## 4 Case Studies  
The case study was conducted based on the modified IEEE 33-node hybrid AC/DC distribution system [19]. As shown in Figure 4, the solid red lines represent AC branches and the dashed blue lines represent DC branches. The rated voltages of the AC and DC distribution network are 12.66 and 15 kV, respectively. The voltage limitation range was set to [0.95, 1.05] p.u. There are two gas-fired units with the capacity of 300 kW, and three VSCs and four wind generators with the capacity of 500 kW in the hybrid system. The electricity price of main grid is 0.12 $/kWh at hour 7-22 and 0.06 $/kWh at other times. The operation parameters of different facilities and the cost coefficients are listed in Tables 1-5. The unit generating cost of gas-fired units and power fluctuation cost in Table 5 were obtained from [29], the unit network loss cost was obtained from [21], and the unit penalty costs for wind curtailment and load shedding can be found in [30]. The load demand and wind power curves are shown in Figure 5. The power output predictions of four wind generators are the same, and the wind generators in the AC distribution network are running at a constant power factor of 0.85. In this study, the solving tool Yalmip was adopted to develop the above application programs and then solved by Cplex in the MATLAB platform [31]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bus Node** & \(\mathbf{Q_{\text{step}}^{\text{CB}}}\)/kVar & \(\mathbf{N_{\text{max}}^{\text{CB}}}\) & \(\mathbf{y_{\text{max}}^{\text{CB}}}\) \\ \hline
2 & 60 & 5 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of capacitor bank. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bus Node** & \(\mathbf{Q_{\text{max}}^{\text{SVC(AG)}}}\)/kVar & \(\mathbf{S_{\text{max}}^{\text{SVC(AG)}}}\)/kVA & \(\mu\) \\ \hline
7, 21, 30 & 600 & 1500 & 0.866 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of gas-fired units. Figure 4: The modified IEEE 33-node hybrid AC/DC distribution network. Figure 5: Wind power output and load curves. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Bus Node** & \(\mathbf{Q_{\text{step}}^{\text{CB}}}\)/kVar & \(\mathbf{N_{\text{max}}^{\text{CB}}}\) & \(\mathbf{y_{\text{max}}^{\text{CB}}}\) \\ \hline
2 & 60 & 5 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters ofenergy storage system. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Bus Node** & \(\mathbf{P_{\text{max}}^{\text{ESS}}}\)/kW & \(\mathbf{E_{\text{max}}^{\text{ESS}}}\)/\% & \(\mathbf{E_{\text{int}}^{\text{ESS}}}\)/\% & \(\mathbf{\eta_{\text{ch}}}\) & \(\mathbf{\eta_{\text{dis}}}\) & \(\mathbf{y_{\text{max}}^{\text{ESS}}}\) \\ \hline
14, 28 & 300 & 1800 & 30 & 0.9381 & 1.1066 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters ofvoltage source converter. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bus Node** & \(\mathbf{P_{\text{min}}^{\text{G}}}\)/kW & \(\mathbf{P_{\text{max}}^{\text{G}}}\)/kW & \(\mathbf{Q_{\text{max}}^{\text{G}}}\)/kW \\ \hline
6, 23 & 30 & 300 & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters for cost. The following cases were considered to demonstrate the effectiveness of proposed model:  
* Day-ahead scheduling for the hybrid distribution system with CB and ESS considering the wind power prediction curve;
* Two-stage stochastic scheduling for the hybrid distribution system with CB considering th wind power scenario set; and
* Two-stage stochastic scheduling for the hybrid distribution system with CB and ESS considering the wind power scenario set.