*3.1. Test Eco-CACC-I for BEVs*

The simulated test road consisted of a single signalized intersection with a control length starting 200 m upstream and ending 200 m downstream of the intersection (total length of 400 m). An automated connected vehicle, a 2015 Nissan Leaf equipped with the Eco-CACC-I system, was assumed to follow the optimal speed profile calculated by the Eco-CACC-I algorithm in that 400-m distance. Combinations of different speed limits (25, 30, 40, and 50 mph), signal indication offsets (15, 20, 25, and 30 s) and road grades (+3% and −3%) were tested. Given that the test results for the Nissan Leaf under various speed limits were very similar, the test results for the 25-mph speed limit alone are presented in Figures 2 and 3.

**Figure 2.** Nissan Leaf speed profile by BEV Eco-Cooperative Adaptive Cruise Control at Intersections (BEV Eco-CACC-I) for a speed limit of 25 mph.

**Figure 3.** Nissan Leaf BEV Eco-CACC-I energy consumption for a speed limit of 25 mph.

Figure 2 demonstrates the test results under a 25-mph speed limit for different signal timings and road grade values. Note that the vehicle with an initial speed of 25 mph did not need to slow down for the 15-s red indication, so the plots for this case were not included. Each image in Figure 2 presents the sampling of numerous feasible solutions (speed profiles) for each combination of parameters. For instance, the right bottom image in Figure 2 includes 29 curves. Each curve represents a feasible solution when a vehicle approaches a signalized intersection with a certain deceleration level (*ai*). The downstream throttle level was the optimal throttle corresponding to the minimal energy consumption given the upstream deceleration level of *ai*. Each feasible solution is plotted in a different color, and the optimal solution, which corresponds to the minimal energy consumption trajectory, is presented in a bold red color. It should be noted that all the images in the left column in Figure 2 show that the speed profile associated with the maximum deceleration level was the optimal solution for the uphill direction. Furthermore, all the images in the right column in Figure 2 show that the speed profile associated with the minimum deceleration level was the optimal solution for the downhill direction.

The corresponding energy consumption levels for each feasible solution (speed profile) are presented in Figure 3. Note that the solution index in the *x*-axis represents the 1st solution, 2nd solution ... *n*th solution, ordered in ascending order by deceleration levels. All the images in the left column in Figure 3 show that the upstream trip regenerated minimum electric power; much less battery power was regenerated than was consumed. In this case, the cruise speed was the most important factor in identifying the optimal solution, as higher cruise speeds associated with higher deceleration levels result in less energy consumption for the entire trip. Consequently, the maximum deceleration level corresponds to the optimal solution for a BEV driving in the uphill direction. All the images in the right column in Figure 3 illustrate that the upstream trip generated equal or slightly higher electric power than the battery power consumed during the downstream trip due to the impact of gravity in the downhill direction. In this case, the deceleration level was the most important factor in identifying the optimal solution. Lower deceleration levels correspond to longer deceleration times and more regenerative electric power upstream of the intersection, which can result in lower energy consumption for the entire trip. Therefore, the minimal deceleration level corresponds to the optimal solution for a BEV driving in the downhill direction.

The Nissan Leaf is a compact BEV with an 80-HP engine; to investigate the impact of engine size on the optimal control strategy, a 2015 Tesla Model S with a much more powerful 283 HP engine was also tested. The same simulation was conducted assuming a connected and automated Tesla Model S equipped with the Eco-CACC-I controller. The simulation results were very similar to the Nissan Leaf results. There were two main differences. First, downstream of the intersection, the Tesla could accelerate to the maximum allowed speed (speed limit) much more quickly in the downhill direction given that the vehicle is more powerful than the Nissan Leaf. Second, the energy consumption for the Tesla Model S was higher since it weighs more. However, the energy consumption curves across the solutions from minimum to maximum deceleration levels showed the same trends, so the same optimal solution could be found for both vehicles. Given that the test results for the Nissan Leaf are already illustrated, the plots for the Tesla are not presented here. According to the test results for the two BEVs, the optimal solutions for the downhill and uphill directions can be summarized as follows:

	- -Upstream—lower cruise speed produces longer brake time and more regenerative energy.
	- - Downstream—lower cruise speed means more energy consumption downstream; however, the benefit of energy regeneration upstream exceeds the additional needs for energy downstream.
	- - Upstream—different from the solution for the downhill direction, the vehicle regenerates minimum energy by decelerating in the uphill direction.
	- - Downstream—the vehicle needs the maximum cruise speed while proceeding through the intersection so that the downstream trip requires less energy.
