CN113075503B - Double-end traveling wave distance measurement method and system for direct-current transmission line - Google Patents
Double-end traveling wave distance measurement method and system for direct-current transmission line Download PDFInfo
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Abstract
The invention relates to a double-end traveling wave distance measurement method and a double-end traveling wave distance measurement system for a direct current transmission line. The method comprises the following steps: for the adaptability problem of the wavelet transform singular point detection technology to the traveling wave head calibration, the improved Hilbert-Huang transform with the complete self-adaptive decomposition capability is provided, and the traveling wave head is calibrated by utilizing the peak frequency point of high-frequency mutation; for the problem that the arrival time of the traveling wave head and the traveling wave velocity are difficult to organically unify, the method proposes that the Newton interpolation algorithm is used for gradually compensating the wave velocity, the wave velocity after each compensation is substituted into a distance measurement formula considering the change of the wave velocity, and the algorithm terminates the circulation after the convergence precision of the distance measurement result meets the set convergence condition, so as to obtain the distance measurement result gradually approaching the real fault distance. The invention has the advantages that: the calibration of the traveling wave head is reliable and accurate, the arrival time of the traveling wave head and the traveling wave speed can be unified, the ranging accuracy is high, the ranging result is stable and reliable, the requirement on the sampling frequency is not high, and the engineering realization is facilitated.
Description
Technical Field
The invention belongs to the field of fault location of extra-high voltage direct current transmission lines, and particularly relates to a double-end traveling wave distance measurement method and system for a direct current transmission line.
Background
At present, theoretical research on fault location of a direct current transmission line is divided into a traveling wave method, a natural frequency method and a fault analysis method from three angles of time, frequency and space. Along with the application of engineering practice, a development trend which takes a traveling wave method as a main part and assists improvement of the distance measurement precision by a natural frequency and fault analysis method is gradually formed in the field of fault distance measurement. The traveling wave method is classified into a single-ended method and a double-ended method according to its principle. In the single-ended traveling wave distance measurement method, when a high-resistance ground fault occurs, the amplitude of a reflected wave head is too small to capture, so that the single-ended method fails to measure the distance, and therefore the double-ended method is frequently adopted in engineering to measure the distance. In the double-end traveling wave distance measurement method, the calibration of the traveling wave head and the organic integration of the arrival time of the traveling wave head and the traveling wave speed are the main factors influencing the distance measurement precision.
Wavelet Transformation (WT) has been used as the mainstream method of the discontinuity detection technology in the power system, however, the time-frequency localization analysis result of the Wavelet Transformation on the signal is influenced by the Wavelet basis and the decomposition scale, and once the Wavelet basis and the decomposition scale are selected, it must be used to analyze various kinds of fault signals. The characteristics of different fault types, different fault degrees and fault information are different, and the self-adaptability problem during wavelet decomposition exists when wavelet transformation is performed on signals under different fault conditions by using a fixed wavelet basis and a decomposition scale.
When a fault occurs in a direct current line, a fault step wave is generated at a fault point, a step signal comprises frequency components from 0 to infinity, and the amplitude of the component with higher frequency is smaller. The fault traveling wave is affected by the dispersion effect of the traveling wave by the line in the process of propagating along the line, so that phase deviation occurs between frequency components, the amplitude of each frequency component is attenuated, the result is expressed as the distortion of the shape of a wave head, the front edge of the wave head is composed of high-frequency components, and the tail part of the wave head contains high-frequency and low-frequency components. And if the amplitude resolution limit of the traveling wave detection device in the actual engineering is not considered, determining the wave speed of the fault traveling wave by the wave speed of the highest-frequency component at the front edge of the wave head, wherein the wave speed of the traveling wave is equal to the light speed. However, in practical engineering, the amplitude resolution of the traveling wave detection device is always limited, and it is impossible to detect an infinitely small signal. When the line far end and the high resistance earth fault occur, the amplitude attenuation effect on the traveling wave is enhanced, and at this time, the amplitude of the highest frequency component traveling wave at the front edge of the wave head may be smaller than the amplitude resolution of the traveling wave detection device, so that the wave speed of the fault traveling wave is determined by the wave speed of the second high frequency component traveling wave, and the actual wave speed schematic diagram is shown in fig. 1. From the above analysis, different fault distances and different transition resistances will have different degrees of influence on the traveling wave speed. However, in the actual traveling wave ranging method, for convenience of calculation, the traveling wave speed is generally taken as a fixed value close to the light speed according to engineering operation experience, and the problem that the used wave speed and the arrival time of the traveling wave head are difficult to organically unify exists, so that the precision of the traveling wave ranging method is influenced.
Disclosure of Invention
The invention aims to provide a method and a system for measuring the distance of double-end traveling waves of a direct-current transmission line, so as to solve the problems.
In order to realize the purpose, the invention adopts the following technical scheme:
a double-end traveling wave distance measurement method for a direct current transmission line comprises the following steps:
Step 3, subtracting L from the total length L of the line 0 Obtaining the fault distance L-L between the fault point and the inversion side 0 Respectively combine l 0 、L-l 0 As Newton interpolation polynomial P n (l) The input quantity of (2) is solved to respectively obtain the wave velocity v when the traveling wave reaches the distance measuring devices at the two ends M0 、v N0 ；
Step 4, mixing v M0 、v N0 Substituting into a double-end traveling wave distance measurement formula considering the wave velocity change to obtain the fault distance l after the first iteration 1 At this time l 1 Bi | (R) | 0 The actual fault distance is closer;
step 5, adding l 1 、L-l 1 As Newton interpolation polynomial P n (l) Repeating the steps 3 and 4 to obtain a distance measurement result vector [ l ] gradually approaching to the real fault distance along with the increase of the iteration times 0 l 1 l 2 … l k-1 l k ]；
Step 6, setting the convergence precision of the algorithm to obtain the final ranging result l = (l) k +l k-1 )/2。
Further, in step 1: the calibration of the traveling wave head adopts improved Hilbert-Huang transformation, which specifically comprises the following steps:
aiming at modal aliasing and false component phenomena generated during empirical mode decomposition in Hilbert-Huang transform HHT, gaussian white noise is added into an original signal, and then improved Hilbert-Huang transform of empirical mode decomposition is carried out, wherein the improved Hilbert-Huang transform comprises the following steps of:
adding a group of white Gaussian noises w (t) into an original signal S (t) to obtain a new signal S (t);
S(t)＝s(t)+w(t) (1)
EMD decomposition is carried out on the new signal S (t) to obtain n inherent mode functions imf with the frequency arranged from high to low in sequence n A component;
adding different white Gaussian noise w into the original signal j (t) (j =1 to m) m times in total;
for eliminating the influence caused by Gaussian white noise, m imfs are processed jk Component averaging:
for the highest frequency imf 1 The components are subjected to Hibert transformation to obtain corresponding instantaneous amplitude A (t) and instantaneous phase
The instantaneous frequency f (t), wherein,
finally, imf is drawn according to f (t) 1 And (5) component time-frequency diagrams.
Further, the arrival time of the highest frequency component detected in the wave head is defined as the arrival time of the fault traveling wave at which the fault transient voltage waveform exhibits a sharp abrupt change at imf 1 The time-frequency images of the components show a high frequency abrupt change that is noticeable.
Further, in step 2, the traditional double-end traveling wave ranging formula is as shown in formula (6):
in the formula: t is t 0 The absolute time when a fault occurs on the line; t is t 1 The moment when the initial traveling wave head of the fault point reaches the M end is the moment; t is t 2 The time when the initial traveling wave head of the fault point reaches the N end is the time; v. of fix Represents a fixed empirical wave speed; l is the total length of the line.
Solving to obtain:
further, in step 4, a double-end traveling wave ranging formula considering the change of the wave velocity is shown as formula (8):
in the formula: l is the total length of the line, v M 、v N Respectively representing the wave speed when the traveling wave reaches the rectifying side and the inverting side distance measuring device, and l is the fault distance obtained by solving.
Solving to obtain:
further, specifically: v is to be M0 、v N0 Substituting into a double-end traveling wave distance measurement formula, t, considering the change of wave speed 0 The absolute time when a fault occurs on the line; t is t 1 The moment when the initial traveling wave head of the fault point reaches the M end is the moment; t is t 2 The time when the initial traveling wave head of the fault point reaches the N end is the time; v. of M 、v N Respectively representing the wave speed, x, of the fault travelling wave arriving at the rectifying side and the inverting side M 、x N Respectively represents the distance between a fault point and two ends of the rectifying station and the inversion station, F represents the fault point, and L is the total length of the line.
Further, in step 5, fitting v (l) by using a newton interpolation algorithm comprises the steps of:
when n =1, n represents the order of the interpolating polynomial, and there are two interpolating nodes l 0 、l 1 Recording a first order interpolation polynomial as P 1 (l) It satisfies P 1 (l 0 )＝v(l 0 )，P 1 (l 1 )＝v(l 1 ) Structure P of 1 (l) Is composed of
P 1 (l) Viewed as interpolation by the zeroth order P 0 (l)＝v(l 0 ) Corrected to obtain, i.e.
P 1 (l)＝P 0 (l)+a 1 (l-l 0 ) (11)
In the formula, a 1 Coefficient of first order difference quotient for function v (l), denoted v [ l ] 0 ,l 1 ]Then there is
When n =2, there are three interpolation nodes/ 0 、l 1 、l 2 Recording a second-order interpolation polynomial as P 2 (l) It satisfies P 2 (l 0 )＝v(l 0 )，P 2 (l 1 )＝v(l 1 )，P 2 (l 2 )＝v(l 2 ) Structure P of 2 (l) Is composed of
In the same way, P 2 (l) Viewed as being interpolated by a first order P 1 (l)＝P 0 (l)+a 1 (l-l 0 ) Is corrected by
P 2 (l)＝P 1 (l)+a 2 (l-l 0 )(l-l 1 ) (14)
In the formula, a 2 A second order difference quotient coefficient of the function v (l), denoted as v [ l ] 0 ,l 1 ,l 2 ]Then there is
Obtaining an expression of an n-order Newton interpolation polynomial according to a recursion method as
P n (l)＝P 0 (l)+a 1 (l-l 0 )+a 2 (l-l 0 )(l-l 1 )+…+a n (l-l 0 )(l-l 1 )…(l-l n-1 ) (16)
In the formula, a n Coefficient of quotient of order n of difference, denoted as v [ l ], for function v (l) 0 ,l 1 ,…,l n ]
P n (l) I.e. an interpolating polynomial function for wave velocity compensation instead of the unknown function v (l).
Further, a direct current transmission line bi-polar travelling wave range finding system includes:
the time calibration module is used for calibrating the time t when the voltage traveling wave reaches the rectifying side and the inverting side distance measuring device by utilizing improved Hilbert-Huang transformation after a fault occurs 1 、t 2 。
The initial value calculation module of the fault distance is used for calculating t 1 、t 2 Substituting into the traditional double-end traveling wave distance measurement formula to obtain an initial value of the fault distance, and recording as l 0 ；
The wave speed acquisition module for subtracting L from the total length L of the line when the traveling wave reaches the distance measuring devices at two ends 0 Obtaining the fault distance L-L between the fault point and the inversion side 0 Respectively mixing l 0 、L-l 0 Solving as the input quantity of Newton interpolation polynomial to respectively obtain the wave velocity v when the traveling wave reaches the distance measuring devices at the two ends M0 、v N0 ；
A fault distance obtaining module for obtaining v M0 、v N0 Substituting into a double-end traveling wave distance measurement formula considering the wave velocity change to obtain the fault distance l after the first iteration 1 At this time l 1 Bi | (R) | 0 The actual fault distance is closer;
the distance measuring module of the real fault distance is used for measuring the true fault distance 1 、L-l 1 As Newton interpolation polynomial P n (l) Repeating the steps 4 and 5 to obtain a ranging result vector [ l ] gradually approaching to the real fault distance along with the increase of the iteration times 0 l 1 l 2 … l k-1 l k ]。
The distance measurement result acquisition module is used for setting the convergence precision of the algorithm to obtain the final distance measurement result l = (l) k +l k-1 )/2。
Compared with the prior art, the invention has the following technical effects:
the invention adopts the improved Hilbert-Huang algorithm to calibrate the wave head, and solves the problem of self-adaptability of wavelet base selection when the travelling wave head is calibrated by utilizing wavelet transformation.
The invention adopts Newton interpolation algorithm to compensate the wave velocity, solves the problem that the wave velocity used and the arrival time of the traveling wave head are difficult to be organically unified, and eliminates the influence of the problem of changing the wave velocity on the distance measurement precision of the traveling wave method.
The invention has high ranging precision, stable and reliable ranging result and low requirement on sampling frequency, and is beneficial to engineering realization.
Drawings
Fig. 1 is a schematic diagram of an actual wave velocity.
Fig. 2 is a fault voltage waveform diagram.
FIG. 3 is a time-frequency diagram of the imf1 component.
FIG. 4 is a schematic diagram of a simulation system model.
FIG. 5 is a graph showing the variation of wave velocity with the distance to failure and the transition resistance.
Fig. 6 is a diagram illustrating a conventional double-ended traveling wave ranging principle.
Fig. 7 is a schematic diagram of double-ended traveling wave ranging in consideration of a wave velocity change characteristic.
FIG. 8 is a flow chart of the method presented herein.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
calibration of traveling wave heads using improved hilbert-yellow transform
Hilbert-Huang transform (HHT) is a time-frequency local processing method with self-adaptive analysis capability on various fault signals, does not have a fixed prior base, and is completely self-adaptive to the local processing of the signals. In view of the modal aliasing and spurious component phenomena generated during empirical mode decomposition in HHT transforms, professor Flandrin and professor Huang propose an Improved Hilbert-yellow transform (IHHT) that adds white gaussian noise to the original signal and then performs empirical mode decomposition, the steps of which are as follows:
a new signal S (t) is obtained by adding a set of white Gaussian noises w (t) to the original signal S (t).
S(t)＝s(t)+w(t) (1)
EMD decomposition is carried out on the new signal S (t) to obtain n inherent mode functions (imf) with the frequencies sequentially arranged from high to low n ) And (4) components.
Adding different white Gaussian noise w into the original signal j (t) (j =1 to m), m times in total.
For eliminating the influence caused by Gaussian white noise, m imfs are subjected to jk Component averaging:
to the imf of the highest frequency 1 The components are subjected to Hibert transformation to obtain corresponding instantaneous amplitude A (t) and instantaneous phase
The instantaneous frequency f (t), wherein,
finally, imf is drawn according to f (t) 1 And (5) component time-frequency diagrams.
The arrival time of the highest frequency component detectable in the wave head, defined as the arrival time of the fault traveling wave for this purpose, at which the fault transient voltage waveform exhibits a sharp abrupt change, at imf 1 The time-frequency images of the components show obvious high-frequency abrupt changes, which are shown in fig. 2 and 3.
Compensation of travelling wave speed by Newton's interpolation
It can be known from analysis in the research background that different fault distances and different transition resistances will have different degrees of influence on the traveling wave speed. In order to research the relationship between the traveling wave speed, the fault distance and the transition resistance, a +/-800 kV bipolar extra-high voltage direct current transmission engineering simulation model shown in figure 4 is used for simulating the wave speed change conditions under the condition of single-pole grounding faults of which the positions 100km, 300km, 600km, 800km, 1200km and 1400km away from a rectifying side are grounded through transition resistances of 0 omega, 100 omega and 300 omega respectively, and the wave speed change curve is shown in figure 5. As can be seen from fig. 5, at any fault point in the full-length range of the line, when the transient resistance is changed from 0 Ω to 100 Ω or 300 Ω, the range of the change in the wave speed of the traveling wave due to the transient resistance is small, and the degree of the change is approximately negligible compared with the range of the change in the wave speed due to the same transient resistance at different fault distances, that is, the actual traveling wave speed can be approximately regarded as a unitary function of the fault distance, that is, v = v (l).
Considering that the functional relationship between the traveling wave speed and the fault distance is influenced by a plurality of factors in practical engineering and is difficult to be substituted, the problem can be solved by considering a function fitting method. According to the interpolation concept, if a polynomial function P (l) can be constructed and can satisfy P (l) k )＝v(l k ) (k =0,1, \8230;, n), then P (l) can be fitted as a known interpolation function to v (l) for solving for wave velocity values at other unknown fault distances.
Currently, the mature and programmed interpolation algorithms include lagrangian interpolation, newton interpolation, hermitian interpolation and the like. When the Lagrange interpolation is utilized, when interpolation nodes are increased, all Lagrange interpolation basis functions need to be recalculated, when the method is applied to the fault distance measurement problem, reprogramming is needed when a group of fault data is newly added, and the algorithm continuity is poor. The Hermite interpolation can not only meet the condition that function values on interpolation nodes are equal, but also meet the condition that a first derivative function value on the interpolation nodes is also equal, and the corresponding algorithm programming is complex. Compared with the Newton interpolation algorithm and the Newton interpolation algorithm, the Newton interpolation algorithm can meet the problem requirements, meanwhile, the algorithm programming is simple, and the convergence speed of the interpolation remainder is high.
The step of fitting v (l) by using a Newton interpolation algorithm is as follows:
when n =1, (n represents interpolation)Polynomial order, in which case there are two interpolation nodes l 0 、l 1 ) Recording a first order interpolation polynomial as P 1 (l) It satisfies P 1 (l 0 )＝v(l 0 )，P 1 (l 1 )＝v(l 1 ) Can construct P 1 (l) Is composed of
P 1 (l) Can be regarded as a zero-order interpolation P 0 (l)＝v(l 0 ) Corrected to obtain, i.e.
P 1 (l)＝P 0 (l)+a 1 (l-l 0 ) (7)
In the formula, a 1 Coefficient of first order difference quotient for function v (l), denoted v [ l ] 0 ,l 1 ]Then there is
When n =2, (there are three interpolation nodes/ 0 、l 1 、l 2 ) Recording a second-order interpolation polynomial as P 2 (l) It satisfies P 2 (l 0 )＝v(l 0 )，P 2 (l 1 )＝v(l 1 )，P 2 (l 2 )＝v(l 2 ) Can construct P 2 (l) Is composed of
In the same way, P 2 (l) Can be regarded as being formed by a first order interpolation P 1 (l)＝P 0 (l)+a 1 (l-l 0 ) Is corrected by
P 2 (l)＝P 1 (l)+a 2 (l-l 0 )(l-l 1 ) (10)
In the formula, a 2 A second order difference quotient coefficient of the function v (l), denoted as v [ l ] 0 ,l 1 ,l 2 ]Then there is
When n =3, the number of the bits is increased,
……
according to the recursion method, the expression of n-order Newton interpolation polynomial is obtained
P n (l)＝P 0 (l)+a1(l-l 0 )+a 2 (l-l 0 )(l-l 1 )+…+a n (l-l 0 )(l-l 1 )…(l-l n -1) (12)
P n (l) I.e. an interpolated polynomial function for wave speed compensation instead of the unknown function v (l). In the formula, a n Coefficient of quotient of n order difference, denoted v [ l ], for function v (l) 0 ,l 1 ,…,l n ]Then there is
With the simulation system shown in FIG. 4, the total length of the line is 1 500km, and from 50km of the line, a unipolar metallic ground fault is set with a step length of 100km, and an interpolated node vector l of the fault distance is obtained 15 Calculating data in Matlab to obtain wave velocity vector v 15 From l 15 、v 15 Structure P 14 (l) For compensation of wave velocity.
According to the construction idea of the Newton interpolation polynomial, the high-order interpolation polynomial can be regarded as being obtained by successively modifying the low-order interpolation polynomial, and the algorithm has good continuity. At the same time, the coefficient of the contrast quotient a n The determination of (a) also has a recurrences of an obvious rule. Along with the increase of the number of interpolation nodes, the order of the interpolation polynomial is gradually improved, and the fitting degree of the interpolation function and the original function is gradually improved.
The invention provides a double-end traveling wave distance measurement method for an extra-high voltage direct current transmission line with higher distance measurement precision, and particularly relates to calibration of a traveling wave head by using improved Hilbert-Huang transformation and compensation of traveling wave speed by using a Newton interpolation algorithm so as to achieve the purposes of accurate calibration of the traveling wave head and unification of the traveling wave speed and the arrival time of traveling waves. The specific implementation of the method provided herein is described with reference to (fig. 6-8), and the specific process is as follows:
firstly, after a fault occurs, the time t when the voltage traveling wave reaches the distance measuring devices at the rectifying side and the inverting side is calibrated by utilizing an improved Hilbert-Huang algorithm 1 、t 2 Then the distance is substituted into the traditional double-end traveling wave distance measurement formula (15) corresponding to the figure 6 (l in the figure 6 is the distance between the fault point F and the M end; t 0 The absolute time when a fault occurs on the line; t is t 1 The moment when the initial traveling wave head of the fault point reaches the M end is the moment; t is t 2 The time when the initial traveling wave head of the fault point reaches the N end is the time; v. of fix Represents a fixed empirical wave speed; l is the total line length).
Solving to obtain:
an approximation l of the fault distance can be obtained without taking into account the change in wave speed 0 Then subtracting L from the total length L of the line 0 Obtaining the fault distance L-L between the fault point and the inversion side 0 。
Secondly, respectively adding l 0 、L-l 0 As Newton interpolation polynomial P n (l) The input quantity of (2) is solved to respectively obtain the wave velocity v when the traveling wave reaches the distance measuring devices at the two ends M0 、v N0 。
Finally, v is M0 、v N0 Substituting into the double-ended traveling wave ranging formula (17) corresponding to FIG. 7 (t in FIG. 7) considering the variation of the wave velocity 0 The absolute time when a fault occurs on the line; t is t 1 The moment when the initial traveling wave head of the fault point reaches the M end is obtained; t is t 2 The time when the initial traveling wave head of the fault point reaches the N end is the time; v. of M 、v N Are respectively provided withRepresenting the wave speed, x, of the fault travelling wave arriving at both ends of the rectifying side and the inverting side M 、x N Respectively representing the distance between a fault point and two ends of the rectifying station and the inversion station, F representing the fault point, and L representing the total length of the line).
Solving to obtain:
an approximation of the ratio l can be obtained 0 Closer to the true fault distance 1 。
Then mix l 1 、L-l 1 Repeating the steps in the second step and the last step as the input quantity of the Newton interpolation polynomial, and obtaining the ranging result l gradually approaching to the real fault distance along with the increase of the iteration times 0 l 1 l 2 … l k-1 l k ]Defining a fluctuation coefficient λ = | l k -l k-1 I, λ will gradually approach zero. In theory λ can be set to be infinitesimal, but taking λ to 0.003 has sufficient ranging accuracy due to engineering practice and convergence speed of the algorithm. The final ranging result is
The ranging process of the method provided by the invention is shown in fig. 8.
Table 1 to table 4 show the ranging results of the method proposed herein, verifying the effectiveness of the proposed method.
According to the principle of using the newton interpolation algorithm to compensate the wave velocity, the convergence of the algorithm is affected by the initial value of the given wave velocity (the fixed empirical wave velocity in the conventional distance measurement formula) and the order of the newton interpolation polynomial. In order to analyze the influence of different given wave velocity initial values on the convergence condition of the algorithm, the wave velocity initial values are respectively set as c and 0.94c wave velocity vector v 15 The average value of (1) is (generally, the fixed empirical wave velocity is 0.94c in engineering practice), and then convergence conditions when unipolar metallic earth faults occur at positions l =100km, 300km, 600km, 800km, 1200km and 1400km are calculated respectively. At this time, the Newton interpolation polynomial is taken as P 14 (l) And carrying out wave velocity compensation. The ranging results are shown in table 1. In the table: l represents the true fault distance; 9 of 9/99.99991 represents the number of iterations, and 99.99991 represents the ranging results.
TABLE 1 Convergence using different initial values of wave velocity
As can be seen from table 1, the method has high ranging accuracy in the whole length range of the line no matter what value the initial value of the given wave velocity is. When faults are close to two ends of a line, the convergence speed of the line is slightly different along with different initial values of given wave speeds; in the case of a fault in the middle of the line, the convergence speed is hardly affected by the initial value of the given wave speed.
In order to verify that the convergence condition of the algorithm is influenced by different orders of Newton interpolation polynomials, from the position of 50km of a line, unipolar metallic earth faults are respectively set with the step length of 50km and 100km to obtain respective Newton interpolation polynomials P 28 (l)、P 14 (l) And calculating convergence conditions at positions l =100km, 300km, 600km, 800km, 1200km and 1400km in sequence. At this moment, the wave velocity initial values are respectively the average values of the respective wave velocity vectors
The ranging results are shown in table 2.
TABLE 2 Convergence for different numbers of interpolation nodes
From table 2, it can be seen that the convergence accuracy of the proposed algorithm is improved with the increase of the number of interpolation nodes in the full-length range of the line, and at the same time, the method has higher ranging accuracy already when n = 14. When the two ends of the line have faults, the more interpolation nodes are, the slower the convergence speed is; when the fault is close to the middle of the line, the convergence speed is less influenced by the number of interpolation nodes.
In order to verify the applicability of the algorithm in the whole line full-length range, the distance measurement performance of the algorithm at other fault distances except for the known interpolation node needs to be verified. Table 3 shows the ranging results after the occurrence of the unipolar ground fault at l =130km, 370km, 690km, 960km, 1 180km, 1 420km. At this moment, the wave velocity initial values are respectively the average values of the respective wave velocity vectors
The ranging results are shown in table 3.
TABLE 3 Convergence at unknown interpolated nodes
From table 3, the algorithm has high ranging accuracy at any fault distance, and has general applicability in the full-length range of the line.
To verify the transition resistance capability of the proposed algorithm, table 4 gives the ranging results when different transition resistance faults occur at line 960 km. At this time, P is taken by interpolation polynomial 14 (l) Initial value of wave velocity
In the table: r represents transition resistance; d represents a ranging result; ε represents the absolute error.
TABLE 4 ranging results for different transition resistances
From table 4, it can be seen that the ranging method has stable accuracy under different transition resistance faults, and also has high ranging accuracy and strong resistance to transition resistance under high resistance ground fault.
Claims (7)
1. A double-end traveling wave distance measurement method for a direct current transmission line is characterized by comprising the following steps:
step 1, after a fault occurs, firstly, the time t when voltage traveling waves reach a rectifying side distance measuring device and an inverting side distance measuring device is calibrated by utilizing improved Hilbert-Huang transformation 1 、t 2 ；
Step 2, mixing t 1 、t 2 Substituting into the traditional double-end traveling wave distance measurement formula to obtain an initial value of the fault distance, and recording as l 0 ；
Step 3, subtracting L from the total line length L 0 Obtaining the fault distance L-L between the fault point and the inversion side 0 Respectively mixing l 0 、L-l 0 As Newton interpolation polynomial P n (l) The input quantity of (2) is solved to respectively obtain the wave velocity v when the traveling wave reaches the distance measuring devices at the two ends M0 、v N0 ；
Step 4, mixing v M0 、v N0 Substituting into a double-end traveling wave distance measurement formula considering wave velocity change to obtain a fault distance l after first iteration 1 At this time l 1 Bi | (R) | 0 The actual fault distance is closer;
step 5, then 1 、L-l 1 As Newton interpolation polynomial P n (l) Repeating the steps 3 and 4 to obtain a ranging result vector [ l ] gradually approaching to the real fault distance along with the increase of the iteration times 0 l 1 l 2 … l k-1 l k ]；
Step 6, setting the convergence precision of the algorithm to obtain the final ranging result l = (l) k +l k-1 )/2；
In the step 1: the calibration of the traveling wave head adopts improved Hilbert-Huang transformation, which specifically comprises the following steps:
aiming at modal mixing and false component phenomena generated during empirical mode decomposition in Hilbert-Huang transform HHT, gaussian white noise is added into an original signal, and then improved Hilbert-Huang transform of empirical mode decomposition is carried out, wherein the improved Hilbert-Huang transform comprises the following steps:
adding a group of white Gaussian noises w (t) into an original signal S (t) to obtain a new signal S (t);
S(t)＝s(t)+w(t) (1)
EMD decomposition is carried out on the new signal S (t) to obtain n intrinsic mode functions imf with frequencies arranged from high to low in sequence n A component;
adding different white Gaussian noise w into the original signal j (t) (j =1 to m) m times in total;
for eliminating the influence caused by Gaussian white noise, m imfs are subjected to jk Component averaging:
for the highest frequency imf 1 The components are subjected to Hibert transformation to obtain corresponding instantaneous amplitude A (t) and instantaneous phase
The instantaneous frequency f (t), wherein,
finally, imf is drawn according to f (t) 1 And (5) component time-frequency diagrams.
2. The double-ended traveling wave distance measuring method for the direct current transmission line according to claim 1, wherein the highest frequency component detected in the wave head arrivesMoment, defined as the arrival moment of this fault traveling wave, at which the fault transient voltage waveform exhibits a sharp abrupt change, at imf 1 The time-frequency image of the component shows a distinct high frequency jump.
3. The double-ended traveling wave distance measurement method of the direct current transmission line according to claim 1, wherein in step 2, a traditional double-ended traveling wave distance measurement formula is shown as formula (6):
in the formula: t is t 0 The absolute time when a fault occurs on the line; t is t 1 The moment when the initial traveling wave head of the fault point reaches the M end is the moment; t is t 2 The time when the initial traveling wave head of the fault point reaches the N end is the time; v. of fix Represents a fixed empirical wave velocity; l is the total length of the line;
solving to obtain:
4. the double-end traveling wave distance measurement method of the direct current transmission line according to claim 1, wherein in the step 4, the double-end traveling wave distance measurement formula considering the wave velocity change is represented by the following formula (8):
in the formula: l is the total length of the line, v M 、v N Respectively representing the wave speed when the traveling wave reaches the rectifying side distance measuring device and the inverting side distance measuring device, and l is the fault distance obtained by solving;
solving to obtain:
5. the double-ended traveling wave distance measurement method for the direct current transmission line according to claim 4, specifically comprising: v is to be M0 、v N0 Substituting into a double-end traveling wave ranging formula considering the change of wave velocity, t 0 The absolute time when a fault occurs on the line; t is t 1 The moment when the initial traveling wave head of the fault point reaches the M end is the moment; t is t 2 The time when the initial traveling wave head of the fault point reaches the N end is the time; v. of M 、v N Respectively representing the wave speed, x, of the fault travelling wave arriving at the rectifying side and the inverting side M 、x N Respectively represent the distance between the fault point and the two ends of the rectifier station and the inverter station, F represents the fault point, and L is the total length of the line.
6. The double-ended traveling wave distance measurement method of the direct current transmission line according to claim 1, wherein in step 5, the step of fitting v (l) by using a Newton's interpolation algorithm comprises the following steps:
when n =1, n represents the order of the interpolating polynomial, and there are two interpolating nodes l 0 、l 1 Recording a first order interpolation polynomial as P 1 (l) It satisfies P 1 (l 0 )＝v(l 0 )，P 1 (l 1 )＝v(l 1 ) Structure P of 1 (l) Is composed of
P 1 (l) Viewed as interpolation by the zeroth order P 0 (l)＝v(l 0 ) Corrected to obtain, i.e.
P 1 (l)＝P 0 (l)+a 1 (l-l 0 ) (11)
In the formula, a 1 Coefficient of first order difference quotient for function v (l), denoted v [ l ] 0 ,l 1 ]Then there is
When n =2, there are three interpolation nodes/ 0 、l 1 、l 2 Recording a second-order interpolation polynomial as P 2 (l) It satisfies P 2 (l 0 )＝v(l 0 )，P 2 (l 1 )＝v(l 1 )，P 2 (l 2 )＝v(l 2 ) Structure P of 2 (l) Is composed of
In the same way, P 2 (l) Viewed as being interpolated by a first order P 1 (l)＝P 0 (l)+a 1 (l-l 0 ) Is corrected by
P 2 (l)＝P 1 (l)+a 2 (l-l 0 )(l-l 1 ) (14)
In the formula, a 2 A second order difference quotient coefficient of the function v (l), denoted as v [ l ] 0 ,l 1 ,l 2 ]Then there is
Obtaining an expression of an n-order Newton interpolation polynomial according to a recursion method as
P n (l)＝P 0 (l)+a 1 (l-l 0 )+a 2 (l-l 0 )(l-l 1 )+…+a n (l-l 0 )(l-l 1 )…(l-l n-1 ) (16)
In the formula, a n Coefficient of quotient of n order difference, denoted v [ l ], for function v (l) 0 ,l 1 ,…,l n ]
P n (l) I.e. for the wave velocity instead of the unknown function v (l)A compensated interpolation polynomial function.
7. A direct current transmission line double-end traveling wave distance measuring system is characterized by comprising:
the time calibration module is used for calibrating the time t when the voltage traveling wave reaches the rectifying side and the inverting side distance measuring device by utilizing improved Hilbert-Huang transformation after a fault occurs 1 、t 2 ；
The calibration of the traveling wave head adopts improved Hilbert-Huang transformation, which specifically comprises the following steps:
aiming at modal mixing and false component phenomena generated during empirical mode decomposition in Hilbert-Huang transform HHT, gaussian white noise is added into an original signal, and then improved Hilbert-Huang transform of empirical mode decomposition is carried out, wherein the improved Hilbert-Huang transform comprises the following steps:
adding a group of white Gaussian noises w (t) into an original signal S (t) to obtain a new signal S (t);
S(t)＝s(t)+w(t) (1)
EMD decomposition is carried out on the new signal S (t) to obtain n inherent mode functions imf with the frequency arranged from high to low in sequence n A component;
adding different white Gaussian noise w into the original signal j (t) (j =1 to m) m times in total;
for eliminating the influence caused by Gaussian white noise, m imfs are processed jk Component averaging:
for the highest frequency imf 1 The components are subjected to Hibert transformation to obtain corresponding instantaneous amplitude A (t) and instantaneous phase
The instantaneous frequency f (t), wherein,
finally, imf is drawn according to f (t) 1 A component time-frequency diagram;
the initial value calculation module of the fault distance is used for calculating t 1 、t 2 Substituting into the traditional double-end traveling wave distance measurement formula to obtain an initial value of the fault distance, and recording as l 0 ；
The wave speed obtaining module is used for subtracting L from the total length L of the line when the traveling wave reaches the distance measuring devices at the two ends 0 Obtaining the fault distance L-L between the fault point and the inversion side 0 Respectively mixing l 0 、L-l 0 The input quantity of the Newton interpolation polynomial is solved to respectively obtain the wave velocity v when the traveling wave reaches the distance measuring devices at the two ends M0 、v N0 ；
A fault distance obtaining module for obtaining v M0 、v N0 Substituting into a double-end traveling wave distance measurement formula considering the wave velocity change to obtain the fault distance l after the first iteration 1 At this time l 1 Than l 0 The actual fault distance is closer;
the distance measuring module of the real fault distance is used for measuring the true fault distance 1 、L-l 1 As Newton interpolation polynomial P n (l) Repeating the steps 4 and 5 to obtain a ranging result vector [ l ] gradually approaching to the real fault distance along with the increase of the iteration times 0 l 1 l 2 … l k-1 l k ]；
The distance measurement result obtaining module is used for setting algorithm convergence precision to obtain a final distance measurement result l = (l) k +l k-1 )/2。
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