Energy-optimal speed control for electric vehicles under vehicle-to-infrastructure (V2I) environment

As the world moves toward sustainability, many talents and resources are now allocated for electrifying transportation systems that could significantly reduce carbon emissions, operate vehicles more efficiently, and reduce oil dependency. Many state and local governments also have committed themselves to promoting electric vehicles (EVs). With this momentum, it is not difficult to see that in the near future EVs could gain a significant market penetration. We will soon face one of the biggest challenges: how to improve efficiency for the EV transportation system.

To address this challenge, this research proposes an operational method, combined with the highly promising Vehicle-to-Infrastructure (V2I) technology, to optimize each individual EV’s energy consumption through optimizing the vehicle speed pattern with smoother deceleration and acceleration rates. An analytical model is developed in this research for EV traveling on signalized arterials. In this model, the EV’s optimal speed control has been formulated as a multi-stage optimal control problem. The real-time traffic conditions including signal status changes and intersection queue lengths provided by V2I technology are treated as the input for this model, and the multi-stage design makes the proposed model suitable for real-time application.

The first critical step is to develop an energy consumption model for EVs. In order to be suitable for real-time applications, this research develops a simple energy consumption model based on the fundamental theory of vehicle dynamics. This model first determines the required tractive efforts through deriving major resistances; then, based on the relationship between the electrical losses and current, this model analytically describes EV’s instantaneous power as a function of real-time velocity, acceleration, and roadway grade. The integration of the instantaneous power over the trip time gives an estimation of the overall energy consumption for a trip.

The proposed energy consumption model is evaluated using an EV conversion vehicle converted from a 1987 Nissan D21 pickup. A data collection system has also been developed to collect in-use EV data and vehicles’ driving information. The data collection system consists of a CAN bus data logger (through BMS) to collect in-use vehicle data, a Smartphone (or tablet) for data transmission (through Bluetooth) and vehicle trajectory collection, and a database for data storage. 5 months of data was collected and used to first evaluate instantaneous power estimation model. The evaluation result shown in Fig 1. indicates that the proposed simple estimation model can accurately estimate EVs’ instantaneous power. Fig 2. further shows the consistence between the measured and estimated EV power values through a scatter plot. We also compare the measured and estimated energy for each trip. Fig 3. clearly shows that the proposed model can successfully estimate trip energy usage. The average mean absolute error (MAE) for all 41 trips is 15.6%.




Fig 1. Measured power vs. estimated power (time series plot)




Fig 2. Measured power vs. estimated power (scatter plot)




Fig 3. Measured vs. estimated EV trip energy consumption


This research then models the EV’s optimal speed control at signalized intersection as a multi-stage optimal control problem. In this model, each individual intersection is treated as a “stage”, and an optimal control model is developed to minimize an individual EV’s electricity usage. The objective function is to minimize the overall energy consumption for an EV traveling through a corridor consisting of multiple signalized intersections, subject to the state constraint, queue limitation constraint, travel time constraint, and boundary constraints.  An approximation model is further developed to improve the computation efficiency.

The proposed model is evaluated using a six-intersection signalized arterial corridor (Fig 4.). During the test, V2I technology is assumed available to provide real-time traffic information including signal timings and intersection queues. The evaluation results show that following the speed profile suggested by the proposed model (Fig 5.), the energy saving is as high as 47.7% without any additional travel time (236 seconds) as shown in Table 1. Future research will be focusing on how to achieve a system optimum which not only benefits the energy saving for individual vehicles but for the whole system.




Fig 4. Test site: Trunk Highway 55 (from Google map)




Fig 5. Optimal speed profile


Table 1: Electric Vehicle Performance Comparisons

Performance Measurements

No Control

Optimal Control

Approximation Model

Total Travel Time (Second)




Energy Consumption (kWh)




Energy Efficiency

(kWh/100 mile)




Energy Saving (%)






Xinkai Wu, professor, school of transportation science and engineering, Beihang University, E-mail:




[1] Wu, X., He, X., Yu. G., Harmandayan, A, Wang, Y. (2015). Energy Optimal Speed Control for Plug-in Electric Vehicles on Signalized Arterials, IEEE TRANSACTIONS ON ITS, VOL. 16, NO. 5, OCTOBER 2015.

[2] Wu, X., Freese, D., Cabrera, A., Kitch, A. W. (2015). Electric Vehicles’ Energy Consumption Measurement and Estimation, Transportation Research–Part D, 34(2015), 52-67.