# Flexibility Based Day-Ahead Generation-Reserve Bilevel Decision Model
## 4 Case Studies
### Flexibility Based Reserve Decision Method  
Traditional reserve decision model only considers uncertainty in the system, but the flexibility based reserve model proposed in this paper has comprehensively considered the uncertainty and fluctuation of net load as well as the forced outage of conventional unit. Under the joint influence of uncertainty and fluctuation, the system needs reserve in both up and down directions. In order to demonstrate the effectiveness of the proposed method in a more intuitive way, the flexibility based reserve only considered the uncertainty and fluctuation of load in this case. The LOFP is set as  
Figure 4: Output data of two wind farms in northwest China. Figure 3: Total load curve of the IEEE-118 bus system. 5%, and the load prediction errors SD is 3% of forecasted load. Figure 5 shows the comparison of reserve between the proposed method and the traditional method, which values the reserve as 10% of forecasted load. As showed in Figure 5, the reserve obtained by the proposed method is less than the traditional method most of the time. However, when the load sees a rapid rising, such as around six o'clock, the up flexibility reserve is greater than the traditional one; and when the load sees a rapid dropping such as around 22 o'clock, the down flexibility reserve is greater than the traditional one. This indicates that the traditional reserve model may not be able to satisfy the ramping requirement of the system when load changes rapidly. For traditional reserve model, the operator will increase the reserve ratio if the reserve fails frequently but the insufficient of reserve may have caused losses already before the operator takes action. The risk of loss flexibility is uncontrollable. What is more, increasing the reserve ratio for all time interval will lead to a waste of system resources, which is uneconomical. Meanwhile, at the load rising stage, e.g., 5-10 a.m., the up flexibility reserve is greater than the down flexibility reserve; at the load dropping stage, e.g., 0-3 a.m., the up flexibility reserve is smaller than the down flexibility reserve. The flexibility based reserve is a measure of system ramping. It captures the characteristics of system power changes between adjacent time. It shows a better performance of indicating the potential changes of the system power, which the traditional one fails to measure. This shows that the proposed method can more accurately describe the net load characteristics. It can be seen that the proposed flexibility based reserve decision method is more applicable to the reliable operation of the power system containing fluctuating RE. In order to analyze the influence of RE upon the flexibility based reserve, flexibility based reserve (\(R_{\text{DW}}\)) comprehensively considering load and wind farm A and flexibility based reserve (\(R_{\text{D}}\)) only considering the load fluctuation were compared, and the difference between \(R_{\text{DW}}\)-\(R_{\text{D}}\) could directly reflect the influence of wind farm fluctuation upon flexibility reserve. The curve is as shown in Figure 6.  
Due to the intensive uncertainty and fluctuation of the wind farm, the introduction of the wind farm increases the up and down flexibility based reserves of the system in general. According to the statistical results of historical data, when the wind farm output is high, the downward ramping probability is larger than upward ramping; when the wind power output is low, it is the opposite. With wind farm A taken into consideration, when the wind farm output is high, for example at 3 a.m., the downward ramping probability of the wind power is greater, so the increment of the up reserve is larger than that of the down reserve. Particularly, when the wind farm output approximates to the rated value, its downward fluctuation probability is far larger than the upward fluctuation. At this moment, the up reserve significantly increases while the down reserve may drop.