Lap Time Optimization of a Sports Series Hybrid Electric Vehicle Roberto Lot and Simos A. Evangelou Abstract—This paper illustrates a methodology for the lap time optimization of a race series hybrid electric vehicle based on the indirect optimal control approach. More specifically, for a vehicle with given characteristics running on a given track, the optimal trajectory and powertrain power flow that minimize the lap time are found. The paper presents a parametric model of a sports series hybrid electric vehicle, illustrates the optimization method and discusses simulation results. Index Terms—hybrid electric vehicle, vehicle dynamics, op- timal control, lap time optimization. I. I NTRODUCTION H YBRID electric vehicles (HEVs) are becoming more popular due to their potential to address climate change and the demand for a limited, but increasingly expensive, supply of fossil fuels. In addition, a new category of sports and race HEVs is emerging [1], [2]. Although the synergy between multiple energy sources in HEV powertrains is normally used to bring reductions in fuel consumption and noxious emissions, in racing the main interest is about performance and lap time minimization. In the case of road HEVs various control techniques have been proposed in the literature for the powertrain energy management, ranging from rule-based to optimisation-based [3]–[9]. This paper presents a global optimisation-based con- trol approach that utilises indirect optimal control techniques to optimise not only the powertrain energy flow but also the trajectory of a racing HEV inside a given race circuit. The methodology is established by utilising symbolic dynamic vehicle modelling of appropriate complexity, together with computationally efficient optimal control software [10]. II. MATHEMATICAL MODEL The powertrain of a Series Hybrid Electric Vehicle (S- HEV) is schematized in Figure 1 and consists of three branches: the spark ignition engine, the battery and the trans- mission. In driving operating conditions, i.e. while cruising at a constant speed or accelerating, power is request to drive the vehicle. The spark ignition (SI) engine is mechanically connected to the permanent magnet synchronous (PMS) generator, which converts the engine mechanical power P e into the electric AC power P g . The rectifier takes this AC power and converts it to DC power P r , which is provided to the DC link. In the other branch, the battery (possibly) provides additional power P bl to the DC/DC converter, which steps up the battery voltage to v dc and provides power P b to the DC link. The overall DC link power P r + P b is converted Manuscript received March 6, 2013; revised April 3, 2013. R. Lot is with Department of Industrial Engineering, University of Padova, 35100 Padova, Italy e-mail: roberto.lot at unipd.it S. A. Evangelou is with the Departments of Electrical and Electronic, and Mechanical Engineering, Imperial College London, London, UK e-mail: s.evangelou at imperial.ac.uk from DC into AC by the inverter, which supplies the electric power P i to the PMS motor. The latter is connected to the wheels by means of a fixed ratio transmission, and the vehicle is finally driven with power P t . While braking, power is driven through the transmission to recharge the battery. Additionally, mechanical brakes extract power P h which is transformed into heat and definitively dissipated. Optionally, the battery may be recharged by the SI engine when a power surplus is available. In summary, the S-HEV has three in- dependent power sources, respectively battery P b , generator P g and brakes P h power, that may be variously combined to obtain the desired values of vehicle speed and acceleration. In particular, the battery may conveniently provide boost power while the vehicle is accelerating. However, the battery energy is limited to the value which may be recovered during each lap, hence it is scarse and it is important to use boost effectively and to optimize the whole power management process. Finally, as a race driver is free to select his preferred trajectory inside the track, to minimize the lap time it is also necessary to optimize the trajectory and speed profile at the same time as optimizing the power flow in the vehicle. Details of the mathematical model of the S-HEV vehicle and its powertrain, the formulation of the minimum lap time problem and some simulation results are discussed in the next sections. A. Powertrain The first power branch (Figure 1) includes the SI engine, the PMS generator and the AC/DC converter. Modelling in detail such elements is not trivial and out of the scope of this work. For the purpose of lap time optimization, the essential feature of this power branch is that the SI engine is not mechanically connected to the vehicle transmission and so it may deliver the maximum available power regardless of the vehicle speed. The total power provided by this branch is found by considering that the SI engine is a source of (limited) power P e , which is then reduced while flowing through the PMS generator and AC/DC converter, that have efficiencies (assumed constant) η g and η r respectively: P r = η r η g P e (1) Fig. 1. Powertrain architecture of a Series Hybrid Electric Vehicle (purple arrows indicate power losses). Proceedings of the World Congress on Engineering 2013 Vol III, WCE 2013, July 3 - 5, 2013, London, U.K. ISBN: 978-988-19252-9-9 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2013