## 5 Case Study
### Scenario 1
#### 5.1.4 Results and Analysis of the Distributed Optimal Dispatching on Day 2 of Scenario 1  
The net power curve of each MG and total net power curve on Day 2 of Scenario 1 are represented in Figure 13. Figure 14 shows the PV power, WT power and load power in each MG.  
Figure 11: Power loss cost comparison between with and without optimization of power loss on Day 1 of Scenario 1.  
Figure 12: Iterative process of the primal residual and dual residual on Day 1 of Scenario 1 ((**a**) Primary residual; (**b**) Dual residual).  
Compared to Day 1, there is more wind power and less PV power on Day 2 because of weather variations; thus, the total net load power is lower on this day. Apparently, the net load in Periods 5-20, 32-46, 49-57 and 92-96 is negative, when the excess renewable energy needs to be stored by BESS. In other periods, the MGs would choose to discharge by BESS or purchase power from the main grid.  
When the renewable energy cannot meet the power demands, discharging by BESS or purchasing electricity from the main grid would be selected by MGs for stable operation. The scheduling results of BESS and purchasing electricity based on ADMM in Scenario 2 are shown in Figure 15.  
In Figure 15, we can find that the storage energy of BESSs is utilized as the first priority when there is a shortage of RESs, such as Periods 21-31, 47-48 and 60-71. Then, the MG should purchase  
Figure 14: The PV power, WT power and load power in each MG on Day 2 of Scenario 1 (**(a)** MG1; (b) MG2; (c) MG3).  
Figure 15: Scheduling results of BESS and purchasing power based on ADMM on Day 2 of Scenario 1 (**(a)** MG1; (b) MG2; (c) MG3).  
Figure 13: Net power curve of each MG and total net power curve of coalition on Day 2 of Scenario 1.  
power from the main grid to satisfy its local demands, such as Periods 67-91. In addition, Figure 16 shows the decided exchange power via the distribution line among MGs. The optimal variables and net load in MG1 are represented as Figure 17.  
As shown in Figure 17, we find that MG1 can satisfy its local load by exchanging energy with other MGs, discharging by BESS or purchasing electricity from the main grid considering purchasing electricity cost, energy storage cost, load characteristic and power loss cost.  
In order to clarify the advantages of proposed method in this paper, the power loss cost comparison between with and without optimization of power loss is represented in Figure 18.  
Figure 16: Decided exchange power among MGs on Day 2 of Scenario 1.  
Figure 17: The optimal variables and net load in MG1 on Day 2 of Scenario 1.  
Figure 18: Power loss cost comparison between with and without optimization of power loss on Day 2 of Scenario 1.  
According to Figure 18 and Table 3, we find that the power loss is reduced by 5.39% compared to the case without optimization of power loss cost based on the same basic data. Through the method in this paper, the power loss cost can be reduced effectively.  
Figure 19 represents the iterative process of the primal residual and dual residual. It is clear that the algorithm can achieve convergence in 30-60 iterations for most time slots, which shows that ADMM has a better convergence performance.