## 1 Introduction  
Load forecasting is a crucial part of power system operation and management. Accurate power load forecasting helps system operators better understand power demand and identify potential supply problems, enabling more rational generation scheduling and improved operational efficiency of the power system [1, 2, 3, 4, 5, 6]. Current load forecasting methods are broadly categorized into two research directions: traditional statistical methods and modern intelligent approaches [7, 8, 9, 10, 11]. Traditional forecasting methods are based on statistical knowledge to analyze the load development law and the correlation of external factors, which can realize the prediction of the future load development trend, including regression analysis [12], time-series method [13], Kalman filter method [14], exponential smoothing method [15] and so on. In [16], a gradient boosting based multiple kernel learning framework of regression for short-term load forecasting is proposed. A method for extracting features from load series data to improve the accuracy of load forecasting is proposed in [17], which simplifies the data features through the trend,periodicity and randomness of the time series and reduces the noise-induced errors to enhance the identification and understanding of power data features. In [18], a generalized method of linear state-space model is proposed to solve the short-term load forecasting problem, which alternately estimates the unknown matrices and states by introducing a blind Kalman filtering algorithm within an expectation-maximization framework. In [19], a new hybrid forecasting model for load forecasting by exponential smoothing, which is based on a new mechanism for dynamically adjusting the smoothing coefficients used is proposed. Modern intelligent prediction methods mainly include artificial neural network method [20], support vector machine method [21], deep reinforcement methods [22] and so on [23]. In [24], a two-step power load forecasting mechanism combining back propagation neural network and radial basis function neural network is presented. In [25], a model for forecasting electric load based on deep residual networks is proposed. To enhance the prediction accuracy, an improved support vector machine integrated with intelligent methods for feature selection and parameter optimization in [26], which applies minimal redundancy maximal relevance to derive informative features from candidate features and uses second-order oscillation and repulsion particle swarm optimization for optimizing parameters. A deep reinforcement learning model with a new asynchronous deep deterministic policy gradient method is proposed for short-term load forecasting in [27], and a new adaptive early forecasting method is proposed to reduce the time cost of model training by adaptively judging the training situation of the agent. There are many external environmental factors that will have an impact on the load change in addition to the electricity load itself when performing load forecasting, including temperature, wind speed, rainfall and humidity [28]. Therefore, exploring the relationship between such external factors and load changes can help to improve load forecasting accuracy [29]. Currently, the Granger causality test is a method to analyze the causal relationship between variables, which plays an important role in identifying the key factors affecting the changes in electricity load. However, the traditional Granger causality test method mainly considers whether there is a linear relationship between the two objects from the perspective of the mean and does not explore the complex relationship between the variables in depth. The test statistic constructed based on the conditional mean model for hypothesis testing is unable to examine the non-negligible quartiles, and the causality of the tails is difficult to be reflected. In other words, existing methods inadequately capture nonlinear and distributional relationships between meteorological factors and load, especially at distribution tails.