Wavelets Based Identification and Classification of Faults in Transmission Lines

Wavelets Based Identification and Classification of Faults in Transmission Lines 1 B Narsimha Reddy, 2 P Chandrasekar 1,2EEE Department, MGIT Abstract: - Optimal operation of a power system depends on how a fault location is accurately and quickly located, so that restoration and maintenance of power is accomplished. Fault detection, fault classification, needs to be performed using a fast responsive algorithm at different levels of a power system. Effect of factors such as fault impedance, fault inception angle (FIA), and fault distance, which cause disturbances in power line can be countered by Wavelet multi resolution analysis (MRA). The method of fault discrimination proposed in this work is on the basis of the three-phase current and voltage waveforms measured during the occurrence of fault in the power transmission-line. Further, a superior technique, viz. Wavelet Singular Entropy (WSE) is applied both at transmission line and transformer level which minimizes the noise in the fault transients and is unaffected by the transient magnitude. The proposed algorithm is verified using MATLAB/Simulink software and the obtained results prove that both MRA and WSE based fault detection and classification methods are practically feasible and reliable. Keywords Wavelet transform (WT), Multi-resolution analysis (MRA), Wavelet Singular Entropy (WSE), fault detection, fault Classification, fault location. I. INTRODUCTION Fault detection and classification are two of the most important tasks involved in transmission-line relaying [19]. They must be accomplished and as fast and accurate as possible to de-energize the system from the harmful faults and restore the system after faults. Interruption of power flow in a power line is mainly due to the occurrence of faults at various levels. Reliability and economical aspects of power transfer can be enhanced due to accurate and fast fault detection Wavelet Transform (WT) [18] conducts both time and frequency domain analysis of current signals and transients in voltage waveforms. Overhead lines are affected by transients, due to the travelling wave phenomenon after the inception of fault. With the analysis of the faults due to induced transients one can gather handy information which covers a wide range of aspects like location and detection of fault and also about the implementation of high performing protective relays. Identification of mother wavelet signifies the preciseness of wavelet analysis. The choice of the appropriate mother wavelet depends on the nature of the signal and on the type of information to be extracted from the signal. In this thesis Wavelet multi resolution analysis is identified as the best possible solution for information extraction from transient signals caused by faults. Dominant second and third order harmonics, termed as d6 coefficients are analyzed whereas d4 coefficient is the mother wavelet. By applying wavelet MRA technique [6], extraction of sixth level detailed coefficient from the current signal after summation is performed. The existence of a fault is identified based on the detail coefficients summation magnitude, a generalized algorithm has been implemented for the transmission line faults classification. The wavelet singular entropy (WSE) highlights the advantages of wavelet transform [18], singular value decomposition [14], and Shannon entropy [16]. WSE is immune to not being affected by the transient magnitude and the noise in the transients of the fault and so it can be used to automatically extract features from transients due to faults and express the fault features efficiently and quantitatively even in the scenario of high-noise and low-magnitude fault transients. WSE can also be used for extraction of features from fault transients quantitatively and automatically. II. FAULT CLASSIFICATION USING WAVELET TRANSFORM Filter bank theory [1] is the basis for the formulation of the discrete wavelet transform (DWT). At level (k), the above technique can be implemented by using a high pass and a low pass filters efficiently. Down sampling of the results is performed by a factor two and the two filters are applied to the output of the low pass filter from the earlier stage. The high pass filter is obtained from the mother wavelet function and further measures the details in a certain input. Similarly, the low pass filter delivers a smoothed version of the input signal and is derived from a scaling function, which is associated to the mother wavelet function [2] & [3]. For a function f (t), its continuous wavelet transform (WT) can be calculated from the following equation: 6

Fig.1.Discreet Wavelet Transform (DWT) representation of a Signal. A. Wavelet Decomposition Scheme using Multi- Resolution Analysis: The wavelet function generates a detail version of the decomposed signal and the scaling function generates the approximated version of the signal that is decomposed. Conversion of scale versus time signal to amplitude versus time signal is performed by Wavelet transforms. The MRA utilizes the scaling functions along with the wavelet functions as building blocks for decomposition and construction of signal at different levels of resolution. Wavelet is a waveform of limited duration has an average value of zero. In general the implementation of discrete wavelet transform is done by using multi resolution analysis. The transmission line faults in power system are usually classified as Symmetrical faults and Unsymmetrical fault whereas the three-phase fault is termed as a symmetrical type of fault. B. Wavelet Singular Entropy The proposed WSE will be suitable and useful for measuring the uncertainty and complexity of the analyzed signals, and will provide an intuitive a quantitative outcome for the fault diagnosis which can be utilize to overcome the drawbacks in the previous methodologies. Let s (t), which is a discrete sequence with n samples, be the signal sequence to be analyzed as follows 1) First, analyze the s(t) by WT, where the db4 mother wavelet and 12-scaled WT are chosen in the transformation. Then, a 12 n WT-coefficient matrix A can be obtained by means of (2) 2) Second, decompose the matrix A with SVD in (4), and a singular-value array can be obtained as {λ1,λ2,.λr}, where r is the rank of the diagonal matrix Λ. The value of r may be very large and the value of as well as its embodied information will decrease with the increase of i. In order to reduce the computing cost and keeping the hypostasis of Λ, the tiny singular values are neglected in our application and the original singular values are represented by k pieces of singular values (λ1,λ2,.λk) (1 k r) which must satisfy the stipulation of λk/λ1 0.01% consequently, the value of k should be different under various situations, and these k pieces of singular values are called the effective singular values, which will make the calculation of WSE become much faster and more effective. 3) Third, in order to obtain the entropy of the singular value array, the probability pi associated with λi, is defined as follows Where k is the number of effective singular values involved in WSE calculation. WSE can be used to extract features from fault transients quantitatively and automatically. It is immune to the noise and many other uncertain factors in the system. Further it is independent on the magnitude and energy of the transients. Fig.2. Representation of Multi-Resolution Analysis 7

Fig 3. Flow chart for WSE Computation III. FAULT CASES STUDY AND RESULTS A 3 phase transmission line of rating 400kV and length of line is 300km has been considered for the study. The circuit diagram of the transmission line fault analysis is represented by Fig.4. Fig 4.Power system model The fault analysis of transmission lines consists of transient phenomena. Therefore, the positive, negative and zero sequence parameters of the source as well as transmission lines are required. The fault currents simulated using MATLAB shown in figures for fault condition of L-G, L-L, and L-L-L. More ever, the sampling time taken for the analysis is 80us, which relates to a sampling frequency of 12.5 khz, and the total number of wavelet levels considered is 10. Hence a tenth level wavelet output corresponds to a frequency band of 6.25-12.5 khz. Down sampling by two done at succeeding levels lead to a third level output corresponding to a frequency band of 97-195 Hz, i.e. it consists of 2nd and 3 rd Harmonics components and are predominant in the situation of transmission line faults. The wavelet toolbox in MATLAB has been used for DWT operation. Different decomposition levels such as a3 (Approximation at level three); detail levels one, two, three, represented as d1, d2, d3, respectively can be extracted using wavelet toolbox. The tables give summations of wavelet coefficients of 3 rd values for current in phases A, B and C respectively for L-L-L fault for different fault inception angles and fault locations. Similarly we can tabulate for other type of fault also. For all other faults such as single line to ground (L-G), double line to ground (L-LG), double line (L-L), and three phase symmetrical (L-L-L) faults also have been extensively investigated for about 1000 simulations with different values of fault impedance value and fault inception angles. Thus it was verified that the algorithm consistently yielded right classification and all cases have not been reported as it would turn to be voluminous [1]. Different types of power system faults are created using simulation model as shown, at different fault distances having different fault inception angles with different fault resistance. The wave forms are shown below, Fig 5: Ia, Ib, Ic for LG Fault at D==100Km, FIA=0, Sequence Parameters of Source and Line The fault analysis of transmission lines includes transient phenomena. Therefore, the positive, negative and zero sequence parameters of the source as well as transmission lines are necessary. Source and transmission line are shown in table. An active load of 500MW and a reactive load of 20MVAR (inductive) are analyzed. Fig 6: Ia, Ib, Ic for LG Fault at D==200Km, FIA=0, Rf=1Ω 8

Fig 7: Ia, Ib, Ic for LLG Fault at D==200Km, FIA=60, Rf=1Ω Fig:12 Ia, Ib, Ic for ABC Fault at D==200Km, FIA=60, Fig 8: Ia, Ib, Ic for ABG Fault at D==200Km, FIA=60, Fig :13 Ia, Ib, Ic for AB Fault at D==200Km, FIA=0, Fig 9: Ia, Ib, Ic for AB Fault at D==200Km, FIA=60, Fig:14 Ia, Ib, Ic for ABG Fault at D==200Km, FIA=0, Rf=1Ω Fig 10: Ia, Ib, Ic for ABC Fault at D==200Km, FIA=0, Fig 11: Ia, Ib, Ic for AB Fault at D==100Km, FIA=0, Fig:15 Ia, Ib, Ic for ABC Fault at D==100Km, FIA=0, In order to reduce the computational burden the sampling frequency should not be too high but it should be high enough to capture the information of fault. By randomly shifting the point of fault on transmission line, more number of simulations was being carried out. The generated current signal for each case is analyzed using wavelet transform. A sampling frequency of 12.5 khz is selected. Daubechies wavelet Db4 is used as mother wavelet since it has good performance results for power system fault analysis. Detail coefficients of fault current signal in 6th level (d6), gives the frequency components corresponding to second and third harmonics. On this basis, summation of 6th level detail coefficients of the three phase currents Ia, Ib and Ic are being used for the 9

purpose of detection and classification of faults in the transmission line. IV. FAULT DETECTION AND CLASSIFICATION ALGORITHM In the simulation model, different types of faults are created at different FIA. The current wave forms are shown in the figures. Let Sa, Sb, Sc be the summation of sixth level detail coefficients for current signals for a, b, c phases respectively. Tables below show the values of Sa, Sb, Sc for different types of faults. From these tables it is observed that the magnitudes of Sa, Sb, Sc increases whenever any fault occurs in a transmission line. Based on the sampling rate the signal is divided into 12 decomposition levels. Among different levels only 6th level is consider for analysis because the frequency corresponding to this level is covering 2nd and 3rd harmonics which are dominant in the fault conditions. Table: 1 L-G fault with different fault distances the coefficients of any two phases is not equal), which is used to discriminate L-G from L-L-G. Table: 4 L-L-L fault with different fault distances the From Table-4: (L-L-L Fault) The summation of detail coefficients of three phases sum is zero but all three phase summation values are different, in L-L fault two phases have a same value, which is used to discriminate L-L from L-L-L. From Table-1: (L-G Fault) The summation of detail coefficients of all three phases sum is not equal to zero for L-G and L-L-G, which is used to discriminate L-G, L-L-G from L-L and L-L-L, Faulty phase summation value is very high compared to healthy phases. Healthy phase summation values are almost equal. Table: 2 L-L fault with different fault distances the From Table-2: (L-L Fault) The summation coefficients in any two phases are equal and the third phase value is very less compared to two faulty phases. Table: 3 L-L-G fault with different fault distances the From Table-3: (L-L-G Fault) The summation of detail coefficients sum is not equal to zero and all three phases Fig 16 Algorithm for fault classification Algorithm Explanation: The transmission line faults in a power system are usually classified as L-G, L-L-G, L-L and L-L-L. Let Sa, Sb, Sc be the coefficients obtained from the summation of 6th level wavelet detail coefficients for currents in phases A,B, and C. B. WSE Implementation When the algebraic sum of Sa, Sb, Sc is zero, then it can be either L-L-L or L-L. To differentiate these two, the summation of any two phases is zero, and remaining healthy coefficient is very small value in L-L fault. Algebraic sum is not equal to zero, then it be either L-G or L-L-G. If the absolute values of any two coefficients have different summation values (summation 10

are equal and much smaller than absolute value of remaining coefficients, then it is L-G fault. If the absolute value of any two coefficients is not equal to zero and is always much higher than the absolute value of remaining coefficients, then it is a L-L-G. The results tabulated show the efficiency of the fault classification of algorithm using db4 wavelet for different fault locations, fault resistances and FIA and the algorithm was verified. Maximum entropy value will gives the faulty section in the transmission line and it also verified by using the summation of the detailed coefficients method. Table 5 Effective Wavelet Singular Entropy Values of the PHASE- A Fault Transients Table 6 Effective Wavelet Singular Entropy Values of the PHASE- B Fault Transients V. CONCLUSION Wavelet multi resolution (MRA) analysis is found to be most suitable for extracting the information from transient fault signals. Second and third order harmonics are dominant in the fault signals and are hence chosen for the analysis (d6 coefficients) and Db4 as mother wavelet. Using wavelet MRA technique, the summation of detail coefficients for sixth level are extracted from the current signal. From the magnitude of detail coefficient summations, the presence of fault in a particular phase is detected. A generalized algorithm based on wavelets has been verified for the classification of transmission line faults. The most important of this algorithm is independent of fault location, impedance and inception angle. The WSE technique is proposed by combining WT with SVD as well as the Shannon entropy. It provides a quantitative output which can act as an automatic feature extraction technique in fault detection. The test results prove that the WSE is sensitive to sudden changes in transient signals, and is immune to noise. WSE can be used to detect the faults under various situations even with the low-magnitude transient where other methodologies encounter problems. REFERENCES [1]. M. Jayabharata Reddy, and D.K. Mohanta, A wavelet-fuzzy combined approach for classification and location of transmission line faults,international journal of Electrical Power and Energy system, Volume 29, Issue 9, pp 669-678, November 2007. [2]. Omar AS, Combined fuzzy-logic wavelet-based fault classification technique for power system relaying, IEEE Trans. On Power Delivery, Vol.19, No. 2, pp.582-589, July 2004. [3]. Biswarup Das and J.Vittal Reddy, Fuzzy-Logic- Based Fault classification, IEEE Trans. On power Delivery, Vol.20, No.2, pp 609-616, April, 2005. [4]. M. M. Tawfik and M. M. Morcos, ANN-Based Techniques for Estimating Fault Location on Transmission Lines using Prony Method, IEEE Trans. On Power Delivery, Vol. 16, No. 2, pp. 219-224, April 2001. [5]. Gopalakrishnan, M. Kezunovic, S. M. Mckenna, D. M. Hamai, Fault Location using the Distributed Parameter Transmission Line Model, IEEE Trans. On Power Delivery, Vol. 15, pp. 1169-1174, October, 2000. [6]. D. Chanda, N. K. Kishore, A. K. Sinha, A Wavelet Multi resolution Analysis for Location of Faults on Transmission Lines, Electrical Power & Energy Systems, Vol. 25, pp.59-69, October, 2003. [7]. H. Osman and O. P. Malik, Protection of Parallel Transmission Lines using Wavelet Transform, IEEE Transactions On Power Delivery, Vol. 19, No. 1, pp. 49-55, October, 2004. [8]. Ferrero A, Sangiovanni S, Zappitelli E, A fuzzy-set approach to fault type identification in digital relaying, IEEE Trans. On Power Delivery, Vol. 10, No.1, pp. 169-175, July, 2003. [9]. M. Jaya Bharata Reddy, D. K. Mohanta and B. M. Karan, Power System Disturbance Recognition using Wavelet and S-Transform Techniques, International Journal of Emerging Electric Power Systems, Vol. 1, Issue. 2, pp. 1-16, October, 2004. [10]. Wavelet Toolbox Users Guide by the Math Works, http//:www.mathworks.com, 2006. [11]. Z. Y. He, X. Q. Chen, and G. M. Luo, Wavelet entropy measure definition and its application for transmission line fault detection and identification (part I: Definition and methodology), in Proc. IEEE Int. Conf. Power System Technology, Oct. 2006, pp. 1 6. 11

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