# A Simple Multi-Parameter Method for Efficient Charging Scheduling of Electric Vehicles
## 2 Materials and Methods
### EVs' Charging Scheduling Method  
#### 2.2.1 Selection of Charge Type  
The examined PL is considered to be equipped with 3 types of charging stations, as shown in Table 2. One-phase 32A and three-phase 16A chargers are adequate to charge all types of PEVs. Only two DC chargers were used as they are more expensive than the other two types and because a small number of EVs would require using them. The majority of drivers using DC chargers are those who have an emergency trip, low SoC and limited time for charging. It was also assumed that each charging point and PEV supports bidirectional energy flow. In Table 2, the power range of each charger type is also shown. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**EV Model** & \begin{tabular}{c} **EV Appearance** \\ **Possibility** \\ \end{tabular} & \
\begin{tabular}{c} **Battery Capacity** \\ **(kWh)** \\ \end{tabular} &
\begin{tabular}{c} **On-Board Charger** \\ **Limitation (kW)** \\ \end{tabular} \\ \hline Nissan Leaf [34] & 0.45 & 40 & 3.6 \\ Tesla Model 3 Standard & & & \\ Range Plus [35] & 0.35 & 50 & 11 \\ BMW 3 120 Ah [36] & 0.2 & 42.2 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: EV model, appearance possibility in the PL, battery capacity and on-board charger limitation. Figure 2: Numbers (per 15 min) of the arrivals, departures of EVs and the EVs participating in the proposed charging schedule. When an EV is connected to the charging pole, a sign-on session is initiated, the charging pole is activated and the arrival time and SoC of the EV battery are sent to the PL operator together with the departure time and SoC\({}_{\text{t}}\) set by the EV driver. The PL operator is responsible for the charging and discharging of the EVs according to the applied charging schedule and all the technical and operation constraints at EV, PL and distribution network levels. First, it is checked if the SoC\({}_{\text{A}\text{r}}\) of the \(i\)th incoming EV is higher than the respective SOC\({}_{\text{t}}\). In this case, the EV will not participate in the proposed charging scheduling method, as shown in Equation (2). According to the available dataset, 793 EVs arrived at the PL during the examined 24 h, and 432 of them participated in the proposed charging schedule method (this group of EVs will be referred to as EV\({}_{\text{CS}}\)). Then, it is checked if there is enough time to charge the EV in an AC charger (denoted by the binary variable AC\({}_{\text{Charger}}\)), as shown in Equation (3):  
\[\text{AC}_{\text{Charger}}(\text{i})=\!\left\{ \begin{array}{ll}1,&\text{E}_{ \text{max}}^{\text{charger}}(\text{i})\ \geq\ \text{E}_{\text{req}}(\text{i})\,\ \ \forall\ \text{i}\ \in\ \text{EV}_{\text{CS}}\\ 0,&\text{otherwise}\end{array} \right. \tag{3}\]  
where \(\text{E}_{\text{max}}^{\text{charger}}(\text{i})\) is the maximum energy the EV charger could give to the \(i\)th EV if it operates with its nominal power during the entire parking time period, and \(\text{E}_{\text{req}}(\text{i})\) is the energy required for the \(i\)th EV to reach its SoC\({}_{\text{t}}\) at its disconnection time. The type of AC charger depends on the on-board charger power limit and it is decided according to the following equations:  
\[\text{AC}_{\text{Charger}(\text{1}-\text{ph, 32A})}(\text{i})=\!\left\{ \begin{array}{ll}1,&\text{P}_{\text{Max}}^{\text{Charger}}(\text{i})\ \leq\ 7.4\ \text{kW}\\ 0,&\text{otherwise}\end{array} \right.\quad\forall\ \text{i}\ \in\ \text{EV}_{\text{CS}} \tag{4}\]  
\[\text{AC}_{\text{Charger}(\text{3}-\text{ph,16A})}(\text{i})=\!\left\{ \begin{array}{ll}1,&\text{7.4 }<\ \text{P}_{\text{Max}}^{\text{Charger}}(\text{i})\ \leq\ 11\ \text{kW}\\ 0,&\text{otherwise}\end{array} \right.\quad\forall\ \text{i}\ \in\ \text{EV}_{\text{CS}} \tag{5}\]  
where \(\text{P}_{\text{Max}}^{\text{Charger}}(\text{i})\) is the maximum (nominal) power of the charging power converter of the \(i\)th EV. If there is not adequate time for the EV to charge its battery with an AC charger, the availability of DC chargers is checked.