CEME Collaborator Professor Bulent Sarlioglu and Research Assistant Justin Paddock – University of Wisconsin-Madison

Cooling electric machines designed for power levels at the megawatt scale is necessary to increase their power density. An analytical approach was initially adopted for modeling the windings and heat exchangers’ thermal behavior to scale in-slot heat exchangers and flat winding concepts.
A simplified flat-winding and heat exchanger configuration within a single machine slot was formed. The winding is represented as a single conductor with a constant current running through it, and the heat exchanger is assumed to be interfaced with the winding in the radial direction. The heat exchanger is placed between the stator iron and winding, which exposes the winding directly to the air gap. It is assumed there is an adiabatic boundary at the winding and air-gap interface and a convective boundary between the winding and the heat exchanger fluid. The slot, winding, and heat exchanger configuration geometry are represented as rectangular extrusions that conveniently form the thermal problem in Cartesian coordinates. A general schematic of the setup is provided in Figure 1.

Figure 1. Schematic of a single-layer winding configuration with in-slot heat exchanger for a single machine slot.

The resistive losses through the conductor can be estimated using the conductor geometry, the copper electrical resistivity, and the current through the conductor. Fourier’s law is applied to approximate a one-dimensional temperature distribution within the winding, assuming the resistive losses are generated as heat uniformly through the conductor. This solution allows for the maximum temperature and its location within the winding to be identified. An equivalent thermal resistance approach is used to model the boundary condition at the interface between the winding and heat exchanger. This involves estimating the convection resistance by applying a convection correlation for the coolant flow within the duct, a conduction resistance through the heat exchanger walls, and the contact resistance at the interface.
The model can estimate the maximum slot (and conductor) current density with a series of design-related inputs: the maximum permitted winding temperature, the geometric characteristics of the winding and heat-exchanger configuration within the slot, the flow performance within the internal flow path of the heat exchanger, and the materials and coolant properties. This analytical approach allows for efficient assessment of numerous design configurations. With appropriate constraints imposed, a design parameter space can be set up, allowing for use of optimization techniques to find a winding and heat-exchanger configuration that maximizes slot-current density,
The ability to integrate multiple winding regions and heat exchangers will be incorporated into the model, allowing for exploring additional designs of interest. This will first be implemented by “stacking” the winding regions and heat exchangers in a single direction (one-dimensional) and then placing them at arbitrary locations within the slot (two-dimensional). After successful implementation, designs of various winding and heat-exchanger configurations at representative slot geometries at high-power levels can be analyzed with greater accuracy and optimized for maximum current density.