## 6 Conclusions  
This paper systematically applies the BASPCE surrogate model to PRPF. Moreover, the GSA based on BASPCE is introduced in the ALSC evaluation to analyze the impact of power stations on the system's LSC. The test results on the IEEE 39-bus system validate the feasibility and effectiveness of the proposed method. Detailed conclusions are drawn below. The BASPCE model can efficiently handle RPF with high accuracy and speed for probabilistic ALSC evaluation, as well as GSA based on RPF. More specifically, the distribution of ALSC obtained by the BASPCE is more than \(97\%\) similar to the reference. Furthermore, for ALSC evaluation, compared with the PRPF based on the original model, the PRPF based on BASPCE can reduce computation time by approximately tenfold without compromising accuracy. For GSA, since more rounds of MCS are required, the speed advantage of BASPCE becomes more pronounced, thus reducing computation time by over 30 times. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **BASPCE** & **MCS** & **HPEM** \\ \hline Time/s & 219.46 & 6548.95 & 133.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computation time of GSA based on different methods. The results of the GSA can quantify the impact of uncertainties in renewable energy stations on LSC, and the ranking derived from GSA indices can assist in identifying the most critical renewable energy power stations. The limitations of this study mainly lie in two aspects: first, the limitation of the RPF approach. RPF is a simple and effective approach for evaluating ALSC; however, its underlying assumption, a fixed load growth direction, may prevent it from identifying the maximum loading point. Therefore, developing more flexible methods that can account for varying load growth directions represents an important direction for future research. Second, the limitation of the GSA indices: The GSA indices lack physical interpretability and only provide a relative ranking of influence. Therefore, a promising future direction is to develop a physically meaningful, station-level LSC index. Conceptualization, J.Z. and J.T. ; methodology, J.Z., K.F., W.H. and Y.Z. ; software, J.Z., Y.Z. and Q.S. ; validation, K.F, Q.S. and J.T. ; formal analysis, W.H. and Q.S. ; investigation, J.Z., K.F. and Y.Z. ; resources, K.F., W.H. and Y.C. ; data curation, Y.Z. and Q.S. ; writing--original draft preparation, J.Z. and Y.Z. ; writing--review and editing, Y.C. and J.T. ; visualization, K.F. and W.H. ; supervision, J.T. ; project administration, J.Z. and Y.C. ; funding acquisition, J.Z., K.F. and W.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the Science and Technology Program of China Southern Power Grid Co., Ltd., grant number YNKJXM20222174. Not applicable. Data Availability Statement: Data are available on reasonable request. Author [PERSON], [PERSON] and [PERSON] was employed by the company Yunnan Power Grid Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The authors declare that this study received funding from China Southern Power Grid Co., Ltd. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article, or the decision to submit it for publication. The following abbreviations are used in this manuscript: \begin{tabular}{l l} LSC & load supply capability \\ GSA & global sensitivity analysis \\ ALSC & available load supply capability \\ LHS & Latin hypercube sampling \\ MCS & Monte Carlo simulation \\ TSC & total supply capability \\ PSC & power supply capability \\ RPF & repeated power flow \\ OPF & optimal power flow \\ CPF & continuation power flow \\ PRPF & probabilistic RPF \\ PCE & polynomial chaos expansion \\ BASPCE & basis-adaptive sparse polynomial chaos expansion \\ LAR & least angle regression \\ LOO & leave-one-out \\ \end{tabular}