## 4 Case Studies
### System Description  
The modified 24-bus power system is shown in Figure 2[37]. The modified system contains five coal-fired power generators, two wind turbines, and thirty-four branches. The expansion plan is to build a WT and ES at several predetermined locations. The predetermined locations of the WT and ES are marked in Figure 2. In this paper, the WT and ES were considered to belong to the same investor. The detailed parameter of the existing generators [37; 38], the WT to be planned, and the ES to be planned [39; 40] are shown in Tables 1-3, respectively. The scenario generation of the wind power output and power load based on the method proposed in Section 2.2 are shown in Figures 3 and 4, respectively. The number of scenarios before and after the scenario reduction were set to 10,000 and 3, respectively. The reference values of the power loads are listed in Table 4. The parameters of the time-of-use tariff are shown in Table 5.  
Figure 5a. Since wind turbines already existed in bus 7 and bus 18 in the original system, the carbon intensities of bus 7 and bus 18 in Figure 5a are relatively low. Comparing Figure 5a,b, it can be found that the carbon intensities of bus 1 and its surrounding buses in Figure 5b are significantly reduced due to the deployment of wind turbines at bus 1. At the same time, new energy storage is planned at bus 8 in the proposed model, which can stimulate energy storage for wind power accommodation. As a result, there was also a visible reduction in the carbon intensities of bus 8 and its surrounding buses.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Generator No.**} & \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Capacity/(MW)**} & **Cost** & **Carbon** \\  & & & **Coefficient/(USD/MWh)** & **Intensity/(tCO\({}_{2}\)/MWh)** \\ \hline G1 & Wind turbine & - & 30 & 0 \\ G2 & Coal-fired & 400 & 38 & 1.31 \\ G3 & Wind turbine & 300 & 30 & 0 \\ G4 & Coal-fired & 591 & 42 & 1.25 \\ G5 & Coal-fired & 215 & 38 & 1.31 \\ G6 & Wind turbine & - & 30 & 0 \\ G7 & Wind turbine & 400 & 30 & 0 \\ G8 & Coal-fired & 400 & 42 & 1.25 \\ G9 & Coal-fired & 300 & 30 & 1.31 \\ G10 & Wind turbine & - & 30 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of generators.  
Figure 2: The modified IEEE 24-bus power system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(v_{ci}\) & 3 m/s & \(\xi_{c}^{1}\) & 3.77 \\ \(v_{r}\) & 7 m/s & \(\xi_{c}^{2}\) & 5.22 \\ \(v_{co}\) & 25 m/s & \(\xi_{c}^{3}\) & 6.22 \\ \(\xi_{k}^{1}\) & 1.14 & \(\xi_{c}^{4}\) & 9.04 \\ \(\xi_{k}^{2}\) & 1.75 & \(\xi_{c}^{WT}\) & 1095 USD/kW \\ \(\xi_{k}^{3}\) & 3.64 & \(P_{N,max}^{WTG}\) & 700 MW \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the wind turbine generator to be planned.  
Figure 4: (a) Power load deviation before and after the scenario reduction; (b) power load of reduced scenarios.  
Figure 3: (a) Wind speed before and after the scenario reduction; (b) wind power output of reduced scenarios.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(\gamma_{loss}\) & 2\%/month & \(N_{Y,ES}\) & 8 Years \\ \(c_{E}^{ES}\) & 100 USD/kW & \(\Gamma\) & 4 \\ \(c_{E}^{PS}\) & 250 USD/kWh & \(\gamma_{rec}\) & 0.1 \\ \(c_{Y}^{int}\) & 25 5/(kW-Year) & \(\alpha_{min},\alpha_{max}\) & 10\%, 90\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of energy storage to be planned.