## 5 Case Studies and Simulation Results
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Value (Unit)** \\ \hline m & Vehicle mass & 1000 kg \\ \(\rho_{a}\) & Air density & 1.22 kg/m\({}^{3}\) \\ r & Overall gear ratio & 2.6 \\ \(f_{r}\) & Rolling resistance coefficient & 0.01 \\ \(C_{d}\) & Aerodynamic drag coefficient & 0.3 \\ \(A_{f}\) & Frontal area & 1.6 m\({}^{2}\) \\ \(r_{d}\) & Wheel radius & 0.28 m \\ \(v_{l}(s)\) & Lower speed limit & 0 mph \\ \(v_{u}(s)\) & Upper speed limit & 35 mph \\ \(a_{max,acc}\) & Maximum acceleration & 4 m/s\({}^{2}\) \\ \(a_{max,dec}\) & Maximum deceleration & \(-\)4 m/s\({}^{2}\) \\ \(v_{w}\) & Wind speed & 0 mph \\ \(\alpha\) & Grade & 0\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: EV parameters. Figure 6: Speed profile for scenario 1 **(a)** speed vs. distance; **(b)** speed vs. time. Figure 8: _Cont._  
Figure 7: Speed profile for scenario 2 (**a**) speed vs. distance; (**b**) speed vs. time. Figure 8 illustrates the battery voltage and recaptured energy during acceleration/cruising and deceleration obtained from MATLAB/SIMULINK using the generated speed profile obtained from MILP. It can be observed that during deceleration, the battery voltage increases as energy is pushed back to the battery in both scenarios. Moreover, as can be seen in the second scenario, more energy is recuperated during low speeds, as more current is pushed back to the battery compared to the first scenario within the same interval. According to Table 3, the total energy required for the AEV to complete the route under study is 57.57 Wh for scenario 1 and 56.35 Wh for scenario 2. Although the energy  
Figure 8: Reference speed, motor speed, motor torque, battery current, battery voltage, and recaptured energy obtained from the MATLAB/SIMULINK model: (**a**) scenario 1; (**b**) scenario 2. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Scenario 1** & **Scenario 2** \\ \hline Total energy (Wh) & 57.57 & 56.25 \\ \hline Energy consumption during acceleration/cruising (Wh) & 63.68 & 64.03 \\ \hline Energy recovered through RB (Wh) & 6.11 & 7.78 \\ \hline Energy recovery improvement (scenario 2 vs. scenario 1) & 27\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy extraction and consumption for each scenario. consumption during acceleration/cruising is slightly higher for scenario 2 (proposed method) compared to scenario 1 (base case), the energy recovered through RB is noticeably higher for scenario 2 compared to scenario 1. This increase in recovered energy is almost 27%, and this results in a lower total energy consumption in scenario 2 compared to scenario 1. The reason for this is that by considering the RB dynamic LSB and integrating it into the calculation during the optimization stage, the proposed approach avoids operating the electric motor as a generator when the operating points fall below the dynamic LSB. This ensures that the optimum speed profile generated by MILP achieves the maximum amount of energy harvested during RB. This is also evident when comparing the results of the speed profiles generated for the two scenarios. It can be observed that when the vehicle approaches a stop sign, in the first scenario, the speed decreases almost linearly with a high deceleration rate, while in contrast, in the second scenario, deceleration is achieved with a comparatively lower rate, resulting in an extension of the overall RB region and a lower braking torque. In turn, these factors result in operation above the dynamic LSB, which allows more RB opportunities for the proposed approach.