DETECTION OF HIGH IMPEDANCE FAULTS BY DISTANCE RELAYS USING PRONY METHOD

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1 DETECTION OF HIGH IMPEDANCE FAULTS BY DISTANCE RELAYS USING PRONY METHOD Abilash Thakallapelli, Veermata Jijabai Technological Institute Abstract Transmission lines are usually suspended from steel towers and provided with one or more earth wires. Therefore the earth fault resistance during flash over on the isolators is only few ohm. In the case of rare arc faults, at mid-span, or during flash over to trees, very high impedance faults may result. Depending on the setting of the zones in R-direction, a maximum of some tens of ohms can be detected. Larger resistances are outside the reach of the distance protection, and must be detected by a separate earth fault protection. Distance relays must operate whenever a fault occurs. Therefore, detecting high impedance faults is an important issue since the relay should be able to differentiate the fault condition and load condition. This paper presents a new method for detecting a high impedance fault, based on extracting components of the current waveform using the Prony method. The merit of the method is demonstrated by simulating different high impedance fault conditions using the MAT- LAB/SIMULINK. Index Terms Distance relay, high impedance faults, prony method, decaying dc component Introduction The technology of relays has moved on from the electro mechanical, through electronic, semiconductor and integrated circuit, to microprocessor. Today, the microprocessor based distance relays have been widely used in the main protection relay of EHV/UHV transmission lines. Distance protection is a universal short-circuit protection. It s mode of operation is based on the measurement and evaluation of the short circuit impedance, which in the classic case is proportional to the distance to the fault. Distance protection determines the fault impedance from the measured short-circuit voltage and current at the relay location. The measured fault impedance is then compared with the known line impedance. If the measured fault impedance is smaller than the set line impedance, an internal fault is detected and a trip command issued to the circuitbreaker. This implies that the distance protection in its simplest form can reach a protection decision with the measured voltage and current at the relay location. For this basic protection decision no further information is required and the protection therefore does not have to depend on any additional equipment or signal transmission channels. Due to inaccuracies in the distance measurement, resulting from measuring errors, transformation errors and the inaccuracy of the line impedance, which is usually based on a calculation and not a measurement, a protection reach setting of 100% of the line length with distance zone is not possible in practice. A security margin (10-15%) from the remote end of the line must be selected for the so called under-reaching stage (1 st zone) to ensure secure protection and external faults. The remainder of the line is covered by an over-reaching stage (2 nd zone), which, to ensure selectivity, must be time-delayed relative to the protection of adjacent line [1].The traditional distance relay measures the fault loop impedance from relay location, which includes the fault line impedance from relay location to fault point and fault path resistance. Under the conditions of loading part of the fault resistance is then translated into inductance or capacitance, causing over-reach or under-reach of the distance relay working on reactance [2], and the high fault path resistance will also cause under-reach for distance relay. When the fault is through a high path resistance the fault current component may be less than the load current in a heavy-load condition. It is possible that the estimated fault impedance is actually determined by the load current and path resistance. As to be shown in this paper, when a fault simulated with high path resistance within the reach of zone-1 distance relay the estimated fault impedance for traditional distance relay is far beyond the reach distance relay. In [3], a fault impedance estimation algorithm of phaseground fault for ground distance relaying based on the negative-, zero- and comprehensive negative zero-sequence current component. Only the single-phase faults have been simulated and the method has not been applied to symmetrical faults. In [4], presented a new algorithm of accurate fault location for EHV/UHV transmission lines based on distributed parameter model, which assumes the fault path is resistive. The fault location function was given with a non-linear equation, and the iterative solution technique is needed for obtaining the fault location. This paper presents a new fault detector for distance relay that avoids the disadvantages of previous schemes while it ISSN NO: VOLUME 2, ISSUE 2, MAY

2 maintains the required selectivity. This detector is based on the extraction of the current waveform components using the Prony method, which is briefly described first. Proposed algorithm that detects faults by monitoring the presence of decaying dc in current waveform is discussed next. Finally, the performance of the proposed scheme is studied by simulating various faults using MATLAB/SIMULINK. Prony method Prony analysis is a signal processing method that extends Fourier analysis. It is a technique of analyzing signals to determine model, damping, phase, frequency and magnitude information contain within the signal. Prony method is a technique for modeling sampled data as a linear combination of exponential, it has a close relationship to least squares linear prediction algorithm used for AR (Autoregressive) and ARMA (Autoregressive moving average) parameter estimation. The matrix of the time-index z element has a Vandermonde structure. If a method can be found to separately determine the z-elements, then equation 2 represents a set of linear simultaneous equations that can be solved for the unknown vector of the complex amplitudes. Prony s contribution was the discovery of such a method. The key to the separation is to recognize that equation 1 is the solution to some homogenous linear constant-coefficient difference equation. In order to find the form of this difference equation, first we must define the polynomial that has the exponents as its roots, (2) There are three basic steps in the Prony method: Step 1:Determine the linear prediction parameters the available data. that fit Step 2:Find the roots of the polynomial formed in step 1, find the prediction coefficient that will yield the estimates of damping and sinusoidal frequencies of each of the exponential term. Step 3:With the solution obtain in step 2; we obtain a second linear equation. With the equation, we yield the estimate of the exponential amplitude and sinusoidal initial phase. A. Prony Analysis Concept Since there are many data sample that are being used, such as the exponential parameters, then an exact exponential fit to the data may be made. Consider the p-exponent discrete time function [5] If the product of 3 is expand into power series, then polynomial may be represented as the summation With the complex coefficient a[m] such that a[0] = 1. Shifting the index on equation 1from n to n-m and multiplying by the parameter a[m] results, Forming similar products a[0]x[n],, a[m-1]x[n-m-1] and summing produces (3) (4) (5) 2p complex samples x[1],,x[2p] are used to fit an exact exponential model to the 2p complex parameters h1,,hp, z1,,zp. The p equation of 1 for 1<n<p may be expressed in matrix form as : (1) Which is valid for p+1 <= n <= 2p. making the substitution (6) ISSN NO: VOLUME 2, ISSUE 2, MAY

3 The right hand equation then sums up in equation 7 may be recognized as the polynomial defines by the equation 4, evaluated at each of its roots, yielding the zero result indicated. Hence the equation P>7 is the linear difference equation whose homogeneous solution is given by equation 1, the polynomial 4 is the characteristic equation associated with this linear difference equation. The p equations representing the valid values of a[n] the satisfy the equation 7 may be expressed as the p x p matrix equation (7) (10) Prony calculates the modal information, such as frequency, amplitude, damping, and phase shift; these can be used to reconstruct the original signal or to make inferences about the system conditions that affected the signal. The fact that Prony can be used for system stability and protection purposes makes it a good candidate for the modern concept of wide-area protection and emergency control [6]. Proposed algorithm Fig. 1 shows a typical current waveform during a fault in a two-machine system. Fig. 2 shows the operating region of the distance relay. Equation 8 demonstrates that, with 2p complex data samples, it is possible to decouple the and parameters. The complex polynomial coefficients a[1],, a[p], which are functions of only the time dependent components of the exponential model, from a linear predictive relationship among the time samples. (8) The Prony procedure to fit p exponentials to 2p data samples may be summarized in three major steps as explain earlier in this chapter. The damping and sinusoidal frequency may be determined from the root using the relationships To complete the prony procedure, the roots computed in the second step are then used to construct the matrix element of 2, which is then solved for the p complex parameters h[1],, h[p]. The amplitude and the initial phase may be determined from each hi parameter with the relationships (9) Fig. 1 Current waveform during a fault The above distance relay is set to operate for fault impedance below 200 ohm, Fig. 1 indicates it is an fault, but distance relay unable to detect it as fault, and point (R=220 & L= 45%) falls out of the operating region. In the case of rare arc faults, at mid-span, or during flash over to trees, very high impedance faults may result. Depending on the setting of the zones in R-direction, a maximum of some tens of ohms can be detected. Larger resistances are outside the reach of the distance protection, and must be detected by a separate earth fault protection. Distance relays must operate whenever a fault occurs. Therefore, detecting high impedance faults is an important issue since the relay should be able to differentiate the fault condition and load condition. This differentiation can be done by prony method. Fig. 3 shows the Thevenin equivalent of a fault in a power system. Applying Kirchhoff s voltage law leads to the following differential equation [7]. ISSN NO: VOLUME 2, ISSUE 2, MAY

4 The presence of decaying dc at least in one phase implies that the fault had occurred and the relay must be unblocked. Simulation results To investigate the merit of the proposed algorithm, a power system shown in Fig. 5 is modeled using MATLAB/ SI- MULINK. Fig. 2 Distance Relay Operating Region Fig. 3 Thevenin equivalent of a fault in a power system By solving (11), the current will be as follows (11) A fault having resistance 220 ohms happens at 0.02 s and is cleared 1 s. This causes high impedance faults. Different phase to earth faults are now simulated. Since the method depends on the relationship between faults and occurrence of decaying dc component in the signals, this behavior should be investigated and demonstrated. The decaying dc component depends on many factors in the network and hence it needs to be shown that the scheme is selective under all such factors. The time constant and amplitude of the decaying dc are unknown and depend on the fault resistance, fault position and the fault incipient time [9]. Detailed studies of different fault conditions and results are presented below and in Table I. Fig. 4 show amplitude of decaying dc component of the current waveform of phase c at each time window. It is clear that amplitude of decaying dc component increases after inception of the fault. Table I shows current waveform components during one data window for different faults and no fault. The values have been shown in the order of the amplitude values. In Table I, the values are components of current waveforms during one data window (50 samples) of the signal. For instance for Ia, in presence of three-phase fault, components that build up the current waveform in that interval (one window) are as follow: a sine function with frequency of 4.99 Hz ( 5 Hz) with amplitude of and damping of and decaying dc (frequency of 4.79 Hz) with amplitude of and damping of and so on. (12) According to equation 12, fault current comprises a decaying dc part [8], while there is no such a part in current waveform during normal load condition. Therefore, presence of decaying dc in current waveform can be used as a sign for detecting fault. It is noticeable that if, then there is no decaying dc in the current waveform in the phase under study. As there is 120 degrees phase shift between different phases in three-phase, there is decaying dc in other phases. According to Table I, in the case of the fault there is decaying dc at least in two phases while there is no decaying dc during normal condition. Therefore, in order to detect high fault, current waveform components are calculated using Prony method. If the decaying dc amplitude is among the two first biggest amplitudes for three successive windows, fault has happened and the relay should operate. As Tables 1,2,3 show, there is a decaying dc during the fault at least in two phases, while it is not so during normal condition. As mentioned before, sensing decaying dc component of current waveform can be a suitable property for detecting high impedance fault. ISSN NO: VOLUME 2, ISSUE 2, MAY

5 Frequency Damping Factor Amplitude Line to Line Fault LLG Fault LLL Fault Load Frequency Damping Factor Amplitude Line to Line Fault LLG Fault International Journal of Advanced Technology & Engineering Research (IJATER) The fact that the proposed method is based on detecting presence of decaying dc in current waveform, not calculating exact amount, makes it able to high impedance fault from normal condition very fast. If the proposed method was based on calculating exact amount of decaying dc, (for instance there was a predefined value that should have reached) it would impose extra delay to the algorithm. The proposed method is based on relative presence of decaying dc in current waveform which makes it possible to detect symmetrical faults in fraction of a cycle as demonstrated in simulation results. Therefore it operates properly even in the fault cases with fast decaying dc components. Fig. 4. Amplitude of decaying dc versus time during threephase fault. Table 1.Phase A Current Waveform Components During Different Faults and Load Ia e+03 0 Table 2.Phase B Current Waveform Components During Different Faults and Load Ib Fig. 5 Schematic of a simulated power system ISSN NO: VOLUME 2, ISSUE 2, MAY

6 LLL Fault Load Frequency Damping Factor Amplitude Line to Line Fault LLG Fault LLL Fault Load International Journal of Advanced Technology & Engineering Research (IJATER) e e Table 3.Phase C Current Waveform Components During Different Faults and Load Ib Conclusion e e e e e+03 0 This paper introduced a new method for detecting high impedance fault during the, which may be used for unblocking the distance relay. This method is based on the presence of decaying dc component in the current waveform as a sign of the fault occurrence. The use of this method improves distance relay dependability by unblocking it during high impedance fault occurs. The merit of the proposed method was demonstrated by simulating various fault cases in a typical power system. The ease of implementation as well as accuracy and high speed of fault detection are important advantages of the proposed method. Acknowledgments The author is thankful to Mr. Rachit Mehra for the support and guidance to develop this document. References [1] Numerical distance protection: principles and application / Gerhard Ziegler. [Siemens].-Erlangen: Publicis- MCD-Verl., [2] XU Z.Y., XU G., RAN L., YU S., YANG Q.X.: A new impedance algorithm for distance relaying on a transmission line, IEEE Trans. Power Deliv., 2008, (accepted for publication). [3] Z.Y. Xu, S.J. Jiang Q.X. Yang1, T.S. Bi: Ground distance relaying algorithm for high resistance fault, Published in IET Generation, Transmission & Distribution, ISSN pp [4] Takagi T., Yamakoshi Y., Baba J., Uemura K., Sakaguchi T.: A new algorithm of an accurate fault location for EHV/UHV transmission lines: part 1 Fourier transformation method, IEEE Trans. Power Apparatus Syst., 1981, PAS-100, (3), pp [5] Digital spectral Analysis by Marple.S, Lawrence.Jr. [6] M. M. Tawfik and M. M. Morcos, ANN-based techniques for estimating fault location on transmission line using Prony method, IEEE Trans. Power Del., vol. 16, no. 2, pp , Apr [7] L. V. Der Siuis, Transients in Power Systems. New York: Wiley, [8] Saeed Lotfifard, Jawad Faiz, and Mladen Kezunovic, Detection of Symmetrical Faults by Distance Relays During Power Swings, IEEE Trans. Power Del.,VOL. 25, NO. 1, Jan [9] V. Balamourougan and T. S. Sidhu, A new filtering technique to eliminate decaying DC and harmonics for power system phasor estimation, in Proc. Power India Conf., India, Apr. 2006, pp Biographies ISSN NO: VOLUME 2, ISSUE 2, MAY

7 ABILASH THAKALLAPELLI received the B.Tech. degree in Electrical & Electronics Engineering from the Acharya Nagarjuna University, Guntur, Andhra Pradesh, in 2010, and currently pursuing the M.Tech. degree in Electrical Engineering from the Veermata Jijabai Technological Institute, Mumbai, Maharashtra. His research areas include power system protection, signal processing, and its application to transients and protection of power systems. Abilash Thakallapelli may be reached at ISSN NO: VOLUME 2, ISSUE 2, MAY