CN116699308A - T-type hybrid line fault positioning method based on traveling wave time difference - Google Patents
T-type hybrid line fault positioning method based on traveling wave time difference 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
- 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
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/088—Aspects of digital computing
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- 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 T-shaped hybrid line fault positioning method based on the traveling wave time difference comprises the following steps: step1, determining a fault branch; step2, determining a fault section; step3, judging the fault distance; step4, wave speed compensation; repositioning the fault distance obtained in Step3. Firstly, judging a fault branch by utilizing a T-shaped line distribution parameter equation; then calculating the time difference of the fault traveling wave reaching bus bars at two ends at the end point and the middle point of the mixed line as the setting value of the fault area; finally, obtaining a result by using a fault distance equation; the distance calculation formula is suitable for fault location of n-section overhead line-cable mixed lines, and the wave speed in the calculation formula is closer to an actual value after Newton interpolation.
Description
Technical Field
The invention relates to the technical field of fault positioning of transmission lines, in particular to a T-shaped hybrid line fault positioning method based on traveling wave time difference.
Background
Along with the change of social production development demands, the traditional single overhead line can not meet the requirement of urban construction. In order to reduce the occupation rate of overhead lines to the land without affecting the overall appearance of the city, the utilization rate of underground cables is continuously increased, and cables with T-shaped branches-overhead lines gradually become a general line connection mode. However, the underground cable has insulation aging problems with the lapse of time, and the overhead line is subject to various failures due to environmental influences. Once the fault is not quickly repaired, huge economic loss is caused, so that the rapid fault identification method has important practical significance.
At present, fault location research on a single overhead line or a cable line is relatively mature, and the effect on engineering application is very remarkable. Because the mixed line wave impedance has more discontinuous points, multiple refraction and reflection will occur in the traveling wave propagation process, and the traditional single line positioning method is not applicable any more. The existing hybrid line positioning method based on the traveling wave time difference utilizes the time difference that the traveling wave of the fault point reaches the two ends of the bus to determine the fault section, and the fault time difference is brought into a distance formula with the traveling wave velocity to obtain a positioning result. The distance formula in the method is only suitable for the specific line, the empirical wave speed in the formula is not consistent with the wave speed changed in the actual engineering, and the positioning result has larger error.
Disclosure of Invention
The invention aims to solve the technical problem of providing a T-shaped hybrid line fault positioning method based on traveling wave time difference, and the method for judging the fault branch by using a distribution parameter model not only can rapidly identify the fault branch, but also can be used for correcting the parameters of a power transmission line.
In order to solve the technical problems, the invention adopts the following technical scheme:
the T-shaped hybrid line fault positioning method based on the traveling wave time difference comprises the following steps: step1, determining a fault branch; establishing a T-shaped cable-overhead line hybrid circuit model in a normal running state, calculating terminal voltage from the first section voltage by using a distribution parameter model, and judging which branch is in fault according to an equivalent relation between voltage values of the cable terminal voltages at all ends to nodes along the overhead line;
step2, determining a fault section; selecting any section in the non-fault section branch, establishing a double-end hybrid transmission line model with the fault section branch, wherein the model comprises an intersection point of a hybrid line, a midpoint of the hybrid line and a fault set point, establishing a corresponding relation table of time difference of fault traveling waves of each point reaching bus bars at two ends and fault section positions, and obtaining the position information of the current fault section by referring to the corresponding relation table according to the obtained time difference of the current fault traveling waves reaching bus bars at two ends;
step3, judging the fault distance; comparing the time difference of the initial traveling wave reaching the buses at the two ends with a preset time difference, determining a fault section on a fault branch, and calculating a fault distance;
step4, wave speed compensation; processing traveling wave data obtained by the traveling wave sampling device through a dynamic mode decomposition algorithm to obtain a Teager energy curve, correcting the wave speed at the highest energy point which is the arrival time of the traveling wave through a Newton interpolation method, and repositioning the fault distance obtained in Step3.
The specific steps of Step1 are as follows:
establishing a T-shaped cable-overhead line hybrid circuit model in a normal operation state, wherein L is A 、L B 、L C Respectively the lengths of the cables in the three branches, U T Is the intersection voltage of three branches, U 1 、U S1 、U S2 、I A The voltage at the end of the M terminal, the voltage at the two ends of the M terminal cable and the branch current at the M terminal are respectively; u (U) 2 、U S3 、U S4 、I B The voltage is respectively N-terminal voltage, N-terminal cable voltage and N-terminal branch current; u (U) 3 、U S5 、U S6 、I C The voltage is the S terminal voltage, the voltage at two ends of the S terminal cable and the S terminal branch current respectively;
assuming that the line parameters are known, for a single transmission line, the end voltage can be calculated from the head-end voltage using a distribution parameter model as shown in equation (5):
vector U T1 、U T2 、U T3 The voltages from the voltages of the cable ends of the M end, the N end and the S end to the node T are calculated along the overhead line respectively, Z C Is the characteristic impedance of the line;
when the T-shaped circuit section fails, a distribution parameter model is adopted to calculate U respectively T1 、U T2 、U T3 Judging a fault branch by comparing the magnitude relation of the fault branch; as calculated U T1 ＝U T2 ≠U T3 The M branch and the N branch are equal in voltage amplitude and same in direction, and are different from the S branch in different directions, so that faults can be judged to occur in the S branch; in order to prevent the high-resistance grounding condition from causing different calculated voltage amplitudes and directions, the amplitudes and the vectors are respectively used as criteria to obtain results, as shown in formulas (6) and (7):
U Ti 、U Tj calculating voltage for non-faulty branch, U Tk Calculating voltages, K, for the faulty branches, respectively 1 、K 2 Setting value K for voltage amplitude of non-fault branch 3 Setting value for the voltage amplitude of the fault branch.
In Step1, in the equation (5), the voltage at both ends of the cable is an unknown value, and the voltage at this point can be calculated by using a non-contact type space electric field sensor measurement method:
the cable end voltage measurement flow is divided into three parts: the system comprises an electric field sensor, a signal conditioning unit and a data processing unit; the device is divided into an induction pole and a grounding pole, and the distance between the two poles is d; e (t) is a cable for emitting an electric field, and the sensor senses a magnetic field to output a current i;
the signal conditioning unit amplifies the current signal and is further used for subsequent data processing; the data processing unit searches an optimal solution in the relation between the electric field and the voltage by using a fitting relation between the magnetic field and the voltage and acquires a voltage optimal value by using a genetic algorithm;
u can be utilized in T-type circuit T1 ＝U T2 ＝U T3 This feature establishes an fitness function, specifically:
j is an fitness function; n is the number of sampling points; u (U) T1 (i)、U T2 (i)、U T3 (i) And (3) for the terminal voltage obtained by calculating the initial ends of the three branches, the original line parameters are brought into a distribution parameter model calculation formula, an optimal solution is searched through a genetic algorithm, J is less than or equal to 1% as a convergence condition, and a parameter result is output.
The specific process of Step2 is as follows:
assuming that the M branch fails, N, S branch is a normal branch, and selecting any one of the N branch or the S branch and the M branch to form a double-end hybrid transmission line model; l (L) MB 、L DE 、L HN For the length L of the three overhead lines in the mixed line BD 、L EH The length of the cable is two sections; A. c, E, H, J is the midpoint of the hybrid line, B, D, G, I is the intersection of the hybrid line, F is the fault setpoint, v c 、v 0 Respectively representing the propagation speed of fault traveling waves in the cable and the overhead line;
when a fault occurs at the A, C, E, H, J point, the time difference of the fault traveling wave reaching buses at two ends is as follows:
when a fault occurs at the B, D, G, I point, the time difference of the fault traveling wave reaching buses at two ends is as follows:
the time difference that the fault traveling wave reaches the acquisition points at the two ends is deltat, and when the line actually breaks down, the fault point area judgment result and the type of the traveling wave received by the M end for the second time are shown in the table 1.
Table 1 time-difference comparison results
The specific steps of Step3 are as follows:
step2, after judging a fault branch according to line parameters, selecting a non-fault branch to form a double-end hybrid transmission line model, calculating the time difference delta t of the fault initial traveling wave reaching buses at two ends, and comparing the delta t with the preset point time difference delta t x Comparing, determining fault section on fault branch, and performing fault distance L F The calculation process is as follows:
step3.1, when a fault occurs in the left half section of the overhead line, the M end receives reflected waves of which the second traveling wave is a fault point; l (L) MX1 The distance from the connecting point before the fault section overhead line to the M-end bus is determined through time difference comparison; t is t m2 、t m1 The time for the fault traveling wave to reach the M-terminal bus for the second time and the first time respectively; fault ranging is defined as:
step3.2, when a fault occurs in the right half section of the overhead line, the M end receives the second traveling wave as a reflected wave of the mixed line connection point; l (L) MX2 The distance from the connecting point after the fault section overhead line to the M-end bus is determined through time difference comparison; fault ranging is defined as:
step3.3, when a fault occurs in the left half section of the cable, the M end receives the second traveling wave as a fault point reflected wave; l (L) MX3 The distance from the connecting point before the cable line of the fault section to the bus at the M end is determined through time difference comparison; fault ranging is defined as:
step3.4, when a fault occurs in the right half section of the cable, the M end receives the second traveling wave as a reflected wave of the mixed line connection point; l (L) MX4 The distance between the connecting point of the cable line of the fault section and the bus at the M end is determined after the comparison of the time difference; fault ranging is defined as:
step3.5 when Δt equals to the pre-calculated Δt x When the fault point is located at the key point or the connection point of the hybrid line; l (L) MX5 Is the hybrid line midpoint or junction distance; fault ranging is defined as:
L F ＝L MX5 (15)。
the specific steps of Step4 are as follows:
step4.1, the traveling wave data x= [ X ] can be obtained through the traveling wave sampling device 1 ,x 2 ,x 3 …x i ]Wherein x is i Representing the sampling value at the ith moment, and forming two different matrixes X by linear mapping of discrete sampling data 1 ，X 2 Expressed as:
X i+1 ＝AX i (16)
X 1 ＝[x 1 ,x 2 ,x 3 ,...x n-1 ] (17)
X 2 ＝[x 2 ,x 3 ,x 4 ...x n ] (18)
a is the state matrix of the discrete system, matrix X 1 ,X 2 The relation is:
X 2 ＝Ax 1 (19)
first pair mapping matrix X 1 Performing singular decomposition:
X 1 ＝B∑V T (20)
A'＝BAB' (21)
b, V is a unitary matrix, A' is an approximation matrix of the state matrix A, and Σ is a singular diagonal matrix;
at this time, after solving by minimization, a is approximately equal to a':
A≈A'＝B T X 2 V∑ -1 (22)
the dimension reduction of the high-dimensional state matrix is realized in the approximation process, and the traveling wave fault characteristic information in the matrix A' is reserved; to obtain fault information, the matrix a' is decomposed:
A'w i ＝c i w i (23)
w i ,c i for the eigenvectors and eigenvalues of matrix A', w will be i ,c i Forming a new matrix W, C:
A'W＝CW (24)
in order to obtain the modal quantity containing the traveling wave fault information, defining the phi column vector of the matrix as one decomposed modal quantity, and then:
φ＝X 2 V∑ -1 W (25)
the Teager energy operator can reflect the energy change of the signal, and obtains the instantaneous energy at the moment of change through differential operation, namely:
setting sampling frequency, intercepting a set number of sampling points for sampling, decomposing the decoupled alpha modulus of the sampling points by the DMD to obtain a Teager energy curve, wherein the highest energy point detected in the wave head is the traveling wave reaching moment, and the traveling wave energy is detected to be suddenly changed at the moment, and the method is particularly shown in figures 10 and 11.
In Step4, after Step4.1 is completed, the following steps are further provided:
step4.2, selecting the fault distance obtained by carrying out uncorrected wave velocity calculation and carrying into a positioning formula as an approximation value l 0 When the polynomial degree n=1, i.e. the first order polynomial is H 1 (l 0 )＝v 1 (l 0 ) The constructor is:
H 1 ＝v(l 0 )+a 1 (l-l 0 ) (27)
a 1 as a function H 1 The specific expression is:
when n=2, the basis function adds a second order polynomial on the basis of the first order polynomial to satisfy H 2 (l 2 )＝v(l 2 )，H 2 (l1)＝v(l 1 ) Constructing a function:
H 2 ＝H 1 +a 2 (l-l 0 )(l-l 1 ) (29)
in which a is 2 Is the second order difference quotient coefficient, recorded as
The Newton's interpolation polynomial expression can be obtained according to the recurrence method:
the n-order difference quotient coefficient expression is:
the invention provides a T-shaped hybrid line fault positioning method based on traveling wave time difference, which is based on traveling wave time difference; firstly, judging a fault branch by utilizing a T-shaped line distribution parameter equation; then calculating the time difference of the fault traveling wave reaching bus bars at two ends at the end point and the middle point of the mixed line as the setting value of the fault area; finally, obtaining a result by using a fault distance equation; the distance calculation formula is suitable for fault location of n sections of overhead line-cable mixed lines, and the wave speed in the calculation formula is closer to the actual value after Newton interpolation; aiming at the problem of fault location of a T-shaped hybrid line, a T-shaped hybrid line fault location method based on traveling wave time difference is provided; firstly, judging a fault branch by utilizing a T-shaped line distribution parameter equation; then calculating the time difference of the fault traveling wave reaching bus bars at two ends at the end point and the middle point of the mixed line as the setting value of the fault area; finally, obtaining a result by using a fault distance equation; the distance calculation formula is suitable for fault location of n-section overhead line-cable mixed lines, and the wave speed in the calculation formula is closer to an actual value after Newton interpolation.
The invention has the following beneficial effects:
(1) The T-shaped line characteristic is utilized, the simultaneous three-terminal distribution voltage equation is utilized to select a fault branch, and the method is simple to operate. In addition, the method for judging the fault branch by using the distribution parameter model not only can rapidly identify the fault branch, but also can be used for correcting the parameters of the power transmission line;
(2) The fault distance formula is applicable to fault setting of n-section hybrid lines and has universality. Secondly, the distance measurement process and the calculation formula are easy to realize, and the applicability is realized;
(3) The time of the fault traveling wave reaching the bus is identified by using a dynamic mode decomposition algorithm, and compared with the traditional wavelet algorithm, the algorithm has stronger self-adaption capability and is more sensitive to energy mutation points.
Drawings
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
FIG. 1 is a schematic flow diagram of a method for locating faults of a T-type hybrid line based on traveling wave time difference;
FIG. 2 is a schematic diagram of a traveling wave fault;
FIG. 3 is a first diagram of traveling wave fault analysis;
FIG. 4 is a second traveling wave fault analysis chart;
FIG. 5 is a schematic diagram of a traveling wave catadioptric system;
FIG. 6 is a schematic diagram of a uniform line parameter model;
FIG. 7 is a schematic diagram of a T-type cable-overhead hybrid circuit model;
FIG. 8 is a schematic diagram of an electric field sensor;
FIG. 9 is a power distribution plot of a spatial magnetic field sensor
FIG. 10 is a graph of the traveling wave propagation of a hybrid line model of a double-ended transmission line with M and N branches combined;
FIG. 11 is a schematic diagram of a single phase ground fault traveling wave;
FIG. 12 is a schematic diagram of Teager energy curves.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, the method for positioning the fault of the T-type hybrid line based on the traveling wave time difference comprises the following steps:
step1, determining a fault branch; establishing a T-shaped cable-overhead line hybrid circuit model in a normal running state, calculating terminal voltage from the first section voltage by using a distribution parameter model, and judging which branch is in fault according to an equivalent relation between voltage values of the cable terminal voltages at all ends to nodes along the overhead line;
step2, determining a fault section; selecting any section in the non-fault section branch, establishing a double-end hybrid transmission line model with the fault section branch, wherein the model comprises an intersection point of a hybrid line, a midpoint of the hybrid line and a fault set point, establishing a corresponding relation table of time difference of fault traveling waves of each point reaching bus bars at two ends and fault section positions, and obtaining the position information of the current fault section by referring to the corresponding relation table according to the obtained time difference of the current fault traveling waves reaching bus bars at two ends;
step3, judging the fault distance; comparing the time difference of the initial traveling wave reaching the buses at the two ends with a preset time difference, determining a fault section on a fault branch, and calculating a fault distance;
step4, wave speed compensation; processing traveling wave data obtained by the traveling wave sampling device through a dynamic mode decomposition algorithm to obtain a Teager energy curve, correcting the wave speed at the highest energy point which is the arrival time of the traveling wave through a Newton interpolation method, and repositioning the fault distance obtained in Step3.
And (3) analyzing the traveling wave propagation principle of the mixed line:
traveling wave generation principle:
the double-end power transmission line is the most basic model in the structure type of the power transmission line, and the fault positioning method research of the complex line can be changed from the model; as shown in FIG. 2, E m And E is n The power supply voltage is the power supply voltage at two sides of the double-end power transmission line; z is Z m And Z n Respectively, the impedance in the power supply side circuit; when the line fails, the voltage at the failure point changes suddenly, and the transient traveling wave process occurs in the line.
By using superposition principle analysis, the fault point can be regarded as voltage +U in non-fault state f And fault component-U f The superposition, as shown in figure 3; excluding the influence of the normal voltage component, and analyzing the line condition under the fault component alone, as shown in fig. 4; the line under the action of the fault component has no influence of electromotive force, and the fault point can be regarded as an additional voltage source with opposite polarity and same amplitude as the normal voltage, and the voltage source is a wave source for generating travelling waves.
Refraction and reflection characteristics of traveling wave:
the traveling wave can be reflected and refracted at the point where the line parameter is suddenly changed or the wave impedance is suddenly changed; in the hybrid line, the connection point of the overhead line and the cable and the fault occurrence point meet the travelling wave refraction and reflection condition; in fig. 5, u1q, u2q, and u1f represent incident waves, refraction waves, and reflection waves of the traveling wave, respectively.
Refractive index alpha A And reflection coefficient beta A Can be expressed as:
when the uniform power distribution network mixing line works in a sinusoidal steady state, circuit parameters in the power distribution network mixing circuit are sinusoidal; thus, the grid related parameters along the transmission line can be represented by a vector; the formula is as follows:
where γ is the line propagation constant, A, B is the integral constant of the uniform line current-voltage expression, expressed as:
the specific steps of Step1 are as follows:
FIG. 6 is a schematic diagram of a hybrid T-cable-overhead line circuit model in normal operating conditions, wherein L A 、L B 、L C Respectively the lengths of the cables in the three branches, U T Is the intersection voltage of three branches, U 1 、U S1 、U S2 、I A The voltage at the end of the M terminal, the voltage at the two ends of the M terminal cable and the branch current at the M terminal are respectively; u (U) 2 、U S3 、U S4 、I B The voltage is respectively N-terminal voltage, N-terminal cable voltage and N-terminal branch current; u (U) 3 、U S5 、U S6 、I C Respectively S terminal voltage, S terminal cable two terminal voltage and S terminal branchA road current;
assuming that the line parameters are known, for a single transmission line, the end voltage can be calculated from the head-end voltage using a distribution parameter model as shown in equation (5):
vector U T1 、U T2 、U T3 The voltages from the voltages of the cable ends of the M end, the N end and the S end to the node T are calculated along the overhead line respectively, Z C Is the characteristic impedance of the line;
when the T-shaped circuit section fails, a distribution parameter model is adopted to calculate U respectively T1 、U T2 、U T3 Judging a fault branch by comparing the magnitude relation of the fault branch; as calculated U T1 ＝U T2 ≠U T3 The M branch and the N branch are equal in voltage amplitude and same in direction, and are different from the S branch in different directions, so that faults can be judged to occur in the S branch; in order to prevent the high-resistance grounding condition from causing different calculated voltage amplitudes and directions, the amplitudes and the vectors are respectively used as criteria to obtain results, as shown in formulas (6) and (7):
U Ti 、U Tj calculating voltage for non-faulty branch, U Tk Calculating voltages, K, for the faulty branches, respectively 1 、K 2 For the voltage amplitude setting value of the non-fault branch, 0.9 and 1.01K are generally taken according to the error magnitude 3 And 1.13 is taken as a fault branch voltage amplitude setting value.
In Step1, in the equation (5), the voltage at both ends of the cable is an unknown value, and the voltage at this point can be calculated by using a non-contact type space electric field sensor measurement method:
the cable end voltage measurement flow is divided into three parts: the system comprises an electric field sensor, a signal conditioning unit and a data processing unit; the schematic diagram of the electric field sensor is shown in fig. 8; the device is divided into an induction pole and a grounding pole, and the distance between the two poles is d; e (t) is a cable for emitting an electric field, and the sensor senses a magnetic field to output a current i; FIG. 9 shows the power distribution points of the spatial magnetic field sensor, and shows that the sensor has good effect in the 45-135-degree induced magnetic field, namely the sensitivity is highest when the signal receiving direction of the sensor is vertical to the power transmission line;
the signal conditioning unit amplifies the current signal and is further used for subsequent data processing; the data processing unit searches an optimal solution in the relation between the electric field and the voltage by using a fitting relation between the magnetic field and the voltage and acquires a voltage optimal value by using a genetic algorithm;
in addition, the method for discriminating the fault branch by using the distribution parameter model not only can rapidly identify the fault branch, but also can be used for correcting the parameters of the power transmission line. The line parameters are often affected by external environment or weather, so that errors exist between the line parameters and the specified parameters; u can be utilized in T-type circuit T1 ＝U T2 ＝U T3 This feature establishes an fitness function, specifically:
j is an fitness function; n is the number of sampling points; u (U) T1 (i)、U T2 (i)、U T3 (i) And (3) for the terminal voltage obtained by calculating the initial ends of the three branches, the original line parameters are brought into a distribution parameter model calculation formula, an optimal solution is found through a genetic algorithm, and in consideration of an error range, J is less than or equal to 1% as a convergence condition, and a parameter result is output.
The specific process of Step2 is as follows:
assuming that the M branch fails, N, S branch is a normal branch, and selecting any one of the N branch or the S branch and the M branch to form a double-end hybrid transmission line model; l (L) MB 、L DE 、L HN For three sections of overhead in the mixed lineLine length, L BD 、L EH The length of the cable is two sections; A. c, E, H, J is the midpoint of the hybrid line, B, D, G, I is the intersection of the hybrid line, F is the fault setpoint, v c 、v 0 Respectively representing the propagation speed of fault traveling waves in the cable and the overhead line;
when a fault occurs at the A, C, E, H, J point, the time difference of the fault traveling wave reaching buses at two ends is as follows:
when a fault occurs at the B, D, G, I point, the time difference of the fault traveling wave reaching buses at two ends is as follows:
the time difference that the fault traveling wave reaches the acquisition points at the two ends is deltat, and when the line actually breaks down, the fault point area judgment result and the type of the traveling wave received by the M end for the second time are shown in the table 1.
Table 1 time-difference comparison results
The specific steps of Step3 are as follows:
step2, after judging a fault branch according to line parameters, selecting a non-fault branch to form a double-end hybrid transmission line model, calculating the time difference delta t of the fault initial traveling wave reaching buses at two ends, and comparing the delta t with the preset point time difference delta t x Comparing, determining fault section on fault branch, and performing fault distance L F The calculation process is as follows:
step3.1, when a fault occurs in the left half section of the overhead line, the M end receives reflected waves of which the second traveling wave is a fault point; l (L) MX1 The distance from the connecting point before the fault section overhead line to the M-end bus is determined through time difference comparison; t is t m2 、t m1 The time for the fault traveling wave to reach the M-terminal bus for the second time and the first time respectively; fault ranging is defined as:
step3.2, when a fault occurs in the right half section of the overhead line, the M end receives the second traveling wave as a reflected wave of the mixed line connection point; l (L) MX2 The distance from the connecting point after the fault section overhead line to the M-end bus is determined through time difference comparison; fault ranging is defined as:
step3.3, when a fault occurs in the left half section of the cable, the M end receives the second traveling wave as a fault point reflected wave; l (L) MX3 The distance from the connecting point before the cable line of the fault section to the bus at the M end is determined through time difference comparison; fault ranging is defined as:
step3.4, when a fault occurs in the right half section of the cable, the M end receives the second traveling wave as a reflected wave of the mixed line connection point; l (L) MX4 The distance between the connecting point of the cable line of the fault section and the bus at the M end is determined after the comparison of the time difference; fault ranging is defined as:
step3.5 when Δt equals to the pre-calculated Δt x When the fault point is located at the key point or the connection point of the hybrid line; l (L) MX5 Is the hybrid line midpoint or junction distance; fault ranging is defined as:
L F ＝L MX5 (15)。
the specific steps of Step4 are as follows:
step4.1, a dynamic pattern decomposition algorithm, is a modal analysis algorithm. The method can effectively process the nonstationary signals, extract key characteristic values and reduce modal aliasing influence caused by low-frequency components; the traveling wave data X= [ X ] can be obtained by the traveling wave sampling device 1 ,x 2 ,x 3 …x i ]Wherein x is i Representing the sampling value at the ith moment, and forming two different matrixes X by linear mapping of discrete sampling data 1 ，X 2 Expressed as:
X i+1 ＝AX i (16)
X 1 ＝[x 1 ,x 2 ,x 3 ,...x n-1 ] (17)
X 2 ＝[x 2 ,x 3 ,x 4 ...x n ] (18)
a is the state matrix of the discrete system, matrix X 1 ,X 2 The relation is:
X 2 ＝Ax 1 (19)
first pair mapping matrix X 1 Performing singular decomposition:
X 1 ＝B∑V T (20)
A'＝BAB' (21)
b, V is a unitary matrix, A' is an approximation matrix of the state matrix A, and Σ is a singular diagonal matrix;
at this time, after solving by minimization, a is approximately equal to a':
A≈A'＝B T X 2 V∑ -1 (22)
the dimension reduction of the high-dimensional state matrix is realized in the approximation process, and the traveling wave fault characteristic information in the matrix A' is reserved; to obtain fault information, the matrix a' is decomposed:
A'w i ＝c i w i (23)
w i ,c i for the eigenvectors and eigenvalues of matrix A', w will be i ,c i Forming a new matrix W, C:
A'W＝CW (24)
in order to obtain the modal quantity containing the traveling wave fault information, defining the phi column vector of the matrix as one decomposed modal quantity, and then:
φ＝X 2 V∑ -1 W (25)
the Teager energy operator can reflect the energy change of the signal, and obtains the instantaneous energy at the moment of change through differential operation, namely:
setting a sampling frequency of 1MHz, intercepting 1000 sampling points for sampling, decomposing the decoupled alpha modulus of the sampling points by a DMD to obtain a Teager energy curve, wherein the highest energy point detected in the wave head is the moment when the traveling wave reaches, and the moment when the traveling wave energy is detected to be suddenly changed is shown as shown in figures 11 and 12.
In Step4, after Step4.1 is completed, the following steps are further provided:
step4.2, selecting the fault distance obtained by carrying out uncorrected wave velocity calculation and carrying into a positioning formula as an approximation value l 0 When the polynomial degree n=1, i.e. the first order polynomial is H 1 (l 0 )＝v 1 (l 0 ) The constructor is:
H 1 ＝v(l 0 )+a 1 (l-l 0 ) (27)
a 1 as a function H 1 The specific expression is:
when n=2, the basis function is increased on the basis of the first order polynomialSecond order polynomials satisfy H 2 (l 2 )＝v(l 2 )，H 2 (l1)＝v(l 1 ) Constructing a function:
H 2 ＝H 1 +a 2 (l-l 0 )(l-l 1 ) (29)
in which a is 2 Is the second order difference quotient coefficient, recorded as
The Newton's interpolation polynomial expression can be obtained according to the recurrence method:
the n-order difference quotient coefficient expression is:
the function constructed by Newton interpolation is a process from a low-order interpolation polynomial to a high-order interpolation polynomial which is continuously increased, and has good continuity. Along with the increment of polynomial orders, the obtained approximate wave speed and the approximate fault distance gradually converge towards the true value, and the fault positioning accuracy is increased.
Researchers find that a functional relationship exists between the traveling wave velocity and the fault distance, but the functional relationship cannot be algebraized, and a fitting means is needed to solve the problem; and obtaining a polynomial function H taking the fault distance l as an independent variable and the traveling wave velocity v as a dependent variable by using a fitting algorithm.
When the existing Lagrangian algorithm is calculated, the repeated calculation of the basis function is needed to be considered for the newly added or reduced interpolation points, the process is complicated, and the overall calculated amount is increased; the defect of the Lagrange polynomial is avoided by improving the basis function of the Newton interpolation polynomial, the new interpolation points are added by only adding the polynomial on the basis of the original basis function, the calculated amount is greatly reduced, and the operation time is shortened.
Claims (7)
1. The T-shaped hybrid line fault positioning method based on the traveling wave time difference is characterized by comprising the following steps of:
step1, determining a fault branch; establishing a T-shaped cable-overhead line hybrid circuit model in a normal running state, calculating terminal voltage from the first section voltage by using a distribution parameter model, and judging which branch is in fault according to an equivalent relation between voltage values of the cable terminal voltages at all ends to nodes along the overhead line;
step2, determining a fault section; selecting any section in the non-fault section branch, establishing a double-end hybrid transmission line model with the fault section branch, wherein the model comprises an intersection point of a hybrid line, a midpoint of the hybrid line and a fault set point, establishing a corresponding relation table of time difference of fault traveling waves of each point reaching bus bars at two ends and fault section positions, and obtaining the position information of the current fault section by referring to the corresponding relation table according to the obtained time difference of the current fault traveling waves reaching bus bars at two ends;
step3, judging the fault distance; comparing the time difference of the initial traveling wave reaching the buses at the two ends with a preset time difference, determining a fault section on a fault branch, and calculating a fault distance;
step4, wave speed compensation; processing traveling wave data obtained by the traveling wave sampling device through a dynamic mode decomposition algorithm to obtain a Teager energy curve, correcting the wave speed at the highest energy point which is the arrival time of the traveling wave through a Newton interpolation method, and repositioning the fault distance obtained in Step3.
2. The method for positioning a T-type hybrid line fault based on traveling wave time difference according to claim 1, wherein the Step1 specifically comprises the steps of:
establishing a T-shape under normal operation stateCable-overhead hybrid circuit model, where L A 、L B 、L C Respectively the lengths of the cables in the three branches, U T Is the intersection voltage of three branches, U 1 、U S1 、U S2 、I A The voltage at the end of the M terminal, the voltage at the two ends of the M terminal cable and the branch current at the M terminal are respectively; u (U) 2 、U S3 、U S4 、I B The voltage is respectively N-terminal voltage, N-terminal cable voltage and N-terminal branch current; u (U) 3 、U S5 、U S6 、I C The voltage is the S terminal voltage, the voltage at two ends of the S terminal cable and the S terminal branch current respectively;
assuming that the line parameters are known, for a single transmission line, the end voltage can be calculated from the head-end voltage using a distribution parameter model as shown in equation (5):
vector U T1 、U T2 、U T3 The voltages from the voltages of the cable ends of the M end, the N end and the S end to the node T are calculated along the overhead line respectively, Z C Is the characteristic impedance of the line;
when the T-shaped circuit section fails, a distribution parameter model is adopted to calculate U respectively T1 、U T2 、U T3 Judging a fault branch by comparing the magnitude relation of the fault branch; as calculated U T1 ＝U T2 ≠U T3 The M branch and the N branch are equal in voltage amplitude and same in direction, and are different from the S branch in different directions, so that faults can be judged to occur in the S branch; in order to prevent the high-resistance grounding condition from causing different calculated voltage amplitudes and directions, the amplitudes and the vectors are respectively used as criteria to obtain results, as shown in formulas (6) and (7):
U Ti 、U Tj calculating voltage for non-faulty branch, U Tk Calculating voltages, K, for the faulty branches, respectively 1 、K 2 Setting value K for voltage amplitude of non-fault branch 3 Setting value for the voltage amplitude of the fault branch.
3. The method for positioning a T-type hybrid line fault based on traveling wave time difference according to claim 2, wherein in Step1, in the equation (5), the voltage at two ends of the cable is an unknown quantity, and the voltage at the point can be calculated by using a non-contact type space electric field sensor measurement method:
the cable end voltage measurement flow is divided into three parts: the system comprises an electric field sensor, a signal conditioning unit and a data processing unit; the device is divided into an induction pole and a grounding pole, and the distance between the two poles is d; e (t) is a cable for emitting an electric field, and the sensor senses a magnetic field to output a current i;
the signal conditioning unit amplifies the current signal and is further used for subsequent data processing; the data processing unit searches an optimal solution in the relation between the electric field and the voltage by using a fitting relation between the magnetic field and the voltage and acquires a voltage optimal value by using a genetic algorithm;
u can be utilized in T-type circuit T1 ＝U T2 ＝U T3 This feature establishes an fitness function, specifically:
j is an fitness function; n is the number of sampling points; u (U) T1 (i)、U T2 (i)、U T3 (i) And (3) for the terminal voltage obtained by calculating the initial ends of the three branches, the original line parameters are brought into a distribution parameter model calculation formula, an optimal solution is searched through a genetic algorithm, J is less than or equal to 1% as a convergence condition, and a parameter result is output.
4. The method for positioning a T-type hybrid line fault based on traveling wave time difference according to claim 3, wherein the Step2 comprises the following specific steps:
assuming that the M branch fails, N, S branch is a normal branch, and selecting any one of the N branch or the S branch and the M branch to form a double-end hybrid transmission line model; l (L) MB 、L DE 、L HN For the length L of the three overhead lines in the mixed line BD 、L EH The length of the cable is two sections; A. c, E, H, J is the midpoint of the hybrid line, B, D, G, I is the intersection of the hybrid line, F is the fault setpoint, v c 、v 0 Respectively representing the propagation speed of fault traveling waves in the cable and the overhead line;
when a fault occurs at the A, C, E, H, J point, the time difference of the fault traveling wave reaching buses at two ends is as follows:
when a fault occurs at the B, D, G, I point, the time difference of the fault traveling wave reaching buses at two ends is as follows:
the time difference that the fault traveling wave reaches the acquisition points at the two ends is deltat, and when the line actually breaks down, the fault point area judgment result and the type of the traveling wave received by the M end for the second time are shown in the table 1.
Table 1 time-difference comparison results
5. The method for positioning a T-type hybrid line fault based on traveling wave time difference according to claim 4, wherein the Step3 comprises the following specific steps:
step2 judges the fault according to the line parametersAfter the branches, selecting a non-fault branch to form a double-end hybrid transmission line model, calculating the time difference delta t of fault initial traveling wave reaching buses at two ends, and comparing delta t with the preset point time difference delta t x Comparing, determining fault section on fault branch, and performing fault distance L F The calculation process is as follows:
step3.1, when a fault occurs in the left half section of the overhead line, the M end receives reflected waves of which the second traveling wave is a fault point; l (L) MX1 The distance from the connecting point before the fault section overhead line to the M-end bus is determined through time difference comparison; t is t m2 、t m1 The time for the fault traveling wave to reach the M-terminal bus for the second time and the first time respectively; fault ranging is defined as:
step3.2, when a fault occurs in the right half section of the overhead line, the M end receives the second traveling wave as a reflected wave of the mixed line connection point; l (L) MX2 The distance from the connecting point after the fault section overhead line to the M-end bus is determined through time difference comparison; fault ranging is defined as:
step3.3, when a fault occurs in the left half section of the cable, the M end receives the second traveling wave as a fault point reflected wave; l (L) MX3 The distance from the connecting point before the cable line of the fault section to the bus at the M end is determined through time difference comparison; fault ranging is defined as:
step3.4, when a fault occurs in the right half section of the cable, the M end receives the second traveling wave as a reflected wave of the mixed line connection point; l (L) MX4 Is obtained by comparing time differencesThe distance from the connecting point behind the cable line of the fault section to the M-end bus is determined; fault ranging is defined as:
step3.5 when Δt equals to the pre-calculated Δt x When the fault point is located at the key point or the connection point of the hybrid line; l (L) MX5 Is the hybrid line midpoint or junction distance; fault ranging is defined as:
L F ＝L MX5 (15)。
6. the method for positioning a T-type hybrid line fault based on traveling wave time difference according to claim 5, wherein the Step4 specifically comprises the steps of:
step4.1, the traveling wave data x= [ X ] can be obtained through the traveling wave sampling device 1 ,x 2 ,x 3 …x i ]Wherein x is i Representing the sampling value at the ith moment, and forming two different matrixes X by linear mapping of discrete sampling data 1 ，X 2 Expressed as:
X i+1 ＝AX i (16)
X 1 ＝[x 1 ,x 2 ,x 3 ,...x n-1 ] (17)
X 2 ＝[x 2 ,x 3 ,x 4 ...x n ] (18)
a is the state matrix of the discrete system, matrix X 1 ,X 2 The relation is:
X 2 ＝Ax 1 (19)
first pair mapping matrix X 1 Performing singular decomposition:
X 1 ＝B∑V T (20)
A'＝BAB' (21)
b, V is a unitary matrix, A' is an approximation matrix of the state matrix A, and Σ is a singular diagonal matrix;
at this time, after solving by minimization, a is approximately equal to a':
A≈A'＝B T X 2 V∑ -1 (22)
the dimension reduction of the high-dimensional state matrix is realized in the approximation process, and the traveling wave fault characteristic information in the matrix A' is reserved; to obtain fault information, the matrix a' is decomposed:
A'w i ＝c i w i (23)
w i ,c i for the eigenvectors and eigenvalues of matrix A', w will be i ,c i Forming a new matrix W, C:
A'W＝CW (24)
in order to obtain the modal quantity containing the traveling wave fault information, defining the phi column vector of the matrix as one decomposed modal quantity, and then:
φ＝X 2 V∑ -1 W (25)
the Teager energy operator can reflect the energy change of the signal, and obtains the instantaneous energy at the moment of change through differential operation, namely:
setting sampling frequency, intercepting a set number of sampling points for sampling, decomposing the decoupled alpha modulus of the sampling points by the DMD to obtain a Teager energy curve, wherein the highest energy point detected in the wave head is the traveling wave reaching moment, and the traveling wave energy is detected to be suddenly changed at the moment, and the method is particularly shown in figures 10 and 11.
7. The method for locating a fault in a T-type hybrid line based on traveling wave time difference as set forth in claim 6, wherein Step4, after Step4.1 is completed, further comprises the steps of:
step4.2, choose not corrected waveThe fault distance obtained by taking the speed calculation into the positioning calculation is taken as an approximation value l 0 When the polynomial degree n=1, i.e. the first order polynomial is H 1 (l 0 )＝v 1 (l 0 ) The constructor is:
H 1 ＝v(l 0 )+a 1 (l-l 0 ) (27)
a 1 as a function H 1 The specific expression is:
when n=2, the basis function adds a second order polynomial on the basis of the first order polynomial to satisfy H 2 (l 2 )＝v(l 2 )，H 2 (l1)＝v(l 1 ) Constructing a function:
H 2 ＝H 1 +a 2 (l-l 0 )(l-l 1 ) (29)
in which a is 2 Is the second order difference quotient coefficient, recorded as
The Newton's interpolation polynomial expression can be obtained according to the recurrence method:
the n-order difference quotient coefficient expression is:
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| CN117406022A (en) * | 2023-10-19 | 2024-01-16 | 国网湖北省电力有限公司荆门供电公司 | Travelling wave speed dynamic correction method suitable for high-voltage line length change |
| CN117406022B (en) * | 2023-10-19 | 2024-05-17 | 国网湖北省电力有限公司荆门供电公司 | Travelling wave speed dynamic correction method suitable for high-voltage line length change |
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| CN117406022A (en) * | 2023-10-19 | 2024-01-16 | 国网湖北省电力有限公司荆门供电公司 | Travelling wave speed dynamic correction method suitable for high-voltage line length change |
| CN117406022B (en) * | 2023-10-19 | 2024-05-17 | 国网湖北省电力有限公司荆门供电公司 | Travelling wave speed dynamic correction method suitable for high-voltage line length change |
| CN117192292A (en) * | 2023-11-07 | 2023-12-08 | 昆明理工大学 | Lightning grounding electrode line fault distance measurement method and system |
| CN117192292B (en) * | 2023-11-07 | 2024-02-06 | 昆明理工大学 | Lightning grounding electrode line fault distance measurement method and system |
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