## 3 Numerical Results and Discussions
### Discussion  
Most of the existing PQD detection schemes have been evaluated over generic electricity channels using only Gaussian noise (AWGN). Hence, the PQD detection analysis under practically severe SG channel conditions, including random phase offset, impulsive noise, and low SNR (\(\leq\)40 dB), has been limited. For instance, a numerical comparison between fixed PQD and random PQD in Tables 4 and 5 indicates that the PQD detection performance is considerably dependent upon the random phase offset. The impulsive noise, which is mainly due to the power switch ON/OFF or man-made EMI, can also substantially affect the performance of PQD detection or localization [2] (Tables 4-8).  
Throughout this section, we analyze the proposed WPTM-based PQD detection system model numerically under such severe electricity channel conditions and compare it with the existing system models. Specifically, in case of PQD events with a fixed phase offset (see fixed PQD in Tables 3-5), there is no significant difference in DR between the proposed and conventional methods (there is even some more difference of FER over IMPN channels). However, in case of PQD events with random phase offset (see random PQD in Tables 4 and 5), the proposed method using WPTM-based metrics (MV and RMS) is relatively superior to conventional wavelet-based (WC-Det and W-Den) or non-wavelet-based (S-Tran) methods, especially over IMPN.  
When considering the precise detection or localization of PQD events with a limited duration, double-edge-based detection is more favorable than conventional single-edge-based detection. In particular, for random PQD (i.e., PQD event signal with a uniformly distributed random phase: \(\varphi_{m}\sim U[0,\,2\pi)\)) in Table 5, the simulation results obtained for AWGN or IMPN indicate that the proposed scheme using MV or RMS metric is much superior to the existing wavelet-based or non-wavelet-based scheme in terms of double-edge-based detection performance (DR or FER). Especially for the IMPN channel with a very low SNR (\(\leq\)25 dB), the DR difference between the proposed and existing schemes increases further.  
The simulation results in Tables 6 and 7 indicate that the proposed PQD detection algorithm (see Figure 1 in Section 2), which has an adaptive impulsive denoising function, improves the robustness under the IMPN channel conditions. Specifically, Table 6 shows that the adaptive impulsive denoising step effectively eliminates impulsive noise; thus, the proposed MV or RMS significantly reduces FER while maintaining a suitable DR. Table 7 also shows that the presented algorithm works well for various PQD events, including harmonics, interruption, notch, oscillatory transient, and swell (or sag) with harmonics, as well as pure sag or swell. According to the simulation results, MV is superior to RMS in terms of DR, whereas RMS is superior to MV in terms of FER.  
Through the simulated experiment of real network distribution models (Table 8), we verify that the proposed MV or RMS scheme guarantees better DR and FER over both AWGN and IMPN channels, as compared to the existing scheme (WC-Det). In particular, the performance difference between the proposed and existing schemes further increases as the SNR decreases (Tables 5 and 8).  
The results of the numerical analysis indicate that the proposed PQD detection scheme with WPTM-based metrics is more reliable and has better detection capability under severe random electricity channel conditions than the conventional schemes.