## 5 Result and Discussion
### Simulation Results
#### 5.2.2 Actual Power System  
We evaluated the practical applicability of the proposed approach for large-scale power systems, by applying the results of our work to an actual power system in Shandong, China, called the Changdao project [37], consisting of 128 buses and 7 MGs as shown in Figure 10. All of the MGs were constantly connected to the DN by means of a single tie-line. The maximum limit of the tie-line flow was 1000 kW. The scheduling period was considered to be a single day. The data for every MG and the capacity parameters were listed in Table 6. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Scenario**} & \multicolumn{2}{c}{**Operation Cost (\$/h)**} & \multirow{2}{*}{**Note**} \\ \cline{2-3} \cline{2-3}  & **DSO** & **MGO** & \\ \hline Scenario A & 864,274 & 512,638 & No bi-level model with Case 2 \\ Scenario B & 862,716 & 517,874 & Proposed bi-level model with Case 2 \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of operational costs for scenarios in Case 2. The scheduled power scheme for Case 2 with an energy band of 60% is shown in Figure 11. As can be seen from Figure 11b, the BESS was charged for longer, from 04:00 to 07:00, than in Case 1, with the MTs also generating additional power. These results indicate that the proposed bi-level optimization model with the energy band can effectively improve reliable operations between the DSO and MGO. Table 7 compares the operational costs for each case. In the base case, the operational cost was $1,454,549/h when no power was purchased from the DN. In comparison, the operational costs for Cases 1 and 2 were $1,447,154/h and $1,450,047/h, respectively. Although the operational cost for the proposed scheme (Case 2) was 0.2% ($2893/h) higher than that for Case 1, it was lower than that for the case in which no power was purchased from the DN by approximately 0.3% ($4532/h). Therefore, the proposed bi-level optimization model based on a 60% energy band provides superior balance for economical and reliable operation between the DSO and MGO. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type**} & **Minimum Power** & **Maximum Power** & **Number of** & **Ramp up/down** \\  & **(kW)** & **(kW)** & **Units** & **Rate (kW/min)** \\ \hline MT & 0 & 1000 & 11 & 500/400 \\ WT & 0 & 1000 & 11 & - \\ PV & 0 & 1500 & 10 & - \\ ESS & \(-\)1500 & 1500 & 7 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Capacity parameters. Figure 10: Actual power system in China. Table 8 presented a comparison of the operational costs for each scenario in Case 2. To confirm the results, we assumed the same scenario as in the IEEE test system described previously. According to the comparison results, the MG operational cost for Scenario A was $1,387,562/h, which was lower than that for Scenario B, namely $1,450,047/h, but the operational cost of the DSO for Scenario A is higher than that for Scenario B. It can be observed that the proposed bi-level model can reduce the DSO operational cost although the MGO operational cost increases, because the MG operational cost can be reduced by the proposed tie-line control strategy. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**Operation Cost (\$/h)**} & \multirow{2}{*}{**Note**} \\ \cline{2-3} \cline{2-3}  & **DSO** & **MGO** \\ \hline Base & 2,081,643 & 1,454,549 & No purchase of power from DN \\ Case 1 & 2,548,231 & 1,447,154 & Purchase of power from DN through tie-line \\ Case 2 & 2,320,075 & 1,450,047 & Purchase of power from DN within energy band of 60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of operational costs for each case. Figure 11: Scheduled power scheme for Case 2 within energy band of 60%: (**a**) Results for energy band, (**b**) Scheduled power volumes for distributed units. Table 9 displayed the optimal results of the proposed approach for each case.