment to the misalignment of the coils [22; 23]; a finite element model was developed by the authors in [22] in order to compute the self- and mutual-inductances at different alignment conditions. The aim of this paper is the optimization of the compensation network (CN) of a dynamic WPTS. The considered CN has a general topology where three reactances arranged in a T circuit are connected at each of the coils of the WPTS. This topology, denoted as TT, is rather general and has been considered as a starting framework in [24], even if in that paper only some particular cases have been analyzed in depth. Determination of the TT network reactances by inverting the mathematical system of equations that relate them to the WPTS performance is a difficult operation because of the rather complex CNs topology. Hence, simplifying hypotheses are introduced in order to solve the equations in closed form at the price of losing the certainty of obtaining an optimal solution [25]. Other authors avoid any simplification and reach an analytical solution, but they add some hypothesis regarding the reactances that constitute the CN and impose that both its sections are of LCC type, i.e., formed by an inductor and two capacitors [26] or derived from this arrangement [27]. The approach followed in this paper disperses with any limitation on the nature of the reactances and is based on the use of the lumped parameters, the self- and mutual-inductances computed by the FEA, to design an optimized CN that allows the highest power transfer to the load in dynamic conditions with a good efficiency; in fact, both these goals are usually considered when dealing with wireless systems [28; 29]. This approach leads to a multi-objective formulation of the design problem. The bi-objective NSGA-II algorithm in the class of genetic algorithms has been chosen to solve the optimization problems [30; 31; 32; 33; 34; 35; 36]. Genetic algorithms and optimization have also been used in [37] to work out the reactances of a double LCC CN, and for other aspects related to WPTS design with a single objective minimization approach, for example, in [38] to find the parameters of the WPTS controller and in [39] to optimize the coils layout. The presented results are related to an existing prototypal WPTS that was sized to transfer a power of 600 W to charge a minister battery [40]. The prototype was designed as a static WPTS and it is equipped with a couple of circular coils.