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Thermal Slot Model for Random Wound Electrical Machines Using Statistical Approach

Mathieu Kirouac, Maxim Bergeron, Jérôme Cros, Philippe Viarouge

The heating estimation of random wound coils in electrical machines is a challenge: the number of wires per slot is generally high and the wires are randomly distributed in the slot. This paper presents an original statistical modelling method to evaluate the steady state thermal coil behaviour. This method takes into account the fill factor and can model different wires arrangements using a statistical distribution. The coil section is discretised as a thermal resistances network. Each round wire is associated to a node and linked to others using combined thermal resistances. First, we present the method used to fill the slot with round wires and estimate the gap between them. A mean thermal resistance between two wires is calculated using one-dimensional and bi-dimensional thermal resistances. We also compute extreme values for this resistance. Both values give a baseline to simulate random wires arrangements by using probability density functions. We explain how to take account the boundary conditions and solve the problem. The 2D slot model version is validated by finite elements analysis and experimental comparisons. According to the experimental results, it was possible to identify the best random distribution of thermal resistances which represents the wire arrangement in slot geometry. Finally, we present how to make a 3D model version and we present a case study of a concentrated winding for a permanent magnet machine.