# Flexibility Based Day-Ahead Generation-Reserve Bilevel Decision Model
## 4 Case Studies
### Flexibility Based Generation-Reserve Bilevel Decision Model  
In order to verify the accuracy of the proposed model, four scenarios were studied in the first case of Section 4.3. The parameters of each scenario are listed in Table 2.  
The obtained unit commitment schemes of the four scenarios were the same. As the predicted value of the load and wind power remained consistent, the objective function value of the four scenarios were the same, which was \(\$1.96\times 10^{6}\). As all solution are obtained through one iteration, the solution time is about 52 min. Figure 7 shows the UC scheme of partial conventional units. In Figure 7, the gray represents unit on operation while the white represents unit shutdown. The comparison of reserve in different scenarios is shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Computing** & **Serial** & **2 Threads** & **4 Threads** & **6 Threads** & **8 Threads** \\
**Means** & **Computing** & **Parallelism** & **Parallelism** & **Parallelism** & **Parallelism** \\ \hline Calculation & & & & & \\ Time & 1207 s & 924 s & 642 s & 563 s & 526 s \\ \hline \end{tabular}
\end{table} 
Table 1: Computing time of different computing means. \begin{table}
\begin{tabular}{c c c} \hline
**Scenarios** & **LOFP** & **Load Prediction Errors** & **Wind Power Prediction** \\  & & **SD in Percentage of** & **Errors SD in Percentage of** \\  & & **Forecasted Load** & **Forecasted Wind Power** \\ \hline Scenario 1 & 5\% & 3\% & 5\% \\ Scenario 2 & 2\% & 3\% & 5\% \\ Scenario 3 & 5\% & 5\% & 5\% \\ Scenario 4 & 5\% & 3\% & 3\% \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of each scenario. Figure 6: \(R_{\text{DW}}\)–\(R_{\text{D}}\) curve. The comparison of scenario 1 and 2 shows the influence of different flexibility requirements upon reserve. When the flexibility requirement rises, the system reserve significantly increases. The  
Figure 8: Comparison of reserve in different scenarios. (**a**) Comparison of the up reserve; (**b**) comparison of the down reserve. Figure 7: Unit commitment of partial units. comparison of scenario 1 and 3 displays the impact of load prediction error upon reserve. Compared to scenario 1, the load prediction error in scenario 3 is larger, and the reserve significantly increases. The reserve of scenario 4 is almost the same with scenario 1. This is because the total capacity of wind power is relatively small, so the increase in wind power output fluctuation caused by the increase in wind power prediction error has less impact on system flexibility. The above simulation results showed that the reserve increased as flexibility requirement rose. When the uncertainty of the system diminishes, such as the lowered load prediction SD and wind speed prediction SD, the operating reserve will decrease. Those cases listed above demonstrate that the reserve capacity obtained by the proposed model could accurately reflect the system uncertainty and flexibility, hence verifying the validity of the proposed model and algorithm. In order to further analyze the influence of wind power upon the operating reserve, the system reserve was calculated under different wind power penetration rates. In scenario 1, the total wind power capacity was 350 MW, with a penetration rate of 5%. The scenarios of no wind power and integrated wind power capacity of 800 MW, 1250 MW and 1800 MW were calculated separately, corresponding to wind power penetration rates of 0%, 10%, 15% and 20%, respectively. The solution information is listed in Table 3.  
When the wind power penetration rate was relatively low, the UC scheme of initial solution by the upper level model could provide sufficient reserve capacity. However, the uncertainty in the system increased with the rising of the wind power penetration rate. Although wind power generation cost was neglected, the unit generation cost increased as wind power penetration increased.