CN111738128A - Series fault arc detection method based on morphological filtering and MMG - Google Patents

Series fault arc detection method based on morphological filtering and MMG Download PDF

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CN111738128A
CN111738128A CN202010554111.2A CN202010554111A CN111738128A CN 111738128 A CN111738128 A CN 111738128A CN 202010554111 A CN202010554111 A CN 202010554111A CN 111738128 A CN111738128 A CN 111738128A
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徐通通
陈浩
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Shandong Zhuowen Information Technology Co ltd
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Abstract

The invention relates to a series fault arc detection method based on morphological filtering and MMG, which comprises the following steps of 1) data sampling: 2) calculating the number of zero crossings of the data; 3) judging the type of the load network according to the number of zero crossings; 4) morphological filtering of the sampled data: carrying out corrosion expansion operation on the sampling data in the step 1), and then carrying out morphological opening and closing operation; 5) solving the morphological gradient value by MMG: extracting the abrupt change characteristics in the current signal waveform to be analyzed by utilizing multi-resolution morphological gradient operation, and solving the morphological gradient value rhom(ii) a 6) Comparing the morphological gradient values ρmAnd setting a threshold value, ifmIf the value is larger than the threshold value, the fault arc is judged to be generated. The detection method can accurately and quickly extract the fault characteristics presented by the singular points of the signals by utilizing mathematical morphology, so thatThe morphology can not be influenced by the position of the fault point and different loads of the line, and whether the fault occurs in the line can be accurately judged.

Description

Series fault arc detection method based on morphological filtering and MMG
Technical Field
The invention relates to a series fault arc detection method based on morphological filtering and MMG, and belongs to the technical field of power system maintenance.
Background
Arcing is the phenomenon in which circuit current breaks down the air, producing a strong gas discharge. This often occurs when circuit insulation ages and contact connections relax. Fault arcing is an important factor among many that causes power system failures. The fault arc may be classified into a series fault arc and a parallel fault arc according to the generation position of the arc. The current amplitude of the parallel fault arc can reach 75-500A, the current amplitude of the series fault arc cannot jump, and the traditional analysis method is difficult to detect and analyze. After the series fault arc is generated, the fault arc current of only 2-10A can generate local high temperature of 2000-4000 ℃, and the arc current of 0.5A is enough to cause fire. Therefore, an electrical fire accident is more easily caused by series fault electric arcs, and in addition, if the fault electric arcs occur in the power distribution cabinet and cannot be eliminated in time, the middle-low voltage bus can be possibly broken down, so that the power supply system is unstable, a large-area power failure can be caused in serious conditions, and even casualties and heavy economic losses are caused.
At present, the method for judging the fault arc mainly judges the distortion of voltage and current signals, such as Fourier transform analysis and wavelet transform analysis, and artificial intelligence algorithms such as a convolutional neural network and a probabilistic neural network. These methods all have the problems of large calculation amount, long time consumption and high requirement on hardware processing capacity.
The morphological filtering is nonlinear transformation based on mathematical morphology, and according to the geometric structural characteristics of signals or images, the signals are locally detected and corrected by using structural elements, so that the purposes of extracting the signals and inhibiting noise are achieved. The Multi-resolution Morphological Gradient operation (MMG) is a Morphological Gradient operation of Multi-resolution analysis, can meet the requirement of high-sensitivity singularity detection, and reflects the degree of signal waveform mutation. The method comprises the steps of filtering noise interference in a current signal by using morphological filtering, extracting abrupt change characteristics of current waveforms before and after occurrence of a series fault arc by using MMG (millimeter-wave generator), further obtaining morphological gradient values of line current waveforms under normal working conditions and during occurrence of the fault arc, and accurately judging whether the line has an arc fault by comparing sizes of the morphological gradient values of the line current waveforms before and after the occurrence of the fault.
The morphological filtering and MMG calculation amount is small, the calculation speed is high, the method is very suitable for detecting the fault arc in the environment of the Internet of things (such as in a distribution box), and the method has important significance for maintaining the safety of a power grid and reducing casualties and property loss.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a series fault arc detection method based on morphological filtering and MMG.
The technical scheme of the invention is as follows:
a series fault arc detection method based on morphological filtering and MMG comprises the following steps:
1) data sampling: collecting current data in a circuit, wherein the sampling frequency is set to be 64 times of the power frequency, namely sampling is carried out for 64 times in each period of a current waveform;
2) calculating the number of zero crossings of data: calculating the number of zero crossing points of the data obtained by sampling in the step 1);
3) judging the type of the load network according to the number of zero crossings: comparing the number of zero crossing points in one period with a judgment threshold, wherein the zero crossing points are nonlinear loads when the zero crossing points are larger than the judgment threshold, and the zero crossing points are linear loads when the zero crossing points are smaller than the judgment threshold;
4) morphological filtering of the sampled data: carrying out corrosion expansion operation on the sampling data in the step 1), and then carrying out morphological opening and closing operation;
5) solving the morphological gradient value by MMG: extracting the abrupt change characteristics in the current signal waveform to be analyzed by utilizing multi-resolution morphological gradient operation, and solving the morphological gradient value rhom；
6) Comparing the form gradient value with a set threshold value: setting the shape gradient threshold of the linear load to be T1The morphological gradient threshold of the nonlinear load is T2(ii) a Calculating a morphological gradient value ρ of a signal of sampled datamIf ρmIf the value is larger than the threshold value, the fault arc is judged to be generated.
Preferably, in step 3), the judgment threshold value for the number of zero-crossing points of the current in one period is set to be 5.
Preferably, in step 4), if f (x) is the acquired one-dimensional input signal, g (x) is used as the structural element, C and D are the domains of f (x) and g (x), respectively, C ═ 1,2, …, M }, D ═ 1,2, …, N }, where M and N are integers, and M ≧ N, the expansion and corrosion of the structural element g (x) to the target signal f (x) are defined as:
Figure BDA0002543667790000021
Figure BDA0002543667790000022
Figure BDA0002543667790000023
and Θ is the sign of the expansion operation and the sign of the erosion operation, respectively, x and y are the coordinates, x is time, y is the amplitude of the current, g (y) is the result of the operation of the structural element g (x) on the amplitude y;
the morphological open-close operation is defined as follows:
Figure BDA0002543667790000031
Figure BDA0002543667790000037
the method can obtain opening operation and closing operation based on expansion and corrosion operation in mathematical morphology, and combines the opening operation and the closing operation to form a new operation form, namely morphology opening and closing operation and morphology closing and opening operation, and the formula is as follows:
Figure BDA0002543667790000039
Figure BDA0002543667790000038
reconstructing the opening and closing operation and the closing and opening operation to form a new filter, wherein the newly constructed filter is as follows, a one-dimensional input signal f (x) is filtered and output as y (x) through the opening and closing operation and the closing operation:
y(x)＝λ1OC(f(x))+λ2CO(f(x))
wherein y (x) is the filtered signal, f (x) contains the original signal and noise, λ1And λ2Are weight coefficients.
Preferably, in step 5), a basic morphological gradient is used, defined as the difference between the original signal f (x) after erosion and expansion by the structural element g (x), expressed as:
Figure BDA0002543667790000032
in order to extract abrupt change features in a signal waveform to be analyzed, a flat structural element is designed, which has different origin positions and can be changed, as shown in the following:
Figure BDA00025436677900000310
Figure BDA00025436677900000311
in the formula, the structural element g+For extracting the rising edge, g, of the waveform-For extracting the falling edge in the waveform,
Figure BDA0002543667790000033
and glEach represents g+And g-The width of the structural element l is 21-αl1，l1For the initial width of the structure element in the first layer, α is the number of analysis layers for the multiresolution morphological gradient computation, from which analysis, the multiresolution morphological gradient ραIs defined as:
Figure BDA0002543667790000034
Figure BDA0002543667790000035
Figure BDA0002543667790000036
for a particular signal f (x), the morphological gradient values it solves
Figure BDA0002543667790000041
The invention has the beneficial effects that:
1. the detection method of the invention is carried out in the time domain when the mathematical morphology is applied to analyze the signal, does not relate to the conversion of the time-frequency domain, and the mathematical morphology has no multiplication and division operation in the operation process and only addition and subtraction operation, so the calculation amount is small and the calculation speed is high.
2. According to the detection method, the mathematical morphology can accurately and quickly extract the fault characteristics presented by the signal singular points, so that the morphology can be free from the influence of the positions of fault points and different loads of a line, and whether the line has faults or not can be accurately judged.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a waveform diagram of arc voltage and arc current when a fault arc occurs in a linear load.
Fig. 3 is a graph of the results of the second set of linear load fault arc current shape filtering in example 2.
Fig. 4 is a graph of the multi-resolution morphological gradient operation results of three sets of linear load signals.
Fig. 5 is a graph of the second set of nonlinear load fault arc current shape filtering results in example 3.
FIG. 6 is a graph of the multi-resolution morphological gradient operation results of three sets of nonlinear loading signals.
Detailed Description
The present invention will be further described by way of examples, but not limited thereto, with reference to the accompanying drawings.
Example 1
As shown in fig. 1, the present embodiment provides a series fault arc detection method based on morphological filtering and MMG, which includes the following steps:
1) and (6) sampling data. The invention collects current data in the circuit to detect fault arc, and the sampling frequency is set to be 64 times of power frequency, namely, the current waveform is sampled for 64 times in each period.
2) And calculating the number of zero-crossing points of the data. And (3) calculating the number of zero crossing points of the data obtained by sampling in the step 1).
When a fault arc occurs, voltage drop exists, and the arc current in the same line is lower than the normal working current; the maximum current rising rate of the current waveform is increased, a section of zero current area appears near the zero crossing point of the arc current waveform, the current amplitude is almost zero at the moment, and when the zero crossing point is reached, the arc can be combusted again, so that the phenomenon is a zero break phenomenon; the time point at which the "zero-break" phenomenon occurs is called the zero-crossing point. When an arc occurs, a large amount of high frequency noise appears in the arc voltage and current waveforms, as shown in fig. 2.
3) And judging the type of the load network according to the number of zero crossing points. A linear load is a load whose current waveform approximates a standard sine wave when a sinusoidal voltage is applied across the load, and whose impedance does not change when the voltage applied across the load changes. A non-linear load is one in which, when a sinusoidal voltage is applied across the load, the current waveform flowing through the load is no longer sinusoidal, and when the voltage across the load changes, the load impedance changes, not always a constant.
Ideally, the number of zero-crossing points of the nonlinear load current is about 10-20, and the number of zero-crossing points of the linear load current is 0-2. Considering that linear load and nonlinear load exist in household electricity at the same time, the judging threshold value of the zero crossing point number of current in one period is set to be 5, if the zero crossing point number of current sampling in one period is more than 5, the current sampling is judged to be the nonlinear load, and if the zero crossing point number is less than 5, the current sampling is the linear load.
4) The sampled data is morphologically filtered. This involves two steps. Firstly, carrying out corrosion expansion operation on data; then, morphological opening and closing operations are performed on the data.
The erosion-dilation operation is defined as follows. The mathematical morphology describes the signal to be analyzed in a set form, and valuable information in the target signal is extracted by detecting the target signal through structural elements. The structural element is also a signal, commonly referred to in the morphological arts as a "probe". Mathematical morphology involves two basic operations, dilation and erosion. Let f (x) be the acquired one-dimensional input signal (i.e. the current signal acquired in step 1), and g (x) be a "probe" that can be used as a structural element (also a signal) to collect target signal information, so as to extract useful information for the feature analysis and description of the signal. C and D are the definition fields of f (x) and g (x), respectively, C is {1,2, …, M }, D is {1,2, …, N }, wherein M and N are integers, and M is larger than or equal to N. The swelling and erosion of the structural element g (x) to the target signal f (x) is defined as:
Figure BDA0002543667790000051
(fΘg)(x)＝min{f(x+y)-g(y)}
Figure BDA0002543667790000052
and Θ is the sign of the expansion operation and the sign of the erosion operation, respectively, x and y are the coordinates, x is time, y is the magnitude of the current, g (y) is the result of the operation of the structuring element g (x) on the magnitude y. Dilation and erosion are the basic operators of mathematical morphological transformations, whose arithmetic processes are of an unrecoverable nature.
The morphological opening/closing operation is defined as follows. Other operators, such as open and close operations, can be derived based on dilation and erosion operations in mathematical morphology.
Figure BDA0002543667790000053
Figure BDA0002543667790000054
The on and off operations can filter noise in images and signals, with the on operation mainly filtering peak noise and the off operation mainly filtering trough noise. In the morphological filtering process, a good filtering effect cannot be obtained by using the on operation or the off operation alone. Therefore, the opening operation and the closing operation can be combined to form a new operation form, namely, the form opening and closing operation and the form closing and opening operation. Such as the formula:
Figure BDA0002543667790000063
Figure BDA0002543667790000064
the open operation can filter scattered points or burrs in the signal, and the signal is smoothed. Therefore, the output amplitude of the signal after the on/off operation is smaller than that of the original signal, and the output amplitude of the signal after the on/off operation is larger than that of the original signal. When filtering a signal, the best filtering effect cannot be obtained by selecting only one operator, and normally, the on-off operation and the off-on operation are reconstructed to form a new filter. The filter constructed by the invention is as follows, a one-dimensional input signal f (x) is filtered and output as y (x) through the opening and closing operation and the closing operation:
y(x)＝λ1OC(f(x))+λ2CO(f(x))
wherein y (x) is the filtered signal, f (x) contains the original signal and noise, λ1And λ2Are weight coefficients.
5) MMG solution of morphological gradient values
In signal processing, morphological gradients are parameters used to characterize the degree of signal mutation. If the change in gradient value increases, it indicates that the signal has a sudden change at that point. And the size of the gradient value can reflect the degree of abrupt change of the signal waveform. The signals can be processed by gradient operation to highlight edge information. The present invention uses a basic morphological gradient, defined as the difference of the original signal f (x) after erosion and expansion of the structural element g (x). Expressed as:
Figure BDA0002543667790000061
in practical application, the common morphological gradient operation is difficult to meet the requirement of high-sensitivity singularity detection. Therefore, the method of multi-resolution analysis can be introduced into mathematical morphology, and a new operation form, namely multi-resolution morphological gradient operation, is formed. In order to extract the mutation characteristics in the waveform of the signal to be analyzed, the invention designs a flat structural element which has different origin positions and can be changed. As follows:
Figure BDA0002543667790000065
Figure BDA0002543667790000066
in the formula, the structural element g+For extracting the rising edge, g, in the waveform-For extracting the falling edge in the waveform.
Figure BDA0002543667790000062
And glEach represents g+And g-The origin position of (a). Width of structural element l 21-αl1，l1To the initial width of the structuring element at the first level, α is the number of analysis levels for the multi-resolution morphological gradient operation.
From the above analysis, the multi-resolution morphological gradient ραIs defined as:
Figure BDA0002543667790000071
Figure BDA0002543667790000072
Figure BDA0002543667790000073
alpha and l have important effects on the structural elements. When alpha and l are increased, the structural elements are more favorable for extracting the mutation characteristics of the signal to be analyzed, and the result is more accurate, but the calculation amount is increased, and the calculation time is also prolonged. When α and l are reduced, the amount of calculation can be reduced and the operation speed can be increased, but useful information in the signal may be missed. Therefore, the reasonable selection of the structural elements can reduce the calculation amount and shorten the calculation time while acquiring the characteristics of the signal to be analyzed.
In this embodiment, a layer of MMG transform with a length of 11 points of the structural element is taken to analyze the line current waveform, that is, α is taken to be 1, and l is taken to be 11. The structural elements are as follows:
g+＝[1.000,0.995,0.980,0.954,0.917,0.866,0.800,0.714,0.600,0.436,0]
g-＝[0,0.436,0.600,0.714,0.800,0.866,0.917,0.954,0.980,0.995,1.000]
6) and comparing the form gradient value with a set threshold value.
The shape gradient threshold of the linear load is set to 0.3, and the shape gradient threshold of the nonlinear load is set to 0.8. Calculating a morphological gradient ρ of a signal of the sampled datamIf ρmIf the value is larger than the threshold value, the fault arc is judged to be generated.
Herein ρmThe formula of the three multi-resolution morphological gradients is a generalized expression and does not refer to the operation of a certain signal. For a particular signal f (x), the morphological gradient values it solves
Figure BDA0002543667790000074
Example 2
A series fault arc detection method based on morphological filtering and MMG selects 3 groups of different linear loads in Matlab environment and collects current signal data of the linear loads. The rated current values of the lines in normal operation are respectively I1NNot 0.19A (group 1)、I2N0.67A (group 2) and I3N1.33A (group 3) with a current frequency of 50 Hz. The fault arc current of the group 2 load is selected as a research object, and filtering processing is carried out according to the morphological filtering principle, and the result is shown in fig. 3. Fig. 3(a) shows a current waveform at the time of occurrence of a fault arc, and fig. 3(b) shows a waveform after morphological filtering processing. The graph shows that the current waveform obtained after morphological filtering can retain the characteristics of the fault arc when the fault arc occurs while filtering noise.
3 complete current cycles are selected respectively under the normal working condition and the fault arc condition of 3 groups of different loads to carry out multi-resolution morphological gradient operation, and the operation result is shown in figure 4.
The threshold determination was performed for three sets of waveforms, with the results as follows:
table one: fault arc determination of linear load current waveform
Figure BDA0002543667790000081
Example 3
A series fault arc detection method based on morphological filtering and MMG selects 3 groups of different nonlinear loads under Matlab environment, the current rated values of a test line in normal operation are respectively that I1N is 0.6A (group 1), I2N is 1.33A (group 2) and I3N is 3.2A (group 3), and the current frequency is 50 Hz. The 2 nd group of fault arc currents are selected as the study objects, and the filtering processing is performed according to the morphological filtering principle, and the result is shown in fig. 5, wherein fig. 5(a) is the waveform when the fault arc occurs, and fig. 5(b) is the waveform after the filtering processing. It can be seen from the figure that the current waveform obtained after morphological filtering filters noise. The characteristics of the fault arc when it occurs can be preserved.
3 complete current cycles are selected respectively under the normal working condition and the fault arc condition of 3 groups of different loads to carry out multi-resolution morphological gradient operation, and the operation result is shown in figure 6.
The threshold determination was performed for three sets of waveforms, with the results as follows:
table two: fault arc determination of non-linear load current waveform
Figure BDA0002543667790000082
The embodiment shows that the serial fault arc detection method based on the morphological filtering and the MMG can accurately identify the existence of the fault arc, and the accuracy rate reaches 100%.

Claims (4)

1. A series fault arc detection method based on morphological filtering and MMG is characterized by comprising the following steps:
1) data sampling: collecting current data in a circuit, wherein the sampling frequency is set to be 64 times of the power frequency, namely sampling is carried out for 64 times in each period of a current waveform;
2) calculating the number of zero crossings of data: calculating the number of zero crossing points of the data obtained by sampling in the step 1);
3) judging the type of the load network according to the number of zero crossings: comparing the number of zero crossing points in one period with a judgment threshold, wherein the zero crossing points are nonlinear loads when the zero crossing points are larger than the judgment threshold, and the zero crossing points are linear loads when the zero crossing points are smaller than the judgment threshold;
4) morphological filtering of the sampled data: carrying out corrosion expansion operation on the sampling data in the step 1), and then carrying out morphological opening and closing operation;
5) solving the morphological gradient value by MMG: extracting the abrupt change characteristics in the current signal waveform to be analyzed by utilizing multi-resolution morphological gradient operation, and solving the morphological gradient value rhom；
6) Comparing the form gradient value with a set threshold value: setting the shape gradient threshold of the linear load to be T1The morphological gradient threshold of the nonlinear load is T2(ii) a Calculating a morphological gradient value ρ of a signal of sampled datamIf ρmIf the value is larger than the threshold value, the fault arc is judged to be generated.
2. The serial fault arc detection method based on morphological filtering and MMG as claimed in claim 1, wherein in step 3), the judgment threshold of the number of current zero-crossing points in one period is set to 5.
3. The method according to claim 1, wherein in step 4), let f (x) be the acquired one-dimensional input signal, g (x) be the structural element, C and D be the domain of f (x) and g (x), respectively, C ═ 1,2, …, M }, D ═ 1,2, …, N }, where M and N are both integers, and M ≧ N, the structural element g (x) defines the expansion and corrosion of the target signal f (x) as:
Figure FDA0002543667780000011
(fΘg)(x)＝min{f(x+y)-g(y)}
Figure FDA0002543667780000012
and Θ is the sign of the expansion operation and the sign of the erosion operation, respectively, x and y are the coordinates, x is time, y is the amplitude of the current, g (y) is the result of the operation of the structural element g (x) on the amplitude y;
the morphological open-close operation is defined as follows:
Figure FDA0002543667780000021
Figure FDA0002543667780000026
the method can obtain opening operation and closing operation based on expansion and corrosion operation in mathematical morphology, and combines the opening operation and the closing operation to form a new operation form, namely morphology opening and closing operation and morphology closing and opening operation, and the formula is as follows:
Figure FDA0002543667780000028
Figure FDA0002543667780000029
reconstructing the opening and closing operation and the closing and opening operation to form a new filter, wherein the newly constructed filter is as follows, a one-dimensional input signal f (x) is filtered and output as y (x) through the opening and closing operation and the closing operation:
y(x)＝λ1OC(f(x))+λ2CO(f(x))
wherein y (x) is the filtered signal, f (x) contains the original signal and noise, λ1And λ2Are weight coefficients.
4. The method according to claim 3, wherein in step 5) a basic morphological gradient is used, defined as the difference of the original signal f (x) after erosion and expansion by the structural element g (x), expressed as:
Figure FDA0002543667780000027
in order to extract abrupt change features in a signal waveform to be analyzed, a flat structural element is designed, which has different origin positions and can be changed, as shown in the following:
Figure FDA0002543667780000022
g-＝{gl,gl-1,Λ,g2,g1}
in the formula, the structural element g+For extracting the rising edge, g, of the waveform-For extracting the falling edge in the waveform,
Figure FDA0002543667780000023
and glEach represents g+And g-The width of the structural element l is 21-αl1，l1α is a multi-resolution morphological ladder for the initial width of the structuring element in the first layerNumber of analysis layers of degree calculation, from the above analysis, multi-resolution morphological gradient rhoαIs defined as:
Figure FDA0002543667780000024
Figure FDA0002543667780000025
Figure FDA0002543667780000031
for a particular signal f (x), the morphological gradient values it solves
Figure FDA0002543667780000032
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