Maximum-distance Race Strategies for a Fully Electric Endurance Race Car

TL;DR

This paper develops a bi-level optimization framework to determine maximum-distance strategies for fully electric endurance race cars, optimizing stint length, charge time, and pit stops to improve race performance.

Contribution

It introduces a novel convex lap time model and a mixed-integer second order conic program for global optimization of electric race strategies.

Findings

Optimized strategies significantly increase race distance.

Flat-out strategies can be highly detrimental.

Joint optimization outperforms fixed pit stop approaches.

Abstract

This paper presents a bi-level optimization framework to compute the maximum-distance stint and charging strategies for a fully electric endurance race car. Thereby, the lower level computes the minimum-stint-time Powertrain Operation (PO) for a given battery energy budget 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 multiple laps and force-based electric motor 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 to the global optimum with off-the-shelf optimization algorithms. Finally, we showcase our framework on a 6 h race around the Zandvoort circuit. Our results show that a flat-out strategy can be extremely detrimental, and that, compared to when the stints are optimized for a fixed number of pit stops, jointly optimizing the stints and number of pit stops can increase the driven distance of several laps.