# Applications of Probabilistic Forecasting in Demand Response
## 3 Results
### Application 3: Establishing an Hourly Strategy for the Target Day
From a practical point of view, and to implement a demand increase, the setpoint of the WH thermostat is changed from 58-60 \({}^{\circ}\)C to 63-65 \({}^{\circ}\)C during the \"WH extra-storage\" period (Figure 16a). On the other side, EH and WH QHCGs are controlled through pulse-wave-modulated \"ON/OFF\" signals to reduce demand (\"DR clipping\" label in Figure 13a). The change in the thermostat setting (a surplus around 1-2 \({}^{\circ}\)C) is applied to increase demand (\"DR storage\" label, Figure 13a). Figure 15: Response of QHCGs (26 October): (**a**) performance of EH QHCGs, (**b**) example of comfort surveillance during DR performance on EH and WH groups. Once the targets, the performance of load groups, and the surveillance of customer comfort have been stated through some examples, it seems necessary to avoid an excessive repetition of the basic steps of the methodology for each end-use and day. For this reason, the main results showing the compliance with the objectives of this section are summarized in Figures 17 and 18 for the three selected days. Figures 17 and 18 show the results for the LQR and \(QRF\) methods, respectively. These Figures show the energy purchased in markets (forecasted 48 h ahead through quantile 0.5 and labelled \"Demand 48 h, 0.5\") and the revisited demand, 1 h ahead (\"Demand 1 h, 0.5\"),  
Figure 16: Response of QHCGs (7 February): (**a**) DR target and baseline for WH QHCG, (**b**) DR performance of WH groups in the daily period. Figure 17: Results for Application 3: fitting of short-term 1 h demand forecast to purchased energy (48 h forecast through LQR) and overall demand flexibility of EH and WH QHCGs: (**a**) 26 October; (**b**) 2 December; (**c**) 7 February. both forecasted through \(QRF\) and LQR. As stated before, a 1 h forecast is considered as the estimator for the actual demand. Moreover, the overall flexibility of both QHCG groups (\"DR effort\") and the adjustment of forecasted \"actual demand\" through DR (labelled \"Demand after DR\") are also shown in Figures 17 and 18. At first sight, the performance of QHCGs can be considered good enough in most of the time periods both to decrease and also to increase demand (a non-usual DR policy for loads). Figure 18 shows the performance of DR but for \(QRF\) forecasts. The labels and days are the same, but logically forecast levels change (errors and patterns) and consequently flexibility requirements. Some external factors can explain the patterns of demand from 1 h to 48 h forecasts. For instance, in Figures 17a and 18a, demand rises from 10 h to 14 h, perhaps due to a change in the external temperature that was not well forecasted by meteorological models 48 ahead. In this scenario, the aggregator requests flexibility to QHCGs to avoid penalties due to demand unbalance. In addition, demand decreases in the afternoon in Figure 18a (Demand (1 h, 0.5)) with respect to 48 h forecasts (Demand (48 h, 0.5)) but this pattern changes for the same day in Figure 17a when a different forecast method is applied. In this way, the aggregator needs to increase or decrease their aggregated QHCG demand according to energy bid levels sent to markets 48 h ago, irrespective of the previous flexibility trends required some hours before for the same day. In both cases, demand flexibility covers to a considerable extent and with good accuracy those needs. It is also interesting to consider some insights from previous figures. First, the reader should note that soft changes in demand levels (from 48 h to 1 h forecasts) give a better fitting of flexibility to required levels (e.g., Figure 17c). Second, the required flexibility levels for the LQR method are higher than for the \(QRF\) method (around 100 kW up or down  
Figure 18: Results for Application 3: fitting of short-term 1 h demand forecast to purchased energy (48 h forecast through \(QRF\)) and overall demand flexibility of EH and WH QHCGs: (**a**) 26 October; (**b**) 2 December; (**c**) 7 February. in most cases).