CN116256597A - Time domain fault distance measurement method and system for high-voltage transmission line - Google Patents

Time domain fault distance measurement method and system for high-voltage transmission line Download PDF

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CN116256597A
CN116256597A CN202310260599.1A CN202310260599A CN116256597A CN 116256597 A CN116256597 A CN 116256597A CN 202310260599 A CN202310260599 A CN 202310260599A CN 116256597 A CN116256597 A CN 116256597A
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transmission line
equation
voltage
line
matrix
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党三磊
杨路
张鼎衢
王岩
宋强
胡珊珊
黄智坤
谢东
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Guangdong Power Grid Co Ltd
Measurement Center of Guangdong Power Grid Co Ltd
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Guangdong Power Grid Co Ltd
Measurement Center of Guangdong Power Grid Co Ltd
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    • 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
    • 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
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/085—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution lines, e.g. overhead
    • 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
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y04S10/52—Outage or fault management, e.g. fault detection or location

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Abstract

The invention discloses a time domain fault distance measurement method and a time domain fault distance measurement system for a high-voltage power transmission line, wherein the method comprises the steps of obtaining and establishing a power transmission line telegram equation according to a line structure and power transmission line parameters of the high-voltage power transmission line; carrying out differential discretization on a telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation; performing matrix transformation on the first-order differential equation to obtain a matrix form equation, and performing space integral transformation on the matrix form equation to obtain a space integral equation; and measuring the position of the fault point of the high-voltage transmission line according to synchronous measurement information and a space integral equation at two ends of the fault line by using the principle of voltage continuity along the transmission line. The embodiment realizes the efficient determination of the fault point position, is not influenced by the calculation conditions such as differential format, step length and the like, and has high ranging precision.

Description

Time domain fault distance measurement method and system for high-voltage transmission line
Technical Field
The invention relates to the field of fault location of high-voltage transmission lines, in particular to a time domain fault location method and a time domain fault location system of a high-voltage transmission line.
Background
High-voltage transmission lines are pulse-striking of the power system, are also the place where the most faults occur in the power system, and are extremely difficult to find. Fault location is the inspection of a high-voltage transmission line, also known as fault location, and refers to determining the location of a fault point. The fault point is found rapidly and accurately after the line fault, so that the method has very important effects on timely repairing the line and ensuring reliable power supply, and safety, stability and economic operation of the power system, and the rapid and accurate distance measurement method for the power transmission line fault is one of the research hot spots of the power system.
The fault distance measuring method of the power transmission line mainly comprises a frequency domain method, a traveling wave method and a time domain method at present, wherein the frequency domain method is simple and reliable, but is easily influenced by factors such as transition resistance, sampling frequency and line symmetry, and the measuring precision is difficult to guarantee. The traveling wave method is not influenced by the transition resistance, the distance measurement precision is higher, but the wave head is difficult to accurately extract, the wave speed is difficult to accurately determine, and the equipment is expensive, so that the application is limited; the time domain rule is to establish a calculus equation in a time domain containing fault information according to a circuit theory by utilizing transient state information when a line is in fault, and calculate the fault position of the power transmission line by carrying out differential calculation on the calculus equation in the time domain, but the calculation accuracy and stability are greatly affected by differential format and step length, are affected by calculation conditions, have no stability, and cannot be ensured.
Disclosure of Invention
The time domain fault location method and the time domain fault location system for the high-voltage transmission line provided by the invention realize efficient determination of the fault point position, are not influenced by calculation conditions such as differential format, step length and the like, and have high location precision.
In order to solve the technical problems, an embodiment of the present invention provides a time domain fault location method for a high-voltage transmission line, including:
acquiring and establishing a transmission line telegraph equation according to the line structure and the transmission line parameters of the high-voltage transmission line;
carrying out differential discretization on a telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation;
performing matrix transformation on the first-order differential equation to obtain a matrix form equation, and performing space integral transformation on the matrix form equation to obtain a space integral equation;
and measuring the position of the fault point of the high-voltage transmission line according to synchronous measurement information and a space integral equation at two ends of the fault line by using the principle of voltage continuity along the transmission line.
By implementing the embodiment of the invention, a power transmission line telegraph equation is established according to the line structure and the power transmission line parameters of the high-voltage power transmission line and the power transmission line distribution parameter model; carrying out differential discretization on a telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation; performing matrix transformation on the first-order differential equation to obtain a matrix form equation, and performing space integral transformation on the matrix form equation to obtain a space integral equation; and according to the synchronous measurement information and a space integral equation at two ends of the fault line, solving the fault point position of the high-voltage transmission line by using the principle of voltage continuity along the transmission line. The first-order differential equation after differential discretization is subjected to matrix conversion and space integral conversion, and the fault point position of the high-voltage transmission line is obtained according to synchronous measurement information at two ends of the fault line, so that the method is not influenced by calculation conditions such as differential format, step length and the like, the algorithm is unconditionally stable, the stability is realized, the ranging precision is high, the calculation efficiency is high, and the fault point position is efficiently measured.
As a preferred scheme, a power transmission line telegraph equation is obtained and established according to the line structure and the power transmission line parameters of the high-voltage power transmission line, and the method specifically comprises the following steps:
acquiring a power transmission line distribution parameter model of a high-voltage power transmission line, and determining a line structure and power transmission line parameters according to the power transmission line distribution parameter model; wherein the transmission line parameters include transmission line length, resistance, inductance, conductance, and capacitance;
according to the line structure and the transmission line parameters, a transmission line telegraph equation is established, and the formula is as follows:
Figure BDA0004131086240000021
Figure BDA0004131086240000022
where u (x, t) is the power line voltage at position x at time t, i (x, t) is the power line current at position x at time t, R is the resistance per unit length of the power line, L is the inductance per unit length of the power line, G is the conductance per unit length of the power line, C is the capacitance per unit length of the power line, and L is the power line length.
As a preferred scheme, the telegraph equation of the transmission line is subjected to differential discretization in a time domain, and a first-order differential equation is established, which is specifically as follows:
according to known parameter conditions, carrying out differential discretization on a telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation, wherein the formula is as follows:
Figure BDA0004131086240000031
Figure BDA0004131086240000032
wherein Δt is the time step, u k ＝u(x,kΔt)，i k =i (x, kΔt), k is the number of calculation steps, k=0, 1,2, … M;
the known parameter conditions are:
u(x,0)＝h 1 (x)
i(x,0)＝h 2 (x)
u(0,t)＝u s (t)
i(l,t)＝F 2 [u(l,t)]
wherein h is 1 (x) For the transmission line voltage at position x at time t=0, h 2 (x) For the transmission line current at position x at time t=0, u s (t) input voltage at position x=0, F 2 [u(l,t)]For the line current at time t at position x=l, l is the line end of the line.
As a preferred scheme, the first-order differential equation is subjected to matrix transformation to obtain a matrix form equation, which specifically comprises the following steps:
carrying out matrix transformation on the power transmission line voltage and the power transmission line current to obtain a first matrix, wherein the formula is as follows:
X＝(u 1 ，…u M ，i 1 ，…i M ) T
wherein X is a first matrix;
carrying out matrix transformation on the inductance of the unit length of the power transmission line, the power transmission line current, the capacitance of the unit length of the power transmission line and the power transmission line voltage to obtain a second matrix, wherein the formula is as follows:
Figure BDA0004131086240000033
wherein F is a second matrix;
and (3) carrying out matrix transformation on the transmission line parameters to obtain a third matrix, wherein the formula is as follows:
Figure BDA0004131086240000041
wherein H is a third matrix;
according to the first matrix, the second matrix and the third matrix, converting the first-order differential equation into a matrix form to obtain a matrix form equation, wherein the method specifically comprises the following steps:
Figure BDA0004131086240000042
as a preferred scheme, space integral conversion is performed on the matrix form equation to obtain a space integral equation, which specifically comprises:
according to differential equation theory, performing integral conversion on the matrix form equation to obtain a first equation; the first equation is specifically:
Figure BDA0004131086240000043
wherein H is a third matrix, and X is a first matrix;
according to the length and the equal division of the power transmission line, calculating the space step length, wherein the formula is as follows:
λ＝l/M
wherein lambda is the space step length, M is the equal division and l is the length of the transmission line;
according to the space step length, an equal step length space point is obtained, specifically:
x j ＝jλ,j＝0,1,2,L
according to the space points with equal step length, carrying out space transformation on the first equation to obtain a second equation; wherein the second equation is specifically:
Figure BDA0004131086240000051
when the preset condition is met, carrying out equation conversion on the second equation to obtain a space integral equation; the space integral equation is specifically:
Figure BDA0004131086240000052
as a preferred scheme, the fault point position of the high-voltage transmission line is measured according to synchronous measurement information and a space integral equation at two ends of the fault line by a voltage continuity principle along the transmission line, specifically:
synchronously acquiring a measured value of a starting end of a fault line and a measured value of an end of the fault line, substituting and solving a space integral equation, and respectively calculating a first line voltage and a second line voltage; the starting end measured value comprises a voltage value of the starting end and a current value of the starting end, and the tail end measured value comprises a voltage value of the tail end and a current value of the tail end;
and measuring the fault point position of the high-voltage transmission line according to the principle of voltage continuity along the transmission line, the first line voltage and the second line voltage.
As a preferred scheme, according to the principle of voltage continuity along the transmission line, the first line voltage and the second line voltage, the fault point position of the high-voltage transmission line is measured, specifically:
according to the characteristic that voltages at fault points are equal, calculating a position function when the voltage value of the first line and the voltage value of the second line are equal, wherein the formula is as follows:
δ＝|U mn (x,t)-U nm (x 1 ,t)|
wherein delta is a position x position function, U mn (x, t) is the first line voltage, U nm (x 1 T) is a second line voltage;
and deriving the position function, and calculating the position point of the position function when the minimum value of the position function is calculated to obtain the position of the fault point of the high-voltage transmission line.
In order to solve the same technical problem, the embodiment of the invention also provides a time domain fault distance measurement system of the high-voltage transmission line, which comprises: the system comprises a telegraph equation module, a differential equation module, a space integral equation module and a position solving module;
the telegram equation module is used for acquiring and establishing a telegram equation of the power transmission line according to the line structure and the power transmission line parameters of the high-voltage power transmission line;
the differential equation module is used for carrying out differential dispersion on the telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation;
the space integral equation module is used for carrying out matrix transformation on the first-order differential equation to obtain a matrix form equation, and carrying out space integral transformation on the matrix form equation to obtain a space integral equation;
the position solving module is used for measuring the position of the fault point of the high-voltage transmission line according to synchronous measurement information and a space integral equation at two ends of the fault line through the principle of voltage continuity along the transmission line.
Preferably, the space integral equation module comprises a matrix conversion unit and a space integral conversion unit;
the matrix transformation unit is used for performing matrix transformation on the first-order differential equation to obtain a matrix form equation, and specifically comprises the following steps:
carrying out matrix transformation on the power transmission line voltage and the power transmission line current to obtain a first matrix, wherein the formula is as follows:
X＝(u 1 ，…u M ，i 1 ，…i M ) T
wherein X is a first matrix;
carrying out matrix transformation on the inductance of the unit length of the power transmission line, the power transmission line current, the capacitance of the unit length of the power transmission line and the power transmission line voltage to obtain a second matrix, wherein the formula is as follows:
Figure BDA0004131086240000061
wherein F is a second matrix;
and (3) carrying out matrix transformation on the transmission line parameters to obtain a third matrix, wherein the formula is as follows:
Figure BDA0004131086240000062
wherein H is a third matrix;
according to the first matrix, the second matrix and the third matrix, converting the first-order differential equation into a matrix form to obtain a matrix form equation, wherein the method specifically comprises the following steps:
Figure BDA0004131086240000071
the space integral conversion unit is used for carrying out integral conversion on the matrix form equation according to the differential equation theory to obtain a first equation; the first equation is specifically:
Figure BDA0004131086240000072
wherein H is the third matrix and X is the first matrix;
according to the length and the equal division of the power transmission line, calculating the space step length, wherein the formula is as follows:
λ＝l/M
wherein lambda is the space step length, M is the equal division and l is the length of the transmission line;
according to the space step length, an equal step length space point is obtained, specifically:
x j ＝jλ,j＝0,1,2,L s
according to the space points with equal step length, carrying out space transformation on the first equation to obtain a second equation; wherein the second equation is specifically:
Figure BDA0004131086240000073
when the preset condition is met, carrying out equation conversion on the second equation to obtain a space integral equation; the space integral equation is specifically:
Figure BDA0004131086240000074
as a preferred scheme, the solving position module comprises a synchronous measuring unit and a fault point determining unit;
the synchronous measurement unit is used for synchronously collecting a measured value of a starting end of a fault line and a measured value of an end of the fault line, substituting and solving a space integral equation, and respectively calculating a first line voltage and a second line voltage; the starting end measured value comprises a voltage value of the starting end and a current value of the starting end, and the tail end measured value comprises a voltage value of the tail end and a current value of the tail end;
the fault point determining unit is used for calculating a position function when the voltage value of the first line and the voltage value of the second line are equal according to the characteristic that the voltages at the fault points are equal, and the formula is as follows:
δ＝|U mn (x,t)-U nm (x 1 ,t)|
wherein delta is a position x position function, U mn (x, t) is the first line voltage, U nm (x 1 T) is a second line voltage;
and deriving the position function, and calculating the position point of the position function when the minimum value of the position function is calculated to obtain the fault point position of the high-voltage transmission line.
Drawings
Fig. 1: the method is a flow diagram of one embodiment of a time domain fault location method of a high-voltage transmission line;
fig. 2: the invention provides a power transmission line distribution parameter model diagram of an embodiment of a time domain fault distance measuring method of a high-voltage power transmission line;
fig. 3: the invention provides a power transmission fault line diagram of one embodiment of a time domain fault location method of a high-voltage power transmission line;
fig. 4: the invention provides a structural schematic diagram of an embodiment of a time domain fault distance measuring system of a high-voltage transmission line.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
Referring to fig. 1, a flow chart of a time domain fault location method for a high voltage transmission line according to an embodiment of the present invention is shown. The time domain fault distance measurement method is suitable for the high-voltage transmission line, the transmission line telegraph equation is converted into the space integral equation through fine integration, the fault point position of the high-voltage transmission line is effectively measured, the influence of calculation conditions such as differential format and step length is avoided, and the distance measurement precision is high. The time domain fault location method comprises steps 101 to 104, wherein the steps are as follows:
step 101: and acquiring and establishing a transmission line telegraph equation according to the line structure and the transmission line parameters of the high-voltage transmission line.
In the embodiment, a telegraph equation of the power transmission line is established based on a power transmission line distribution parameter model according to the line structure and the power transmission line parameters of the high-voltage power transmission line.
Optionally, step 101 includes obtaining a power transmission line distribution parameter model of a high-voltage power transmission line, and determining a line structure and power transmission line parameters according to the power transmission line distribution parameter model; wherein the transmission line parameters include transmission line length, resistance, inductance, conductance, and capacitance;
according to the line structure and the transmission line parameters, a transmission line telegraph equation is established, and the formula is as follows:
Figure BDA0004131086240000091
Figure BDA0004131086240000092
where u (x, t) is the power line voltage at position x at time t, i (x, t) is the power line current at position x at time t, R is the resistance per unit length of the power line, L is the inductance per unit length of the power line, G is the conductance per unit length of the power line, C is the capacitance per unit length of the power line, and L is the power line length.
In this embodiment, as shown in fig. 2, in the power transmission line distribution parameter model, R is a resistance of a unit length of a power transmission line, L is an inductance of a unit length of the power transmission line, G is a conductance of a unit length of the power transmission line, C is a capacitance of a unit length of the power transmission line, and L is a length of the power transmission line. The telegraph equation for the power line is the following:
Figure BDA0004131086240000093
Figure BDA0004131086240000094
where u (x, t) is the power line voltage at position x at time t and i (x, t) is the power line current at position x at time t. u and i are functions of space x and time t.
Step 102: and carrying out differential discretization on the telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation.
In this embodiment, the opposite telegraph equation is differentially discretized in the time domain, and a first-order differential equation of the space is established.
Optionally, step 102 specifically includes performing differential discretization on a telegraph equation of the power transmission line in a time domain according to a known parameter condition, and establishing a first-order differential equation, where the formula is as follows:
Figure BDA0004131086240000101
Figure BDA0004131086240000102
wherein Δt is the time step, u k ＝u(x,kΔt)，i k =i (x, kΔt), k is the number of calculation steps, k=0, 1,2, … M;
the known parameter conditions are:
u(x,0)＝h 1 (x)
i(x,0)＝h 2 (x)
u(0,t)＝u s (t)
i(l,t)＝F 2 [u(l,t)]
wherein h is 1 (x) A transmission line voltage at the time t=0 for the position x, i.e. a voltage at the time t=0 for the transmission line at the position x; h is a 2 (x) For the transmission line current at time t=0 for position x, i.e.Current of the transmission line at the time t=0 at the position x; u (u) s (t) is the input voltage at position x=0, i.e. at x=0; f (F) 2 [u(l,t)]For the transmission line current at the time t at the position x=l, i.e. the current at the time t at the position x=l (line end), l is the line end of the transmission line.
Step 103: and performing matrix transformation on the first-order differential equation to obtain a matrix form equation, and performing space integral transformation on the matrix form equation to obtain a space integral equation.
In this embodiment, by solving the differential equation, the voltage and current values at any point along the power transmission line at any time can be obtained.
Optionally, the first-order differential equation is subjected to matrix transformation to obtain a matrix equation, which specifically comprises the following steps:
carrying out matrix transformation on the power transmission line voltage and the power transmission line current to obtain a first matrix, wherein the formula is as follows:
X＝(u 1 ，…u M ，i 1 ，…i M ) T
wherein X is a first matrix;
carrying out matrix transformation on the inductance of the unit length of the power transmission line, the power transmission line current, the capacitance of the unit length of the power transmission line and the power transmission line voltage to obtain a second matrix, wherein the formula is as follows:
Figure BDA0004131086240000103
wherein F is a second matrix;
and (3) carrying out matrix transformation on the transmission line parameters to obtain a third matrix, wherein the formula is as follows:
Figure BDA0004131086240000111
wherein H is a third matrix;
according to the first matrix, the second matrix and the third matrix, converting the first-order differential equation into a matrix form to obtain a matrix form equation, wherein the method specifically comprises the following steps:
Figure BDA0004131086240000112
optionally, space integral conversion is performed on the matrix form equation to obtain a space integral equation, which specifically includes:
according to differential equation theory, performing integral conversion on the matrix form equation to obtain a first equation; the first equation is specifically:
Figure BDA0004131086240000113
wherein H is a third matrix, and X is a first matrix;
according to the length and the equal division of the power transmission line, calculating the space step length, wherein the formula is as follows:
λ＝l/M
wherein lambda is the space step length, M is the equal division and l is the length of the transmission line;
according to the space step length, an equal step length space point, namely a series of space points with equal step length lambda, is obtained, specifically:
x j ＝jλ,j＝0,1,2,L
according to the equal step space point, the first equation is spatially transformed to obtain a second equation, and when x=jλ, the second equation specifically comprises:
Figure BDA0004131086240000114
when the preset condition is met, carrying out equation conversion on the second equation to obtain a space integral equation; the space integral equation is specifically:
Figure BDA0004131086240000121
in the present embodiment, the preset condition is x j <x≤x j+1 When x is j <x≤x j+1 When the second equation performs the equation conversion process, the equation conversion process is:
Figure BDA0004131086240000122
step 104: and measuring the position of the fault point of the high-voltage transmission line according to synchronous measurement information and a space integral equation at two ends of the fault line by using the principle of voltage continuity along the transmission line.
In this embodiment, the position of the fault point is obtained according to the principle of voltage continuity along the transmission line by using the synchronous measurement information at both ends of the fault line.
Optionally, step 104 includes steps 1041 to 1042, where each step is specifically as follows:
step 1041: synchronously acquiring a measured value of a starting end of a fault line and a measured value of an end of the fault line, substituting and solving a space integral equation, and respectively calculating a first line voltage and a second line voltage; the initial end measured value comprises a voltage value of the initial end and a current value of the initial end, and the terminal end measured value comprises a voltage value of the terminal end and a current value of the terminal end.
In this embodiment, the voltage and current values along the line of the power transmission line based on the measured data at both ends can be calculated by using the synchronous measurement information at both ends of the fault line (refer to the voltage value u (0, t) and the current value i (0, t) at the line start x=0, and the voltage value u (l, t) and the current value i (l, t) at the line end x=l). As shown in fig. 3, when a fault occurs at the point F, the voltage and current values are synchronously collected at the M end and the N end of the transmission line. Acquiring data of an M end and an N end, and respectively solving a first line voltage U at any point on an MF section and an NF section at any moment according to a space integral equation mn (x, t) and a second line voltage U nm (x 1 T), x is the distance from the point on the MF segment of the line to the M end, x 1 Is the distance of the point on the line NF segment from the N-terminal. Since there is a short-circuit current at the fault, the line voltage-current distribution calculated from the M-point voltage-current value is correct in the MF segment and incorrect in the FN segment; similarly, from the N point voltageThe line voltage current distribution calculated by the current value is correct in the NF section and incorrect in the MF section.
Step 1042: and measuring the fault point position of the high-voltage transmission line according to the principle of voltage continuity along the transmission line, the first line voltage and the second line voltage.
In this embodiment, according to the principle of voltage continuity along the transmission line, the positions of the fault points can be obtained by calculating the voltages along the transmission line from the measured data at the two ends of the line, where the voltages are equal at the fault points.
Optionally, step 1042 is specifically: according to the characteristic that voltages at fault points are equal, calculating a position function when the voltage value of the first line and the voltage value of the second line are equal, wherein the formula is as follows:
δ＝|U mn (x,t)-U nm (x 1 ,t)|
wherein delta is a position x position function, U mn (x, t) is the first line voltage, U nm (x 1 T) is a second line voltage;
and deriving the position function, and calculating the position point of the position function when the minimum value of the position function is calculated to obtain the position of the fault point of the high-voltage transmission line.
In this embodiment, according to the principle of continuity of the transmission line voltage, only at the fault point F, there are the following cases:
U mn (x,t)＝U nm (x 1 ,t)
let δ be the difference between the first line voltage and the second line voltage, i.e.:
δ＝|U mn (x,t)-U nm (x 1 ,t)|
delta is a function of the position x, and in theory delta is 0 at the fault point, and the existence of calculation errors which are unavoidable in actual engineering is a small value. The fault point can be determined by deriving x when determining the delta minimum.
By implementing the embodiment of the invention, a transmission line telegraph equation is established according to a transmission line distribution parameter model of the high-voltage transmission line; carrying out differential discretization on a telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation; performing matrix transformation on the first-order differential equation to obtain a matrix form equation, and performing space integral transformation on the matrix form equation to obtain a space integral equation; and according to the synchronous measurement information and a space integral equation at two ends of the fault line, solving the fault point position of the high-voltage transmission line by using the principle of voltage continuity along the transmission line.
The first-order differential equation after differential discretization is subjected to matrix conversion and space integral conversion, and the fault point position of the high-voltage transmission line is obtained according to synchronous measurement information at two ends of the fault line, so that the method is not influenced by calculation conditions such as differential format, step length and the like, the algorithm is unconditionally stable, the stability is realized, the ranging precision is high, the calculation efficiency is high, and the fault point position is efficiently measured.
Example two
Correspondingly, referring to fig. 4, fig. 4 is a schematic structural diagram of a second embodiment of a time domain fault location system of a high-voltage transmission line according to the present invention. As shown in fig. 4, the time domain fault distance measurement system of the high-voltage transmission line comprises a telegram equation module 401, a differential equation module 402, a space integral equation module 403 and a solution position module 404;
the telegram equation module 401 is configured to acquire and establish a telegram equation of the power transmission line according to the line structure and the power transmission line parameters of the high-voltage power transmission line;
the differential equation module 402 is configured to perform differential discretization on a telegraph equation of the power transmission line in a time domain, and establish a first-order differential equation;
the space integral equation module 403 is configured to perform matrix transformation on the first-order differential equation to obtain a matrix equation, and perform space integral transformation on the matrix equation to obtain a space integral equation;
the spatial integral equation module 403 includes a matrix conversion unit 4031 and a spatial integral conversion unit 4032;
the matrix transformation unit 4031 is configured to perform matrix transformation on the first-order differential equation to obtain a matrix equation, which specifically is:
carrying out matrix transformation on the power transmission line voltage and the power transmission line current to obtain a first matrix, wherein the formula is as follows:
X＝(u 1 ，…u M ，i 1 ，…i M ) T
wherein X is a first matrix;
carrying out matrix transformation on the inductance of the unit length of the power transmission line, the power transmission line current, the capacitance of the unit length of the power transmission line and the power transmission line voltage to obtain a second matrix, wherein the formula is as follows:
Figure BDA0004131086240000141
wherein F is a second matrix;
and (3) carrying out matrix transformation on the transmission line parameters to obtain a third matrix, wherein the formula is as follows:
Figure BDA0004131086240000151
/>
wherein H is a third matrix;
according to the first matrix, the second matrix and the third matrix, converting the first-order differential equation into a matrix form to obtain a matrix form equation, wherein the method specifically comprises the following steps:
Figure BDA0004131086240000152
the space integral conversion unit 4032 is configured to perform integral conversion on the matrix equation according to the differential equation theory, so as to obtain a first equation; the first equation is specifically:
Figure BDA0004131086240000153
wherein H is the third matrix and X is the first matrix;
according to the length and the equal division of the power transmission line, calculating the space step length, wherein the formula is as follows:
λ＝l/M
wherein lambda is the space step length, M is the equal division and l is the length of the transmission line;
according to the space step length, an equal step length space point is obtained, specifically:
x j ＝jλ,j＝0,1,2,L
according to the space points with equal step length, carrying out space transformation on the first equation to obtain a second equation; wherein the second equation is specifically:
Figure BDA0004131086240000154
when the preset condition is met, carrying out equation conversion on the second equation to obtain a space integral equation; the space integral equation is specifically:
Figure BDA0004131086240000161
the solving position module 404 is used for measuring the position of the fault point of the high-voltage transmission line according to the synchronous measurement information and the space integral equation at the two ends of the fault line by using the principle of voltage continuity along the transmission line.
The solution position module 404 includes a synchronous measurement unit 4041 and a failure point determination unit 4042;
the synchronous measurement unit 4041 is configured to collect a measured value of a start end of a fault line and a measured value of an end of the fault line synchronously, and substitute and solve a space integral equation to calculate a first line voltage and a second line voltage respectively; the starting end measured value comprises a voltage value of the starting end and a current value of the starting end, and the tail end measured value comprises a voltage value of the tail end and a current value of the tail end;
the fault point determining unit 4042 is configured to calculate a location function when the first line voltage value and the second line voltage value are equal according to the characteristic that voltages at the fault points are equal, where the formula is:
δ＝|U mn (x,t)-U nm (x 1 ,t)|
wherein delta is a position x position function, U mn (x, t) is the first line voltage, U nm (x 1 T) is the firstVoltage along the second line;
and deriving the position function, and calculating the position point of the position function when the minimum value of the position function is calculated to obtain the fault point position of the high-voltage transmission line.
The time domain fault location system of the high-voltage transmission line can implement the time domain fault location method of the high-voltage transmission line in the method embodiment. The options in the method embodiments described above are also applicable to this embodiment and will not be described in detail here. The rest of the embodiments of the present application may refer to the content of the method embodiments described above, and in this embodiment, no further description is given.
The frequency domain method is simple and reliable, but the measurement accuracy is difficult to guarantee. The traveling wave method is not affected by the transition resistance, but the wave head is difficult to accurately extract and the wave speed is difficult to accurately determine, and the application is limited due to expensive equipment. The accuracy and stability of the computation are greatly affected by the differential format and the computation step size by the conventional time domain method. The time domain fault distance measuring system of the high-voltage transmission line based on the fine integration method is a time domain semi-analytic method, has the characteristics of unconditional stability of an algorithm, high distance measuring precision and the like, is not limited in application, and can be widely popularized and used.
The foregoing embodiments have been provided for the purpose of illustrating the general principles of the present invention, and are not to be construed as limiting the scope of the invention. It should be noted that any modifications, equivalent substitutions, improvements, etc. made by those skilled in the art without departing from the spirit and principles of the present invention are intended to be included in the scope of the present invention.

Claims (10)

1. A time domain fault location method for a high voltage transmission line, comprising:
acquiring and establishing a transmission line telegraph equation according to the line structure and the transmission line parameters of the high-voltage transmission line;
performing differential discretization on the telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation;
performing matrix transformation on the first-order differential equation to obtain a matrix form equation, and performing space integral transformation on the matrix form equation to obtain a space integral equation;
and measuring the position of the fault point of the high-voltage transmission line according to synchronous measurement information at two ends of the fault line and the space integral equation by using the principle of voltage continuity along the transmission line.
2. The time domain fault location method of high voltage transmission line according to claim 1, wherein the obtaining and establishing a transmission line telegram equation according to the line structure and transmission line parameters of the high voltage transmission line specifically comprises:
acquiring a power transmission line distribution parameter model of the high-voltage power transmission line, and determining the line structure and the power transmission line parameters according to the power transmission line distribution parameter model; wherein the transmission line parameters include transmission line length, resistance, inductance, conductance, and capacitance;
according to the line structure and the power transmission line parameters, a power transmission line telegraph equation is established, and the formula is as follows:
Figure FDA0004131086230000011
Figure FDA0004131086230000012
where u (x, t) is the power line voltage at position x at time t, i (x, t) is the power line current at position x at time t, R is the resistance per unit length of the power line, L is the inductance per unit length of the power line, G is the conductance per unit length of the power line, C is the capacitance per unit length of the power line, and L is the power line length.
3. The time domain fault location method of high voltage transmission line according to claim 2, wherein the differential discrete is performed on the transmission line telegraph equation in the time domain, and a first order differential equation is established, specifically:
according to known parameter conditions, carrying out differential discretization on the telegraph equation of the power transmission line in a time domain, and establishing the first-order differential equation, wherein the formula is as follows:
Figure FDA0004131086230000021
Figure FDA0004131086230000022
wherein Δt is the time step, u k ＝u(x,kΔt)，i k =i (x, kΔt), k is the number of calculation steps, k=0, 1,2, … M;
the known parameter conditions are:
u(x,0)＝h 1 (x)
i(x,0)＝h 2 (x)
u(0,t)＝u s (t)
i(l,t)＝F 2 [u(l,t)]
wherein h is 1 (x) For the transmission line voltage at position x at time t=0, h 2 (x) For the transmission line current at position x at time t=0, u s (t) is the input voltage at the position x=0, F 2 [u(l,t)]For the line current at time t at position x=l, l is the line end of the line.
4. The time domain fault location method of high voltage transmission line according to claim 3, wherein the first order differential equation is transformed into a matrix form equation, specifically:
and performing matrix transformation on the power transmission line voltage and the power transmission line current to obtain a first matrix, wherein the formula is as follows:
X＝(u 1 ，…u M ，i 1 ，…i M ) T
wherein X is the first matrix;
and performing matrix transformation on the inductance of the unit length of the power transmission line, the power transmission line current, the capacitance of the unit length of the power transmission line and the power transmission line voltage to obtain a second matrix, wherein the formula is as follows:
Figure FDA0004131086230000023
wherein F is the second matrix;
and performing matrix transformation on the transmission line parameters to obtain a third matrix, wherein the formula is as follows:
Figure FDA0004131086230000031
wherein H is the third matrix;
according to the first matrix, the second matrix and the third matrix, the first-order differential equation is converted into a matrix form to obtain a matrix form equation, specifically:
Figure FDA0004131086230000032
5. the time domain fault location method of high voltage transmission line according to claim 4, wherein the performing space integral conversion on the matrix equation to obtain a space integral equation is specifically:
according to differential equation theory, carrying out integral conversion on the matrix form equation to obtain a first equation; wherein, the first equation is specifically:
Figure FDA0004131086230000033
wherein H is the third matrix and X is the first matrix;
according to the length and the equal division of the power transmission line, calculating a space step length, wherein the formula is as follows:
λ＝l/M
wherein lambda is the space step length, M is the equal fraction, and l is the length of the transmission line;
according to the space step length, an equal step length space point is obtained, specifically:
x j ＝jλ,j＝0,1,2,L
according to the equal step space points, performing space transformation on the first equation to obtain a second equation; wherein the second equation is specifically:
Figure FDA0004131086230000034
/>
when a preset condition is met, carrying out equation conversion on the second equation to obtain the space integral equation; the space integral equation is specifically:
Figure FDA0004131086230000041
6. the time domain fault location method of high voltage transmission line according to claim 1, wherein the fault point position of the high voltage transmission line is measured according to the synchronous measurement information at two ends of the fault line and the space integral equation by using the principle of voltage continuity along the transmission line, specifically:
synchronously collecting a measured value of a starting end of the fault line and a measured value of an end of the fault line, substituting and solving the space integral equation, and respectively calculating a first line voltage and a second line voltage; the starting end measured value comprises a voltage value of the starting end and a current value of the starting end, and the tail end measured value comprises a voltage value of the tail end and a current value of the tail end;
and measuring the fault point position of the high-voltage transmission line according to the principle of the voltage continuity of the transmission line along the line, the first line voltage and the second line voltage.
7. The time domain fault location method of a high voltage transmission line according to claim 6, wherein the fault point location of the high voltage transmission line is measured according to a principle of continuity of voltage along the transmission line, the first voltage along the line and the second voltage along the line, specifically:
according to the characteristic that voltages on fault points are equal, calculating a position function when the voltage value of the first line and the voltage value of the second line are equal, wherein the formula is as follows:
δ＝|U mn (x,t)-U nm (x 1 ,t)|
wherein delta is the position function of position x, U mn (x, t) is the first line voltage, U nm (x 1 T) is the second line voltage;
and deriving the position function, and calculating a position point when the position function is minimum to obtain the position of the fault point of the high-voltage transmission line.
8. A time domain fault location system for a high voltage transmission line, comprising: the system comprises a telegraph equation module, a differential equation module, a space integral equation module and a position solving module;
the telegraph equation module is used for acquiring and establishing a telegraph equation of the power transmission line according to the line structure and the power transmission line parameters of the high-voltage power transmission line;
the differential equation module is used for carrying out differential dispersion on the telegraph equation of the power transmission line in a time domain, and establishing a first-order differential equation;
the space integral equation module is used for carrying out matrix transformation on the first-order differential equation to obtain a matrix form equation, and carrying out space integral transformation on the matrix form equation to obtain a space integral equation;
the position solving module is used for measuring the position of the fault point of the high-voltage transmission line according to the synchronous measurement information at the two ends of the fault line and the space integral equation through the principle of voltage continuity along the transmission line.
9. The time domain fault location system of a high voltage transmission line according to claim 8, wherein the spatial integral equation module comprises a matrix conversion unit and a spatial integral conversion unit;
the matrix transformation unit is used for performing matrix transformation on the first-order differential equation to obtain a matrix equation, and specifically comprises the following steps:
and performing matrix transformation on the power transmission line voltage and the power transmission line current to obtain a first matrix, wherein the formula is as follows:
X＝(u 1 ，…u M ，i 1 ，…i M ) T
wherein X is the first matrix;
and performing matrix transformation on the inductance of the unit length of the power transmission line, the power transmission line current, the capacitance of the unit length of the power transmission line and the power transmission line voltage to obtain a second matrix, wherein the formula is as follows:
Figure FDA0004131086230000051
wherein F is the second matrix;
and performing matrix transformation on the transmission line parameters to obtain a third matrix, wherein the formula is as follows:
Figure FDA0004131086230000061
wherein H is the third matrix;
according to the first matrix, the second matrix and the third matrix, the first-order differential equation is converted into a matrix form to obtain a matrix form equation, specifically:
Figure FDA0004131086230000062
the space integral conversion unit is used for carrying out integral conversion on the matrix form equation according to the differential equation theory to obtain a first equation; wherein, the first equation is specifically:
Figure FDA0004131086230000063
wherein H is the third matrix and X is the first matrix;
according to the length and the equal division of the power transmission line, calculating a space step length, wherein the formula is as follows:
λ＝l/M
wherein lambda is the space step length, M is the equal fraction, and l is the length of the transmission line;
according to the space step length, an equal step length space point is obtained, specifically:
x j ＝jλ,j＝0,1,2,L
according to the equal step space points, space s transformation is carried out on the first equation, and a second equation is obtained; wherein the second equation is specifically:
Figure FDA0004131086230000064
when a preset condition is met, carrying out equation conversion on the second equation to obtain the space integral equation; the space integral equation is specifically:
Figure FDA0004131086230000071
10. the time domain fault location system of high voltage transmission line according to claim 8, wherein the solution location module comprises a synchronous measurement unit and a fault point determination unit;
the synchronous measurement unit is used for synchronously collecting a measured value of a starting end of the fault line and a measured value of an end of the fault line, substituting and solving the space integral equation, and respectively calculating a first line voltage and a second line voltage; the starting end measured value comprises a voltage value of the starting end and a current value of the starting end, and the tail end measured value comprises a voltage value of the tail end and a current value of the tail end;
the fault point determining unit is used for calculating a position function when the voltage value of the first line and the voltage value of the second line are equal according to the characteristic that the voltages on the fault points are equal, and the formula is as follows:
δ＝|U mn (x,t)-U nm (x 1 ,t)|
wherein delta is the position function of position x, U mn (x, t) is the first line voltage, U nm (x 1 T) is the second line voltage;
and deriving the position function, and calculating a position point when the position function is minimum to obtain the fault point position of the high-voltage transmission line.
CN202310260599.1A 2023-03-17 2023-03-17 Time domain fault distance measurement method and system for high-voltage transmission line Pending CN116256597A (en)

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