Transmission Ratio Design for Electric Vehicles via Analytical Modeling and Optimization

TL;DR

This paper introduces an analytical modeling and optimization approach for electric vehicle transmission design, demonstrating how to improve efficiency by selecting optimal transmission ratios with a case study on BMW i3.

Contribution

It presents a novel analytical loss model for electric machines and derives an optimal transmission ratio, enabling efficient comparison of transmission technologies in EVs.

Findings

CVT can improve efficiency by over 3% compared to fixed-gear transmissions.

The loss model can be fitted accurately with only three sample points.

The approach facilitates integrated design of e-machine and transmission.

Abstract

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.