# Applications of Probabilistic Forecasting in Demand Response
## 3 Results
### Application 3: Establishing an Hourly Strategy for the Target Day  
The third application involves probabilistic forecasting with a 1 h horizon to establish an effective DR strategy. The goal is to correct deviations between the electricity purchased (hourly baseline for a specific day) and actual consumption. To achieve this, we use 1 h horizon probability forecasts to estimate the energy to be saved or increased each hour, thereby setting a DR schedule for aggregation. The process is as follows:  
* Step 1: Select a day from the test period and obtain the hourly predicted baseline (purchased energy) for that day with a 48 h horizon, as in other applications. * Step 2: Obtain the probabilistic forecasts (predicted quantiles) with a 1 h horizon for all hours of the selected day. * Step 3: For each hour of the selected day, estimate the probability that actual consumption will be lower or higher than the purchased energy. This involves determining the position of the purchased energy among the predicted quantiles with a 1 h horizon. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{_QRF_} & \multicolumn{2}{c}{_LQR_} \\ \hline
**Day** & **WH** & **EH** & **WH** & **EH** \\ \hline
26 October & 620 & 575 & 640 & 595 \\ \hline
2 December & 870 & 625 & 735 & 530 \\ \hline
7 February & 455 & 435 & 445 & 420 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Approximate number of loads to be involved in DR policies by day. Figure 10: Example of Application 2 for three days in the test period. Coverage probability of 70% and method _QRF_: (**a**) purchased energy, and predicted quantiles 0.15 and 0.85 using the QRF48 model on 7 February 2011; (**b**) energy to rise and fall according to step 2 on 7 February 2011; (**c**) purchased energy, predicted quantiles 0.15 and 0.85 and DR efforts on 26 October 2010; (**d**) purchased energy, predicted quantiles 0.15 and 0.85 and DR efforts on 2 December 2010. For instance, if the purchased energy at hour \(h\), \(E_{h}\), is between the \(\hat{Q}_{h,0.05}\) and \(\hat{Q}_{h,0.06}\) predicted quantiles, we estimate \(p_{h}=P(Y_{h}<E_{h})=0.05\), where \(Y_{h}\) denotes the actual consumption at hour \(h\). * Step 4: Establish criteria to determine DR actions, applying them only when there is a high certainty that saving or increasing energy is needed: If \(p_{h}\) is in the range [0.25, 0.75], no DR actions are applied. If \(p_{h}<0.25\), there is a high likelihood that actual demand will exceed purchased energy. In this case, DR actions are taken at hour \(h\) to save the energy difference between \(\hat{Q}_{h,0.5}\) (the predicted median with a 1 h horizon) and the purchased energy \(E_{h}\). If \(p_{h}>0.75\), there is a high likelihood that actual demand will be less than purchased energy. In this case, DR actions (DR > 0, see Figure 11) are taken at hour \(h\) to increase the energy difference between \(E_{h}\) and \(\hat{Q}_{h,0.5}\) (the predicted median with a 1 h horizon). To better illustrate the procedure from a practical point of view, and to present some different possibilities for the aggregator, three different days during the test period have been considered: 26 October and 2 December 2010, and 7 February 2011. The choice of these days is justified by the forecasted demand (and the considered representative quantiles) and the weather conditions that drive flexible end-use (WH and EH) demand. Due to these boundary conditions, the necessary flexibility requires different values and trends in different periods. Figure 12a,b shows the demand quantile 0.50 for 48 h and 1 h forecasts for two of the three selected days with the \(QRF\) and LQR methods, labelled as \"Demand (time-horizon, quantile)\". These figures correspond to steps 1 and 2 of the proposed method/process. Note that flexibility requirements are different. As has been discussed before, in the short term, a 1 h forecast is more accurate (Table 4) and will drive the target for demand flexibility.