**1. Introduction**

Disturbance in the power system is a significant concern for many electric utilities due to its impact on the operation and reliability of the overall system. Besides, it may cause damage to vital equipment in the power system such as a generator, transmission line, and transformer in case the operator does not address the fault with speed and accuracy, which results in large scale electric outage, economic losses, and the possibility of loss of life. Thus, the protection system with the ability to accurately identify, locate, and classify faults in the power system needs to be implemented into the system to ensure the quick and correct response to fault clearing.

The algorithm to detect and classify faults in power transmission lines has been widely developed based on different types of methodologies. The wavelet transform is one of the popular methods for fault detection and discrimination due to its ability to analyze high-frequency components [1–6]. The discrete wavelet transform (DWT)-based methodology has been used for the detection of transmission line faults [1]. Three-phase voltage signals are decomposed by the Daubechies wavelet (db4). By considering the results, the coefficient details at level 4 clearly distinguish the different types of faults in the power system. The new differential relaying scheme based on the transient energy extracted using the DWT in the current signals of each line distinguishes between external and internal faults under all operating conditions [2]. This paper proposed an adaptive technique to detect low-impedance faults (LIFs) and high-impedance faults (HIFs) and classified LIFs in transmission systems depending on the DWT. The current of each phase is analyzed by using the DWT (db1), and faults are classified through comparison with the current approximation coefficient (Sg) and current detail coefficients (Da, Db, and Dc) [3]. This reveals that the wavelet transform is significant in the detection and classification of faults in power systems. However, the algorithm can be improved by using artificial intelligence (AI).

AI has been combined with wavelets to improve the accuracy of fault classification algorithms in electrical systems [7–12]. AI enhances accuracy and reduces the time to classify faults. Wavelets with neural networks (NNs) have been used to detect and identify fault types in transmission line systems [7–11]. The algorithm makes use of wavelet transform-based approximate coefficients of three-phase voltage and current signals obtained over a quarter cycle to detect and classify faults. Fault detection and classification and fault location estimation are carried out using an artificial neural network (ANN), and the alienation coefficients of current signals are used as ANN input [7]. This paper presents an application of NNs and wavelet transforms for fault classification in transmission lines in comparison with particle swarm optimization–artificial neural network (PSO–ANN)-, back-propagation neural networks (BPNN)-, and support-vector machines (SVM)-based classification schemes. The PSO–ANN technique has a very high accuracy (99.912%) in the classification of power system faults [11]. This paper presents a survey and review of the research and developments in the field of fault detection, classification, and location in transmission networks [12].

In addition, wavelets are used to detect faults or abnormalities in transformers [13–22]. They are used to detect vibrations or electrical signals. Transformer vibration signals are decomposed into several empirical wavelet functions. The signals are calculated to construct the eigenvectors of the transformer vibration signals for classifying three different working conditions (normal conditions, winding axial deformation, and winding radial deformation) [13]. Most papers use wavelets to classify inrush and internal and external faults. The differential current is used as input for the wavelet transform to analyze faults [14–21]. The boundary wavelet transform is implemented in the differential protection of power transformers to distinguish internal faults from other disturbances. The method is designed for real-time applications and implemented in a digital signal processor for real-time analysis [14]. The algorithm distinguishes between internal faults and inrush currents in power transformers. Fault currents are analyzed by using the DWT to evaluate their remarkable characteristic values, and the highest values produced by the total wavelet correlation matrix are used to identify inrush and internal fault currents in power transformers. The results are validated with an experimental test setup [18]. Moreover, the algorithm can identify fault occurrence with the continuous wavelet transform (CWT) and improve conventional current differential protection methods in the presence of current transformer (CT) saturation [20]. A spectrum of wavelets has been used for the prediction of winding insulation defects in transformers [21].

From the literature review, it can be seen that the wavelet transform methodology has been widely used in power system fault analysis. However, many studies only focus on transmission lines or transformers, and few have combined the two components when analyzing systems. Most of the references use wavelets to detect and identify fault types in electrical systems, but they do not analyze the mother wavelet [1–17,20,21]. Additionally, there are research articles that compare mother wavelets [18,19,22,23]. They study the comparative use of 16 different wavelets for fault classification in overhead transmission line systems. However, it is revealed that the Db4 wavelet completely satisfies the fault classification algorithm [23].

Another point is that the result from a simulation that has been widely used may not correctly represent the actual system in the real world due to some parameter and factor that has been simplified, which might affect the result. In terms of wavelet transform application, the research using wavelets to detect and discriminate fault types on power systems might not take effects from different mother wavelets into consideration when evaluating the performance of the algorithm. Thus, this paper presents the effect of mother wavelets on the performance of fault classification algorithms in the

power system. The result in terms of accuracy between di fferent mother wavelets was evaluated by using an experimental setup modeled after the actual system with a transmission line connected to the power transformer.

The paper is divided into six sections as follows. The second section provides the fundamentals and theory of the DWT. The experimental setup and system characteristics are presented in Section 3. The details of the fault classification algorithm used in this study are contained in Section 4. The results and conclusions of the study are summarized in Sections 5 and 6, respectively.

#### **2. Fundamentals and Theory**

The wavelet transform is a method based on signal processing that was developed from Fourier and short-Fourier transforms for suitable specific applications. The time width and frequency can be adjusted for optimal analysis.

The wavelet theory based on mathematics integrates small signals into one signal. The small signal is the wavelet, which has a specific character because the wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. Therefore, any signals in the wavelet theory are a combination of wavelet groups that are structured from the same function. This function is the origin wavelet called the mother wavelet. The signals are caused by the mother wavelet stretching (scaling: a) or shrinking (shifting: k) the wavelet itself, which occurs as a position change along the time axis.

DWT signal analysis can select many scales (m) and many positions (k) for integrated wavelets and can form a signal at the interest scale. When integrating the signal at all resolutions, the actual input signal is received. In multilevel analysis, the scale of analysis is reduced by two times. Hence, this is a DWT-type dyadic wavelet transform, as described in Equation (1) [24].

$$DWT(m,n) = \frac{1}{\sqrt{2^m}} \sum\_{k} f(k)\psi\left[\frac{n-k2^m}{2^m}\right] \tag{1}$$

where

m, n, k = Integers Ψ = Mother wavelet n=Numberofdata

 points

m = Scaling

k = Shifting

Signals are decomposed by the wavelet. The mother wavelet is a filter signal that separates the following two channels:


The high-frequency component will be used to analyze signal during transient state.

The mother wavelets used in the DWT are db, sym, coif, and bior [24]. Each mother wavelet provides a di fferential coe fficient because of its di fferential characteristic signal, as shown in Figure 1.

**Figure 1.** Characteristic signals of the mother wavelets.

The Daubechies (db) mother wavelet has asymmetric basic functions, while the symlets (Sym) mother wavelet has the least asymmetric basic functions. The biorthogonal (Bior) mother wavelet has symmetric basic functions, and the coif1 mother wavelet has nearly asymmetric basic functions. It is necessary to choose a suitable mother wavelet for increased efficiency.
