## 2 Case Studies
Scenario 2 also used MST to generate the connection topology, similar to scenario 1, so the topology obtained was exactly the same as script Scenario 2 optimized the cross-section of the cable and used a large number of cables with a cross-section of 185 mm\({}^{2}\) to 500 mmAlthough this optimization increased the cost of medium-voltage cable from 1.27 million US dollars to 2.25 million US dollars in script 1, it also caused a significant drop in the overall topological resistance level, which reduced the annual power loss from 3495.23 MWh/a to 1202.85 MWh/a, resulting in a 65.7% reduction in power loss costs. In a comprehensive comparison, the total cost of scenario 2 was 22.2% lower than that of scenario It can be concluded that the optimization of the cable cross section can effectively reduce the development cost of the power system. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Scenario 1** & **Scenario 2** & **Scenario 3** \\ \hline Total cost \(C_{total}\) (million USD) & 8.62 & 6.71 & 6.24 \\ Medium-voltage cable total length (km) & 50.32 & 50.32 & 53.09 \\ Annual energy loss (MWh/a) & 3495.23 & 1202.85 & 973.27 \\ Medium-voltage cable cost (million USD) & 1.37 & 2.25 & 2.01 \\ Total construction cost (million USD) & 1.27 & 1.27 & 1.32 \\ Energy loss cost (million USD) & 4.25 & 1.46 & 1.18 \\ Substation cost (million USD) & 1.01 & 1.01 & 1.01 \\ High-voltage cable cost (million USD) & 0.72 & 0.72 & 0.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of key economic parameters of topology. Figure 5: The resistances and reactances of the cables. Scenario 3 carried out the coupling optimization of the connection topology and the cable cross-section, and the structure of the optimal topology obtained was significantly different from the topology generated by the MST (scenario 1 and scenario 2), wherein the number of branches were increased to 5 and the number of wind turbines per branch were 5, 7, 4, 4 and Scenario 3 allowed for an appropriate increase in the length of the cable in exchange for the best match of the topology and cable cross-section, so the total length of the medium-voltage cable was increased by 5.5% over scenario 1 and scenario Compared to scenario 1, scenario 3 employed cables with large cross-sections, resulting in a significant reduction in energy loss costs of 72.2%. Compared to scenario 2, the optimal topology used in scenario 3 adopted more branches to reduce the current in each branch, thereby reducing the use of large cables with a cross-section of 240 mm\({}^{2}\) or more, thus successfully reducing the cost of the medium-voltage cable by 10.7%. At the same time, facilitated by the optimal matching of the connection topology to the cable cross section, the annual energy loss was further reduced to 973.27 MWh/a. In addition, the total cost of scenario 3 decreased by 27.6% and 7%, respectively, relative to scenario 1 and scenario These results show that the best match between the two were achieved by optimizing the coupling between the connection topology and the cable cross-section optimization, which could significantly reduce the power loss of the power system and achieve the goal of minimum total cost. Figure 6: Topology optimization based on minimum spanning tree (MST) and cable cross-section planning according to the principle of maximum current carrying capacity (Scenario 1). Figure 7: Topology optimization based on MST and optimization of the cable cross-sections (Scenario 2).