## 6 Case Studies
### Analysis of the Influence of DG Permeability Constraint on System Reliability  
In order to disscuss the influence of the \(DG\) permeability constraint on system reliability, we set Case 5, and the specific description is as follows:  
Case 5: Network reconfiguration is considered and a robust planning model is adopted, but the \(DG\) permeability constraint is ignored. The planning scheme and various costs obtained from the simulation are shown in Table 4.  
In order to disscuss the influence of \(DG\) permeability constraint on system reliability, we compare the results of Case 4 and Case 5. As shown in Table 5, the total installed capacity of \(DG\) in Scenario 5 has increased by 100 kW compared to the total installed capacity of \(DG\) in Scenario 4, resulting in an increase of USD 62,000 in investment costs. But the \(DG\) operation cost and \(DG\) proactive management cost decrease by USD 38,800 and USD 42,400, respectively. The reason is that the planning model in Case 5 ignores \(DG\) constraints, resulting in lower utilization of \(DG\), resulting in lower operating and management costs for \(DG\). In addition, in order to maintain the balance of the power grid, the purchase of electricity from the grid increased in Case 5 compared with Case 4, so that the power purchase cost increased by USD 50,000 in Case 5. It can be seen that it is crucial to consider \(DG\) permeability constraints during the \(DG\) planning stage, which can increase the absorption capacity of renewable energy and help build a low-carbon and friendly power system. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & \multicolumn{4}{c}{**Case 4**} & \multicolumn{4}{c}{**Case 5**} \\ \cline{3-10}  & **Bus** & **7** & **14** & **24** & **25** & **7** & **14** & **24** & **25** \\ \hline Investment & \multirow{3}{*}{Element Type} & \multirow{3}{*}{\(WTG\)} & \multirow{3}{*}{\(WTG\)} & \multirow{3}{*}{\(PVG\)} & \multirow{3}{*}{\(PVG\)} & \multirow{3}{*}{\(WTG\)} & \multirow{3}{*}{\(WTG\)} & \multirow{3}{*}{\(PVG\)} & \multirow{3}{*}{\(PVG\)} \\ Decision & & & & & & & & & \\ \cline{3-10}  & & Capacity (kW) & 300 & 300 & 600 & 600 & 300 & 400 & 600 & 600 \\ \hline \multirow{7}{*}{Cost (10\({}^{4}\) USD)} & Network loss cost & \multicolumn{4}{c}{5.32} & \multicolumn{4}{c}{10.32} \\  & \(DG\) Investment Cost & \multicolumn{4}{c}{126.61} & \multicolumn{4}{c}{132.81} \\ \cline{1-1}  & \(DG\) operation cost & \multicolumn{4}{c}{43.72} & \multicolumn{4}{c}{39.84} \\ \cline{1-1}  & \(DG\) Proactive Management Cost & \multicolumn{4}{c}{35.02} & \multicolumn{4}{c}{30.78} \\ \cline{1-1}  & Power purchase cost & \multicolumn{4}{c}{450.3} & \multicolumn{4}{c}{495.3} \\ \cline{1-1}  & Reconstruction cost & \multicolumn{4}{c}{1.92} & \multicolumn{4}{c}{2.01} \\ \cline{1-1}  & Total cost & \multicolumn{4}{c}{662.89} & \multicolumn{4}{c}{711.06} \\ \hline \end{tabular}
\end{table} 
Table 4: Planning results of Case 4 and Case 5. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline Computation Time & 100.23 s & 858.06 s & 163.58 s & 1176.09 s \\ \hline \end{tabular}
\end{table} 
Table 3: The computation times of Case 1 to Case 4. It is consistent with the conclusion in Section 6.1, and the system does not need to be reconstructed frequently. The reason is that the system has a good adaptability to the uncertainty of load, wind power and photovoltaic due to a robust planning model adopted in both Scenario A and Scenario B. Therefore, the total installed \(DG\) capacity of Scenario A and Scenario B is the same, which is 2500 kW. The reconstruction cost of Scenario B is lower than that of Scenario A. At the same time, the network loss cost of Scenario B is greatly reduced, and the annual average comprehensive cost is reduced by USD 360,100. Therefore, it is still advantageous to consider network reconfiguration when using robust programming model.