CN114755530A - Robust fault positioning method for power transmission line - Google Patents

Robust fault positioning method for power transmission line Download PDF

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CN114755530A
CN114755530A CN202210418317.1A CN202210418317A CN114755530A CN 114755530 A CN114755530 A CN 114755530A CN 202210418317 A CN202210418317 A CN 202210418317A CN 114755530 A CN114755530 A CN 114755530A
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童晓阳
董星星
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Southwest Jiaotong University
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    • G—PHYSICS
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    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
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Abstract

The invention discloses a robust fault positioning method for a power transmission line, and belongs to the technical field of fault positioning of power systems. And establishing a secondary nonlinear overdetermined equation set of the fault position at each sampling moment after a fault occurs in one cycle by using the measured value of the grid synchronous phasor measuring device and adopting a node voltage equation before and after the fault. To quantify the measurement error, a residual error is added to the system of equations. And solving a plurality of groups of equation sets containing residual errors by using a Levenberg-Marquardt method to obtain the fault position at each moment and form a fault position array. And aiming at noise and abnormal large numbers, a probability screening and smoothing filtering method is provided, abnormal data are respectively screened from the fault positions at each moment, smoothing filtering and replacing are carried out, and the average value of an array is calculated to obtain the final fault position. The fault positioning method can effectively improve the fault positioning precision of the power transmission line, is not influenced by fault positions, transition resistances and fault types, and has strong anti-interference capability and good robustness.

Description

Robust fault positioning method for power transmission line
Technical Field
The invention belongs to the technical field of power system line fault positioning.
Background
The research of transmission line fault location has great engineering value and practical significance, and the Synchronous Phasor Measurement Unit (PMU) technology is mature applied to the power system. Because PMU is expensive, it is necessary to research an accurate fault location method of a power transmission line under a finite synchrophasor measurement unit PMU.
At present, most of line fault positioning documents represent each measurement value as a function of a fault position, and the fault position is solved by methods such as static state estimation and Newton-Raphson. But most of the existing fault location literature regards measurement noise as white gaussian noise. The document "Zhao J.A Robust Dynamic State and Parameter Estimation Framework for Smart Grid Monitoring and Control [ D ]. Virginia Tech, 2018" states that from synchronous phasor measurement unit PMU data from the american Pacific north National Laboratory, a gaussian distribution is obtained in which the synchronous phasor measurement unit PMU voltage current amplitude error is not standard, where two peaks occur, i.e. non-gaussian noise, the document "wang, sun-shine, south-shine, wangke, houda. the generator Dynamic State Estimation method taking into account the influence of Parameter uncertainty [ J ]. power system automation, 2020, 44 (04): 110-.
Document "Fu J, Song G, De Schuter B. infiluence of measurement elementary on parameter estimation and fault location for transmission lines [ J ]. IEEE Transactions on Automation Science and Engineering, 2020, 18 (1): 337 and 345' analyze the influence of the measurement uncertainty on the parameter estimation and fault location of the power transmission line, and reduce the measurement uncertainty by using the maximum likelihood method, but the error of the measurement parameter is assumed to be obeyed to the normal distribution, so that certain limitation exists.
The literature, "zhangshengpo, wide area backup protection research based on estimation and node fault injection current under a finite synchrophasor measurement unit PMU [ D ]. southwest university of transportation, 2021", researches on collecting voltages of PMU nodes of regional boundary synchrophasor measurement units in a power grid by using a wide area communication network, calculating positive sequence voltages of PMU nodes of synchrophasor measurement units not arranged in each region, and provides a method for determining fault regions and fault lines.
The existing literature considers less adverse effects of non-Gaussian distribution noise, random noise and abnormal large numbers on the fault positioning accuracy, and certain robustness is insufficient in practical engineering application.
Disclosure of Invention
The invention aims to provide a robust fault positioning method for a power transmission line, which can effectively solve the technical problems of accurate fault positioning under various fault situations and no influence of fault positions, fault types and transition resistances.
The invention aims to realize the purpose through the following technical scheme, and discloses a robust fault positioning method for a power transmission line, which comprises the following steps of:
collecting voltages of synchronous Phasor Measurement Units (PMUs) on boundary nodes of each area in a power grid in real time through a wide area communication network, and determining the voltages of the nodes without the PMUs by using the conventional calculation method for the nodes without the PMUs in each area so as to determine a fault area and a fault line in the fault area; aiming at each sampling time in the period from 2 nd to 3 rd cycle after the fault occurs in the fault line, positive sequence voltages of all nodes in the power grid are utilized to respectively establish a node voltage equation before and after the fault, and an original fault position secondary nonlinear overdetermined equation set at each sampling time is constructed through derivation;
step two, the original fault position secondary nonlinear overdetermined equation set at each sampling moment comprises two equations, measurement errors existing in fault positioning affect the equation set, the measurement errors are comprehensively considered, and a residual variable epsilon is defined1The residual variable ε2Their random variation range is [ -0.015, -0.005 [ -0.015 [ -0.005 [ ]]∪[0.005，0.015]Interval, adding them to the right side of equal sign of two equations in the secondary nonlinear over-determined equation system of original fault positionForming a group of fault position secondary nonlinear over-determined equations containing residual variables; then the same treatment is carried out, and nine groups of residual variables epsilon are defined continuously1The residual variable ε2Then, the two equations are respectively added to the right sides of equal signs of two equations in the original fault position secondary nonlinear over-determined equation set, and ten sets of fault position secondary nonlinear over-determined equation sets containing residual variables are formed in total;
respectively solving ten sets of secondary nonlinear overdetermined equations of fault positions containing residual variables at each moment by adopting a Levenberg-Marquardt nonlinear least square method to obtain corresponding ten fault positions, and then solving the average value of the ten fault positions to serve as the line fault position at the sampling moment; forming a line fault position array X of the same fault point at the line fault positions at each sampling moment;
step four, aiming at the fault position of each sampling moment in the line fault position array X, a probability discrimination and smooth filtering method is provided for filtering, and abnormal data are discriminated by adopting a probability distribution-based principle; carrying out smooth filtering processing on each abnormal data and replacing; processing the fault position at each sampling moment to obtain a line fault position array X of the same fault point after filteringR；
Step five, the filtered line fault position array XRAnd calculating an average value to obtain a final line fault position.
Aiming at the line fault position at each sampling moment in the line fault position array X, a probability discrimination and smooth filtering method is provided for filtering, and the method specifically comprises the following steps:
for the line fault position array X, l is the length of the array X, l is 60, four line fault positions with the maximum and minimum amplitudes are respectively eliminated from the line fault position array X, and the array X 'is obtained as [ X'1，x′2…，x′m]Where m is the length of the array X ', m is 52, and the average μ of the array X' is calculated as:
Figure BDA0003605051240000021
in formula (II), x'τIs the τ th element in array X';
the standard mean square error σ of the array X' is calculated as:
Figure BDA0003605051240000022
according to the probability distribution principle, the data within 1 time of standard mean square error of an array mean accounts for 68.27%; the method judges data except for 1 time of standard mean square error of the mean value of the array as abnormal data or outlier data, and then carries out smoothing treatment on the abnormal data or the outlier data so as to inhibit the abnormal data or the outlier data;
for the h data X in the line fault position array XhH is more than or equal to 1 and less than or equal to l if data xhIn the interval [ mu-sigma, mu + sigma]Then, the data x is processedhJudging the data to be abnormal data;
for exception data xhBefore the index number h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]First three adjacent data x ofh-3、xh-2、xh-1After h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]X is the 1 st adjacent data ofvV is the index number of the data in the array X, v is more than or equal to h +1 and less than or equal to l, four data are selected in total, and the average value of the four data is calculated to be gamma, then:
γ＝(xh-3+xh-2+xh-1+xv)/4 (3)
if h is less than or equal to 3, selecting 4 adjacent data meeting [ mu-sigma, mu + sigma ] before and after the point h, and solving a mean value gamma;
using mean value gamma to replace current abnormal data xh。
Compared with the prior art, the invention has the beneficial technical effects that:
the method comprises the steps of determining a fault area and a fault line under a finite synchrophasor measurement unit (PMU) by using the existing method, considering the ground admittance of the line, establishing a fault position quadratic nonlinear overdetermined equation set by adopting a node voltage equation before and after the fault, and facilitating the accuracy of a fault position solution model by introducing the ground admittance of the line.
In the operation process of a power grid, line parameters and measurement data are influenced by weather and geographic factors, so the method takes the line parameters and measurement errors into consideration, introduces residual variables into a secondary nonlinear over-determined equation set of the fault position, and solves the equation set by using a Levenberg-Marquardt method, so that the fault position obtained by solving fully considers the influence of the measurement errors and the line parameters on the fault positioning result, and the method has better fault tolerance of the measurement errors and the parameter errors.
And aiming at the noise and abnormal numbers possibly existing in fault positioning, a probability discrimination and smooth filtering method is provided, and the fault position at each moment is subjected to filtering processing to obtain the final accurate fault position. Therefore, the interference caused by noise and abnormal numbers to the fault position solving can be effectively inhibited, and the solved fault position is more accurate.
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FIG. 1 is a flow chart of the present invention.
FIG. 2 shows a circuit L according to the inventionijAnd (5) a schematic diagram of a power grid structure when a fault occurs.
Fig. 3 is a system for testing IEEE 39 nodes according to an embodiment of the present invention.
FIG. 4 is a voltage curve of the node voltage of embodiment 29 with 20dB of white Gaussian noise added.
FIG. 5 is a graph of the result of fault location under white Gaussian noise of 20dB added to the node voltage in embodiment 29 of the present invention.
Fig. 6 is a fault location result curve under different filtering methods according to an embodiment of the present invention.
Detailed Description
The present invention uses a distributed parameter line model. If on line LijIs faulty, the length between the fault point f and the node i and the line L are setijThe ratio of the total length is a fault position x, the x is an unknown variable, and the length between a fault point f and a node j is equal to the line LijThe ratio of the total length is (1-x), BijIs a line LijAdmittance to ground, jxBij/2 denotes the line-to-ground admittance from the fault point f to the node i, j (1-x) Bij/2 is the line-to-ground admittance, Z, from fault point f to node jijIs a line LijThe impedance of (c).
For a positive sequence network, the number of nodes of a power grid is assumed to be n, n is a positive integer, and a line LijThe node voltage equation for the grid before the fault is expressed as:
Figure BDA0003605051240000041
in the formula, the variable superscript 0 represents the voltage and current before the fault,
Figure BDA0003605051240000042
is the positive sequence voltage of each node,
Figure BDA0003605051240000043
is the injection current of each node, Y is the node admittance matrix;
provided with a line LijAnd (3) generating a fault at the middle f point, considering that a fault point f is added into the node admittance matrix Y and is set as the n +1 th node, before the fault occurs, the injection current of the fault point f is 0, and then a node voltage equation with n +1 nodes before the fault occurs is expressed as:
Figure BDA0003605051240000044
in the formula, the prime mark ' in the element superscript in the extended node admittance matrix Y ' represents the changed admittance element after adding the fault point f, including Y 'ii、Y′ij、Y′ji、Y′jjAnd newly added admittance element Y'i(n+1)、Y′(n+1)i、Y′j(n+1)、Y′(n+1)j、Y′(n+1)(n+1)They are as follows:
Figure BDA0003605051240000045
when the line L isijAfter a fault, the node voltage equation for a system with n +1 nodes is expressed as:
Figure BDA0003605051240000051
in the formula, U 'and I' are positive sequence voltage and injection current of each node after failure,
Figure BDA0003605051240000052
is the injection current at fault point f;
subtracting formula (5) from formula (7) yields:
Figure BDA0003605051240000053
in the formula (I), the compound is shown in the specification,
Figure BDA0003605051240000054
is the positive sequence voltage fault component of each node,
Figure BDA0003605051240000055
is the positive sequence voltage fault component of fault point f,
Figure BDA0003605051240000056
unfolding the ith row of equation (8) yields:
Figure BDA0003605051240000057
expanding line j of equation (8) yields:
Figure BDA0003605051240000058
for the transformation of the formula (9), only the i, j and n +1 terms are reserved on the left side of the formula (9) equation, and the three terms comprise an unknown variable x and an unknown variable
Figure BDA0003605051240000059
The remaining terms are known variables, which are right-shifted to the right of the equation, i.e.:
Figure BDA00036050512400000510
order to
Figure BDA00036050512400000511
Rewriting formula (11) as:
Figure BDA00036050512400000512
similarly, for the transformation of the formula (10), only the i, j and n +1 terms are reserved on the left side of the formula (10), and the three terms comprise an unknown variable x and an unknown variable
Figure BDA00036050512400000513
The remaining terms are known variables, which are right-shifted to the right of the equation, i.e.:
Figure BDA00036050512400000514
order to
Figure BDA00036050512400000515
Rewriting formula (13) as:
Figure BDA0003605051240000061
substituting formula (6) for formula (12) yields:
Figure BDA0003605051240000062
the finishing method comprises the following steps:
Figure BDA0003605051240000063
order to
Figure BDA0003605051240000064
Rewrite equation (16) to:
Figure BDA0003605051240000065
the two sides of the formula (17) are multiplied by x respectively to obtain:
Figure BDA0003605051240000066
similarly, formula (6) is substituted for formula (14) to obtain:
Figure BDA0003605051240000067
the finishing method comprises the following steps:
Figure BDA0003605051240000068
order to
Figure BDA0003605051240000069
Rewriting equation (20) as:
Figure BDA00036050512400000610
the two sides of equation (21) are multiplied by (1-x) respectively to obtain:
Figure BDA00036050512400000611
subtracting the formula (22) from the formula (18), and eliminating the unknown variable
Figure BDA00036050512400000612
Obtaining:
Figure BDA00036050512400000613
sorted into complex coefficient one-dimensional quadratic equations for fault location x:
Figure BDA00036050512400000614
order:
Figure BDA0003605051240000071
Figure BDA0003605051240000072
Figure BDA0003605051240000073
equation (24) becomes a complex coefficient one-dimensional quadratic equation with respect to the fault location x:
ax2+bx+c＝0 (25)
respectively taking the real part coefficients a of the complex coefficients in equation (25)1、b1、c1Coefficient of imaginary part a2、b2、c2Two unitary quadratic equations are obtained to form a secondary nonlinear overdetermined equation set of the original fault position, which is as follows:
Figure BDA0003605051240000074
step twoThe primary fault position secondary nonlinear overdetermined equation set at each sampling moment comprises two equations, measurement errors existing in fault positioning affect the equation set, the measurement errors are comprehensively considered, and a residual variable epsilon is defined1The residual variable ε2Their random variation range is [ -0.015, -0.005 [ -0.015 [ -0.005 [ ]]∪[0.005，0.015]Adding the interval to the right sides of equal signs of two equations in the original fault position secondary nonlinear over-determined equation set to form a group of fault position secondary nonlinear over-determined equation set containing residual variables; then the same treatment is carried out, and nine groups of residual variables epsilon are defined continuously1The residual variable ε2Then, adding the two equations to the right of equal sign of two equations in the original fault position secondary nonlinear over-determined equation set respectively to form ten sets of fault position secondary nonlinear over-determined equation sets containing residual variables in total;
by solving the quadratic nonlinear overdetermined equation system of the formula (26) by using a least square method, the fault position x of the fault line can be obtained, but the formula (26) does not consider the measurement error possibly existing in the actual engineering.
The invention considers the influence of measurement error and introduces a residual variable epsilon1、ε2And respectively adding the two equations to the right of the equal sign of the equation (26) of the quadratic nonlinear overdetermined equation set to obtain an equation (27):
Figure BDA0003605051240000075
in which the residual variable ε1The residual variable ε2Has a value range of [ -0.015, -0.005 [ ]]∪[0.005，0.015]。
Aiming at each sampling time in the cycle period from 2 nd to 3 rd after the line fault, forming a group of fault position secondary nonlinear overdetermined equations containing residual variables according to the formula (27); then the same treatment is carried out, and nine groups of residual variables epsilon are defined1The residual variable ε2Respectively adding the two secondary nonlinear over-determined equations to the right of equal sign of two equations of the original fault position secondary nonlinear over-determined equation set to form ten sets of fault position secondary nonlinear over-determined equations containing residual variablesGroup, as follows:
Figure BDA0003605051240000076
in the formula, epsilon1_q、ε2_qAre all [ -0.015, -0.005 [)]∪[0.005，0.015]Q represents the q-th set of equations, q 1, 2.
Respectively solving ten sets of secondary nonlinear overdetermined equations of fault positions containing residual variables at each moment by adopting a Levenberg-Marquardt nonlinear least square method to obtain corresponding ten fault positions, and then solving the average value of the ten fault positions to serve as the line fault position at the sampling moment; forming a line fault position array X of the same fault point at the line fault positions at each sampling moment;
step four, aiming at the fault position of each sampling moment in the line fault position array X, a probability discrimination and smooth filtering method is provided for filtering, and abnormal data are discriminated on the basis of a probability distribution principle; carrying out smooth filtering processing on each abnormal data, and replacing; processing the fault position at each sampling moment to obtain a line fault position array X of the same fault point after filteringR；
For the line fault position array X, if l is the length of the array X, and l ═ 60, four line fault positions with the maximum and minimum amplitudes are respectively eliminated from the line fault position array X, and the array X '═ X'1，x′2…，x′m]M is the length of the array X ', m is 52, and the average of the array X' is calculated as:
Figure BDA0003605051240000081
in formula (II), x'τIs the τ th element in array X';
the standard mean square error σ of the array X' is calculated as:
Figure BDA0003605051240000082
according to the probability distribution principle, namely that data within 1 time of standard mean square error of an array mean accounts for 68.27%, the invention judges data outside 1 time of standard mean square error of the array mean as abnormal data or outlier data, and then carries out smoothing treatment on the abnormal data or outlier data so as to inhibit the abnormal data or outlier data;
for the h data X in the line fault position array XhH is more than or equal to 1 and less than or equal to l if data xhIn the interval [ mu-sigma, mu + sigma]Then, the data x is processedhJudging the data to be abnormal data;
for exception data xhBefore the index number h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]First three adjacent data x ofh-3、xh-2、xh-1After h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]Is xvV is the index number of the data in the array X, v is more than or equal to h +1 and less than or equal to l, four data are selected in total, the mean value of the four data is calculated to be gamma, and then:
γ＝(xh-3+xh-2+xh-1+xv)/4 (3)
if h is less than or equal to 3, selecting 4 adjacent data meeting [ mu-sigma, mu + sigma ] before and after the point h, and solving a mean value gamma;
using mean value gamma to replace current abnormal data xh；
Processing the fault position at each sampling moment to obtain a line fault position array X of the same fault point after filteringR；
Step five, the filtered line fault position array X is processedRCalculating the average value to obtain the final line fault position
Figure BDA0003605051240000083
Figure BDA0003605051240000084
In the formula, xRuIs an array XRWherein u is the data and l is the array XRL is 60.
Because the fault position array X is a discrete array, the accuracy of the predicted value of the common Kalman filtering is not high when the current value is seriously deviated from the mean value and is not in the range of [ mu-sigma, mu + sigma ] (such as abnormal large number). The probability discrimination and smoothing filtering method provided by the invention can better eliminate the influence of noise, abnormal numbers and the like on fault positioning by using data before and after the current sampling moment.
In order to verify the performance of the robust fault positioning method for the three-position power transmission line provided by the invention, various fault conditions which may occur in the actual working state of the line need to be considered, so that line faults under different transition resistances, fault positions and fault types are set in the IEEE 39 node test system of FIG. 3, a PMU layout mode of a synchronous phasor measurement device is provided in FIG. 3, and the accuracy of the robust fault positioning method for the power transmission line is verified through a simulation result. The sampling frequency is 3kHz, the system frequency is 60Hz, and the fault types are A phase grounding short-circuit fault AG, A phase and B phase short-circuit fault AB, A phase and B phase grounding short-circuit fault ABG and three-phase grounding short-circuit fault ABC.
The fault location error is defined as follows:
Figure BDA0003605051240000091
the positioning results of the faults of the lines 26-29 under different fault types, transition resistances and positions are shown in table 1, wherein the 3 rd column is the fault position preset from the node 26 in the lines 26-29, which is the ratio of the length between the fault point and the node 26 to the total length of the line, and the 4 th column is the fault position solved by the method.
TABLE 1 localization results for faults occurring in lines 26-29 under different fault types, transition resistances, and locations
Figure BDA0003605051240000092
As can be seen from the table 1, the method provided by the invention is not affected by fault types, transition resistances and fault positions, has high positioning precision, has a positioning error below 1 percent, and meets the engineering positioning requirements.
The fault location results of the A-phase short circuit faults of different lines at different positions under the condition that the transition resistance is 300 omega are shown in table 2, and L in the table 226-29The line 26-29 is shown to have a fault, the left side is the line starting point number, the right side is the line terminal point number, and the 2 nd list head 'preset fault position 0.1' in table 2 shows that the ratio of the length between the preset fault point and the line starting point to the total length of the line is 0.1; the 3 rd list header of table 2, preset fault location 0.5, indicates that the ratio of the length between the preset fault point and the line starting point to the total line length is 0.5, and the 4 th list header of table 2, preset fault location 0.9, indicates that the ratio of the length between the preset fault point and the line starting point to the total line length is 0.9; the data in columns 2, 3 and 4 in table 2 are the fault locations solved by the present invention.
As can be seen from the table 2, the method provided by the invention is suitable for the faults of each line, is not influenced by the fault positions, and has higher positioning accuracy.
TABLE 2 Fault location results of A-phase short circuit faults of different lines at different positions of 300 Ω of transition resistance
Figure BDA0003605051240000101
In practical engineering applications, there may be some deviation or error in the line parameters and measurements. Corresponding simulation is set to verify the fault tolerance of the method to system parameters and measurement errors, node admittance offset of lines 26-29 is set in table 3, an AG fault occurs at a position where the ratio of the lengths of fault points and nodes 26 in the lines 26-29 to the total length is 0.1, and a transition resistor is 300 omega, an AG fault occurs at a position where the ratio of the lengths of the fault points and nodes 26 in the lines 26-29 to the total length is 0.5, and the voltage of the node 26 is offset at the transition resistor 300 omega.
As can be seen from table 3, the line measurement parameter has a certain influence on the method provided by the present invention, but even if the offset of the admittance of the node 26 in table 3 reaches 10%, the error of line fault location still does not exceed 2%, even if the voltage offset of the node 26 in table 4 reaches 5%, the error of line fault location reaches 2.59%, and the present invention has a good fault tolerance capability against line parameter offset and measurement error.
TABLE 3 Fault location results in admittance shift at node 26 of lines 26-29
Figure BDA0003605051240000102
TABLE 4 Fault location results when node 26 voltages of lines 26-29 are shifted
Figure BDA0003605051240000111
The fault location of the power transmission line may have random interference and abnormal large number, and in order to overcome the defects of the fault location method of the power transmission line, the invention provides a probability discrimination and smoothing filtering method for discriminating and filtering abnormal data.
In order to verify the influence of random noise and abnormal large numbers on the fault positioning method, the conditions that 20db of noise and 5 random abnormal large numbers exist in the voltage of the node 29 when the line 26-29 has a fault are simulated respectively.
Table 5 shows the fault location result of adding 20db gaussian white noise to the node 29 voltage when AG fault occurs at different positions of the lines 26 to 29, column 3 in table 5 shows the fault location preset at the distance node 26 in the lines 26 to 29, which is the ratio of the length between the fault point and the node 26 to the total length of the lines, table 6 shows the fault location result of adding 20db gaussian noise to the node 29 voltage when AG fault occurs at different positions of the lines 26 to 29, which has 5 random abnormal large numbers, and column 3 in table 6 shows the fault location preset at the distance node 26 in the lines 26 to 29, which is the ratio of the length between the fault point and the node 26 to the total length of the lines.
TABLE 5 Fault location results of 20db noise added to node 29 voltage when AG faults occur at different locations of lines 26-29
Figure BDA0003605051240000112
TABLE 6 Fault location results with 20db noise added to node 29 voltage and 5 random abnormal large numbers when AG faults occur at different positions of lines 26-29
Figure BDA0003605051240000113
As can be seen from tables 5 and 6, the method provided by the invention has better noise resistance and abnormal large number resistance, and has stronger robustness.
In order to further verify the effectiveness of the method on noise resistance and abnormal numbers, the method selects a Kalman filtering method commonly used in the current engineering to carry out a comparison experiment.
Fig. 4 is a graph of the magnitude of the voltage at node 29 with 20db noise added to the voltage at line 26-29 and without the noise added, and it can be seen from fig. 4 that the magnitude of the voltage at node 29 is greatly distorted after 20db noise is added.
Fig. 5 is a fault location curve of node 29 voltage with 20db gaussian noise and without noise when AG fault occurs in lines 26-29, and it can be seen from fig. 5 that the first cycle after fault occurs at time 0.3ms is a transient process, i.e. the fault location fluctuation is large between 0.3ms and 0.317 ms. The fault position is in a stable state between the 2 nd cycle and the 3 rd cycle after the fault, namely 0.317ms to 0.337ms, and the fluctuation of the fault positioning result is small, so the data between the 0.317ms to 0.337ms of the 2 nd cycle and the 3 rd cycle after the fault is selected for fault positioning.
FIG. 6 is a fault location at 60 sampling times within 20ms of the 2 nd cycle when an AG fault occurs in a line 26-29, wherein X-noise is a fault location curve obtained by using the fault location method of the present invention without probability discrimination and smoothing filtering under the condition that 20db of noise is added to the node 29 voltage;
the X-ALN is a fault position curve obtained by utilizing the method of the invention under the condition that 20db of noise is added into the 29 voltage of the node and random 5 distortion data are added, but probability discrimination and smooth filtering do not exist;
the X-KF is a fault position curve obtained by using the method and Kalman filtering under the condition that 20db of noise is added into 29 voltages of the nodes and 5 random distortion data are added;
the X-PSF is a fault position curve obtained by adding 20db of noise into the 29 voltage of the node and adding 5 random distortion data by using the method and the probability screening and smoothing filtering of the invention.
The filtering result in fig. 6 is shown in table 7, and it can be seen from table 7 that, compared with kalman filtering, the probabilistic smoothing filtering provided by the present invention has stronger filtering capability on random noise and abnormal large numbers, the positioning error is below 1%, the fault positioning accuracy is higher, and the present invention has stronger engineering value.
Table 7 shows the fault location results of different filtering methods under the conditions that 20db noise is added to the voltage of the node 29 and 5 random abnormal numbers exist when AG faults occur in the lines 26-29
Figure BDA0003605051240000121

Claims (2)

1. A robust fault positioning method for a power transmission line is suitable for high-voltage power transmission lines of 220kV and above, and comprises the following steps:
collecting voltages of synchronous Phasor Measurement Units (PMUs) on boundary nodes of each area in a power grid in real time through a wide area communication network, and determining the voltages of the nodes without the PMUs by using the conventional calculation method for the nodes without the PMUs in each area so as to determine a fault area and a fault line in the fault area; aiming at each sampling time in the period from 2 nd to 3 rd cycle after the fault occurs in the fault line, positive sequence voltages of all nodes in the power grid are utilized to respectively establish a node voltage equation before and after the fault, and an original fault position secondary nonlinear overdetermined equation set at each sampling time is constructed through derivation;
step two, the secondary nonlinear overdetermined equation set of the original fault position at each sampling moment comprises two equations, and the measurement error caused by fault positioning is givenThe system of equations brings influence, measurement errors are comprehensively considered, and a residual variable epsilon is defined1The residual variable ε2Their random variation range is [ -0.015, -0.005 [ -0.015 [ -0.005 [ ]]∪[0.005，0.015]Adding the interval to the right sides of equal signs of two equations in the original fault position secondary nonlinear over-determined equation set to form a group of fault position secondary nonlinear over-determined equation set containing residual variables; then the same treatment is carried out, and nine groups of residual variables epsilon are defined continuously1The residual variable ε2Then, adding the two equations to the right of equal sign of two equations in the original fault position secondary nonlinear over-determined equation set respectively to form ten sets of fault position secondary nonlinear over-determined equation sets containing residual variables in total;
respectively solving ten sets of secondary nonlinear overdetermined equations of fault positions containing residual variables at each moment by adopting a Levenberg-Marquardt nonlinear least square method to obtain corresponding ten fault positions, and then solving the average value of the ten fault positions to serve as the line fault position at the sampling moment; forming a line fault position array X of the same fault point at the line fault positions at each sampling moment;
step four, aiming at the fault position of each sampling moment in the line fault position array X, a probability discrimination and smooth filtering method is provided for filtering, and abnormal data are discriminated by adopting a probability distribution-based principle; carrying out smooth filtering processing on each abnormal data and replacing; processing the fault position at each sampling moment to obtain a line fault position array X of the same fault point after filteringR；
Step five, the filtered line fault position array X is processedRAnd (5) calculating an average value to obtain a final line fault position.
2. The robust fault location method for the power transmission line according to claim 1, characterized in that: aiming at the line fault position at each sampling moment in the line fault position array X, a probability discrimination and smooth filtering method is provided for filtering, and the method specifically comprises the following steps:
for the line fault location array X, let l be the length of array XAnd l is 60, four line fault positions with the maximum and minimum amplitudes are respectively removed from the line fault position array X, and the array X 'is obtained as [ X'1，x′2…，x′m]Where m is the length of the array X ', m is 52, and the average μ of the array X' is calculated as:
Figure FDA0003605051230000011
x 'in the formula'τIs the τ th element in array X';
the standard mean square error σ of the array X' is calculated as:
Figure FDA0003605051230000012
the data within 1 time standard mean square error of an array mean is 68.27% according to the probability distribution principle; the method judges data except for 1 time standard mean square error of the mean value of the array as abnormal data or outlier data, and then carries out smoothing treatment on the abnormal data or the outlier data so as to inhibit the outlier data or the outlier data;
for the h data X in the line fault position array XhH is more than or equal to 1 and less than or equal to l if data xhIn the interval [ mu-sigma, mu + sigma]Then, the data x is processedhJudging the data to be abnormal data;
for exception data xhBefore the index number h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]First three adjacent data x ofh-3、xh-2、xh-1After h in the array X is selected, the [ mu-sigma, mu + sigma ] is satisfied]X is the 1 st adjacent data ofvV is the index number of the data in the array X, v is more than or equal to h +1 and less than or equal to l, four data are selected in total, the mean value of the four data is calculated to be gamma, and then:
γ＝(xh-3+xh-2+xh-1+xv)/4 (3)
if h is less than or equal to 3, selecting 4 adjacent data meeting [ mu-sigma, mu + sigma ] before and after the point h, and solving a mean value gamma;
using the mean value gamma to replace the currentAbnormal data x ofh。
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