CN110031788A - A kind of hollow coil current transformer error environment correlation analysis - Google Patents
A kind of hollow coil current transformer error environment correlation analysis Download PDFInfo
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Abstract
The invention discloses a kind of hollow coil current transformer error environment correlation analysis, include the following steps: in assessment time window according to acquisition data building original matrix；The original matrix is extended based on Kalman filter, establishes higher-dimension random matrix；The higher-dimension random matrix is standardized, so that it is converted to row vector mean value 0, the non-Hermite Matrix that variance is 1；Influence amount relevance evaluation matrix is obtained according to the non-Hermite Matrix；Hollow coil current transformer error environment relevance evaluation index is obtained according to the influence amount relevance evaluation matrix, and the correlation between hollow coil current transformer error and environment parameter is assessed according to the influence amount relevance evaluation matrix and the relevance evaluation index.Advantage: can obtain the correlation degree of mutual inductor kinematic error Yu one or more environment parameter in real time, be conducive to control and assess the running error state stability of mutual inductor.
Description
Technical Field
The invention belongs to the field of power transmission and distribution equipment state evaluation, and particularly relates to an air-core coil current transformer error environment correlation analysis method based on a high-dimensional matrix theory.
Background
The piezoelectric current transformer is an important measuring device for providing current information for a transformer substation electric energy metering system, and the operation performance of the piezoelectric current transformer is related to the accuracy of a metering device. The traditional electromagnetic current widely adopted at present has the defects of complex insulating structure, large volume, high manufacturing cost, small magnetic saturation, small dynamic range and the like, and is difficult to meet the technical requirements of an electric power system. The electronic current transformer has the advantages of large dynamic range, wide frequency response range, small volume, light weight and the like, and conforms to the development direction of digitization, intellectualization and networking of a power system. The air-core coil current transformer is one of electronic current transformers, and a series of achievements are obtained after years of exploration and practice along with rapid development of construction of intelligent substations in recent years.
However, the air-core coil current transformer has a complex structure and many inclusion links, and is influenced by environmental parameters such as temperature, humidity, vibration, magnetic field and primary load current in the operation process. The accuracy problems of air-core coil current transformers still account for a large proportion of field operational problems. The fairness of electric energy trade settlement is influenced, and the popularization and application of the hollow coil current transformer are hindered. The internal relation and the influence rule of the transformer error and various environment parameters are disclosed, the main influence quantity is determined, guidance is provided for the design and the process of the hollow coil current transformer, and the method has important significance for the control and the evaluation of the error stability of the hollow coil current transformer.
The prior art comprises a model-based correlation analysis method, a mechanism and a rule of the influence of environmental parameters on the error of a transformer are analyzed according to a mechanism model of the action of the environmental parameters on a hollow coil current transformer, the method is highly dependent on the accuracy of the model, various assumptions and preconditions can also influence the analysis result, different mechanism models are required to be established for different environmental parameters, the universality is poor, and quantitative evaluation indexes of the correlation cannot be obtained.
The prior art also comprises an analysis method based on data driving, an accurate mechanism model is not required to be constructed, and the correlation between the error of the transformer and the environmental parameter is obtained by mining, processing and analyzing the error data and the environmental parameter data of the transformer. However, the relationship between the error of the air coil current transformer and the environmental parameter presents the characteristics of multi-coupling and high randomness, the correlation degree of the transformer error and the environmental parameter is difficult to determine, and the analysis method is not suitable.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides an air core coil current transformer error environment correlation analysis method based on a high-dimensional matrix theory and independent of a mechanism model, and can provide reference for an air core coil current transformer error control method.
In order to solve the technical problem, the invention provides an error environment correlation analysis method for an air-core coil current transformer, which is characterized by comprising the following steps of:
s1: acquiring environmental parameter data and error data of the hollow coil current transformer, and constructing an original matrix according to the acquired environmental parameter data and the error data in an evaluation time window;
s2: expanding the original matrix based on a Kalman filter to establish a high-dimensional random matrix;
s3: standardizing the high-dimensional random matrix to convert the high-dimensional random matrix into a non-Hermite matrix with a row vector mean value of 0 and a variance of 1;
s4: obtaining an influence quantity correlation evaluation matrix according to the non-Hermite matrix;
s5: and obtaining an error environment correlation evaluation index of the air coil current transformer according to the influence quantity correlation evaluation matrix, and evaluating the correlation between the error of the air coil current transformer and an environment parameter according to the influence quantity correlation evaluation matrix and the correlation evaluation index.
Further, in step S1, an environment parameter matrix is constructed by the collected environment parameter dataWherein the element PijThe measured value of the ith measurable environment parameter at the time j is shown, i is the serial number of the measurable environment parameter, i is 1, 2 and … … M, M is the number of the environment parameters, j is the measured serial number, j is 1, 2 and … … T, and T is the measuring times; construction of an error state matrix from collected error dataWherein, the element QijThe measured value of the ith transformer error parameter at the moment j is represented, i is the serial number of the transformer error parameter, i is 1, 2, … … N, N is the number of the transformer error parameters, j is the measured serial number, j is 1, 2, … … T, and the constructed original matrix isWherein k is M + N.
Further, in step S2, the high-dimensional random matrix obtained after the expansion isk ' is the number of the expanded state parameters, and the value range of N ' meets the condition that k '/T belongs to (0, 1)]And T is the number of measurements.
Further, in step S3, the non-Hermite matrix isWherein Represents a sample xiAverage value of (a), σ (x)ij) Represents a sample xiStandard deviation of (1), xiIs a high-dimensional random matrix D3Row vector of (2), xi＝(xi1,xi2,...,xiT) I is more than or equal to 1 and less than or equal to k ', k' is the number of the expanded state parameters, T is the number of measurements, yijIs a high-dimensional random matrix D3Variable x in (1)ijAnd obtaining new variables after the standardization mode.
Further, the step S4 is specifically:
calculating a singular value equivalence matrix D of the non-Hermite matrixu；
According to the singular value equivalence matrix DuCalculating a matrix product Z;
obtaining an error state evaluation matrix Z according to the matrix product Z2。
Further, the matrix productL1, the error state evaluation matrixWherein,ziis a row vector of matrix Z, Zi＝(zi1,zi2,...,ziT),1≤i≤k'，Is a matrix Z2The row vector of σ (z)i) Denotes ziK' is the number of state parameters after expansion, and T is the number of measurements.
Further, in step S5, the relevance estimation index includes dMSRAnd IMSRWherein d isMSR＝εev-εref，dMSRIntegration over time of IMSR：Wherein, t1And t2Indicating the start time and the end time of the evaluation,λifor the eigenvalues of the corresponding original matrix, λwiFor eigenvalues of the corresponding reference matrix, n and n2E () representing eigenvalue sample expectations for the corresponding original and reference matrices, respectivelyThe reference matrix is composed of an air coil error state matrix and a Gaussian white noise matrix, wherein D1Is an environment parameter matrix; dNThe noise matrix has the same dimensionality as the environment parameter matrix, elements of the noise matrix are random variables which obey standard normal distribution, and the amplitude is the same as the amplitude of Gaussian white noise superposed in matrix extension.
An error state monitoring system of an air-core coil current transformer is characterized by comprising an original matrix building module, a high-dimensional random matrix building module, a standardization processing module, an influence quantity correlation evaluation matrix module and a correlation evaluation module;
the original matrix construction module is used for acquiring environmental parameter data and error data of the hollow coil current transformer and constructing an original matrix according to the acquired environmental parameter data and the error data in an evaluation time window;
the high-dimensional random matrix construction module is used for expanding the original matrix based on a Kalman filter to establish a high-dimensional random matrix;
the standardization processing module is used for standardizing the high-dimensional random matrix to convert the high-dimensional random matrix into a non-Hermite matrix with a row vector mean value of 0 and a variance of 1;
the influence quantity correlation evaluation matrix module is used for obtaining an influence quantity correlation evaluation matrix according to the non-Hermite matrix;
the correlation evaluation module is used for obtaining an error environment correlation evaluation index of the air coil current transformer according to the influence quantity correlation evaluation matrix and evaluating the correlation between the error of the air coil current transformer and an environment parameter according to the influence quantity correlation evaluation matrix and the correlation evaluation index.
Further, the original matrix construction module is used for constructing the environment parameter matrix through the collected environment parameter dataWherein the element PijThe measured value of the ith measurable environment parameter at the time j is shown, i is the serial number of the measurable environment parameter, i is 1, 2 and … … M, M is the number of the environment parameters, j is the measured serial number, j is 1, 2 and … … T, and T is the measuring times; construction of an error state matrix from collected error dataWherein, the element QijThe measured value of the ith transformer error parameter at the moment j is represented, i is the serial number of the transformer error parameter, i is 1, 2, … … N, N is the number of the transformer error parameters, j is the measured serial number, j is 1, 2, … … T, and the constructed original matrix isWherein k is M + N.
Further, the high-dimensional random matrix built by the high-dimensional random matrix building module isk ' is the number of the expanded state parameters, and the value range of N ' meets the condition that k '/T belongs to (0, 1)]And T is the number of measurements.
Further, the non-Hermite matrix obtained by the processing of the standardized processing module is the non-Hermite matrixWherein Represents a sample xiAverage value of (a), σ (x)ij) Represents a sample xiStandard deviation of (1), xiIs a high-dimensional random matrix D3Row vector of (2), xi＝(xi1,xi2,...,xiT) I is more than or equal to 1 and less than or equal to k ', k' is the number of the expanded state parameters, T is the number of measurements, yijIs a high-dimensional random matrix D3Variable x in (1)ijAnd obtaining new variables after the standardization mode.
Further, the influence quantity correlation evaluation matrix module is used for calculating a singular value equivalence matrix D of the non-Hermite matrixuFrom said singular value equivalence matrix DuCalculating matrix product Z, and obtaining error state evaluation matrix Z according to the matrix product Z2；
The matrix productThe error state evaluation matrixWherein,ziis a row vector of matrix Z, Zi＝(zi1,zi2,...,ziT),1≤i≤k'，Is a matrix Z2The row vector of σ (z)i) Denotes ziK' is the number of the extended state parameters, T is the number of measurements
Further, the relevance assessment indicator includes dMSRAnd IMSRWherein d isMSR＝εev-εref，dMSRIntegration over time of IMSR：Wherein, t1And t2Indicating the start time and the end time of the evaluation,λifor the eigenvalues of the corresponding original matrix, λwiFor eigenvalues of the corresponding reference matrix, n and n2E () representing eigenvalue sample expectations for the corresponding original and reference matrices, respectivelyThe reference matrix is composed of an air coil error state matrix and a Gaussian white noise matrix, wherein D1Is an environment parameter matrix; dNThe noise matrix has the same dimension as the environment parameter matrix, the elements are random variables obeying standard normal distribution, and the amplitude is the same as the amplitude of the Gaussian white noise superposed in the matrix extension
The invention achieves the following beneficial effects:
according to the method, no physical model is required to be established, no assumed condition or simplified condition is required, the internal relation between the transformer error and the environment parameter is quantized into the correlation evaluation index according to the error data and the environment parameter data of the hollow coil current transformer, the correlation degree between the transformer operation error and one or more environment parameters can be obtained in real time according to the size and the variation trend of the correlation evaluation index, and the error state stability in the transformer operation can be favorably controlled and evaluated.
Drawings
FIG. 1 is a schematic view of an evaluation flow of the present invention;
FIG. 2 is a schematic diagram of an error state online monitoring platform of the air-core coil current transformer;
FIG. 3 is an influence quantity correlation evaluation matrix Dev1A distribution map of eigenvalues of;
FIG. 4 is an influence quantity correlation evaluation matrix Dev2A distribution map of eigenvalues of;
FIG. 5 is a correlation evaluation matrix D for the influence quantityev1The correlation evaluation index change trend graph is obtained;
FIG. 6 is a correlation evaluation matrix D for the influence quantityev2The index change trend graph is evaluated according to the relevance.
The system comprises an air-core coil current transformer 1, an electromagnetic current transformer 2, an environment monitoring unit 3, an optical fiber remote transmission unit 4, a signal acquisition unit 5, a data processing unit 6, a time synchronization unit 7, a switch 8 and a server 9.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
According to the method, a high-dimensional random matrix is only needed to be established according to the error data and the environmental parameter data of the hollow coil current transformer, and the correlation evaluation index is obtained from the high-dimensional random matrix, reflects the statistical distribution rule of elements of the high-dimensional random matrix and can be used for representing the correlation between the error state of the transformer and the environmental parameter, so that the correlation of the error state of the transformer can be analyzed.
The invention discloses an air-core coil current transformer error environment correlation analysis method based on a high-dimensional matrix theory, which comprises the following steps of:
step 1: on-line monitoring of errors and environmental parameters of the hollow coil current transformer, and constructing an environmental parameter matrix, an error state matrix and an original matrix in an evaluation time window;
because the time series data obtained by online monitoring has time-varying characteristics, a sliding time window real-time processing method is adopted, namely the end time of the time window at the previous moment is the start time of the time window at the next moment, the environmental parameters and error data at the current moment and the historical moment are obtained, the data at each sampling moment are arranged according to the time series, and the data at the current moment and the historical moment can be contained in the original matrix. The length of the sliding time window ranges from 100 to infinity(s), and preferably the length of the sliding time window can be selected to be 1800 s.
The error type of the air-core coil current transformer comprises a specific difference and an angular difference, the environment parameter type comprises a non-electric parameter and an electric parameter, the electric parameter can be divided into a magnetic field parameter and a primary load current parameter (load parameter for short), and the non-electric parameter can be divided into a temperature parameter, a humidity parameter and a vibration parameter. In each intercepted evaluation time window, M environmental parameters are measured for T times, and N mutual inductor error data are measured for T times. The value range of M is 1-5, and preferably, M is selected to be 5; the value range of N is 1-2, and preferably, N is selected to be 2; the value range of T is 300 to infinity, and T is preferably selected to be 360. All measurement data may constitute the original matrix D:
wherein k is M + N, xijDenotes the value of the ith parameter measured j, i is the number of the parameter, i is 1, 2, … … k, j is the number of the measurement times, j is 1, 2,……T。
step 2: expanding the original matrix D by a Kalman filter based on a single state quantity to obtain a high-dimensional random matrix D3；
Because the types of error data and environment parameters of the air-core coil current transformer are less, even if the error data and the environment parameters are combined, the dimension of the constructed influence quantity correlation evaluation matrix is still less, and the construction condition of a high-dimensional random matrix cannot be met. In order to solve the problem, a matrix expansion method based on a Kalman filtering equation of a single state quantity is adopted.
Based on the kalman filter equation, the accurate measurement value of the measurement system is estimated as: wherein x iskFor the amount of system state space, x, at the current timek+1Is the next time system state space quantity, ykIs a system measurement value ξkModel noise of 0 mean ηkNoise was measured for 0 mean.
Changing measurement noise ηkMay be used to obtain multiple sets of kalman filter output values, ηkCan be in the range of 0.1Vrms～10VrmsWherein V isrmsIs the effective value of the Kalman filter input signal. The output of the Kalman filter is used as a matrix row, the state parameters are changed from k to k ', the dimension of the matrix is expanded, and the value range of k ' needs to ensure that k '/T belongs to (0, 1)]Preferably, k' is chosen to be 20, from which a high-dimensional random matrix D is constructed3：
And step 3: for high-dimensional random matrix D3Performing standardization to convert into lineA non-Hermite matrix with a vector mean of 0 and a variance of 1;
for matrix D3Becomes a non-Hermite matrix D after undergoing the following normalization operationstd：Wherein Represents a sample xiAverage value of (a), σ (x)ij) Represents a sample xiStandard deviation of (1), xi＝(xi1,xi2,...,xiT) Where 1. ltoreq. i. ltoreq. N' is a matrix D3The row vector of (2). Such that the matrix D after the normalization operationstd＝(yij)k'×TSatisfy the requirement ofWherein, yi＝(yi1,yi2,...,yiT),1≤i≤N’。
And 4, step 4: establishing an influence quantity correlation evaluation matrix through links of singular value equivalent matrix calculation, matrix product calculation and evaluation matrix calculation;
firstly, a singular value equivalent matrix D of a non-Hermite matrix is obtainedu：
Wherein,representation matrix DstdU is a haar unitary matrix.
Subsequently, the matrix product Z is calculated:wherein D isu,iEach independent singular value equivalent matrix is represented, and the value range of L is 1 to infinity, preferably L is 1.
Finally, based on matrix product Z, obtaining influence quantity correlation evaluation matrix Z2：
Wherein,zi＝(zi1,zi2,...,ziT) I is more than or equal to 1 and less than or equal to k' is a row vector of the matrix Z,is a matrix Z2The row vector of σ (z)i) Denotes ziStandard deviation of (2).
And 5: establishing an error environment correlation evaluation index of the air-core coil current transformer, wherein the evaluation index is represented by linear characteristic value statistics; matrix Z is evaluated according to influence quantity correlation2And analyzing the correlation between the error of the hollow coil current transformer and the environmental parameter according to the correlation evaluation index.
The linear eigenvalue statistic can reflect the eigenvalue distribution condition of a random matrix, for a random matrix, a single eigenvalue cannot reflect the statistical rule of matrix elements in an evaluation time window, and the trace of the matrix can reflect the statistical characteristics of the matrix elements. The reference matrix can be formed by an air core coil error state matrix and a Gaussian white noise matrixWherein D isNThe noise matrix has the same dimension as the environment parameter matrix, the elements are random variables which obey standard normal distribution, and the amplitude is the same as the amplitude of Gaussian white noise superposed in matrix extension. Eigenvalues of the reference matrix may constitute eigenvalue samplesError state evaluation matrix Z2The eigenvalues may constitute an eigenvalue sample V ═ λ1,λ2,…λnCalculate the central moment of the matrixAndwherein λ iswiFor eigenvalues of the corresponding reference matrix, λiFor eigenvalues corresponding to the original matrix, n and n2The number of eigenvalues corresponding to the original matrix and the reference matrix, respectively. E () represents a feature value sample expectation. Defining a relevance evaluation index dMSR： dMSR＝εev-εref，dMSRIntegration over time of IMSR：Wherein t is1And t2Indicating the start time and the end time of the evaluation.
If the correlation exists between the error of the hollow coil current transformer and the environmental parameter, the singular value equivalent matrix of the random matrix constructed by the transformer error data and the environmental parameter data meets the single-loop theorem, and the characteristic values are uniformly distributed in a ring with a specific inner radius and a specific outer radius; otherwise, the distribution of the characteristic values changes and the distribution is not uniform.
For a further understanding of the invention, the following brief description of the single-ring theorem in the present invention is provided:
in practical application, if the matrix isIs a non-Hermite matrix, and the row vectors of the matrix A satisfy the conditions that the mean value is 0 and the variance is 1. For a plurality of non-Hermite matrices AiDefining the matrix productWherein A isu,iIs AiThe singular value equivalence matrix of. Will matrix A2Normalized to AstdSo that it satisfies σ2(ai) 1/n, wherein aiIs a matrix AstdThe row vector of (A)stdThe limiting spectral distribution of (a) converges to a probability density function of, with probability 1:in the formula (12), c is m/n ∈ (0, 1)]， m,n→∞。AstdThe characteristic value of (2) is distributed in a complex plane as a circular ring, and the radius of the inner ring is (1-c)L/2And the radius of the outer ring is 1. In the case of a normal device state, the matrix AstdThe following properties are satisfied: the normalized product matrix obtained by the singular value equivalent matrix through haar unitary matrix transformation should satisfy the single-loop theorem.
The invention is further described with reference to the following figures and specific examples. The examples are illustrative and are intended to be illustrative of the invention and should not be construed as limiting the invention.
As shown in fig. 1, the present invention analyzes the correlation between the error of the air coil current transformer and the environmental parameter according to the following steps:
(1) build the air core coil current transformer error state monitoring platform as shown in figure 2, the platform includes: the system comprises an environment monitoring unit 3, an optical fiber remote transmission unit 4, a signal acquisition unit 5, a data processing unit 6 and a time synchronization unit 7. A0.2-level air-core coil current transformer 1 and a 0.2-level electromagnetic current transformer 2 are installed in the platform. The output of the electromagnetic current transformer 2 is used as a standard signal, and the comparison result of the error of the hollow coil current transformer 1 can be obtained. The environment monitoring unit 3 can collect environment parameters of the installation position of the mutual inductor, including parameters such as temperature, humidity, vibration, magnetic field and the like; the optical fiber remote transmission unit 4 standardizes the data of the environment monitoring unit 3 and sends the data to a data processing unit 6; the data processing unit 6 transmits the data to the server 9 through the switch 8, and the monitoring data are stored in the server 9; the signal acquisition unit 5 can acquire output data of the digital electromagnetic current transformer; the data processing unit 6 receives the output data of the signal acquisition unit 5 and the sampling value message data of the air-core coil current transformer 1 at the same time. Constructing an original random matrix D according to the environmental parameters and the error data of the hollow coil current transformer 1; the clock synchronization unit 7 constructs a synchronous clock system of the whole system and is responsible for synchronizing the optical fiber remote transmission unit 4, the data processing unit 6 and the signal acquisition unit 5.
(2) Based on a Kalman filter, expanding the matrix D to form a high-dimensional random matrix D3. The method comprises the steps of forming original matrixes by utilizing ratio difference data, angle difference data, non-electrical parameter data and electrical parameter data of the air-core coil current transformer, and expanding the original matrixes by adopting a Kalman filter-based matrix expansion method, wherein scales of the original matrixes and the expanded matrixes are shown in a table 1. The error and the environmental parameter of the air-core coil current transformer are calculated once every 10min, the length of a sliding time window is 24h, the total number of the calculation is 144, the number is the column number of an original matrix, and after the expansion is carried out by utilizing a Kalman filter, a 20 multiplied by 144 expansion matrix is formed.
Because only the phase of the electronic transformer is calculated, the number of rows of the original matrix is 1, the phase of the electronic transformer is calculated for 1 time every 10s, the length of the sliding time window is 1h, and the total number of the rows is 360, namely the number of columns of the original matrix, and after the expansion by using the Kalman filter, a 150 multiplied by 360 expansion matrix is formed.
TABLE 1 high dimensional matrix Scale
(3) Using equation (4) to matrix D3Performing standardized conversion to obtain matrix Dstd。
(4) The influence quantity correlation evaluation matrix Z is obtained by using the formula (6) to the formula (8)2。
(5) Forming an error state matrix by using the ratio difference data of the hollow coil current transformer, forming an environment parameter matrix by using the temperature parameter data, and combining the error state matrix and the environment parameter matrix into an influence quantity correlation evaluation matrix Dev1The matrix size is 40 × 144; an influence quantity correlation evaluation matrix D is formed by utilizing the specific difference data and the humidity parameter data of the air-core coil current transformerev2The matrix size is likewise 40 × 144. The sliding time window is 1800s, D in FIG. 3 and D in FIG. 4ev1And Dev2Comparing fig. 3 and fig. 4, it can be seen that Dev1The eigenvalue distribution of the singular value equivalence matrix is more dispersed, and part of eigenvalues exceed the limitation of a circular ring; dev2The eigenvalues of the singular value equivalence matrix are distributed more intensively and are basically distributed in a ring.
The correlation evaluation index is calculated according to the formulas (9) to (10), and fig. 5 and 6 are respectively the data Dev1And Dev2The obtained correlation evaluation index change trend graph shows that the evaluation matrix Dev1In other words, the evaluation index dMSRRises to around 0.35, IMSR273.15 is achieved; for evaluation matrix Dev2In other words, the evaluation index dMSRAlways kept near 0, IMSR43.8, much smaller than the matrix Dev1I of (A)MSRThis indicates that the air-core coil current transformer has a strong correlation between the ratio difference and the temperature and a weak correlation between the ratio difference and the humidity.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (13)
1. An error environment correlation analysis method for an air-core coil current transformer is characterized by comprising the following steps:
s1: acquiring environmental parameter data and error data of the hollow coil current transformer, and constructing an original matrix according to the acquired environmental parameter data and the error data in an evaluation time window;
s2: expanding the original matrix based on a Kalman filter to establish a high-dimensional random matrix;
s3: standardizing the high-dimensional random matrix to convert the high-dimensional random matrix into a non-Hermite matrix with a row vector mean value of 0 and a variance of 1;
s4: obtaining an influence quantity correlation evaluation matrix according to the non-Hermite matrix;
s5: and obtaining an error environment correlation evaluation index of the air coil current transformer according to the influence quantity correlation evaluation matrix, and evaluating the correlation between the error of the air coil current transformer and an environment parameter according to the influence quantity correlation evaluation matrix and the correlation evaluation index.
2. The method for analyzing the error environment correlation of the air-core coil current transformer according to claim 1, wherein in step S1, the environment parameter matrix is constructed by the collected environment parameter dataWherein the element PijThe measured value of the ith measurable environment parameter at the time j is shown, i is the serial number of the measurable environment parameter, i is 1, 2 and … … M, M is the number of the environment parameters, j is the measured serial number, j is 1, 2 and … … T, and T is the measuring times; construction of an error state matrix from collected error dataWherein, the element QijThe measured value of the ith transformer error parameter at the moment j is represented, i is the serial number of the transformer error parameter, i is 1, 2, … … N, N is the number of the transformer error parameters, j is the measured serial number, j is 1, 2, … … T, and the constructed original matrix isWherein k is M + N.
3. The method for analyzing the correlation between the error environments of the air-core coil current transformer and the air-core coil current transformer according to claim 1, wherein in step S2, the high-dimensional random matrix obtained after the expansion isk ' is the number of the expanded state parameters, and the value range of N ' meets the condition that k '/T belongs to (0, 1)]And T is the number of measurements.
4. The air core coil current transformer error environment correlation analysis method as claimed in claim 1, wherein in step S3, the non-hermitian matrix isWherein Represents a sample xiAverage value of (a), σ (x)ij) Represents a sample xiStandard deviation of (1), xiIs a high-dimensional random matrix D3Row vector of (2), xi＝(xi1,xi2,...,xiT) I is more than or equal to 1 and less than or equal to k ', k' is the number of the expanded state parameters, T is the number of measurements, yijIs variable x in high-dimensional random matrixijAnd obtaining new variables after the standardization mode.
5. The method for analyzing the correlation between the error environments of the air-core coil current transformer according to claim 1, wherein the step S4 specifically comprises:
calculating a singular value equivalence matrix D of the non-Hermite matrixu；
According to the singular value equivalence matrix DuCalculating a matrix product Z;
obtaining an error state evaluation matrix Z according to the matrix product Z2。
6. Air core coil current transformer error environment dependent according to claim 5Method for sexual analysis, characterized in that said matrix productThe error state evaluation matrixWherein,ziis a row vector of matrix Z, Zi＝(zi1,zi2,...,ziT),1≤i≤k'，Is a matrix Z2The row vector of σ (z)i) Denotes ziK' is the number of state parameters after expansion, and T is the number of measurements.
7. The air-core coil current transformer error environment correlation analysis method as claimed in claim 1, wherein in step S5, the correlation evaluation index includes dMSRAnd IMSRWherein d isMSR＝εev-εref，dMSRIntegration over time of IMSR：Wherein, t1And t2Indicating the start time and the end time of the evaluation,λifor the eigenvalues of the corresponding original matrix, λwiFor eigenvalues of the corresponding reference matrix, n and n2E () representing eigenvalue sample expectations for the corresponding original and reference matrices, respectivelyThe reference matrix is composed of an air coil error state matrix and a Gaussian white noise matrix, wherein D1Is an environment parameter matrix; dNThe noise matrix has the same dimensionality as the environment parameter matrix, elements of the noise matrix are random variables which obey standard normal distribution, and the amplitude is the same as the amplitude of Gaussian white noise superposed in matrix extension.
8. An error state monitoring system of an air-core coil current transformer is characterized by comprising an original matrix building module, a high-dimensional random matrix building module, a standardization processing module, an influence quantity correlation evaluation matrix module and a correlation evaluation module;
the original matrix construction module is used for acquiring environmental parameter data and error data of the hollow coil current transformer and constructing an original matrix according to the acquired environmental parameter data and the error data in an evaluation time window;
the high-dimensional random matrix construction module is used for expanding the original matrix based on a Kalman filter to establish a high-dimensional random matrix;
the standardization processing module is used for standardizing the high-dimensional random matrix to convert the high-dimensional random matrix into a non-Hermite matrix with a row vector mean value of 0 and a variance of 1;
the influence quantity correlation evaluation matrix module is used for obtaining an influence quantity correlation evaluation matrix according to the non-Hermite matrix;
the correlation evaluation module is used for obtaining an error environment correlation evaluation index of the air coil current transformer according to the influence quantity correlation evaluation matrix and evaluating the correlation between the error of the air coil current transformer and an environment parameter according to the influence quantity correlation evaluation matrix and the correlation evaluation index.
9. The air core coil current transformer error condition monitoring system of claim 8, wherein the primitive matrix construction module is configured to construct the ambient parameter matrix from the collected ambient parameter dataWherein the element PijThe measured value of the ith measurable environment parameter at the time j is shown, i is the serial number of the measurable environment parameter, i is 1, 2 and … … M, M is the number of the environment parameters, j is the measured serial number, j is 1, 2 and … … T, and T is the measuring times; construction of an error state matrix from collected error dataWherein, the element QijThe measured value of the ith transformer error parameter at the moment j is represented, i is the serial number of the transformer error parameter, i is 1, 2, … … N, N is the number of the transformer error parameters, j is the measured serial number, j is 1, 2, … … T, and the constructed original matrix isWherein k is M + N.
10. The air core coil current transformer error state monitoring system of claim 8, wherein the high-dimensional random matrix established by the high-dimensional random matrix construction module isk ' is the number of the expanded state parameters, and the value range of N ' meets the condition that k '/T belongs to (0, 1)]And T is the number of measurements.
11. The air core coil current transformer error condition monitoring system of claim 8, wherein the non-Hermite matrix processed by the normalization processing module is the non-Hermite matrixWherein Represents a sample xiAverage value of (a), σ (x)ij) Represents a sample xiStandard deviation of (1), xiIs a high-dimensional random matrix D3Row vector of (2), xi＝(xi1,xi2,…,xiT) I is more than or equal to 1 and less than or equal to k ', k' is the number of the expanded state parameters, T is the measurement times, yij is the variable x in the high-dimensional random matrixijAnd obtaining new variables after the standardization mode.
12. The air core coil current transformer error condition monitoring system of claim 8, wherein the influence quantity correlation evaluation matrix module is configured to calculate a singular value equivalence matrix D of the non-hermitian matrixuFrom said singular value equivalence matrix DuCalculating matrix product Z, and obtaining error state evaluation matrix Z according to the matrix product Z2；
The matrix productThe error state evaluation matrixWherein,ziis a row vector of matrix Z, Zi＝(zi1,zi2,…,ziT),1≤i≤k'，Is a matrix Z2The row vector of σ (z)i) Denotes ziK' is the number of the extended state parameters, T is the number of measurements
13. The air core coil current transformer error condition monitoring system of claim 8, wherein the correlation evaluation indicator comprises dMSRAnd IMSRWherein d isMSR＝εev-εref，dMSRIntegral over time ofWherein, t1And t2Indicating the start time and the end time of the evaluation,λifor the eigenvalues of the corresponding original matrix, λwiFor eigenvalues of the corresponding reference matrix, n and n2E () representing eigenvalue sample expectations for the corresponding original and reference matrices, respectivelyThe reference matrix is composed of an air coil error state matrix and a Gaussian white noise matrix, wherein D1Is an environment parameter matrix; dNThe noise matrix has the same dimensionality as the environment parameter matrix, elements of the noise matrix are random variables which obey standard normal distribution, and the amplitude is the same as the amplitude of Gaussian white noise superposed in matrix extension.
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