Battery model impact on time-optimal co-design for electric racing cars: review and application

The sustainable mobility trend touches the racing world as well, from the hybridization of Formula 1 (F1) and Le Mans Hypercars to the fully electric Formula E racing class. In this scenario, the research community is studying how to push electric racing vehicles to their limit, combining vehicle dynamics and energy management, to successfully solve the minimum lap time problem. Recently, this class of problems has been enlarged towards optimal sizing, with a particular interest in batteries, which represent the main bottleneck for electric vehicle performance. In this work, starting from a thorough review of literature approaches, we define a general optimization framework of minimum lap and race time problems for electric vehicles, suitable to figure out the impact of different modeling choices on both problem structure and optimal variables profiles. Exploiting a case study on Generation 3 (Gen 3) of Formula E cars, we delve into the impact of battery models' complexity on both optimal sizing and optimal battery usage. We show how highly detailed models are necessary to study the evolution of both battery and vehicle control variables during the race, while, simple models are more than sufficient to address the battery sizing problem.