Transmission Ratio Design for Electric Vehicles via Analytical Modeling and Optimization

In this paper we present an effective analytical modeling approach for the design of the transmission of electric vehicles. Specifically, we first devise an analytical loss model for an electric machine and show that it can be accurately fitted by only sampling three points from the original motor map. Second, we leverage this model to derive the optimal transmission ratio as a function of the wheels' speed and torque, and use it to optimize the transmission ratio. Finally, we showcase our analytical approach with a real-world case-study comparing two different transmission technologies on a BMW i3: a fixed-gear transmission (FGT) and a continuously variable transmission (CVT). Our results show that even for e-machines intentionally designed for a FGT, the implementation of a CVT can significantly improve their operational efficiency by more than 3%. The provided model will ultimately bridge the gap in understanding how to efficiently specify the e-machine and the transmission technology in an integrated fashion, and enable to effectively compare single- and multi-speed-based electric powertrains.