## 3 Numerical Results and Discussions
### Effect of Adaptive Impulsive Denoising  
In Table 6, we assume that a sag signal of 80% \(pu\) under the randomly phased IMPN conditions with SNR = 20 to 40 dB, \(\mu\) = 400, and \(\psi\) = 0.02% is generated. The results in Table 6 show that the proposed scheme with the adaptive denoising function (see Step 4 in Figure 1) effectively eliminates impulsive noise. In addition, the proposed algorithm considerably reduces the FER under severe impulsive electricity channel conditions, even at a very low SNR (\(\leq\)25 dB). Moreover, the proposed scheme with adaptive impulsive denoising (case (b) in Table 6) exhibits more improved FER and DR than the same scheme without adaptive impulsive denoising (i.e., only with wavelet-based Gaussian denoising; case (a) in Table 6). Specifically, by adding the impulsive denoising function, the proposed MV and RMS methods exhibit an improved DR of 7.5% and 8.6% (or 11.3% and 13.7%) at SNR = 35 dB (or SNR = 25 dB), respectively, while considerably reducing the FER. At SNR = 40 dB, the proposed algorithm with the impulsive denoising step (Step 4) exhibits a slightly better (\(<\)1.3%) DR while maintaining a suitable FER. As a result, we confirm that adaptive impulsive denoising makes the proposed detection algorithm more robust to a real IMPN environment.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**SNR** & **Metric** & **(a) w/o Impulsive Denoising** & **(b) w/Impulsive Denoising** \\ \hline \multirow{2}{*}{40 dB} & MV & 89.6/89.9 & 90.1/11.7 \\  & RMS & 88.5/89.6 & 89.8/7.5 \\ \hline \multirow{2}{*}{35 dB} & MV & 78.8/94.5 & 86.3/9.2 \\  & RMS & 77.2/94.1 & 85.8/8.0 \\ \hline \multirow{2}{*}{25 dB} & MV & 49.2/88.7 & 60.5/14.0 \\  & RMS & 45.3/88.2 & 59.0/15.1 \\ \hline \multirow{2}{*}{20 dB} & MV & 13.8/90.8 & 34.5/14.9 \\  & RMS & 10.4/90.3 & 32.7/17.3 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Performance comparison (DR/FER (%)) between (a) random PQD detection without impulsive denoising and (b) random PQD detection with impulsive denoising, where an 80% \(pu\) sag signal over IMPN with SNR = 20, 25, 35, or 40 dB; \(\mu\) = 400; and \(\psi\) = 0.02% is assumed.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Fixed POD**} & \multicolumn{3}{c}{**Random PQD**} & \multicolumn{3}{c}{**Random PQD**} \\  & \multicolumn{3}{c}{**(SNR = 35 dB)**} & \multicolumn{3}{c}{**(SNR = 35 dB)**} & \multicolumn{3}{c}{**(SNR = 40 dB)**} \\ \cline{3-11}  & & \multicolumn{3}{c}{**AWGN**} & \multicolumn{3}{c}{**IMPN**} & \multicolumn{3}{c}{**AWGN**} & \multicolumn{3}{c}{**IMPN**} & \multicolumn{3}{c}{**AWGN**} & \multicolumn{3}{c}{**IMPN**} \\ \cline{3-11}  & & **(a)** & **(b)** & **(a)** & **(b)** & **(a)** & **(b)** & **(a)** & **(b)** & **(a)** & **(b)** \\ \hline \multirow{2}{*}{Prop.} & MV & 100 & 100 & 100 & 82.3 & 78.5 & 86.3 & 84.0 & 89.0 & 87.9 & 90.1 & 89.4 \\  & RMS & 100 & 100 & 100 & 81.8 & 77.7 & 85.8 & 82.0 & 88.9 & 87.7 & 89.8 & 89.0 \\ \hline \multirow{3}{*}{Conv.} & WC-Det. & 100 & 100 & 98.8 & 93.0 & 76.4 & 70.8 & 59.4 & 56.6 & 80.2 & 78.8 & 76.6 & 76.0 \\  & W-Den. & 100 & 99.5 & 98 & 86.8 & 47.8 & 43.9 & 37.4 & 31.4 & 72.2 & 64.3 & 59.2 & 57.2 \\ \cline{1-1}  & S-Tran. & 100 & 100 & 100 & 100 & 18.7 & 22.3 & 22.0 & 21.5 & 21.8 & 18.5 & 17.5 & 28.0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Double-edge-based PQD detection performance (DR (%)) of the proposed and conventional (WC-Det, W-Den, and S-Transform) algorithms, where (a) a sag signal with 80% \(pu\) or (b) SWELL: a swell signal with 120% \(pu\) is used over AWGN or IMPN with SNR = 35 dB or 40 dB.