###### Abstract
Hence, in contrast to the existing WTM-based direct correlation metrics [1], the proposed WPTM-based indirect correlation metrics exhibit an exponentially increased degrees of freedom (i.e., \(DoF=P=2^{l}-1\) at level \(l\) (except approximation)). The impulsive noise that is mainly generated by the power switch ON/OFF or manade electromagnetic interference (EMI) substantially hinders the PQD detection or localization [2]. However, it is not easily removable by using wavelet denoising alone, because of its broadband characteristics; thus, the PQD detection performance is considerably degraded. Throughout this paper, this impulsive noise disturbing wavelet- or wavelet packet-based PQD signal detection is differentiated from the transient events defined by the IEEE standard [9]. In particular, the presented PQD detection algorithm has an adaptive impulsive denoising step that makes it more robust to real channel conditions, including impulsive noise, than conventional schemes. Specifically, in the adaptive impulsive denoising step, if the signal sample is above a threshold \(TH\) (= three-sigma level), a standard median (SM) plus WT-based denoising filter that can efficiently remove both impulsive noise and AWGN is chosen. Otherwise, a WT-based denoising filter that can only remove AWGN is chosen [10]. Numerical results prove that the presented WPTM-based PQD detection algorithm with larger degrees of freedom not only improves the correlation characteristics but is also more robust to random phase \(\varphi_{m}\), impulsive noise, and low signal-to-noise ratio (SNR \(\leq\) 25 dB). Moreover, it also shows that the proposed algorithm with a threshold modification step reduces the false edge detection rate (FER) under such critical channel conditions. The main contributions of this paper are listed as follows:  
1. We define WPTM using WPC and propose a PQD feature detection (or localization) algorithm using WPTM-based metrics (such as RMS and MV). Hence, the presented WPTM-based PQD detection scheme, with larger degrees of freedom (\(DoF=2^{l}-1\)), exhibits better correlation properties than the existing WTM-based PQD detection schemes (\(DoF=two\) or three). 2. For the WPTM-based PQD detection, we also define and use a modified threshold (\(TH_{M}\)) rather than a conventional universal threshold (\(TH_{U}\)), which makes it more robust to practically severe power signal conditions, including random phase offset and low SNR (\(\leq\)25 dB)
3. In the presented PQD detection procedure [see the details in Section 2.2], we add the SM plus wavelet filter-based adaptive denoising step after the pure power signal removal process (which follows the PQD feature strengthening process [7]), the so-called preprocessing stage, that effectively removes both impulsive noise and AWGN. Next, the proposed PQD detection stage using MV or RMS metric is executed. In particular, the MV metric uses the MV-based indirect correlation between WPCs instead of the conventional direct correlation between WCs. 4. A numerical analysis is performed for the proposed scheme (Section 3) under random power signal conditions and compared with the existing schemes. For reliable PQD localization, double edge-based detection is used and compared with the conventional single edge-based detection. In the numerical evaluation, various standard PQD event signals, including voltage sag, voltage swell, interruption, harmonics, notch, and so on, are generated and tested based on IEEE-1159. In addition, we implement a power distribution network using MATLAB(r) Simulink(r) (Natick, MA, USA) to create several PQD events and test the proposed scheme for the PQD signals generated by the network, for further validating our proposed system model. Via the numerical analysis, we prove that the proposed scheme is superior to the conventional wavelet-based, wavelet-correlation-based, or non-wavelet-based schemes.