CN112698147A - Power line fault point positioning method based on instantaneous phase consistency - Google Patents

Power line fault point positioning method based on instantaneous phase consistency Download PDF

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CN112698147A
CN112698147A CN202011394682.0A CN202011394682A CN112698147A CN 112698147 A CN112698147 A CN 112698147A CN 202011394682 A CN202011394682 A CN 202011394682A CN 112698147 A CN112698147 A CN 112698147A
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phase
voltage
current
fault point
fault
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CN112698147B (en
Inventor
张捷
罗建
何建军
谢兵
肖波
张洪涛
吴松麟
朱彬
杨凌
周玉宇
李怀政
吕培庚
韦嘉
唐启军
刘蕾
余渌绿
曾彦珺
杨帆
康宇轩
邹刚
尹颢涵
秦涛
王珊
龙文
谢清宇
刘海龙
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Chongqing University
State Grid Corp of China SGCC
Chongqing City Power Supply Co of State Grid Chongqing Electric Power Co Ltd
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Chongqing University
State Grid Corp of China SGCC
Chongqing City Power Supply Co of State Grid Chongqing Electric Power 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
    • G01R31/081—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
    • 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
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/52—Testing for short-circuits, leakage current or ground faults
    • 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
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/58—Testing of lines, cables or conductors
    • 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 provides a power line fault point positioning method based on instantaneous phase consistency, which comprises the following steps: determining a search step length, and generating a plurality of fault points to be determined in a fault circuit; respectively establishing constraint relations of transient voltage and current phase consistency on the transition resistor aiming at different line fault types based on transient voltage and current phase consistency on the short circuit transition resistor; and (4) calculating the instantaneous phase consistency of the voltage current on the transition resistor of each fault point to be determined one by one, wherein the fault point to be determined with the highest consistency is the determined fault point. The positioning method can position the fault points of the power line layer by layer, is effective and reliable, and can accurately position simple short-circuit faults of the power electronic grid.

Description

Power line fault point positioning method based on instantaneous phase consistency
Technical Field
The invention relates to the field of electrical engineering, in particular to a power line fault point positioning method based on instantaneous phase consistency.
Background
The power line is one of the most important elements in the power system, and plays a role in transmitting and distributing electric energy, and meanwhile, the power line is the most concentrated link of fault occurrence in the power system. With increasingly complex structures of power systems, uncertain factors of power grid operation increase, and difficulty in locating fault points of power lines also gradually increases. The existing power line fault point positioning method mainly comprises a traveling wave method and a fault analysis method. However, the traveling wave method has high requirements on the sampling rate of the device, and is easily affected by the network structure, the bus connection mode, the fault type, the transition resistance and the like. Compared with a traveling wave method, the fault analysis method has low requirement on the sampling rate and strong adaptability, can adopt data at any time interval after the fault without being limited to a traveling wave head, and is more beneficial to automatic realization. However, the conventional common fault analysis method mostly adopts double-ended or single-ended power frequency fault components and centralized line parameters, and cannot fundamentally avoid the influence of transition resistance. In addition, due to the existence of a large number of power electronic devices in the power grid, in the fault transient process of the power grid, the current magnitude and the phase are related to the control mode and the current limiting measure of the power electronic devices, and the traditional fault analysis method is not easy to process transient data in a short window.
Disclosure of Invention
In view of the deficiencies in the prior art, it is an object of the present invention to address one or more of the problems in the prior art as set forth above. For example, it is an object of the present invention to provide a method for determining a power line fault point that is efficient and reliable.
In order to achieve the above object, the present invention provides a power line fault point location method based on instantaneous phase consistency, which may include the following steps: determining a search step length, and generating a plurality of fault points to be determined on a fault line; respectively establishing constraint relations of transient voltage and current phase consistency on the transition resistor aiming at different line fault types based on transient voltage and current phase consistency on the short circuit transition resistor; and (4) calculating the instantaneous phase consistency of the voltage current on the transition resistor of each fault point to be determined one by one, wherein the fault point to be determined with the highest consistency is the determined fault point.
Compared with the prior art, the invention has the beneficial effects that: the positioning method is simple, convenient, quick, effective and reliable, and can accurately position simple short-circuit faults of the power electronic grid.
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The above and other objects and features of the present invention will become more apparent from the following description taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a diagram illustrating a distribution of points of fault to be determined in accordance with an exemplary embodiment of the present invention based on an instantaneous phase-aligned power line point of fault localization method;
FIG. 2 is a schematic diagram illustrating an A-phase single-phase ground fault in an exemplary embodiment of a power line fault location method based on instantaneous phase alignment according to the present invention;
FIG. 3 illustrates an B, C two-phase short circuit fault schematic diagram of an exemplary embodiment of a power line fault point location method based on instantaneous phase alignment according to the present invention;
FIG. 4 illustrates an B, C two-phase ground fault diagram of an exemplary embodiment of a power line fault location method based on instantaneous phase alignment according to the present invention;
fig. 5 shows an A, B, C three-phase ground fault diagram of an exemplary embodiment of the power line fault point location method based on instantaneous phase alignment of the present invention.
Detailed Description
Hereinafter, a power line fault point locating method based on instantaneous phase coincidence according to the present invention will be described in detail with reference to the accompanying drawings and exemplary embodiments.
Fig. 1 shows a distribution diagram of fault points to be determined according to an exemplary embodiment of the power line fault point locating method based on instantaneous phase consistency. Fig. 2 is a schematic diagram of an a-phase single-phase ground fault according to an exemplary embodiment of the power line fault location method based on instantaneous phase alignment. Fig. 3 shows B, C two-phase short circuit fault diagram of an exemplary embodiment of the power line fault point location method based on instantaneous phase alignment according to the present invention. Fig. 4 shows B, C two-phase ground fault diagram of an exemplary embodiment of the power line fault point location method based on instantaneous phase alignment according to the present invention. Fig. 5 shows an A, B, C three-phase ground fault diagram of an exemplary embodiment of the power line fault point location method based on instantaneous phase alignment of the present invention.
Specifically, the positioning method of the invention is based on the principle of transient phase consistency of transient voltage and current on the short circuit transition resistor for positioning. The fault transient voltage across the transition resistor is in phase with the current, "phase" refers to the instantaneous phase that is changing over time and remains the same. The fault point is determined on the basis of the fact that no instantaneous phase constraint exists at the non-fault point of the fault line.
Provided with a pair of voltages u having a phase-constrained relationshipR(t) and a current iR(t), which can be represented sinusoidally as:
Figure BDA0002814287840000031
in the formula of UR(t)、IR(t) represents the instantaneous magnitudes of the voltage and current, respectively, and has:
Figure BDA0002814287840000032
Figure BDA0002814287840000036
the instantaneous initial phases of the voltage and the current are respectively as follows according to the triangle identity transformation:
Figure BDA0002814287840000033
wherein A isuR(t)、BuR(t) and AiR(t)、BiR(t) coefficient polynomials resulting from the voltage current fitting and the sinusoidal representation, respectively. The instantaneous initial phase coincidence can be expressed as:
Figure BDA0002814287840000034
the tangent is calculated on both sides of the above equation, and the relationship of the instantaneous phase coincidence can also be expressed as:
Figure BDA0002814287840000035
the invention provides a power line fault point positioning method based on instantaneous phase consistency. In an exemplary embodiment of the power line fault point locating method based on instantaneous phase consistency of the present invention, the locating method may include:
s01, determining a search step length, and generating a plurality of fault points to be determined on a fault line;
s02, respectively establishing constraint relations of transient phase consistency of the transient voltage and the current on the transition resistor aiming at different line fault types based on the transient phase consistency of the transient voltage and the current on the short circuit transition resistor;
and S03, calculating the instantaneous phase consistency of the voltage current on the transition resistance of each fault point to be determined one by one, wherein the fault point to be determined with the highest consistency is the determined fault point.
In this embodiment, for S01, specifically, an enumeration method may be used to determine an appropriate enumeration step Δ S as needed, and obtain a series of fault points S to be determined in a fault linej(j ═ 1,2,3 …), as shown in fig. 1. SfIs SjTo determine a point of failure, M, N represents the two ends of the line. And verifying each fault point to be determined one by one, and verifying whether the transient phase consistency constraint relation is met on the transition resistance of the fault point to be determined, wherein the fault point to be determined with the highest consistency is the determined fault point.
In this embodiment, the different line fault types include a single-phase ground short fault, a two-phase ground short fault, and a three-phase ground short fault. For each fault type, the fault point can be determined separately by the following method.
For a single-phase short-circuit fault, as shown in fig. 2, phase a is assumed to be grounded (of course, any phase may be grounded). The three-phase voltages u at the theoretical fault point F can be obtained through the electrical quantity and the line parameters of the M, N terminalFa(t)、uFb(t) and uFc(t) three-phase currents are iFa(t)、iFb(t) and iFc(t)，uFa(t) and iFa(t) denotes A-phase voltage and current, uFb(t) and iFb(t) represents the B-phase voltage and current, uFc(t) and iFc(t) represents a C-phase voltage and a current. i.e. iFaM(t) shows phase A current from one end M of the line at the theoretical fault point F, iFaN(t) represents phase a current from one end N of the line at the theoretical fault point F. Phase A transition resistance Ra(t) the voltage and current are uFa(t)、iFa(t), representing its sine:
Figure BDA0002814287840000041
wherein, UFa(t)、IFa(t) represents the instantaneous magnitudes of the voltage and current respectively,
Figure BDA0002814287840000043
for an instantaneous initial phase, AuFa(t)、BuFa(t) and AiFa(t)、BiFa(t) respectively represent coefficient polynomials of the voltage-current sinusoidal expression.
According to the formulae (4) and (5), the A-phase transition resistance RaThe instantaneous phase constraint relationship on (t) is expressed as:
Figure BDA0002814287840000042
the theoretical fault point F is a constraint relation which theoretically completely meets transient voltage and current transient phase consistency on the transition resistor at the fault point F. However, in an actual application process, on one hand, the influence of errors between items, calculation accuracy and the like needs to be considered, and on the other hand, the generated fault point to be determined may not coincide with the actually occurring fault point, and the generated fault point to be determined may be in the vicinity of the actually occurring fault point, so that the fault point to be determined may not fully satisfy equation (7). Based on this, the determination of the failure point may be performed according to a criterion function, i.e. the criterion function may be:
f(Sj)＝|AuSja(t)·BiSja(t)-AiSja(t)·BuSja(t)| (8)
wherein S isjTo generateTo determine any of the fault points, AuSja(t)、BuSja(t) and AiSja(t)、BiSja(t) points S of failure to be determinedjThe fitted sine of the voltage and current at the transition resistance represents the resulting coefficient polynomial.
The criterion function f (S)j) The point corresponding to the minimum value is determined as the fault point, i.e. the point
f(Sf)＝min(f(Sj)) (j＝1,2,3...) (9)
Point SfI.e. the final determined failure point.
For a two-phase short fault, assume B, C phases are shorted as shown in FIG. 3. The three-phase voltage at the theoretical fault point F is uFa(t)、uFb(t) and uFc(t) three-phase current is iFa(t)、iFb(t) and iFc(t)。iFbM(t) represents phase B current from one end M of the line at theoretical fault point F, iFbN(t) represents phase B current from one end N of the line at the theoretical fault point F. i.e. iFcM(t) C-phase current from one end M of the line at the theoretical fault point F, iFcN(t) represents the phase C current from one end N of the line at the theoretical fault point F. B, C interphase transition resistance R added at theoretical fault point FbcVoltage u on (t)Rbc(t) current iRbc(t) are respectively:
Figure BDA0002814287840000051
will voltage uRbc(t) current iRbc(t) written as a sine expression:
Figure BDA0002814287840000052
wherein u isFb(t)、uFc(t) represents the b-phase and c-phase voltages of the transition resistance at the theoretical fault point F, iFb(t) represents the transition resistance b phase current at the theoretical fault point F, the b phase is any phase in the three-phase circuit, AuRbc(t)、BuRbc(t) and AiRbc(t)、BiRbc(t) respectively represent coefficient polynomials of the voltage-current sinusoidal expression.
Transition resistance RbcThe constraint relation of the instantaneous phase consistency of the voltage and the current exists in (t):
Figure BDA0002814287840000053
according to a constraint relation (12) of voltage and current instantaneous phase consistency, a criterion function is established as follows:
Figure BDA0002814287840000054
similarly, each fault point to be determined is calculated by using the formula (13), and the fault point to be determined corresponding to the obtained minimum value is the determined fault point.
For a two-phase ground fault, as shown in fig. 4, assume B, C that two phases are grounded. The three-phase voltage at the theoretical fault point F is uFa(t)、uFb(t)、uFc(t) and three-phase currents iFa(t)、iFb(t)、iFc(t)。iFbM(t) represents phase B current from one end M of the line at theoretical fault point F, iFbN(t) represents phase B current from one end N of the line at the theoretical fault point F. i.e. iFcM(t) C-phase current from one end M of the line at the theoretical fault point F, iFcN(t) represents the phase C current from one end N of the line at the theoretical fault point F. Respectively calculating grounding resistance R added at fault point FbcgVoltage u on (t)Rbcg(t) and a current iRbcg(t) are respectively:
Figure BDA0002814287840000055
will voltage uRbcg(t) and a current iRbcg(t) written as a sine expression:
Figure BDA0002814287840000056
wherein u isFg(t) represents an intermediate variable, iFb(t) and iFc(t) respectively representing the b-phase and c-phase currents of the transition resistance at a theoretical fault point F, AuRbcg(t)、BuRbcg(t) and AiRbcg(t)、BiRbcg(t) respectively represent coefficient polynomials of the voltage-current sinusoidal expression.
B-phase transition resistance R added at fault point FbVoltage u on (t)Rb(t) current iRb(t) are respectively:
Figure BDA0002814287840000061
and the B phase is transited to the resistance RbVoltage u on (t)Rb(t) current iRb(t) are respectively expressed as sine expressions:
Figure BDA0002814287840000062
wherein u isFb(t) represents the phase voltage of the transition resistance b at the theoretical fault point F, AuFb(t)、BuFb(t) and AiFb(t)、BiFb(t) respectively represent coefficient polynomials of the voltage-current sinusoidal expression.
C-phase transition resistance R added at fault point FcVoltage u on (t)Rc(t) current iRc(t) are respectively:
Figure BDA0002814287840000063
and the C phase transition resistance RcVoltage u on (t)Rc(t) current iRc(t) are respectively expressed as sine expressions:
Figure BDA0002814287840000064
wherein u isFc(t) respectively represent the phase voltage of the transition resistance c at the theoretical fault point F, AuFc(t)、BuFc(t) and AiFc(t)、BiFc(t) is divided intoCoefficient polynomials are expressed as sinusoidal expressions of voltage and current.
According to the ground resistance Rbcg(t) the instantaneous phases of the voltage and current are consistent, and an intermediate variable u is obtainedFg(t) is:
Figure BDA0002814287840000065
therefore, the resistance R is grounded at three resistorsbcg(t) transition resistance Rb(t) and transition resistance Rc(t) each satisfies instantaneous phase consistency, which translates into two new constraint equations on B, C phase resistances:
Figure BDA0002814287840000066
as a criterion for locating a fault point, the ground resistance Rbcg(t) solution is not needed, and only the existence of the grounding resistance R on the point to be tested needs to be verifiedbcg(t) two constraint equations in the equation (21) are satisfied simultaneously. Thus, two constraint equations are coupled, eliminating Rbcg(t), obtaining a fault point positioning criterion function of the two-phase grounding short circuit as follows:
Figure BDA0002814287840000071
wherein,
Figure BDA0002814287840000072
wherein S isjTo be determined at any one of the fault points, AuSjb(t)、BuSjb(t) and AiSjb(t)、BiSjb(t) respectively representing points of failure S to be determinedjThe voltage and current of the b-phase transition resistance is fitted with a sine to obtain a coefficient polynomial AuSjc(t)、BuSjc(t) and AiSjc(t)、BiSjc(t) respectively representing points of failure S to be determinedjFitting a sine to the voltage and current of the c-phase transition resistor to obtain a coefficient polynomial, wherein the b-phase and the c-phase are three-phase powerAny two phases in the way, the criterion function f (S)j) And obtaining the point corresponding to the minimum value as the determined fault point.
Similarly, the minimum value obtained by equation (22) is the final determined failure point for the failure point to be determined.
For a three-phase short-circuit to ground fault, as shown in fig. 5, A, B and C phases of the circuit are grounded simultaneously, and the voltage of the three phase at the theoretical fault point F is uFa(t)、uFb(t)、uFc(t) three-phase current is iFa(t)、iFb(t)、iFc(t)。iFaM(t) shows phase A current from one end M of the line at the theoretical fault point F, iFaN(t) represents phase a current from one end N of the line at the theoretical fault point F. i.e. iFbM(t) represents phase B current from one end M of the line at theoretical fault point F, iFbN(t) represents phase B current from one end N of the line at the theoretical fault point F. i.e. iFcM(t) C-phase current from one end M of the line at the theoretical fault point F, iFcN(t) represents the phase C current from one end N of the line at the theoretical fault point F. Calculating the ground resistance R added at the fault point FabcgVoltage u on (t)Rabcg(t) current iRabcg(t) and are respectively expressed as sine expressions:
Figure BDA0002814287840000073
uFg(t) represents an intermediate variable, iFa(t)、iFb(t) and iFc(t) respectively representing transition resistance a-phase, b-phase and c-phase currents at a theoretical fault point F, AuRabcg(t)、BuRabcg(t) and AiRabcg(t)、BiRabcg(t) coefficient polynomials respectively representing sinusoidal expressions of voltage and current,
solving the A-phase transition resistance R at the theoretical fault point FaVoltage u on (t)Ra(t) and a current iRa(t) and are respectively expressed as sinusoidal expressions:
Figure BDA0002814287840000074
wherein u isFa(t) the transition resistance A phase voltage at the theoretical fault point F, AuFa(t)、BuFa(t) and AiFa(t)、BiFa(t) coefficient polynomials respectively representing sinusoidal expressions of voltage and current,
solving the B-phase transition resistance R at the theoretical fault point FbVoltage u on (t)Rb(t) and a current iRb(t) and are respectively expressed as sine expressions:
Figure BDA0002814287840000081
wherein u isFb(t) the transition resistance B phase voltage at the theoretical fault point F, AuFb(t)、BuFb(t) and AiFb(t)、BiFb(t) coefficient polynomials respectively representing sinusoidal expressions of voltage and current,
calculating C-phase transition resistance R at theoretical fault point FcVoltage u on (t)Rc(t) and a current iRc(t)，
Figure BDA0002814287840000082
Wherein u isFc(t) respectively representing the voltage of the transition resistance C phase at the theoretical fault point F, AuFc(t)、BuFc(t) and AiFc(t)、BiFc(t) respectively represent coefficient polynomials of the voltage-current sinusoidal expression.
According to the ground resistance Rabcg(t) the instantaneous phases of the voltage and current are consistent, and an intermediate variable u is obtainedFg(t) is:
Figure BDA0002814287840000083
according to the ground resistance Rabcg(t) transition resistance Ra(t) transition resistance Rb(t) and transition resistance Rc(t) are each satisfied instantaneouslyPhase consistency, can be translated into A, B and three new constraint equations on phase C:
Figure BDA0002814287840000084
as a positioning criterion of a fault point, the common transition resistance R does not need to be solvedabcg(t), only the existence of R at the fault point to be determined is verifiedabcg(t) three constraint equations in equation (29) are satisfied simultaneously. Thus, simultaneous triad, elimination of Rabcg(t), the fault point positioning criterion function of the three-phase grounding short circuit is as follows:
Figure BDA0002814287840000085
wherein,
Figure BDA0002814287840000091
wherein S isjTo be determined at any one of the fault points, AuSja(t)、BuSja(t) and AiSja(t)、BiSja(t) respectively representing points of failure S to be determinedjThe voltage and current of the a-phase transition resistance is fitted with a sine to obtain a coefficient polynomial AuSjb(t)、BuSjb(t) and AiSjb(t)、BiSjb(t) respectively representing points of failure S to be determinedjThe voltage and current of the b-phase transition resistance is fitted with a sine to obtain a coefficient polynomial AuSjc(t)、BuSjc(t) and AiSjc(t)、BiSjc(t) respectively representing points of failure S to be determinedjA coefficient polynomial obtained by fitting a sine to the voltage and current of the c-phase transition resistor, wherein the b-phase and the c-phase are any two phases in a three-phase circuit, and the criterion function f (S)j) And obtaining the point corresponding to the minimum value as the determined fault point.
In this embodiment, the positioning method may further include calculating a transient voltage and current distribution on the line, and obtaining a voltage and a current at any point on the line. Namely, in order to verify whether each fault point to be determined meets the constraint relation of voltage and current instantaneous phase consistency, the voltage and the current of each fault point to be determined need to be obtained. For example, finding the voltage and current at any point on the line may include the steps of:
s100, collecting transient voltage and current during fault from two ends of a line, respectively representing the transient voltage and current into transient signal sine expressions, and solving each order of derivative;
transient voltage and current data i during power grid fault acquisition from two ends of lineM(t)、uM(t)、iN(t) and uN(t) respectively representing them as transient signal sinusoidal expressions comprising:
Figure BDA0002814287840000092
wherein iM(t) represents the transient current at the line M,
Figure BDA00028142878400000914
Figure BDA0002814287840000093
IM(t)、
Figure BDA0002814287840000094
and
Figure BDA0002814287840000095
respectively representing transient current i of M ends of the lineM(t) instantaneous amplitude, instantaneous initial phase and instantaneous phase;
Figure BDA0002814287840000096
wherein,
Figure BDA0002814287840000097
UM(t)、
Figure BDA0002814287840000098
and
Figure BDA0002814287840000099
representing the transient voltage u at the line M terminalM(t) instantaneous amplitude, instantaneous initial phase and instantaneous phase;
Figure BDA00028142878400000910
wherein,
Figure BDA00028142878400000911
IN(t)、IN(t) and
Figure BDA00028142878400000912
are respectively N-terminal transient current iN(t) instantaneous amplitude, instantaneous initial phase and instantaneous phase;
Figure BDA00028142878400000913
wherein,
Figure BDA0002814287840000101
UN(t)、
Figure BDA0002814287840000102
and
Figure BDA0002814287840000105
are respectively N-terminal transient voltage uN(t) instantaneous amplitude, instantaneous initial phase and instantaneous phase;
let iM(t)、uM(t)、iN(t) and uN(t) A (t), B (t) in the sinusoidal expression of (t) satisfy the following relationships:
B(t)＝H[A(t)] (36)
wherein A (t) is
Figure BDA0002814287840000106
And
Figure BDA0002814287840000107
b (t) is one of
Figure BDA0002814287840000108
Figure BDA0002814287840000109
And
Figure BDA00028142878400001010
one of A (t), B (t) and iM(t)、uM(t)、iN(t) and uN(t) corresponds to the sinusoidal expression, H represents the hilbert transform of the signal;
selecting A (t), determining B (t), and obtaining transient voltage and current data iM(t)、uM(t)、iN(t) and uNThe derivatives of each order of (t).
And S200, calculating the transient voltage and current distribution on the line based on the line distribution parameter model.
Based on the distributed parameter line model, with any end of the circuit as the starting end, for example, with the end M of the line as the starting end (the method is consistent with the method with the end N of the other end of the line as the starting end), the voltage and current at the point S at any distance x (x ≦ l) from the end M can be obtained by measuring the voltage and current at the starting end M:
Figure BDA0002814287840000103
wherein,
Figure BDA0002814287840000104
wherein u isS(t) represents the voltage of a point S to be solved at x (x is less than or equal to l) at the end M at any end of the line, uM(t) represents the transient voltage at the line M, i is the voltage to ground, iM(t) represents the transient current at the line M terminal, iS(t) represents the current of a point S at x (x is less than or equal to l) at the M end at any end of the line, R, L, C and G respectively represent the resistance, the inductance, the capacitance and the conductance of a unit length, l is the total length of the line, iM (2j-i)(t)、uM (2j-i)(t) is the (2j-i) order derivative of the current and voltage at the M end at the t moment, iM (2j-i+1)(t)、iM (2j-i-1)(t) is the (2j-i +1), (2j-i-1) order derivative of the M terminal current at the time t, uM (2j-i-1)(t)、uM (2j-i-2)And (t) are respectively (2j-i-1) and (2j-i-2) order derivatives of the M end voltage at the time t, wherein the M end is an initial end, and the positive direction of the current is that the initial end points to a point to be solved. In the above, the distributed parameter line model may be a distributed parameter line model commonly used in the art.
Of course, the positioning method of the present invention may use the method of the present invention to obtain the voltage and current of any point on the line, and the method of the present invention to obtain the voltage and current of each fault point to be determined is not limited to the above-mentioned methods of S100 to S200, and may also use other methods in the art to obtain the voltage and current.
In this embodiment, the positioning method may further include determining a rough fault section on the line before the step of determining the search step size. And determining a search step size in the determined approximate fault interval to generate a fault point to be determined.
In conclusion, the positioning method can be used for positioning the fault points of the power line layer by layer, is effective and reliable, and can be used for accurately positioning simple short-circuit faults of the power electronic grid.
Although the present invention has been described above in connection with exemplary embodiments, it will be apparent to those skilled in the art that various modifications and changes may be made to the exemplary embodiments of the present invention without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (10)

1. A power line fault point positioning method based on instantaneous phase consistency is characterized by comprising the following steps:
determining a search step length, and generating a plurality of fault points to be determined on a fault line;
respectively establishing constraint relations of transient voltage and current phase consistency on the transition resistor aiming at different line fault types based on transient voltage and current phase consistency on the short circuit transition resistor;
and (4) calculating the instantaneous phase consistency of the voltage current on the transition resistor of each fault point to be determined one by one, wherein the fault point to be determined with the highest consistency is the determined fault point.
2. The instantaneous phase consistency-based power line fault point locating method according to claim 1, wherein the different line fault types comprise a single-phase ground fault, a two-phase ground fault and a three-phase ground fault, and the locating method further comprises establishing a criterion function according to a constraint relation of instantaneous phase consistency of voltage and current on the transition resistor to determine the consistency of the instantaneous phase of the voltage and current on the transition resistor.
3. A method as claimed in claim 2, wherein for the single-phase short-to-earth fault, the criterion function is:
f(Sj)＝|AuSja(t)·BiSja(t)-AiSja(t)·BuSja(t)|，
wherein S isjTo be determined at any one of the fault points, AuSja(t) and BuSja(t) as the point of failure S to be determinedjCoefficient polynomial in a voltage-fitting sinusoidal expression at transition resistance, AiSja(t) and BiSja(t) as the point of failure S to be determinedjFitting a current at the transition resistance to a coefficient polynomial in a sinusoidal expression, the criterion function f (S)j) And obtaining the fault point to be determined corresponding to the minimum value as the determined fault point.
4. The power line fault point locating method based on instantaneous phase consistency according to claim 3, wherein establishing a constraint relation of instantaneous phase consistency of voltage currents on transition resistors for the single-phase ground short-circuit fault comprises:
supposing that any phase a in the three-phase circuit is short-circuited, the voltage u of the transition resistor at the theoretical fault point F is obtainedFa(t) and a current iFa(t) and expressing the voltage and current as sinusoidal expressions, respectively:
Figure FDA0002814287830000011
wherein, UFa(t)、IFa(t) represents the instantaneous magnitudes of the voltage and current respectively,
Figure FDA0002814287830000012
for an instantaneous initial phase, AuFa(t)、BuFa(t) coefficient polynomial representing the voltage sine expression, AiFa(t)、BiFa(t) a coefficient polynomial representing a current sine expression;
the constraint relation of the instantaneous phase consistency of the voltage current on the transition resistor is established as follows:
Figure FDA0002814287830000021
5. a method as claimed in claim 2, wherein for the two-phase short-circuit fault, the criterion function is:
Figure FDA0002814287830000022
wherein S isjFor any one of the points of failure to be determined,
Figure FDA0002814287830000023
for the fault point S to be determinedjTo transition resistanceRbc(t) fitting the voltage of (t) to a coefficient polynomial obtained from a sinusoidal expression,
Figure FDA0002814287830000024
Figure FDA0002814287830000025
for the fault point S to be determinedjA coefficient polynomial obtained by sine-fitting the current at the transition resistance, the criterion function f (S)j) And obtaining the fault point to be determined corresponding to the minimum value as the determined fault point.
6. The power line fault point positioning method based on instantaneous phase consistency according to claim 5, wherein establishing a constraint relation of instantaneous phase consistency of voltage currents on transition resistors for the two-phase short-circuit fault comprises:
assuming that two-phase short circuit occurs to any two phases b and c in the three-phase circuit, calculating the transition resistance R at the theoretical fault point FbcVoltage u of (t)Rbc(t) and a current iRbc(t) and expressing the voltage and current as sinusoidal expressions, respectively:
Figure FDA0002814287830000026
wherein u isFb(t)、uFc(t) represents the b-phase and c-phase voltages of the transition resistance at the theoretical fault point F, iFb(t) represents the transition resistance b phase current at the theoretical fault point F, the b phase is any phase in the three-phase circuit, AuRbc(t)、BuRbc(t) and AiRbc(t)、BiRbc(t) coefficient polynomials respectively representing a voltage-current sine expression;
the constraint relation of the instantaneous phase consistency of the voltage current on the transition resistor is established as follows:
Figure FDA0002814287830000027
7. a method as claimed in claim 2, wherein for the two-phase short-to-earth fault a criterion function is:
Figure FDA0002814287830000028
wherein,
Figure FDA0002814287830000029
wherein S isjTo be determined at any one of the fault points, AuSjb(t)、BuSjb(t) indicates a fault point S to be determinedjCoefficient polynomial obtained by fitting voltage of b-phase transition resistance to sinusoidal expression, AiSjb(t)、BiSjb(t) indicates a fault point S to be determinedjThe current fitting sine of the b-phase transition resistance expresses the obtained coefficient polynomial, AuSjc(t)、BuSjc(t) indicates a fault point S to be determinedjCoefficient polynomial obtained by fitting voltage of c-phase transition resistance to sinusoidal expression, AiSjc(t)、BiSjc(t) indicates a fault point S to be determinedjA coefficient polynomial obtained by fitting a sine expression to the current of the c-phase transition resistor, wherein the b-phase and the c-phase are any two phases in a three-phase circuit, and the criterion function f (S)j) And obtaining the point corresponding to the minimum value as the determined fault point.
8. The power line fault point locating method based on instantaneous phase consistency according to claim 7, wherein establishing a constraint relationship of instantaneous phase consistency of voltage currents on transition resistors for the two-phase ground short circuit fault comprises:
assuming that any two phases b and c in the three-phase circuit are grounded, calculating the grounding resistance R at the theoretical fault point FbcgVoltage u on (t)Rbcg(t) and a current iRbcg(t) and the voltage and the current are represented asThe sine expression is:
Figure FDA0002814287830000031
wherein u isFg(t) represents an intermediate variable, iFb(t) and iFc(t) respectively representing the b-phase and c-phase currents of the transition resistance at a theoretical fault point F, AuRbcg(t)、BuRbcg(t) coefficient polynomial representing the voltage sine expression, AiRbcg(t)、BiRbcg(t) coefficient polynomials respectively representing the current sine expressions,
solving b-phase transition resistance R at theoretical fault point FbVoltage u on (t)Rb(t) and a current iRb(t) and are respectively expressed as sine expressions:
Figure FDA0002814287830000032
wherein u isFb(t) represents the phase voltage of the transition resistance b at the theoretical fault point F, AuFb(t)、BuFb(t) coefficient polynomial representing the voltage sine expression, AiFb(t)、BiFb(t) coefficient polynomials respectively representing the current sine expressions,
solving the c-phase transition resistance R at the theoretical fault point FcVoltage u on (t)Rc(t) and a current iRc(t) and are respectively expressed as sine expressions:
Figure FDA0002814287830000033
wherein u isFc(t) respectively represent the phase voltage of the transition resistance c at the theoretical fault point F, AuFc(t)、BuFc(t) coefficient polynomial representing the voltage sine expression, AiFc(t)、BiFc(t) coefficient polynomials respectively representing current sine expressions;
based on ground resistance RbcgElectricity on (t)Instantaneous phase coincidence of piezoelectric current, intermediate variable uFg(t) is:
Figure FDA0002814287830000041
according to the ground resistance Rbcg(t) transition resistance Rb(t) and transition resistance Rc(t) all respectively satisfy instantaneous phase consistency, and the constraint relation of the voltage current instantaneous phase consistency is obtained as follows:
Figure FDA0002814287830000042
9. a method as claimed in claim 2, wherein for the three-phase short-to-earth fault, the criterion function is:
Figure FDA0002814287830000043
wherein,
Figure FDA0002814287830000044
wherein S isjTo be determined at any one of the fault points, AuSja(t)、BuSja(t) and AiSja(t)、BiSja(t) respectively representing points of failure S to be determinedjThe voltage and current of the a-phase transition resistance is fitted with a sine to obtain a coefficient polynomial AuSjb(t)、BuSjb(t) and AiSjb(t)、BiSjb(t) respectively representing points of failure S to be determinedjThe voltage and current of the b-phase transition resistance is fitted with a sine to obtain a coefficient polynomial AuSjc(t)、BuSjc(t) and AiSjc(t)、BiSjc(t) respectively representing points of failure S to be determinedjVoltage current fitting sine of C-phase transition resistanceExpressing the obtained coefficient polynomial, wherein the phase b and the phase c are any two phases in a three-phase circuit, and the criterion function f (S)j) And obtaining the point corresponding to the minimum value as the determined fault point.
10. The power line fault point locating method based on instantaneous phase consistency according to claim 9, wherein establishing a constraint relationship of instantaneous phase consistency of voltage currents on transition resistors for the three-phase ground short circuit fault comprises:
calculating the grounding resistance R at the theoretical fault point FabcgVoltage u on (t)Rabcg(t) and a current iRabcg(t) and are respectively expressed as sine expressions:
Figure FDA0002814287830000045
uFg(t) represents an intermediate variable, iFa(t)、iFb(t) and iFc(t) respectively representing transition resistance a-phase, b-phase and c-phase currents at a theoretical fault point F, AuRabcg(t)、BuRabcg(t) and AiRabcg(t)、BiRabcg(t) coefficient polynomials respectively representing sinusoidal expressions of voltage and current,
solving the a-phase transition resistance R at the theoretical fault point FaVoltage u on (t)Ra(t) and a current iRa(t) and are respectively expressed as sinusoidal expressions:
Figure FDA0002814287830000051
wherein u isFa(t) the transition resistance a phase voltage at the theoretical fault point F, AuFa(t)、BuFa(t) and AiFa(t)、BiFa(t) coefficient polynomials respectively representing sinusoidal expressions of voltage and current,
solving b-phase transition resistance R at theoretical fault point FbVoltage u on (t)Rb(t) and a current iRb(t) and are respectively expressed as sine tablesThe expression is as follows:
Figure FDA0002814287830000052
wherein u isFb(t) represents the phase voltage of the transition resistance b at the theoretical fault point F, AuFb(t)、BuFb(t) and AiFb(t)、BiFb(t) coefficient polynomials respectively representing sinusoidal expressions of voltage and current,
solving the c-phase transition resistance R at the theoretical fault point FcVoltage u on (t)Rc(t) and a current iRc(t)，
Figure FDA0002814287830000053
Wherein u isFc(t) respectively represent the phase voltage of the transition resistance c at the theoretical fault point F, AuFc(t)、BuFc(t) and AiFc(t)、BiFc(t) coefficient polynomials respectively representing a voltage-current sine expression;
based on ground resistance Rabcg(t) instantaneous phase alignment of voltage and current, intermediate variable uFg(t) is:
Figure FDA0002814287830000054
according to the ground resistance Rabcg(t) transition resistance Ra(t) transition resistance Rb(t) and transition resistance Rc(t) all respectively satisfy instantaneous phase consistency, and the constraint relation of the voltage current instantaneous phase consistency is obtained as follows:
Figure FDA0002814287830000055
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