A Closed-Form Analytical Method for Reliable Estimation of Equivalent Thermal Conductivity of Windings With Round-Profile Conductors

Overheating of windings is one of the key factors limiting the power density of electric machines. However, thermal modeling of windings is challenging due to the extremely fine and heterogeneous structures. Without adequately addressing the microscopic heat flux field in windings, the commonly used models, even those with conductor insulation accounted for, may give divergent estimations for the equivalent thermal conductivity of windings. Considering the negligible thermal resistance of conductors, we propose a perfect-conductor methodology for thermal modeling of windings, which enables us to derive a closed-form solution to the heat flux field in the impregnation between round wires. From this heat flux solution, the effective thermal resistance of the impregnation, which constitutes the vast majority of that of the whole winding, can then be calculated, based on which a homogenization model is obtained for the equivalent thermal conductivity of the winding. A comparative study confirms that the present perfect-conductor model is more reliable than those commonly used ones. Although only windings formed with round wires are considered here, the perfect-conductor methodology can also facilitate addressing the heat flux profile for other winding constructions.