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.

中文翻译：

---

可靠估计圆形导体绕组等效热导率的闭式分析方法

绕组过热是限制电机功率密度的关键因素之一。然而，由于极细且异质的结构，绕组的热建模具有挑战性。在没有充分解决绕组中的微观热通量场的情况下，即使是考虑了导体绝缘的模型，常用的模型也可能会对绕组的等效热导率做出不同的估计。考虑到导体的热阻可忽略不计，我们提出了一种用于绕组热模型的理想导体方法，这使我们能够得出圆线之间浸渍中热通量场的封闭形式解。通过这种热通量解决方案，浸渍的有效热阻占整个绕组的绝大部分，然后，可以计算出绕组的等效热导率，并据此获得均质化模型。一项比较研究证实，目前的理想导体模型比常用的模型更可靠。尽管此处仅考虑由圆线形成的绕组，但是理想导体方法也可以帮助解决其他绕组结构的热通量分布问题。