A hybrid Wavelet-ANN protection scheme for series compensated EHV transmission line

Abstract

The paper presents a novel idea of protection of the multi-terminal Extra High Voltage (EHV) transmission line having multiple Series compensation. A statistical learning perspective for improved classification of faults using Artificial Neural Networks (ANN) has been proposed. The protective scheme uses single end cur-rent data of three phases of line to detect and classify faults. A Multiresolution Analysis (MRA) wavelet transform is employed to decompose the signals acquired and further processed to extract statistical features. The statistical features learning algorithm utilizes a set of ANN structures with a different combination of Neural Network parameters to determine the best ANN topology for Classifier. The algorithm generates different fault patterns arising out of different fault scenarios and altering system parameters in the test system. The features are selected based on ANOVA F-test statistics to determine relevance and improve classification accuracy. The features thus selected from fault patterns are given to the Hybrid Wavelet-ANN structure. The ANN once trained on a part of data set is later tested on the other part of unseen patterns and further validated on rest of the patterns. To provide a comparative Support Vector Machine Classifier is used to classify the fault patterns. A 5 fold cross validation is used on the data set to check the accuracy of SVM. It is shown that the proposed method using Pattern Recognition using Hybrid structure provides a high accuracy with reliability in identifying and classifying fault patterns as opposed to SVM.

Keywords

Series compensation multi-resolution analysis (MRA)artificial neural network SVM feature selection

1 Introduction

The electrical power grid is ever expanding due to increasing power requirements and hence protection of such large complex dynamic system components interacting is susceptible to disturbances or faults. The increase in line loading and inability to carry large power necessitates providing series compensation in EHV systems. The series compensation of transmission lines has been found useful in increasing transient stability limits, increasing power transfer capability, power loss reduction to name a few. Several studies have been done using Series Compensation devices to control the Reactance of EHV line. However, it has resulted into several challenges to Protection engineers.

The protective relaying schemes suggested by researchers for protecting EHV lines includes approaches such as adaptive Kalman filtering [1], traveling waves scheme [2 –4] discrete wavelet transforms [4, 5], fuzzy logic [6, 7], Artificial Neural Networks (ANN) [8 –11], Wavelet transforms [12, 13].

The pattern recognition technique can be suitably applied for discrimination between the faulty and healthy power system. The use of ANN can assist in identifying occurrences of different types of faults and segregate from three phases the one involved in a fault. The ANNs have the very good capability to generalize and hence can be adopted for fault classification task. Several researchers have suggested techniques which utilize Neural Network and Fuzzy systems for power networks. The ANN has been shown as a method giving superior results with voltage and current signals used for pattern classification [14, 15]. Xuan et al. [16] have shown the application of ANN as pattern recognition tool to render adaptive scheme to protective relay used for series compensated line. An algorithm is given by Parikh et al. [17] uses a Radial Basis Function (RBF) kernel function for SVM employed for identification of faults. Authors have used DWT signal processing for this method. The fault detection algorithm is followed by a classification done by using SVM is shown by Parikh et al. [18]. The ANFIS based scheme on a double circuit system has been shown in [19]. A detailed review of methods used in Series Compensated lines is given in [20]. The use of statistical feature selection has been reported in [21, 22].

The paper has been organized four sections, wherein Section 2 discusses selected test system, Section 3 includes the proposed Algorithm which includes the use of MRA and Feature Extraction, Section 4 deals with Artificial Neural Network and parameter selection, Section 5 the use of SVM and Section 6 provides the Simulation Results.

2 System under consideration

Here a multi-terminal EHV transmission line is considered, as indicated in Fig. 1 for verifying the proposed protective algorithm. The multi-terminal system includes three buses (B1, B2, and B3) spanned over a length of 900 km length. It has two compensating devices shown as C1 and C2 respectively. The system under consideration is shown with a single line diagram consists of a six generators with 13.8 KV, 60 Hz having 350 MVA capacity each at one end and 735 KV, 60 Hz generator representing infinite bus at the other end. The power is transmitted over a total length of 900 km length. The line length between buses B1 and B2 is 600 km and that between B2 and B3 is 300 kms.

The transmission line contains with itself in each phase a series compensation module which has a series capacitor, a metal oxide varistor (MOV) protecting the capacitor, and a parallel gap protecting the MOV. When the energy dissipated in the MOV exceeds beyond a threshold level, the gap simulated by a circuit breaker is fired.

In order to increase the transmission line power transfer capability, series compensation is provided by the use of capacitors representing 40% of the transmission line reactance. The protective scheme consists of three lines CT’s at the single end to collect three phase currents and presents it to the Relaying Algorithm to perform the task of identifying and classifying the various faults in the system.

3 The proposed methodology

The proposed methodology adopted for the classifying the faults is shown in Fig. 2 with a flowchart. The system simulations with a different type of fault conditions are conducted on MATLAB 2010^® software using the Simulink library at a sampling frequency of 20 kHz. Firstly, the fault classification algorithm selects different types of faults with associated parameters like ground fault resistance, fault inception angle, the level of compensation in the line & source impedance, to generate various fault patterns. A single end three phase current based Relay classification module is used. As a part of the algorithm three-phase currents from CT’s are recorded in the memory. Later these signals are given to multi-resolution wavelet transform, having multiple numbers of filter banks to capture the low frequency and high-frequency components in the signal. Thus obtained spectral information is passed through a statistical feature extraction unit. The statistical features are so selected that it represents the characteristic indicator of each type. The statistical features are later presented to ANN structure to determine the efficacy of the Classifier. The critical features within the fault patterns preprocessed and analyzed through Multiresolution analysis provides a margin of similarity between faults occurring at different locations on the transmission line and with different fault resistances.

3.1 MRA and feature extraction

A wavelet transform is a tool for analyzing signals which are discontinuous and time varying in nature. The wavelet transform has attained a lot of attention in recent years for researchers in studying the behavior of signals in the joint time-frequency domain. As opposed to STFT (short time Fourier Transform), Multiresolution Analysis by Wavelets provide an excellent opportunity to study different frequency content within the signal at different levels of resolutions. As an outcome, it provides a good time as well as frequency resolution to capture the variation in signal properties for faults occurring before and after capacitor bank.

Wavelet transform can be effectively used to capture the transient behavior of power systems such as fault scenarios in time and frequency domains. This helps in providing information about high-frequency components for small durations and low-frequency components existing for a long duration of time of different fault scenarios.

The DWT (Discrete Wavelet Transform) utilizes two filter banks successively, namely low pass filter and high pass filter. Figure 3 indicates the overall structure of a typical MRA done by Wavelet transform. $y_{low} [n] = \sum_{- \infty}^{+ \infty} s [n] * u [2 n - k]$ (1) $y_{high} [n] = \sum_{- \infty}^{+ \infty} s [n] * v [2 n - k]$ (2)

The signal (s) is made to pass through two filter banks subsequently, a low pass and high pass filter. It is illustrated by Equations 1 and 2 how the signal (s) is operated by a dyadic function by mother wavelet transform. The same has been highlighted by Fig. 3 where the signal is firstly divided into two halves in frequency band & applied to low pass and high pass filters. The output of the low pass filter is further divided into two halves and applied to the second stage of low pass and high pass filters. The multiple levels of filter banks employed here extracts the detailed information on the applied signal (s) at every stage of decomposition. The approximate and detailed components are further given to a “feature extraction” module to extract 11 different statistical components. These statistical features used describe the correlation and variance within the feature vectors to a degree of probability which best match a particular fault pattern. The ANOVA [23] based method is suggested to derive significant features which can be used for giving better accuracy in prediction. The feature extraction process selected aids in reducing the dimensionality of fault patterns stored. The p-value calculated from F-statistic confirms the test of the null hypothesis. The resultant features selected have between lower and higher limits a confidence interval of more than 95% for the true mean of each set. The selection procedure of statistical feature vectors through ANOVA provides better learning instances and classification accuracy. The outcome of the feature selection process is later presented to ANN.

3.2 Fault analysis with different parameters

A detailed study of Fault Analysis is done by applying Multiresolution Wavelet transform in discrete form. The Figs. 4 and 5 indicates the decomposition of a signal (s) which has resulted because of a single phase to ground fault on the test system shown in Fig. 1. In Fig. 4, the three current waveforms are shown as “s” have resulted due to three different ground fault resistances: 1, 10 and 50 ohms respectively. With the application of Daubachies-4 mother wavelet transform and 8th level of decomposition, the signals spectral content at different levels of decomposition is shown below each of the respective signals. The sequence of the wavelet decompositions is ordered in the form of approximate and detailed information (a8, d8 to d1).

Whereas, Fig. 5 indicates five different waveforms shown as a signal as “s” which has resulted due to single line to ground (LG) fault occurring at a different section of transmission taken from relaying point viz. 50,100,150,200, and 250 km. The study of this decomposition process clearly shows that the detailed components D4 and D5 localizes the fault pattern better and carries the useful information about the fault. The approximate coefficient indicates a slow varying change in the signal information for the entire period and DC level drift. The energy level of each of the detailed components provides a way to identifying and classifying the fault patterns which arises because of the different operating condition of the power system.

4 Neural network classifier

The Artificial Neural Networks (ANN) are the abridged models designed to mimic the capability of the biological neural structure of a humanbrain.

ANNs are rigged up from several neurons which constitute the fundamental processing unit of the entire structure. One neuron is further connected to another neuron by connecting link. Each neuron receives several inputs which are processed by ‘weights’. The weights indicate the interconnection strength between various neurons. The weights undergo a change during training process in order to correctly associate a particular pattern to the desired output. The sum total of weighted output is made to pass through a non-linear function called as ‘activation function’ or ‘Transfer function’, in addition to a threshold referred as ‘bias’ to produce anoutput.

Here in our work, we have used a feed forward ANN with back propagation learning algorithm. The ANN structure comprises of 11 input layer neurons, 11 hidden layer neurons, and 5 output neurons. The hidden layer utilizes a ‘tansig’ transfer function and the output layer utilizes a ‘softmax’ transfer function.

The ANN structure is trained and tested with various learning algorithms to verify the accuracy of the classifier and finally “Levenberg-Marquardt” is selected as training algorithm for the Classification. The 5 outputs class labels of the ANN structure are coded as given in Table 1 to produce “1” for a correct class and “0” for incorrect class.

Table 2 highlights the various parameters used for training, testing and validating of the fault patterns. The ANN structure target output classes are verified against the generated outputs for the unseen patterns. The performance of the ANN classifier in classifying the patterns is checked through the “Cross-Entropy” measure of the network.

5 SVM based classifier

Support Vector Machines (SVM) uses the idea of producing decision planes that decide decision boundaries between data set containing different class values. The linear discriminant function used here can be represented by the following equation: $f (x) = w^{T} x + w_{0}$ (3)w₀ is the bias term, vector w is weight vector, which is the space of respective hyperplanes creating support vectors from the origin. The SVM then can be used for classification purpose. The resulting equation is of the form linear discriminant, $y = w^{T} φ (x) + w_{0}$ (4)

Where φ is the function which translates the non-linear feature space to linear space.

The principle of structural risk minimization to optimize the given problem to minimize the cost function given below:

$\begin{matrix} J (w, ξ) & = & \frac{1}{2} {∥ w ∥}^{2} + C \sum ξ_{i} \\ y_{i} (w \cdot φ (x_{i}) + b \geq 1 - ξ_{i} \\ ξ_{i} \geq 0, for i = 1, 3, \dots l \end{matrix}$ (5)

Here C is a regularization parameter and ξi is a degree of error for non-separable data set points. y_i represents class label associated with the ith data point. The solution to the above equation minimizing the cost function is subject to constraints given in equation can be handled with the following formulation which Maximizes: $L_{D} = \sum_{i} α_{i} - \frac{1}{2} \sum_{i, j} α_{i} α_{j} y_{i} y_{j} K (x_{i,} x_{j})$ (6)

Subject to condition

$\begin{matrix} 0 \leq α_{i} \leq C \\ \sum_{i} α_{i} y_{i} = 0 \end{matrix}$ (7)

Here, αi’s represented the Lagrangian multipliers & K (x, y) represent the kernel which is a non-linear function given by $K (x, y) = φ (x) \cdot φ (y)$ (8)

The solution can be expressed by the weight-plane intercept equation given below $w_{0} = \sum_{i}^{Ns} α_{i} y_{i} φ (x_{i})$ (9)

Here Ns – represent the support vectors.

$\begin{matrix} If {f (x)}_{w = w_{0}} < 0 \\ If {f (x)}_{w = w_{0}} > 0 \end{matrix}$ (10)

The polynomial kernel function provides a better classification accuracy as it can separate a highly complex multi-featured multi-class problem. A degree polynomial kernel function can be expressed as follows $k (x, y) = (x^{T} y + c)^{d}$ (11)

We have used quadratic kernel function for the classification problem which has is obtained by putting the value of d = 2. This results into following form $k (x, y) = {(\sum_{i = 1}^{n} x_{i} y_{i} + c)}^{2}$ (12)

6 Simulation results

The extensive simulation of the test system shown in Fig. 1 is done with various parameters as indicated in Table 3. A total of 1650 patterns is captured to investigate the efficacy of the proposed algorithm. The test results on the system with the finally selected ANN structure with parameters used & indicated in Table 2 are shown in Fig. 7. The training functions selected for testing performance of ANN are indicated in Table 4 with results shown in Fig. 8. It was observed that for LG, LL and LLG fault the classifier has given 100% and more than 98.3% correct results for later two cases. But with LLL fault and LLLG, the miss-classified patterns amounts to 8.1% and 7% respectively. It is found that the misclassification is due to ANN being unable to identify between presence and absence of ground along with LLL fault. The overallclassification accuracy results to 98.3% which proves to be high with such large data set considered.

The classification accuracy produced by a quadratic kernel SVM is presented in Table 5. The performance of SVM is 100% for LG and LL faults. But for the rest three type of scenarios it poorly performances when compared against ANN. The LLLG fault is misclassified with only 93.3% of total cases.

7 Conclusion

The paper presents a novel statistical feature extraction based methodology applied to detection and classification of faults in EHV transmission line system with fixed series compensation. The proposed algorithm uses a multi-resolution wavelet transform for decomposing the signal to 8th level. The statistical features extracted from the wavelet decomposition are presented to an ANN structure, which is trained, tested and validated over different fault patterns. The learning algorithm and the structure have been optimally selected through the algorithm to provide better classification over a wide range of fault patterns through ANOVA F-test statistics. The best performing learning scheme is taken for the final classification purpose. Further, SVM with a quadratic kernel function is used to check the performance of the classifier. The comparison between and ANN and SVM is presented which highlights the strength of proposed algorithm using ANN provides high accuracy. The training methodology of selected features plays a vital role in the improvement of overall classification accuracy. Various types of faults with associated fault position, fault inception angle, fault resistance, etc. have been studied extensively with simulation studies conducted. The classification accuracy is high and the algorithm provides a robust performance over a wide variety of fault conditions tested on the given system.

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