## 1 Introduction  
In recent years, the vigorous development of renewable energy, the rise of Industry 4.0, and the transformation of traditional industries into high-tech industries, a large number of power electronic instruments and equipment have become widely used. However, due to the tight interconnection of power networks, voltage waveforms can be affected by system failures or the switching actions of devices, resulting in transient changes and waveform distortions that lead to power quality and stability problems. This may affect power supply stability, cause power interruptions, and even cause equipment damage and industrial operation losses. Therefore, the industry, government, and academia are paying close attention to the measurement and analysis of power quality and related research [1; 2; 3; 4]. Good power quality is critical in power systems. Several studies have been conducted on the detection and classification of power quality disturbances (PQDs). The detection algorithms for signal processing, such as Fourier transform [5; 6; 7], short-time Fourier transform (STFT) [8; 9], wavelet transform (WT) [10; 11], S-transform (ST) [12; 13; 14], Hilbert-Huang transform (HHT) [15], and chaos synchronization [16] are commonly used for power quality analysis. Artificial intelligence schemes containing support vector machines (SVM) [17; 18], particle swarm optimization and support vector machines (PSO-SVM) [19], and neural networks [20; 21; 22] have been widely utilized for classifying power quality disturbances in accordance with the features extracted by signal processing algorithms. [PERSON] et al. proposed an improved generalized discrete Fourier transform (GDFT) for harmonic extraction, which plays a key role in power quality assessment [5]. [PERSON] et al. used a protection method based on the application of STFT as the major signal processing algorithm for meshed multi-terminal voltage source converter-high-voltage direct current (VSC-HVDC) grids [8]. [PERSON] et al. utilized a recognition technique that contains the tunable-Q wavelet transform (TQWT) and dual multiclass support vector machines (MSVM) for detection of PQDs [10]. [PERSON] and [PERSON] proposed a method based on S-transform and the rule-based decision tree for detection and recognition of PQDs under noiseless and noisy situations [12]. [PERSON] et al. used an integrated intelligence method of Hilbert-Huang transform, and weighted bidirectional extreme learning machine (WBLM) with empirical mode decomposition (EMD) to detect and recognize PQDs [15]. [PERSON] et al. applied the extension recognition algorithm combined with a chaos synchronization-based method, which can detect small dynamic variations in system signals, in order to analyze different power quality problems [16]. [PERSON] et al. developed a hybrid classification technique based on particle swarm optimization and support vector machines (PSO-SVM) for categorizing the features extracted by wavelet transform and diagnosing the various types of faults in a smart grid [19]. [PERSON] et al. presented an algorithm based on improved principal component analysis (IPCA) for extracting the features of PQDs and 1-dimensional convolution neural networks (1-D-CNN), which were used to obtain the highest classification accuracy of PQDs [20]. As shown in the above literature review, most previous studies regarding the detection of PQDs described just a single method for signal processing, and extracted the limited features from the original signal. Existing research in extracting fewer and meaningful features has ignored the role of combining of discrete wavelet transform (DWT) and [PERSON]'s theorem. This study intends to take the advantage of [PERSON] and [PERSON]'s theorem to reduce the large number of data and utilize the extension neural network [8], with the aim to shorten the detection time and obtain maximum classification accuracy in PQDs.