CN112345895B - Series arc fault detection method based on discriminant analysis strategy - Google Patents
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Abstract
The invention discloses a series arc fault detection method based on a discriminant analysis strategy, which is characterized in that an arc generating circuit is detected through a current sensor and a data acquisition card, current data in the arc generating circuit is acquired through a computer, characteristic transformation is implemented, a current characteristic matrix is constructed and standardized processing is implemented to obtain a new characteristic matrix, a Fisher discriminant analysis algorithm is utilized to obtain a classification transformation matrix, and the classification characteristic matrix and a residual error matrix are calculated. The collected current data are constructed into a current data vector, the mean value, the standard deviation kurtosis, the skewness, the root mean square, the peak factor, the shape factor, the pulse factor, the edge factor and the maximum logarithm are obtained through feature transformation, a feature vector is constructed, and the feature vector is subjected to standardization processing to obtain a detection index. The method has the advantages that only current data under different loads when the circuit normally operates are needed, current data under an arc fault state do not need to be simulated or actually sampled, and negative effects on the whole circuit are small.
Description
Technical Field
The invention relates to an arc fault detection method, in particular to a series arc fault detection method based on a discriminant analysis strategy.
Background
With the trend of increasing complexity and diversification of electric equipment, the problem of electric safety is a non-negligible problem. According to the statistics of the national fire department, the fire caused by the problems of short circuit, overload, electric leakage and the like of electrical equipment is the main cause of fire. The current electric equipment is generally provided with circuit units such as a circuit breaker, a fuse, electric leakage protection and the like, so that the problems of short circuit, overload and electric leakage are solved respectively. In addition to these three typical and common types of electrical equipment faults, an arc fault refers to an electrical fault in which an unintended arc occurs in a live line. According to the connection relationship between the electric Arc and the circuit when the electric Arc Fault occurs, the electric Arc Fault can be divided into Series Arc Fault (SAF), parallel Arc Fault (PAF), ground Arc Fault (GAF) and the like. The parallel arc fault and the grounding arc fault are equivalent to a short-circuit fault due to large current during fault, and a circuit breaker or a fuse can be directly operated to play a protection role. When a series arc fault occurs, the load current is smaller than the normal working current due to the self impedance, and the circuit breaker and the fuse cannot take corresponding actions. Therefore, series arc fault detection is a weak link in current power supply and distribution system fault detection.
Generally, the task of detecting the series arc fault mainly lies in successfully detecting whether the fault occurs or not, and the diagnosis of the type of the arc fault is performed after corresponding protective measures are taken. There are basically two main types of strategies for implementing series arc fault detection: firstly, the arc fault detection is implemented by installing a physical sensing device to acquire physical characteristic signals in real time; second, data-driven arc fault detection is implemented using current or voltage signals in the circuit. The former requires installation of hardware equipment, increases the investment cost of the equipment, and is limited by the installation location space. In contrast, the latter belongs to software detection, and online real-time monitoring of series arc faults can be realized only by using a proper data mining algorithm. Therefore, implementing data-driven series arc fault detection is currently the main direction of research.
It is noted that under normal operating conditions, series arcs can exhibit different characteristics of change in current in the circuit due to different loads and complex operating conditions. The traditional implementation of arc fault detection by using data is mainly based on the idea of multi-class classification, such as the use of decision trees, neural networks, support vector machines, bayesian classifiers, and the like. In addition, in consideration of the current change characteristics, the current signal is subjected to characteristic transformation such as time domain characteristic analysis and frequency domain characteristic analysis, and then classification is performed by using the transformed characteristics, thereby diagnosing the series arc fault. From this point of view, the feature selection plays a key role, that is, it needs to select a proper feature to improve the precision effect of classification, which derives a new problem. The data-driven serial arc fault detection is implemented, the characteristics are analyzed and converted through a time domain or a frequency domain, the multi-working-condition characteristics of a serial circuit need to be considered, the characteristics are extracted through the converted characteristics, the characteristic components are fully utilized, and the arc fault is timely and effectively detected.
Disclosure of Invention
The invention aims to solve the main technical problems that: the purpose of series arc fault detection can be achieved only according to current data under different load conditions. Specifically, the method firstly carries out time domain and frequency domain feature analysis on current data under different load conditions under normal working conditions, then converts the time-frequency domain features into feature signals and residual error signals for classification by utilizing discriminant analysis, and finally carries out fault detection on the classification feature signals and the residual error feature signals respectively.
The technical scheme adopted by the method for solving the problems is as follows: a series arc fault detection method based on a discriminant analysis strategy comprises the following steps:
step 1: the method comprises the following steps of detecting an arc generating circuit through a current sensor and a data acquisition card, acquiring current data in the arc generating circuit through a computer, and dividing the acquired current data into three types: resistive load current data
Inductive load current data
And non-linear load current data
Wherein,
represents 1 XN 1 A vector of real numbers of the dimensions,
represents 1 XN 2 The vector of real numbers of the dimension(s),
represents 1 XN 3 Real number vector of dimension, N 1 ，N 2 ，N 3 Respectively representing the number of resistive load current data, the number of inductive load current data and the number of nonlinear load current data;
step 2: performing characteristic transformation on the three types of current data obtained in the step 1 to obtain a resistive load current characteristic matrix
Inductive load current signature matrix
And a non-linear load current signature matrix
Wherein,
represents n 1 A real number matrix of x 10 dimensions,
represents n 3 X 10 dimensional real number matrix, n 1 ，n 2 ，n 3 Respectively represents Z 1 ，Z 2 ，Z 3 The number of the row vectors of (a),
and step 3: constructing a current feature matrix Z = [ Z ] 1 T ，Z 2 T ，Z 3 T ] T And standardizing each column vector in Z to obtain a new feature matrix
Wherein the upper symbol T represents the transpose of a matrix or vector, n = n 1 +n 2 +n 3 ，R n×10 A real number matrix representing n × 10 dimensions;
and 4, step 4: discrimination by FisherThe analysis algorithm obtains a classification transformation matrix W belonging to R 10×2 And calculating a classification feature matrix
Sum residual matrix
Wherein the load matrix
And 5: and (3) carrying out singular value decomposition on the residual matrix E: e = UAV T And calculating a transformation matrix Q = VA -1 (ii) a Wherein U and V represent unitary matrix of singular value decomposition, the diagonal elements in diagonal matrix A are composed of singular values;
step 6: according to the formula psi = diag { UU T Calculating a detection index vector psi and determining a maximum value of psi as psi 0 ；
And 7: the current data collected at the sampling moment are formed into a current data vector x t Where t represents the latest sampling instant, x is obtained by feature transformation t Mean value m of t Standard deviation of delta t Degree of kurtosis alpha t Deviation of degree beta t Root mean square upsilon t Crest factor gamma t Shape factor η t Pulse factor e t Edge factor f t Maximum logarithm of g t (ii) a And constructing a feature vector z t ＝[m t ，δ t ，α t ，β t ，υ t ，γ t ，η t ，e t ，f t ，g t ]∈R 1×10 For feature vector z t Carrying out standardization processing to obtain new characteristic vector
And 8: using formulas
Computing residual vector E t And detecting the index psi t ＝E t E t T ；
And step 9: and judging whether the step 8 meets the condition: psi t ≤ψ 0 (ii) a If yes, the series arc fault does not occur, and the steps 7 to 9 are repeated to continue to detect the arc fault of the arc generating circuit; if not, detecting the series arc fault.
Preferably, the specific implementation method for performing feature transformation on the three types of current data obtained in step 1 in step 2 is as follows:
setting the window length as L and the moving step length as D,
step 2.1: initializing j =1;
step 2.2: mixing X 1 The current interval vector q is composed of the (j-1) × L +1 to the (j × L) th elements j ∈R 1×L (ii) a Wherein R is 1×L A real number vector representing 1 × L dimensions;
step 2.3: respectively calculating mean values m according to formulas (1) to (R) j Standard deviation of delta j Degree of kurtosis alpha j Deviation of degree beta j Root mean square upsilon j Crest factor gamma j Shape factor η j Pulse factor e j Edge factor f j Maximum logarithm of g j ：
η j ＝υ j /m j ⑦
f j ＝q j (max)/m j ⑧
g j ＝log 10 (q j (max)) ⑩
Step 2.4: constructing a feature vector z j ＝[m j ，δ j ，α j ，β j ，υ j ，γ j ，η j ，e j ，f j ，g j ]∈R 1×10 And then judging whether the conditions are met: (j + 1). Times.L > N 1 (ii) a If not, after j = j +1 is set, returning to the step (2.2); if yes, all the obtained eigenvectors form a resistive load current characteristic matrix
Preferably, X in step 2.2 is 1 Is replaced by X 2 、X 3 And respectively obtaining the inductive load current characteristic matrixes according to the implementation processes of the step 2.1 to the step 2.4
And a non-linear load current signature matrix
Preferably, the latest sampling time is set as t, and the current data I acquired at the latest sampling time in the step 7 is set as t And the first L-1 thereofCurrent data I at the sampling instants t-1 ，I t-2 ，…，I t-L+1 Built into a current data vector x t ＝[I t ，I t-1 ，…，I t-L+1 ]∈R 1×L (ii) a Coupling X in step 2.2 1 Is replaced by x t Obtaining x t Mean value m of t Standard deviation of delta t Degree of kurtosis alpha t Degree of deviation beta t Root mean square upsilon t Crest factor gamma t Shape factor η t Pulse factor e t Edge factor f t Maximum logarithm of g t 。
By carrying out the steps described above, the advantages of the method of the invention are introduced as follows:
firstly, the method processes the multi-load characteristic of current data by discriminant analysis, thereby detecting whether a fault occurs by using residual errors; secondly, the method can judge whether the circuit generates the electric arc only by utilizing the current data under different loads when the circuit normally operates without simulating or actually sampling the current data under the electric arc fault state, thereby trying to reduce the influence on the circuit caused by the traditional data acquisition through equipment and realizing the purpose of minimizing the negative influence on the whole circuit; finally, the method provided by the invention uses the time domain characteristics of the current signal to carry out data mining, and is simpler and more practical.
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FIG. 1 is a schematic flow chart of the method of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the invention discloses a series arc fault detection method based on a discriminant analysis strategy. A specific embodiment of the method of the present invention is further set forth below in conjunction with fig. 1.
And constructing an arc generating circuit, namely connecting resistive, inductive and nonlinear loads with an arc generator and a current sensor respectively to form the arc generating circuit.
Step 1: by current sensors and data acquisitionThe card detects the arc generating circuit, and acquires current data in the arc generating circuit through the computer, and divides the acquired current data into three types: resistive load current data
Inductive load current data
And non-linear load current data
Wherein,
represents 1 XN 1 The vector of real numbers of the dimension(s),
represents 1 XN 2 Real number vector of dimension, N 1 ，N 2 ，N 3 Respectively representing the data number of resistive load current, inductive load current and nonlinear load current;
and 2, step: setting the window length as L and the moving step length as D, and performing characteristic transformation on the three types of current data to obtain a resistive load current characteristic matrix
Inductive load current signature matrix
And a non-linear load current signature matrix
Wherein,
represents n 1 A real number matrix of x 10 dimensions,
represents n 3 X 10 dimensional real number matrix, n 1 ，n 2 ，n 3 Respectively represents Z 1 ，Z 2 ，Z 3 The specific implementation process of the number of row vectors of (2) is as follows,
step 2.1: initializing j =1;
step 2.2: mixing X 1 The current interval vector q is composed of the (j-1) × L +1 to the (j × L) th elements j ∈R 1×L (ii) a Wherein R is 1×L A real number vector representing 1 × L dimensions;
step 2.3: calculating mean value m according to above formula (1) to formula (R) j Standard deviation of delta j Degree of kurtosis alpha j Deviation of degree beta j Root mean square upsilon j Crest factor gamma j Shape factor η j Pulse factor e j Edge factor f j Maximum logarithm of g j ；
Step 2.4: constructing a feature vector z j ＝[m j ，δ j ，α j ，β j ，υ j ，γ j ，η j ，e j ，f j ，g j ]∈R 1×10 And then judging whether the conditions are met: (j + 1). Times.L > N 1 (ii) a If not, after j = j +1 is set, returning to the step (2.2); if yes, all the obtained eigenvectors form a resistive load current characteristic matrix
Mixing X in the step 2.2 1 Is replaced by X 2 、X 3 And according to the implementation process from step 2.1 to step 2.4, the inductive load current characteristic matrixes can be respectively obtained
And a non-linear load current signature matrix
By standardizationProcessing to obtain a new feature matrix
Where the upper index T represents the transpose of the matrix or vector, n = n 1 +n 2 +n 3 ，R n×10 Representing a matrix of real numbers of dimension n x 10.
Step 4, obtaining a classification transformation matrix W belonging to R by utilizing a Fisher discriminant analysis algorithm 10×2 And calculating a classification feature matrix
Sum residual matrix
Wherein the load matrix
The specific implementation process of the Fisher discriminant analysis algorithm is as follows:
step 4.1: new feature matrix
Front n in (1) 1 The row vectors of the rows form a matrix
N of (1) 1 +1 line to nth line 1 +n 2 The row vectors of the rows form a matrix
After n in (1) 3 The row vectors of the rows form a matrix
Step 4.2: separately computing matrices
And
line mean vector mu of 1 ，μ 2 ，μ 3 The calculation method of the line mean vector is as follows: adding the row vectors in the matrix, and dividing the sum by the number of the row vectors;
step 4.3: the covariance matrix C between classes is calculated according to the formula 0 And within-class covariance matrix C 1 ：
In the above formula, the first and second carbon atoms are,
representation matrix
The row vector of the j-th row in (1), i ∈ {1,2,3}, j ∈ {1,2, …, n i }；
Step 4.4: calculation matrix C = C 1 -1 C 0 Maximum two eigenvalues λ 1 And λ 2 And its corresponding feature vector w 1 And w 2 Reconstructing a classification transformation matrix W = [ W = [) 1 ，w 2 ]；
And 5: and (3) performing singular value decomposition on the residual matrix E: e = UAV T And calculating a transformation matrix Q = VA -1 (ii) a Wherein U and V represent unitary matrix of singular value decomposition, the diagonal elements in diagonal matrix A are composed of singular values;
step 6: according to the formula psi = diag { UU T Calculating a detection index vector psi and determining a maximum value of psi as psi 0 (ii) a Wherein diag { } denotes an operation of converting an element on a diagonal of the matrix in braces into a column vector;
and 7: current data I acquired at the latest sampling moment t And first L-1 sampling timeCurrent data of the moment I t-1 ，I t-2， …，I t-L+1 Built into a current data vector x t ＝[I t ，I t-1 ，…，I t-L+1 ]∈R 1×L (ii) a Where t represents the latest sampling instant. Mixing X in the step 2.2 1 Is replaced by x t Respectively calculate to obtain x t Mean value m of t Standard deviation of delta t Degree of kurtosis alpha t Deviation of degree beta t Root mean square upsilon t Crest factor gamma t Shape factor eta t Pulse factor e t Edge factor f t Maximum logarithm of g t (ii) a And constructing a feature vector z t ＝[m t ，δ t ，α t ，β t ，υ t ，γ t ，η t ，e t ，f t ，g t ]∈R 1×10 And carrying out the same standardization processing as the step 3 to obtain a new feature vector
And 8: using formulas
Computing residual vector E t And detecting the index psi t ＝E t E t T ；
And step 9: psi is judged in step 8 t Whether the condition is satisfied: psi t ≤ψ 0 (ii) a If yes, the series arc fault does not occur, and the steps 7 to 9 are repeated to continue to detect the arc fault of the arc generating circuit; if not, the series arc fault is detected, so that the detection of the arc generating circuit is realized, measures are convenient to take to break the circuit, and the generation of serious accidents is avoided.
The above-mentioned embodiments are only preferred embodiments of the present invention, and the description thereof is more specific and detailed, but not to be construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.
Claims (4)
1. A series arc fault detection method based on a discriminant analysis strategy is characterized by comprising the following steps:
step 1: the method comprises the following steps of detecting an arc generating circuit through a current sensor and a data acquisition card, acquiring current data in the arc generating circuit through a computer, and dividing the acquired current data into three types: resistive load current data
Inductive load current data
And non-linear load current data
Wherein,
represents 1 XN 1 A vector of real numbers of the dimensions,
represents 1 XN 2 The vector of real numbers of the dimension(s),
represents 1 XN 3 Real number vector of dimension, N 1 ，N 2 ，N 3 Respectively representing the number of resistive load current data, the number of inductive load current data and the number of nonlinear load current data;
step 2: performing characteristic transformation on the three types of current data obtained in the step 1 to obtain a resistive load current characteristic matrix
Inductive load current signature matrix
And a non-linear load current signature matrix
Wherein,
represents n 1 A real number matrix of x 10 dimensions,
represents n 3 X 10 dimensional real number matrix, n 1 ，n 2 ，n 3 Respectively represents Z 1 ，Z 2 ，Z 3 The number of the row vectors;
and step 3: constructing a current characteristic matrix Z = [ Z ] 1 T ，Z 2 T ，Z 3 T ] T And standardizing each column vector in Z to obtain a new feature matrix
Wherein the upper symbol T represents the transpose of a matrix or vector, n = n 1 +n 2 +n 3 ，R n×10 A real number matrix representing n × 10 dimensions;
and 4, step 4: obtaining a classification transformation matrix W epsilon R by utilizing a Fisher discriminant analysis algorithm 10×2 And calculating a classification feature matrix
Sum residual matrix
Wherein the load matrix
And 5: and (3) carrying out singular value decomposition on the residual matrix E: e = UAV T And calculating a transformation matrix Q = VA -1 (ii) a Wherein U and V represent unitary matrix of singular value decomposition, the diagonal elements in diagonal matrix A are composed of singular values;
step 6: according to the formula psi = diag { UU T Calculating a detection index vector ψ, and determining a maximum value of ψ as ψ 0 ；
And 7: the current data collected at the sampling moment are formed into a current data vector x t Where t represents the latest sampling instant, x is obtained by feature transformation t Mean value m of t Standard deviation of delta t Degree of kurtosis alpha t Deviation of degree beta t Root mean square upsilon t Crest factor gamma t Shape factor eta t Pulse factor e t Edge factor f t Maximum logarithm of g t (ii) a And constructing a feature vector z t ＝[m t ，δ t ，α t ，β t ，υ t ，γ t ，η t ，e t ，f t ，g t ]∈R 1×10 For feature vector z t Carrying out standardization processing to obtain new characteristic vector
And 8: using formulas
Computing residual vector E t And detecting the index psi t ＝E t E t T ；
And step 9: and judging whether the step 8 meets the condition: psi t ≤ψ 0 (ii) a If yes, the series arc fault does not occur, and the steps 7 to 9 are repeated to continue to detect the arc fault of the arc generating circuit; if not, detecting the series arc fault.
2. The method for detecting the series arc fault based on the discriminant analysis strategy as claimed in claim 1, wherein the specific implementation method for performing the feature transformation on the three types of current data obtained in step 1 in step 2 is as follows:
setting the window length as L and the moving step length as D,
step 2.1: initializing j =1;
step 2.2: mixing X 1 The current interval vector q is composed of the (j-1) × L +1 to the (j × L) th elements j ∈R 1×L (ii) a Wherein R is 1 ×L A real number vector representing 1 × L dimensions;
step 2.3: respectively calculating mean values m according to formulas (1) to (R) j Standard deviation delta j Degree of kurtosis alpha j Deviation of degree beta j Root mean square upsilon j Crest factor gamma j Shape factor η j Pulse factor e j Edge factor f j Maximum logarithm of g j ：
η j ＝υ j /m j ⑦
f j ＝q j (max)/m j ⑧
g j ＝log 10 (q j (max)) ⑩
Step 2.4: constructing a feature vector z j ＝[m j ，δ j ，α j ，β j ，υ j ，γ j ，η j ，e j ，f j ，g j ]∈R 1×10 And then judging whether the conditions are met: (j + 1). Times.L > N 1 (ii) a If not, after j = j +1 is set, returning to the step (2.2); if yes, all the obtained eigenvectors form a resistive load current characteristic matrix
3. The tandem arc fault detection method based on discriminant analysis strategy as claimed in claim 2, wherein X in step 2.2 1 Is replaced by X 2 、X 3 And respectively obtaining the inductive load current characteristic matrixes according to the implementation processes of the step 2.1 to the step 2.4
And a non-linear load current signature matrix
4. The method of claim 2, wherein the setting is based on a discriminant analysis strategy for series arc fault detectionThe latest sampling time is t, and the current data I acquired at the latest sampling time in the step 7 t And current data I of the first L-1 sampling moments t-1 ，I t-2 ，…，I t-L+1 Built into a current data vector x t ＝[I t ，I t-1 ，…，I t-L+1 ]∈R 1×L (ii) a Mixing X in step 2.2 1 Is replaced by x t Obtaining x t Mean value m of t Standard deviation of delta t Degree of kurtosis alpha t Deviation of degree beta t Root mean square upsilon t Crest factor gamma t Shape factor η t Pulse factor e t Edge factor f t Maximum logarithm of g t 。
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