CN114371361A - Power transmission line single-end fault location method based on multivariate model fusion analysis - Google Patents

Power transmission line single-end fault location method based on multivariate model fusion analysis Download PDF

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CN114371361A
CN114371361A CN202111283974.1A CN202111283974A CN114371361A CN 114371361 A CN114371361 A CN 114371361A CN 202111283974 A CN202111283974 A CN 202111283974A CN 114371361 A CN114371361 A CN 114371361A
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fitting
fault distance
model
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李斌
胡泽鹏
何佳伟
姚斌
盛亚如
谢仲润
王文博
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Tianjin University
Xian Jiaotong University
NARI Group Corp
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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    • 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
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Abstract

The invention discloses a power transmission line single-end fault location method based on multivariate model fusion analysisq(1)Calculating the voltage and current to a new initial point x by using a Bergeron modelq(1)And (4) calculating the fault distance x by using the lumped parameter model fitting again based on the voltage and the current at the new calculation starting pointq(2)The final fault distance x is obtainedq＝xq(1)+xq(2). Compared with the prior art, the method can reduce the distance measurement error of the concentrated parameter line model caused by neglecting the line distributed capacitance.

Description

Power transmission line single-end fault location method based on multivariate model fusion analysis
Technical Field
The invention relates to the field of relay protection of power systems, in particular to a power transmission line single-end fault location algorithm based on multivariate model fusion and maximum error estimation
Background
With the development of national economy, the demand of long-distance and large-range power transmission is increased, and meanwhile, high-voltage power transmission lines are widely distributed, and the terrain of passing through areas is complex and changeable. The fault location is rapidly and accurately carried out after the transmission line has a fault, so that the fault is rapidly repaired, the stability of a power system is improved, and the fault location method is also very important for normal operation of national economy.
The single-ended impedance method for fault location only needs to measure information of one end of the power transmission line, and has the advantages of low requirement on hardware, easiness in implementation, stable algorithm and the like, so that the method is widely applied. The traditional fault location uses a line model based on centralized parameters, and when the fault location is applied to a longer power transmission line, the influence of line distributed capacitance becomes non-negligible, and a larger error is caused to the remote fault location precision. Therefore, it is very important to research a fault location model and algorithm suitable for long lines and improve the accuracy of fault location.
Disclosure of Invention
Based on the prior art, the invention provides a power transmission line single-end fault location method based on multivariate model fusion analysis, a time domain equation set is constructed based on the lumped parameter line model to fit and calculate the fault distance, and the final fault distance is obtained.
The invention is realized by the following technologies:
a power transmission line single-end fault location method based on multivariate model fusion analysis specifically comprises the following steps:
step 1: estimating the fault distance by a lumped parameter line model, wherein:
based on a lumped parameter line model, a difference equation of the fault phase voltage and the fault phase current which are continuously acquired by the protection device and are within the length of a unit data window is arranged into a matrix form:
U＝Iβ
and solving and calculating to obtain a fault distance x calculated by unit data window fitting, wherein a fault distance solving expression is as follows:
β＝(ITI)-1ITU，β＝[x R'F]T
wherein x is fault distance, U is fault phase voltage matrix, I is fault phase current matrix, beta is coefficient matrix to be solved, and R'FEquivalent transition resistance;
step 2: judging whether the fitting calculation reaches a steady state;
and step 3: after the steady state is reached, calculating to obtain a current fault distance calculation value xnDetermining a new calculation starting point x by considering the margin corresponding to the maximum model errorq(1)The expression is as follows:
Figure BDA0003332151570000021
wherein k isxIs a margin coefficient, xnFor steady state calculation results of fault location based on lumped parameter line models, Ecmax(ω,x,RF) Is an error calculation formula generated by neglecting distributed capacitance, wherein Y ═ r1+jωl1，W＝jωc1，RFRepresenting a transition resistance value, taking a maximum value according to the actual system condition, wherein omega is frequency;
and 4, step 4: calculating the voltage and the current from the protective installation position to the starting point x by using a Bergeron modelq(1)；
And 5: based on a new calculation starting point xq(1)Calculating the fault distance by using the lumped parameter line model;
step 6: judging whether the fitting calculation enters a steady state again;
and 7: after the fitting calculation is judged to reach the steady state, a fault distance calculation result x is obtained based on the new calculation starting pointq(2)；
And 8: finally obtaining a fault distance calculation result xq＝xq(1)+xq(2)。
Compared with the prior art, the power transmission line single-end fault location method based on the multivariate model and the maximum error has the following beneficial effects:
1) the distance measurement error generated by neglecting the line distributed capacitance of the line model with the centralized parameters can be reduced;
2) the influence of the line distributed capacitance can be almost ignored, and the fault location accuracy of the long-distance transmission line is greatly improved.
Drawings
Fig. 1 is a flowchart of a transmission line single-ended fault location method based on multivariate model fusion analysis.
Fig. 2 is a schematic diagram of a single-ended fault of a power transmission line.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a power transmission line single-end fault location algorithm based on multivariate model fusion analysis, which comprises the steps of firstly estimating and solving a fault distance through a time domain equation based on a lumped parameter line model, determining a new calculation starting point by considering a certain margin under the condition that the maximum location error range caused by distributed capacitance is ignored in an accurate estimation lumped model after judging that fitting calculation enters a steady state, calculating voltage and current at a protection installation position to the new starting point through the distributed parameter line model, and solving the fault distance of a power transmission line based on the lumped parameter line model based on the new starting point to obtain a final fault distance.
As shown in fig. 1, which is a flowchart of a power transmission line single-ended fault location method based on multivariate model fusion analysis of the present invention, firstly, parameter identification calculation is performed on sampled data based on a lumped parameter line model; after the stable state of the fitting calculation is judged, the fault distance is estimated and solved through a time domain equation, and the fault distance value x corresponding to the current sampling sequence n is calculatednUnder the condition of accurately estimating the maximum range error range of the centralized model caused by neglecting distributed capacitance, a certain margin is considered to determine a new calculation starting point xq(1)(ii) a Calculating the voltage and the current from the fault protection position to the starting point x by using a Bergeron modelq(1)(ii) a Base ofAt the new calculation starting point xq(1)Calculating the fault distance by using the lumped parameter line model; judging again that the fitting calculation enters a steady state, and obtaining a calculation starting point x based on a new valueq(2)Obtaining a fault distance result of xq＝xq(1)+xq(2)。
Fig. 2 is a schematic diagram of a single-ended fault of a power transmission line. A single-phase earth fault occurs at line F, r0、l0Zero sequence resistance and inductance, r, respectively, per unit length of the line1、l1Resistance and inductance, R, respectively, per unit length of the lineFTo transition resistance, iFX is the fault distance for the current flowing through the transition resistance.
Step 1: estimating a fault distance through a centralized parameter line model; wherein:
taking the occurrence of a single-phase earth fault as an example, the fault phase (a-phase) voltage u of discrete sampled data at the installation site is protectedmA(n)) is represented by the following formula:
umA(n)＝[(imA(n)+3krim0(n))r1+(imA(n+1)+3krim0(n+1)-imA(n-1)-3krim0(n-1))l1/(2Δt)]x+im0(n)R'F (1)
wherein n is a sampling sequence, delta t is a sampling interval, R'F＝CFRF，CFTo protect the zero sequence shunt coefficient of the installation, umA(n) the faulted phase voltage of the sampling sequence n, imA(n)、imA(n +1) are the fault phase current of the sampling sequence n and the fault phase current of the sampling sequence n +1 respectively,i m0(n)、im0(n +1) is the fault phase zero sequence current of the sampling sequence n and the fault phase zero sequence current of the sampling sequence n +1, Kr＝(ro-r1)/3r1、Kl＝(lo-l1)/3l1Are respectively a resistance zero sequence compensation coefficient and an inductance zero sequence compensation coefficient, R'FEquivalent transition resistance;
selecting a certain data window length, and organizing a difference equation of the fault phase voltage and the fault phase current acquired by the protection device within the unit data window length into a matrix form, wherein the expression is as follows:
U＝Iβ (2)
wherein:
U＝[umA(n-k+1),umA(n-k+2),...umA(n)]T
Figure BDA0003332151570000051
β＝[x R'F]T
p(n)＝imA(n)+3kri0(n)
pd(n)＝[imA(n+1)+3kli0(n+1)-imA(n-1)-3kli0(n-1)]/(2Δt)
wherein U is a fault phase voltage matrix, I is a fault phase current matrix, p (n) is a current sampling sequence, and pd(n) is a current sampling point differential derivative sequence; t represents matrix transposition; k is the number of sampling points used for fitting calculation in a unit data window, and beta is a coefficient matrix; the coefficient matrix β is expressed as follows:
β＝(ITI)-1ITU (3)
wherein, ITTransposing a matrix for fault phase current;
in combination with the formula:
β＝(ITI)-1ITU，β＝[x R'F]T (4)(5)
solving and calculating to obtain a fault distance x and an equivalent transition resistance R 'calculated by unit data window fitting'F；
Step 2, judging whether the fitting calculation reaches a steady state;
judging whether the fitting calculation enters a steady state or not according to the stability of the calculation result, wherein the specific judgment method comprises the following steps:
define the fit error within the unit data window as:
Figure BDA0003332151570000052
continuously performing fitting calculation on the protection sampling data by adopting a sliding data window to obtain a sequence E of fitting errorsr＝[Er(1),Er(2),…,Er(Cn)]，CnSolving the C < th > of the fault distance for the current time-domain differential equationnCalculating a result of the secondary fitting;
the value of the fitting error reflects the stability of the differential equation in the fitting calculation unit data window, when the transient process is severe, the differential equation cannot be stably solved, the fitting error is large, and when the calculation starts to enter a stable state, the fitting error approaches zero; the invention takes whether the value of the fitting error is continuously smaller than the threshold value in the set data window as the judgment whether the fitting calculation enters the steady state:
Er(i)＜Er(set),i＝Cn,Cn-1,…,Cn-nw (7)
wherein n iswFitting times to account for the calculated continuity;
step 3, after the steady state is reached, calculating to obtain a fault distance value x corresponding to the current sampling sequence nnCombined with a certain margin to determine a new calculation starting point xq(1)The expression is as follows:
Figure BDA0003332151570000061
wherein k isxIs a margin coefficient, xnFor steady state calculation results of fault location based on lumped parameter line models, Ecmax(ω,x,RF) Is an error calculation formula generated by neglecting distributed capacitance, wherein Y ═ r1+jωl1，W＝jωc1，RFRepresents a transition resistance value, omega is a frequency;
determining measurements based on lumped parameter single-ended ranging generated by ignoring distributed capacitance based on line parameter and theoretical derivationRange to error; the voltage at any point x on the line can be calculated by the long line equation and can be determined by the voltage at the protective installation
Figure BDA0003332151570000062
Electric current
Figure BDA0003332151570000063
And calculating to obtain:
Figure BDA0003332151570000064
wherein γ is the propagation coefficient, ZcIs the line wave impedance;
taylor first order expansion of the above formula at x ═ 0 yields:
Figure BDA0003332151570000065
wherein R is2(x) The lagrange residue for the taylor first order expansion is shown as follows:
Figure BDA0003332151570000066
when formula (7) ignores the Lagrange remainder and transforms to the time domain, the lagrangian remainder is the time domain lumped parameter line equation, namely, only the resistance and the inductance of the transmission line are considered, the distributed capacitance of the line is ignored, and R can be known2(x) Namely, is the source of error in the lumped parameter line model;
the exact fault distance is calculated as follows:
Figure BDA0003332151570000071
wherein:
Figure BDA0003332151570000072
Figure BDA0003332151570000073
therefore, the method comprises the following steps:
xCALC-xCALC_1≤xCALC_2
therefore, the calculation error with the maximum fault distance of the lumped parameter line model is xCALC_2(ii) a Due to R2(x) In
Figure BDA0003332151570000074
Failure to determine an accurate value, resulting in xCALC_2An accurate calculated value cannot be obtained, but the voltage between the head end of the line and a fault point can be known through the derivation process of the Lagrange remainder term, so that the voltage is satisfied
Figure BDA0003332151570000075
Thus x can be obtainedCALC_2The value range of (a) is shown as the following formula:
Figure BDA0003332151570000076
wherein Z ismFor apparent impedance of the head end of the line, the equivalent gamma model of the transmission line is ZmExpressed as:
Figure BDA0003332151570000077
substituting the formula into the formula (8) and finishing to obtain an expression of the maximum error:
Figure BDA0003332151570000078
wherein, Y ═ r1+jωl1，W＝jωc1；
Obtaining a ranging error expression generated by neglecting distributed capacitance in single-ended ranging based on the centralized parameters, and calculating the maximum range of the distributed capacitance error in real time according to the actual line parameters and the actual engineering condition constraints;
step 4, calculating the voltage and the current from the fault protection position to the starting point x by utilizing a Bergeron modelq(1)Finally obtaining a fault distance measurement result;
taking the single-phase system as an example, um、imIn order to protect the voltage and current at the installation site, x is the distance from one point of the line to the protection installation site of the line, and then the voltage and current at the point can be calculated by the voltage and current at the protection installation site:
Figure BDA0003332151570000081
in the above formula:
Figure BDA0003332151570000082
Figure BDA0003332151570000083
Figure BDA0003332151570000084
wherein D ise(τ) is the delay factor, i.e., f (t + τ) ═ De(τ) f (τ), τ x/v, v is the wave velocity,
Figure BDA0003332151570000085
is the wave impedance of the lossless line; x can be calculated by combining phase-mode transformationqThe voltage current at (c);
step 5, based on the new calculation starting point xq(1)Calculating the fault distance by using the lumped parameter line model;
step 6, judging whether the fitting calculation enters a stable state again;
and 7, judging that the calculation reaches the steady state based on xqThe line fault distance at the moment is solved through a time-domain differential equation, and when the calculation result reaches the steady-state judgment of the formula (2), the calculation result x of the fault distance at the moment based on a new calculation starting point is obtainedq(2)；
Step 8, obtaining a fault distance result as xq＝xq(1)+xq(2)。
It should be noted that the invention is not limited to the above-mentioned method steps and calculation procedures, the above-mentioned embodiments are only illustrative and not restrictive, and those skilled in the art can make various changes and modifications in the invention without departing from the spirit and scope of the invention as claimed.

Claims (2)

1. A power transmission line single-end fault location method based on multivariate model fusion analysis is characterized by specifically comprising the following steps:
step 1: estimating the fault distance by a lumped parameter line model, wherein:
based on a lumped parameter line model, a difference equation of the fault phase voltage and the fault phase current which are continuously acquired by the protection device and are within the length of a unit data window is arranged into a matrix form:
U＝Iβ
and solving and calculating to obtain a fault distance x calculated by unit data window fitting, wherein a fault distance solving expression is as follows:
β＝(ITI)-1ITU，β＝[x R'F]T
wherein x is fault distance, U is fault phase voltage matrix, I is fault phase current matrix, beta is coefficient matrix to be solved, and R'FEquivalent transition resistance;
step 2: judging whether the fitting calculation reaches a steady state;
and step 3: after the steady state is reached, calculating to obtain a current fault distance calculation value xnDetermining a new calculation starting point x by considering the margin corresponding to the maximum model errorq(1)The expression is as follows:
Figure FDA0003332151560000011
wherein k isxIs a margin coefficient, xnFor steady state calculation results of fault location based on lumped parameter line models, Ecmax(ω,x,RF) Is an error calculation formula generated by neglecting distributed capacitance, wherein Y ═ r1+jωl1，W＝jωc1，RFRepresenting a transition resistance value, taking a maximum value according to the actual system condition, wherein omega is frequency;
and 4, step 4: calculating the voltage and the current from the protective installation position to the starting point x by using a Bergeron modelq(1)；
And 5: based on a new calculation starting point xq(1)Calculating the fault distance by using the lumped parameter line model;
step 6: judging whether the fitting calculation enters a steady state again;
and 7: after the fitting calculation is judged to reach the steady state, a fault distance calculation result x is obtained based on the new calculation starting pointq(2)；
And 8: finally obtaining a fault distance calculation result xq＝xq(1)+xq(2)。
2. The power transmission line single-ended fault location method based on the multivariate model and the maximum error as claimed in claim 1, wherein whether the calculation result reaches a steady state is judged according to the real-time fitting calculation result of the fault distance, and the specific steps are as follows:
define the fit error within the unit data window as:
Figure FDA0003332151560000021
by sampling the protectionContinuously fitting and calculating the data by adopting a sliding data window to obtain a sequence E of fitting errorsr＝[Er(1),Er(2),…,Er(Cn)]，CnSolving the C < th > of the fault distance for the current time-domain differential equationnCalculating a result of the secondary fitting;
when the transient process is violent, the differential equation can not obtain a stable solution, the fitting error is large, and the fitting error approaches zero after the calculation starts to enter a stable state; and (3) judging whether the value of the fitting error is continuously smaller than a threshold value in a set data window as whether the fitting calculation enters a steady state:
Er(i)＜Er(set),i＝Cn,Cn-1,…,Cn-nw
wherein, CnSolving the C < th > of the fault distance for the current time-domain differential equationnThe result of the sub-fitting calculation, nwTo account for the number of fits that calculate continuity.
CN202111283974.1A 2021-11-01 2021-11-01 Power transmission line single-end fault location method based on multivariate model fusion analysis Pending CN114371361A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115508671A (en) * 2022-11-10 2022-12-23 国网天津市电力公司电力科学研究院 Fault positioning method and system based on line voltage lowest point calculation

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115508671A (en) * 2022-11-10 2022-12-23 国网天津市电力公司电力科学研究院 Fault positioning method and system based on line voltage lowest point calculation
CN115508671B (en) * 2022-11-10 2023-03-28 国网天津市电力公司电力科学研究院 Fault positioning method and system based on line voltage lowest point calculation

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