# Applications of Probabilistic Forecasting in Demand Response
## 3 Results
### Application 3: Establishing an Hourly Strategy for the Target Day
In our case, quantile 0.50 with a horizon of 48 h has been chosen as the baseline for demand without DR. Obviously, the \"real\" load can increase and decrease in different magnitudes throughout the selected days with respect to the baseline in different periods. This represents interesting performance tests for demand flexibility (DR) and PBLM performance and usefulness. According to step 3, the aggregator (and considering the number of loads defined in the previous subsection, i.e., Application 2) defines a target hour ahead (Target2 in Figure 13) to reduce or increase demand in each group of responsive loads (QHCG) with respect to the QHCG baseline demand. An example for EH and WH aggregated control groups on 26 October is depicted in Figure 13.  
It is also interesting to analyze the stress that each load group suffers due to the compliance of DR targets. This can be considered through an effort curve (the ratio between the increase/decrease in each end-use demand over the baseline level for this end-use). Figure 14 shows this daily curve on 26 October again. In Figure 14a, each group develops a similar flexible pattern of demand, and it is seen that the effort does not surpass 0.3 p.u. Figure 11: Example of application of step 4. The purchased energy \(E_{h}\) in markets is compared with 1 h predictions (quantiles are selected by the energy aggregator). If \(E_{h}\) is greater than energy defined by bands (in red), DR actions should increase demand—for example, through energy storage (DR > 0). If the blue curve is under the demand band, DR should be applied to clip demand (DR < 0). According to the experience of each aggregator with its customers' response, these efforts can be changed and QHCG targets can be different. For example, another option to be considered is to \"specialize\" each QHCG in a flexible task, i.e., WHs only increase demand and HVAC shaves demand. This is presented in Figure 14b. In this paper, this scenario is not considered because the main interest is to show the ability of flexible loads to perform in complex DR contexts. Nevertheless, draft results show that this specialization does not have a significant impact on the overall results, but from the point of view of energy efficiency this option could be of interest. For these reasons, a more detailed study will be presented in a future paper. According to the DR targets that have been presented in Figure 13a,b, the QHCGs' response has been simulated, hour by hour, during a day. Figure 15a presents the performance of EH QHCGs with respect to the DR targets presented in Figure 13a. The figure shows that the DR targets are not reached perfectly, mainly because PBLM limits fast changes in demand (e.g., from 19 h to 20 h) to avoid short peaks and demand rebounds after clipping periods. As stated before, DR requires a surveillance of flexibility effects in load service (i.e., assuming some minimum thresholds for customer comfort--in our case, temperatures inside the dwelling or hot water temperatures, Section 2). The effects are depicted in Figure 15b through PBLM state variables (indoor temperature in the case of EH, or temperatures in the water tank in the case of WHs). Another example is presented in Figure 16. On 7 February, the aggregator required (Figure 12b) an almost rising profile of demand to account for an excess of energy forecasted in the 48 h horizon (LQR method). This involved a non-typical DR action (i.e., a rise in demand). Figure 16a represents the target for WH loads, and Figure 16b presents simulation results though PBLMs. As can be seen, WH QHCGs can also follow changes in demand specified by a target (Target2 WH in Figure 13b) with good accuracy but filtering fast changes in the demand reference/target. To simplify the simulation and avoid overdamping, the control reference signal applies every 15 min, and any change is implemented in PBLM scripts if the foreseen change in demand (Target 2) is less than 0.03 p.u., i.e., a deadband is applied in PBLM control procedures.