## 1 Introduction
However, there are two main research gaps in the existing studies. The first gap is that no work has studied how to improve the computational efficiency of the probabilistic evaluation of the LSC. In recent years, with the rapid increase in the number of uncertainty sources in power systems, there has been a growing interest in the uncertainty quantification of the LSC evaluation [4; 7; 8]. As to the authors' knowledge, most existing works use the simulation methods to calculate the probabilistic RPF (PRPF), which require enormous rounds of deterministic calculations to ensure the convergence. This necessitates significant data storage and computational resources, which are not conducive to real-time grid dispatch and analysis. Therefore, improving the efficiency of probabilistic LSC evaluation is a meaningful but overlooked problem. Polynomial chaos expansion (PCE) is a commonly used method for enhancing computational efficiency in uncertainty quantification, which has been successfully applied in various fields such as optimal power flow [16], fault location [17], and economic dispatch [18]. The fundamental idea of PCE is to use a set of orthogonal polynomials to approximate the original system model. Basis-adaptive sparse polynomial chaos expansion (BASPCE) is an advanced method that employs the basis-adaptive procedure to automatically select the appropriate truncation strategy and uses a sparse-adaptive scheme to address the curse of dimensionality. Therefore, this paper employs BASPCE to establish a surrogate model for the whole process of the ALSC evaluation to enhance the computational efficiency of probabilistic ALSC evaluation. The second research gap is that no studies have yet analyzed the impact of renewable energy generation on the system's LSC. Existing works typically focus on the LSC of the power system or distribution systems, and even though the systems they studied include renewable energy generation, they do not quantify this impact. The inherent uncertainty of renewable energy generation can affect the system's LSC, making it essential to use specific indices to quantify and evaluate this impact. These indices can also serve as the LSC indices for renewable energy power stations (currently, only the system's LSC indices exist), providing valuable references for the planning and dispatch of renewable energy generation. In other words, shifting the research focus from the power system to a specific renewable energy power station is highly significant. Global sensitivity analysis (GSA) is a method capable of analyzing the impact of renewable energy generation on the system's LSC. This technique measures the influence of input random variables on the probabilistic characteristics of the target output variable [19; 20]. Specifically, the outputs of renewable energy power stations can be considered as input random variables, and their GSA indices can be computed with respect to the LSC. Based on the results of the GSA indices, the importance of each renewable energy power station can be ranked. In engineering practice, specific operational strategies can be formulated for the controllable equipment of the important renewable energy power stations based on these rankings, thereby enhancing the performance of the LSC. In general, the research aim of this paper is to study the influence of the uncertainties caused by renewable energy generation on the power system's LSC. The main innovations and contributions of this paper are summarized as follows:  
1. A novel PRPF method is proposed for the probabilistic evaluation of ALSC. This method works based on BASPCE, which can enhance computational efficiency while holding high accuracy. 2. The GSA is introduced systematically into the LSC evaluation to rank the importance of renewable energy power stations in contributing to the system's LSC. 3. To validate the effectiveness of the proposed method, experiments are conducted on the modified IEEE 39-bus system.