CN110488218B - Electric energy meter running state evaluation method and evaluation device - Google Patents

Electric energy meter running state evaluation method and evaluation device Download PDF

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CN110488218B
CN110488218B CN201910790547.9A CN201910790547A CN110488218B CN 110488218 B CN110488218 B CN 110488218B CN 201910790547 A CN201910790547 A CN 201910790547A CN 110488218 B CN110488218 B CN 110488218B
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CN110488218A (en
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杜杰
程瑛颖
张家铭
周全
侯兴哲
肖冀
张晓勇
冯凌
黄磊
李刚
谭时顺
周峰
胡建明
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Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd
State Grid Corp of China SGCC
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Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd
State Grid Corp of China SGCC
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Abstract

The invention belongs to the technical field of electric power metering and inspection, and particularly relates to an electric energy meter operation state evaluation method and an electric energy meter operation state evaluation device. According to the method, various index data of the electric energy meter are preprocessed in a unified mode, and time series data representation is completed; then, integrating time sequence data by adopting a real-time separation window technology, and calculating and analyzing statistic time sequence characteristics of the time sequence data of the multi-dimensional electric energy meter in real time on the basis of a random matrix theory; further adopting a DTW clustering algorithm to calculate the similarity of time sequence data, thereby clustering and grading the random matrix statistics; and finally, analyzing the clustering result to obtain the evaluation grade range of the running state of the electric energy meter, and finishing the evaluation of the real-time running state of the electric energy meter. The method does not depend on scores but on the similarity between sequences to carry out state classification, has good noise immunity and timeliness, and can more accurately classify the state intervals; meanwhile, the method has better applicability to the spatiotemporal characteristics of data.

Description

Electric energy meter running state evaluation method and evaluation device
Technical Field
The invention belongs to the technical field of electric power metering and inspection, and particularly relates to an electric energy meter operation state evaluation method and an electric energy meter operation state evaluation device.
Background
Along with the continuous development of intelligent distribution network scale, the continuous expansion in power supply region and the intelligent degree of strapping table constantly promote, the information acquisition system coverage rate of smart meter crescent, and the electric wire netting operation in-process is detected, the monitoring data volume is the finger number level and is increased. Therefore, the running state of the electric energy meter also presents more complex and sudden characteristics. Currently, for the evaluation and treatment of the operation state of the electric energy meter, an electric power company mainly determines the operation state of the electric energy meter by a field detection mode. However, the operation state of the electric energy meter is greatly influenced by factors such as atmospheric environment in the actual inspection process, and meanwhile, the measurement of the electric energy meter is also greatly affected by the change of the load, or the accurate operation state of the electric energy meter cannot be obtained. In order to effectively solve the dynamic problems, the correlation between various influencing factors and the running state of the electric energy meter needs to be researched and analyzed so as to comprehensively evaluate the running state of the electric energy meter.
With the driving production of big data, the analysis method based on big data mining is applied to various industries, and the analysis method driven by data, such as machine learning, is gradually applied to more frontier fields. In a novel power grid structure, the real-time operation state of a power grid is analyzed by utilizing a big data technology, and the operation trend of the power grid is predicted to become a new research hotspot.
At present, multi-index correlation analysis aiming at the running state of an electric energy meter is mainly divided into two types: an evaluation model based on theoretical mechanism indexes and an evaluation method based on big data drive. For an index model constructed based on a theoretical mechanism, the effectiveness of an analysis result mainly depends on the accuracy of an index system of the mechanism model. Thus, it is less versatile in its practical applicability to evaluate more complex or special operating conditions. And the intelligent evaluation method based on big data can effectively solve the problems. Based on the characteristics of the time sequence data of the electric energy meter, the multivariate and synchronism of the time sequence data are fully utilized, and the random matrix theory can be used as a novel analysis method of the large electric power data to research and solve the problems of more complex time sequence correlation influence factors and the like. The algorithm in the prior art is single, data cannot be comprehensively analyzed and processed from the whole to the local, and in addition, the defects in the aspects of calculation accuracy, robustness, reliability, timeliness and the like are obvious.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an electric energy meter running state evaluation method and an electric energy meter running state evaluation device.
The application provides an electric energy meter running state evaluation method. Firstly, preprocessing the big power data uniformly to finish the representation of time series data. The time series data was then integrated using a moving-split window (MSW) technique. Secondly, calculating and analyzing the time sequence data of the multi-dimensional electric energy meter in real time on the basis of a random matrix theory to obtain statistic time sequence characteristics. Further, aiming at the problem, the improved DTW clustering algorithm is adopted to calculate the similarity of time sequence data, so that the clustering of the random matrix statistics is graded. And finally, analyzing the clustering result to obtain the evaluation grade and range of the running state of the electric energy meter, and finishing the evaluation of the real-time running state of the electric energy meter. It is worth noting that two random matrix models are constructed in the method and applied to real-time evaluation of the running state of the whole batch of electric energy meters and the running state of a single electric energy meter respectively. Therefore, the time sequence data processing and analysis from whole to local are comprehensive, and the running state of the electric energy meter can be effectively evaluated, analyzed and predicted in real time. Finally, the novel electric energy meter running state evaluation method is applied to corresponding example analysis, and compared with a traditional Principal Component Analysis (PCA) evaluation method for research, a series of experimental analysis and results prove the robustness, reliability and timeliness of the method, and a new thought is provided for application research of the power grid detection technology. The method specifically comprises the following steps:
A. collecting the sampling time TiThe method comprises the steps that sequential data collected by the electric energy meter are represented by utilizing a big data principle and a real-time separation window method, and standard product matrixes respectively representing the running states of the whole electric energy meter and the single electric energy meter are generated;
B. performing feature visualization on the two standard product matrixes by using a random matrix model, monitoring the stability of the running state of the electric energy meter, calculating linear feature statistics, and outputting a time sequence feature evaluation curve;
C. clustering and grading the output time sequence characteristic evaluation curve by using an improved DTW clustering algorithm, constructing an evaluation system from the whole to the local, comprehensively monitoring and evaluating the running state of the electric energy meter in real time, and generating a system analysis result;
D. and outputting the real-time running states of the single and integral electric energy meters according to the system analysis result so that the equipment management personnel can correspondingly process the electric energy meters according to the feedback information.
Further, the time series data in the step A comprise daily measurement point current, voltage, electric energy, electric power and voltage phase angle of the electric energy meter.
Further, the step a specifically includes the following steps:
a.1, selecting n electric energy meters as an integral space sample, recording the dimension number of relevant influence factors of time sequence data which can be acquired by the electric energy meters as v, and acquiring sampling time T under the dimension of a certain relevant influence factoriData x ofnThe column vector is formed of
xn(Ti)＝[x1,x2,...,xn]T (1)；
Wherein, TiThe sampling time interval is set according to the actual acquisition requirement, so that a complete time sequence matrix is obtained under the dimensionality of all relevant influence factors
Figure GDA0003177791790000031
Is shown as
Figure GDA0003177791790000032
A.2, for a certain electric energy meter, v relevant influence dimensions are in TiData x collected at a sampling instantvThe column vector is formed of
xv(Ti)＝[x1,x2,...,xv]T (3)
Wherein x isn(Ti) And xv(Ti) All the same T based on all the electric energy metersiSample time data, hence xv(Ti) The complete timing matrix can be represented as
Figure GDA0003177791790000033
A.3, mixing
Figure GDA0003177791790000034
And
Figure GDA0003177791790000035
replacing by matrix X;
a.4, generating by using a real-time separation window methodForming a time sequence matrix, and adopting a moving window w ═ iw×jwWherein w ═ iw×jw(iw＝1,2,…,N, j w1,2, …, N), the matrix X is generated into a window timing matrix XwThereby respectively obtaining
Figure GDA0003177791790000041
And
Figure GDA0003177791790000042
respectively, the window timing sequence matrix of
Figure GDA0003177791790000043
And
Figure GDA0003177791790000044
a.5, combining the matrix XwThe elements in (A) are normalized according to the following formula (5) to obtain a standard non-Hermitian matrix
Figure GDA0003177791790000045
Figure GDA0003177791790000046
Wherein the content of the first and second substances,
Figure GDA0003177791790000047
are respectively
Figure GDA0003177791790000048
Mean and standard deviation of;
Figure GDA0003177791790000049
are respectively
Figure GDA00031777917900000410
Average and standard deviation of, and
Figure GDA00031777917900000411
thus obtaining
Figure GDA00031777917900000412
And
Figure GDA00031777917900000413
are respectively not Hermitian
Figure GDA00031777917900000414
And
Figure GDA00031777917900000415
a.6, calculated according to the following equation (6)
Figure GDA00031777917900000416
And
Figure GDA00031777917900000417
singular equivalence matrix of
Figure GDA00031777917900000418
And
Figure GDA00031777917900000419
Figure GDA00031777917900000420
wherein U is a Haar unitary matrix;
a.7, calculating the matrix product according to the following formula (7) to respectively obtain a standard product matrix of
Figure GDA00031777917900000421
And
Figure GDA00031777917900000422
Figure GDA00031777917900000423
wherein the matrix product
Figure GDA00031777917900000424
L represents the number of non-Hermitian matrixes, and the variance satisfies sigma2(Z)＝1/iw，
Figure GDA00031777917900000425
And
Figure GDA00031777917900000426
will be used as a standard product matrix for random matrix model analysis.
Random Matrix Theory (RMT) is used as an important tool for mathematical statistics, and by performing statistical analysis on data characteristics of a complex system, random characteristics of data are evaluated, so that the overall behavior characteristics of actual data are obtained through analysis, and the structure and properties of the complex system are explained. In recent years, as a leading-edge research hotspot, the random matrix theory has been widely applied and researched in numerous fields such as finance, traffic and communication. The method for analyzing the big electric power data based on the stochastic matrix theoretical model is already applied to an electric power grid system.
Further, the step B specifically includes the following steps:
b.1, replacing the two standard product matrixes by a matrix M into
Figure GDA0003177791790000051
And
Figure GDA0003177791790000052
b.2, setting M as an s-order matrix non-Hermitian matrix and the characteristic value as lambdai(i ═ 1,2, …, s), for all eigenvalues, a one-dimensional empirical spectral distribution function is defined as follows:
Figure GDA0003177791790000053
where, # Set refers to the number of elements in the Set,due to most of the eigenvalues lambdaiIs complex, and therefore the two-dimensional empirical spectral distribution function defining matrix M is:
Figure GDA0003177791790000054
b.3, setting matrix M ═ MijIs a non-Hermitian random matrix of order s, and all elements in the matrix satisfy the same distribution independently, expecting E (m)ij) 0, variance E (| m)ij|2) For L non-Hermitian matrices, a standard product matrix is obtained according to equation (7) when i, j tend to infinity, and the row-column ratio p is i/j (p e (0, 1)]) Keeping constant, standard product matrix
Figure GDA0003177791790000055
The empirical spectral distribution function of (a) obeys the single-loop law of consistent convergence, and its probability density function f can be expressed as:
Figure GDA0003177791790000056
b.4, for s-order non-Hermitian random matrix M which satisfies independent same distribution, M is equal to { Mij}, expect E (m)ij) 0, variance E (| m)ij|2) 1, a covariance matrix S of the matrix M is calculated according to equation (11),
Figure GDA0003177791790000057
when i, j tends to infinity, and the row-column ratio p ═ i/j (p ∈ (0, 1)]) While held constant, the covariance matrix S satisfies the M-P law, i.e., the probability density function f that the ESD of the matrix S converges to equation (12)M-P：
Figure GDA0003177791790000058
Wherein the content of the first and second substances,
Figure GDA0003177791790000059
and
Figure GDA00031777917900000510
respectively an supremum limit and a infimum limit of the covariance matrix S;
b.5, introducing the MSR measurement of the mean spectral radius for analysis:
the MSR is defined as the average distance between each point and the central point of all the eigenvalues of the random matrix M on the complex plane, and is defined as follows:
Figure GDA0003177791790000061
wherein R isMSRAnd calculating and analyzing the time sequence characterization matrix for the average spectrum radius of all the characteristic values based on the average spectrum radius, and outputting a time sequence characteristic evaluation curve.
Clustering is a basic problem in data mining, and is also an important algorithm in machine learning. In the clustering problem, various clustering algorithms are proposed for different sample data. Compared with static data, time series data has higher dimensionality and structural complexity, and meanwhile, the integrity of the sequence during clustering is ensured, so that the clustering is more difficult. The objective of time series data clustering is to divide each sequence in a time series data set into different subsets, and require that the sequence similarity in the same subset be large and the difference between subsets be large. A Dynamic Time Warping (DTW) algorithm was proposed by Itakura, a scholars in japan as the earliest problem of processing time series clustering matching, and is an algorithm based on a dynamic programming concept, and was used to solve the speech rate change problem in speech recognition at the earliest. Bemdt and lifford applied it for the first time in 1994 to the analysis of time series. On the basis of the DTW algorithm, various improved algorithms are proposed aiming at different problems. Pentitjean et al propose a DTW center-of-gravity averaging algorithm based on this, and find the center time series of the time series set. The Yaoyang and the like combine the DTW algorithm and the hidden Markov model to carry out sequence extraction and sequencing on the flight path of the aerial target. The decoction sensitivity and the like propose a sequence clustering design based on DTW and a local adjacent map, can accurately determine the cluster number of clustering, and mark out core points and edge points.
Further analysis is required for the temporal characteristics of the Mean Spectral Radius (MSR) derived from the random matrix. The method and the device divide the running state of the electric energy meter by the MSR data in a clustering mode, and output different evaluation state grade division ranges.
Further, the step C specifically includes the steps of:
c.1, assuming that there are two time series data S and O, the lengths are i and j, respectively, and are expressed as:
Figure GDA0003177791790000062
two different time series elements si，OjThe distance measure δ between them is defined as follows:
Figure GDA0003177791790000071
where δ is a distance measure between two time series elements;
and C.2, taking one time sequence as a reference template, calculating the shortest distance from each point in the reference template to each point in the other time sequence, wherein the shortest point pair set can form a regular path W:
W＝w1,w2,…,wk (16)
wherein, wkAnd (3) performing iterative computation based on the point pair with the shortest distance of each point pair in the sequence to obtain the similarity DTW (S, T) of the two time sequences:
Figure GDA0003177791790000072
c.3, further developing to obtain:
Figure GDA0003177791790000073
and C.4, solving a penalty coefficient alpha by combining a DTW algorithm of the penalty coefficient, and multiplying the result of the original algorithm to obtain the updated inter-sequence distance:
Figure GDA0003177791790000074
wherein Num (W) is the number of point pairs with the shortest distance, comLeniRepresents the length between the point pair when i equals j;
and C.5, carrying out clustering grading of different grades by using a binary tree traversal algorithm according to the similarity of the distances between the sequences.
Further, the clustering classification in the step C.5 comprises four grades of good, normal, early warning and abnormal.
The invention also provides an electric energy meter running state evaluation device, and the evaluation method comprises the following steps:
a data acquisition unit for acquiring sampling time TiTime sequence data of the electric energy meter;
and the data processing unit is used for processing the time sequence data acquired by the data acquisition unit so as to construct an evaluation system from the whole to the local, comprehensively monitor and evaluate the running state of the electric energy meter in real time and generate a system analysis result.
Further, still include:
and the data display unit is used for outputting the real-time running states of the single and integral electric energy meters according to the system analysis result so that the equipment management personnel can correspondingly process the electric energy meters according to the feedback information.
Further, the time series data includes the number of electric energy meters, a current phase angle, a voltage phase angle, electric power, voltage, current, electric energy, a frequency fluctuation value, a power factor, a power direction, a load current, and a sampling time.
The invention has the beneficial effects that:
1. according to the method, various index data of the electric energy meter are preprocessed in a unified mode, and time series data representation is completed; then, integrating time sequence data by adopting a real-time separation window technology, and calculating and analyzing statistic time sequence characteristics of the time sequence data of the multi-dimensional electric energy meter in real time on the basis of a random matrix theory; further adopting a DTW clustering algorithm to calculate the similarity of time sequence data, thereby clustering and grading the random matrix statistics; and finally, analyzing the clustering result to obtain the evaluation grade range of the running state of the electric energy meter, and finishing the evaluation of the real-time running state of the electric energy meter. The method has good robustness, reliability and timeliness;
2. the invention constructs two random matrix models which are respectively applied to the real-time evaluation of the running state of the whole batch of electric energy meters and the running state of a single electric energy meter, so that the electric energy meters are subjected to time sequence data processing and analysis from whole to local, the running states of the electric energy meters can be effectively evaluated, analyzed and predicted in real time, and the time-space characteristics of the data are well applicable.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic flow chart of a method for evaluating an operating state of an electric energy meter according to the present invention;
FIG. 2 is a flow chart illustrating a method for processing the time series data in FIG. 1;
FIG. 3 is a schematic diagram of a time-series data matrix structure of an index of the whole electric energy meter shown in FIG. 2;
FIG. 4 is a schematic diagram of a time-series matrix structure of each indicator of the single electric energy meter in FIG. 2;
FIG. 5 is a graph of the spectral distribution of eigenvalues at steady state and non-steady state;
FIG. 6 is a diagram showing the basic effect of M-P law under different loads;
FIG. 7 is a graph of a time series data linear feature statistic distribution;
FIG. 8 is a schematic diagram of a DTW clustering algorithm;
FIG. 9 is a single-loop-law distribution plot of timing data according to an embodiment;
FIG. 10 is a graph of M-P law distribution of time series data according to an embodiment;
FIG. 11 is a time-series linear feature statistic distribution graph according to an embodiment;
FIG. 12 is a DTW clustering effect diagram according to an embodiment;
FIG. 13 is a graph illustrating distance measurements of timing data according to an embodiment;
fig. 14 is a schematic diagram of a single energy meter timing LES according to an embodiment.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and therefore are only examples, and the protection scope of the present invention is not limited thereby.
It is to be noted that, unless otherwise specified, technical or scientific terms used herein shall have the ordinary meaning as understood by those skilled in the art to which the invention pertains.
In the description of the present application, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and are therefore not to be considered limiting of the invention.
In this application, unless expressly stated or limited otherwise, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can include, for example, fixed connections, removable connections, or integral parts; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
The application provides an electric energy meter running state evaluation method. The method specifically comprises the following steps: as shown in figure 1 of the drawings, in which,
1) firstly, the electric energy meter is used as an intelligent metering instrument and can simultaneously acquire a plurality of dimensional time sequence data. The N time sequence variable analysis of the electric energy meters provides that the specific sampling time is Ti (i is 1,2, …, N), and the sampling interval can be set artificially (the system analyzes the data of the daily samples 24, 48 and 96 points). Therefore, based on the big data principle and technology (real-time separation window technology), multi-dimensional data are processed in real time, and the time sequence data representation of the electric energy meter is completed. Two standard product matrixes and a standard product random matrix of the running state of the single electric energy meter are generated respectively as a whole.
2) Secondly, two standard product matrixes are analyzed based on a random matrix theory. After data are standardized, the characteristics of a single-ring law and an M-P law of the random matrix are analyzed, the visualization of the time sequence data characteristics of the electric energy meter is completed, the radius of an inner ring is compared, and the stability of the running state of the electric energy meter can be monitored. Then, linear feature statistics (MSR) are calculated, and a time series feature evaluation curve is output. The characteristics of calculation and analysis mainly comprise time sequence variation characteristics of v indexes of the n integral electric energy meters and time sequence variation characteristics of v indexes of a single electric energy meter.
3) And then, analyzing the characteristics of the output overall time sequence curve of multiple dimensions, namely, the system utilizes an improved DTW clustering algorithm to perform clustering classification according to the MSR time sequence change of the matrix so as to evaluate and predict the running states of the n ammeters. Further, the time sequence curve characteristics of v indexes of a single electric energy meter, namely the MSR time sequence change of the matrix, are subjected to clustering analysis, an evaluation system from the whole to the local is constructed, and the running state of the electric energy meter is comprehensively monitored and evaluated in real time. Overall, for the time sequence variation characteristic curve of the matrix, the results obtained by the electric energy meters in different states have a large difference, which is specifically expressed in the overall trend of the curve: for an electric energy meter with good running condition, the slope of the characteristic curve is approximately unchanged after smoothing treatment; and the slope of the characteristic curve of the electric energy meter with poorer running conditions is reduced more after smoothing. Therefore, the time sequence curve distance of the electric energy meter in different running states is obvious, and clustering can be well carried out in different states by using the improved DTW clustering algorithm. And further setting a threshold value for the curve distance based on the time sequence curve characteristics of the typical electric energy, so that the clustering result represents different state evaluations. Further, clustering evaluation is carried out on the time sequence curve characteristics and the template sequence of each index state of a single electric meter, so that multiple measurement indexes of the single electric meter are monitored and evaluated in real time. Aiming at large data volume, the method applies the moving window method to the improved DTW method so as to solve the influence of the calculation rate caused by high time complexity.
4) And finally, outputting the real-time running state of each and the whole batch of electric energy meters according to the system analysis result. At this moment, according to the feedback information, the equipment management personnel need to overhaul or replace the electric energy meter in time.
1 electric energy meter time sequence data processing
The big data principle is a novel mathematical principle for calculating, analyzing and processing all data involved in a problem, wherein the big data has the characteristic of 5V (Volume, Velocity, Value, Veracity). The big data principle taking data driving as a core idea is essentially a combination of methodology and cognition in measurement statistics, feature analysis and behavior decision, and is a cognitive explanation of the principle and the trend of a data main body. The key role of the big data technology is to specialize and visually analyze and process mass data information, which must rely on distributed processing of cloud computing, distributed databases, cloud storage and virtualization technologies. With the driving development of big data, application research based on big data principle and technology plays a wide role in various fields. In recent years, with the magnitude increase of large electric power data, a novel idea is provided for power grid application research by an analysis method of the operation situation of the electric power system based on massive large electric power data.
The method specifically comprises the following steps: as shown in figure 2 of the drawings, in which,
firstly, aiming at the time sequence data processing of the overall evaluation of the running state of the electric energy meter, n electric energy meter nodes are selected as an overall space sample. And simultaneously, recording the dimension number of relevant influence factors (time sequence indexes) of the time sequence data which can be acquired by the electric energy meter as v. Therefore, under the dimension of a certain relevant influence factor, n electric energy meter nodes are at TiData x collected at a sampling instantnThe column vectors formed are:
xn(Ti)＝[x1,x2,...,xn]T (1)
wherein, TiAnd setting the sampling time interval according to the actual acquisition requirement. Thus a complete time series matrix
Figure GDA0003177791790000121
Can be expressed as:
Figure GDA0003177791790000122
and secondly, processing the time sequence data of the running state of the single electric energy meter. Similarly, for n electric energy meter nodes and T of v relevant influence factor dimensionsiThe sampling instants represent time series data. Different from the overall evaluation data processing mode, for the evaluation of the operation state of a single electric energy meter, the variable needing to be controlled is n. Thus, for a meter, the v correlation influence dimensions are at TiData x collected at a sampling instantvThe column vectors formed are:
xv(Ti)＝[x1,x2,...,xv]T (3)
wherein x isn(Ti) And xv(Ti) All the same T based on all the electric energy metersiThe time of day data is sampled. Thus xv(Ti) The complete timing matrix can be represented as:
Figure GDA0003177791790000123
the two data matrix generation forms are shown in fig. 3-4, wherein fig. 3 shows a time sequence data matrix structure diagram of a certain index of the whole electric energy meter; fig. 4 shows a schematic diagram of a time-series matrix structure of indexes of a single electric energy meter.
The subsequent normalization method is the same for both time series matrices. In this case, the calculation steps are to be combined uniformly
Figure GDA0003177791790000131
And
Figure GDA0003177791790000132
replaced by a matrix X. For the timing matrix, a real-time split window technique is used, i.e. using w ═ iw×jwMoving window of size, generating window timing matrix XwWherein w ═ iw×jw(iw＝1,2,…,N, j w1,2, …, N) to yield respectively
Figure GDA0003177791790000133
And
Figure GDA0003177791790000134
respectively, the window timing sequence matrix of
Figure GDA0003177791790000135
And
Figure GDA0003177791790000136
the method synchronously calculates the historical data and the real-time data, and can effectively represent the time sequence data. Next, the matrix X is divided according to equation (5)wConversion to standard non-Hermitian matrix
Figure GDA0003177791790000137
Figure GDA0003177791790000138
Wherein the content of the first and second substances,
Figure GDA0003177791790000139
are respectively
Figure GDA00031777917900001310
Mean and standard deviation of;
Figure GDA00031777917900001311
are respectively
Figure GDA00031777917900001312
Average and standard deviation of, and
Figure GDA00031777917900001313
thus obtaining
Figure GDA00031777917900001314
And
Figure GDA00031777917900001315
are respectively not Hermitian
Figure GDA00031777917900001316
And
Figure GDA00031777917900001317
then, it is calculated according to equation (6)
Figure GDA00031777917900001318
And
Figure GDA00031777917900001319
singular equivalence matrix of
Figure GDA00031777917900001320
And
Figure GDA00031777917900001321
Figure GDA00031777917900001322
wherein, U is a Haar unitary matrix.
Finally, calculating the matrix product according to the formula (7) to respectively obtain a standard product matrix of
Figure GDA00031777917900001323
And
Figure GDA00031777917900001324
Figure GDA00031777917900001325
wherein the matrix product
Figure GDA00031777917900001326
L represents the number of non-Hermitian matrixes, and the variance satisfies sigma2(Z)＝1/iw。
Figure GDA00031777917900001327
And
Figure GDA00031777917900001328
will be used as a standard product matrix for random matrix model analysis. The above process shows the time sequence data representation aiming at the electric energy meter data completely, and prepares data for constructing a random matrix model.
The electric energy meter is used as a power system device and comprises static data information and dynamic acquisition data information, wherein the static data information of the electric energy meter mainly comprises attribute data such as a model, a production batch, a manufacturer, a power supply unit and an installation month, and the time sequence data information which can be acquired by the electric energy meter comprises time sequence combination data such as daily measurement point current, voltage, electric energy, electric power, voltage phase angle and the like. The method and the device have the advantages that through time sequence data analysis, the running state of the electric energy meter is effectively evaluated in real time, and the timeliness and the reliability are superior. Meanwhile, the evaluation of the running state of the electric energy meter can be divided into overall evaluation and individual evaluation, namely, a comprehensive evaluation system from the whole to the individual.
2 random matrix model construction
In the mathematical statistical principle, a random matrix refers to a matrix containing a plurality of random variables, and is widely applied to data statistical analysis. In 1951, Random Matrix Theory (RMT) was proposed and developed by the physicist Wigner when performing spectral interpretation. For more complex quantum physical systems, the trend of the whole system is predicted by the characteristic analysis of the random matrix theory, and the average of actual possible interaction is reflected. Over a half-century of development, random matrix theory has been used to solve many of the problems of scientific research and engineering practice. Among them, random matrix theory based on big data has recently become a new research focus.
The random matrix can be divided into an infinite-dimension random matrix and a finite-dimension random matrix according to the difference of dimensions. The finite-dimension random matrix theory pushes the theoretical analysis of the wireless-dimension random matrix to the practical application of the finite dimension, namely, the dimension of the matrix is not limited by the infinite dimension requirement of the finite-dimension random matrix theory. Therefore, when the ratio of the row dimension and the column dimension of the stochastic matrix is kept constant, the time-series linear characteristics of the stochastic matrix, such as an Empirical Spectral Distribution (ESD) function, conform to various statistical theorems, including semi-circular law (semi-circular law), M-P law (Marchenko-patrur law), single-ring law (single ring theory), and the like. Therefore, based on the time series data representation of the first part, a random matrix model is further constructed, and based on the characteristic analysis of the law, relevant statistics are calculated. And finally, analyzing the time sequence characteristics of the random matrix in real time to obtain the statistic characteristics of the data. In the aspect of actual data processing effect, the analysis method based on the random matrix theory has good robustness, and can be self-adaptively stable to bad data or phenomena such as data loss and abnormity.
2.1 empirical spectral distribution function
Since the post-processing methods for the standard product matrix are the same, the two standard product matrices are defined as
Figure GDA0003177791790000151
And
Figure GDA0003177791790000152
replacing by a matrix M, wherein M is an s-order matrix non-Hermitian matrix and the characteristic value is lambdai(i ═ 1,2, …, s). For all eigenvalues, we define a one-dimensional empirical spectral distribution function as follows:
Figure GDA0003177791790000153
where, # Set refers to the number of elements in the Set. Due to most of the eigenvalues lambdaiIs complex, and therefore the two-dimensional empirical spectral distribution function defining matrix M is:
Figure GDA0003177791790000154
the theoretical objective of the random matrix is to study the empirical spectral distribution function F of a given random matrix MMConvergence of (x, y). While the Limit Spectral Distribution (LSD) of the matrix has a stochastic nature.
2.2 monocyclic law
Let matrix M ═ { M ═ MijIs an s-order non-Hermitian random matrix (non-square matrix) and all elements in the matrix satisfy independent equal distribution (IID), with E (m) expectedij) 0, variance E (| m)ij|2) 1. For the L non-Hermitian matrices, a standard product matrix is obtained according to equation (7). When i, j tends to infinity, and the row-column ratio p ═ i/j (p ∈ (0, 1)]) Keeping constant, standard product matrix
Figure GDA0003177791790000155
The empirical spectral distribution function (PDF) f of (1) obeys the uniform convergence of the single-loop law, which can be expressed as:
Figure GDA0003177791790000156
according to the single-loop law, the characteristic value lambdaiDistributed on the complex plane on the outer ring with radius 1 and with radius (1-p)L/2The effect of the inner ring is schematically shown in fig. 5. Specific analysis of the distribution of the characteristic values shows that the characteristic values are spectral distributions in a stable state as shown in 5 (a); as shown in fig. 5(b), for the spectrum distribution of the characteristic value in the unstable state, when the system receives a signal, the load increases and the system is in the unstable state, part of the characteristic value will be distributed in the Inner ring (Inner Circle), that is, the system will have a certain probability of unstable state. When most of the feature values are within the inner ring, the system is at risk of crashing.
2.3 Marchenko-Passtur's law
Similarly, for s-order non-Hermitian random matrix satisfying independent equal distribution, M is { M }ij}, expect E (m)ij) 0, variance E (| m)ij|2) 1. The covariance matrix S of the matrix M is calculated according to equation (11).
Figure GDA0003177791790000161
When i, j tends to infinity, and the row-column ratio p ═ i/j (p ∈ (0, 1)]) While held constant, the covariance matrix S satisfies the M-P law, i.e., the ESD of the matrix S converges to the probability density function f of equation 12M-P：
Figure GDA0003177791790000162
Wherein the content of the first and second substances,
Figure GDA0003177791790000163
and
Figure GDA0003177791790000164
the supremum and the infimum of the covariance matrix S are respectively. The basic effect graph of the M-P law is shown in FIG. 6.
Calculating to obtain a probability density function curve of the characteristic value, wherein the characteristic value of the covariance matrix meets the M-P law distribution when no additional influence load exists; when the load is increased, the system is in an unstable state, and the distribution of the characteristic values of the system does not meet the M-P law any more.
2.4 time-series linear feature statistics
According to the single-loop law and the M-P law, the EDS of the system in different states is different, and the reflecting of the time sequence characteristics needs to further select the statistic with more real-time performance. Therefore, for the electric energy meter time sequence data, linear eigen value statistical (LES) will be used as a more effective statistical index of the random matrix M, and the statistical rule thereof is reflected to a greater extent. For this, Mean Spectral Radius (MSR) statistics were introduced for analysis.
The MSR is defined as the average distance between each point and the central point of all the eigenvalues of the random matrix M on the complex plane, and is defined as follows:
Figure GDA0003177791790000165
wherein R isMSRThe spectral radii are averaged for all feature values. As shown in fig. 7, the analysis shows that the time series curve of the average spectrum radius effectively analyzes the overall development trend of the system. And calculating and analyzing the time sequence characterization matrix based on the average spectrum radius to obtain an average spectrum radius time sequence change curve, and further, performing clustering analysis on the time sequence curve to divide a state range.
3 clustering and grading by using improved DWT clustering algorithm
Dynamic Time Warping (DTW) clustering algorithm is a typical recursive optimization algorithm, which compresses or stretches data segments by solving distances corresponding to each point in a time sequence one by one, and eliminates the interference of time asynchronization, thereby matching the similarity of two time sequences.
Suppose there are two pieces of time-series data S and O, i and j, respectively, of length, expressed as:
Figure GDA0003177791790000171
two different time series elements si，OjThe distance measure δ between them is defined as follows:
Figure GDA0003177791790000172
where δ is a distance measure between two time series elements. After defining the distance, the time sequence clustering problem can be converted into the matching with the shortest distance between the point pairs in the iterative time sequence set, namely, one sequence is taken as a reference template, the shortest distance from each point in the reference template to each point in the other sequence is calculated, and the shortest point pair set can form a regular path W:
W＝w1,w2,…,wk (16)
wherein, wkIs the shortest distance point pair of each point pair in the sequence. Based on the similarity, the similarity DTW (S, T) of the two time sequences can be obtained through iterative calculation:
Figure GDA0003177791790000173
further development yields:
Figure GDA0003177791790000174
when the sequence which is similar to the template sequence in an increasing and decreasing mode appears, interference is generated on the same sequence distance of different phases, and therefore the clustering effect of the DTW algorithm is influenced. Based on the problem, the DTW algorithm combined with a penalty coefficient is applied by referring to an optimal path planning principle. And solving the penalty coefficient alpha and multiplying the result of the original algorithm to obtain the updated inter-sequence distance.
Figure GDA0003177791790000181
Wherein Num (W) is the number of point pairs with the shortest distance, comLeniDenotes the length between the point pairs when i equals j. When α is smaller, this means that the larger the number of dot pairs when i is j, the more the two sequences tend to be the same data sequence with different phases, and the closer the distance between the two sequences, the smaller the interference of the increasing and decreasing similarity sequence. Meanwhile, aiming at high complexity brought by electric meter big data, a fast-DTW algorithm is combined to apply data point compression to optimize the clustering operation speed in one step. The calculated linear characteristic statistic (MSR) of the electric energy meter in a normal working state has small fluctuation, so that when the MSR time series data SMSRIn satisfies SMSR[j]-SMSR[j-1]<ε, can be approximated as SMSR[j]＝SMSR[j-1]And mixing SMSR[j]And SMSR[j-1]Point merging is used for compressing the length of the time sequence and accelerating the calculation. The overall improved DTW algorithm effect is schematically shown in FIG. 8.
The method and the device are based on a random matrix theory and a clustering algorithm, analyze time sequence data characteristics and evaluate the real-time running state of the electric energy meter. For the running state of the electric energy meter, the time sequence data are analyzed more timely. Compared with the analysis of relevant static relevant influence factors, the characteristic analysis of the time sequence data can reflect the real-time running state of the electric energy meter, and meanwhile trend prediction is made on the running state of the electric energy meter.
The invention also provides an electric energy meter running state evaluation device, and the evaluation method comprises the following steps:
a data acquisition unit for acquiring sampling time TiTime sequence data of the electric energy meter;
and the data processing unit is used for processing the time sequence data acquired by the data acquisition unit so as to construct an evaluation system from the whole to the local, comprehensively monitor and evaluate the running state of the electric energy meter in real time and generate a system analysis result.
Further, still include:
and the data display unit is used for outputting the real-time running states of the single and integral electric energy meters according to the system analysis result so that the equipment management personnel can correspondingly process the electric energy meters according to the feedback information.
Further, the time series data includes the number of electric energy meters, a current phase angle, a voltage phase angle, electric power, voltage, current, electric energy, a frequency fluctuation value, a power factor, a power direction, a load current, and a sampling time.
Examples
100 electric energy meters (n is 100) in the same batch are selected for analysis, and 10 indexes (v is 10) of current phase angle, voltage phase angle, electric power, voltage, current, electric energy, frequency fluctuation, power factor, power direction and load current are selected as indexes, wherein the data comprises normal electric energy meter measurement data and abnormal electric energy meter data. In the analysis of this example, 96 points of data are sampled daily (Ti is 15min), and in order to reflect the time sequence characteristics of the data characteristics and fully utilize the historical data characteristics, a time sequence interval with a moving distance smaller than a moving window is set, that is, the window w is 100 × 4, the moving distance is 2, and the moving times are 1000 times. And sequentially carrying out single-loop law and M-P law analysis, LES calculation, clustering and state analysis on the time sequence data based on the proposed evaluation method.
Aiming at the running state analysis of the whole electric energy meter, single-loop law characteristic value spectrum distribution and M-P law distribution of time sequence data are calculated by utilizing python 3.7, and two indexes (voltage and electric power) with abnormal values are analyzed at T50Time and T500The single-loop law and M-P law distributions at time, where P of both laws remains constant (P-4/100-0.04)<1) The distribution diagrams are shown in fig. 9 and 10.
According to the distribution of characteristic values of the single-loop law, the characteristic value distribution at T50Voltage data and electric power data measured by the electric energy meters are integrally stable at any moment, and the individual electric energy meters have abnormal measurement conditions at the initial time; when at T500Time of day, voltageAnd 4 abnormal values of the electric power measurement data, namely abnormal operation conditions of a plurality of electric energy meters. Further, T was analyzed50Time and T500And analyzing the distribution condition of the characteristic values of the time sequence data by the electric energy meter based on the M-P law at the moment.
Likewise, T is analyzed using calculations50Time and T500And analyzing the distribution condition of the M-P law of the time sequence data according to the eigenvalue probability density distribution of the covariance matrix at the moment. By comparison, at T50The characteristic value of the covariance matrix at the moment accords with the probability density distribution of an M-P law, namely the whole operation is normal; at T500At the moment, compared with M-P Ddensity, a certain deviation occurs, namely, the running states of the partial electric energy meter for measuring the voltage and the electric power are abnormal.
The single-loop law and the M-P law preliminarily evaluate the overall running state of the electric energy meter, and T can be displayed in the real-time monitoring process0Time to T1000And (4) evaluating the overall operation state in real time according to the change condition of the moment. Further, the time sequence characteristics of the LES are calculated and analyzed to locate the abnormal power meter, and the LES result graph of this example is shown in fig. 11.
The change situation of the time-series linear feature statistic of 100 electric energy meters (n is 100) under the voltage and electric power indexes is observed, the overall MSR stably changes, the trend is the same, and the partial MSRs deviate from the overall situation. Therefore, the whole electric energy meter is in a stable operation state, and meanwhile, the situation that the plurality of electric energy meters are abnormal in measurement in the time sequence process also occurs. And comparing the single-loop law with the M-P law analysis, the change of the running state of the electric energy meter is also verified, and the qualitative analysis is completed. Further, performing quantitative analysis, performing fast-DTW cluster analysis based on the electric energy meter time sequence characteristic statistics, calibrating the interval range for the time sequence data, and evaluating the state.
By setting a clustering time window WtThe size is 500, the step length is 500, and 100 electric meters are measured from T0Time to T1000MSR historical time sequence data S of timeMSR1,SMSR2,...,SMSR100Inputting improved DTW algorithm, clustering, and arranging and outputting according to distance similarity by using binary tree[i]Can realize according toAnd the data are clustered and output according to the same-grade requirement, and the grading division of the state of the electric meter is realized. The method adopts four grade modes of good, normal, early warning and abnormity. The left side of fig. 12 takes the voltage index data as an example, and the classification result is shown in a binary tree form, in which MSR time series data of 100 meters in the second layer are classified into four classes, and an enlarged view is shown in the middle of fig. 12, and a distance DTW (S, O) from each class to the template data of the good meter is selected and calculatedn(n∈[1,2,3,4]) The smaller the DTW (S, O), the better the state of the electric energy meter. The distance size of the time series data in the right side of fig. 12 is: DTW (S, O)2>DTW(S,O)1>DTW(S,O)3>DTW(S,O)4The enlarged view is shown in FIG. 13, and it can be found that (i) is good, that (i) is normal, that (iii) is early warning, and that (iv) is abnormal.
The electric energy meter state classification obtained by the clustering result is shown in table 1, the abnormal serial numbers are respectively 25, 37, 69 and 82, and the evaluation grade division of the electric energy meter state is completed. Comparing the actual detection results, wherein the serial number of the abnormal electric energy meter is the same as the analysis result. The electric power index can be analyzed in the same way. And comparing the multiple groups of indexes with the positionable specific abnormal electric energy meter and the specific abnormal index. And finally, further analyzing the time sequence linear characteristic statistic variation of all indexes of the single electric energy meter.
TABLE 1 DTW clustering Range and distribution
Figure GDA0003177791790000211
And analyzing the abnormal electric energy meter No. 69 according to the clustering analysis result. As shown in fig. 14, the average spectrum radius abnormality of multiple indexes occurs in 10 indexes of No. 69 electric energy meter, and the voltage, electric power and electric energy measurement of the electric energy meter is abnormal by combining the single-loop law and the M-P law distribution. Thus, the operation state evaluation of the single electric meter is completed.
The above example analysis research is distributed according to a single-ring law and an M-P law, and the operation state of the electric energy meter is judged in advance on the whole. And analyzing the time sequence characteristics of the electric energy meter by using a fast-DTW clustering algorithm according to the time sequence change of the linear feature statistics (MSR) to evaluate the time sequence running state of the whole electric energy meter. And simultaneously, performing LES time sequence analysis on the electric energy meter diagnosed with the abnormality, and displaying specific abnormality measurement indexes. Therefore, comprehensive evaluation and prediction of the electric energy meter from the whole to the individual are completed.
The results of the above example verify the effectiveness of the method for evaluating the running state of the electric energy meter. In this section, the superiority and timeliness of the method of the present application are verified by comparing Principal Component Analysis (PCA). PCA is essentially a data-based dimension reduction and simplification analysis method, and is a common algorithm for processing multidimensional index data analysis processing at present. Therefore, based on the above example as well, the evaluation of the operating state of the electric energy meter is scored by using the principal component analysis method. For the evaluation of the running state of the electric energy meter, a PCA principal component index weight system needs to be constructed as shown in Table 2:
TABLE 2 PCA index weights
Figure GDA0003177791790000212
As shown in table 2, for controlling variables, the evaluation dimension of the PCA time series data is consistent with the evaluation method proposed in the present application, i.e. 10 time series indexes are the same. Meanwhile, the abnormality of the power representation number is also used as one of the evaluation indexes. The electric energy meters for test evaluation in the comparative study are 100 electric energy meters for example analysis. The PCA was used to weight and score 100 meters in the experiment, and the score table is shown in table 3:
TABLE 3 PCA score
Figure GDA0003177791790000221
Compared with the experimental result based on the research, the range accuracy of the PCA evaluation score is not high due to the fact that the abnormal condition of the electric energy representation number does not occur. The PCA has the advantages of convenient evaluation, small calculated amount and low timeliness, cannot fully utilize historical time sequence data for evaluation, only evaluates the current state, cannot predict the subsequent running state of the electric energy meter, and depends on the actually measured data of the electric energy meter to obtain grade scoring, and the existence of noise has great influence on the scoring-based PCA algorithm. The actual running state evaluation of the electric energy meter needs better time sequence evaluation, the clustering algorithm does not depend on the score but carries out state classification by the similarity between sequences, the anti-noise performance and the timeliness are good, and the state interval can be accurately classified. Meanwhile, the method has better applicability to the spatiotemporal characteristics of data.
The application designs an electric energy meter running state evaluation method based on a random matrix theory and a DTW clustering algorithm. Firstly, all index data of the electric energy meter are preprocessed in a unified mode, and time series data representation is completed. And then, integrating time sequence data by adopting a real-time separation window technology, and calculating and analyzing statistic time sequence characteristics of the time sequence data of the multi-dimensional electric energy meter in real time on the basis of a random matrix theory. Further, the similarity of time sequence data is calculated by adopting a DTW clustering algorithm, so that the random matrix statistic is clustered and graded. And finally, analyzing the clustering result to obtain the evaluation grade range of the running state of the electric energy meter, and finishing the evaluation of the real-time running state of the electric energy meter.
The method has the innovation point that two random matrix models are constructed and are respectively applied to the evaluation of the running state of the whole batch of electric energy meters and the running state of a single electric energy meter, so that the running state of the electric energy meter can be effectively evaluated and analyzed in real time from integral to local comprehensive data processing and analysis, and the method has good applicability to the time-space characteristics of data. The proposed method was compared to the conventional PCA assessment method in the case analysis. Experimental results show that the method can effectively divide the running state and the grade of the electric energy meter.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. An electric energy meter running state evaluation method is characterized in that: the method specifically comprises the following steps:
A. collecting the sampling time TiThe method comprises the steps that sequential data collected by the electric energy meter are represented, and standard product matrixes respectively representing the running states of the whole electric energy meter and the single electric energy meter are generated;
the step A specifically comprises the following steps:
a.1, selecting n electric energy meters as an integral space sample, recording the dimension number of relevant influence factors of time sequence data acquired by the electric energy meters as v, and setting the sampling time as TiN electric energy meters at TiData x collected at a sampling instantnThe column vector formed is xn(Ti) Complete time series matrix in the dimension of relevant influence factors
Figure FDA0003177791780000011
Is shown as
Figure FDA0003177791780000012
A.2, for a certain electric energy meter, v relevant influence dimensions are in TiData x collected at a sampling instantvThe column vector formed is xv(Ti) The time sequence matrix of the single electric energy meter is expressed as
Figure FDA0003177791780000013
A.3, mixing
Figure FDA0003177791780000014
And
Figure FDA0003177791780000015
replacing by matrix X;
and A.4, generating a time sequence matrix by using a real-time separation window method, wherein the adopted moving window is w ═ iw×jwWherein w ═ iw×jw(iw＝1,2,…,N,jw1,2, …, N), the matrix X is generated into a window timing matrix Xw；
A.5, combining the matrix XwThe elements in (1) are normalized according to the following formula (3) to obtain a standard non-Hermitian matrix
Figure FDA0003177791780000016
Figure FDA0003177791780000017
Wherein the content of the first and second substances,
Figure FDA0003177791780000018
are respectively
Figure FDA0003177791780000019
Mean and standard deviation of;
Figure FDA00031777917800000110
are respectively
Figure FDA00031777917800000111
Average and standard deviation of, and
Figure FDA00031777917800000112
a.6, calculation according to the following formula (4)
Figure FDA00031777917800000113
Singular equivalence matrix of
Figure FDA00031777917800000114
Figure FDA0003177791780000021
Wherein U is a Haar unitary matrix;
a.7, calculating the matrix product according to the following formula (5) to obtain a standard product matrix of
Figure FDA0003177791780000022
Figure FDA0003177791780000023
Wherein the matrix product
Figure FDA0003177791780000024
L represents the number of non-Hermitian matrixes, and the variance satisfies sigma2(Z)＝1/iw，
Figure FDA0003177791780000025
The standard product matrix is used as a random matrix model for analysis;
B. performing characteristic visualization on the two standard product matrixes, monitoring the stability of the running state of the electric energy meter, calculating linear characteristic statistics, and outputting a time sequence characteristic evaluation curve;
C. and clustering and grading the output time sequence characteristic evaluation curve, constructing an evaluation system from the whole to the local, comprehensively monitoring and evaluating the running state of the electric energy meter in real time, and generating a system analysis result.
2. The method for evaluating the operating condition of the electric energy meter according to claim 1, characterized in that: further comprising the steps of:
D. and outputting the real-time running states of the single and integral electric energy meters according to the system analysis result so that the equipment management personnel can correspondingly process the electric energy meters according to the feedback information.
3. The method for evaluating the operating condition of the electric energy meter according to claim 2, characterized in that: the step B specifically comprises the following steps:
b.1, replacing the standard product matrix with a matrix M to obtain Z ~;
b.2, setting M as an s-order matrix non-Hermitian matrix and the characteristic value as lambdaiI-1, 2, …, s, for all eigenvalues, a one-dimensional empirical spectral distribution function is defined as follows:
Figure FDA0003177791780000026
where, # Set refers to the number of elements in the Set, and the two-dimensional empirical spectrum distribution function defining the matrix M is:
Figure FDA0003177791780000027
b.3, setting matrix M ═ MijIs a non-Hermitian random matrix of order s, and all elements in the matrix satisfy the same distribution independently, expecting E (m)ij) 0, variance E (| m)ij|2) For L non-Hermitian matrices, a standard product matrix is obtained according to equation (7) when i, j tend to infinity, and the row-column ratio p is i/j (p e (0, 1)]) When the standard product matrix Z-is kept constant, the empirical spectrum distribution function of the standard product matrix Z-obeys the consistent convergence of a single-loop law, and the probability density function f is expressed as:
Figure FDA0003177791780000031
b.4, for s-order non-Hermitian random matrix M which satisfies independent same distribution, M is equal to { Mij}, expect E (m)ij) 0, variance E (| m)ij|2) Calculating a covariance matrix S of the matrix M according to equation (9) as 1,
Figure FDA0003177791780000032
when i, j tends to infinity, and the row-column ratio p ═ i/j (p ∈ (0, 1)]) When kept constant, the covariance matrix S satisfies the M-P law, i.e., the probability density function f of the matrix S, where ESD converges to equation (10)M-P：
Figure FDA0003177791780000033
Wherein the content of the first and second substances,
Figure FDA0003177791780000034
and
Figure FDA0003177791780000035
respectively an supremum limit and a infimum limit of the covariance matrix S;
b.5, introducing the MSR measurement of the mean spectral radius for analysis:
the MSR is defined as the average distance between each point and the central point of all the eigenvalues of the random matrix M on the complex plane, and is defined as follows:
Figure FDA0003177791780000036
wherein R isMSRAnd calculating and analyzing the time sequence characterization matrix for the average spectrum radius of all the characteristic values based on the average spectrum radius, and outputting a time sequence characteristic evaluation curve.
4. The method for evaluating the operating condition of the electric energy meter according to claim 3, characterized in that: the step C specifically comprises the following steps:
c.1, assuming that there are two time series data S and O, the lengths are i and j, respectively, and are expressed as:
Figure FDA0003177791780000037
two different time series elements Si，OjThe distance measure δ between them is defined as follows:
Figure FDA0003177791780000041
where δ is a distance measure between two time series elements;
c.2, constructing a regular path W formed by the shortest distance point pair set:
W＝w1,w2,…,wk (14)
wherein, wkThe shortest distance point pair of each point pair in the two time sequences is shown;
and C.3, iterating on the basis of the regular path to obtain the similarity DTW (S, T) of the two time sequences:
Figure FDA0003177791780000042
and C.4, solving a penalty coefficient alpha by combining a DTW algorithm of the penalty coefficient, and multiplying the result of the original algorithm to obtain the updated inter-sequence distance:
Figure FDA0003177791780000043
wherein Num (W) is the number of point pairs with the shortest distance, comLeniRepresents the length between the point pair when i equals j;
and C.5, carrying out clustering grading of different grades by using a binary tree traversal algorithm according to the similarity of the distances between the sequences.
5. The method for evaluating the operating condition of the electric energy meter according to claim 4, wherein: and C.5, clustering grades comprise four grades of good, normal, early warning and abnormal.
6. An evaluation device using an electric energy meter operation state evaluation method according to any one of claims 1 to 5, characterized in that: the method comprises the following steps:
a data acquisition unit for acquiring sampling time TiTime sequence data of the electric energy meter;
and the data processing unit is used for processing the time sequence data acquired by the data acquisition unit so as to construct an evaluation system from the whole to the local, comprehensively monitor and evaluate the running state of the electric energy meter in real time and generate a system analysis result.
7. The electric energy meter operation state evaluation device according to claim 6, wherein: further comprising:
and the data display unit is used for outputting the real-time running states of the single and integral electric energy meters according to the system analysis result so that the equipment management personnel can correspondingly process the electric energy meters according to the feedback information.
8. The electric energy meter operation state evaluation device according to claim 6, wherein: the time sequence data comprises the number of electric energy meters, current phase angles, voltage phase angles, electric power, voltage, current, electric energy, frequency fluctuation values, power factors, power directions, load current and sampling moments.
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