A Support Vector Machine Based Fault Diagnostic Technique In Power Distribution Networks

Abstract

In this paper, a method for detection and classification of faults in an electrical power distribution system is presented. Digsilent Power Factory software was used to model a section of a 66 kV power system. Fault incidents were instantiated based on Electromagnetic Transient study on the model. The signal obtained from fault incidences were subsequently fed as input to discrete wavlet transform in order to obtained fault features and subsequently the extracted features were then fed into a support vector machine (SVM) and artificial neural network (ANN) for fault classification and detection.

In addition, a Gaussian Process Regression (GPR) technique was employed for estimation of fault locations along the distribution line. Fault detection, classification and location estimation scheme were developed in MATLAB. The method showed that most faults on electric power distribution network can be classified with a good accuracy and minimum fault estimation error. The method is further validated on a real world power system. A hybrid method comprising of DWT-SVM and GPR is thus proposed for detection, classification and estimation of fault location in a distribution network.

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Introduction

An electric power system is important for economic development and security of nations. Power security requires that electric power is always available at any time to any comsumer at any place. However, electric power utilities often find it difficult to maintain uninterrupted electrical power supply to the end users as a result of unpredictability of occurrence of faults. Faults in distribution lines are difficult to eradicate completely, it is therefore important to develop a scheme that can detect, examine the type of fault and estimate the fault distance quickly and accurately [1].

Researchers have proposed various type of schemes that could be used to classify and locate faults in a distribution line [1]. Impedance measurement based technique and Travelling wave based technique come on top of the list. Techniques that are based on the use of impedance method use fundamental frequency component of current and voltage.

The method is not expensive; however, it gives incorrect results for large fault resistance [2]. In distribution lines fault estimation has been a subject of interest for years. The relationship between the forward and backward waves travelling is the basis of travelling wave technique. This technique has attracted a widespread attention because it can estimate different type of faults and find a high impedance fault in distribution network with a good level of accuracy.

However the technique requires a high sampling rate, which is difficult to implement in the field [3], [4]. In recent time, Wavelet Transform (WT) has been used for signal analysis and signal decomposition in various fields. WT decomposes a signal into a series of components, each of which corresponds to a time-domain signal that covers a specific frequency band containing coarse and more detailed information. A fault feature extraction technique based on WT is proposed in [5]. Entropy and other characteristics of signal of a decomposed signal components are then used as signal features. Few of entropy measures that are commonly used in conjunction with wavelets are; Wavelet Singular Entropy (WSE), Wavelet Energy Entropy (WEE). Wavelet Distance Entropy (WDE) and Wavelet Time Entropy (WTE) presented in [6]. A method that uses and of a cycle data window for fault feature extraction is also proposed in [7].

Although fault incidences at distribution network level do not pose a major problem to power system stability, however they often lead to loss of revenue. Thus it is imperative that a faulty section is isolated as fast as possible. In order to alleviate the impact of fault on network, methods based on Computational Intelligence (CI) have been proposed for fault diagnosis. Such method includes the Probabilistic Neural Network (PNN) proposed in [8]; Rough Membership Neural Network (RMNN) in conjunction with wavelet proposed in [9]. One major drawback of techniques based on CI is that, they require a huge training data set, as well as a high computational time

It has been suggested that methods that use Structural Risk Minimization (SRM) such as Support Vector Machines (SVMs) may give a better accuracy with a less computaton time. Consequently, in [5] and [1] , techniques based on SVM for fault detection and classification has been proposed. An advanced fault signal processing technique proposed in [10] has also received a wide attention. Although, Gaussian process regression technique has been used to solved various regression problems in other fields [11], however it has received a less attention in power system.

The remaining sections of the paper are set as follow. A discussion of the Discrete Wavelet Transform (DWT), SVM , ANN, and feature extraction process is given in Section II. In Section III, the proposed technique is discussed. The results are presented in Section IV, and lastly, a conclusion is drawn in Section V.

Discrete Wavelet Transform (DWT)

Wavelet transform (WT) analysis is a mathematical signal processing tool which has gained the interest of many researchers in recent years. Wavelets can decompose a signal into various frequency components. It is mostly used in power system applications for transient signal analysis, because it can extract both information in time and frequency domains simultaneously. Continuous Wavelet Transforms (CWT) and DWT have emerged as powerful tools for signal processing analysis and have some advantages over the traditional Fourie analysis [12], [13]. The mathematical representation of CWT for a given signal with respect to a mother wavelet is:

1. where a is the scale factor and b is the translation factor. DWT is defined as:
2. Where and in Eq. 1 are changed to be the functions of integers in Eq. 2. DWT can be used to decompose non-stationary signals containing both low and high frequency components.

Support Vector Machine (SVM)

The use of empirical data modelling is a major challenge in many engineering applications. In empirical data modelling a process of inductive reasoning is used to build up a model of the system, with the expectation that the model can generalise both seen and unseen data [14]. Quantitative and and qualitative measures are used as performace indices for empirical model. A support vector machine (SVM) uses a statistical and adaptive learning scheme. SVMs were initially developed to solve classification problems in statistical learning theory and Structural Risk Minimization (SRM). In SVM, input vectors are mapped into a high dimensional feature space, such that related data points are separated with hyperplane into distinct classes [5]. The optimal separating hyperplane of such problems could be obtained through quadratic programming method. Computing a hyperplane is equivalent to solving the optimization problem given in Eq. (3) subject to where is the ith example and is the class label which is either +1 or -1. The dual form of the optimisation problem posed in Eq. (3) is Eq. (4).

The input data mapping into a high dimensional feature space is ususally done through the aid of a kernel function in cases where data cannot be linearly separated. The choice of a kernel function employed for data classification is hghly dependent on the structure of data. Some commonly used kernel functions are linear, quadratic, radial bias function and sigmoid [5].

Artificial Neural Network (ANN)

Artificial neural networks may be considered as a simplified model of the human brain which can be used to perform certain applications. It is a powerful tool for pattern recognition and classification; hence it can be used for fault detection in distribution power networks [15]. The attributes of ANN cannot be ignored. ANN has impresive performance characteristics, such as noise immunity, robustnesss and generalization capability.

Gaussian Process Regression (GPR)

Supervised learning schemes may be divided into two categories, classification and regression schemes. The outputs of classification schemes are discrete in nature, such as class labels, however, for regression schemes, their output are real numbers. The output of regression schemes can be used in estimation of continuous quantities. Gaussian Process (GP) regression scheme is an example of a regression scheme. On an elementary basis, one may think of a GP as defining a distribution over a set of functions, and inference taking place directly in function space, this is termed as the function-space view [16]. A GPR scheme predicts a value of a response variable given a new input and the training data. The Bayesian analysis of a standard linear regression model with Gaussian noise is given in Eq. (5).

Where is the input vector, is a vector of weights of the model, is the function value and is the observed target value. In many cases, a bias vector is included, and this is denoted by . In addition, this may be implemented by augmenting the input vector with an additional element whose value is always one [16]. It is generally assumed that the values of differ from the function values by an additive noise. The additive noise components are from independent identically distributed Gaussian distributions with zero mean and variance .

The probability density of a set of observations given the parameters, which is factored over cases in the training set is given in Eq. (7) [16].

Where donates the Euclidean length of vector . In the Bayesian formalism, a priori over the parameters need to be specified, expressing the belief about the parameters. The mean is equated to zero for the Gaussian prior with covariance matrix on the weights.

Inference in the Bayesian linear model is based on the posterior distribution over weights, computed by Bayes rule.

Where the normalising constant is the weight and is given by Eq. (9) combines the likelihood and the prior, resulting in a capture of the knowledge about the parameters.

Signal Processing and Feature Extraction

Fault current signals are often contaminated with harmonic content at high-frequency oscillations and DC offset. DWT has been shown to be an effective tool for signal decomposition and feature extraction. Symlet wavelet family are modifications to Daubechies family. Symlet 4 (sym4), Symlet 6 (sym6) and Symlet 8 (sym8) are widely used wavelets in image processing [11]. Once a signal is decomposed into components, statistical features are then extracted from the components and used as inputs for training and testing purposes.

Fault Classification and Detection

Four SVMs subsystems were trained to detect and classify faults in their corresponding phases. SVMA was trained to detect and classify faults in phase A. SVMB and SVMC were used to detect and classify faults in their corresponding phases. Furthermore, SVMG is used to classify and detect faults corresponding to ground faults. The output of each SVM is either +1 or -1. For each of the three phases, +1 means a fault has occurred in their corresponding phase and -1 means no fault has occurred. In addition, we also investigated the effectiveness of ANN classifier.

Fault Location

Estimation of fault location is vital for reliability of power system. An accurate fault location estimation can enable a quick restoration of power supply. GPR is used for estmation of fault location. Four GPRs were trained to estimate fault location in their corresponding phase. The mean square error (MSE) is used to evaluate the error between the actual fault location and the predicted fault location.

In order to study the viability of the proposed method, a representation of a electric power distribution network was studied. The electric power system distribution network studied is a reduced representation of a 66 kVEskom power distribution network. Various types of faults such as Single line to ground (LG), line to line (LL), line to line to ground (LLG) and three-phase (LLL) faults were investigated on the reduced 66 kV network. The parameters used for simulations are given in Table I, and a simplified diagram of the reduced network is shown in Figure 3.

Fault Type

LG, LLG, LL, LLL

Fault Location

10%, 25%, 45%, 75%, 95%

Fault Resistance (Ω)

0, 10, 100, 150

Loading

100%

Delmas SS 66 kVNevile SS 66 kV

36.5 km

The data set is divided into two cases, fault and non-fault cases. The total number of non-fault cases is 20500, while that of fault cases is 20000. The proposed scheme is trained using 80% of the data set and tested using 20% of the data set. Samples of fault features waveform extracted for LG, LL, LLG and LLL are presented from Fig. 4 to Fig. 7.

Results and Discussion

The statistical features obtained from DWT mother wavelets are presented in Table II in form of standard deviation and mean. It is easy to see that sym4 has the lowest standard deviation.

statitstical features of some of symlet wavelets

The output indication of SVM enables the protection mechanism to make an informed decision. The output of SVM is either +1 or -1. The presence of a fault on a line is singaled by +1 indicates, otherwise it is -1, which indicates the absence of a fault.

The accuracy of the two classifiers are presented in Table IV. The ratio of thevnumber of correctly classified fault cases to the total number of tested cases is used to determine classification accuracy. It is easy to see that for all phases, SVM yielded better results than ANN scheme.

The estimates of fault locations obtained through the GPR scheme is presented in Table IV. The actual location and type of faults are presented in column 1 and column 2 of Table IV respectively, while the other columns in the table represent mean square error (MSE) of fault location on each of the phases and the neutral line.

The proposed scheme is compared with some schemes in the literature and the result is presented in Table VI. It seems there is only a maginal difference between the proposed scheme in this paper and the one proposed in [1].

The parameters of source at the two substations used in this work are presented in Table VII.

Network Data:

Conclusions

A method that can detect, classify and estimate fault location in an electic power distribution network is presented in this paper. The method uses one cycle of fault current measurements at the source terminal after an occurrence of a fault. DWT that uses sym4 as a mother wavelet is used for signal decomposition and extraction of fault features. Statistical features are then used to train SVM and ANN schemes for fault classification and detection. In addition, a GPR scheme is also used to estimate fault locations on an electric distibution network. Thus a scheme that comprises of DWT-SVM and GPR is proposed. The proposed scheme shows a good fault classification capabilities and a reduced error in estimation of fault location in an electric power distribution network.

References

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3. L. Eriksson, M. M. Saha and G. D. Rockefeller, 'An accurate fault locator with compensation for apperant reactance in the fault resistance resulting from remote-end feed,' IEEE Trans. Power Application System, vol. 104, no. 2, pp. 1424-1436, 1985.
4. X. Dong, W. Kong and T. Cui, 'Fault classification and faulted phase selection based on the initial current travelling wave,' IEEE Trans. Power Delivery, vol. 24, no. 2, pp. 552-559, 2009.
5. X. G. Magagula, Y. Hamam, J. A. Jordaan and A. A. Yusuff, 'Fault Detection And Classification Method Using DWT And SVM In A Power Distribution Network,' in IEEE-PES-IAS Power Africa, Acra, Ghana, 2017.