## 4 Case Studies
The simulation results for the above cases are listed in Table 6. When the active and reactive power load at all the nodes were increased by 12.5%, the simulation results for the above four cases are listed in Table 7.  
From Table 6, it can be seen that: (1) The power loss cost, the power purchasing cost, and power fluctuation penalty costs of the main grid in Case 2 were reduced prominently compared to Case 1, and a similar situation occurs between Case 3 and Case 4, which indicates that considering ESSs can improve the economical performance of the dispatch solution; (2) the various costs in Case 1 are less than the corresponding values in Case 3, and a similar situation exists between Cases 2 and 4. Yet, the deterministic scheduling model is adopted in Cases 1 and 2 while the two-stage stochastic scheduling model is implemented in Cases 3 and 4. Apparently, wind power uncertainty is not taken into consideration in the deterministic scheduling model, which is inconsistent with the actual situation. By contrast, the wind power scenario set has been introduced by the proposed model in Cases 3 and 4 to describe wind power fluctuation in real time. In other words, the influence of wind power uncertainty on the dispatch solution is integrated into the decision process. As a result, the two-stage stochastic scheduling model has increased the operation cost compared with the deterministic scheduling model, but the reliability of the dispatch solution has been improved. From Table 7, it can be found that load shedding happened in Cases 1 and 3 with the increase of the active and reactive power load, in which ESSs are not integrated in the hybrid AC/DC distribution network. Considering ESSs in Cases 2 and 4 can prominently enhance the economy and reliability of system operation compared with Cases 1 and 3. Furthermore, the operation status of regulating facilities, such as VSC and ESS, is investigated as follows. For the deterministic scheduling model in Case 2, the transferred active/reactive power by the VSC facilities and the charging/discharging power by ESS are shown in Figures 6 and 7, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Power Purchasing Cost (\$)** & **Power Fluctuation Penalty Cost (\$)** & **Power Loss (kW)** & **Load Shedding(kW)** \\ \hline Case 1 & 2463.86 & 178.81 & 186.47 & 0 \\ Case 2 & 2343.83 & 57.95 & 181.62 & 0 \\ Case 3 & 2487.71 & 240.71 & 225.78 & 0 \\ Case 4 & 2427.25 & 75.05 & 203.12 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation results for different cases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Power Purchasing Cost (\$)** & **Power Fluctuation Penalty Cost (\$)** & **Power Loss (kW)** & **Load Shedding(kW)** \\ \hline Case 1 & 3230.61 & 178.56 & 273.38 & 62.23 \\ Case 2 & 3118.27 & 52.73 & 268.27 & 0 \\ Case 3 & 3249.85 & 235.76 & 319.21 & 110.34 \\ Case 4 & 3134.96 & 80.01 & 276.65 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Simulation results for different cases. It can be seen that: (1) VSC3 operates under the working mode of inverting while VSC1 and VSC2 operate under the working mode of rectifying; (2) as shown in Figure 7, the positive values of power denote that ESS works in the charging state and the negative values mean it works in the discharging state. Combined with the load curves in Figure 5, during the load valley periods of 1 to 8, ESS stored the surplus energy generated by wind generators and the main grid. During the load increasing period of 10 to 20, ESS discharged the previous stored energy to satisfy the balance of supply and demand. By this means, the power fluctuation of the main grid can be alleviated. Meanwhile, ESS can store energy when the electricity price is lower and discharge energy when the electricity price is higher to reduce the power purchasing cost from the main grid.