On the Optimal Speed Profile for Electric Vehicles

Abstract

The main question in eco-driving is-what speed or torque profile should the vehicle follow to minimize its energy consumption over a certain distance within a desired trip time? Various techniques to obtain globally optimal energy-efficient driving profiles have been proposed in the literature, involving optimization algorithms such as dynamic programming (DP) or sequential quadratic programming. However, these methods are difficult to implement on real vehicles due to their significant computational requirements and the need for precise a-priori knowledge of the scenario ahead. Although many predictions state that electric vehicles (EVs) represent the future of mobility, the literature lacks a realistic analysis of optimal driving profiles for EVs. This paper attempts to address the gap by providing optimal solutions obtained from DP for a variety of trip times, which are compared with simple intuitive speed profiles. For a case study EV, the results show that the DP solutions involve forms of Pulse-and-Glide (PnG) at high frequency. Hence, detailed investigations are performed to: i) prove the optimality conditions of PnG for EVs; ii) show its practical use, based on realistic electric powertrain efficiency maps; iii) propose rules for lower frequency PnG operation; and iv) use PnG to track generic speed profiles. INDEX TERMS Dynamic programming, eco-driving, electric vehicles, speed profile, optimization, pulse-and-glide.

Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency

“…If, on the other hand, there is no jerk limitation, any powertrain topology can quickly set an efficient load point, resulting in almost equal energy consumptions among the topologies. If no comfort is considered, the speed profile of the 1M1G topology results in P&G, similar to Reference [12]. This is energy optimal but unrealistic for passenger trips.…”

“…Energy-efficient driving methodologies may be divided into online and offline applications. DP is often used as an offline method ( [10] p. 164), [11][12][13], since it can compute the global optimal solution using nonlinear functions and efficiency maps present as look-up tables (LUT). Online applications may be used in a model predictive control (MPC) and react to changing boundary conditions, such as leading vehicles.…”

“…The required electrical power, gained by motor efficiency maps, is non-convex, since efficiency drops for low torques and speeds ( Figure A1 in Appendix A). So et al [12] use DP with an efficiency map of an electric motor for an electric powertrain with one motor and a single-speed transmission and showed that energy-efficient driving of an electric powertrain may result in P&G. Except works that use DP, all further reviewed studies approximate the power of the electric motor by quadratic functions of torque and speed or minimize acceleration. If acceleration is minimized, the energy demand must be calculated retrospectively.…”

Contributions of vehicle dynamics to the energy efficient operation of road and rail vehicles

“…Most of the literature focuses on internal combustion engine (ICE) or hybrid electric vehicles (HEVs), but So et al [90] provide a mathematical proof that PnG is also the optimal strategy for electric vehicles, when the desired motor torque is smaller than the torque at which the powertrain efficiency peaks for the specific speed. Owing to the periodic nature of PnG, the real-life implementation of this eco-driving technique can deteriorate driving comfort requiring careful selection of the PnG period and duty cycle.…”

A GA-based Approach to Eco-driving of Electric Vehicles Considering Regenerative Braking

“…In [10], Pontryangin's minimum principle based co-optimization strategy of speed trajectory and power management has been proposed for fuel-cell/battery electric vehicle. In [11], an optimal speed profile has been computed for eco-driving using constant pedal position technique. In [12], an eco-driving at signalized intersections for EV with the support of vehicle infrastructure system technologies has been proposed.…”