# Applications of Probabilistic Forecasting in Demand Response
## 1 Introduction
The addition of these explanatory variables, particularly those related to electricity prices, significantly improves the model's predictive accuracy compared to other state-of-the-art models in a case study of regional load prediction in China. The authors acknowledge the limitations of their proposed model, noting that the variables related to DR are restricted to price factors and do not dynamically interact with the forecasted load. Research published in the international literature focuses on developing optimal STLF models, both deterministic and probabilistic, and has recognized the need to integrate DR programs and actions into these models. However, how DR could be leveraged to improve the performance of STLF models has not yet been thoroughly analyzed. It is important to note that certain electricity market participants, such as retailers and aggregators, rely on the forecasts generated by STLF models to trade energy in the day-ahead market, aligning their bids with the expected demand of their customers for each of the 24 h of the following day. In this context, this article presents an example of how DR actions can first reduce the forecasting errors of STLF models, which provide the expected demand for the following day, thereby influencing the amount of energy purchased in the day-ahead market. This reduction in forecasting errors subsequently leads to a decrease in potential penalties for imbalances between the electricity purchased and consumed. In recent years, several studies have addressed the integration of machine learning (ML) models with the potential activation of DR actions. In most cases, these models are designed for short-term load forecasting, while in other instances, they aim to directly adjust the actual load curve to match the initially predicted one. Table 1 provides a summary of relevant studies, detailing the ML techniques employed, the objectives pursued, and the advantages or limitations associated with each approach. The table also provides a brief summary of the characteristics of the method proposed in this article, which will be detailed in the following sections. As shown in Table 1, ML models have a broad range of applications in the activation of DR strategies, each with specific objectives. Nevertheless, they all share the general goals of reducing peak load, ensuring grid stability, lowering costs, and facilitating the integration of renewable energy into electricity grids. However, few studies focus on developing models for load aggregators to plan DR actions [20,26]. These studies aim to maximize the benefits of aggregators while reducing electricity purchasing costs for their customers, but do not consider the assessment of uncertainty in load forecasts. The uncertainty assessment is of particular interest in the case of DR action-planning decisions. This article aims to fill this gap with a probabilistic approach. The main contributions of this article are linked to the use of probabilistic rather than point prediction and its applications in DR. The contributions can be listed as follows:  
1. Given a set of consumers and various load types, such as Electric Heating and Water Heaters, we show how to determine the maximum percentage of predictive uncertainty that can be mitigated by DR actions. This approach enables the aggregator to estimate, at least one day in advance, the likelihood of successfully adjusting the final consumption through DR to meet the purchased energy, thereby establishing the desired balance between supply and demand. 2. In this context, we also demonstrate how to determine the number of consumers required to cover a predetermined level of predictive uncertainty. This will enable the aggregator to plan, at least one day in advance, which loads and how many should be available to participate in DR actions to effectively address the specified uncertainty. 3.