CN117406022A - Travelling wave speed dynamic correction method suitable for high-voltage line length change - Google Patents
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Abstract
The invention belongs to the field of relay protection of power systems, and discloses a traveling wave speed dynamic correction method suitable for high-voltage line length change. According to the technology, under the condition that the load of the high-voltage transmission line changes, basic parameters of the transmission line are corrected through state monitoring data of the transmission line, so that the traveling wave speed of the current line length is dynamically corrected, and the fault positioning accuracy can be effectively improved when the line breaks down. The technology firstly analyzes and demonstrates the conversion relation between the line length and the capacitance inductance parameter when the power transmission line is lengthened, and further proposes the state monitoring data of the power transmission line, defines the ratio coefficient, and utilizes the least square method to realize the real-time solution of the line length equation based on the lowest point coordinate and the tail end coordinate of the catenary; and further, based on the principle of constant quality under the change of the length of the transmission line, curve integration is applied to correct the average height of the transmission line to the ground and the radius of the transmission line, so that the updating calculation of capacitance and inductance parameters is realized, and finally, the dynamic correction of the traveling wave speed is achieved. The technology is novel, real-time line parameter correction can be achieved, accurate positioning after faults is achieved, and the fault repairing efficiency is effectively improved when the fault repairing method is applied to the high-voltage transmission line with complex topography.
Description
Technical Field
The invention relates to a traveling wave speed dynamic correction method suitable for high-voltage line length change, which aims to meet the requirement of accurate positioning during high-voltage transmission line faults and improve the quick operation and maintenance of a system.
Background
The high-voltage transmission line is an important component of a power system, is a connecting bridge for generating and using electricity, and is safe and stable to operate, and the safety and reliability of the whole power network are related. The current high-voltage transmission line in China has large span, complex traversing topography, polymorphic environment, high probability of line fault occurrence, and more than thousand times of annual tripping times of the current transmission line above 110kV according to statistics of power related departments, and becomes an electrical element which is most prone to fault in a power system.
The fault, especially permanent fault, of the line can be eliminated and recovered rapidly by accurate positioning of the fault. The traveling wave fault location method is used as a novel fault location technology, has high ranging precision and small influence by high-resistance grounding, and is widely applied to overhead lines of various voltage classes in China. However, the errors of the length parameters and the wave speed parameters used in the traveling wave calculation process still have a certain influence on the ranging result; particularly, as the number of ultra-high voltage and ultra-high voltage transmission lines is continuously increased, more transmission lines with larger span are generated, and the change of the line length of the large-span transmission lines is more obvious, so that people gradually pay attention to the influence of the line length on the travelling wave ranging result.
Aiming at the problem of line length change, a plurality of researches are currently carried out, and literature (Xie Liwei, li Yong, luo Longfu, and the like) discloses a multi-branch line fault positioning method based on pole symmetrical decomposition, china motor engineering report, 2021,41 (21): 7326-7338.) is used for achieving the purpose of eliminating the influence of the wave speed on a positioning result by establishing an equation set of the wave speed, the distance and the moment when the wave head reaches, and eliminating the parameter of the wave speed in the solving process, but the wave speed is continuously changed along with the propagation distance in the propagation process, so the method has a certain limitation. Patent (Shu Hongchun; zhong Tongyun; tian Xincui) discloses a double-end fault distance measuring method for a same-tower double-circuit direct-current transmission line with wave speed correction, and an authorized bulletin number CN 106093708B) aims at inaccurate wave speed caused by inaccurate line parameters, sets ground faults at intervals of 10km in the whole line length range of the same-tower double-circuit direct-current transmission line, obtains wave speed of the ground faults, and further obtains the wave speed of a line mode fault voltage traveling wave by adopting an iteration method based on a multipoint curve. But this approach does not account for line parameter variations that occur during actual operation. The invention calculates the line parameters in real time based on the real-time state monitoring of the power transmission line, dynamically updates the traveling wave speed, and can accurately realize the traveling wave fault location when the line fails, with high accuracy.
Disclosure of Invention
In the actual operation process of the high-voltage transmission line, the high-voltage transmission line is affected by dynamic load current, the heating degree of the transmission line is different, the length of the transmission line is changed, the line parameters are further affected, and at the moment, if a line fault occurs, larger errors are brought about by traveling wave fault positioning realized based on fixed parameters. In order to solve the secondary problem, the method acquires the actual space position of the line based on the state monitoring of the power transmission line on the basis of establishing a conversion relation model of capacitance inductance parameters and line length, realizes the real-time calculation of line length change, realizes the correction of the average height of the wire to the ground and the correction of the radius of the wire based on the relation between the line length and the space arrangement, and finally dynamically calculates the wave velocity so as to achieve the aim of improving the accuracy of the positioning of the traveling wave fault.
The technical scheme adopted by the invention is as follows:
a dynamic correction method for travelling wave speed suitable for the change of high-voltage line length includes such steps as real-time calculation of the conversion relation between capacitor and inductor parameters and line length, correction of average height of wire to ground, correction of radius of wire and dynamic correction of travelling wave speed. The method comprises the following specific steps:
step 1: based on a three-phase transmission line capacitance and inductance parameter calculation model required by wave speed calculation, when the line length changes, the three-phase transmission line capacitance and inductance parameter calculation model is converted into basic parameters to be corrected, namely the average height of the lead pair on the ground and the radius of the lead.
Step 2: and (3) applying a catenary equation and a line minimum point coordinate and a line end coordinate to realize parameter calculation based on line length stroke deformation, and further applying integration to calculate the actual line length.
Step 3: and calculating the average ground correction height of the wire based on the relation between the line length equation and the height difference and the span of the tower heights at the two ends of the line.
Step 4: based on the principle of unchanged line length change quality, a model with equal volume is established, the corrected sectional area of the wire is obtained, and then the radius of the corrected transmission line is calculated.
Step 5: based on the corrected wire parameters, dynamically calculating real-time wave velocity, and calculating a mean value by applying multi-point wave velocity calculation to serve as the final wave velocity of traveling wave fault positioning.
The invention has the beneficial effects that:
(1) Based on power transmission line state monitoring, real-time calculation of the length of a power transmission line is realized, and the use and the efficiency of the current equipment are effectively combined;
(2) Dynamically correcting the traveling wave speed, and when a line fails, ensuring accurate line parameters and high positioning accuracy;
(3) The technical principle of correcting the height of the lead to the ground and the radius of the lead is simple, the lead is easy to realize, and the lead is favorable for popularization in engineering.
Drawings
Fig. 1 is a schematic diagram of a wire arrangement and a parameter definition diagram thereof.
Fig. 2 is a schematic diagram of a catenary rectangular coordinate system.
Fig. 3 is a schematic diagram of the correction of the average height.
Fig. 4 is a schematic sectional area correction calculation diagram.
Fig. 5 is a schematic diagram of a transmission line conductor arrangement.
Fig. 6 is a schematic diagram of the height of the power line to ground in a suspended state.
Fig. 7 is a schematic view of sag of a power transmission line in a suspended state.
Fig. 8 is a waveform diagram of the head end of the fault traveling wave wavelet transform without correction wave speed.
Fig. 9 is a waveform diagram of the end of the wavelet transform of the fault traveling wave without the modified wave velocity.
Fig. 10 is a waveform diagram of the head end of a fault traveling wave wavelet transform including a modified wave velocity.
Fig. 11 is a waveform diagram of the end of the wavelet transform of the traveling wave of the fault containing the corrected wave velocity.
Detailed Description
The invention provides a traveling wave speed dynamic correction method suitable for high-voltage line length change, which specifically comprises the following steps:
step 1: conversion relation between capacitance inductance parameter and line length
The transmission line is uniformly distributed with an inductance L along the length direction of the line, a capacitance C is uniformly distributed between the transmission line and the ground, and the wave velocity of the traveling waveFrom this, it is clear that the wave speed is related to the inductance and capacitance parameters.
The basic formula involved in capacitance parameter calculation is
Wherein j=1, 2,3, represents a three-phase wire, P ii Is the self potential coefficient of the wire, P ij Is the mutual potential coefficient between the wires i and j. As shown in FIG. 1, h i For the average height of the wire i to the ground, r i For the radius of the wire i, D ij D is the distance between the mirror images of conductor i and conductor j ij Epsilon is the distance between conductor i and conductor j 0 Is the dielectric constant of air.
The basic formula involved in inductance parameter calculation is
Wherein Z is ii Z is the self-impedance of the wire ij R is the transimpedance between conductors i and j d Is a direct current resistance of a wire, alpha R As Bessel function, D g To account for the equivalent depth of the ground mirror image when the ground inductance is accounted for,r' is the average radius of the wire and ω is the system angular frequency.
From equations (1) and (2), it can be seen that the variation of the capacitance and inductance parameters, ultimately also the average height h of the wire pair i ' and wire radius r i ' forehead change.
Step 2: real-time calculation of line length change
(1) Line length Cheng Bianxing
As shown in fig. 2, a plane rectangular coordinate system is established with the low suspension point a as the origin of coordinates. a is the distance between the lowest point O and the line suspension point perpendicular to the specific load direction, l is the span, h is the distance difference between the two suspension points along the specific load direction, and is called the altitude difference for short, and beta is the included angle between the connecting line of the two suspension points and the perpendicular to the specific load direction, and is called the altitude difference angle for short. When β=0, the suspension points on both sides of the catenary are equal in height; gamma is the line specific load vertically downward in the direction and sigma 0 Is the axial stress at the lowest point. At this time, the line catenary equation
Wherein gamma is the line specific load vertically downward in the direction and sigma 0 For axial stress at the lowest point, a is the distance between the lowest point and the suspension point of the line measuring end perpendicular to the specific load direction. The equation reflects the change in the horizontal height y of the lower column of the vertical two-line column as the horizontal distance x changes. When the line length changes, the unknown quantity a and sigma exist in the equation 0 Gamma. a can generally be defined by the stateMonitoring gives, but sigma 0 Gamma cannot be monitored.
Defining the coefficient variable k of the stress ratio, settingThe catenary variance is then transformed to a variance containing only one unknown quantity, as in equation (4)
(2) And calculating a parameter k. Based on the prior video monitoring technology, the distance difference h along the specific load direction between two line towers as shown in figure 2 is obtained, and the horizontal height-h of a line with a being the vertical distance from the line to the low tower is obtained a The gear distance l is used for obtaining two coordinate points (a, -h) a ) (l, h), substituting into the formula (4) to obtain the formula (5)
Setting an initial value k of the coefficient of the stress ratio based on the formula (5) 0 In k 0 ±30％k 0 The range, using a least squares algorithm, the two equations yield the parameter k at the minimum difference.
(3) And calculating the catenary length. After the catenary equation is obtained, the calculation of the wire length can be obtained by integration using the arc length differential equation, according to equation (6), at this timeBased on this, it is possible to obtain:
and integrating the two ends of the formula (7) to obtain the following steps:
from formulas (5) and (7), it is possible to obtain:
the integral calculation of the arc length between 0 and l based on the catenary equation can obtain the line length as shown in the formula (9)
Step 3: average height correction of wire to ground
As shown in fig. 3, in the scene of considering the actual line length of the transmission line, the bottom of the tower where the lowest suspension point is located is taken as the origin to be established
And (5) a coordinate system. According to step 2, the updated stress ratio coefficients are knownThe catenary equation y' (x) for the current wire can be written in columns, then the point-to-ground height h (x) on the catenary can be expressed as:
h(x)＝h l +y′(x) (10)
in the formula, h l Is the tower height. Further, calculating the sum of the heights of the transmission lines to the ground based on the actual line length by using an integral method, and dividing the sum by the gear distance l to obtain a corrected average height h of the transmission lines to the ground i ' as shown in formula (11);
step 4: wire radius correction
In consideration of the correction of the radius of the wire of the actual wire length, the sectional area of the wire needs to be corrected first, then the outer diameter of the wire is calculated according to the corrected sectional area, and the establishment mode of the coordinate system in the calculation process is consistent with that of fig. 3. As shown in fig. 4, a line expansion analysis of a length dx of the wire is taken, and when dx→0 is defined by integration, the wire is "Qu Bianzhi", and as shown in the enlarged part of fig. 4, the radian of the wire can be ignored, and the wire is equivalent to a cylinder with delta angle with the x axis.
The initial section area of the wire is recorded as S when the initial wire length L is calculated, and the initial section area is calculated according to the actual wire lengthThe cross-sectional area at the time of calculation is +.>As shown, the height of the equivalent cylinder can be expressed as +.>According to the catenary equation of the transmission line, the included angle delta between any point on the line and the x axis can be calculated:
δ＝arctany′(x) (12)
in general, the change of the wire mass and density along with the change of the wire length is very small, and can be approximately considered as unchanged, so that the mass and the volume of the wire are consistent with the initial state. Based on the criterion that the wire mass is constant, i.e. the total volume is constant, the following equations can be listed using the curve integral equation:
wherein L is the initial line length, S is the initial sectional area of the lead, and the actual line lengthThe actual cross-sectional area is +.>l is the gear distance, and the included angle between the delta wire and the horizontal line.
The corrected wire cross-sectional area is:
because the single high-voltage transmission line is formed by twisting a plurality of strands of aluminum wires and copper wires, the cross section is correctedProduct ofThe calculation of the wire radius cannot simply take the stranded wires into account as a circular model. Let a high voltage transmission line be composed of m high voltage transmission lines with diameter d 1 And n aluminum wires with diameter d 2 The copper wires are twisted, the effect of the change of the wire length on all wire cores is considered to be consistent, the change of the diameter of the wire cores is recorded as xi, and according to a sectional area calculation formula of the multi-strand wire, the following equation is provided:
solving the equation to obtain the diameter (d) of the corrected single-strand aluminum wire 1 ζ), the diameter of the single strand copper wire is (d 2 - ζ). According to the circumscribed circle diameter algorithm of the multi-strand wires, when the number of the wire cores is different, the wire core diameter is multiplied by different coefficients k m 、k n The calculation formula of the outer diameter of the wire is d=k m (d 1 -ξ)+k n (d 2 - ζ). Taking LGJ-300/25 type wire as an example, which is formed by twisting 48 aluminum wires and 7 copper wires, the table look-up is available, 48 cores=6d 1 7 core = 3d 2 Then the wire outer diameter d=6d 1 +3d 2 。
To sum up, the corrected transmission line radius r i ' can be expressed as:
step 5: dynamic correction of traveling wave velocity
According to the corrected wire radius r i ' and pair average height h i And', substituting the inductance parameter and the capacitance parameter to calculate to obtain an inductance matrix L ' and a capacitance matrix C ' based on the actual line length. Obtaining a corrected 1-mode component L through a phase-mode conversion process by using the corrected inductance matrix and capacitance matrix (1)′ 、C (1)′ Finally obtaining the corrected wave velocity in the gearIn addition, substituting the modified 1-mode component into the wave impedance calculation formula to obtain the wave impedance +.>And substituting the accurate positioning result in the calculation of the forward wave process and the backward wave process.
A complete power transmission line comprises a plurality of gear distances, the height differences and the ratio coefficient are different, the sag changes of the power transmission lines are inconsistent, and each gear distance has a corrected wire radius and a pair average height, so that the complete power transmission line corresponds to a plurality of corrected wave speeds.
Assuming that a complete transmission line contains n spans, the modified wave speed can be represented by a matrix as:
v (1)′ ＝[v 1 (1)′ ,v 2 (1)′ ,v 3 (1)′ ,L,v n (1)′ ] (17)
taking the average value of n modified wave speedsAs the wave velocity used in the calculation of the double-end traveling wave method, so as to achieve the purpose of correcting the positioning result.
And (3) carrying out calculation analysis: calculation example 1: transmission line wave speed correction calculation
Taking a circuit between two towers for three-phase power transmission as an example, as shown in FIG. 5, the outer diameter of a wire is 23.94mm, and the calculated sectional area is 338.99mm 2 Is formed by stranding 24 aluminum wires with the diameter of 3.99mm and 7 copper wires with the diameter of 2.66mm, and k is formed by stranding m ＝4，k n =3. As shown in FIG. 5, the three phases of the lead are horizontally arranged, the phase-to-phase horizontal distance is 13m,4 phases are split, the split phase distance is 0.45m, and the direct current resistor R d The ground resistivity was 100 Ω·m, and the average height was 22 m=0.108 Ω/km. The ground wire model is 2 XLHGJJ-90, the horizontal distance is 22.5m, the ground wire diameter is 14.84mm, the direct current resistance is 0.374 ohm/km, and the average height is 40m.
And calculating the corrected wire radius and the average height of the pair according to various parameters of the line to obtain a decoupled inductance and capacitance modulus matrix. As shown in fig. 6 and 7, the maximum sag of the current line is about 21m, and the minimum point of the wire is about 23.71m from the ground according to the data in the figure, so as to simulate the height and sag of the span transmission line based on the catenary equation. According to formula (11), the average height h of the wire pair obtained by integration is utilized i As can be seen from the variation of the level difference and sag, the overall height of the wire pair to ground is greater than 22m, and the average height of the wire pair is widely different from the given calculation parameters.
The integrated wire cross-sectional area is calculated according to formulas (12), (13) and (14)The change of the sectional area delta S is approximately equal to 2.5711mm 2 . Substituting the corrected sectional area into the equation (15), solving the diameter change xi of each wire core with the diameter of about 0.014326mm, and obtaining the corrected wire radius r according to the equation (16) i ′＝11.87989mm。
According to the inductance and capacitance matrix calculation flow, table 1 shows the comparison of various parameters before and after the correction of the lead.
Table 1 comparison of parameters before and after correction
Comparing the data in table 1, it can be seen that the change in the length of the transmission line causes the radius of the transmission line to change from the average height to the average, consistent with the theoretical portion. By comparing the capacitance and inductance modulus matrix before and after correction, it can be obtained that the wire line mode capacitance, inductance and zero mode capacitance based on the actual line length model are different from those when the span model is used, and different wave speed values are obtained. According to the calculation result, since there is a certain gap between the change Δv= 67.307km/s of the wave velocity values before and after correction, it is necessary to consider the change in the wave velocity of the traveling wave in the actual line length scene so as to minimize the range error as much as possible.
Calculation example 2: traveling wave fault location
In order to verify the effect of the wave speed correction method in double-end traveling wave fault positioning, a 500kV line model with 300 gear distances is built, the length of each gear is 428.246m after correction, and the total length of the simulation line is 128.4738km. According to Table 1, the average wave velocity before correction of the line isThe average wave speed after correction is
The inductance and capacitance modulus parameters before and after correction and the traveling wave velocity expansion traveling wave fault location simulation calculation are respectively used in table 1. Setting that single-phase earth faults occur at the positions 8km, 30km, 64km, 100km and 123km away from the head end, wherein the fault moment is 0.035s, the sampling frequency is 1MHz, the faults continue to the end of simulation, and the maximum value of a wavelet mode is obtained for fault voltage traveling waves recorded at two ends so as to obtain the arrival moment of the wave head. Table 2, table 3 shows the first fault head arrival time (starting from the fault occurrence time), fault ranging results and errors when calculated using different parameters. Taking a fault distance of 30km as an example, fig. 8 and 9, and fig. 10 and 11 show wavelet transformation diagrams of line mode fault traveling waves acquired at two ends of a line, and the corresponding time of an initial wave head mode maximum value is amplified and identified.
Table 2 fault location results using uncorrected modulus parameters & wave speed
TABLE 3 fault location results using corrected modulus parameter & wave speed
Comparing table 2 with table 3, the error is larger when the line mode component and the wave speed obtained by calculating given parameters are used for fault location, and considering that the allowable error of the current traveling wave method is generally within 300m, the error is close to 600m when the fault distance is 30km according to the data in table 2, and exceeds the allowable error. The arrival time of the wave head changes when the double-end traveling wave fault positioning is carried out by using the corrected line parameters and the wave speed, the final ranging errors are smaller than 50m, and the positioning precision is obviously improved. Based on the above, the wave speed correction method provided by the patent can effectively reduce the ranging error and further accurately position the result.
Claims (6)
1. A traveling wave speed dynamic correction method adapting to the length change of a high-voltage line is characterized in that: the correction method comprises the steps of conversion relation between capacitance and inductance parameters and line length, real-time calculation of line length change, correction of average height of a wire to ground, correction of radius of the wire and dynamic correction of traveling wave speed.
2. The method for dynamically correcting the traveling wave velocity adapted to the length change of the high-voltage line according to claim 1, wherein the method comprises the following steps: the conversion relation between the capacitance inductance parameter and the line length comprises the following steps: for any three-phase power transmission line, when capacitance and inductance parameters are calculated, the self potential coefficient, mutual potential coefficient, line self impedance and mutual impedance of the wire are mainly calculated, and when the line length is changed, the basic parameters used are directly influenced to be h i 、r i Wherein h is i The average height of the conducting wire i to the ground is set; r is (r) i For the radius of wire i, i=1, 2,3, representing a three-phase wire.
3. The method for dynamically correcting the traveling wave velocity adapted to the length change of the high-voltage line according to claim 1, wherein the method comprises the following steps: the real-time calculation of the line length change comprises the following steps: when the high-voltage line transmits different loads, the line heats for a long time, the line length changes due to the fact that the line length arc sags greatly, and in the process of calculating the line length changes in real time, the specific steps are as follows:
step 1:line length Cheng Bianxing: according to the equation of the catenary of the lineWherein gamma is the line specific load vertically downward in the direction and sigma 0 For axial stress at the lowest point, a is the distance between the lowest point and the suspension point of the line measuring end, which is perpendicular to the specific load direction, the equation reflects the change of the horizontal height y of the lower tower of the vertical two line towers along with the change of the horizontal distance x, and the specific coefficient is defined>The linear length difference is deformed to +>
Step 2: calculating a parameter k: based on the existing video monitoring technology, obtaining a distance difference h along the specific load direction between two line towers, wherein the vertical distance of a-line path is lower than the horizontal height-h of a tower a The gear distance l is used for obtaining two coordinate points (a, -h) a ) (l, h) substituting a line catenary equation, and calculating a parameter k by using a least square algorithm;
step 3: the integral calculation of the arc length between 0 and l based on the catenary equation can obtain the line length as shown in the formula (1)
4. The method for dynamically correcting the traveling wave velocity adapted to the length change of the high-voltage line according to claim 1, wherein the method comprises the following steps: the step of wire average ground height correction is as follows: based on the catenary equation y' (x), any point-to-ground height h (x) thereof is expressed as h (x) =h l +y′(x)，h l The tower height is the reference coordinate; calculating the sum of the heights of the transmission lines to the ground based on the actual line length by using an integral method, and dividing the sum by the gear distance l to obtain a corrected average height h of the transmission lines to the ground i ' e.g. formula (2)
5. The method for dynamically correcting the traveling wave velocity adapted to the length change of the high-voltage line according to claim 1, wherein the method comprises the following steps: the wire radius correction steps are as follows:
step 1: for a section of line, the mass m=ρvg, ρ line density, V is the volume, based on the principle of constant mass, that is, the volume V is constant, after the line becomes longer, the line sectional area is changed, and an equation is establishedWherein L initial line length, initial sectional area of S conductor, actual line length +.>The actual cross-sectional area is +.>l is the gear distance, the included angle between the delta wire and the horizontal line is calculated to obtain the corrected wire sectional area
Step 2: because the single high-voltage transmission line is formed by twisting a plurality of strands of aluminum wires and copper wires, the cross section area is correctedThe calculation of the wire radius cannot be considered simply as a round model, assuming a high voltage transmission line consisting of m strands of diameter d 1 And n aluminum wires with diameter d 2 Is formed by twisting copper wires according to a sectional area calculation formula of the multi-strand wireζ is the variation of the core diameter, and the diameter of the corrected single strand aluminum wire is (d 1 ζ), the diameter of the single strand copper wire is (d 2 ζ), according to the circumscribed circle diameter algorithm of the multiple strands, the core diameter needs to be multiplied by different coefficients k when the core numbers are different m 、k n Corrected transmission line radius r i ' is->
6. The method for dynamically correcting the traveling wave velocity adapted to the length change of the high-voltage line according to claim 1, wherein the method comprises the following steps: the step of dynamic correction of the traveling wave velocity is as follows:
step 1: dynamically calculating inductance parameters and capacitance parameters based on the corrected wire radius and the pair-average height, and obtaining corrected 1-mode component L through phase-mode conversion (1)′ 、C (1)′ Correcting the wave velocity at this time
Step 2: for a power transmission line with n monitoring spans, the modified wave speed can be expressed as v by a matrix (1)′ ＝[v 1 (1)′ ,v 2 (1)′ ,v 3 (1)′ ,L,v n (1)′ ]Taking an average valueAs the wave velocity used in the calculation of the fault traveling wave positioning method, the purpose of correcting the positioning result is achieved.
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