Simple Loss Model of Battery Cables for Fast Transient Thermal Simulation

In electric vehicles, currents with high-frequency ripples flow in the power cabling system due to the switching operation of power converters. Inside the cables, a strong coupling between the thermal and electromagnetic phenomena exists, since the temperature and Alternating Current (AC) density distributions in the strands affect each other. Due to the different time scales of magnetic and heat flow problems, the computational cost of Finite Element Method (FEM) numeric solvers can be excessive. This paper derives a simple analytical model to calculate the total losses of a multi-stranded cable carrying a Direct Current (DC) affected by a high-frequency ripple. The expression of the equivalent AC cable resistance at a generic frequency and temperature is derived from the general treatment of multi-stranded multi-layer windings. When employed to predict the temperature evolution in the cable, the analytical model prevents the use of complex FEM models in which multiple heat flow and magnetic simulations have to be run iteratively. The results obtained for the heating curve of a 35 mm2 stranded cable show that the derived model matches the output of the coupled FEM simulation with an error below 1%, whereas the simple DC loss model of the cable gives an error of 2.4%. While yielding high accuracy, the proposed model significantly reduces the computational burden of the thermal simulation by a factor of four with respect to the complete FEM routine.