# V2G Strategies to Flatten the Daily Load Curve in Seoul, South Korea
## 2 Daily Load Curve Evaluation Method
### Charging and Discharging Modeling of EVs by Location
#### 2.1.2 Probability Density Function of EV Charge Start Time at Home
The difference between control mode 1, control mode 2, and the uncontrolled mode is caused by the fact that SMP rates are relatively high from 8:00 a.m. to 2:00 p.m. In addition, as shown in the charging probability density function of uncontrolled discharge and controlled discharge in the home, shown in Figure 3, it can be seen that the probability density gradually increases from 4:00 p.m. to 8:00 p.m. in the case of the uncontrolled mode. After that, it gradually decreases until 11:00 p.m., and it decreases rapidly from midnight to around 5:00 a.m. In particular, the charge probability density is at its maximum at 8:00 p.m. On the other hand, the results of the controlled mode are not significantly different from those of the uncontrolled mode. However, control mode 1 shows a relatively low afternoon charging probability density and a slightly higher charging probability density from midnight to 5:00 a.m. due to the influence of the TOU tariff. The reason is that TOU tariffs are very low from 11 p.m. to dawn. However, as shown in Figure 3, in the case of control mode 2, it can be seen that the probability density is slightly lower in the afternoon and slightly higher in the morning than in control mode 1. Figures 6-8 show the EV charge/discharge density function calculated through the uncontrolled mode using only vehicle inflow and outflow modeling, and control mode 1 and control mode 2 modeling using the vehicle's SMP rate and TOU rate system, respectively. Analyzing Figures 6-8, it can be seen that the discharge probability is high in the grid off-peak time zone, and that the charge probability is high in the peak time zone in the uncontrolled mode compared to the controlled mode. In addition, it can be seen that the case of control mode 2 has a higher charging probability in the grid off-peak time zone and a higher discharge probability in the peak time zone compared to control mode 1. Therefore, it can be seen that control mode 2 is most effective for grid leveling. Figure 6: Charging and discharging probability density function by hour for the uncontrolled mode (vehicle operation). 2.1.4. Calculating the SOC Condition of the EV Battery  
The initial battery SOC at the time of going from home to work and vice versa is calculated using Equation (5), which considers the mean driving distance predetermined for EV charging:  
\[soc_{0}=\left(1-\frac{\alpha}{d_{R}}\right)\times 100\% \tag{5}\]  
where \(\alpha\) is the daily driving distance and \(d_{R}\) is the EVs' maximum driving distance. A daily driving distance of 46.2 km from home to work and vice versa was used to calculate the initial battery SOC\({}_{0}\) based on a charging station in Seoul using Equation (5). The distance was obtained from the 2010 Vehicle Driving Distance Analysis Report published by the Seoul Metropolitan Police Agency [24]. Meanwhile, the maximum driving distance of the EVs was set to 180 km according to the EVs' efficiency of 0.16 kWh/km when using a Nissan Altra 29 kWh lithium-ion battery [25]. We used constant values for the initial SOC\({}_{0}\) and charging times for each electric vehicle because we applied the average values for evaluating the daily load curves for charging electric vehicles on a large scale, such as a big city. Therefore, based on the 46.2 km daily driving distance from home to work and vice versa, the initial battery SOC\({}_{0}\) at the time of starting from home to work and vice versa was calculated as 74%. Therefore, the initial battery SOC\({}_{0}\) after 2 days of driving would be 0.49 if the initial battery SOC\({}_{0}\) was high enough not to require recharging after 1 day of driving  
Figure 8: Charging and discharging density function by hour for control mode 2 (vehicle operation + SMP\({}_{2}\), TOU\({}_{2}\) tariff). Figure 7: Charging and discharging probability density function by hour for control mode 1 (vehicle operation + SMP\({}_{1}\), TOU\({}_{1}\) tariff). from home to work and vice versa, and it would need recharging after 2 days of driving the same distance.