# 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  
As assumed before, the hourly charging probability density function for electric vehicles at home was applied to the difference between hourly inflow and outflow traffic based on a driving time of 1 h to work in Seoul in the morning, calculated for the uncontrolled mode (Equation (3)). Controlled modes for minimizing grid effects were calculated as in Equation (4) by applying the difference between inflow and outflow traffic and TOU charges over time. The probability density function of the uncontrolled mode charge start time at home was calculated according to Equation (3) for electric vehicles departing from the city center used by owners to drive from work to home outside the city. Moreover, it was considered that these electric vehicles were likely to be charged after a certain amount of time (say, 1 h) away from the city center. The reason why the probability density function for the controlled mode charge start time at home was calculated according to Equation (4) was that the electric vehicle was likely to be charged during the time period when the TOU charge was low after arriving at home. In Equation (3) and (4), whole vehicle(t) means the entire running vehicle at time t, and \(EVs_{outflow}(t)\) and \(EVs_{inflow}(t)\) are, respectively, the outflow and inflow vehicles in the city center by time zone at actual operation time t. TOU(t) represents the TOU rate at time t.  
**Equation (3):** Probability of charge start time at home (uncontrolled mode):  
Figure 3: Discharge probability density in the controlled mode at workplace. Figure 2: Discharge probability density in the uncontrolled mode at workplace. \[P_{uh}(t)=\frac{\left(EVs_{outflow}(t)-EVs_{inflow}(t)\right)}{\textit{whole EVs}} \tag{3}\]  
**Equation (4)**: Probability of charge start time at home (controlled mode):  
\[P_{ch}(t)=\frac{\left(EVs_{outflow}(t)-EVs_{inflow}(t)\right)}{\textit{whole EVs}} \div T\textsl{OU}(t) \tag{4}\]  
Figure 4 shows the expected charging probability density in the uncontrolled mode at the household considering the difference between incoming and outgoing traffic. In addition, Figure 4 shows the charging probability density results including TOU rates for comparison with the charging probability density using only traffic modeling. Figure 5 shows the charging probability densities in the controlled mode where TOU rates are tuned lower during the afternoon hours. That is, as the TOU rate decreases during the off-peak hours from midnight to 5:00 a.m., it can be seen that the charging probability density increases relatively during the same time period. In particular, as shown in Figure 4, when the TOU 2 rate is applied rather than the TOU 1 rate from 6:00 p.m. to 5:00 a.m., the charging probability density is high from 6:00 p.m. to midnight, and it can be seen that the grid leveling effect is the greatest. Figure 4: Charging probability density in the uncontrolled mode at home. Figure 5: Charging probability density in the controlled mode at home. 2.1.3. Analysis of the Probability Density Function for Charging and Discharging EVs  
As can be seen in the discharge probability density function of uncontrolled discharge and controlled discharge in the workplace, which is shown in Figure 1, in the case of the uncontrolled mode, the probability density gradually increases from 6:00 a.m. to 8:00 a.m., and then gradually decreases from 9:00 a.m. The rate of decrease, meanwhile, increases in the afternoon. In particular, the discharge probability density is at its maximum at 8:00 a.m. In the case of control mode 1, the difference is small due to the influence of SMP deliberation, but the probability density is somewhat higher than that of the non-controlled mode. However, for control mode 2 (Figure 2), unlike control mode 1, the probability density increases from 6:00 a.m. to 7:00 a.m., increases rapidly from 8:00 a.m. to 9:00 a.m., stays almost the same until noon, and then slowly decreases. It reaches its maximum between 8:00 a.m. and 9:00 a.m.