### Related Work  
In the literature, diverse PQD feature detection schemes using Fourier transform (FT), Short-time Fourier transform (STFT), phased-locked loop (PLL), Hilbert-Huang transform (HHT), S-transform, WT [1; 4; 11; 12], and WPT [7; 13] have been proposed.  
FT extracts the frequency components of PQD event signals but does focus on the analysis of stationary signals [10]. STFT, also termed as windowed FT, overcame the limitations of FT by segmenting the signal into narrow time intervals; however, it cannot simultaneously provide suitable frequency and time resolutions [14]. In [15], PLL-based PQD detection was proposed; however, a small distortion of the main voltage substantially degraded the detection performance. The authors in [3] presented an S-transform-based technique, where the denoising threshold was determined with the energy congregation level; however, this technique incurred a highly complex noise level estimation. In [16], the authors introduced HHT to detect and analyze PQDs, where MM was used to suppress the noise level. However, HHT is sensitive to the noise superimposed on an electric signal [17].  
WT allows simultaneous signal localization in the time and frequency domains, which is a favorable characteristic for the analysis and detection of nonstationary transient signals [1; 4; 18; 19], such as PQD, as compared to the other schemes mentioned above, including FT and STFT [10; 14]. Recently, [PERSON] et al. showed that the spatial correlation between adjacent WCs is robust to nonlinear PQD signals over power signal channels [1]. WPT, which is an extended version of WT, allows the further decomposition of both high-frequency components (details) and low-frequency components (approximations) [7; 13]. As the WPT output (i.e., WPCs) has larger degrees of freedom than the WT output (i.e., WCs), feature detection using WPCs exhibits a better spatial correlation property than wavelet-correlation-based-detection (WC-Det). Very recently, in [7], the authors presented a feature detection scheme using an MV-based indirect correlation. However, they used a universal threshold \(TH_{U}\) for feature detection, which yields a large FER over severe power signal channels with random phase offset and impulsive noise.  
In the present study, we extend our previous study [20] further by proposing an updated PQD detection algorithm that includes a preprocessing stage to make it more robust to severe power channel conditions like random phase \(\varphi_{m}\) and low signal-to-noise ratio. Furthermore, we elaborate our previous study by adding an adaptive impulsive denoising function to the proposed algorithm, and thoroughly analyzing the presented system model under impulsive electricity channel conditions. With the help of numerical analysis, the proposed system model is proved to be superior to the conventional wavelet-based, wavelet-correlation-based, or non-wavelet-based schemes.  
The remainder of this paper is organized as follows. In Section 2, we briefly introduce the PQD signal model, address the proposed detection system model with adaptive denoising, explain WPT including how to decompose a PQD signal into different WPCs, define WPTM and WPTM-based metrics (MV and RMS), and present WPTM-based PQD feature detection using MV or RMS metric. Section 3 presents the numerical results of the proposed system model and a discussion on these results. Section 4 concludes the paper.