## 5 Simulation Results and Discussion  
### Description of the Test System  
This study uses the IEEE 34 distribution system as the test system. The EVs are added randomly at buses 816, 824, 854, 842, and 846, as shown in Figure 1. The residential load profile for this study is taken from [47] and the charging/discharging price is taken from [48]. This study assumes all EVs are a Nissan Leaf model, and the battery size and the range under full charge are 24 kWh and 170 km, respectively [49]. A Board Level II Type charger is assumed to be used in this study. This is a single-phase AC IEC 61851-1 standard charger that connects to AC with a rating of 240 V and 32 A [50]. The driving behavior is generated randomly for all EV users based on data from [51]. The arrival/departure times (Figure 4) are randomly generated from [34]. Moreover, a daily distance of around 40-75 km a day is used to calculate the initial state of charge given by Equation (26) and is also shown in Figure 5. Different EV penetration levels have been used for this study, and the details are given in Table 2.  
\[SOC_{Initial}=100\%\times\frac{(D_{M}-D_{D})}{D_{M}} \tag{26}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Phase A**} & \multicolumn{4}{c}{**Phase B**} & \multicolumn{4}{c}{**Phase C**} \\ \hline
**EV Bus Connection** & **816** & **824** & **854** & **842** & **846** & **816** & **824** & **854** & **842** & **846** & **816** & **824** & **854** & **842** & **846** \\ \hline
30\% (162 EVs) & 22 & 1 & 0 & 21 & 0 & 5 & 0 & 41 & 15 & 21 & 0 & 21 & 15 & 0 & 0 \\
50\% (271 EVs) & 32 & 11 & 0 & 31 & 0 & 20 & 0 & 51 & 25 & 31 & 0 & 31 & 35 & 4 & 0 \\
75\% (407 EVs) & 45 & 23 & 4 & 43 & 10 & 23 & 4 & 63 & 37 & 43 & 13 & 43 & 37 & 15 & 4 \\
100\% (542 EVs) & 55 & 32 & 13 & 52 & 19 & 32 & 13 & 72 & 46 & 51 & 22 & 52 & 46 & 24 & 13 \\ \hline \hline \end{tabular}
\end{table}
Table 2: EV penetration for different phases and nodes.  
Uncontrolled Charging: EV charging when the users arrives (the arrival time is assigned randomly from 5:00 p.m. to 12:00 a.m., as shown in Figure 4).  
Randomly as:  
Method 1: CC, VUF, VD with P-V2G (both system and customer objectives) [29; 30]  
Method 2: CC, BC (only customer objective) [26; 27; 28]  
Method 3: VUF, VD with Q-V2G (only system objective) [31; 32; 33; 34]  
All the results are only shown for bus 846 and in the 5 p.m.-10 a.m. time period, which represents the worst-case scenarios for this study. Tables 3 and 4 show the simulation parameters for the constraints and PSO used in this study, respectively.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(E_{0}\) & 24 kWh \\ \(E_{Driving}\) & 0.4 p.u \\ \(E_{V2G}\) & 0.3 p.u \\ \(P_{Dis}^{Max}\) & 7.68 kW \\ \(P_{Dis(t,n)}^{Max}\) & 7.2 kW \\ \(C_{t}\) & Obtained from Figure 6 \\ \(R_{V2G}\) & 0.324 EUR/kWh \\ \(SOC_{Initial}\) & Obtained from Figure 5 \\ \(SOC_{final}\) & \(\geq\)95\% \\ \(\Delta t\) & 1 h \\ \(\eta_{i,t}^{Cig}\) & 93\% \\ \(\eta_{i,t}^{Dchg}\) & 93\% \\ \(C_{C}\) & 110.97 EUR/kWh \\ \(C_{SLV}\) & 60\% of \(C_{C}\) \\ \(S_{f}\) & 2.22 \\ \(K_{w}\) & 0.00015 kWh/kWh \\ \(C_{L,NoV2G}\) & 1035.19 days (3 years) \\ \(C_{L,V2G}\) & 706.214 days (2 years) \\ \(w_{p,NoV2G}\) & 0.179 EUR/kWh \\ \(w_{p,V2G}\) & 0.122 EUR/kWh \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters for constraints.  
Figure 7: Residential load profile with different electric load profiles.