## 4 Numerical Results
### Simulation Results
The total DG accommodation capacities of seven Pareto frontier solutions are shown in Figure 6. The optimal compromise solution (i.e., solution 3) has a 78.9-MW DG accommodation capacity on the premise of obtaining joint optimal values of multiple objectives. Its DG accommodation capacity is the second largest, following solution 2. Furthermore, the penetration of DG in solution 3 is 28.9%, showing that the distribution network in solution 3 has a better accommodation capacity for DG. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Objective**} & \multirow{2}{*}{\begin{tabular}{c} **Daily Energy** \\ **Supply of DG** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Voltage** \\ **Amplitude** \\ **Deviation** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Line Capacity** \\ **Margin** \\ **Decision-Making** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **The Optimal** \\ **Station (Mixed** \\ **Strategy Nash** \\ **Solution (TOPSIS** \\ **Method )** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **The Optimal** \\ **Solution (TOPSIS** \\ **Method )** \\ \end{tabular} } \\ \cline{1-1}  & & & & & **Decision-Making** \\ \hline Daily energy supply of DG & 1.000 & 0.000 & 0.5821 & 0.7996 & 0.7996 \\ Voltage amplitude deviation & 0.2442 & 1.000 & 0.456 & 0.4508 & 0.4508 \\ Line capacity margin & 0.000 & 0.4867 & 1.000 & 0.8582 & 0.8582 \\ \hline \hline \end{tabular} Note: TOPSIS = Technique for order preference by similarity to ideal solution.  
\end{table} 
Table 2: The optimal boundary solutions and compromise solutions of the multi-objective optimization model. Figure 5: The distribution map of objective functions of external archives. The specific PV and WF accommodation capacities of each node to be built under two different scenes are shown in Figure 7. In scene A, the number of DG nodes to be built is large and the distribution is scattered. Thus, the total DG accommodation capacity of the distribution network in this area could be maximized on the premise of ensuring the flexibility of the distribution network, in which several nodes do not need to connect large-capacity DG equipment. In scene B, the actual accommodation capacity of the PV nodes to be built is larger and more centralized than for the corresponding nodes in scene A. The optimal compromise solutions for DG accommodation capacity under two scenes are shown in Table 4. It can be seen from Table 4 that when the number of DG connection nodes in the distribution network is reduced, the fitness of each objective function and the total DG accommodation capacity \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Case**} & **Upper Limit of the** & **Objective Function Value** \\  & **Expected Value (\(u_{1}\), \(u_{2}\), \(u_{3}\))** & **of Nash Equilibrium** \\  & **Decision-Making** & **Solutions** \\ \hline
1 & (0.5,0.5,0.5) & \(-0.8094\) & 3 \\
2 & (0.5,0.7,0.7) & \(1.2094\) & 3 \\
3 & (0.7,0.7,0.7) & \(-1.4094\) & 3 \\
4 & (0.5,0.7,0.9) & \(-1.4094\) & 3 \\
5 & (1.0,1.0,1.0) & \(-3.000\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Solutions of the mixed strategy Nash equilibrium decision-making method with different \(u_{i}\). Figure 6: The total accommodation capacity of DG corresponding to the Pareto frontier solution set. Figure 7: The DG accommodation capacity of each node under two scenes. of the optimal compromise solution of the DG configuration are reduced simultaneously. This is because of the limitation of the line capacity; the DG capacity of a single node is limited and the reduction of the connection nodes directly leads to the reduction of the total accommodation capacity. Thus, the dispatchable DG power is also reduced accordingly. At the same time, more decentralized DG connection nodes can provide voltage support and alleviate the pressure of power transmission. The fitness function value of the line capacity margin which represents the average of all line capacity margin values is 58.1% for scene A.