CN114755530B - Robust fault positioning method for power transmission line - Google Patents

Robust fault positioning method for power transmission line Download PDF

Info

Publication number
CN114755530B
CN114755530B CN202210418317.1A CN202210418317A CN114755530B CN 114755530 B CN114755530 B CN 114755530B CN 202210418317 A CN202210418317 A CN 202210418317A CN 114755530 B CN114755530 B CN 114755530B
Authority
CN
China
Prior art keywords
fault
array
data
line
fault position
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210418317.1A
Other languages
Chinese (zh)
Other versions
CN114755530A (en
Inventor
童晓阳
董星星
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southwest Jiaotong University
Original Assignee
Southwest Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southwest Jiaotong University filed Critical Southwest Jiaotong University
Priority to CN202210418317.1A priority Critical patent/CN114755530B/en
Publication of CN114755530A publication Critical patent/CN114755530A/en
Application granted granted Critical
Publication of CN114755530B publication Critical patent/CN114755530B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • 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
    • G01R31/088—Aspects of digital computing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

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 the fault location of the transmission line has great engineering value and practical significance, and the Synchronous Phasor Measurement Unit (PMU) technology is mature and 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 treats the 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 synchrophasor measurement unit PMU data from the american Pacific north Laboratory, a gaussian distribution is obtained in which the synchrophasor measurement unit PMU voltage-current amplitude error is not standard, where two peaks occur, i.e. non-gaussian noise, the document "Wang Yi, sun Yonghui, south east bright, wang Kaike, hou Dongchen. Generator Dynamic State Estimation method considering Parameter uncertainty effects [ J ]. Power system automation, 2020, 44 (04): 110-118 "also indicate that noise pollution of the synchrophasor measurement unit PMU measurements by communication channel noise deviates from the gaussian distribution assumption.
Document "Fu J, song G, de Schuter B. Infection of measurement elementary on parameter estimation and fault location for transmission lines [ J ]. IEEE Transactions on Automation Science and Engineering,2020, 18 (1): 337-345' analyzes the influence of the uncertainty of measurement on the parameter estimation and fault location of the transmission line, and utilizes the maximum likelihood method to reduce the uncertainty of measurement, but the error of the measurement parameter is assumed to obey normal distribution, so that certain limitation exists.
Document Zhang Shengpeng, a wide area backup protection research based on estimation and node fault injection current under a finite synchrophasor measurement unit PMU [ D ]. Southwest traffic university, 2021 "researches a method of collecting voltages of PMU nodes of area 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 area, and determining a fault area and a fault line.
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 defined 1 The residual variable ε 2 Their 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 variable epsilon are defined continuously 1 The residual variable ε 2 Then, 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; for each exceptionCarrying out smooth filtering processing on the data and replacing the data; processing the fault position at each sampling moment to obtain a line fault position array X of the same fault point after filtering R ；
Step five, the filtered line fault position array X R And 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 =60, four line fault positions with the maximum amplitude and the minimum amplitude are respectively eliminated from the line fault position array X, and an array X '= [ X' 1 ，x′ 2 …，x′ m ]M is the length of array X ', m =52, and the average μ of array X' is calculated as:
Figure BDA0003605051240000021
x 'in the formula' τ Is the τ th element in array X';
the standard mean square error σ of the array X' is calculated as:
Figure BDA0003605051240000022
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 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 X h H is more than or equal to 1 and less than or equal to l if data x h In the interval [ mu-sigma, mu + sigma]Then, the data x is processed h Judging the data to be abnormal data;
for exception data x h Selecting the index number h in the array X to satisfy [ mu-sigma,μ+σ]first three adjacent data x of h-3 、x h-2 、x h-1 After h in the array X is selected, the [ mu-sigma, mu + sigma ] is satisfied]X is the 1 st adjacent data of v V 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＝(x h-3 +x h-2 +x h-1 +x v )/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 x h 。
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, therefore, 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 influences 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.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a line of the present inventionRoad L ij And (4) 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 fault location result of the node voltage of embodiment 29 with 20dB of white Gaussian noise added.
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 L ij F point f of (a) is failed, and the length between the failure point f and the node i and the line L are set ij The 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 L ij The ratio of the total length is (1-x), B ij Is a line L ij Is guided by the earth, jxB ij /2 denotes the line-to-ground admittance from the fault point f to the node i, j (1-x) B ij /2 is the line-to-ground admittance, Z, from fault point f to node j ij Is a line L ij The 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 L ij The 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, is greater than>
Figure BDA0003605051240000043
Is the injection current of each node, and Y is the node admittance matrix;
provided with a line L ij Failure at the intermediate f-point, taking into account the nodeAdding a fault point f into the admittance matrix Y, setting the fault point f as an n +1 th node, wherein before a 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′ jj And 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 respectively as follows:
Figure BDA0003605051240000045
when the line L is ij After 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 the fault,
Figure BDA0003605051240000052
is the injection current at fault point f;
subtracting equation (5) from equation (7) yields:
Figure BDA0003605051240000053
in the formula (I), the compound is shown in the specification,
Figure BDA0003605051240000054
is positive sequence voltage fault division of each nodeVolume, or>
Figure BDA0003605051240000055
Is the positive sequence voltage fault component of the fault point f, is greater than or equal to>
Figure BDA0003605051240000056
Expanding the ith row of equation (8) to obtain:
Figure BDA0003605051240000057
unfolding the jth line 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 equation (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
by substituting formula (6) for formula (12), we obtain:
Figure BDA0003605051240000062
the finishing method comprises the following steps:
Figure BDA0003605051240000063
order to
Figure BDA0003605051240000064
Rewrite equation (16) as:
Figure BDA0003605051240000065
multiplying x on both sides of the formula (17) to obtain:
Figure BDA0003605051240000066
similarly, substituting equation (6) into equation (14) yields:
Figure BDA0003605051240000067
the finishing method comprises the following steps:
Figure BDA0003605051240000068
order to
Figure BDA0003605051240000069
Rewriting equation (20) as:
Figure BDA00036050512400000610
multiplying both sides of the formula (21) 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:
ax 2 +bx+c＝0 (25)
respectively taking the real part coefficient a of the complex coefficient in equation (25) 1 、b 1 、c 1 Coefficient of imaginary part a 2 、b 2 、c 2 Two 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 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 defined 1 The residual variable ε 2 Their 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 continuously 1 The residual variable ε 2 Then, 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 epsilon 1 、ε 2 And respectively adding the two equations to the right of equal sign of the equation (26) in the quadratic nonlinear overdetermined equation set to obtain an equation (27):
Figure BDA0003605051240000075
in the formula, the residual variable ε 1 The residual variable ε 2 Has 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 defined 1 The residual variable ε 2 Respectively 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 equation sets containing residual variables in total, wherein the following steps are as follows:
Figure BDA0003605051240000076
in the formula, epsilon 1_q 、ε 2_q Are 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, firstly based on the probability distribution principle,screening abnormal data; 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 filtering R ；
Regarding the line fault position array X, if l is the length of the array X, l = =60, four line fault positions with the maximum amplitude and the minimum amplitude are respectively eliminated from the line fault position array X, and an array X '= [ X' 1 ，x′ 2 …，x′ m ]M is the length of array X ', m =52, and the average of array X' is calculated as:
Figure BDA0003605051240000081
in formula (II), x' τ Is 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 value accounts for 68.27%, the invention judges data outside 1 time of standard mean square error of the array mean value 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 X h H is more than or equal to 1 and less than or equal to l, if data x h In the interval [ mu-sigma, mu + sigma]Then, the data x is processed h Judging the data to be abnormal data;
for exception data x h Before the index number h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]First three adjacent data x of h-3 、x h-2 、x h-1 After h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]X is the 1 st adjacent data of v V 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＝(x h-3 +x h-2 +x h-1 +x v )/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 x h ；
Processing the fault position at each sampling moment to obtain a line fault position array X of the same fault point after filtering R ；
Step five, the filtered line fault position array X R Calculating the average value to obtain the final line fault position
Figure BDA0003605051240000083
Figure BDA0003605051240000084
In the formula, x Ru Is an array X R Wherein u is the data and l is the array X R L =60.
Because the fault position array X is a discrete array, the accuracy of the predicted value of the commonly used 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 smooth filtering method provided by the invention can better eliminate the influence of noise, abnormal numbers and the like on fault positioning by utilizing 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 a node test system of fig. 3IEEE 39, a layout mode of a PMU (phasor measurement unit) 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 divided into an A-phase grounding short-circuit fault AG, an A-phase and B-phase short-circuit fault AB, an A-phase and B-phase grounding short-circuit fault ABG and a three-phase grounding short-circuit fault ABC.
The fault location error is defined as follows:
Figure BDA0003605051240000091
the results of locating faults in lines 26-29 for different fault types, transition resistances, and locations are shown in table 1, where column 3 is the fault location in lines 26-29 preset from node 26, which is the ratio of the length between the fault point and node 26 to the total length of the line, and column 4 is the fault location solved by the present invention.
TABLE 1 location results of faults occurring in the lines 26-29 under different fault types, transition resistances and positions
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 2 26-29 The 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 "preset fault position 0.5" in table 2 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 "preset fault position 0.9" in table 2 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 capability of the method to system parameters and measurement errors, node admittance offset of the lines 26-29 is set in the table 3, AG fault occurs at the position where the ratio of the lengths of the fault point and the node 26 in the lines 26-29 to the total length is 0.1, and the transition resistance is 300 omega, AG fault occurs at the position where the ratio of the lengths of the fault point and the node 26 in the lines 26-29 to the total length is 0.5, the transition resistance is 300 omega, and voltage of the node 26 is offset.
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
In order to overcome the defects of the transmission line fault location method, 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 result with 20db noise added to node 29 voltage and 5 random abnormal large numbers when AG fault occurs 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 in resisting noise and abnormal numbers, the method selects a Kalman filtering method commonly used in the current engineering to carry out comparison experiments.
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 0.3ms is a transient process, i.e. the fault location fluctuates greatly 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 adding 20db of noise into the 29-node voltage and adding 5 random distortion data by using Kalman filtering by using the method of the invention;
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 (1)

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 original fault position secondary nonlinear overdetermined equation set at each sampling moment comprises two equations, the measurement error existing in fault positioning influences the equation set, the measurement error is comprehensively considered, and a residual variable epsilon is defined 1 The residual variable ε 2 Their 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 continuously 1 The residual variable ε 2 Then, 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 fault position secondary nonlinear overdetermined equations 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 filtering R ；
Step five, the filtered line fault position array X R Calculating an average value to obtain a final line fault position;
aiming at the line 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 the method specifically comprises the following steps:
for the line fault position array X, l is the length of the array X, l =60, four line fault positions with the maximum amplitude and the minimum amplitude are respectively eliminated from the line fault position array X, and an array X '= [ X' 1 ，x′ 2 …，x′ m ]M is the length of array X ', m =52, and the average μ of array X' is calculated as:
Figure FDA0004084878200000011
in formula (II), x' τ Is the τ th element in array X';
the standard mean square error σ of the array X' is calculated as:
Figure FDA0004084878200000012
the data within 1 time standard mean square error of an array mean is 68.27% according to the probability distribution principle; judging data except for the data with the standard mean square error of 1 time of the average value of the array as abnormal data or outlier data, and then smoothing the data so as to inhibit the data;
for theH data X in line fault position array X h H is more than or equal to 1 and less than or equal to l if data x h In the interval [ mu-sigma, mu + sigma]Then, the data x is processed h Judging the data to be abnormal data;
for exception data x h Before the index number h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]First three adjacent data x of h-3 、x h-2 、x h-1 After h in the array X is selected, the requirement of [ mu-sigma, mu + sigma ] is satisfied]X is the 1 st adjacent data of v V 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＝(x h-3 +x h-2 +x h-1 +x v )/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 x h 。
CN202210418317.1A 2022-04-20 2022-04-20 Robust fault positioning method for power transmission line Active CN114755530B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210418317.1A CN114755530B (en) 2022-04-20 2022-04-20 Robust fault positioning method for power transmission line

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210418317.1A CN114755530B (en) 2022-04-20 2022-04-20 Robust fault positioning method for power transmission line

Publications (2)

Publication Number Publication Date
CN114755530A CN114755530A (en) 2022-07-15
CN114755530B true CN114755530B (en) 2023-03-28

Family

ID=82331081

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210418317.1A Active CN114755530B (en) 2022-04-20 2022-04-20 Robust fault positioning method for power transmission line

Country Status (1)

Country Link
CN (1) CN114755530B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116520073B (en) * 2023-03-17 2024-01-30 上海交通大学 Fault positioning method for power supply system of submarine observation network

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105652147A (en) * 2015-09-09 2016-06-08 三峡大学 Single/double-circuit power-transmission-line whole-line high-precision fault range finding method
CN113777440A (en) * 2021-08-05 2021-12-10 杭州华辰电力控制工程有限公司 Method for positioning single-phase earth fault of current collection circuit of photovoltaic power station

Family Cites Families (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1289913C (en) * 2003-09-03 2006-12-13 武汉大学 Accurate trouble-locating method for electricity transmission lines with SC
US8514057B2 (en) * 2010-11-16 2013-08-20 Aruba Networks, Inc. Locating devices in a wireless network
US20120310555A1 (en) * 2011-05-31 2012-12-06 Gaarder Paal Even Method and Apparatus for Monitoring Power Transmission in an Electric Power Transmission Network
CN107247215B (en) * 2017-07-14 2019-08-06 国网上海市电力公司 Distribution Network Failure population location algorithm based on Multipoint synchronous measurement data
CN107505534B (en) * 2017-07-14 2020-02-04 国网上海市电力公司 Distribution network fault genetic search positioning method
CN107329045B (en) * 2017-07-14 2020-02-07 国网上海市电力公司 Least square positioning method for distribution network fault
CN107478941B (en) * 2017-07-14 2019-08-06 国网上海市电力公司 Distribution network failure simulated annealing localization method based on Multipoint synchronous measurement data
CN107942202A (en) * 2017-12-28 2018-04-20 国网山东省电力公司济南供电公司 A kind of two ends of electric transmission line Method of Traveling Wave Fault Ranging based on over-determined systems
CN108872792B (en) * 2018-07-16 2019-05-21 西南交通大学 A kind of electric transmission line fault detection method
DE102018211881A1 (en) * 2018-07-17 2020-01-23 Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. Method and device for initial estimation of the movement parameters of a movement model when tracking a moving object with projecting measurements
CN109100614B (en) * 2018-09-28 2021-01-05 东北大学 Power transmission line fault positioning method based on PMU device
CN111257696B (en) * 2020-03-03 2021-05-04 西南交通大学 Estimation-based power transmission line fault detection method under limited PMU
CN111308270B (en) * 2020-03-06 2021-08-17 西南交通大学 Power transmission line fault detection method based on node fault injection current
DE102020107950A1 (en) * 2020-03-23 2021-09-23 Sick Ag Procedure for fault detection and safe sensor system
CN113189402B (en) * 2021-04-27 2023-09-05 国网陕西省电力公司营销服务中心(计量中心) Low-voltage distribution line impedance identification method and system
CN113900046A (en) * 2021-09-30 2022-01-07 国网四川省电力公司南充供电公司 Line zero sequence parameter identification method and device based on wave recording data before and after fault

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105652147A (en) * 2015-09-09 2016-06-08 三峡大学 Single/double-circuit power-transmission-line whole-line high-precision fault range finding method
CN113777440A (en) * 2021-08-05 2021-12-10 杭州华辰电力控制工程有限公司 Method for positioning single-phase earth fault of current collection circuit of photovoltaic power station

Also Published As

Publication number Publication date
CN114755530A (en) 2022-07-15

Similar Documents

Publication Publication Date Title
Pegoraro et al. Line impedance estimation based on synchrophasor measurements for power distribution systems
CN108152675A (en) It is determined and fault zone localization method based on the fault moment of Random Matrices Theory
Ahsaee et al. A novel fault-location algorithm for long transmission lines compensated by series FACTS devices
CN108957225B (en) Direct-current distribution line single-end fault location method considering cable distribution capacitance
CN109523165B (en) Voltage sag state estimation method based on limited information
CN111679158A (en) Power distribution network fault identification method based on synchronous measurement data similarity
CN101349731B (en) Real time evaluating method of voltage stability
CN109387744B (en) Distribution network line fault point positioning method and device based on singular value decomposition
CN106054023B (en) The method of two sides system impedance is estimated in a kind of transmission line of electricity single end distance measurement
CN114755530B (en) Robust fault positioning method for power transmission line
CN102967779A (en) Identifying method of distribution parameters of transmission line
Zhang et al. Time‐domain single‐ended fault location method that does not need remote‐end system information
CN106443253A (en) Power transmission line parameter identification method based on PMU (phasor measurement unit) data
CN108828292B (en) Zinc oxide arrester resistive current online monitoring method considering influence of grounding bar
CN109270406B (en) Method for calculating transition resistance based on double-end asynchronous electrical quantity
Gurusinghe et al. Efficient algorithms for real‐time monitoring of transmission line parameters and their performance with practical synchrophasors
CN111221811A (en) Low-voltage distribution network line parameter estimation method based on centralized meter reading system
CN107505534B (en) Distribution network fault genetic search positioning method
CN107528323B (en) Optimal configuration method of dynamic reactive power compensation device
CN103972889B (en) A kind of distribution line impedance on-line identification method
CN110932755A (en) Distributed low-voltage distribution network line parameter estimation method based on recursive least square method
Davis et al. Estimation of transmission line parameters from historical data
Zhou et al. Fault locating and severity assessment for power distribution systems based on elasticity network topology mapping
CN109375058B (en) Fault line identification method based on multipoint monitoring and current-voltage difference second-order difference
Goklani et al. Quantification of minimum unbalance required for accurate estimation of sequence parameters of transmission line using PMU data

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant