# Applications of Probabilistic Forecasting in Demand Response
## 1 Introduction  
The societal commitment to energy transition and the increasing integration of renewable energy sources into electrical grids have rendered the availability of accurate and reliable short-term electric power consumption forecasting models critical. These models enable stakeholders in the electrical system to make appropriate decisions to anticipate load fluctuations, optimize energy generation and distribution, and minimize operational and environmental costs. The methods described in the international literature for short-term load forecasting can be categorized into two groups: deterministic or point forecast methods, and probabilistic methods. The distinction between these two categories is based on how they deal with uncertainty in predictions. In deterministic methods, the focus is on providing a single expected load value as the forecast. These methods do not explicitly account for uncertainty, and they offer the single point estimate of load value without information about the potential range of outcomes or the level of confidence in the prediction. On the other hand, probabilistic methods go further by not only providing a point estimate but also offering additional information that allows you to assess the uncertainty associated with that estimation. These methods provide a probability distribution or a set of probabilitiesthat describe the possible range of load values and the likelihood of each value occurring. This added information is valuable for making more informed decisions. One of the decisions that these stakeholders can make focuses on the field of electric power distribution, particularly in actions known as demand response. Demand response (DR) is an integral component of modern electrical system management [1; 2] contributing to the reduction in capacity requirements and costs, facilitating greater integration of renewable energy, and lowering overall system emissions [3]. As electrical systems become more complex and power generation more variable due to the inclusion of renewable sources, the ability to adjust electricity demand in real time has become a vital tool for maintaining the stability and efficiency of the grid. DR materializes in the adaptation of electricity consumption by end-users in response to external signals. These signals can be changes in electricity prices during periods of high demand or incentives offered by grid operators to reduce load during critical periods. DR programs can be roughly classified into three groups based on who initiates the demand reduction action: (a) rate-based or price programs, where utilities vary electricity prices to motivate customers to adjust their consumption patterns; (b) incentive or event-based programs, where utilities or aggregators request or control customer load reductions through signals or commands; and (c) demand reduction bids, where customers initiate and offer load reductions to utilities at specified prices [4]. This paper focuses on programs classified in the second group, where utilities are expected to implement an efficient incentive system to adequately compensate customers who adjust their consumption in response to signals indicating the execution of DR actions. The initial step in compensating customers who have engaged in these actions involves assessing their actual level of commitment. This requires evaluating the degree to which they have adjusted their consumption patterns in response to the utility's signals. In this task, forecasting customers' load is essential, particularly in the short term, which involves predictions up to seven days in advance. The body of scientific literature on STLF models is extensive and diverse, although it is primarily focused on deterministic models--that is, models that do not provide information about uncertainty in prediction.