CN112557812B - Small current ground fault positioning method and system based on Hausdorff distance - Google Patents
Small current ground fault positioning method and system based on Hausdorff distance Download PDFInfo
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Abstract
The invention discloses a method and a system for positioning a low-current ground fault based on a Hausdorff distance, wherein the method comprises the following steps: monitoring the zero sequence voltage of a system bus in real time; when the zero sequence voltage of the bus is greater than a set threshold value, fault positioning is carried out; sampling the bus zero-sequence voltage of a first period after a fault and the zero-sequence current of each monitoring point of a fault line; extracting bus transient zero-sequence voltage in a characteristic frequency band and transient zero-sequence current of each monitoring point of a fault line; calculating projection components of each monitoring point of the fault line, and calculating improved Hausdorff distance values of adjacent monitoring points; and judging the fault section according to the solved improved Hausdorff distance value. The method determines the fault section by utilizing the characteristic of obvious difference of transient zero-sequence currents on two sides of the fault point, and has obvious positioning effect.
Description
Technical Field
The invention relates to a small current ground fault positioning method and system based on a Hausdorff distance, and belongs to the technical field of power distribution network fault positioning.
Background
The low-current grounding mode is a grounding mode commonly adopted by medium-voltage power distribution networks in China, when a low-current grounding system has a single-phase grounding fault, line voltage between three phases still keeps symmetrical, the system is allowed to continuously operate for 1-2 hours, and if the fault cannot be timely removed, insulation breakdown between lines can be caused, so that the fault range is enlarged. Therefore, how to quickly locate the fault section in the low-current grounding system is a big problem in the relay protection technology.
Currently, research on the positioning of a low-current ground fault section is greatly advanced, and most of the research is developed on the basis of fault line selection. In a power distribution network with ungrounded neutral points, section positioning is carried out by utilizing the amplitude and direction of power frequency zero sequence current and a zero sequence reactive power direction method; in a resonant grounded power distribution network, a zero sequence active power method is adopted to indicate faults, and the influence of arc suppression coil current is overcome by using active current components generated by parallel resistors of the arc suppression coils; in addition, additional current signals are detected using line mounted fault indicators, and the fault section is located using the additional signal characteristics of flowing from the bus to the fault line and returning from the fault point. Compared with the method, the method for fault location by using the transient quantity is not influenced by arc suppression coils, can quickly and accurately locate the fault section, has wide application prospect, and can be successfully applied to the transmission line and also can be used for location measurement on the power distribution network with longer line length and less branches by adopting the traveling wave principle; the transient reactive power direction method needs to acquire fault transient voltage and current of a line at a detection point, perform Hilbert transform on the fault transient zero-sequence voltage, obtain average power of the fault transient zero-sequence voltage and the transient zero-sequence current, and judge a fault section by a symbol of the average power; at the present stage, a large amount of research is carried out by domestic and foreign scholars on a method for positioning a fault section by utilizing the similarity of transient zero-mode current waveforms at the upstream and the downstream of a fault point, and the method has a good field application effect and higher reliability.
The above methods are classified into two major categories, using steady-state quantities and transient quantities. Positioning of a fault section by using steady-state fault characteristics including a zero-sequence current group amplitude-to-amplitude ratio phase method and a zero-sequence reactive power direction method is influenced by noise and arc suppression coils, so that positioning failure is caused. The additional signal method includes an S signal injection method, etc., which has disadvantages in that additional signal injection equipment is required, field operation difficulty is increased, and when the fault resistance is large, it is difficult to perform positioning processing, and it is not suitable for a fault in which an intermittent arc exists. Compared with the method, the method for fault location by using the transient quantity is not influenced by the arc suppression coil, can quickly and accurately locate the fault section, and has wide application prospect. The traveling wave ranging method has been successfully applied to the transmission line, but it is difficult to implement fault ranging considering many factors such as short circuit of the distribution network, many branches, and the presence of aerial cable mixture. The method for positioning the fault section according to the waveform similarity of the transient zero-sequence currents at the upstream and the downstream of the fault point has a positioning blind area, large communication data volume and requires accurate time synchronization of all detection points. In addition, the method for realizing fault location by using empirical mode decomposition can cause the amplitude of transient zero-sequence current to be greatly reduced under severe fault conditions, thereby causing location failure. In addition, with the access of a large number of cable lines, the actual distribution network fault condition is more complex, and the transient state information is more abundant, so that the research on a reliable positioning method for the power distribution network of the cable-overhead mixed line is of great significance.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a small-current ground fault positioning method and system based on a Hausdorff distance.
The technical scheme adopted for solving the technical problems is as follows:
on one hand, the small-current ground fault positioning method based on the Hausdorff distance provided by the embodiment of the invention comprises the following steps:
monitoring the zero sequence voltage of a system bus in real time;
when the zero sequence voltage of the bus is greater than a set threshold value, fault positioning is carried out;
sampling the bus zero-sequence voltage of a first period after a fault and the zero-sequence current of each monitoring point of a fault line;
extracting bus transient zero-sequence voltage in a characteristic frequency band and transient zero-sequence current of each monitoring point of a fault line;
calculating projection components of each monitoring point of the fault line, and calculating improved Hausdorff distance values of adjacent monitoring points;
and judging the fault section according to the solved improved Hausdorff distance value.
As a possible implementation manner of this embodiment, the starting of fault location when the bus zero-sequence voltage is greater than a set threshold specifically includes:
when the zero sequence voltage U of the system bus0Greater than kUNIn which U isNAnd if the voltage is the rated voltage of the bus and k is a threshold coefficient, starting a fault positioning program.
As a possible implementation manner of this embodiment, the extracting of the bus transient zero-sequence voltage and the transient zero-sequence current of each monitoring point of the fault line in the characteristic frequency band specifically includes:
selecting fault characteristic information in an SFB frequency band as fault characteristic quantity;
and extracting the transient zero-sequence voltage of the bus and the transient zero-sequence current of each monitoring point of the fault line by using a finite-length single-bit impulse response filter.
As a possible implementation manner of this embodiment, the formula for obtaining the projection component of each monitoring point of the fault line is as follows:
in the formula (I), the compound is shown in the specification,
is the bus transient zero-sequence voltage,
is the transient zero-sequence current of the fault line monitoring point,
is a transient zero sequence current
In-bus transient zero sequence voltage
The projected vector of (c).
As a possible implementation manner of this embodiment, the formula for calculating the improved Hausdorff distance value of the adjacent monitoring point is as follows:
H(i,j)＝max(h(i0i,i0j),h(i0j,i0i)) (14)
in the formula, H (i, j) is the Hausdorff distance of the adjacent sections i, j, and represents the mismatching degree of the transient zero sequence current, i0i、i0jTransient zero sequence currents of adjacent sections i, j, respectively, h (i)0i,i0j),h(i0j,i0i) Are respectively transient zero sequence current i0i、i0jBetweenThe one-way Hausdorff distance.
As a possible implementation manner of this embodiment, the determining the fault section according to the solved improved Hausdorff distance value specifically includes:
selecting the maximum value H in the improved Hausdorff distance valuesmaxIf H ismaxGreater than the sum of the improvements of other adjacent monitoring points, the maximum value HmaxThe section is a fault section; if H is presentmaxAnd if the sum of the improvements of other adjacent monitoring points is less than the sum of the improvements of other adjacent monitoring points, the downstream section of the most tail monitoring point is a fault section.
On the other hand, the small-current ground fault positioning system based on the Hausdorff distance provided by the embodiment of the invention comprises:
the voltage real-time monitoring module is used for monitoring the zero sequence voltage of the system bus in real time;
the threshold value judging module is used for positioning faults when the zero sequence voltage of the bus is greater than a set threshold value;
the fault data sampling module is used for sampling the bus zero-sequence voltage of the first period after the fault and the zero-sequence current of each monitoring point of the fault line;
the characteristic quantity extraction module is used for extracting bus transient zero-sequence voltage in a characteristic frequency band and transient zero-sequence current of each monitoring point of a fault line;
the distance value calculation module is used for calculating the projection component of each monitoring point of the fault line and calculating the improved Hausdorff distance value of the adjacent monitoring points;
and the fault section judgment module is used for judging the fault section according to the solved improved Hausdorff distance value.
As a possible implementation manner of this embodiment, the threshold is kUNWherein U isNAnd if the voltage is the rated voltage of the bus and k is a threshold coefficient, starting a fault positioning program.
As a possible implementation manner of this embodiment, the characteristic amount extraction module includes:
the fault characteristic quantity selecting module is used for selecting fault characteristic information in an SFB frequency band as fault characteristic quantity;
and the filter module is used for extracting the transient zero-sequence voltage of the bus and the transient zero-sequence current of each monitoring point of the fault line by using the finite-length single-bit impulse response filter.
As a possible implementation manner of this embodiment, the fault section judgment is specifically configured to:
selecting the maximum value H in the improved Hausdorff distance valuesmaxIf H is presentmaxGreater than the sum of the improvements of other adjacent monitoring points, the maximum value HmaxThe section is a fault section; if H is presentmaxAnd if the sum of the improvements of other adjacent monitoring points is less than the sum of the improvements of other adjacent monitoring points, the downstream section of the most tail monitoring point is a fault section.
The technical scheme of the embodiment of the invention has the following beneficial effects:
the invention takes the transient zero-sequence voltage of a bus and the transient zero-sequence current of each monitoring point of a fault line as fault characteristic quantities, designs a band-pass filter to extract the transient characteristic quantities of characteristic frequency bands, projects the extracted transient information, calculates the projected numerical value by using an improved Hausdorff distance algorithm, and then positions a fault section according to a set fault criterion. The method determines the fault section by utilizing the characteristic of obvious difference of transient zero-sequence currents on two sides of the fault point, and has obvious positioning effect.
Compared with the prior art, the invention has the following advantages:
(1) the grounding device is suitable for different neutral point grounding modes;
(2) the fault characteristic quantity in the characteristic frequency band is orthogonalized, so that the influence of noise on a positioning result can be effectively avoided, and the method has stronger anti-interference capability;
(3) the method is improved on the basis of the traditional Hausdorff distance algorithm, the similarity of waveforms of a fault section and a healthy section is calculated, mean (min | | a-b | |) is used for replacing max (min | | | a-b | |), and the effect is better than that of the traditional Hausdorff distance algorithm;
(4) the invention only needs to extract the transient zero sequence voltage of the bus, and has no requirement on the zero sequence voltage of each outgoing line; the data calculation amount is not large, and only the characteristic information (10ms) of the latter half period of the fault needs to be uploaded.
Description of the drawings:
FIG. 1 is a flow diagram illustrating a method for low current ground fault location based on Hausdorff distance in accordance with an exemplary embodiment;
FIG. 2 illustrates a functional block diagram of a Hausdorff distance-based low current ground fault location system in accordance with an exemplary embodiment;
FIG. 3 is a low current ground fault transient equivalent circuit diagram;
fig. 4 is a zero sequence equivalent network diagram of a power distribution network;
FIG. 5 is a phasor diagram of a projection component calculation;
fig. 6 is a flow chart of fault location using the method of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the following figures:
in order to clearly explain the technical features of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings. The following disclosure provides many different embodiments, or examples, for implementing different features of the invention. To simplify the disclosure of the present invention, the components and arrangements of specific examples are described below. Furthermore, the present invention may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. It should be noted that the components illustrated in the figures are not necessarily drawn to scale. Descriptions of well-known components and processing techniques and procedures are omitted so as to not unnecessarily limit the invention.
As shown in fig. 1, a method for positioning a low-current ground fault based on a Hausdorff distance provided by an embodiment of the present invention includes the following steps:
monitoring the zero sequence voltage of a system bus in real time;
when the zero sequence voltage of the bus is greater than a set threshold value, fault positioning is carried out;
sampling the bus zero-sequence voltage of a first period after a fault and the zero-sequence current of each monitoring point of a fault line;
extracting bus transient zero-sequence voltage in a characteristic frequency band and transient zero-sequence current of each monitoring point of a fault line;
calculating projection components of each monitoring point of the fault line, and calculating improved Hausdorff distance values of adjacent monitoring points;
and judging the fault section according to the solved improved Hausdorff distance value.
As a possible implementation manner of this embodiment, the starting of fault location when the bus zero-sequence voltage is greater than a set threshold specifically includes:
when the zero sequence voltage U of the system bus0Greater than kUNIn which U isNAnd if the voltage is the rated voltage of the bus and k is a threshold coefficient, starting a fault positioning program.
As a possible implementation manner of this embodiment, the extracting of the bus transient zero-sequence voltage and the transient zero-sequence current of each monitoring point of the fault line in the characteristic frequency band specifically includes:
selecting fault characteristic information in an SFB frequency band as fault characteristic quantity;
and extracting the transient zero-sequence voltage of the bus and the transient zero-sequence current of each monitoring point of the fault line by using a finite-length single-bit impulse response filter.
As a possible implementation manner of this embodiment, the formula for obtaining the projection component of each monitoring point of the fault line is as follows:
in the formula (I), the compound is shown in the specification,
is the bus transient zero-sequence voltage,
is the transient zero sequence current of the fault line monitoring point,
is a transient zero sequence current
In-bus transient zero sequence voltage
The projected vector of (c).
As a possible implementation manner of this embodiment, the formula for calculating the improved Hausdorff distance value of the adjacent monitoring point is as follows:
H(i,j)＝max(h(i0i,i0j),h(i0j,i0i)) (14)
in the formula, H (i, j) is Hausdorff distance of adjacent sections i, j, and represents mismatching degree of transient zero sequence current, i0i、i0jTransient zero sequence currents of adjacent sections i, j, respectively, h (i)0i,i0j),h(i0j,i0i) Are respectively transient zero sequence current i0i、i0jOne-way Hausdorff distance in between.
As a possible implementation manner of this embodiment, the determining the fault section according to the solved improved Hausdorff distance value specifically includes:
selecting the maximum value H in the improved Hausdorff distance valuesmaxIf H is presentmaxGreater than the sum of the improvements of other adjacent monitoring points, the maximum value HmaxThe section is a fault section; if H ismaxAnd if the sum of the improvements of other adjacent monitoring points is less than the sum of the improvements of other adjacent monitoring points, the downstream section of the most tail monitoring point is a fault section.
As shown in fig. 2, an embodiment of the present invention provides a small-current ground fault location system based on a Hausdorff distance, including:
the voltage real-time monitoring module is used for monitoring the zero sequence voltage of the system bus in real time;
the threshold value judging module is used for positioning faults when the zero sequence voltage of the bus is greater than a set threshold value;
the fault data sampling module is used for sampling the bus zero-sequence voltage of the first period after the fault and the zero-sequence current of each monitoring point of the fault line;
the characteristic quantity extraction module is used for extracting bus transient zero-sequence voltage in a characteristic frequency band and transient zero-sequence current of each monitoring point of a fault line;
the distance value calculation module is used for calculating the projection component of each monitoring point of the fault line and calculating the improved Hausdorff distance value of the adjacent monitoring points;
and the fault section judgment module is used for judging the fault section according to the solved improved Hausdorff distance value.
As a possible implementation manner of this embodiment, the threshold is kUNWherein U isNAnd if the voltage is the rated voltage of the bus and k is a threshold coefficient, starting a fault positioning program.
As a possible implementation manner of this embodiment, the characteristic amount extraction module includes:
the fault characteristic quantity selecting module is used for selecting fault characteristic information in an SFB frequency band as fault characteristic quantity;
and the filter module is used for extracting the transient zero-sequence voltage of the bus and the transient zero-sequence current of each monitoring point of the fault line by using the finite-length single-bit impulse response filter.
As a possible implementation manner of this embodiment, the fault section judgment is specifically configured to:
selecting the maximum value H in the improved Hausdorff distance valuesmaxIf H is presentmaxGreater than the sum of the improvements of other adjacent monitoring points, the maximum value HmaxThe section is a fault section; if H is presentmaxAnd if the sum of the improvements of other adjacent monitoring points is less than the sum of the improvements of other adjacent monitoring points, the downstream section of the most tail monitoring point is a fault section.
The following describes the related art and principles related to the present invention.
1 fault transient current characteristic of low current grounding system
FIG. 3 is a low current grounding transient equivalent circuit. U shape0kA zero sequence virtual voltage source which is a fault point; l isPExpressed as 3 times the equivalent inductance of the arc suppression coil; r is the sum of the upstream line mode of a fault point of the fault line, a zero mode and 3 times of transition resistance; l is fault point of fault lineThe sum of the upstream line mode and zero mode inductance; c is the sum of the distributed capacitances of all outgoing lines of the system to the ground.
After the small current grounding system has single-phase grounding fault, the transient current flowing through the fault point consists of transient capacitance current and transient inductance current, i.e. if＝iC+iLAnd the frequency and the amplitude of the two are different, so that the two can not be mutually counteracted to be zero in the transient process, and the transient grounding current i flowing through the fault pointfIs composed of
In the formula ICm、ILmRespectively the amplitude of the capacitance current and the amplitude of the inductance current flowing through a fault point when the single-phase earth fault is in a stable state; tau isC、τLIs a time constant;
is the resonant angular frequency of the lc-loop. The first term in the formula (1) is the difference between the steady-state capacitance current and the inductance current, namely a steady-state component, because the over-compensation effect of the arc suppression coil can greatly influence the amplitude and the polarity of the steady-state component, and further influence the single-phase earth fault detection in the resonant earth system, i is extracted from the steady-state componentfOf (a) a transient component ifs
In the equivalent zero sequence network shown in fig. 4, C01、C02、C0GRespectively, the line 1, the line 2 and the ground capacitance of the generator end; c0a、C0b、C0d、C0eThe capacitance to ground of the lines 5ab, bf, fd, de sections, respectively; the f point is a failure point. U shape0fThe voltage is a fault point zero-sequence virtual voltage source and is equal to the fault point transient zero-sequence voltage in numerical value. When single-phase earth fault occurs, compared with non-fault line, the transient zero-sequence current on the fault line,the polarities of the two are opposite, and the amplitude of the former is larger than that of the latter; because the length of the line at the upstream of the fault point is far longer than that of the line at the downstream, the amplitude of the transient zero-sequence current at the upstream of the fault point is far longer than that at the downstream, and the polarities of the transient zero-sequence current at the upstream of the fault point and the transient zero-sequence current at the downstream are opposite. In the research of the zero sequence network of the low-current grounding system, in order to ensure the safe operation of the system, the main network low-current grounding mode is not changed, and the neutral point of the distributed power supply adopts the optimum non-grounding mode, so that the zero sequence network when the active power distribution network has single-phase grounding fault is the same as the zero sequence network of the power distribution network without the distributed power supply, and the access of the distributed power supply does not influence the fault position information contained in the electric quantity for realizing fault detection.
Taking a non-grounded system with a neutral point as an example, a single-phase ground fault occurs at point f in fig. 4, and a transient zero-sequence current i flows through a monitoring point b0bIs equal to i0aAnd the sum of the capacitance-to-ground currents of the section ab, and similarly, the transient zero-sequence current i flowing through the monitoring point d0dIs equal to i0eAnd the sum of the capacitance-to-ground currents between sections de. And transient zero-sequence current i flowing through monitoring point a0aEqual to the sum of the other non-fault line capacitance-to-ground currents.
In an actual power distribution network, because the length of a downstream line of a fault point is far shorter than the length of an upstream line of the fault point and the total length of a sound line, namely the amplitude of transient zero-sequence current at the upstream of the fault point is far longer than that at the downstream of the fault point, and the waveform similarity of the transient zero-sequence current at the upstream of the fault point and the waveform similarity of the transient zero-sequence current at the downstream of the fault point are low; secondly, the section ab has a short distance, and the capacitance current to ground is negligible compared with the sum of the zero sequence capacitance currents of the non-fault line, so that the transient zero sequence currents flowing through the monitoring points a and b are approximately equal, i.e. i0a≈i0b。
2 system characteristic frequency band
2.1 line impedance phase-frequency characteristics
In the zero sequence network of the small current grounding system, when the tail end of the line is open, the impedance Z of the input end of the line isocIs composed of
In formula (3):
is the wave impedance of the line and,
for propagation coefficient, l is the line length.
In the event of a single-phase earth fault, the frequency range of the transient component is typically greater than 200Hz, with the zero-sequence resistance being much smaller than the reactance. Therefore, when the zero sequence impedance at the input end of the line is analyzed, the influence of the zero sequence resistance is ignored. The ingress zero sequence impedance at the fault point can be expressed as
In formula (4): c0、L0The zero sequence capacitance and the zero sequence inductance of the circuit.
Under the condition of series and parallel resonance, the zero sequence resistance is ignored, and the phase-frequency characteristic of the zero sequence impedance at the input end of the circuit has a slight difference from the impedance phase-frequency characteristic when the zero sequence resistance is considered. Thus making
When the frequency range is 0 < fkWherein the line impedance is capacitive, and f ═ fkWhen the circuit is in series resonance for the first time; f > fkThe line impedance is changed alternately in capacitance or inductance with the increase of frequency, and the intervals of the frequency change are not equal. That is, each line can be equivalent to a capacitor or an inductor in different frequency bands along with the increase of frequency.
2.2 determining characteristic frequency band
The tail end of each line in the zero sequence network is in an open circuit state, and when the system Frequency is from 0 to a certain low Frequency Band, each line is capacitive, so that the Selected Frequency is from 0 to the minimum series resonance Frequency Band of all non-fault lines as a characteristic Frequency Band (SFB). In the characteristic frequency band, each non-fault line and each fault line in the zero sequence network are capacitive, and most transient currents are distributed to each non-fault line through the fault line (the transient current amplitude of the non-fault line is inversely proportional to the equivalent capacitive reactance of the non-fault line). Namely, the transient zero-sequence current direction of the fault line flows from the line to the bus, while the transient zero-sequence current of the non-fault line flows from the bus to the line, the polarities of the two are opposite, and the amplitude of the transient zero-sequence current is larger than that of the transient zero-sequence current of the non-fault line; the direction of the upstream transient zero-sequence current of the fault point flows from the fault point to the bus, and the direction of the downstream transient zero-sequence current flows from the fault point to the tail end of the line, and the polarities of the upstream transient zero-sequence current and the downstream transient zero-sequence current are opposite, and generally, the amplitude of the upstream transient zero-sequence current is far larger than that of the downstream transient zero-sequence current.
In a characteristic frequency band, LC series resonance is inevitably generated in the system, the resonance frequency in the resonance process is minimum, the amplitude of the generated transient current is maximum, and most energy in the transient zero sequence current is concentrated. Therefore, the fault characteristic information in the SFB frequency band is selected as the fault characteristic quantity.
2.3 extraction of transient characteristic quantities
Because the zero-sequence network presents the compatibility in the non-fault line and the fault line in the SFB frequency band, the fault characteristic quantity in the text is the transient zero-sequence voltage of the bus and the transient component in the zero-sequence current of each monitoring point, and can be obtained from the formula (2): the transient zero-sequence component is a product of a sine function and an exponential function, and presents an attenuation trend according to an exponential form.
The unit impulse response of the FIR filter is a finite length sequence, and the unit impulse response h (n) is set to have a length L, and the system function H (z) and the difference function y (n) are respectively
The system function of the FIR filter has only zero points, no pole points except the origin, so the FIR filter is stable.
Meanwhile, the window function plays a very important role in the design of the FIR digital filter, and the performance of the designed digital filter can be improved by selecting the proper window function. The width of the transition band can be effectively controlled by adjusting the window length N, and the fluctuation in the transition band can be reduced and the stop band attenuation can be increased by adjusting the shape of the window function. After the window function is adjusted, the main lobe of the spectrum function of the window function contains more energy, the amplitude of the side lobe can be correspondingly reduced, the reduction of the amplitude of the side lobe can reduce the fluctuation of a pass band and a stop band, the attenuation of the stop band is increased, and a proper window function needs to be selected according to actual conditions and technical requirements. Therefore, to reduce spectral energy leakage, we consider here the use of a window function to truncate the signal. Because the main resonant frequency of the transient zero-sequence component is usually greater than 300Hz, in order to suppress interference of power frequency and other low-frequency components, a digital filter is used for extracting fault information in a characteristic frequency band.
3 Fault location principle based on improved Hausdorff distance
3.1 Fault feature quantity orthogonalization processing
In linear algebra, if a set of vectors in the inner product space can form a subspace, the set of vectors is called a base of the subspace. Gram-Schmidt orthogonalization provides a method, which can obtain an orthogonal base of a subspace through a base on the subspace, and can further obtain a corresponding orthonormal base.
Let alpha1,α2,…,αm(m.ltoreq.n) is RnA set of linearly independent vectors of (1), if
Then beta is1,β2,…,βmIs a set of orthogonal vectors. If order
A set of orthonormal vectors e is obtained1,e2,…,em. As shown in figure 5 of the drawings,
is a vector
Sum vector
The included angle therebetween.
From fig. 5, it can be seen that:
in the formula ipIs a transient zero sequence current
In-bus transient zero sequence voltage
A scalar quantity of the projection of (a) onto,
is a transient zero sequence current
In-bus transient zero sequence voltage
The projected vector of (c).
From equation (9), a vector can be obtained
In the vector
The projection components on are:
in the formula (10), the reaction mixture is,
is a vector
Sum vector
The inner product between. According to the formula (10), the projection of the transient zero-sequence current of each monitoring point in the characteristic frequency band on the transient zero-sequence voltage of the bus can be calculated
3.2 principle of positioning
The Hausdorff distance algorithm is applied to image processing and is a fuzzy distance measure used for measuring the similarity between two finite point sets. In image matching identification, an image is taken as a point set, and the matching degree of the image is represented by the similarity degree of two point sets. Assume that there are 2 finite point sets: a ═ a1,a2,…,ai}，B＝{b1,b2,…,bj}。
The improved Hausdorff distance calculation is as follows:
the one-way Hausdorff distance from point set a to point set B is:
the one-way Hausdorff distance from point set B to point set a is:
and | a-B | and | B-a | represent the Euclidean distance between the point set A and the point set B and the point.
The two-way Hausdorff distance between the point set A and the point set B is as follows:
H(A,B)＝max(h(A,B),h(B,A)) (13)
h (A, B) reflects the degree of mismatch between point set A and point set B. The larger H (A, B), the larger the difference between the point set A and the point set B.
If a fault line in a low-current grounding system has m sections, the transient zero-sequence current i of the adjacent sections i and j0i、i0jFrom equation (13), the Hausdorff distance between two adjacent segments is:
H(i,j)＝max(h(i0i,i0j),h(i0j,i0i)) (14)
defining H (i, j) as the mismatching degree of the transient zero sequence current of the adjacent sections i, j, wherein the larger H (i, j) is, the more obvious the difference between the waveforms of the transient zero sequence current is.
When a single-phase earth fault occurs in the system, because the amplitude of the transient zero-sequence current at the upstream of the fault point is far larger than that of the transient zero-sequence current at the downstream, and the polarities of the transient zero-sequence current and the transient zero-sequence current are opposite, the projection component amplitude difference of each monitoring point at two sides of the fault point is large, the waveform similarity is low, and the value of H (i, j) is large; the projection component amplitude difference of each monitoring point at the upstream of the fault point is not large, the waveform similarity is high, the H (i, j) value is small, and each monitoring point at the downstream of the fault point has similar conclusion; (ii) a When the tail end of the line has a fault, the projection component waveform similarity of each adjacent monitoring point of the fault line is high, and the numerical value of H (i, j) is small. Therefore, the maximum value H is selectedmaxIf H ismaxGreater than the sum of other adjacent monitoring points H, i.e. sigma HrestIf the section where the maximum value is located is a fault section; if HmaxLess than Σ HrestThen the downstream section of the endmost monitoring point is determined to be faulty.
3.3 Fault location flow sheet
For a power distribution network with overhead-cable mixed outlet, a fault section positioning flow chart based on the principle is shown in 6. The specific fault location procedure is as follows.
(1) Monitoring system busZero sequence voltage, when U0Greater than kUNTime (U)NThe rated voltage of the bus is adopted, the k value is generally 0.15 according to actual needs), and then the fault locating device is started.
(2) And sampling to obtain the bus zero-sequence voltage of the first period after the fault and the zero-sequence current of each monitoring point of the fault line, and designing a digital filter to extract the bus transient zero-sequence voltage in the characteristic frequency band and the transient zero-sequence current of each monitoring point of the fault line.
(3) And (3) calculating projection components of monitoring points of the fault line by using the formula (10), and calculating improved Hausdorff distance values of adjacent monitoring points by using the projected current through the formula (14).
(4) Selecting the maximum value H according to the solved improved Hausdorff distance valuemaxIf H ismaxGreater than Σ HrestThen maximum value HmaxThe section is a fault section; if H ismaxLess than Σ HrestThen the section downstream of the endmost monitoring point is the failed section.
The invention designs a digital filter to extract transient zero-sequence current of each monitoring point and transient zero-sequence voltage of a bus in a characteristic frequency band, determines a fault section by utilizing the characteristic that the transient zero-sequence current on two sides of a fault point has obvious difference, and has obvious positioning effect.
The waveform difference between the fault section and the healthy section is represented through gram-Schmidt orthogonalization, improvement is carried out on the basis of the existing Hausdorff distance algorithm, and the similarity of the waveforms of the fault section and the healthy section is calculated.
The invention only needs to extract the transient zero sequence voltage of the bus, and has no requirement on the zero sequence voltage of each outgoing line; the data calculation amount is not large, and only the characteristic information (10ms) of the half period after the fault is uploaded.
The foregoing is only a preferred embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements are also considered to be within the scope of the present invention.
Claims (8)
1. A small current ground fault positioning method based on a Hausdorff distance is characterized by comprising the following steps:
monitoring the zero sequence voltage of a system bus in real time;
when the zero sequence voltage of the bus is greater than a set threshold value, fault positioning is carried out;
sampling the bus zero-sequence voltage of a first period after a fault and the zero-sequence current of each monitoring point of a fault line;
extracting bus transient zero-sequence voltage in a characteristic frequency band and transient zero-sequence current of each monitoring point of a fault line;
calculating projection components of each monitoring point of the fault line, and calculating improved Hausdorff distance values of adjacent monitoring points;
judging a fault section according to the solved improved Hausdorff distance value;
the characteristic frequency band is as follows: the tail end of each line in the zero sequence network is in an open circuit state, when the system frequency is from 0 to a certain low frequency band, each line is capacitive, and the frequency is selected from 0 to the minimum series resonance frequency band of all non-fault lines as a characteristic frequency band;
the process of calculating the projection component of each monitoring point of the fault line and calculating the improved Hausdorff distance value of the adjacent monitoring points comprises the following steps:
the formula for solving the projection component of each monitoring point of the fault line is as follows:
in the formula (I), the compound is shown in the specification,
is the bus transient zero-sequence voltage,
is the transient zero-sequence current of the fault line monitoring point,
is a transient zero-sequence current
In-bus transient zero sequence voltage
A projection vector of (a);
the formula for calculating the improved Hausdorff distance value of the adjacent monitoring points is as follows:
H(i,j)＝max(h(i0i,i0j),h(i0j,i0i)) (14)
in the formula, H (i, j) is Hausdorff distance of adjacent sections i, j, and represents mismatching degree of transient zero sequence current, i0i、i0jTransient zero sequence currents of adjacent sections i, j, respectively, h (i)0i,i0j),h(i0j,i0i) Are respectively transient zero sequence current i0i、i0jThe one-way Hausdorff distance between;
and (3) calculating projection components of monitoring points of the fault line by using the formula (10), and calculating improved Hausdorff distance values of adjacent monitoring points by using the projected current through the formula (14).
2. The method for positioning the small-current ground fault based on the Hausdorff distance according to claim 1, wherein the starting of fault positioning when the zero-sequence voltage of the bus is greater than a set threshold value specifically comprises:
when the zero sequence voltage U of the system bus0Greater than kUNIn which U isNAnd if the voltage is the rated voltage of the bus and k is a threshold coefficient, starting a fault positioning program.
3. The method for positioning the small-current ground fault based on the Hausdorff distance according to claim 1, wherein the extracting of the bus transient zero-sequence voltage and the transient zero-sequence current of each monitoring point of the fault line in the characteristic frequency band specifically comprises:
selecting fault characteristic information in an SFB frequency band as fault characteristic quantity;
and extracting the transient zero-sequence voltage of the bus and the transient zero-sequence current of each monitoring point of the fault line by using a finite-length single-bit impulse response filter.
4. The method for positioning the low-current ground fault based on the Hausdorff distance as claimed in claim 1, wherein the fault section judgment is performed according to the solved improved Hausdorff distance value, and specifically comprises:
selecting the maximum value H in the improved Hausdorff distance valuesmaxIf H is presentmaxGreater than the sum of the improvements of other adjacent monitoring points, the maximum value HmaxThe section is a fault section; if H is presentmaxAnd if the sum of the improvements of other adjacent monitoring points is less than the sum of the improvements of other adjacent monitoring points, the downstream section of the most tail monitoring point is a fault section.
5. A small current ground fault positioning system based on Hausdorff distance is characterized by comprising:
the voltage real-time monitoring module is used for monitoring the zero sequence voltage of a system bus in real time;
the threshold value judging module is used for positioning faults when the zero sequence voltage of the bus is greater than a set threshold value;
the fault data sampling module is used for sampling the bus zero-sequence voltage of the first period after the fault and the zero-sequence current of each monitoring point of the fault line;
the characteristic quantity extraction module is used for extracting bus transient zero-sequence voltage in a characteristic frequency band and transient zero-sequence current of each monitoring point of a fault line;
the distance value calculation module is used for calculating the projection component of each monitoring point of the fault line and calculating the improved Hausdorff distance value of the adjacent monitoring points;
the fault section judgment module is used for judging the fault section according to the solved improved Hausdorff distance value;
the characteristic frequency band is as follows: the tail end of each line in the zero sequence network is in an open circuit state, when the system frequency is from 0 to a certain low frequency band, each line is capacitive, and the frequency is selected from 0 to the minimum series resonance frequency band of all non-fault lines as a characteristic frequency band;
the process of calculating the projection component of each monitoring point of the fault line and calculating the improved Hausdorff distance value of the adjacent monitoring points comprises the following steps:
the formula for solving the projection component of each monitoring point of the fault line is as follows:
in the formula (I), the compound is shown in the specification,
is the bus transient zero-sequence voltage,
is the transient zero-sequence current of the fault line monitoring point,
is a transient zero sequence current
In-bus transient zero sequence voltage
A projection vector of (a);
the formula for calculating the improved Hausdorff distance value of the adjacent monitoring points is as follows:
H(i,j)＝max(h(i0i,i0j),h(i0j,i0i)) (14)
in the formula, H (i, j) is the Hausdorff distance of the adjacent sections i, j, and represents the mismatching degree of the transient zero sequence current, i0i、i0jTransient zero sequence currents of adjacent sections i, j, respectively, h (i)0i,i0j),h(i0j,i0i) Are respectively transient zero sequence current i0i、i0jThe one-way Hausdorff distance between;
and (3) calculating projection components of monitoring points of the fault line by using the formula (10), and calculating improved Hausdorff distance values of adjacent monitoring points by using the projected current through the formula (14).
6. The Hausdorff distance-based low-current ground fault location system of claim 5, wherein the threshold is kUNWherein U isNAnd if the voltage is the rated voltage of the bus and k is a threshold coefficient, starting a fault positioning program.
7. The Hausdorff distance-based low current ground fault location system of claim 5, wherein the characteristic quantity extraction module comprises:
the fault characteristic quantity selecting module is used for selecting fault characteristic information in an SFB frequency band as fault characteristic quantity;
and the filter module is used for extracting the transient zero-sequence voltage of the bus and the transient zero-sequence current of each monitoring point of the fault line by using the finite-length single-bit impulse response filter.
8. The Hausdorff distance-based low-current ground fault location system according to claim 5, wherein the fault section determination is specifically configured to:
selecting the maximum value H in the improved Hausdorff distance valuesmaxIf H is presentmaxGreater than the sum of the improvements of other adjacent monitoring points, then the maximum value HmaxThe section is a fault section; if H is presentmaxAnd if the sum of the improvements of other adjacent monitoring points is less than the sum of the improvements of other adjacent monitoring points, the downstream section of the most tail monitoring point is a fault section.
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