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 PDFInfo
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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
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- 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
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- 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
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
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 extractedAndwherein, 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 2And positive sequence currentA 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):
wherein the content of the first and second substances,representing the variation of the phasor of the voltage at the head end and the tail end of the line,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
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:
preferably, in step 1, the step of calculating the propagation coefficient γ and the characteristic impedance Z of the line further includes:
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:
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)
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:
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:
the two forms are the same, the parameters are consistent, and the formula (8) and the formula (9) are subtracted to obtain:
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
preferably, in step 3, the step of calculating the positive sequence voltage and the positive sequence current across the line further includes:
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:
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:
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)
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:
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:
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:
wherein the content of the first and second substances,representing the variation of the phasor of the voltage at the head end and the tail end of the line,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
(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 extractedAnd
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 2And positive sequence currentThe value of (c).
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):
wherein the content of the first and second substances,representing the variation of the phasor of the voltage at the head end and the tail end of the line,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
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:
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:
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
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 extractedAndwherein, 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 2And positive sequence currentN 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):
wherein the content of the first and second substances,representing the variation of the phasor of the voltage at the head end and the tail end of the line,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
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:
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:
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:
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)
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:
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:
the two forms are the same, the parameters are consistent, and the formula (8) and the formula (9) are subtracted to obtain:
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
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:
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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CN110133444A (en) * | 2019-06-05 | 2019-08-16 | 国网江苏省电力有限公司检修分公司 | A kind of Fault Locating Method based on positive sequence voltage variable quantity, apparatus and system |
CN110988594B (en) * | 2019-12-06 | 2022-04-08 | 国网上海市电力公司 | Power distribution network fault position determining method and determining device |
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CN113156266A (en) * | 2021-04-16 | 2021-07-23 | 华中科技大学 | Power distribution network fault positioning method based on voltage distribution and traveling wave characteristics along line |
CN113433417B (en) * | 2021-05-08 | 2022-06-14 | 湖南大学 | Power distribution network fault positioning method and system based on measured voltage difference |
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