## 2 State of the Art of Scientific Literature
### Sizing of Charging Infrastructures  
Scientific publications about EB charging either focus on the infrastructures' sizing [11] and/or the scheduling of the battery charging power [12; 13]. A charging strategy can be defined as the choices of charging frequency, power, start time, and duration [6]. Few studies tackle both the sizing and management problems. [PERSON] et al. [14] compared the impact of normal charging at 90 kW and ultra-fast charging at 480 kW on the on-board battery capacity for improving the autonomy of the bus. Fast charging has been shown to reduce the battery capacity and increase the autonomy. [PERSON] et al. [15] have demonstrated that two 150 kW charging stations and an opportunity charger of 350 kW are needed at the terminals in order to reduce the cost and environmental impact compared to current diesel buses. [PERSON] et al. [16] have focused on the energy management of the bus and the charging strategy. The developed \"ECO-charging\" strategy, using pulsed charging to lessen the battery cooling needs, reduces the average grid load by more than 10% and shifts the charging to off-peak periods. On the other hand, a two-phase optimization framework is proposed to size the charging infrastructure and schedule the charging of EBs with the objective to minimize the total system cost in [6]. The developed rolling-horizon-based charging strategy, which adjusts charging scheduling in real-time based on EB consumption and travel time, reduces the total charging cost by 68.3% compared to uncontrolled charging. In several studies, the sizing of a battery storage is combined with the determination of charging schedules [17; 18; 19]. Most studies only consider the sizing of the charger's rated power and the capacity of stationary storage. They usually consider that the size of the on-board battery of the bus is known. However, Ref. [6] investigated the charger deployment, the on-board battery capacity, the charging schedules, and charging costs, and the study shows the importance of considering the on-board battery.  
Many studies about EB charging consider the influence on transportation or on the utility grid, but not both at the same time [20]. For example, in order to improve the traffic, [PERSON] et al. have analysed passenger loading to optimize the vehicle scheduling plan, locations of starting, and terminal stations for short-turning lines and charging strategies [21]. The proposed strategy led to reduce the total passenger travel time (dwell times at stops and inter-stop travel times) of 15%. On the other hand, [PERSON] et al. have considered mainly grid constraints to optimize the objectives of bus operators such as load balancing via peak shaving and cost minimization with load shifting [22]. The presented methodology is achieved to reduce the peak consumption and total charging cost by 50% and 27%, respectively. [PERSON] et al. optimized the bus planning process considering jointly the transportation system and utility grid [23], and [PERSON] et al. studied the feasibility of simultaneously minimizing the power and the energy of surplus PV production [24]. Both studies showed that joint optimization reduces the charging cost, prevents later conflicts between transportation objectives and electricity network constraints, and increases the rate at which EBs charge using local renewable energy.