## 5 Test Results and Discussion
### Test Setups  
As shown in Figure 3, two wind power stations are connected to nodes 18 and 19 in the standard IEEE 39-bus system (denoted as W1 and W2), while three photovoltaic (PV) power stations are connected to nodes 23, 24, and 25 (denoted as PV1, PV2, and PV3). The penetration rate of renewable energy is 15%. The detailed information on the renewable energy power station is shown in Appendix B. The base load is increased to 1.2 times the value in the standard IEEE 39-bus system. The uncertainties in the PV and wind power  
Figure 2: Schematic diagram of GSA for PRPF. generation, as well as the load, are derived from the data in the Belgian grid dataset [39]. The dataset contains measured and forecasting data for renewable energy power stations and load, from which the forecasting error data can be calculated. Then, non-parametric kernel density estimation can be used to model the marginal distribution of source and load power forecasting errors. The detailed steps for modeling the uncertainty of source and load power can be found in Appendix B. The wind farms are set with a leading power factor of 0.98 [4], the PV power stations are set with zero reactive power [40], and the loads maintain their original power factors. The correlation between loads is set to 0.7 [4], while the other correlations are calculated using the Spearman correlation coefficients based on the Belgian grid dataset. The truncation criterion parameter \(p\) of BASPCE is set to 1-6, and the truncation norm \(q\) is set to 0.8 [41]. The ED sample size \(N_{\text{ED}}\) is 1000. The other parameters setting of the system is shown in Appendix B. The load growth pattern vector in RPF is set as 5% of the base load. To conduct an in-depth analysis of the experimental results, three different scenarios are designed, as shown in Table 1. The penetration rate of renewable energy is a critical issue in modern energy systems. As the development of renewable energy continues, its penetration rate is expected to increase. Therefore, in S2, the installed capacity of each renewable energy station is proportionally scaled up, raising the penetration rate of renewable energy from 15% to 30%, while keeping all other settings consistent with S1. In addition, the correlation among renewable sources, as well as between renewable sources and load, may vary in practice. To investigate the impact of correlation on the results, S3 modifies the correlation coefficients as follows: wind power stations (WPS) and photovoltaic stations (PVS) to 0.7, WPS and load to \(-\)0.2, PVS and load to 0.7, and WPS and PVS to \(-\)0.2. All other settings in S3 are kept the same as in S1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Scenarios** & **Descriptions** \\ \hline S1 & Default setting in Section 5.1. \\ S2 & Penetration rate of renewable energy rises to 30\%. \\  & The correlation coefficients among WPS, among PVS, between WPS and loads, between PVS and PVS are set to 0.7, 0.7, \(-\)0.2, 0.7, \(-\)0.2. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Setting of the test scenarios. Figure 3: Modified IEEE 39-bus system. The frequency histograms of ALSC show that, except for SRS-MCS and LHS-MCS with 1000 samples, the frequency histograms of the other six methods closely match the contour of the reference results in all three scenarios. This indicates that BASPCE achieves the expected good accuracy and can handle over the RPF, with nearly the same accuracy as MCS. To further evaluate the test results, the frequency histogram similarity index (FHSI) is used to quantitatively describe the accuracy of uncertainty quantification methods. FHSI represents the degree of overlap between two frequency histograms; the higher the FHSI value, the greater the accuracy of the uncertainty quantification.