## 5 Example Analysis
CBA, BA and ACA reached convergence at the 48 th, 58 th and 62 nd iteration times respectively, and the final number of Pareto solution sets is 121. It shows that the CBA has the advantage of speed. Figure 4: Wind power generation in typical scenarios (**a**) Wind power generation in scenario 1; (**b**) Wind power generation in scenario 2; (**c**) Wind power generation in scenario 3; (**d**) Wind power generation in scenario 4. The typical output and the probability of each scenario in the spring of each region are substituted into the multi-objective DERs aggregation model, and FMD-CBA is used to select the resources of each region. The obtained Pareto solution sets are shown in Figure 7.  
Figure 5: Photovoltaic generation in typical scenarios (**a**) Photovoltaic generation in scenario 1; (**b**) Photovoltaic generation in scenario 2; (**c**) Photovoltaic generation in scenario 3; (**d**) Photovoltaic generation in scenario 4. Figure 6: Iterative convergence process. The Pareto solution sets obtained by FMD-CBA take into account the global search and the local search. The number of the Pareto solution sets is 121. But in practice, only one planning scheme is adopted when constructing a RA. Therefore, this paper calculates the membership and weight of each objective function through fuzzy compromise programming and then obtains a compromise solution. The compromise solution and the value range of each objective function are shown in Table 3.  
Under this compromise solution, the average daily cost is 5180 USD, the average daily output is 46.5 MWh, the volatility is 0.49, and the aggregation degree is 6.22 MW/km. The corresponding aggregation scheme of the compromise solution is shown in Table 4. '\(\surd\)' represents that the resource participates in the aggregation, '\(\times\)' represents that the resource does not participate in the aggregation, and the blank represents that there are no such resources in this region. The final aggregation scheme includes DG in 13 regions (WP in 1 region and PV in 12 regions), ES in 6 regions and DR in 11 regions. The aggregation scheme corresponds to the compromise solution which considers cost, output characteristics and aggregation degree. The actual output curve of the RA is superimposed by the curves of WP, PV, ES and DR, as shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline
**Number** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** \\ \hline DG & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\times\) \\ ES & & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & & \(\times\) & & & \(\times\) & \(\surd\) \\ DR & & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & & \(\surd\) & & \(\surd\) & & \(\surd\) & & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Final aggregation scheme. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(f_{1}\) (10\({}^{3}\) USD) & \(f_{2}\) (MWh) & \(f_{3}\) & \(f_{4}\) (MW/km) \\ \hline Maximum value & 9.14 & 79.14 & 0.54 & 10.58 \\ Minimum value & 0.48 & 3.8 & 0.45 & 1.04 \\ Compromise Solution & 5.18 & 46.5 & 0.49 & 6.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The value of each objective function. Figure 7: Pareto solution sets. The area of various DERs represents the daily average output value. WP is 35.06 MWh, PV is 7.14 MWh, DR is 7.6 MWh, ES is \(-\)3.3 MWh, and the daily average output of the RA is 46.5 MWh. From Figure 8, DG accounts for the majority of the RA output. Although the capacity of ES and DR is small, the output curve of the RA can be adjusted.