**1. Introduction**

The United States is one of the world's prime petroleum consumers, burning more than 20% of the planet's total refined petroleum, and the surface transportation sector alone accounts for around 69% of the United States' total petroleum usage [1]. This presents the transportation sector with three important challenges: availability of fuel to drive vehicles, emissions of greenhouse gases, and vehicular crashes. It is, therefore, important to reduce petroleum consumption to make surface transportation safer, more efficient, and more sustainable [2].

The advent of communication and information technology has enabled vehicle-to-vehicle and vehicle-to-infrastructure connectivity, so that various data, such as signal phase and timing (SPaT), vehicle trajectory, and velocity, can be transmitted and utilized. The advanced communication abilities of connected vehicles ensures that information is updated at a very high rate, which enables researchers

to develop connected transportation systems meeting safety, economy, and efficiency challenges [3]. Studies have shown that vehicles have high fuel consumption rates when approaching signalized intersections because of vehicle acceleration/deceleration maneuvers during stop-and-go traffic [2,4]. Over the past few decades, researchers have worked on optimizing traffic signal planning to reduce traffic delay and fuel consumption [5,6]. In recent years, a number of studies have focused on developing eco-driving algorithms to help vehicles approach signalized intersections using connected vehicle technologies. These eco-driving strategies aim to provide, in real-time, recommendations to individual drivers or vehicles so that vehicle maneuvers can be appropriately adjusted to reduce fuel consumption and emission levels [7–9].

Most of the studies in this area have been focused on developing eco-driving strategies for internal combustion engine vehicles (ICEVs). For example, Malakorn and Park proposed to reduce vehicle fuel consumption by minimizing vehicle acceleration maneuvers using a cooperative adaptive cruise control system under a connected environment [10]. Another study [2] developed an optimal control strategy by using dynamic programming and recursive pathfinding techniques, and the control logic was validated by an agent-based modeling approach. In addition, a schedule optimization method was proposed in [11] to search for "green-windows" so that vehicles can traverse multiple signalized intersections by minimizing full stops. A further-improved approach was developed by Guan and Frey to generate a brake-specific fuel map so that the optimized gear ratio can be computed to save fuel levels [12].

In addition to the studies that focused on ICEVs, a few studies have investigated eco-driving strategies for battery electric vehicles (BEVs) near signalized intersections. Using SPaT information passed from connected infrastructure, an energy-optimized speed trajectory can be computed for BEVs while traveling on signalized arterials, thus extending the BEV's range. An eco-driving technique for BEVs was developed in [13]. In that work, the vehicle trajectory control problem was formulated as an optimization problem to minimize the summation of vehicle power, and Bellman's dynamic programming algorithm was used to compute the optimal solution. However, a simple energy model was used in this study by assuming that the recharge efficiency is a constant value. Another BEV eco-driving algorithm was proposed in [14]. A VT-Micro model-based energy consumption model was developed for different BEV operation modes (including acceleration, deceleration, idling, and cruising). Subsequently, an eco-driving model, which used the developed energy model, was proposed for a single signalized intersection. Several example trips in the case study illustrate the proposed eco-driving method's ability to reduce energy consumption efficiently. However, the proposed energy consumption model was a statistical model based on limited collected data, thus the accuracy may not be sufficient for developing an optimal control strategy for dynamic vehicle maneuvers. Moreover, the vehicle dynamics model was not considered in the constraints to compute the acceleration level, so the calculation of the optimal solution may use an unrealistic acceleration level.

The same energy consumption model was used in [15] to develop a connected BEV eco-driving system. A model predictive control logic was considered in the control system to force the vehicle to follow the optimal speed trajectory as closely as possible. A field test with four participants demonstrated an average of 22% energy savings for automated driving with the proposed eco-driving system. However, a 2012 Ford Escape with a hybrid engine was used for the field test in this study, and this vehicle was assumed to be representative of an actual BEV's performance.

An analytical model to calculate a BEV's optimum vehicle trajectory was proposed in [16], with the goal of minimizing electricity usage with consideration of intersection queues. Furthermore, an approximation model was proposed to increase computation efficiency for real-time applications. A 47.5% energy savings was found when evaluating field data from a six-intersection corridor. However, the objective function was the summation of energy consumption from the tractive force only, and the braking force was assumed to be 100% transferable to battery power. In addition, the work in [17] provided a solution to minimize BEVs' energy consumption while traversing a sequence of signalized intersections and always getting a green indication. A simple simulation network (AIMSUN) with five

intersections was used in the case study. A sensitivity analysis with different market penetration rates was tested to show a 10% energy savings for a 40% penetration rate. However, the computation of energy consumption in this study did not consider regenerative braking.

There are several issues with the aforementioned studies of BEV eco-driving strategies: a lack of realistic energy consumption models to accurately compute the instantaneous energy consumption when BEVs travel through signalized intersections, and the lack of a vehicle dynamics model to constrain vehicle acceleration maneuvers. In addition, although many previous studies developed eco-driving strategies for ICEVs and BEVs, there is no comparison to demonstrate the differences in the energy-optimal solutions for each. To address these issues, this study develops a connected eco-driving controller for BEVs, called the BEV Eco-Cooperative Adaptive Cruise Control at Intersections (Eco-CACC-I). The developed controller can assist BEVs negotiating signalized intersections by minimizing their energy consumption. The calculation of optimal vehicle trajectory is formulated as an optimization problem subject to the following constraints: (1) vehicle acceleration/deceleration behavior, defined by a vehicle dynamics model; (2) vehicle energy consumption behavior, defined by a BEV energy consumption model; and (3) the relationship between vehicle speed, location, and signal timing, defined by vehicle characteristics and SPaT data shared under a connected vehicle environment. The optimal speed trajectory is computed in real-time by the proposed BEV Eco-CACC-I controller so that a BEV can follow the optimal speed while negotiating a signalized intersection. The proposed BEV controller was tested in a case study to investigate its performance under various speed limits, roadway grades, and signal timings. In addition, a comparison of the optimal speed trajectories for BEVs and ICEVs was conducted to investigate the impact of vehicle engine types on eco-driving solutions. Lastly, the proposed controller was implemented in microscopic traffic simulation software to test its networkwide performance. The test results from an arterial corridor with three signalized intersections demonstrate that the proposed controller can effectively reduce stop-and-go traffic in the vicinity of signalized intersections, and that the BEV Eco-CACC-I controller produces average savings of 9.3% in energy consumption and 3.9% in vehicle delays.

The remainder of this paper is presented as follows. The proposed BEV Eco-CACC-I system and the vehicle dynamics and energy consumption models are described in the next section. Afterward, the details of the proposed system testing on the case study section to investigate the impacts of various factors on system performance are presented. This is followed by implementing the proposed controller into microscopic traffic simulation software to quantify the networkwide impacts. The last section provides conclusions and recommendations for future research.
