###### Abstract  
Wavelet transform modulus (WTM) has been used to detect or localize transient signal discontinuities. A numerical analysis indicated that these power quality disturbance (PQD) events are extremely sensitive to the random phase offset due to shift-variant wavelet or wavelet packet characteristics, which have not been comprehensively discussed yet. In this paper, we define wavelet packet transform modulus (WPTM) and present a WPTM-based PQD feature detection that is robust to severe power signal channels including random phase offset and low signal-to-noise ratio (\(\leq\)25 dB). The presented WPTM-based detection that exhibits an exponentially increased degrees of freedom (_DoF_) and has better correlation properties than existing WTM-based detection of a limited _DoF_ (two or three). We then use a standard median filter to efficiently remove impulsive noise and add a threshold modification step to reduce the false edge detection rate under random phase offset conditions while maintaining a reasonable detection rate. The proposed scheme uses the majority voting-based indirect correlation or root-mean-square metric between wavelet packet coefficients, rather than the conventional wavelet denoising or correlation metric. For a reliable numerical analysis, the proposed scheme uses both double- and single-edge-based detection measures, and the results verify its superiority over the conventional wavelet-based, wavelet-correlation-based, or non-wavelet-based schemes. a 2021 11 2825 11 2021 11 2021 11 2021 11 2021 11 2021 11 2021 11 2021 11 2  
A wavelet transform modulus (WTM) with wavelet decomposition (WD) is often used to detect or localize the discontinuities of transient signals, such as images and PQDs [1; 2]. [PERSON] et al. [1] introduced a PQD detection scheme using the spatial correlation between wavelet coefficients (WCs), which further strengthens the edge points of a PQD signal compared to other signal points. However, this direct spatial correlation (i.e., direct inter-multiplication between WCs) scheme has a limited (two or three) degrees of freedom due to the nature of WD; hereinafter, a dyadic discrete WD or wavelet packet decomposition (WPD) is assumed. For better detection of the edge points of a PQD event signal (i.e., starting and ending edge points), PQD feature strengthening, together with wavelet (or wavelet packet)-based denoising, is often used. Several denoising techniques developed so far use S-transform [3], WT [4], mathematical morphology (MM) [5], and empirical mode decomposition (EMD) [6]. Recently, [PERSON] et al. [7] proposed a localization system using the majority voting (MV)-based interscale and intrascale indirect correlation metrics of WPCs to detect PQDs. They argued that the inherent additive white Gaussian noise (AWGN) in the power transmission system corrupts the detection capability; thus, denoising prior to PQD localization is required to further strengthen the PQD edge points. However, the simulation results indicate that the conventional wavelet or wavelet packet-based PQD feature detection is also highly sensitive to random (start or end) edge occurrence (i.e., random phase offset \(\varphi_{m}\), which is uniformly distributed \(\sim\)\(U[0,\ 2\pi)\)) owing to the shift variance characteristics [8]. This paper proposes a wavelet packet transform modulus (WPTM) using WPD and a WPTM-based PQD detection scheme that is applicable to reliable smart grid construction. In addition, as the detection metric, we define (and use) the MV-based indirect correlation or root mean square (RMS). While WD decomposes only a low-frequency component (approximation) into two subcomponents (i.e., two WCs), WPD decomposes both low-frequency (approximation) and high-frequency (detail) components into two subcomponents (i.e., two wavelet packet coefficients (WPCs)).