# Cooperative Multi-Objective Optimization of DC Multi-Microgrid Systems in Distribution Networks
## 3 Case 3
#### 5.3.2 Outer-Loop Optimization Results  
In case 1, case 2, and case 3, the reactive power output of the DC/AC converters is not optimized. In case 4, the outer-loop reactive power optimization model is used to optimize  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**MGs**} & \multicolumn{2}{c}{\(C_{ex}\)} & \(C_{ci}\) & \(C_{OTC}\) \\  & & **Energy Transaction** & **Carbon Emissions** & **Total Operating** \\  & & **Cost/CNY** & **Cost/CNY** & **Cost/CNY** \\ \hline \multirow{3}{*}{Case 1} & RMG & 2760.0 & 16.3 & 2776.3 \\  & OBMG & 5700.8 & 31.8 & 5732.6 \\  & MMGS & 8460.8 & 48.1 & 8508.9 \\ \hline \multirow{3}{*}{Case 2} & RMG & 2627.8 & 16.3 & 2644.1 \\  & OBMG & 5609.6 & 32.5 & 5642.1 \\  & MMGS & 8237.4 & 48.8 & 8286.2 \\ \hline \multirow{3}{*}{Case 3} & RMG & 2348.9 & 42.9 & 2391.8 \\  & OBMG & 5394.6 & 9.5 & 5404.1 \\ \cline{1-1}  & MMGS & 7743.5 & 52.4 & 7795.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of operating cost in three cases.  
Figure 11: Remaining capacity of EVs in three cases.  
the reactive power output of the DC/AC converters. The optimized reactive power output of the DC/AC converters of RMG and OBMG in case 4 is shown in Figure 12. The converters will absorb or output a certain amount of reactive power to the distribution network at every moment, which is used to optimize the operating network loss of the distribution network, thereby reducing the energy loss cost \(C_{WTC}\) and total carbon emissions \(E_{C}\) of MMGS and the distribution network, and cooperating with the inner-loop model to reduce the total economic cost \(C_{ETC}\) of MMGS. The comparison of the results under the four cases is shown in Table 4.  
By analyzing the distribution network loss under the above different cases, it can be concluded that the reactive power output of the DC/AC converters to the distribution network will affect the distribution network loss. When MMGS is not integrated into the distribution network to work, the original baseline loss \(W_{S}^{B}\) of the distribution network is 14,787.9 kW. The distribution network loss under the first three cases is all greater than \(W_{S}^{B}\), while the distribution network loss under case 4 is less than \(W_{S}^{B}\) and lower than the first three cases. Case 3 and case 4 are a set of comparisons. Under the common premise of using the inner-loop optimization model, case 4 that uses reactive power optimization has lower network loss. Figure 13 is the increased network loss diagram for each period of the distribution network which further proves that intelligently optimizing the reactive power output of DC/AC converters through the outer-loop model can effectively reduce the daily network loss of the distribution network.  
Table 5 is the network loss cost and energy loss cost in four cases. Among the four cases, the network loss cost \(C_{il}\) and the carbon emissions cost \(C_{co}\) derived from the optimization of the outer-loop model are the lowest, which proves that the outer-loop optimization model plays a role in the cooperative optimization of the economic cost of MMGS.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline \(W_{S}^{G}\) & & & & \\ Total Network Loss/kW & & & & \\ \hline \(W_{S}^{B}\) & & & & \\ Increased Network Loss/kW & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of network loss in the four cases.  
Figure 12: (**a**) Reactive power output by the DC/AC converter of OBMG in case 4; (**b**) reactive power output by the DC/AC converter of RMG in case 4.