Mathematical Problems in Engineering

Volume 2015, Article ID 823720, 9 pages

http://dx.doi.org/10.1155/2015/823720

## Locating High-Impedance Fault Section in Electric Power Systems Using Wavelet Transform, -Means, Genetic Algorithms, and Support Vector Machine

Department of Electrical Engineering, Chung Yuan Christian University, 200 Chung Pei Road, Chung Li 320, Taiwan

Received 22 July 2014; Accepted 14 November 2014

Academic Editor: Vishal Bhatnaga

Copyright © 2015 Ying-Yi Hong and Wei-Shun Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

High-impedance faults (HIFs) caused by downed conductors in electric power systems are in general difficult to be detected using traditional protection relays due to small fault currents. The energized downed conductor can pose a safety risk to the public and cause a fire hazard. This paper presents a new method for locating the line (feeder) section of the HIF with the help of limited measurements in electric power systems. The discrete wavelet transform is used to extract the features of transients caused by HIFs. A modified -means algorithm associated with genetic algorithms is then utilized to determine the placement of measurement facilities. The signal energies attained by wavelet coefficients serve as inputs to the support vector machine for locating the HIF line section. The simulation results obtained from an 18-busbar distribution system show the applicability of the proposed method.

#### 1. Introduction

High-impedance faults (HIFs) in general occur in electric distribution systems. HIFs occur when a conductor contacts a tree with a high-impedance or when a broken conductor touches the ground. These faults may impose fire risks and cause electric shock that endangers lives of personnel. Therefore, HIF detection is essential to ensure safety. However, detection of HIFs using traditional protection devices (e.g., overcurrent and distance relay) is difficult because the resulting level of fault current is usually smaller than the nominal current.

Lien et al. proposed a method for detecting HIFs using three-phase energy variance for the second, fourth, and sixth harmonics of unbalanced current. Then counters are designed to detect HIF arcing through statistical confidence [1]. Emanuel et al. proposed that 120 Hz and 180 Hz components may be employed to detect HIFs. The field test was supported by a simple theoretical model and laboratory measurement [2]. Kim et al. used wavelet transform to extract HIF features for developing an HIF indicator [3]. Sedighi et al. presented a statistical pattern recognition, namely, principal component analysis and Bayes classifier, for detecting HIF and discriminating it from other disturbances [4]. Lai et al. used the nearest neighbor rule approach to classify HIF and low-impedance fault (LIF) with the help of wavelet transform and voltage/current rms values [5]. Michalik et al. employed a phase displacement relation between wavelet coefficients of zero sequence voltages and currents to detect HIFs [6]. Sheng and Rovnyak used rms current, harmonic magnitudes, and phases in a decision tree for detecting HIFs [7].

On the other hand, the wavelet transform (WT) has been widely used for analyzing transient signals because of its varied window function for the time domain. The features of signals/functions can be easily extracted/decomposed via multiresolution analysis (MRA) [8]. There are many papers using discrete wavelet transform (DWT) to detect and classify PQ events [9–12]. Furthermore, artificial neural networks (ANNs) can be employed to map the input and output nonlinear relationship. The support vector machine (SVM), which is one of the ANNs, has recently been proposed for nonlinear regression and classification. Dash et al. used three SVMs for training to achieve fault classification, ground detection, and section identification, respectively, for the line using thyristor-controlled compensated compensators [13]. Srinivasan et al. employed SVMs with linear and polynomial kernels developed for signature extraction and device identification [14]. Janik and Lobos used space phasor for feature extraction from three-phase signals to build distinguished patterns for SVM classifiers [15]. Other applications using SVM are, for example, load forecasting [16] and transient stability analysis [17].

In previous methods, “detection” means identification of an HIF in a feeder (or transmission line) [1–4] or in one of the multiple feeders (or transmission lines) [5–7] from the secondary side of a transformer at a substation. Locating a line (feeder) section, where an HIF occurs, has not been addressed in these papers. Moreover, different features, for example, even harmonics [1], low harmonics [2, 7], wavelet coefficients [3–5], voltage/current rms values [5], and phase displacement [6], were considered for detection. There was no salient result showing which features were better.

In this paper, locating the HIF line (feeder) section instead of detecting HIFs is addressed in a distribution system. Placement of multiple measurement facilities is determined first by a modified -means algorithm associated with genetic algorithms. The discrete wavelet transform (DWT) is then used to extract features from these measurement locations for classification. Finally, the SVM is utilized to locate an exact HIF line section.

In Section 2, the problem description and assumptions are provided. The proposed method for locating the HIF section is given in Section 3. Simulation results obtained from an 18-busbar distribution system with HIFs are discussed in Section 4. Concluding remarks are given in Section 5.

#### 2. Problem Description and Assumptions

Power engineers in general deal with the power event according to the following steps: (i) localization, (ii) classification, (iii) locating, and (iv) remedial action. These can be achieved with the help of the power supply monitoring system. When the monitored signals (voltage and current) are measured, the important features can be extracted using digital signal processing techniques. The monitoring system will assimilate the information including the features into useful knowledge/information through soft computing and machine learning for engineers to develop control strategy and to achieve decision-making.

In the last paragraph, “localization” means to identify the time for HIFs to occur. “Classification” indicates that HIFs should be discriminated from other disturbances, for example, load switching and low-impedance (short circuit) fault. “Locating” implies that an exact HIF line section should be identified. The second and third tasks will be emphasized in this paper. After locating the HIF, proper remedial actions will be activated by power engineers.

This paper deals with locating the HIF line section in a distribution system with multiple feeders using a power supply monitoring system including multiple measurement facilities at different lines. Locating a line (feeder) section, where an HIF occurs, has not been addressed in the previous papers. There are several assumptions in this paper as follows.(i)The number of measurement facilities is given. In this paper, it is assumed that the supplier (utility) has a monitoring system including some measurement facilities that can be placed at different locations for recording.(ii)Locating single HIF is considered. The data-window size of the signal for processing in this paper is five cycles. Simultaneous HIFs at different lines hardly occur.(iii)Configuration of the studied distribution system is fixed. If the system topology is changed, the proposed neural network requires retraining. However, possible system configurations are generally known to engineers and the corresponding neural networks should be trained in advance.(iv)The HIF generally occurs at a single phase of a line section. The proposed method employed MATLAB/SIMULINK SimPowerSystems and all the three-phase transient voltages/currents at each busbar/line in the system are obtained.

#### 3. The Proposed Method

The presented method includes three stages: (i) determining measurement sites, (ii) discriminating HIFs from other disturbances, and (iii) locating the HIF. The measurement sites are first determined by modified -means algorithm associated with genetic algorithms. The proposed method then uses the wavelet coefficients of the currents (obtained by the measurements) as the features for classification of disturbances and the inputs of the SVM for locating the HIF.

##### 3.1. Determination of Measurement Sites

In general, the number of power supply monitoring facilities is much smaller than the regular power, voltage, and current meters that are installed at all busbars and lines. Hence, a modified -means algorithm is used to partition the system into clusters ( is the number of power supply measurement facilities). measurement facilities are placed at the lines near the pseudocenters of the clusters. This subsection describes the modified -means algorithm for partitioning the system for placement of the power supply measurement facilities. Moreover, the proposed modified -means algorithm is enhanced from -means [18, 19] and fuzzy--means (FCM) [20, 21] as follows.

Let be an objective: where is the number of clusters; represents the number of data (line section); signifies the vector of the center in the th clustering; is the th (known) data vector for clustering; denotes the characteristic value (0 or 1) as a weighting factor between and . If the minimum of is gained, the sets of vectors are partitioned into clusters and is formulated by Matrix of the characteristic values can be defined as follows:For the th column in the matrix , the sum of all elements equals one and only one element in this column is unity. The traditional -means algorithm did not consider (1), which is implemented in this proposed enhanced -means algorithm.

The unknown variables in the problem of placement of measurement facilities are , , and . Traditional optimization methods involving the gradients of objective function cannot minimize (1) because of discontinuity of the objective function. The genetic algorithm was adopted to minimize (1) herein because the genetic algorithm can deal with binary variable efficiently [22]. The population size, crossover rate, and mutation rate in the genetic algorithm were assigned with 100, 0.9, and 0.01, respectively.

In this paper, represents one of the current vectors (signal energies calculated by DWT) caused by an HIF at a line . The dimension (1 × 3660 herein) of varies with the number of studied cases. Symbols and (3660 in this paper) are the numbers of measurement facilities and the scenarios with HIFs, respectively. Let be the number of the line sections. Then ’s need to be partitioned into clusters. The vector (1 × 3660) consisting of the virtual HIF currents serves as the center in the th cluster. All vectors of the HIF currents ’s in the th cluster geometrically center at . Therefore, the criterion for placing measurement facilities in the electric distribution system is as follows:* place a measurement facility at line **, at which the total Euclidean distance between **’s (HIFs occurring at line **) and ** is minimal, in the **th cluster*.

##### 3.2. Discrete Wavelet Transform (DWT)

Fourier transform (FT) is a suitable approach for studying problems with steady state responses. Short-time Fourier transform (STFT) divides the full-time interval into a number of small/equal-time intervals, which can be individually analyzed using FT. Although the result obtained from STFT contains time and frequency information, the equal-time intervals are fixed. Thus, STFT cannot be used to detect the transient signals. On the other hand, the discrete wavelet transform (DWT) has been widely used for analyzing the transient signals due to its varied scale and wavelet functions [23–25]. The features of signals can be easily extracted via the multiresolution analysis (MRA). DWT avoids the disadvantages of both FT and STFT.

A signal can be represented as a sum of wavelet functions and scale functions with coefficients at different time shifts and scales (frequencies) using DWT. DWT can extract the features of transient signals by decomposing signal components overlapping in both time and frequency [8]. According to DWT, a time-varying function (signal) can be expressed as follows: where and represent the scaling (coarse) coefficient at scale 0 and wavelet (detailed) coefficient at scale , respectively. The symbol represents the translation coefficient. The scales denote the different (high to low) frequency bands. The variable is an integer. The translated and scaled (dilated) version of the wavelet, , used in the multiresolution analysis (MRA), constructs a time-frequency picture of the signal.

There are some other wavelets in the wavelet theory [8]: Haar wavelets have compact support (a finite bounded set) but are discontinuous. Shannon wavelets are very smooth but are not compactly supported and they decay at infinity very slowly. Compared with these wavelets, Daubechies-4 belongs to a class of orthonormal basis-generating, continuous, and compactly supported wavelets. Daubechies-4 is adopted in this paper to extract the features of the line currents at scales 1, 2, and 3 with a sampling rate of 128 points/cycle.

##### 3.3. Multiresolution Analysis (MRA)

As shown in (4), is constructed by and decomposed by at different scales (resolution levels). generates the detailed version of and generates the coarse version of . It can be shown that [8]where and are the low-pass and high-pass filters, respectively [8]. These two equations show that the scaling and wavelet coefficients at different scale levels can be obtained by convolving the expansion coefficients at scale by the time-reversed recursion coefficients and and then downsampling or decimating to give the expansion coefficients at the next level of . The term “downsampling” indicates that the number at lower scale is double compared with that at higher scale due to the filters and . This process is called the “analysis (decomposition)” from the fine scale to the coarse scale. The reverse process, called synthesis (construction), from the coarse scale to the fine scale, is omitted here. Figure 1 illustrates a three-scale MRA decomposition for a signal. The symbols , , and “2” denote the low-pass filter, high-pass filter, and “downsampling,” respectively.