# Analyzing the Impact of Variability and Uncertainty on Power System Flexibility
## 3 Scenarios for Variability and Uncertainty
### Scenario Generation and Sensitivity Analysis  
A scenario-based approach is applied in this study. To clarify the impacts of variability and uncertainty, the following are considered. First, the net load variation appears in every time interval. As every time interval is complex, this complicates the analysis of the results. Thus, to enhance the analyzability and clarity, the most influential time interval, in terms of flexibility, is selected and the  
Figure 1: Triangular distribution for the example. net load variation for the time interval is varied. \(RSP_{t}\) is used as the selection criterion, i.e., the time interval of the largest \(RSP_{t}\) is chosen. Figure 2 represents the forecast net load variation and measured net load variation for the selected time interval. A blue straight line and two red dotted lines for the selected time interval (between \(t_{1}\) and \(t_{2}\)) indicate the forecast net load variation and measured net load variation, respectively. (a) means variability, and (b) and (c) imply uncertainty. Differently with the forecast net load variation, the measured net load variation includes uncertainty. The variability and uncertainty both vary with net load at time \(t_{1}\) and \(t_{2}\). When adjusting the variability, it is assumed that the net load at time \(t_{2}\) is changed, while the net load at time \(t_{1}\) is fixed. This assumption is useful in clarifying scenario generation, and comparing the result of the uncertainty with that of the variability. The uncertainty is represented by some percentage (indicating the standard deviation expressed as a percentage) of the net load at time \(t_{2}\). A change in the variability is accompanied by a change in the uncertainty, because both parameters are dependent on the net load at time \(t_{2}\). Therefore, to keep the uncertainty unchanged with the variability, the same value of the uncertainty of the base case is applied to all scenarios for the variability; the \"base case\" refers to the information of the given system. The scenarios for the increased variability and uncertainty are listed in Table 1. For reference, \"increased variability\" instead of variability is used for scenario generation; it is represented as an increment based on the variability of the base case, and its value is calculated as some percentage of the net load. The increased variability of the base case is thus equal to zero. The effects of increased variability and uncertainty on flexibility change with the net load because the reserve capacity of generating units may vary with the net load. The net load is thus classified into three types: high, medium, and low. Among these types, the medium net load corresponds to the base \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario \#** & **Net Load** & **Increased Variability** & **Uncertainty** \\ \hline S1 & High (\(>\)100\%) & Particular range & Fixed \\ S2 & & Fixed, 0\% & Particular range \\ S3 & Medium (100\%) & Particular range & Fixed \\ S4 & & Fixed, 0\% & Particular range \\ S5 & Low (\(<\)100\%) & Particular range & Fixed \\ S6 & & Fixed, 0\% & Particular range \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Scenarios for three parameters at the selected time interval. Figure 2: Forecast net load variation and measured net load variation. case of the net load (i.e., 100%), and is represented in S3 and S4. The high (low) type is larger (smaller) than 100%, given by S1 and S2 (S5 and S6). Each type depends on the system conditions, e.g., low net load can occur due to use of DSRs in the time period considered. Empirical trials were used to determine the value of each type of net load. For every net load, two kinds of scenarios for variability and uncertainty are considered: one (the other) is when the variability (uncertainty) is fixed and the uncertainty (variability) is changed. The value of the increased variability is 0% for the fixed case, i.e., S2, S4, and S6.