## 1 Introduction
To simulate a more realistic power system operation, this paper proposes an RPF method with multi-slack buses that includes two types of power imbalance allocations and considers the economy of generators in the second power imbalance allocation, which is a novel principle of power imbalance allocation. With wind power, photovoltaic power and other renewable energy generation integrated to the grid, the uncertainty factors in the power system have greatly increased. Therefore, the deterministic power flow is not suitable for solving the problem of probabilistic ALSC evaluation. Probabilistic power flow (PPF) can be introduced to address this issue. PPF can be generally divided into three methods: the Monte Carlo simulation (MCS) method [14], analytical method [15] and approximation method [16]. The analytical method has a high dependence on complicated theory. The approximate method has the disadvantage of low accuracy on the probability distribution. Therefore, the MCS method, with simple calculation and relatively high accuracy, is selected herein. The traditional random-sample Monte Carlo simulation (RS-MCS) achieves a high computational accuracy when the sample size is large enough, but it takes a long time and suffers from low computational efficiency. Therefore, it is usually used as a benchmark for verifying the accuracy of other methods. Latin hypercube sampling (LHS) can efficiently cover the entire distribution range of random input variables. It is advantageous at high sampling efficiency, good robustness and simple implementation. Thus, it has been widely applied in probabilistic power flow calculation and probabilistic ALSC analysis [3; 13]. In the existing studies about probabilistic ALSC evaluation, the probability distributions of uncertainty sources, such as loads, wind power generators and photovoltaic power generators are artificially preset as normal. This does not conform to the actual situation and cannot reflect the operating conditions of the future power grid. If the forecasting techniques are used to predict the probability distributions of these uncertainty sources in advance, based on which the ALSC analysis is conducted, then the forecasting result of ALSC can be obtained. The predicted ALSC can help power grid operators assess the security risk of future power systems, which brings an important guiding significance. Therefore, this is a meaningful, but neglected, problem. In recent years, with the improvement in computing power and big data technology [17], artificial intelligence methods have been widely applied in the field of forecasting. Reference [18] proposes a sliding-window-based LightGBM model for the short-term load forecasting. Reference [19] applies XGBoost to predict photovoltaic production. However, the generalization ability and application scope of a single algorithm are quite limited. In order to further improve the forecasting accuracy and stability, some studies adopt the ensemble learning methods, which refer to the method of combining several different machine learning techniques into one forecasting model. Reference [20] combines the decomposition method and stacking-ensemble learning method to forecast wind power generation. Reference [21] proposes a feature-selective ensemble learning model for long-term regional PV generation forecasting. In addition, reference [22] points out that selecting the optimal model input features is also a critical step in the forecasting problem. Therefore, it is necessary to study a method to identify the critical inputs of the model. Correspondingly, the main contributions of this paper are as follows:  
1. The maximal information coefficient (MIC) is used to select appropriate model input features, and the stacking ensemble learning model is used to predict the wind power, photovoltaic power and load power. Both the MIC feature selection method and stacking ensemble learning model are beneficial for forecasting accuracy improvement. 2. An RPF method considering multi-slack buses is proposed to solve the ALSC evaluation problem.