## 4 Numerical Results
### Simulation Results  
Seven external archival solutions for the maximum accommodation capacity of DG are obtained by the proposed CLPSO algorithm, and the objective function values of each solution are standardized. The proposed method is implemented in CPLEX and solved using the YALMIP (an optimization solution tool which relies on external solvers for the low-level numerical solution of optimization problem) toolbox on a PC with a Core i5 3570 CPU and 4 GB of RAM. The running time using the proposed CLPSO algorithm in the basic case is 58504.2 s, which is acceptable in the optimal planning problem. In order to visually display the distribution of three objective functions corresponding to external archives, the Pareto frontier solution set of three-dimensional objective function space is drawn, as shown in Figure 5. It can be seen from Figure 5 that the solution set in the external archives is distributed at the Pareto optimal frontier, the distances between the external archives are large, and the congestion degree is low. It can be concluded that the external archive solution set obtained by the proposed CLPSO algorithm contains a variety of decision-making solutions that fully consider the mutual dominance of the three objective functions presented in this paper. The optimal compromise solution could fully weigh the interests of each objective function and achieve the comprehensive optimum. The weights of the three objective functions calculated by the entropy weight method are 0.3143, 0.3661, and 0.3196, respectively. The difference of the weights of the three objective functions is not significant, which means that the information entropy provided by each objective function in the proposed optimization model is comparable and the economy and flexibility of the distribution network operation after the connection of DG can be considered comprehensively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**DG Type** & **Accommodation Nodes in Scene A** & **Accommodation Nodes in Scene B** \\ \hline PV & 3, 5, 6, 7, 9, 11, 12, 29, 30, 34, 36, 37, & 3, 9, 34, 36, 50, 51 \\  & 39, 40, 50, 51, 54, 55 & \\ WF & 41 & 41 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The configuration scenes of DG connection nodes. Figure 4: The typical output scenarios of WF and PV in different dispatching periods. The normalized function values of each optimal boundary solution and the optimal solutions with Nash equilibrium decision-making and TOPSIS are presented in Table 2. In Table 2, the line capacity margin is the least among the seven Pareto frontier solutions in the optimal solution for the maximizing daily energy supply of DG. The daily energy supply of DG is least in the optimal solution for minimizing nodal voltage amplitude deviation. This means that there is a game relationship among the three objectives. The optimal solution obtained with the mixed strategy Nash equilibrium decision-making, which is a type of decentralized decision-making method, is the same as that obtained with TOPSIS, which is a type of centralized decision-making method. The result shows that the directions along which the particle swarms search to find the optimal solutions for the two methods are consistent. Moreover, because the three objectives are regarded as non-cooperative decision-making participants in a competitive relationship, the proposed mixed strategy Nash equilibrium decision-making model is more suitable for finding the optimal compromise solution and corresponding DG connection solution for the distribution network in this paper. Table 3 shows the solutions of the mixed strategy Nash equilibrium decision-making with different \(u_{i}\). It shows that the change in values of parameter \(u_{i}\) does not influence the final optimal solution for the mixed strategy Nash equilibrium decision-making, which demonstrates the robustness and adaptability of the proposed decision-making method.