## 1 Introduction  
With the presentation of the goal of \"carbon peaking and carbon neutrality\" in China, the construction of a new electrical power system based on new energy is imminent. Under the new electrical power system architecture, the interaction of renewable energy generations, energy storage and flexible load resources is becoming more frequent. The accuracy and reliable challenges posed by the higher penetration of renewable energy and flexible load resources should be considered significantly. Short-term load forecast is the basis work of power grid dispatching, and it is becoming more important in the new electrical power system [1, 2, 3]. Various short-term load forecasting models and methods have been proposed and applied during the past decades. Typically, load forecasting methods are divided into statistical-based and machine learning-based forecasting methods [4, 5, 6, 7]. Statistical methods include multiple linear regression [8], autoregressive moving average [9], and autoregression [10, 11]. These methods have a distinctive feature with faster calculation speed. However, they also have a weak expressive ability for nonlinear problems. With the development of artificial intelligence technology recently, machine learning methods such as gray system [12], recurrent neural network [13], and extreme learning machine [14] are focused and widely used in load forecasting areas. However, there are gradient extinction and gradient explosion problems in the back propagation of recurrent neural network with the layer increase in the deep structure. Extreme learning machine is a combined stochastic prediction and multiple regression method; its performance reduces with the increasing complexity of load forecasting considering various meteorological and electrical consumption behaviors. The k-fold cross-validation estimator is widely used in classification and regression problems. A global support vector regression metamodeling approach based on the sorted k-fold method is proposed in [15], in which the k number of SVR metamodels are constructed based on a cross-validation technique. A k-fold cross-validation approach based on the DCNN algorithm is used for predicting the melanoma classes in [16], and the k-fold method can achieve a better performance on a small skin cancer data set. Furthermore, load forecasting methods based on combined algorithms emerge continuously, which have achieved results with a faster calculation speed and higher precision. A deep learning bidirectional LSTM neural network is proposed in [17]; the method gives a deep learning structure of bidirectional LSTM to avoid the gradient explosion problem. A hybrid short-term load forecasting is proposed in [18], which uses the combination of correlation analysis and appropriate inputs to the individual Bayesian neural network, but the parallel training and its weight of Bayesian neural network introduce an extra computational burden. A novel hybrid with a new signal decomposition and correlation analysis technique method is proposed in [19]; T-copula is used to compensate the peak load to reduce the forecasting error. A combined method based on the maximum information coefficient, factor analysis, gray wolf optimization and generalized regression neural network is proposed in [20]; the proposed method has a strong global search ability, but it needs enough time for the training and forecasting. The variation of electrical price will influence the consumption of electrical power, which depends on the electrical power curves. So, the electrical price is a key point for the load forecasting. A new approach combining parametric and nonparametric function autoregressive models for the prediction of electricity price is proposed in [21]; it provides insights into the scale and purchase mechanism with the price and demand formation process. The paper provides a new solution from the purchase curve side to improve the forecasting accuracy.