## 5 Test Results and Discussion
### Test Results on GSA  
In this subsection, BASPCE, MCS (with \(10^{4}\) samples), and [PERSON]'s point estimate method (HPEM) are adopted to calculate the \(K\)-\(ST\) index for the GSA of PRPF, where the accuracy and the efficiency are compared. The reference results are obtained by MCS with \(10^{5}\) samples. The \(K\)-\(ST\) index results calculated by different methods in three scenarios are shown in Figures 7-9.  
The primary goal of GSA is to obtain the importance ranking of input random variables, making the accuracy of the importance ranking the most critical aspect. From Figure 7, in S1, it can be observed that both BASPCE and MCS achieve the same importance ranking  
Figure 8: _K-ST_ index results calculated by different methods in S2.  
Figure 7: _K-ST_ index results calculated by different methods in S1.  
Figure 9: _K-ST_ index results calculated by different methods in S3.  
results as the reference method: \(P_{\text{PV1}}>P_{\text{PV2}}>P_{\text{W2}}>P_{\text{W1}}>P_{\text{PV3}}\). This demonstrates that BASPCE can accurately determine the importance ranking of random input variables for the target output. In contrast, the HPEM method produces incorrect results: \(P_{\text{PV1}}>P_{\text{W1}}\)\(>P_{\text{W2}}>P_{\text{PV2}}>P_{\text{PV3}}\). A correct importance ranking is highly meaningful. For example, if it is determined that PV1 has the highest sensitivity to ALSC, indicating that PV1 is the most critical factor, priority should be given to adjusting the PV1 station when ALSC is low (indicating insufficient load supply capability). Such measures could include adjusting the control strategy of the energy storage system, regulating the power output of inverters, etc. The same conclusion can be drawn from S2 and S3: Both BASPCE and MCS are capable of generating the correct importance ranking, whereas HPEM yields a wrong importance ranking. Moreover, it can be observed that the ranking of the importance of renewable energy stations varies across different scenarios. Nevertheless, the BASPCE model consistently demonstrates the ability to obtain accurate rankings under all conditions.  
As for the accuracy of the exact values of the _K-ST_ index, it can be evaluated based on the relative errors labeled on each bar. The relative errors of the BASPCE and MCS methods for the five input random variables are similar, indicating that they have almost the same accuracy. However, HPEM produces some ridiculous results. Specifically, in S1, the relative error of BASPCE ranges from \(-6.9\%\) to \(+6.0\%\), that of MCS from \(-4.2\%\) to \(+6.4\%\), and that of HPEM from \(-95.5\%\) to \(+14.8\%\). In S2, the relative error of BASPCE spans from \(-10.8\%\) to \(+35.4\%\), MCS from \(-24.4\%\) to \(+17.7\%\), and HPEM from \(-98.9\%\) to \(+424.4\%\). In S3, the relative error of BASPCE is between \(-32.7\%\) and \(+2.0\%\), MCS between \(-28.9\%\) and \(+1.8\%\), and HPEM between \(-82.3\%\) and \(+4.3\%\). The low accuracy of HPEM likely stems from its inaccurate probabilistic evaluation of ALSC. For instance, the reference variance value for ALSC is \(0.0140\) in S1, whereas HPEM estimates the variance to be \(0.0008\), with this error propagating and amplifying in the GSA analysis. In other words, the HPEM method is unsuitable for PRPF.  
The computation time of GSA based on the three methods is shown in Table 5. Due to the multiple rounds of MCS required by GSA, the MCS method takes significantly more time than the other two methods. Although HPEM requires the shortest computation time, its low accuracy renders it unsuitable for GSA. BASPCE effectively balances accuracy and efficiency, achieving a fast GSA with high accuracy.