# Applications of Probabilistic Forecasting in Demand Response
## 4 Conclusions  
Probabilistic forecasting is shown as a useful tool in the context of demand response, together with Physical-Based Load Models--an aspect that is reflected throughout the paper by means of three specific applications. On the one hand, it allows us to quantify the percentage of uncertainty that DR actions could potentially cover during a target day for predictions with a horizon of 48 h (the usual time horizon when purchasing the energy on the market). On the other hand, the forecasted quantiles can be used to compute the number of consumers needed for DR actions. Two probabilistic forecasting methods have been used to illustrate the proposed applications: Lineal Quantile Regression and a Quantile Regression Forest. For the analyzed dataset (hourly data of a small city in Spain), the \(QRF\) method showed better performance properties than LQR regarding accuracy, calibration, and sharpness. In both cases, results reveal that the percentage of uncertainty covered by DR is lower in the day hours from 10 a.m. to 8 p.m., as expected. Apart from these two applications, a third one is also developed in detail. Unlike the first application, in Application 3 we do not focus on the theoretical potential of DR but propose a specific strategy based on the quantiles resulting from the probabilistic forecast  
Figure 19: _RMSE_ during the test period before and after applying Application 3 (assuming perfect DR actions): (**a**) comparative results for the LQR method; (**b**) comparative results for the \(QRF\) method; (**c**) comparative results between predictive methods before applying Application 3; (**d**) comparative results between predictive methods after applying Application 3.  
ing. The results reveal a significant reduction in errors (deviations of real consumption from purchased energy) for the two forecasting methods (LQR and _QRF_), with a greater reduction in the case of the one that is less accurate. Consequently, this work shows that demand response can provide high levels of flexibility in the residential sector. This is significant because flexibility needs to increase in the future to avoid security issues and high generation costs, thus achieving balance in the power system. Additionally, this flexibility substantially reduces short-term load forecasting uncertainty, enabling the creation of a new portfolio of more reliable resources on the demand side. Consequently, demand response alleviates some energy and balance concerns for customers, aggregators, distributors, and other stakeholders (e.g., balancing responsible parties) in future scenarios. Moreover, the increase in flexibility (both upward and downward) is particularly valuable when generation sources, primarily renewables, can heighten the volatility of supply resources, thus increasing the probability of imbalances. This is critical from a security of supply perspective. These imbalances can occur at small scales (prosumers) or across the entire power system. The main challenge is to define flexibility targets using short-term load forecasting methods and to analyze the potential flexibility of demand-side resources through simulation models. Additionally, probabilistic methods allow for the consideration of different risk levels according to the profiles of customers and aggregators and, naturally, the potential benefits or revenues associated with those risks in markets or services. Conceptualization: L.A.F.-J., A.G. ([PERSON]), and M.C.R.-A. ; methodology: L.A.F.-J., A.G. ([PERSON]), and M.C.R.-A. ; software: L.A.F.-J., A.G. ([PERSON]), M.C.R.-A., and A.G. ([PERSON]); validation: A.G. ([PERSON]) and A.G. ([PERSON]); formal analysis: L.A.F.-J. and M.C.R.-A. ; investigation: all authors; resources: M.C.R.-A. and A.G. ([PERSON]); writing--original draft preparation: all authors; writing--review and editing: L.A.F.-J., A.G. ([PERSON]), and M.C.R.-A. ; visualization: [PERSON]. ([PERSON]); supervision, [PERSON] and [PERSON]; project administration: [PERSON].