Method for fault location to single-terminal traveling wave

Abstract

A method for fault location to single-terminal traveling wave includes steps as follows. Step (a): recording a waveform of a traveling wave signal of disturbance by a traveling wave device when a line disturbance occurs. Step (b): performing a phase mode transformation on the waveform recorded by the step (a), so as to obtain components of line mode and zero mode of a fault initial traveling wave, and performing a wavelet transform to decompose the components of the line mode to obtain singularities in the waveform of the traveling wave. Step (c): calculating a wavefront slope k of the components of the line mode of the fault initial traveling wave. Step (d): computing a preliminary fault distance D according to the slope k computed in the step (c). Step (e): confirming a fault point according to the preliminary fault distance and wavelet singularities of the components of the line mode. Step (f): end.

Claims

1. A single-terminal traveling wave based fault locating method comprising steps operated by a main site and a plurality of electrical substations connected to the main site via a communication network, each of the electrical substations equipped with a traveling wave recording system, the method comprising: step (a): recording a waveform of a traveling wave signal of a line disturbance by a traveling wave device when the line disturbance occurs; step (b): performing a phase mode transformation on the waveform recorded by the step (a), so as to obtain components of line mode and zero mode of a fault initial traveling wave, and performing a wavelet transform to decompose the components of the line mode to obtain wavelet singularities in the waveform of the traveling wave; step (c): calculating a wavefront slope k of the components of the line mode of the fault initial traveling wave, wherein calculating the wavefront slope k of the components of the line mode of the fault initial traveling wave during the step (c) comprises: defining a wave head corresponding to a maximum value of a first mode which is detected after the wavelet transform of the step (b) as the disturbance initial traveling wave, and normalizing the components of the zero mode of the wave head such that the collected components of the zero mode of the wave head is amplified to a reference value, and rest of values are scaled up, wherein the reference value is 0.5 kA, and wherein the slope of the normalized wave head is computed by selecting points thereof, which is performed by selecting three sampling points from an initial point and linearly fitting the three selected sampling points with a least square method to obtain the slope k; step (d): computing a preliminary fault distance D according to the slope k computed in the step (c); step (e): confirming a fault point according to the preliminary fault distance and the wavelet singularities of the components of the line mode; and step (f): ending the steps.

2. The single-terminal traveling wave based fault locating method of claim 1, wherein the phase mode transformation in the step (b) is performed by applying a Karen Boolean transformation, which has a phase mode transformation matrix as: $S=\left[\begin{array}{ccc}1& 1& 1\\ 1& -2& 1\\ 1& 1& -2\end{array}\right];S^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& -1& 0\\ 1& 0& -1\end{array}\right].$

3. The single-terminal traveling wave based fault locating method of claim 1, wherein the wavelet transform performed on the components of the line mode is implemented by: $\{\begin{array}{c}{S}_{2^j}f\left(n\right)=\underset{k}{.Math.}{h}_k{S}_{2^{j-1}}f\left(n-2^{j-1}k\right)\\ W_{2^j}f\left(n\right)=\underset{k}{.Math.}{g}_k{S}_{2^{j-1}}f\left(n-2^{j-1}k\right)\end{array},$ where j∈[1, ∞]; S.sub.2.sub.jf(n) is an approximation component of a result of the wavelet transform; W.sub.2.sub.jf(n) is a wavelet components of the result of the wavelet transform; {h.sub.k}={0.125, 0.375, 0.375, 0.125} (k=−1, 0, 1, 2); and {g.sub.k}={−2, 2} (k=0, 1).

4. The single-terminal traveling wave based fault locating method of claim 1, wherein the selecting the initial point comprises: setting a threshold value as 0.1 kA with respect to the components of the zero mode of the wave head of the normalized disturbance initial traveling wave, wherein the initial point is a first point that is greater than the threshold value.

5. The single-terminal traveling wave based fault locating method of claim 1, wherein the least square method is performed by formulas: $\{\begin{array}{c}y=kx+b\\ 3b+k\underset{i=1}{\overset{3}{.Math.}}{x}_i=\underset{i=1}{\overset{3}{.Math.}}{y}_i\\ b\underset{i=1}{\overset{3}{.Math.}}{x}_i+k\underset{i=1}{\overset{3}{.Math.}}{x}_i^2=\underset{i=1}{\overset{3}{.Math.}}{y}_i{x}_i\end{array}.$

6. The single-terminal traveling wave based fault locating method of claim 1, wherein computing the preliminary fault distance D in the step (d) is performed by formulas: $k=2700{D^{\left(-0.9990+0.0136\rho \right)}\left(\frac{\rho }{100}\right)}^{-0.4568},$ where k is the wavefront slope, D is the fault distance, and ρ is soil resistivity.

7. The single-terminal traveling wave based fault locating method of claim 1, wherein confirming the fault point in the step (e) comprises: according to the preliminary fault distance D computed in the step (d) and the wavelet singularities of the components of the line mode obtained in the step (b), taking D as a center and setting a range as the center ±D*20%, and selecting a wave head of the traveling wave from the range such that a fault distance is obtained by multiplying a time difference between the fault initial traveling wave and a fault point reflection wave by traveling wave propagation velocity, wherein if there is more than one wave head, min(|D−d|) is applied to, and wherein d is disturbance point distance corresponding to the wave head, and then the fault distance is obtained by multiplying the time difference between the fault initial traveling wave and the fault point reflection wave by the traveling wave propagation velocity.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a schematic diagram of a connection in a traveling wave ranging system;

(2) FIG. 2 is a flowchart of a method for fault location to single-terminal traveling wave; and

(3) FIG. 3 shows a schematic diagram of a line topology and length of a double-terminal 220 kV transmission line.

DETAILED DESCRIPTION

(4) FIGS. 1-2 are the best embodiments of the present invention. The following are in combination with FIGS. 1-2 to further explain the present invention.

(5) A method for fault location to single-terminal traveling wave (i.e. a single-terminal traveling wave based fault locating method) includes steps operated by a traveling-wave ranging system as shown in FIG. 1. The traveling-wave ranging system includes a main site and several electrical substations, such as electrical substation A, electrical substation B, . . . , and electrical substation M. All the electrical substations are connected to the main site via a communication network, and each electrical substation is equipped with a traveling wave recording system. Similar to the existing technology, the traveling wave recording system is implemented by a computer in general, and a traveling wave recording software is executed by the computer. By the traveling wave recording system, the disturbance records recorded by traveling wave signal detection devices in the electrical substations can be received.

(6) As shown in FIG. 2, the method for fault location to single-terminal traveling wave further includes step as follows.

(7) Step 1001: start.

(8) The method for fault location to single-terminal traveling wave is started.

(9) Step 1002: obtaining singularities in waveform of a traveling wave. When line disturbance (i.e. lint fault) occurs, a traveling wave device records a traveling wave signal of the disturbance (e.g. including a waveform). First, a phase mode transformation is performed on the waveform, so as to obtain components of line mode and zero mode of initial traveling wave. The phase mode transformation adopts a Karen Boolean transformation, in which a phase mode transformation matrix thereof is as follows:

(10) $\begin{array}{cc}S=\left[\begin{array}{ccc}1& 1& 1\\ 1& -2& 1\\ 1& 1& -2\end{array}\right];S^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& -1& 0\\ 1& 0& -1\end{array}\right]& \left(1\right)\end{array}$

(11) A wavelet transform is performed for decomposing the components of the line mode to obtain the singularities in the waveform of the traveling wave. The wavelet transform is implemented by Mallat algorithm as follows.

(12) $\begin{array}{cc}\{\begin{array}{c}{S}_{2^j}f\left(n\right)=\underset{k}{.Math.}{h}_k{S}_{2^{j-1}}f\left(n-2^{j-1}k\right)\\ W_{2^j}f\left(n\right)=\underset{k}{.Math.}{g}_k{S}_{2^{j-1}}f\left(n-2^{j-1}k\right)\end{array}& \left(2\right)\end{array}$
where j∈[1, ∞]; S.sub.2.sub.jf(n) is the approximation components of the wavelet transform result; W.sub.2.sub.jf(n) is the wavelet components of the transformation result; {h.sub.k}={0.125, 0.375, 0.375, 0.125}(k=−1, 0, 1, 2); {g.sub.k}={−2, 2}(k=0, 1).

(13) The singularities include initial time of the disturbance, arrival time of a disturbance point reflection wave (i.e. a fault point reflection wave), and arrival time of the reflection wave of an impedance mismatching point on the line.

(14) Step 1003: calculating a wavefront slope of the components of the line mode of the fault initial traveling wave (i.e. the disturbance initial traveling wave).

(15) After the wavelet transform, the wave head corresponding to the maximum value of a first mode which is detected is the disturbance initial traveling wave. The zero mode components of the wave head is normalized, and three sampling points are selected from an initial point for linearly fitting them with a least square method to obtain the wavefront slope k.

(16) The selection method to the initial point is as follows: for the zero mode components of the wave head of the normalized disturbance initial traveling wave, a threshold value is set as 0.1 kA, and the initial point is a first point that is greater than the threshold value.

(17) The least square method is realized by the following formula:

(18) $\begin{array}{cc}\{\begin{array}{c}y=kx+b\\ 3b+k\underset{i=1}{\overset{3}{.Math.}}{x}_i=\underset{i=1}{\overset{3}{.Math.}}{y}_i\\ b\underset{i=1}{\overset{3}{.Math.}}{x}_i+k\underset{i=1}{\overset{3}{.Math.}}{x}_i^2=\underset{i=1}{\overset{3}{.Math.}}{y}_i{x}_i\end{array}& \left(3\right)\end{array}$

(19) Step 1004: calculating a preliminary fault distance (i.e. a preliminary disturbance distance).

(20) The slope k computed in the step 1003 is substituted into the following formula (4) to compute the preliminary fault distance D:

(21) $\begin{array}{cc}k=2700{D^{\left(-0.9990+0.0136\rho \right)}\left(\frac{\rho }{100}\right)}^{-0.4568}& \left(4\right)\end{array}$

(22) Step 1005: the fault point is confirmed according to the preliminary fault distance and the wavelet singularities of the components of the line mode.

(23) According to the preliminary fault distance D computed in the step 1004 and the wavelet singularities of the components of the line mode obtained in the step 1002, with taking D as a center and setting a range as the center ±D*20%, a wave head is selected from the range. A fault distance is obtained by multiplying a time difference between the fault initial traveling wave and the fault point reflection wave by the traveling wave propagation velocity. If there is more than one wave head, min(|D−d|) is applied to, in which d is the disturbance point distance corresponding to the wave head, and then the fault distance is obtained by multiplying a time difference between the fault initial traveling wave and the fault point reflection wave by the traveling wave propagation velocity.

(24) Step 1006: end.

(25) Taking a double-terminal transmission line with 220 kV as an example, a topology and length of the line are shown in FIG. 3. The line is an overhead line, and propagation velocity of traveling wave in the line is 291 m/us. As illustration, a traveling wave detection device is equipped to a node A for collecting traveling wave signals.

(26) PSCAD is applied to establishing a corresponding simulation model. Fault occurs at a node F away from a node A by 60 km. The fault occurrence time is set as 0 s, and the soil resistivity ρ was set as 100 ∩.Math.M.

(27) Step 1001: after the line fault occurs, the acquisition point A collects and uploads a traveling wave signal.

(28) Step 1002: obtaining singularities in waveform of traveling wave.

(29) When line disturbance occurs, a traveling wave device records a traveling wave signal of the disturbance. First, a phase mode transformation is performed on waveform recorded in the step 1001, so as to obtain components of line mode and zero mode of initial traveling wave. A wavelet transform is performed on the component, so as to obtain a list of the singularities in the waveform of the traveling wave.

(30) The phase mode transformation matrix is as follows:

(31) $S=\left[\begin{array}{ccc}1& 1& 1\\ 1& -2& 1\\ 1& 1& -2\end{array}\right];S^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& -1& 0\\ 1& 0& -1\end{array}\right].$

(32) The wavelet transform is performed as follows.

(33) 0$\begin{array}{cc}\{\begin{array}{c}{S}_{2^j}f\left(n\right)=\underset{k}{.Math.}{h}_k{S}_{2^{j-1}}f\left(n-2^{j-1}k\right)\\ W_{2^j}f\left(n\right)=\underset{k}{.Math.}{g}_k{S}_{2^{j-1}}f\left(n-2^{j-1}k\right)\end{array}& \left(2\right)\end{array}$
where j∈[1, ∞]; S.sub.2.sub.jf(n) is the approximation components of the wavelet transform result; W.sub.2.sub.jf(n) is the wavelet components of the transformation result; {h.sub.k}={0.125, 0.375, 0.375, 0.125}(k=−1, 0, 1, 2); {g.sub.k}={−2, 2}(k=0, 1).

(34) TABLE-US-00001 TABLE 1 singularity list possible disturbance singularity time (μs) distance (km) 1 205 — 2 616 60.5 3 822 90.1

(35) TABLE-US-00002 TABLE 2 zero mode component of initial traveling wave zero mode of initial time (μs) traveling wave (kA) after normalizing(kA) 0 0.00459940950968730 0.00980000000000000 1 0.0138454460763030 0.0291917124911631 2 0.0290769626481030 0.0611367721971993 3 0.0480362961866330 0.100900182427558 4 0.0680354190231550 0.142844342752596 5 0.0875682731845390 0.183810597785266 6 0.106025897198460 0.222521772629663

(36) Step 1003: calculating a wavefront slope k of the components of the zero mode of the fault initial traveling wave. As shown in table 2, there are the components of the zero mode of the wave head of the disturbance initial traveling wave and the data generated by normalizing them. According to the normalized data, a first point greater than the threshold value of 0.1 kA is selected as an initial point, and three points from the initial point are selected.

(37) The three selected sampling points (0.1009, 0.1428, 0.1838) are linearly fitted with the least square method, and the slope k is 39.83 A/μs.

(38) The formula of least square method is as follows:

(39) $\begin{array}{cc}\{\begin{array}{c}y=kx+b\\ 3b+k\underset{i=1}{\overset{3}{.Math.}}{x}_i=\underset{i=1}{\overset{3}{.Math.}}{y}_i\\ b\underset{i=1}{\overset{3}{.Math.}}{x}_i+k\underset{i=1}{\overset{3}{.Math.}}{x}_i^2=\underset{i=1}{\overset{3}{.Math.}}{y}_i{x}_i\end{array}& \left(1\right)\end{array}$

(40) Step 1004: substituting the slope k computed in the step 1003 into the following formula (2) to compute a preliminary fault distance D:

(41) $\begin{array}{cc}k=2700{D^{\left(-0.9990+0.0136\rho \right)}\left(\frac{\rho }{100}\right)}^{-0.4568}& \left(2\right)\end{array}$

(42) Step 1005: confirming the fault point according to the preliminary fault distance D and the wavelet singularities of the component in the line. With taking D as a center and setting a range as the center ±D*20%, a wave head is selected from the range. A fault distance is obtained by multiplying a time difference between the fault initial traveling wave and the fault point reflection wave by the traveling wave propagation velocity, which computes that the fault distance is 60.5 km.

(43) The above descriptions are only better embodiments of the present invention, and do not serve as a restriction on the present invention for other forms. A person having ordinary skill in the art may use the above disclosed technical contents to vary or modify it into equivalent embodiment with equivalent variation. However, any simple variation, equivalent variation, and modification made to the above embodiments according to the substantial technology of the present invention, which is not divorced from the technical solution of the present invention, still belongs to the protection scope of the technical scheme of the present invention.