## 3 Numerical Results and Discussions
### Simulation for a Distribution Network  
We implement a simple power distribution network with line faults using MATLAB(r) Simulink(r), as shown in Figure 7a, which generates PQD event signals such as voltage sag and voltage swell, and we test the proposed system model for the created event signals. We also implement a nonlinear load network using MATLAB(r) Simulink(r), as shown in Figure 7b, which generates harmonic voltage disturbance signals. Those models comprise 11 KV, 30 MVA, and 60 Hz three-phase source block feeding through 0.4 KV, 1 MVA delta/wye transformers to a 10 kW resistive and 100 VAR inductive load (whose detailed properties can be referred to from [27]). In a practical network model [27], we can insert line faults generating voltage sag or swell events. The PQD events generated by this network are assumed to have a fixed phase (i.e., fixed PQD). \begin{table}
\begin{tabular}{c c c} \hline \hline
**PQD Events** & **MV** & **RMS** \\ \hline Swell 110\% & 78.5 & 78.2 \\ Sag 90\% & 81.1 & 81.0 \\ Har. 10\% & 100 & 100 \\ Int & 100 & 100 \\ Notch & 100 & 100 \\ Oscillatory transient & 100 & 100 \\ Swell 110\% with Har. 10\% & 100 & 100 \\ Sag 110\% with Har. 10\% & 100 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Detection performance (DR (%)) of double-edge-based random PQD events using the proposed algorithm, where a sag signal with 90% \(pu\), a swell signal with 110% \(pu\), a harmonics signal with 10% \(pu\), interruption, notch, oscillatory transient signal, and swell (or sag) with harmonics are assumed over IMPN channels of SNR = 40 dB, \(\mu\) = 400, and \(\psi\) = 0.02%Figure 7: (**a**) Implemented network model with line faults using Simulink(r), (**b**) Nonlinear load model using Simulink®. Figure 8 shows the voltage sag (Phases A and B) and voltage swell (Phase C) waveforms generated by the corresponding line faults of the power distribution network in Figure 7a. A simulation time of 0.2 s is set and the ode23 tb solver is selected to run the simulation. From the above waveforms shown in Figure 8, we choose Phase B for the voltage sag signal with 78% \(pu\) and Phase C for the voltage swell signal with 111% \(pu\), and then apply our proposed algorithm to the PQD event signals generated over AWGN channels with SNR = 30-35 dB and IMPN channels with SNR = 30-35 dB, \(\mu\) = 400, and \(\psi\) = 0.02%, respectively, to evaluate the detection performance. Table 8 shows the performance of the double-edge-based PQD detection system over AWGN channels with SNR = 30-35 dB and IMPN channels with SNR = 30-35 dB, \(\mu\) = 400, and \(\psi\) = 0.02%. The results of the network distribution model (Figure 7a) and the nonlinear load model (Figure 7b) over AWGN or IMPN channel, as observed in Table 8, verify that the proposed system model is suitable for real grid systems. Compared to the proposed schemes (MV or RMS), the conventional scheme (WC-Det) has a similar DR for sag or swell signals but has a degraded DR for harmonic signals over AWGN or IMPN channels. However, WC-Det has a higher FER than the proposed schemes, especially for PQD over IMPN. Table 8 also shows that both MV and RMS have comparable performance over AWGN and IMPN channels. Figure 8: Voltage sag (Phases A and B) and swell (Phase C) waveforms.