A Fast Extraction Method in the Applicaton of UHV Transmission Line Fault Location *

To aim at the distribution parameter characteristics of UHV transmission line, this paper presents a fast extraction method (FE) to extract the accurate fundamentals of current and voltage from the UHV transmission line transient process, and locates the fault by utilizing two-end unsynchronized algorithm. The simulation result shows that this method has good performance of accuracy and stability, and has better location precision by comparing with results of one cycle Fourier algorithm. Therefore the method can efficiently improve the precision of fault location during the transient process, and makes the error of location results less than 0.5%.


Introduction
Recently, with the development of communication technology and the improvement of electric power automation system, two-terminal fault location method [1][2][3][4][5][6] has been gradually popularized in the power system.With the increasing of UHV long transmission line, two-terminal fault location method that employs the accurate distributed parameter model and need not synchronized data of two-terminal will be applied extensively.Compared with HV and EHV transmission line, UHV transmission line has the characteristics of large transmission capacity, long transmission distance, smaller wave impedance and larger distributed capacitance, so the fault transient process will be more complicated, and accurately acquiring of fault electric quantity would be difficult.Most of existing location algorithms based on phasor method.In the transient process of UHV AC transmission system, the decaying DC offset of fault current and the decaying DC offset of fault voltage introduced by CVT extend the convergence time of the traditional Fourier algorithm, decrease the accuracy of algorithm, and also reduce the precision of electric quantities in the fault transient process.
In order to remove the influence of decaying DC offset, many domestic and foreign scholars have proposed some improved algorithms, such as difference Fourier algorithm [7] and parallel compensation method [8].Although difference Fourier algorithm can suppress the DC offset in a certain extent, it cannot remove the decaying DC offset; meanwhile it also amplifies the content of harmonics.Parallel compensation method required the prior knowledge regarding the time constant of the DC offset, so it is difficult to realize in practical engineering.On the premise of relay protection rapid action, the present algorithm has a high demand of rapidity, which will sacrifice some accuracy and stability.But the UHV transmission line require not only the higher accuracy of fault location, but also protection quick trip over ten milliseconds, then the voltage and current data window would less than one cycle.In order to calculate fault location fast and accurately, it is important to introduce a new phasor extraction algorithm.
Based on Matrix Pencil method [9-12], the Fast Extraction method [13] is established by using matrix similar transformation and QR Factorization.It can quickly extract the fundamental frequency component of UHV transmission line, and remove the effect of decaying DC offset and high order harmonic component of the transient process.This paper uses the Fast Extraction method to identify the fundamental component of fault component within 20 ms, and applies the fundamental to two-terminal fault location scheme for fault location, which greatly improves the accuracy of fault location during transient process, and has a good application prospect.

A Brief Introduction to Fast Extraction Method
When faults occurred in UHV transmission line, fault current consists of a fundamental frequency, a decaying DC offset, and decaying harmonics.Capacitive voltage transformers produce low-frequency transient components having over damped behavior, which resemble DC offset components.So the fault voltage has the same frequency components as the fault current.Therefore the fault signal can be expressed as In (1), k A is the amplitude, and k  is the phase, and Since we know that cos 2 then can be expressed as where 1 0 Since, in practice, one almost always deals with a discrete set of sampled transient data, (4) can be expressed as where n , and is the size of the time-stepping interval used in obtaining the sampled data.
In order to calculate the fundamental component of the input signal, as we all know, the fundamental amplitude is not decay, so let the reference signal is as follows where 1 2 50 / rad s    .So its discrete expression is as follows (7) where , Acco 1 ( ) (2) . From the definitions of measured signal and referhen enced signal, t Left multiplying by the pseudo where     o-inve denotes Moore-Penrose general inv pseud rse).bining erse(i.e.,

Com
(3) with ( 14)-( 16), one can obtain Therefore, the amplitude and the phase angl fundamental components can be obtained by co the eige

The Basic Principle of Fault Location
 .
The following Figure 1 shows a single phase transmis-sion system between two buses.A fault occurs at location F which is x kilometer from bus M, the voltage phasor at fault point F U  can be expressed as where and are the voltage and current at bus N;  is w propag ion coefficient, ave at Theoretically, asynchronous data at both terminals only affect the phase of sinusoidal signal, but has no influence on the magnitudes; therefore the fault point voltage magnitudes measured from two ends are equal, i.e.
Substitution (18) into (19), one can obtain Because the circuit parameters are known electrical quantities of opposite end are also be obtained, so , and the solving (20) can get the fault position x .Also note that the voltage and current of (18)-(20) are decoupling modulus through phase-to-module transformation.The searching method for the fault location is as follows.
Assume 1  is a precision number which less than 1, but close to 1, and 2  is also a precision number which greater than but close to1.Firstly, the transmission line is divided into n sections.If n is even number, then the initial iterative location 1, x is equal to /2 n L ; if n is odd number, then the initial iterative location x is equal to

Simulation and Verification
In order to improve the fault location accuracy of twotermi l location algorithm during the transient process, the Fast Extraction method (FE metho s applied to In practice, digital relays are equipped with analog low-pass antialiasing filters prior to the analog-to-digital onverter.To accurately model the analog process of antialias filtering, the initial sampling rate in the simulations is set to 20 kHz.Then the voltage and current are passed through a second-order low-pass Butterworth filter with a 350-Hz cutoff frequency.The output of this low-pass filter is downsampled to c s f = 4 kHz.MAT-LAB tio is used to verify the location effect of Fast Extracn method, which is also compared with the measured location of Fourier algorithm.
Throughout the entire discussion, represent the location measured by the conventional Fourier method and the proposed method, respectively.AC  and RC  represent the absolute error and the relative error of the fault location given by the conventional Fourier algorithm, respectively.AP  and RP  represent the absolute error and the relative error of the fault location given by the proposed scheme, respectively.These errors are defined as and The following gives an examp of the conventional Fourier algorithm and the proposed method about single-line-to-ground from Jindongnan to illustrate.Fault components of the voltage and the current are show magnitude and phase angle comparisons measured e proposed method and one cycle Fourier algorithm are shown in Figure 3(c)-3(f).The F thod can accurately compute the fundamental c ne t fault, phase-to-phase short circuit gr le as the location effect fault at 326.7km n in Figure 3(a)-3(b).The by th ast Extraction meomponts of the voltage and the current, and filter out the influence of decaying DC offset and harmonics.
The fault location obtained by the positive-sequence fault components, the negative-sequence fault components, and the zero-sequence fault components measured by the conventional Fourier method and the proposed method are shown in Figures 4-6, respectively.The result of the proposed method is almost a straight line, but the result of the traditional Fourier algorithm is an upand-down curve.
Because different fault types all contain positive-sequence fault components, so the following location results are obtained by positive-sequence fault components.Tables 1-5 represent the location performance of the conventional Fourier method and the proposed method, respectively, in terms of error in the measurement of absolute error and relative error for different fault types such as single-line-to-ground fault, high-resistance single-line-to-ground with 500 transition resistance, phaseto-phase short circui ounding fault and three-phase short circuit fault.

fD
and L represent the real fault location and the whole length of transmission line.

Figure 3 . 6 Figure 4 .Figure 5 .Figure 6 .
Figure 3. Fault components of the voltage and the current under single-line-to-ground fault and the magnitude and phase angle comparisons extracted by the Fast Extraction method and one cycle Fourier algorithm.
kilo ter, conductance per kilom r, and ca-

one cycle Fourier algorithm. nce fault tal compo ents compu ed by Fas Extractio
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