CN113253052A - High-voltage direct-current transmission line fault distance measurement method based on improved SMMG - Google Patents
High-voltage direct-current transmission line fault distance measurement method based on improved SMMG Download PDFInfo
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Abstract
The invention relates to a high-voltage direct-current transmission line fault location method based on an improved SMMG, belonging to the field of relay protection fault location; the invention takes into account that when the transmission line has special fault conditions such as high impedance grounding and the like, the traveling wave energy is weak and difficult to detect; in the existing distance measurement method, the difference of the speed of a fault traveling wave reaching the two ends of a rectification side and an inversion side is not considered, so that the distance measurement error is large, and the fault current traveling wave is effectively decomposed by adopting variational mode decomposition; realizing successive transformation of weak signals by using a multi-resolution morphological gradient transformation technical algorithm, accumulating and amplifying the sudden change characteristics of the traveling wave signals, and realizing accurate calibration of the arrival time of the initial fault traveling wave head; and simultaneously, Hilbert transformation is carried out on the high-frequency component of the fault current signal, the frequency of the high-frequency component of the fault current signal which reaches the measurement points at the two ends of the rectification side and the inversion side firstly is determined, the fault current traveling wave speed is further determined, and the detection of the fault position is finally completed.
Description
Technical Field
The invention belongs to the technical field of fault location of relay protection high-voltage direct-current power transmission systems, and particularly relates to a fault location method for cumulatively amplifying weak signals and taking wave speed influence into account.
Background
The high-voltage transmission line is one of the most failed devices in the power system, and the actual direct-current transmission project operation data statistics show that the direct-current transmission line failure accounts for about 50% of the total failure. Once a fault tripping accident occurs to the direct current transmission line, the production operation of national economy is influenced, and inconvenience is brought to the life of people. Therefore, the method for rapidly and accurately finding the fault point after the line fault has important significance for timely repairing the line, and for safe, stable and economic operation of the power system.
At present, for fault location, a large number of experts and scholars provide two main fault location principles of a traveling wave method and a fault analysis method on the basis of a distribution parameter equation describing the electrical quantity characteristics of a long-distance direct-current transmission line. Although the fault analysis method has high stability, a good solution is not provided so far for the problem of low fault point positioning accuracy caused by model errors of the direct-current transmission line, so that fault location of the fault analysis method is not applied to actual direct-current transmission engineering. The fault transient traveling wave of the high-voltage direct-current line is a typical oscillation waveform, the wave head of the fault transient traveling wave is correspondingly gentle, and when the power transmission line has special fault conditions such as high impedance grounding and the like, the traveling wave energy is weak and difficult to detect. The existing wavelet transform modulus maximum detection methods may have false modulus maximum points, EMD-Hilbert and other wave head detection methods may have serious modal mixing and end effect phenomena, which cause large errors or range finding failure. Meanwhile, the fault distance is mostly calculated by adopting empirical wave velocity in the existing method, but actually fault traveling waves with different frequency components have different wave velocities, and the fault traveling waves have certain difference in the wave velocities reaching two ends of the rectification side and the inversion side, and the fault traveling waves also have influence on the distance measurement precision.
Therefore, there is a need in the art for a new solution to solve these problems.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the high-voltage direct-current transmission line fault location method based on the improved SMMG solves the problems that under the condition of special faults, traveling wave signal energy is weak and difficult to detect, and the speed of fault traveling waves reaching the two ends of a rectification side and the speed of fault traveling waves reaching the two ends of an inversion side have difference, so that location precision is affected.
In order to achieve the purpose, the specific technical scheme of the high-voltage direct-current transmission line fault distance measuring method based on the improved SMMG is as follows:
a high-voltage direct-current transmission line fault distance measurement method based on improved SMMG is characterized in that: comprises the following steps which are sequentially carried out,
step one, performing smooth filtering processing on a fault current signal by mathematical morphology open operation, and effectively filtering interference of isolated value points, noise and unstable signals with violent changes.
And step two, decoupling operation is carried out on the fault current traveling wave by adopting a Kerenbel transformation matrix to obtain 1-mode and 0-mode components, so that electromagnetic coupling between the two poles of the high-voltage direct-current power transmission system is eliminated.
Compared with the zero-mode component 1, the mode component is less influenced by the traveling wave dispersion effect and is more stable, and the current traveling wave 1 mode component is selected as a follow-up line fault location input signal.
And step three, carrying out Variable Mode Decomposition (VMD) on the traveling wave 1 mode component of the fault current to obtain Intrinsic Mode Functions (IMF) of different frequencies of the signal, overcoming the problems of endpoint effect and mode component aliasing in the EMD method, having a firmer mathematical theory basis, reducing time sequence non-stationarity with high complexity and strong non-linearity, decomposing to obtain a sub-sequence which comprises a plurality of different frequency scales and is relatively stable, and being suitable for a sequence of the non-stationarity. In order to make the central frequency interval of each modal component clear and make each frequency band bandwidth appropriate, the variational modal decomposition algorithm can effectively decompose the fault current traveling wave. In subsequent researches, Hilbert transformation is required to be carried out on a certain inherent modal function, and the high-frequency component IMF4 is selected for subsequent researches.
And step four, performing cascade multi-resolution morphological gradient transformation (SMMG) transformation on the high-frequency component IMF4 to calibrate the traveling wave head.
The length combination of the structural elements and the order of their concatenation determine the final detection effect of the SMMG. The short structural elements have sensitive detection capability on weak signals, and the long structural elements can further strengthen the change of the weak signals at singular points after the weak signals are processed by the short structural elements. Therefore, SMMG conversion is carried out in a cascading sequence of the short structural elements in front and the long structural elements in back, and a traveling wave head is calibrated;
aiming at the defects of the MMG method, the SMMG technology which is a cascade multi-resolution morphological gradient transformation technology is adopted, the SMMG greatly improves the processing capability of the MMG, endows the original algorithm with higher flexibility and openness, and achieves the purpose of extracting the signal mutation characteristics by designing flat structural elements with variable lengths and different origin positions to match or locally correct the signals, thereby solving the extraction problem of the weak signal characteristics.
And step five, the propagation speed v of the fault traveling wave is a complex function strongly related to the frequency, and the instantaneous frequency reaching the rectification side and the inversion side of the traveling wave head is required to be known when the wave speed is obtained. Hilbert transformation is carried out on the high-frequency component IMF4, the frequency corresponding to the first mutation point in a Hilbert transformation time-frequency diagram is the frequency of the high-frequency component of the fault traveling wave of the rectification and inversion side which is reached firstly, and then the corresponding fault current traveling wave speed at the moment is determined;
the propagation speed v of a certain frequency component in the fault traveling wave is a complex function with strong correlation with frequency, and the expression is shown as the following formula.
In the formula: ω is the angular frequency of the specific frequency component, ω ═ 2 π f; γ (ω) is a phase distortion coefficient of the specific frequency component.
The specific flow of solving the frequency f is as follows:
current 1-mode signal x (t), whose Hilbert transform y (t) is defined as:
forming a conjugate complex pair by Hilbert transform x (t) and y (t), resolving signal z (t) into:
z(t)＝x(t)+jy(t)＝a(t)ejθt
in the formula:
the analytical signals z (t) obtained by the Hilbert transform are represented by the following equations in terms of phase, amplitude and frequency as a function of time. And finding out the wave velocity corresponding to the analytic signal frequency obtained after Hilbert conversion in the corresponding relation curve of the frequency and the wave velocity.
According to the invention, a certain wave velocity to be tested is not singly selected for fault location of the direct current transmission line, and the difference of the wave velocities of fault traveling waves reaching the rectifying side and the inverting side is considered, so that the accuracy of location is further improved.
Substituting the time and wave speed of the traveling wave heads detected at the rectifying side and the inverting side into a distance measurement formula to complete the calculation of the fault distance;
the distances from the fault point to the rectification side and the inversion side are respectively as follows:
LR＝VR(ωR)(TR-T)
LI＝VI(ωI)(TI-T)
according to the formula, the traveling wave fault location result of the direct current transmission line and the time T when the initial wave head of the fault traveling wave reaches two sidesR、TIAnd the corresponding fault traveling wave velocity V at the momentR(ωR)、VI(ωI) Is related to, and VR(ωR)、VI(ωI) Are related to the instantaneous frequency.
Further, the kelvin transformation matrix in the second step is as follows:
wherein u is0、u1Is 0 mode and 1 mode voltage; u. ofp、unThe voltage values of the positive and negative electrodes.
Further, the implementation of the VMD algorithm and the selection of the number of decomposition modes in step three:
the algorithm is realized by the following steps:
VMD is a completely non-recursive modal variation method by decomposing an input signal f into a plurality of discrete modal signals u with specific sparse propertieskTherefore, the frequency domain subdivision of the signal and the effective separation of each component are realized. Signal u of each modekThe bandwidth is calculated as follows:
in the formula: { ukFor the k modal components resulting from the decomposition, { ωkThe frequency center of each modal component.
In order to solve the constraint problem of the formula (1), an augmentation expression as the formula (2) is obtained by introducing a method of combining a secondary penalty factor alpha and a Lagrange multiplier lambda.
By using the Alternative Direction Multiplier Method (ADMM), each modal component and its central frequency calculation formula can be obtained.
In the formula:
the wiener filtering of each modal component can obtain the real part u of each modal component through inverse Fourier transformk(t)；
Which corresponds to the center of frequency of the modal component.
Initiation
Setting n as zero, where n is n +1, and K is a positive integer to be decomposed;
fifthly, Fork is 1: K, and the mode is updated through the formula (3)
Sixthly, Fork is 1: K, and the mode is updated through a formula (4)
When the number of the decomposition modes is 4, the central frequency intervals of all the mode components are clear, the bandwidth of each frequency band is proper, and the variational mode decomposition algorithm can effectively decompose the fault current traveling wave. Therefore, when the fault current traveling wave is processed by using the variational modal decomposition algorithm, the optimal modal number decomposition number K is selected to be 4.
Further, the VMD parameter in step three is set as: k is 4, α is 2000, τ is 0; at the moment, the center frequency interval of each modal component is clear, the bandwidth of each frequency band is proper, and the variational modal decomposition algorithm can effectively decompose the fault current traveling wave;
the VMD algorithm adopted by the invention overcomes the problems of endpoint effect and modal component aliasing in the EMD method, has a firmer mathematical theory basis, can reduce the non-stationarity of time sequences with high complexity and strong nonlinearity, decomposes to obtain relatively stable subsequences containing a plurality of different frequency scales, and is suitable for non-stationarity sequences.
Further, selecting the SMMG long and short elements in the fourth step:
the SMMG has the core idea that the purpose of extracting the signal mutation characteristic is achieved by designing flat structural elements with variable lengths and different origin positions to match or locally correct signals. Selecting initial structural elements with lengths of 8 and 4 to respectively carry out rectification and inversion side 4 th modal component
Cascaded multi-resolution morphological gradient transformation;
selecting initial structures with lengths of 8 and 4 to carry out
Cascaded multi-resolution morphological gradient transforms. Meanwhile, the morphology only relates to addition and subtraction operation, the operation speed is high, the time delay is small, and the requirement of fault location on rapidity is met.
The high-voltage direct-current transmission line fault distance measurement method based on the improved SMMG has the following advantages: according to the invention, a VMD-SMMG-Hilbert conversion combined algorithm is used, aiming at the problems that the traveling wave signal energy is weak and difficult to detect under the special fault condition, the difference of the wave speeds of the fault traveling wave reaching the rectifying side and the inverting side is considered, the fault transient current is effectively decomposed by the VMD algorithm, the SMMG is combined with morphological calculation to realize accurate calibration of a wave head, the instantaneous frequency of the wave head reaching the rectifying side and the inverting side is detected through Hilbert conversion, and the wave speed is further determined. The method has the advantages of high operation speed and small time delay, and meets the requirement of fault location on rapidity; the precise calibration of the weak initial traveling wave head time is realized; the method is basically not influenced by fault types, fault distances and transition resistances under different fault conditions, and has high reliability and positioning accuracy.
Drawings
Fig. 1 is a flow diagram of a fault location method of a high-voltage direct-current transmission line based on an improved SMMG.
Fig. 2 is a schematic diagram of a simulation model of a high-voltage direct-current transmission system in an embodiment of the high-voltage direct-current transmission line fault distance measurement method based on the improved SMMG.
Fig. 3 is a fault traveling wave propagation schematic diagram in an embodiment of the fault location method for the high-voltage direct-current transmission line based on the improved SMMG.
Fig. 4 shows a line fault current signal in an embodiment of the fault distance measuring method of the high-voltage direct-current transmission line based on the improved SMMG.
Fig. 5 shows 4 modes obtained by decomposing a fault current signal by VMD in an embodiment of the fault distance measuring method for the hvdc transmission line based on the improved SMMG.
Fig. 6 is a detection result of a modal 4 component obtained by VMD decomposition of current 1-mode components on a rectifying side and an inverting side in an embodiment of a high-voltage direct-current transmission line fault location method based on an improved SMMG of the present invention.
Fig. 7 is a wave speed and frequency relation curve of a fault traveling wave of the high-voltage direct-current transmission line in an embodiment of a fault location method of the high-voltage direct-current transmission line based on the improved SMMG.
Fig. 8 is a time-frequency diagram obtained after Hilbert transformation of a current traveling wave high-frequency component mode 4 component in an embodiment of the high-voltage direct-current transmission line fault location method based on the improved SMMG.
Detailed Description
In order to better understand the purpose, structure and function of the present invention, a fault location method for a high voltage direct current transmission line based on an improved SMMG according to the present invention is described in further detail below with reference to the accompanying drawings.
A high-voltage direct-current transmission line fault distance measurement method based on improved SMMG comprises the following steps:
step one, preprocessing fault current traveling wave
(1) And the traveling wave recorder records fault current transient components of the rectifying side and the inverting side.
(2) Mathematical morphology open operation has certain smoothing function to the signal, can effectively filter the interference of isolated value point, noise and the violent change non-stationary signal. Firstly, filtering the fault current traveling wave signal through mathematical morphology open operation.
(3) Because electromagnetic coupling exists between two poles of the high-voltage direct-current transmission system, the Kerenbel transformation matrix is adopted to carry out decoupling operation on fault current traveling waves to obtain 1-mode and 0-mode components, compared with the 0-mode component, the 1-mode component is less affected by traveling wave dispersion effect and is more stable, and therefore the 1-mode component of the current traveling waves is selected as a fault location input signal of a subsequent line.
Step two, calibration of traveling wave head
(1) Decomposition of fault current line mode component
A completely non-recursive modal variation method is adopted, and the method decomposes an input signal f into a plurality of discrete modal signals with specific sparse properties to realize the frequency domain subdivision of the signals and the effective separation of each component, namely VMD, wherein VMD parameters are set as: k is 4, α is 2000, and τ is 0. After the fault current traveling wave line mode components are decomposed through the variation mode, four mode components (IMF1-IMF4) are obtained; as shown in fig. 5, when the number of decomposition modes is 4, the center frequency interval of each modal component is clear, the bandwidth of each frequency band is appropriate, and the variational modal decomposition algorithm can effectively decompose the fault current traveling wave. Therefore, when the fault current traveling wave is processed by using the variational modal decomposition algorithm, the optimal modal number decomposition number K is selected to be 4.
The subsequent research on wave velocity is considered, and the wave velocity is related to frequency, so that the IMF4 representing the high-frequency component of the fault current signal is selected for subsequent ranging research.
(2) Calibration of time for wave head to reach rectifying side and inverting side
Aiming at the defects of the MMG method, a cascade multi-resolution morphological gradient transformation technology, namely SMMG, is adopted, the SMMG greatly improves the processing capacity of the MMG, endows the original algorithm with higher flexibility and openness, and realizes the purpose of extracting the signal mutation characteristics by designing flat structural elements with variable lengths and different origin positions to match or locally correct the signals, thereby solving the extraction problem of the weak signal characteristics.
The short structural elements have sensitive detection capability on weak signals, and the long structural elements can further strengthen the change of the weak signals at singular points after the weak signals are processed by the short structural elements. The method comprises the steps of selecting initial structural elements with the lengths of 8 and 4 to respectively carry out rectification and inversion side 4 th modal component (IMF4) in a mode that short structural elements are in front of long structural elements and long structural elements are in back of the short structural elements
And (3) cascading multi-resolution morphological gradient transformation, wherein the test result is shown in figure 6.
Step three, wave velocity determination
(1) Wave velocity versus frequency
Fault traveling waves of different frequency components have different wave velocities. The difference of the wave speeds of the fault traveling wave reaching the rectifying side and the inverting side is considered, and the wave speed corresponding to the frequency when the traveling wave reaches the two sides needs to be researched.
For a high voltage direct current transmission system as shown in fig. 2, assuming that a short circuit fault occurs on the direct current transmission line at a certain time T, the fault traveling wave propagates to both ends of the rectifying side and the inverting side, and is respectively at TR、TIThe time respectively reaches the rectification side and the inversion side, and the time respectively reaches the instantaneous frequency omegaR、ωIFault travelling wave component with associated wave velocity VR(ωR)、VI(ωI)。
The relationship among the instantaneous frequency wave velocity of the fault traveling wave, the arrival time of the initial wave head of the fault traveling wave and the fault distance can be obtained as follows:
LR＝VR(ωR)(TR-T) (7)
LI＝VI(ωI)(TI-T) (8)
L＝LR+LI (9)
as can be seen from the formulas (7) and (8), the traveling wave fault location result of the direct current transmission line and the time T when the initial wave head of the fault traveling wave reaches the two sidesR、TIAnd the corresponding fault traveling wave velocity V at the momentR(ωR)、VI(ωI) Is related to, and VR(ωR)、VI(ωI) Are related to the instantaneous frequency.
(2) Determination of instantaneous frequency
The time when a certain high-frequency component of the initial fault traveling wave head reaches the rectification side and the inversion side is defined as the time when the fault traveling wave reaches the measurement point, the fault traveling wave at the measurement point at the end can present singular change, as shown in fig. 8, the frequency corresponding to the first catastrophe point in the Hilbert transform time-frequency diagram is the frequency of the high-frequency component of the fault traveling wave at the rectification side and the inversion side at the first, and the wave speed corresponding to the frequency is the solved frequency.
Step four, calculating the fault position
And substituting the arrival time and the wave velocity of the wave heads at the two ends into the distance measurement formulas (7) and (8) to complete the search of the fault position.
Example (b):
the invention carries out verification analysis on PSCAD/EMTDC. Firstly, a simulation model of the +/-500 kV bipolar HVDC system shown in FIG. 2 is built. The length of the transmission line is 1000km, an ACSR720/50 type steel core aluminum stranded wire is adopted, the conducting wire 6 is split, the splitting distance is 0.4572m, the calculated radius is 18.1mm, the distance between the double-pole overhead transmission lines is 10m, the distance between the transmission lines and the horizontal ground is 20m, and the line sag is 2m when the system normally operates. Self-resistance 0.04632 omega/km of transmission line and mutual resistance 4.25 multiplied by 10-7Omega/km; self-inductance 0.00182H/km, mutual inductance 0.00097H/km; capacitance to ground of unit length of line 9.98 x 10-9F/km, interelectrode capacitance per unit length 2.12X 10-9F/km。
The rectification station and the inversion station both adopt double 12-pulse converter valves, the rated current is 2kA, and the rated power is 1000 MW. The DC line fault types are divided into a unipolar ground fault and a bipolar ground fault, the rectifying side is taken as a reference side, different fault types are set at positions 100, 500 and 900km away from the rectifying side and transition resistances of 10 or 200 omega respectively, and the sampling frequency is set to be 1MHz on the assumption that the fault occurs at 1.5 s.
When a single-pole ground fault or a double-pole ground fault occurs on the high-voltage direct-current transmission line, fault current initial traveling waves are measured at the two ends of rectification and inversion of the direct-current line, and fault current information is preprocessed through the steps. And step two, calibrating the traveling wave head by VMD-SMMG conversion, and calculating the time of the traveling wave head reaching the two sides of the direct current line. And thirdly, detecting the instantaneous frequency of the fault traveling wave by Hilbert, finding out the wave velocity corresponding to the frequency, and calculating the fault distance according to the formula (7) or the formula (8) as shown in tables 1 and 2.
TABLE 1 simulation calculation results in case of single-pole earth fault
As can be seen from Table 1, the calculated fault distance has a relative error maximum of 0.1395% and a relative error minimum of 0.0014%; when the fault occurs in the middle position of the direct current transmission line, the fault traveling wave distance measurement precision is high; if the fault occurs at the two sides close to the rectification and inversion of the direct current transmission line, the fault traveling wave distance measurement precision is relatively low, but the relative errors are within 0.2 percent; in addition, simulation results show that for single-pole ground faults, the fault location precision based on the VMD-SMMG-Hilbert algorithm is basically not influenced by the transition resistance, and the method has certain engineering application value.
TABLE 2 simulation calculation results in case of bipolar short-circuit fault
As can be seen from Table 2, the calculated relative error of the fault distance has a maximum value of 1.2003% and a minimum value of 0.0034%; when a fault occurs in the middle position of the direct current transmission line, the fault distance measurement precision is low due to the fact that the fault traveling wave is seriously lost in the transmission process of the long-distance transmission line; if the fault occurs at the two sides close to the rectification and inversion of the direct current transmission line, the fault location precision is relatively high, but the relative error is within 1%;
2010, the technical committee on relay protection standardization in the power industry issued an industry standard for fault traveling wave distance measuring devices, namely, for trans-regional long-distance high-voltage transmission lines exceeding 300km, the traveling wave fault positioning error of the trans-regional long-distance high-voltage transmission lines should not exceed 1 km. Simulation shows that the high-voltage direct-current transmission line fault location method based on the improved SMMG meets the industrial standard for fault traveling wave location devices issued by the technical committee of relay protection standardization in the power industry.
In summary, the fault location method of the high-voltage direct-current transmission line based on VMD-SMMG-Hilbert conversion is used for solving the problems that traveling wave signal energy is weak and difficult to detect under the condition of special faults, the speed difference of the fault traveling wave reaching the two ends of the rectification side and the inversion side is considered and the like on the basis of analyzing the relation between the speed of the fault traveling wave and the instantaneous frequency. The method is characterized in that effective decomposition of fault transient current is realized by a VMD algorithm, SMMG is combined with morphological operation to realize accurate calibration of a wave head, and Hilbert conversion is carried out on fault current traveling wave high-frequency components to determine the frequency of the fault current traveling wave high-frequency components which reach measurement points at two ends of a rectification side and an inversion side firstly, and further determine the corresponding fault current traveling wave speed at the moment, thereby realizing effective calibration of the fault initial traveling wave head and organic unification of the fault traveling wave speed at the moment. The method has the advantages of high operation speed and small time delay, and meets the requirement of fault location on rapidity; the precise calibration of the weak initial traveling wave head time is realized; the method is basically not influenced by fault types, fault distances and transition resistances under different fault conditions, has higher reliability and positioning accuracy, and has certain engineering practical value.
Fig. 3 in the description is a schematic diagram of fault traveling wave propagation in this embodiment, and as shown in fig. 3, when a line occurs, a fault traveling wave is transmitted from a fault point to two ends of the line, and a traveling wave recorder at a detection position detects a first fault traveling wave.
Description fig. 4 is a line fault current signal in the present embodiment, in which the solid line portion represents a fault current traveling wave detected at the inverter-side bus bar, and the dotted line portion represents a fault current traveling wave detected at the rectifier-side bus bar.
Fig. 7 in the specification is a curve of the relationship between the wave speed and the frequency of the fault traveling wave of the high-voltage direct-current transmission line in the embodiment. And after the frequency of the initial traveling wave reaching the detection position is calculated in the fifth step, finding the wave velocity corresponding to the initial traveling wave in the graph 7 so as to meet the requirement of calculating the fault distance in the following step.
It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (7)
1. A high-voltage direct-current transmission line fault location method based on an improved SMMG is characterized by comprising the following steps which are sequentially carried out:
step one, performing smooth filtering processing on a fault current signal by mathematical morphology open operation, and effectively filtering interference of an isolated value point, noise and a severely-changed non-stationary signal;
step two, decoupling operation is carried out on fault current traveling waves by adopting a Kerenbel transformation matrix to obtain 1-mode and 0-mode components, so that electromagnetic coupling between the two poles of the high-voltage direct-current power transmission system is eliminated;
thirdly, performing a spatial mode decomposition and VMD decomposition on the 1-mode component of the traveling wave of the fault current to obtain Intrinsic Mode Functions (IMF) of different frequencies of the signal;
selecting a proper inherent mode function to carry out cascade multi-resolution morphological gradient transformation technical transformation, and carrying out cascade multi-resolution morphological gradient transformation technical transformation in a cascade sequence of a short structural element in front and a long structural element in back to calibrate a traveling wave head;
selecting the same inherent mode function to carry out Hilbert transformation, wherein the frequency corresponding to a first catastrophe point in a Hilbert transformation time-frequency diagram is the frequency of the high-frequency component of the fault traveling wave at the rectification and inversion side firstly, and further determining the corresponding fault current traveling wave speed at the moment;
the propagation speed v of a certain frequency component in the fault traveling wave is a complex function with strong correlation with frequency, and the expression is shown as the following formula:
in the formula: ω is the angular frequency of the specific frequency component, ω ═ 2 π f; γ (ω) is a phase distortion coefficient of the specific frequency component;
analyzing a function relation of the phase, the amplitude and the frequency of the signal with respect to time, which is obtained through Hilbert transformation; finding out the wave velocity corresponding to the analytic signal frequency obtained by Hilbert transform in the corresponding relation between the frequency and the wave velocity;
substituting the time and wave speed of the traveling wave heads detected at the rectifying side and the inverting side into a distance measurement formula to complete the calculation of the fault distance;
the distances from the fault point to the rectification side and the inversion side are respectively as follows:
LR＝VR(ωR)(TR-T)
LI＝VI(ωI)(TI-T)
wherein, TR、TIThe moment when the initial wave head of the fault traveling wave reaches the two sides; omegaR、ωIIs the instantaneous frequency; vR(ωR)、VI(ωI) The fault traveling wave speed.
2. The high-voltage direct current transmission line fault location method based on the improved SMMG of claim 1, wherein the Kerenbel transformation matrix in the second step is as follows:
wherein u is0、u1Is 0 mode and 1 mode voltage; u. ofp、unThe voltage values of the positive and negative electrodes.
3. The high-voltage direct current transmission line fault location method based on the improved SMMG as claimed in claim 1, characterized in that the VMD algorithm in the third step is implemented as follows:
decomposing an input signal f into a plurality of discrete mode signals u with specific sparsity propertieskThereby realizing the frequency domain subdivision of the signal and the effective separation of each component; signal u of each modekThe bandwidth is calculated as follows:
in the formula: { ukFor the k modal components resulting from the decomposition, { ωkThe frequency center of each modal component.
4. The high-voltage direct current transmission line fault location method based on the improved SMMG as claimed in claim 3, characterized in that, in order to solve the constraint problem of the formula (1), an augmentation expression as shown in formula (2) is obtained by introducing a method of combining a secondary penalty factor α and a Lagrange multiplier λ:
obtaining each modal component and a central frequency calculation formula thereof by using an alternative direction multiplier method ADMM;
in the formula:
the wiener filtering of each modal component can obtain the real part u of each modal component through inverse Fourier transformk(t)；
The frequency center of the modal component corresponding thereto;
initialization
Setting n as zero, where n is n +1, and K is a positive integer to be decomposed;
② Fork is 1: K, updating the mode by formula (3)
(iii) Fork is 1: K, and the mode is updated by the formula (4)
5. The method for fault location of the high-voltage direct current transmission line based on the improved SMMG as claimed in claim 1, wherein the parameters for decomposition of the spatial mode decomposition in the third step are set as follows: k is 4, α is 2000, and τ is 0.
6. The high-voltage direct current transmission line fault location method based on the improved SMMG of claim 1, wherein in the fourth step, the initial structural elements with the lengths of 8 and 4 are selected as the long and short elements for the transformation of the cascade multi-resolution morphological gradient transformation technology on the high-frequency component IMF4 to respectively carry out rectification and inversion side modal components
Cascaded multi-resolution morphological gradient transforms.
7. The high-voltage direct current transmission line fault location method based on the improved SMMG as claimed in claim 1, wherein the specific process of solving the frequency f in the step five is as follows:
current 1-mode signal x (t), whose Hilbert transform y (t) is defined as:
forming a conjugate complex pair by Hilbert transform x (t) and y (t), resolving signal z (t) into:
z(t)＝x(t)+jy(t)＝a(t)ejθt
in the formula:
the analytic signals z (t) obtained by Hilbert transformation have the functional relations of phase, amplitude and frequency with respect to time, which are respectively shown in the formula; and finding out the wave velocity corresponding to the analytic signal frequency obtained by Hilbert conversion in the corresponding relation curve of the frequency and the wave velocity.
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| CN117192291A (en) * | 2023-10-31 | 2023-12-08 | 国网浙江省电力有限公司宁波供电公司 | Single-phase broken line non-grounding fault positioning method for power distribution network |
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