Optimal Endurance Race Strategies for a Fully Electric Race Car Under Thermal Constraints

This article presents a bi-level optimization framework to compute the offline maximum-distance race strategies for a fully electric endurance race car, whilst accounting for the low-level vehicle dynamics and the thermal limitations of the powertrain components. Thereby, the lower level computes the minimum-stint-time for a given charge time and stint length, whilst the upper level leverages that information to jointly optimize the stint length, charge time, and number of pit stops, in order to maximize the driven distance in the course of a fixed-time endurance race. Specifically, we first extend a convex lap time optimization framework to capture low-level vehicle dynamics and thermal models and use it to create a map linking the charge time and stint length to the achievable stint time. Second, we leverage the map to frame the maximum-race-distance problem as a mixed-integer second-order conic program that can be efficiently solved in a few seconds to the global optimum with off-the-shelf optimization algorithms. Finally, we showcase our framework for a simulated 6 h race around the Zandvoort circuit. Our results show that the optimal race strategy can involve partially charging the battery, and that, compared to the case where the stints are optimized for a fixed number of pit stops, jointly optimizing the stints and number of pit stops can significantly increase the driven distance and hence race performance by several laps.