## 5 Case Study
### Scenario 1
#### 5.1.3 Results and Analysis of the Distributed Optimal Dispatching on Day 1 of Scenario 1  
Figure 5 represents the net electric load of each MG and the total net electric load of the coalition. The PV power, wind power and load power in each MG are shown in Figure 6.  
Obviously, the total net load of this coalition in the periods of 1-17, 36-61 and 91-96 is negative, when BESS needs to absorb the excess renewable energy. While in the remaining periods when total net load is positive, it is necessary to choose to discharge by BESSs or purchase electricity from the main grid to satisfy the total load demand with comprehensive consideration of the purchasing electricity cost, discharging cost of BESSs and power loss cost. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Days**} & **Total Operation** & \multicolumn{2}{c}{**Power Loss Cost**} & \multicolumn{2}{c}{**Power Loss Cost**} & \multirow{2}{*}{**Average Iteration**} \\  & **Cost (CNY)** & & & **Power Loss (CNY)** & \\ \hline Day 1 & 10,449.7 & 900.7 & 697.5 & 33 \\ Day 2 & 5777.4 & 483.9 & 457.9 & 37 \\ Day 3 & 8991.1 & 807.9 & 675.1 & 37 \\ Day 4 & 10,373.1 & 734.2 & 636.2 & 29 \\ Day 5 & 6429.2 & 513.9 & 453.8 & 37 \\ Day 6 & 13,606.4 & 1431.4 & 1063.3 & 30 \\ Day 7 & 11,120.8 & 821.6 & 676.9 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal results on different days for one week. Figure 5: Net power curve of each MG and total net power curve of the coalition on Day 1 of Scenario 1. Figure 6: The PV power, WT power and load power in each MG on Day 1 of Scenario 1 ((a) MG1; (b) MG2; (c) MG3). Figure 7 represents the output power of BESSs and the power purchased from the main grid of each MG.  
As shown in Figure 5, in the periods 1-17, 36-61 and 91-96, the total load demand is less than the total output power of RESs including WTs and PVs; thus, the BESSs are used to store the surplus energy by means of charging. In other periods, when there is a shortage of RESs, each MG can choose to purchase electricity from the main grid or discharge by BESS to meet the load demands for reduction of total operation cost in coalition with a comprehensive consideration of purchasing electricity cost and energy storage cost. Considering that there is less cost in discharging of BESS, it is obvious to find out that BESSs are used to discharge as the first priority in Periods 18-19 and 62-69 when the renewable energy is insufficient. The charge-discharge power of each BESS is optimized based on distributed optimal scheduling algorithm. In Periods 20-35 and 70-90, the output power of BESS is inadequate to satisfy the load demands of MGs in coalition, so that MGs purchase electricity from the main grid. In addition, Figure 8 shows the decided exchange power among MGs of each optimal scheduling period. As shown in Figure 8, we find that the sum of decided exchange power of MGs is zero, which ensures the power balance of the system. When the renewable energy of MG is insufficient, it would import energy from the MG with surplus power as the first priority. For instance, in Periods 1-17, the net load of MG2 is greater than zero, while the RESs in MG1 and MG3 are abundant. Then, the excess power in MG1 and MG3 would be exported to MG2 for the reduction of power loss and operation cost. If RESs of all MGs are surplus, there exists no exchange power generally, such as Periods 41-46. Through distributed optimization based on ADMM, the optimal problem can be solved effectively while satisfying the load demands of MGs in coalition by just sharing the expected exchange power, which protects the privacy of the MGs and ESP. Figure 8: Decided exchange power among MGs on Day 1 of Scenario 1. Figure 7: Scheduling results of BESS and purchasing power based on alternating direction method of multipliers (ADMM) on Day 1 of Scenario 1 (**(a)** MG1; **(b)** MG2; **(c)** MG3). The efficiency of BESS in this study is set as 95%.