# Medium- and Long-Term Load Forecasting for Power Plants Based on Causal Inference and Informer
## 2 Preliminaries  
Since load is highly dependent on external factors such as climate and economy, the influence of external factors should be considered for accurate forecasting. However, the multiple covariance and deeper causal relationships between external factors are ignored in traditional methods. In the present study, the causal relationship between external factors and load was explored using causal inference techniques, which not only increased the performance of the model, but also enhanced its interpretability and robustness. Causal inference has already found numerous applications in fields such as medicine, sociology, and computer science [15; 16; 17; 18; 19], but owing to a shortage of data, causal inference, which is an emerging research area, is not yet widely used in energy forecasting. Nevertheless, it holds great potential in this field. Despite often being used interchangeably, causality and correlation have different meanings. Correlation is a general relationship that refers to the degree of mutual influence between different variables, and this relationship is not concerned with the directionality of the influence relationship between different variables. Causality is typically divided into two components: cause and effect. The presence of a cause results in the occurrence of an effect, and the existence of an effect is, to some degree, attributable to the cause [20]. Correlational inference and causal inference differ significantly in their research focus. The latter focuses on the response of the outcome variable when the causal variable is changed and quantifies the magnitude of the response [21]. There are two common frameworks for causal analysis that are based on observed data: the potential outcome model and the structural causal model. Among the two, the design of potential outcome models is inspired by the concept of randomized controlled trials and potential outcomes in statistics. Unlike the potential outcome model algorithm, which focuses on estimating the effect of a single variable, the structural causal model aims to identify causal relationships among multiple variables. It proposes a causal function model by examining the features of the data distribution between variables resulting from causal mechanisms. The regression model is used to learn the causal functions given the data of the variables. In the present study, a structural causal model based on directed acyclic graphs (DAGs) [22] is used to construct the causal effect assessment model. Therefore, based on the PC algorithm [23] and industry experience with external variables and load, a causal diagram was first constructed, as illustrated in Figure 1. The diagram includes load and the external variables that affect load. The start of the arrow represents the 'cause' and the pointing end of the arrow represents the 'outcome'. The graphical model allows for the visualization of causality and can be used to obtain joint distributions from statistical analysis of observed data. However, the exact causal relationships cannot be obtained from the graphical model alone. Several methods, that is, the intervention, need to be used to change the distribution of the existing data and thus confirm causality. [PERSON] [22] creatively proposed do-calculus to express the intervention. The variables to be examined are denoted as \(X\) and \(Y\). The other covariates are combined into a vector \(Z=(Z_{1},Z_{2},Z_{3},\dots)\). For simplicity, \(X\) is assumed to be a binary variable and can only take the value of 1 or 0. A set of data can be denoted as \(D=(X^{(i)},Y^{(i)},Z^{(i)})\), \(P(Y=y\mid X=x)\) and \(P(Y=yl\,do(X=x))\) have different meanings, with the former representing the probability distribution of \(Y=y\) conditional on \(X=x\) in the original data and the latter representing the probability distribution of \(Y=y\) when \(X=x\) is reached by intervention.