An improved continuum skin and proximity effect model for hexagonally packed wires

This work presents approximate but closed-form expressions for “effective” complex-valued magnetic permeability and electric conductivity that represent the effects of proximity and skin effect losses in wound coil with hexagonally packed wires. Previous work is extended by providing improved accuracy versus finite element results for effective permeability and by providing an expression for effective conductivity, which was previously neglected. These material properties can then be used in 2D/axisymmetric finite element models in which the coil is modeled as a coarsely meshed, homogeneous region (i.e., removing the need for modeling each turn in the coil).