# Applications of Probabilistic Forecasting in Demand Response
## 3 Results
### Application 3: Establishing an Hourly Strategy for the Target Day
This can be partially explained through performance indicators for each forecast method (Tables 5 and 6). Table 8 summarizes the improvement provided after running Application 3 to the three selected days in the test period and for the two probabilistic forecasting methods (LQR and \(QRF\)). Additionally, Table 9 shows the error reduction in terms of the \(RMSE\) when the strategy proposed in Application 3 is applied to all days in the test period. In this case, perfect DR actions are assumed in the following sense: the energy to save or to increase at each hour, determined by the steps described in Application 3, is supposed to be achieved. As it can be seen, the \(QRF\) method is more accurate than the LQR, in the scenario of no DR actions as well as in the case of applying DR according to Application 3. However, the percentage of error reduction is greater for the LQR method, which can be considered an added value: the differences of accuracy among the predictive methods can be cushioned after applying the strategy proposed in Application 3. The evaluation of the error reduction is also depicted in Figure 19, which includes several comparing graphs with the evolution of the \(RMSE\) for all days in the test period. The significant reduction in error after applying Application 3 is latent in Figure 19a,b, corresponding to the LQR and \(QRF\) methods, respectively. On the other hand, Figure 19a,b reveals a better performance of the \(QRF\) method against LQR, which is cushioned after applying Application 3. The lack of accuracy in predictions comes from different sources (weather forecast inaccuracies or the forecast method selected, among others). As we have confirmed, there is a significative difference in 48 h-ahead predictions' accuracy depending on the method employed (LQR versus \(QRF\)), and the impact of those differences was reduced after applying the DR strategy proposed in this paper. That is, the capacity for improvement is greater when the initial 48 h-ahead baseline is worse. Although weather forecast inaccuracies affect demand predictions, it can also be proved that if we had used the real values of climatic factors (instead of their forecasts), the results would not have changed significatively. The reason is similar to before: the 48 h-ahead baseline of demand would be significatively affected by the lack of accuracy in the climatic factors, but not the 1 h-ahead baseline. Therefore, a suitable DR strategy like the one proposed in the paper will be the most important factor to obtain similar results (low deviations between the purchased energy and final consumption). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Day**} & \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{_RMSE_} & \multicolumn{1}{c}{_RMSE_} & \multicolumn{1}{c}{**Percentage of**} \\  & & **(Before Applying App3)** & **(After Applying App3)** & **Error Reduction** \\ \hline \multirow{2}{*}{26 October} & LQR & 301.37 & 178.61 & 40.73\% \\ \cline{2-5}  & \(QRF\) & 210.02 & 14.45 & 29.79\% \\ \hline \multirow{2}{*}{2 December} & LQR & 262.57 & 167.78 & 36.10\% \\ \cline{2-5}  & \(QRF\) & 174.50 & 152.44 & 12.64\% \\ \hline \multirow{2}{*}{7 February} & LQR & 173.73 & 149.91 & 13.71\% \\ \cline{2-5}  & \(QRF\) & 156.52 & 119.44 & 23.69\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Reduction in \(RMSE\) after applying Application 3 to the three selected days. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{_RMSE_} & \multicolumn{1}{c}{_RMSE_} & \multicolumn{1}{c}{_Percentage of_} \\  & **(Before Applying App3)** & **(After Applying App3)** & **Error Reduction** \\ \hline LQR & 313.61 & 185.20 & 40.95\% \\ \hline \(QRF\) & 213.33 & 141.61 & 33.62\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Reduction in \(RMSE\)s after applying Application 3 to the whole test dataset.