## 4 Case Study  
In this paper, the GTFS data are gathered for the city of Compiegne in France. The bus line \"ARC EXPRESS\", which is 20 km long and composed of 12 bus stops, is chosen as the case study (see Figure 6). According to GTFS data, there are 11 routes and 36 trips used for providing transportation services over a day. The services of two buses were defined manually, so they matched the timetable. In order to realize all the trips defined on the timetable, the first bus \"bus n\({}^{\circ}\)1\" begins its service at 06:30 and ends it at 19:15. It performs 11 trips, including 2 between the bus depot and the line terminals. The second bus \"bus n\({}^{\circ}\)2\" operates from 06:10 to 18:50 and performs 15 trips. Both buses have long idle period in the middle of the day. The cumulative distance travelled by bus n\({}^{\circ}\)1 and bus n\({}^{\circ}\)2 are 149 km and 219 km, respectively. Concerning the speed profile between two bus stops, the acceleration is assumed to be constant at \(a=1\) m/s\({}^{2}\)[55]. Speed and acceleration limits are assumed as \(v_{lim}=40\) km/h and \(a_{lim}=1.5\) m/s\({}^{2}\), considering the need of passenger comfort [56]. Figure 6: Bus line ARC EXPRESS in Compiègne [57]. The 12m bus model from BYD has been chosen for this case study [58], and its characteristics are given in Table 2. This EB is equipped with a 422 kWh battery adding 2.8 tons (assuming 150 Wh/kg for lithium iron phosphate battery [1]) to the normal bus weight of 16.7 tons (total weight 19.5 tons). Average power values are assumed for the ventilation \(P_{ventilation}\) and the other auxiliaries \(P_{other}\)[35]. The initial SoC of the EB battery is arbitrarily set to 90%. Available charging powers are taken from the ABB's chargers. Buses can be charged at the depot using a Combined Charging System plug with a power of 100 kW or 150 kW [59]. They can also be charged overnight at the depot with a pantograph at 50 kW [60]. Eventually, on-route charging at bus stops and terminals can be performed via ABB's HVC-Opportunity charger at the power ratings of 150 kW, 300 kW, 450 kW, or 600 kW [60]. Scenarios described hereafter consider a power of 50 kW at the depot and 150 kW, 300 kW, 450 kW, and 600 kW for opportunity charging. The number of boarding/alighting passengers is chosen arbitrarily, and the passenger flow is fixed for all routes of the same length. The number of passengers boarding/alighting is summarized in Table 3 for different lengths of bus sequence and one example for a bus route composed of 10 stops is displayed in Figure 7. The passage rate is assumed to be one passenger every four seconds [35]. An average passenger weight of 68 kg is considered. When computing the necessary energy to reach the next charging station, an arbitrary consumption of 1.3 kWh/km is chosen in order to keep a safety margin for considering the uncertainty on the future bus consumption. \begin{table}
\begin{tabular}{c c c} \hline \hline
**BYD-12 m Bus** & \multicolumn{2}{c}{**PV Panel**} \\ \hline
**Characteristics** & **Value** & **Characteristics** & **Value** \\ \hline Length & 12.2 m & \(P_{STC}\) & 345 W \\ Width & 2.55 m & \(N_{PV}\) & 290 \\ Height & 3.30 m & \(SSTC\) & 1000 W/m\({}^{2}\) \\ Gross vehicle weight & 19.5 t & \(\gamma\) & \(-\)0.29\%/\({}^{\circ}\)C \\ Maximal passenger & 85 & \(NOCT\) & 41.5 \({}^{\circ}\)C \\ capacity & 422 kWh & \(T_{air-test}\) & 20 \({}^{\circ}\)C \\ Battery technology & LFP \({}^{1}\) & \(G_{test}\) & 800 W/m\({}^{2}\) \\ \(soc_{min}\) & 20\% & \(\eta_{syst}\) & 85\% \\ \(soc_{max}\) & 90\% & & \\ \(P_{ventilation}\) & 0.5 kW & & \\ \(P_{other}\) & 2 kW & & \\ \hline \hline \end{tabular} \({}^{\dagger}\) Lithium Iron Phosphate.  
\end{table} 
Table 2: Characteristics of the BYD-12 m bus and the PV panels.