CN109633367B - Power transmission line fault positioning method based on voltage and current changes before and after fault - Google Patents

Power transmission line fault positioning method based on voltage and current changes before and after fault Download PDF

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CN109633367B
CN109633367B CN201811395499.5A CN201811395499A CN109633367B CN 109633367 B CN109633367 B CN 109633367B CN 201811395499 A CN201811395499 A CN 201811395499A CN 109633367 B CN109633367 B CN 109633367B
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fault
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transmission line
line
power transmission
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崔玉
程真何
刘贞瑶
徐皓远
陈轩
梁睿
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Maintenance Branch of State Grid Jiangsu Electric Power Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08Locating faults in cables, transmission lines, or networks
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • YGENERAL 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
    • Y04INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04SSYSTEMS 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
    • Y04S10/00Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y04S10/52Outage or fault management, e.g. fault detection or location

Abstract

The invention discloses a power transmission line fault positioning method based on voltage and current changes before and after a fault. Firstly, a fault location equation is constructed according to a distribution parameter model of the power transmission line, after a fault occurs, positive sequence voltage and positive sequence current variable quantities before and after the fault are calculated by utilizing voltage and current phasor values recorded by PMUs at two ends of the power transmission line, and the positive sequence voltage and the positive sequence current variable quantities are substituted into the constructed fault location equation to calculate the fault position. The method is not influenced by the transition resistance and the initial fault angle, is suitable for various short circuits and ground faults, can effectively determine the fault position when a near bus fault occurs, and has higher precision, reliability and engineering practice significance.

Description

Power transmission line fault positioning method based on voltage and current changes before and after fault
Technical Field
The invention relates to a power transmission line fault positioning method based on voltage and current changes before and after a fault.
Background
The transmission line is used as a core component of the whole power grid, and once a fault occurs, the interruption of power transmission can be caused, so that the normal production and life of people can be seriously influenced. For a long-distance power transmission line, the fault is difficult to find and clear through manual line patrol after the fault occurs, so that the accurate and rapid fault positioning method has important significance for reducing economic loss and improving the system stability.
At present, common transmission line fault positioning methods can be divided into two major categories, namely a traveling wave method and an impedance method. The traveling wave method carries out fault location by detecting the wave head information of fault traveling waves, has very high requirements on the sampling frequency of the traveling wave detection device, and is difficult to be applied in a large scale in an actual power grid. The impedance method is used for solving by deducing a relational expression containing fault distance and system parameters, calculating the fault position, is simple and quick in positioning, can be applied to positioning of various types of faults, can eliminate the influence of fault resistance by utilizing synchronous data at two ends, and has high application value in the field of fault positioning. Therefore, the novel power transmission line fault positioning method with simple research principle, strong practicability and high reliability has important practical significance.
Disclosure of Invention
The invention aims to provide a power transmission line fault positioning method based on voltage and current changes before and after a fault, aiming at the problems in the prior art, and the power transmission line fault positioning can be realized more conveniently and quickly.
In order to achieve the purpose, the invention adopts the technical scheme that:
the power transmission line fault positioning method based on voltage and current changes before and after a fault comprises the following steps:
step 1, establishing a power transmission line distribution parameter model, calculating a propagation coefficient gamma and a characteristic impedance Z of a line, and deducing a fault location equation comprising a fault distance, the propagation coefficient, the characteristic impedance and a double-end electric quantity;
step 2, after a fault is detected on the power transmission line, three-phase voltage and current data recorded by PMUs installed at two ends of the line are respectively extracted
Figure BDA0001875053600000011
And
Figure BDA0001875053600000012
wherein, i is 1, 2, respectively representing before and after fault, M represents line head end, N represents line tail end, and A, B, C represents phase a, phase B, and phase C;
step 3, calculating the positive sequence voltage at two ends of the circuit according to the data in the step 2
Figure BDA0001875053600000013
And positive sequence current
Figure BDA0001875053600000014
A value of (d);
step 4, calculating the variation of voltage and current phasors before and after the fault at two ends of the power transmission line by using the formula (1):
Figure BDA0001875053600000021
Figure BDA0001875053600000022
Figure BDA0001875053600000023
Figure BDA0001875053600000024
wherein the content of the first and second substances,
Figure BDA0001875053600000025
representing the variation of the phasor of the voltage at the head end and the tail end of the line,
Figure BDA0001875053600000026
representing the variation of current phasor at the head end and the tail end of the line;
step 5, substituting the calculation result in the step 4 into the fault location equation deduced in the step 1, and solving the fault distance x1、x2As shown in the formula (2),
Re(A)x1 2+Re(B)x1+Re(C)=0
Im(A)x2 2+Im(B)x2+Im(C)=0 (2)
wherein x is1、x2Represents the distance between the fault point and the line head end M, Re and Im represent the real and imaginary parts, respectively, and
Figure BDA0001875053600000027
Figure BDA0001875053600000028
Figure BDA0001875053600000029
here, L represents the length of the transmission line;
step 6, substituting the preliminary fault distance solved in the step 5 into a formula (3), and selecting a correct fault distance xReAnd xIm
|x1j-x2k|< (3)
Wherein x is1jRepresenting the j solutions, x, obtained by solving the real part equation in step 52kRepresenting k solutions, x, obtained by solving the imaginary part equation in step 5ReRepresenting the correct distance to failure, x, from the real part equationImRepresenting the correct fault distance derived from the imaginary part equation, representing the selection threshold;
and 7, calculating the accurate fault distance X by using the formula (4) according to the selection in the step 6:
Figure BDA00018750536000000210
preferably, in step 1, the step of calculating the propagation coefficient γ and the characteristic impedance Z of the line further includes:
Figure BDA0001875053600000031
Figure BDA0001875053600000032
wherein Z is0Representing the impedance of the line per unit length, Y0Representing the admittance per unit length of the line.
Preferably, in step 1, the step of deriving a fault location equation including a fault distance, a propagation coefficient, a characteristic impedance and a double-ended electrical quantity further includes:
for the power transmission line, a formula for calculating the voltage phasor of any point from two ends of the power transmission line is as follows:
Figure BDA0001875053600000033
Figure BDA0001875053600000034
secondly, when the fault occurs, the positive sequence voltage of the fault point is calculated from the two ends of the line by using the formula (6)
Figure BDA0001875053600000035
Figure BDA0001875053600000036
Figure BDA0001875053600000037
Wherein, L represents the length of the transmission line;
due to the voltage U of the fault point calculated from the two ends of the lineFThe values are equal, resulting in:
Figure BDA0001875053600000038
and similarly, when no fault occurs, for the position x, the voltage calculated from two ends of the line to the position x is equal, and the following results are obtained:
Figure BDA0001875053600000039
the two forms are the same, the parameters are consistent, and the formula (8) and the formula (9) are subtracted to obtain:
Figure BDA00018750536000000310
to simplify the calculation, take the first two terms and the first term for cosh (x) and sinh (x) taylor expansion:
sinh(x)=x
cosh(x)=1+x2 (11)
the simplified hyperbolic sine and cosine functions are substituted into formula (10) and are arranged into a standard form of a unitary quadratic equation, and the real part and the imaginary part of the coefficient A, B, C are respectively taken to obtain a fault location equation:
Re(A)x2+Re(B)x+Re(C)=0
Im(A)x2+Im(B)x+Im(C)=0 (12)
wherein x represents the distance between the fault point and the line head end M, Re and Im represent the real and imaginary parts, respectively, and
Figure BDA0001875053600000041
preferably, in step 3, the step of calculating the positive sequence voltage and the positive sequence current across the line further includes:
Figure BDA0001875053600000042
Figure BDA0001875053600000043
Figure BDA0001875053600000044
wherein a represents an operator, and a-ej120°
Preferably, in step 6, the number j of solutions obtained by the real part equation is 2, and the number k of solutions obtained by the imaginary part equation is 2.
Preferably, in step 6, the value at the time of the selection of the fault distance is taken to be 2 km.
Compared with the prior art, the invention has the beneficial effects that: the invention is not influenced by transition resistance and fault initial angle, is suitable for various short circuit and earth fault on the transmission line, can effectively determine the fault position when the near bus fault occurs, and has higher precision, reliability and engineering practice significance.
Drawings
FIG. 1 is a flow chart of a transmission line fault location method based on voltage and current changes before and after a fault in the present invention;
FIG. 2 is a schematic diagram of a distributed parameter model of the power transmission line of the present invention;
fig. 3 is a schematic diagram of a power transmission line structure according to an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the present invention provides a method for positioning a fault of a power transmission line based on voltage and current changes before and after the fault, which comprises the following steps:
step 1, establishing a power transmission line distribution parameter model shown in fig. 2, calculating a propagation coefficient gamma and a characteristic impedance Z of a line, and deducing a fault location equation containing a fault distance, the propagation coefficient, the characteristic impedance and a double-end electrical quantity.
The method comprises the following specific steps:
calculating a transmission coefficient gamma and a characteristic impedance Z of the power transmission line according to a power transmission line distribution parameter model:
Figure BDA0001875053600000051
Figure BDA0001875053600000052
wherein Z is0Representing the impedance of the line per unit length, Y0Representing the admittance per unit length of the line.
Secondly, based on the distribution parameter model of the power transmission line, a formula for calculating the voltage phasor value of any point from two ends of the line can be deduced as follows:
Figure BDA0001875053600000053
Figure BDA0001875053600000054
wherein M represents the head end of the line, N represents the tail end of the line, and L represents the length of the transmission line.
Thirdly, after the fault occurs, the positive sequence voltage of the fault point is calculated from the two ends of the line by using the formula (6)
Figure BDA0001875053600000055
Figure BDA0001875053600000056
Figure BDA0001875053600000057
Where subscript 2 represents after the failure.
Due to the voltage U of the fault point calculated from the two ends of the lineFThe values are equal, yielding:
Figure BDA0001875053600000058
similarly, when no fault occurs, the voltage calculated from the two ends of the line to the position x is equal for the position x, and the following can be obtained:
Figure BDA0001875053600000061
where the subscript 1 represents before failure occurs.
The equations (8) and (9) have the same form and the parameters are the same, and subtracting the two equations can obtain:
Figure BDA0001875053600000062
wherein the content of the first and second substances,
Figure BDA0001875053600000063
representing the variation of the phasor of the voltage at the head end and the tail end of the line,
Figure BDA0001875053600000064
representing the amount of change in the current phasors at the head end and the tail end of the line.
For simplifying calculation, take the first two terms and the first term respectively by using cosh (x) and sinh (x) Taylor expansion:
sinh(x)=x
cosh(x)=1+x2 (11)
the simplified hyperbolic sine and cosine functions are substituted into formula (10) and are arranged into a standard form of a unitary quadratic equation, and the real part and the imaginary part of the coefficient A, B, C are respectively taken to obtain a fault location equation:
Re(A)x2+Re(B)x+Re(C)=0
Im(A)x2+Im(B)x+Im(C)=0 (12)
wherein x represents the distance between the fault point and the line head end M, Re and Im represent the real and imaginary parts, respectively, and
Figure BDA0001875053600000065
Figure BDA0001875053600000066
Figure BDA0001875053600000067
(2) after a fault is detected on a power transmission line, three-phase voltage and current data recorded by PMUs (Phasor Measurement units) arranged at two ends of the line are respectively extracted
Figure BDA0001875053600000068
And
Figure BDA0001875053600000069
where i is 1 and 2, and represents before and after failure, and A, B, C represents a phase, B phase, and C phase, respectively.
(3) Calculating the positive sequence voltage of the two ends of the line according to the data of the step 2
Figure BDA00018750536000000610
And positive sequence current
Figure BDA00018750536000000611
The value of (c).
Figure BDA0001875053600000071
Figure BDA0001875053600000072
Figure BDA0001875053600000073
Wherein a represents an operator, and a-ej120°
(4) Calculating the variable quantity of voltage and current phasors before and after the fault at two ends of the power transmission line by using the formula (1):
Figure BDA0001875053600000074
Figure BDA0001875053600000075
Figure BDA0001875053600000076
Figure BDA0001875053600000077
wherein the content of the first and second substances,
Figure BDA0001875053600000078
representing the variation of the phasor of the voltage at the head end and the tail end of the line,
Figure BDA0001875053600000079
representing the amount of change in the current phasors at the head end and the tail end of the line.
(5) Substituting the calculation result in the step 4 into a fault positioning equation, and solving the fault distance x1、x2
Re(A)·x1 2+Re(B)·x1+Re(C)=0
Im(A)·x2 2+Im(B)·x2+Im(C)=0 (2)
Wherein x is1、x2Represents the distance between the fault point and the line head end M, Re and Im represent the real and imaginary parts, respectively, and
Figure BDA00018750536000000710
Figure BDA00018750536000000711
Figure BDA00018750536000000712
here, L represents the length of the transmission line.
(6) Substituting the preliminary fault distance solved in the step 5 into a formula (3), and selecting the correct fault distance xReAnd xIm
|x1j-x2k|< (3)
Wherein x is1jRepresents the j solutions obtained by solving the real part equation in step 5, j is 2, x2kRepresents k solutions obtained by solving the imaginary part equation in step 5, k being 2, xReRepresenting the correct distance to failure, x, from the real part equationImRepresenting the correct fault distance from the imaginary equation, and representing the selection threshold, 2 km.
And 7, calculating the accurate fault distance X by using the formula (4) according to the selection in the step 6:
Figure BDA0001875053600000081
examples
And (4) constructing a double-end power transmission line model on the PSCAD/EMTDC, as shown in figure 3. Faults with different fault resistances (10 omega and 200 omega) and different fault types (single-phase grounding and two-phase short circuit) are simulated at different positions of the transmission line, and the total length of the transmission line is 250 km. The fault positioning results obtained by adopting the power transmission line fault positioning method provided by the invention are shown in table 1. In table 1, the fault distance refers to the distance between the fault point and the line head end M, XReRefers to the fault distance, X, solved by the real part equationImReferring to the fault distance solved by the imaginary part equation, the fault positioning error e is defined by the following formula:
Figure BDA0001875053600000082
in the formula (14), X is the solved fault distance, XrFor the true fault distance, L is the length of the transmission line. As can be seen from table 1, the fault location error is not affected by the fault resistance and the fault type, and the location error is less than 1km in each case.
TABLE 1 localization results for different fault resistances and fault types
Figure BDA0001875053600000083
Figure BDA0001875053600000091
The invention discloses a power transmission line fault positioning method based on voltage and current changes before and after a fault. Firstly, a fault location equation is constructed according to a distribution parameter model of the power transmission line, after a fault occurs, positive sequence voltage and positive sequence current variable quantities before and after the fault are calculated by utilizing voltage and current phasor values recorded by PMUs at two ends of the power transmission line, and the positive sequence voltage and the positive sequence current variable quantities are substituted into the constructed fault location equation to calculate the fault position. The method is not influenced by the transition resistance and the initial fault angle, is suitable for various short circuits and ground faults, can effectively determine the fault position when a near bus fault occurs, and has higher precision, reliability and engineering practice significance.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. A power transmission line fault positioning method based on voltage and current changes before and after a fault is characterized by comprising the following steps:
step 1, establishing a power transmission line distribution parameter model, calculating a propagation coefficient gamma and a characteristic impedance Z of a line, and deducing a fault location equation comprising a fault distance, the propagation coefficient, the characteristic impedance and a double-end electric quantity;
step 2, after a fault is detected on the power transmission line, three-phase voltage and current data recorded by PMUs installed at two ends of the line are respectively extracted
Figure FDA0002637899630000011
And
Figure FDA0002637899630000012
wherein, i is 1, 2, respectively representing before and after the fault, M represents the line head end, and A, B, C represents a phase a, a phase B, and a phase C;
step 3, calculating the positive sequence voltage at two ends of the circuit according to the data in the step 2
Figure FDA0002637899630000013
And positive sequence current
Figure FDA0002637899630000014
N represents the line end;
step 4, calculating the variation of voltage and current phasors before and after the fault at two ends of the power transmission line by using the formula (1):
Figure FDA0002637899630000015
Figure FDA0002637899630000016
Figure FDA0002637899630000017
Figure FDA0002637899630000018
wherein the content of the first and second substances,
Figure FDA0002637899630000019
representing the variation of the phasor of the voltage at the head end and the tail end of the line,
Figure FDA00026378996300000110
representing the variation of current phasor at the head end and the tail end of the line;
step 5, substituting the calculation result in the step 4 into the fault location equation deduced in the step 1, and solving the fault distance x1、x2As shown in the formula (2),
Re(A)x1 2+Re(B)x1+Re(C)=0
Im(A)x2 2+Im(B)x2+Im(C)=0 (2)
wherein x is1、x2Represents the distance between the fault point and the line head end M, Re and Im represent the real and imaginary parts, respectively, and
Figure FDA00026378996300000111
Figure FDA00026378996300000112
Figure FDA00026378996300000113
here, L represents the length of the transmission line;
step 6, substituting the preliminary fault distance solved in the step 5 into a formula (3), and selecting a correct fault distance xReAnd xIm
|x1j-x2k|< (3)
Wherein x is1jRepresenting the j solutions obtained by solving the real part equation in step 5,x2kRepresenting k solutions, x, obtained by solving the imaginary part equation in step 5ReRepresenting the correct distance to failure, x, from the real part equationImRepresenting the correct fault distance derived from the imaginary part equation, representing the selection threshold;
and 7, calculating the accurate fault distance X by using the formula (4) according to the selection in the step 6:
Figure FDA0002637899630000021
2. the method for positioning the fault of the power transmission line based on the voltage and current changes before and after the fault according to claim 1, wherein in the step 1, the step of calculating the propagation coefficient γ and the characteristic impedance Z of the line further comprises:
Figure FDA0002637899630000022
Figure FDA0002637899630000023
wherein Z is0Representing the impedance of the line per unit length, Y0Representing the admittance per unit length of the line.
3. The method for positioning the fault of the power transmission line based on the voltage and current changes before and after the fault according to claim 1, wherein in the step 1, the step of deriving a fault positioning equation including a fault distance, a propagation coefficient, a characteristic impedance and a double-ended electrical quantity further comprises:
for the power transmission line, a formula for calculating the voltage phasor of any point from two ends of the power transmission line is as follows:
Figure FDA0002637899630000024
Figure FDA0002637899630000025
secondly, when the fault occurs, the positive sequence voltage of the fault point is calculated from the two ends of the line by using the formula (6)
Figure FDA0002637899630000026
Figure FDA0002637899630000027
Figure FDA0002637899630000028
Wherein, L represents the length of the transmission line;
due to the voltage U of the fault point calculated from the two ends of the lineFThe values are equal, resulting in:
Figure FDA0002637899630000031
and similarly, when no fault occurs, for the position x, the voltage calculated from two ends of the line to the position x is equal, and the following results are obtained:
Figure FDA0002637899630000032
the two forms are the same, the parameters are consistent, and the formula (8) and the formula (9) are subtracted to obtain:
Figure FDA0002637899630000033
to simplify the calculation, take the first two terms and the first term for cosh (x) and sinh (x) taylor expansion:
sinh(x)=x
cosh(x)=1+x2 (11)
the simplified hyperbolic sine and cosine functions are substituted into formula (10) and are arranged into a standard form of a unitary quadratic equation, and the real part and the imaginary part of the coefficient A, B, C are respectively taken to obtain a fault location equation:
Re(A)x2+Re(B)x+Re(C)=0
Im(A)x2+Im(B)x+Im(C)=0 (12)
wherein x represents the distance between the fault point and the line head end M, Re and Im represent the real and imaginary parts, respectively, and
Figure FDA0002637899630000034
4. the method for positioning the fault of the power transmission line based on the voltage and current changes before and after the fault according to claim 1, wherein in the step 3, the step of calculating the positive sequence voltage and the positive sequence current at the two ends of the line further comprises the steps of:
Figure FDA0002637899630000035
wherein a represents an operator, and a-ej120°
5. The method for locating the fault of the power transmission line based on the voltage and current changes before and after the fault according to claim 1, wherein in the step 6, the number j of solutions obtained by a real part equation is 2, and the number k of solutions obtained by an imaginary part equation is 2.
6. The method for locating the fault of the power transmission line based on the voltage and current changes before and after the fault according to claim 1, wherein in the step 6, the value is taken as 2km when the fault distance is selected.
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