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This paper presents models and optimization methods to rapidly compute theachievable lap time of a race car equipped with a battery electric powertrain.Specifically, we first derive a quasi-convex model of the electric powertrain,including the battery, the electric machine, and two transmission technologies:a single-speed fixed gear and a continuously variable transmission (CVT).Second, assuming an expert driver, we formulate the time-optimal controlproblem for a given driving path and solve it using an iterative convexoptimization algorithm. Finally, we showcase our framework by comparing theperformance achievable with a single-speed transmission and a CVT on the LeMans track. Our results show that a CVT can balance its lower efficiency andhigher weight with a higher-efficiency and more aggressive motor operation, andsignificantly outperform a fixed single-gear transmission.

Time-optimal Control Strategies for Electric Race Cars with Different Transmission Technologies