On the Optimal Speed Profile for Electric Vehicles

So, Kai Man; Gruber, Patrick; Tavernini, Davide; Karci, Ahu Ece Hartavi; Sorniotti, Aldo; Motaln, Tomaz · 2020 · Crossref

DOI: 10.1109/access.2020.2982930

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Summary

This paper addresses the challenge of determining optimal speed profiles for electric vehicles (EVs) to minimize energy consumption over a fixed distance within a specific trip time. While dynamic programming (DP) is a standard method for finding globally optimal profiles, its high computational requirements and need for precise a-priori scenario knowledge limit its real-world implementation. Furthermore, existing literature lacks a realistic analysis of optimal driving profiles for EVs, often relying on simplified powertrain efficiency models. This study aims to bridge this gap by comparing DP-derived optimal solutions with intuitive, easy-to-follow speed profiles, specifically investigating the applicability of Pulse-and-Glide (PnG) driving techniques for EVs. The researchers conducted a simulation study using a prototype L7e quadricycle equipped with in-wheel direct drive electric machines. They first evaluated a "Constant Pedal Position Technique" (CPPT), where acceleration, constant speed, and braking phases use fixed torque ratios. A brute-force optimization identified the optimal CPPT (Opt-CPPT) profiles for various distances and average speeds, accounting for realistic powertrain efficiency maps. Subsequently, they employed DP to calculate unconstrained optimal speed profiles. The DP algorithm minimized battery energy consumption and trip time, using a velocity grid and torque steps to generate Pareto fronts of energy consumption versus average speed. The study compared the energy consumption and operational characteristics of Opt-CPPT against DP solutions across different average speeds and distances. The results demonstrate that DP solutions for EVs inherently involve high-frequency Pulse-and-Glide (PnG) patterns, particularly at lower average speeds. At an average speed of approximately 19 km/h, the DP solution consumed 22.7 Wh/km, which was 24.2% less than the Opt-CPPT solution (28.2 Wh/km). This efficiency gain arises because the DP strategy accelerates the vehicle to higher torque levels where the powertrain operates more efficiently (87.9% vs. 68.6%), then freewheels to maintain average speed. In contrast, Opt-CPPT maintains a constant speed at lower, less efficient torque levels. At higher average speeds (e.g., 45 km/h), the efficiency gap narrows significantly (1.4% difference) because the powertrain operates more efficiently at higher speeds and torques. The study also proves analytically that PnG is optimal for EVs under certain conditions and provides rules for implementing lower-frequency PnG to track generic speed profiles. The significance of this work lies in its validation of PnG as an optimal strategy for EVs when realistic powertrain efficiency maps are considered, contradicting earlier assumptions based on simplified models. The findings suggest that while DP provides the theoretical optimum, its complex, high-frequency oscillations are impractical for real-time implementation. Consequently, the paper proposes simplified rules for PnG operation and compares them with intuitive CPPT profiles, offering a pathway for developing practical eco-driving assistance systems. These systems can guide drivers or automated controllers to adopt energy-efficient strategies that balance computational feasibility with significant energy savings, particularly in low-speed urban driving scenarios.

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• eco driving