Analytical Computation for AC Resistance and Reactance of Electric Machine Windings in Ferromagnetic Slots

Under the effects of alternating current (AC), the resistance and reactance of electric machine windings are different from their static state. As electric machine windings usually comprise many conductors, it makes the modeling and analysis very cumbersome using the finite element method. This paper presents an analytical method for computing AC resistance and reactance of electric machine windings placed in ferromagnetic slots, which is more convenient and efficient, and could be extended to the slots with different complex structures. First, the slot is divided into a number of layers based on the concept of discretization. Then, the magnetic field governing equation is established, and the distributions of magnetic field intensity and the current density of conductors under AC conditions are solved. By Poynting's theorem, the complex power flowing into the conductors is calculated, and then the effective resistance and reactance of the windings are obtained. Finally, the deduced analytical solutions are compared with the finite element method, and the results show that they have a good agreement for both single-layer winding and the double-layer windings with current phase difference. The presented analytical model is useful for understanding the AC effects and optimization of electric machine windings placed in ferromagnetic slots.