# A Simple Multi-Parameter Method for Efficient Charging Scheduling of Electric Vehicles
## 2 Materials and Methods  
### Case Study  
This work aims to minimize the charging cost of EVs plugged into the charging stations of a PL considering several technical and operation constraints at EV, parking lot and distribution levels. Some of the input data of the developed model were extracted from the data records of an existing PL in Chania, Greece. This PL does not have charging stations currently, but they are considered to be included in a future investment. Other input data necessary for the simulations were generated using suitable probability distribution functions to simulate the real-world charging situations. A charging schedule method (CS) is designed to ensure the efficient charging and discharging schedule of EVs in real-time at EV and PL levels. The time horizon was divided into time slots with length \(\Delta\)t = 15 min. The residual state-of-charge of the EVs (SoC\({}_{\text{Arr}}\)) when they arrive to the PL is a random number that is assigned to each arriving EV and follows the normal distribution, with \(\mu\) = 55 and \(\sigma\) = 10. To choose the parameters of the normal distribution, we considered that many drivers would probably start travelling from home with a satisfactory SoC of their EVs' batteries. The probability mass function used to estimate the SoC\({}_{\text{Arr}}\) is illustrated in Figure 1. In [22], the authors have extracted from realistic vehicular mobility/parking patterns that 95% of all vehicles have travelled less than 100 km before their arrival to the PLs. Furthermore, the survey in [33] shows that the daily trips were less than 24 km for 85.2% of the studied vehicles. Theoretically, 10% of the EV's battery with efficiency of 161 Wh/km (Nissan Leaf [34]) could cover approximately 24 km. In reality, the distance cannot be calculated precisely because it depends on many factors, such as driver's behavior, weather, etc. Hence, it can be concluded that the normal distribution shown in Figure 1 could adequately describe the residual SoC of the arriving EVs. The calculation of the desirable SoC target (SoC\({}_{\text{t}}\)) is described next. Two factors were considered to calculate SoC\({}_{\text{t}}\). Namely, the traveling distance to the next charging point (NCP) and the range anxiety of the driver (RA). Three different cases were assumed for distance of the next charging point: (1) \"short distance\", (2) \"medium distance\" and (3) \"long distance\", as formulated in (1). More specifically, SoC\({}_{\text{NCP}}\) and SoC\({}_{\text{RA}}\) are random numbers that are separately produced for the \(i\)th EV, as shown in (1), i.e., the function rand(i) produces a random number for the \(i\)th EV ranging between 0 and 1. The possibilities for \"low\", \"medium\" and \"long distance\" were considered equal to 60%, 30% and 10%, respectively [33]. Furthermore, it was assumed that 25%, 60% and 15% of the drivers have low, medium and high range anxiety, respectively. Taking into consideration the fact that an EV with satisfactory SoC has enough energy to cover most of the daily driving requirements, it was assumed that a small number of high range anxiety drivers would occur (15%). In addition, most EV drivers could not estimate the exact SoC to reach the next charging point, and as a result, the medium range anxiety drivers were considered to be the majority. SoC\({}_{\text{t}}\) depends on the distance of the next charging point and the range anxiety of the driver. The higher the range anxiety and distance of the next charging point are, the higher the SoC\({}_{\text{t}}\) is. Finally, SoC\({}_{\text{t}}\) is calculated for the \(i\)th EV according to Equation (1):  
\[\text{SoC}_{\text{t}}(\text{i})=\text{SoC}_{\text{NCP}}(\text{i})+\text{SoC}_ {\text{RA}}(\text{i})\hskip 28.452756 pt\forall\text{i}\ \in\ \text{EV}\]  
\[\text{SoC}_{\text{NCP}}(\text{i})=\left\{