A sectional matrix method for IPT coil shape optimization

In this paper, Neumann´s integral is evaluated for computing self-inductance using a multi-turn sectional matrix method. Analytical equations are derived considering the increase in dimensions of the coil due to an impinging air-gap between the turns. The resulting sectional self-inductance matrix is computed and the concepts of sectional partial self-inductance and sectional partial mutual inductance are introduced. The effects of the various partial inductances are considered as a function of the air-gap, dimensions and turns. Further, the mutual inductance of a pair of coils is considered and the coupling is obtained analytically. The coils considered are to be used for shape optimization of IPT coils. Finally, the results are compared with experimentation. This technique being generic can be applied to a number of different polygonal shapes and can be further simplified by the theory of vector decomposition of current elements. A case study with self-inductance and perimeter as optimization objective is considered.