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This paper presents a modeling and optimization framework to minimize theenergy consumption of a fully electric powertrain by optimizing its design andcontrol strategies whilst explicitly accounting for the thermal behavior of theElectric Motor (EM). Specifically, we first derive convex models of thepowertrain components, including the battery, the EM, the transmission and aLumped Parameter Thermal Network (LPTN) capturing the thermal dynamics of theEM. Second, we frame the optimal control problem in time domain, and devise atwo-step algorithm to accelerate convergence and efficiently solve theresulting convex problem via nonlinear programming. Subsequently, we present acase study for a compact family car, optimize its transmission design andoperation jointly with the regenerative braking and EM cooling controlstrategies for a finite number of motors and transmission technologies. Wevalidate our proposed models using the high-fidelity simulation softwareMotor-CAD, showing that the LPTN quite accurately captures the thermal dynamicsof the EM, and that the permanent magnets' temperature is the limiting factorduring extended driving. Furthermore, our results reveal that powertrainsequipped with a continuously variable transmission (CVT) result into a lowerenergy consumption than with a fixed-gear transmission (FGT), as a CVT canlower the EM losses, resulting in lower EM temperatures. Finally, our resultsemphasize the significance of considering the thermal behavior when designingan EM and the potential offered by CVTs in terms of downsizing.

Energy-optimal Design and Control of Electric Powertrains under Motor Thermal Constraints