CN113051826A - Harmonic source universal uncertainty modeling method based on Gaussian process regression - Google Patents

Harmonic source universal uncertainty modeling method based on Gaussian process regression Download PDF

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CN113051826A
CN113051826A CN202110330962.3A CN202110330962A CN113051826A CN 113051826 A CN113051826 A CN 113051826A CN 202110330962 A CN202110330962 A CN 202110330962A CN 113051826 A CN113051826 A CN 113051826A
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CN113051826B (en
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张逸
刘必杰
邵振国
林芳
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Fuzhou University
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    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G—PHYSICS
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/214—Generating training patterns; Bootstrap methods, e.g. bagging or boosting
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

The invention relates to a harmonic source general uncertainty modeling method based on Gaussian process regression. The method is based on the linear coupling relation between harmonic voltage and harmonic current of an external port of a harmonic source, and the establishment of a harmonic general uncertainty model is realized by combining Gaussian process regression; the method also comprises an online updating strategy of the harmonic general uncertainty model, and the online updating of the harmonic general uncertainty model is realized in a scene needing real-time monitoring and analysis of a harmonic source. The estimation result obtained by the method is Gaussian distribution, and compared with an accurate value model, the uncertainty influence of unaccounted physical factors on the characteristics of the harmonic source can be reflected in the probability sense. Meanwhile, the modeling method has the characteristics of high precision, convenience in parameter solving and the like. In addition, the model updating strategy can accurately track the harmonic characteristic change of the harmonic load, realizes the online updating of the model, and can be used for the aspects of harmonic application to abnormal behaviors of the harmonic load, load change monitoring and the like.

Description

Harmonic source universal uncertainty modeling method based on Gaussian process regression
Technical Field
The invention relates to a harmonic source general uncertainty modeling method based on Gaussian process regression.
Background
In recent years, electric arc furnaces, electric locomotives and other loads with high capacity, nonlinearity and impact properties are continuously connected to an electric power system in a large quantity, meanwhile, the application of power electronic technology in household appliances is very common, so that the loads of residents present harmonic source characteristics with small capacity and dispersibility, the harmonic problem of medium and low voltage distribution networks is increased, in addition, the types of harmonic sources are more abundant and diversified, except for the high-capacity nonlinear loads of the traditional electric locomotives, electric arc furnaces and other loads, inverters required by micro-grids and distributed power supply grid connection and household appliances adopting electronic circuits, and the diversity of topology and control strategies of power electronic circuits can also cause the difference of specific harmonic characteristics; secondly, the mechanism of harmonic generation is increasingly complex, the harmonic emission characteristic of a harmonic source is not only related to the characteristics and working conditions of the harmonic source, but also influenced by other harmonic sources, moreover, the distributed new energy sources such as photovoltaic energy, wind power and the like are greatly influenced by natural conditions and have intermittence, the harmonic characteristic of an electric automobile charging pile is related to the use habits of users and has regularity on a time sequence, namely the harmonic emission characteristic of the harmonic source and electric quantity even non-electric quantity have complex interaction, and the difficulty of harmonic source mechanism analysis is increased day by day
In order to maintain qualified power quality, it is necessary to model harmonic sources to analyze the mechanism of harmonic generation, the influence of harmonic generation, and the interaction influence between harmonic sources or between a harmonic source and a power grid, and it is a prerequisite to evaluate harmonic hazards and make a harmonic suppression strategy, and current harmonic source models can be divided into an accurate model and a general model: the accurate harmonic source model is generally used for deeply researching the harmonic characteristics of a certain harmonic source, so that the universality is not strong, and the application scene limitation is large. Therefore, the frequency domain angle analysis of the general model of the external characteristics of the harmonic source is the key point of the harmonic source modeling research.
The conventional universal harmonic source model is generally a combination of equivalent harmonic sources as basic circuit elements, and the relationship between electrical quantities of external ports of the harmonic source model is one of the most basic methods for constructing the universal harmonic source model, such as a constant current source model, a norton equivalent model and the like, but the types of harmonic sources are various, the harmonic emission characteristics of the harmonic sources and the electrical quantities and even non-electrical quantities have complex interaction, the harmonic characteristics of the harmonic sources are described only by the relationship between the electrical quantities and are inevitably deviated, and the conventional universal model is accurate value estimation, is difficult to fully reflect the uncertain influence of unaccounted physical factors on the characteristics of the harmonic sources, and cannot eliminate potential estimation deviation.
Disclosure of Invention
The invention aims to provide a harmonic source general uncertainty modeling method based on Gaussian process regression, wherein an estimation result obtained by the method is Gaussian distribution, and compared with an accurate value model, the method can reflect the uncertainty influence of unaccounted physical factors on the harmonic source characteristics in a probability sense. Meanwhile, the modeling method has the characteristics of high precision, convenience in parameter solving and the like. In addition, the model updating strategy can accurately track the harmonic characteristic change of the harmonic load, realizes the online updating of the model, and can be used for the aspects of harmonic application to abnormal behaviors of the harmonic load, load change monitoring and the like.
In order to achieve the purpose, the technical scheme of the invention is as follows: a harmonic source general uncertainty modeling method based on Gaussian process regression is characterized in that a harmonic source general uncertainty model is built based on a linear coupling relation between harmonic voltage and harmonic current of a harmonic source external port and combined with Gaussian process regression.
In an embodiment of the present invention, a harmonic source general uncertainty modeling method based on gaussian process regression is implemented as follows:
collecting harmonic monitoring data;
carrying out harmonic monitoring data dimension reduction by using partial correlation;
setting a mean function and a covariance function of Gaussian process regression by combining a harmonic mechanism;
and solving parameters of the harmonic general uncertainty model by using a maximum likelihood method to obtain the harmonic source general uncertainty model.
In an embodiment of the present invention, the method further includes an online update strategy for the harmonic general uncertainty model, and the online update of the harmonic general uncertainty model is realized in a scene where a harmonic source needs to be monitored and analyzed in real time.
In an embodiment of the present invention, the harmonic monitoring data is collected, that is, the harmonic voltage and the harmonic current of the external port of the harmonic source are collected; the harmonic source external characteristics can be approximately expressed by a linear relationship between the harmonic current and the harmonic voltage at the harmonic source external port, as shown in the following formula:
Figure BDA0002996051010000021
in the formula IhIs the h harmonic current; u shapeiIs the ith harmonic voltage; a ish,iThe coupling coefficient of the h harmonic current and the i harmonic voltage is obtained; bhFor the h-th harmonic current and the fundamental current I1The coupling coefficient of (a); chThe constant is used for reflecting the inherent harmonic current emission of the harmonic source which is not influenced by other factors; equation (1) can be written in matrix form as shown in the following equation:
Ih＝AhX+Ch (2)
in the formula, Ah＝[ah,1,ah,2,...,ah,i,bh]I +1 dimensional row vectors; x ═ U1,U2,...,Ui,I1]TAnd is an i + 1-dimensional column vector.
In an embodiment of the present invention, the harmonic monitoring data dimension reduction using partial correlation is implemented as follows:
respectively calculate IhAnd variable U1,U2,...,Ui,I1The partial correlation coefficient between r and rm(m＝1，2，…,i+1)；
Calculating the mean of the partial correlation coefficients
Figure BDA0002996051010000022
Selecting partial correlation coefficient rmGreater than the mean value ravCorresponding variables, and forming the d variables into a harmonic general uncertainty model parameter X after dimensionality reductiond＝[x1,x2,...,xd]And the dimensionality of the parameters of the harmonic general uncertainty model is reduced from the dimension m to the dimension d.
In an embodiment of the present invention, the implementation manner of setting the mean function and the covariance function of the gaussian process regression by combining the harmonic mechanism is as follows:
after the parameter dimension of the harmonic general uncertainty model is reduced from m dimension to d dimension by using partial correlation, the corresponding parameter vector AhAlso decrease to d dimension, denoted as Wh＝[zh,1,zh,2,...,zh,d]Thus, formula (2) can be expressed as follows:
Ih＝WhXd+Ch (3)
taking the formula (3) as a mean function of the Gaussian process; when the covariance function is selected, in order to fully reflect the influence degree of different variables on harmonic characteristics, different parameters are assigned to each variable, so that the following function is selected as the covariance function:
Figure BDA0002996051010000031
in the formula ximIs a variable vector xiThe m-th variable, xjmIs a variable vector xjThe mth variable in (1); sigmafIs the signal variance; sigmamThe variance scale represents the influence capability of different variables.
In an embodiment of the present invention, the harmonic general uncertainty model parameter is solved by using a maximum likelihood method, and an implementation manner of the harmonic source general uncertainty model is obtained as follows:
model parameter set θ ═ { σ ═ σf；σm；Wh；ChThe parameter is identified by a maximum likelihood method; the negative log-likelihood function of the training set sample conditional probability is L (theta) — logp (y | x, theta), the negative log-likelihood function is used for solving partial derivatives of the hyper-parameters theta, and then the partial derivatives are minimized by using a conjugate gradient method to obtain the optimal hyper-parameters; the negative log-likelihood function L (θ) and the partial derivative with respect to the hyper-parameter θ can be represented by:
Figure BDA0002996051010000032
Figure BDA0002996051010000033
wherein
Figure BDA0002996051010000034
α＝C-1y；
Identifying a hyper-parameter θ ═ σ of the modelf；σm；Wh；ChAfter that, the variable x can be predicted by using equations (7) and (8)*Predicted result y of*Mean of gaussian distribution of
Figure BDA0002996051010000035
Sum variance cov (y)*)；
Figure BDA0002996051010000036
Figure BDA0002996051010000037
In an embodiment of the present invention, the implementation manner of the online update strategy of the harmonic general uncertainty model is as follows:
two indexes to be used are introduced: hit rate and coefficient of variation; the hit rate represents the proportion of the actual harmonic current value falling in the selected confidence interval, the accuracy of the prediction result is reflected, and if m points of the N prediction results in one prediction fall in the selected confidence interval, the hit rate of the prediction is as follows:
Figure BDA0002996051010000041
the variation coefficient reflects the discrete degree of the prediction result, if the variation coefficient of a certain prediction result is more than 15%, the discrete degree of the data is considered to be too large, the prediction result is abnormal, and the prediction interval is considered to be not hit; the coefficient of variation is defined as follows:
Figure BDA0002996051010000042
in the formula
Figure BDA0002996051010000043
And dn*Respectively the mean value and the standard deviation of the nth prediction result;
online harmonic generic uncertainty model
Figure BDA0002996051010000044
The specific steps of updating the strategy are as follows:
1) building a general uncertainty model of a harmonic source by using offline data or historical data;
2) setting a monitoring scale data point number D and a hit rate threshold value t;
3) inputting real-time monitoring data into a harmonic source universal uncertainty model constructed by using offline data or historical data by taking the D as a rolling analysis window, comparing and analyzing the actually-measured harmonic current and the harmonic current distribution predicted by the model, and calculating the hit rate and the variation coefficient;
4) in a certain period of time with the data length of D, if the hit rate is greater than t, the harmonic source general uncertainty model is not updated, and the next analysis window is entered; if the hit rate is smaller than the threshold value t, the load is considered to be abnormally operated or changed for a long time at the moment, and the stored D monitoring data are used for updating the general uncertainty model of the harmonic source;
and circulating the steps 3) -4).
The invention also provides a computer readable storage medium having stored thereon computer program instructions executable by a processor, the computer program instructions when executed by the processor being capable of performing the method steps as described above.
Compared with the prior art, the invention has the following beneficial effects: according to the harmonic source general uncertainty modeling method based on the Gaussian process regression, the obtained estimation result is Gaussian distribution, and compared with an accurate value model, the uncertainty influence of unexsidered physical factors on the harmonic source characteristics can be reflected in the probability sense. Meanwhile, the modeling method has the characteristics of high precision, convenience in parameter solving and the like. In addition, the model updating strategy can accurately track the harmonic characteristic change of the harmonic load, realizes the online updating of the model, and can be used for the aspects of harmonic application to abnormal behaviors of the harmonic load, load change monitoring and the like.
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FIG. 1 is a modeling flow of a harmonic source general uncertainty model based on Gaussian process regression according to the present invention.
FIG. 2 is a flow chart of the model online update strategy of the present invention.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The invention relates to a harmonic source general uncertainty modeling method based on Gaussian process regression, which is used for realizing the establishment of a harmonic general uncertainty model based on the linear coupling relation between harmonic voltage and harmonic current of a harmonic source external port and combining Gaussian process regression. The method also comprises an online updating strategy of the harmonic general uncertainty model, and the online updating of the harmonic general uncertainty model is realized in a scene needing real-time monitoring and analysis of a harmonic source.
The following is a specific implementation process of the embodiment of the invention.
As shown in fig. 1, the invention relates to a harmonic source general uncertainty modeling method based on gaussian process regression, which comprises the following steps:
(1) a harmonic general uncertainty modeling method is provided by combining Gaussian process regression based on a linear coupling relation between harmonic voltage and harmonic current of a harmonic source external port.
(2) Based on the modeling method, a model online updating strategy is provided, online updating of the model can be realized in a scene where real-time monitoring and analysis of a harmonic source are needed, and the method can be applied to monitoring abnormal behaviors of harmonic loads, load change and the like.
1. Gauss process regression
The Gaussian process is a statistical learning method and is also a machine learning method based on supervised learning of a Bayesian framework, and the defined expression is as follows: the gaussian process is a collection of random variables, any finite of which conforms to a gaussian distribution.
The nature of a gaussian process can be determined using its mean function m (x) and covariance function k (x, x'), written as:
f～GP(m(x),k(x,x')) (1)
wherein x, x' is ∈ RnFor random variables, the mean function and covariance function are defined by:
Figure BDA0002996051010000051
the mean function m (x) represents the expectation of a function value in the absence of any observed value, and for convenience of explanation, m (x) is set to 0. The covariance function k (x, x') is used for measuring the similarity degree between input samples, the larger the similarity degree of the input samples is, the more likely to obtain similar output values, the value of the output values is related to the selection of the covariance function, the covariance function is a symmetric function meeting the Mercer condition, commonly used covariance functions with square indexes, Matern covariance functions and the like, and a proper covariance function is selected according to the problem to be solved. For the regression problem, consider the following model:
y＝f(x)+ε (3)
wherein x is an n-dimensional random vector; f is a function value; y is an observed value polluted by noise; ε is independent white Gaussian noise, assuming
Figure BDA0002996051010000061
The prior distribution of the observed values y is then:
Figure BDA0002996051010000062
observed value y and predicted value y*The joint prior distribution of (a) is:
Figure BDA0002996051010000063
wherein K (X, X) is a covariance matrix of n multiplied by n order symmetric positive definite; matrix element kij＝k(xi,xj) Is used for measuring xiAnd xjA covariance function of the degree of similarity; k (x)*,X)＝K(X,x*)TFor predicting y*Variable x of*An nx1 order covariance matrix with the input X of the training set; k (x)*,x*) Is x*(ii) its own covariance; i isnIs an n-dimensional identity matrix.
From this, the predicted value y can be calculated*The posterior distribution of (A) is:
Figure BDA0002996051010000064
wherein
Figure BDA0002996051010000065
Figure BDA0002996051010000066
In the formula
Figure BDA0002996051010000067
And cov (y)*) I.e. the variable x*For the predicted result y*Mean and variance of the gaussian distribution.
2. Harmonic source universal uncertainty model based on Gaussian process regression
2.1 selection of mean and covariance functions
The harmonic out-of-source characteristics can be approximated by a linear relationship between the harmonic currents and harmonic voltages at the harmonic source ports, as follows:
Figure BDA0002996051010000068
in the formula IhIs the h harmonic current; u shapeiIs the ith harmonic voltage; a ish,iThe coupling coefficient of the h harmonic current and the i harmonic voltage is obtained; bhIs the coupling coefficient of the h harmonic current and the fundamental current; chIs constant and is used for reflecting harmonic sourceInherent harmonic current emission unaffected by other factors. Equation (9) can be written in matrix form as shown in the following equation:
Ih＝AhX+Ch (10)
in the formula, Ah＝[ah,1,ah,2,...,ah,i,bh]I +1 dimensional row vectors; x ═ U1,U2,...,Ui,I1]TAnd is an i + 1-dimensional column vector.
In order to reduce the model parameters to be identified and simplify the model structure, the method can adopt partial correlation analysis to screen variables so as to achieve the purpose of reducing the dimension of the model parameter X, and comprises the following specific steps:
(1) respectively calculate IhAnd variable U1,U2,...,Ui,I1The partial correlation coefficient between r and rm(m＝1，2，…,i+1)；
(2) Calculating the mean of the partial correlation coefficients
Figure BDA0002996051010000071
(3) Selecting partial correlation coefficient rmGreater than the mean value ravCorresponding variables, and forming the d variables into a reduced-dimension model parameter Xd＝[x1,x2,...,xd]And reducing the dimension of the model parameter from m dimension to d dimension.
(4) Corresponding parameter vector AhAlso decrease to d dimension, denoted as Wh＝[zh,1,zh,2,...,zh,d]Equation (10) can be represented by the following equation:
Ih＝WhXd+Ch (11)
equation (11) is taken as the mean function of the gaussian process. When the covariance function is selected, in order to fully reflect the influence degree of different variables on the harmonic characteristics, different parameters are assigned to each variable, so that the following function is selected as the covariance function:
Figure BDA0002996051010000072
in the formula ximIs a variable vector xiThe m-th variable, xjmThe same process is carried out; sigmafIs the signal variance; sigmamAnd the variance scale embodies the influence capability of different variables.
2.2 solving of model parameters
Model parameter set θ ═ { σ ═ σf；σm；Wh；ChAnd the parameter is identified by using a maximum likelihood method. And (3) the negative log-likelihood function of the conditional probability of the training set sample is L (theta) — logp (y | x, theta), the negative log-likelihood function is used for solving partial derivatives of the hyper-parameter theta, and then the partial derivatives are minimized by using a conjugate gradient method to obtain the optimal hyper-parameter. The negative log-likelihood function L (θ) and the partial derivative with respect to the hyper-parameter θ can be represented by:
Figure BDA0002996051010000073
Figure BDA0002996051010000081
wherein
Figure BDA0002996051010000082
α＝C-1y。
2.3 model outcome prediction
Identifying a hyper-parameter θ ═ σ of the modelf；σm；Wh；ChAfter that, the variable x can be predicted by using the equations (7) and (8)*Predicted result y of*Mean of gaussian distribution of
Figure BDA0002996051010000083
Sum variance cov (y)*). Suppose the actual set of harmonic current values is Y ═ Y1,y2,...,yNThe mean set of the model estimation results is
Figure BDA0002996051010000084
Set of square differences as S*＝{s1*,s2*,...,sN*Get the standard deviation set as D*＝{d1*,d2*,...,dN*}. The size of the confidence interval can be determined according to different confidence level requirements, and the distribution of the prediction result is described by the confidence interval, which is 99.7 percent of the confidence interval
Figure BDA0002996051010000085
For example, there is a 99.7% probability that the actual harmonic current value falls within this interval. 95.45% confidence interval
Figure BDA0002996051010000086
And 68.27% confidence intervals
Figure BDA0002996051010000087
The same is true. The distribution of the harmonic current values predicted by the model reflects possible estimation deviation and uncertain behaviors of a harmonic source from the angle of probability, so that a scheme can be made more flexibly according to the requirements of system conservation and redundancy when harmonic prevention and treatment strategies are customized.
3. Model online update strategy
Theoretically, under the condition of ensuring the accuracy of the method provided by the text, the actually measured harmonic current values should all fall within the confidence interval of model prediction, and if a large number of actually measured values deviate from the predicted confidence interval, the situation that the harmonic characteristics of a harmonic source change or the load in a multi-harmonic source complex network varies is indicated, and the constructed model cannot well describe the changed harmonic characteristics. Based on the analysis, a model online updating strategy is provided under the scene that the harmonic source needs to be monitored and analyzed in real time.
Before the updating strategy is explained in detail, two indexes needed to be used are introduced, namely hit rate and coefficient of variation. The hit rate indicates that the actual harmonic current value falls within a selected confidence interval (e.g., 99.7% confidence interval)
Figure BDA0002996051010000088
) The ratio of (a) reflects the accuracy of the prediction result, and if m points in the N prediction results in one prediction fall in a 99.7% confidence interval, the hit rate of the prediction is as follows:
Figure BDA0002996051010000089
the coefficient of variation reflects the degree of dispersion of the prediction results, and if the coefficient of variation of a certain prediction result is greater than 15%, the degree of dispersion of data is considered to be too large, the prediction result is not normal, and the prediction interval is considered to be not hit. The coefficient of variation is defined as follows:
Figure BDA0002996051010000091
as shown in FIG. 2, the online update strategy for the model is as follows:
(1) building a general uncertainty model of the harmonic source by using the method and using the off-line data or the historical data;
(2) setting a monitoring scale data point number D and a hit rate threshold value t;
(3) d is used as a rolling analysis window, real-time monitoring data are input into a harmonic source model which is constructed by using offline data or historical data, the actually measured harmonic current and the harmonic current distribution predicted by the model are contrastively analyzed, and the hit rate and the variation coefficient are calculated;
(4) in a certain period of time with the data length D, if the hit rate is greater than a threshold value t, the model is not updated, and a next analysis window is entered; if the hit rate index is smaller than the threshold value t, the load is considered to be abnormally operated or changed for a long time at the moment, and the model is updated by using the stored D monitoring data;
(5) and (5) circulating the steps (3) to (4).
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 foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.

Claims (9)

1. A harmonic source general uncertainty modeling method based on Gaussian process regression is characterized in that the harmonic source general uncertainty modeling method is based on the linear coupling relation between harmonic voltage and harmonic current of a harmonic source external port and is combined with Gaussian process regression to achieve the establishment of a harmonic general uncertainty model.
2. The Gaussian process regression-based harmonic source universal uncertainty modeling method as claimed in claim 1, characterized in that the method is implemented as follows:
collecting harmonic monitoring data;
carrying out harmonic monitoring data dimension reduction by using partial correlation;
setting a mean function and a covariance function of Gaussian process regression by combining a harmonic mechanism;
and solving parameters of the harmonic general uncertainty model by using a maximum likelihood method to obtain the harmonic source general uncertainty model.
3. The Gaussian process regression-based harmonic source general uncertainty modeling method according to claim 2, further comprising an online updating strategy for the harmonic general uncertainty model, and the online updating of the harmonic general uncertainty model is realized in a scene where real-time monitoring and analysis of a harmonic source are required.
4. The Gaussian process regression-based harmonic source general uncertainty modeling method as claimed in claim 2, wherein the harmonic monitoring data acquisition is that of harmonic source external port harmonic voltage and harmonic current; the harmonic source external characteristics can be approximately expressed by a linear relationship between the harmonic current and the harmonic voltage at the harmonic source external port, as shown in the following formula:
Figure FDA0002996051000000011
in the formula IhIs the h harmonic current; u shapeiIs the ith harmonic voltage; a ish,iThe coupling coefficient of the h harmonic current and the i harmonic voltage is obtained; bhFor the h-th harmonic current and the fundamental current I1The coupling coefficient of (a); chThe constant is used for reflecting the inherent harmonic current emission of the harmonic source which is not influenced by other factors; equation (1) can be written in matrix form as shown in the following equation:
Ih＝AhX+Ch (2)
in the formula, Ah＝[ah,1,ah,2,...,ah,i,bh]I +1 dimensional row vectors; x ═ U1,U2,...,Ui,I1]TAnd is an i + 1-dimensional column vector.
5. The Gaussian process regression-based harmonic source general uncertainty modeling method as claimed in claim 4, wherein the harmonic monitoring data dimension reduction with partial correlation is implemented as follows:
respectively calculate IhAnd variable U1,U2,...,Ui,I1The partial correlation coefficient between r and rm(m＝1，2，…,i+1)；
Calculating the mean of the partial correlation coefficients
Figure FDA0002996051000000012
Selecting partial correlation coefficient rmGreater than the mean value ravCorresponding variables, and forming the d variables into a harmonic general uncertainty model parameter X after dimensionality reductiond＝[x1,x2,...,xd]And the dimensionality of the parameters of the harmonic general uncertainty model is reduced from the dimension m to the dimension d.
6. The Gaussian process regression-based harmonic source universal uncertainty modeling method as claimed in claim 5, wherein the mean function and covariance function of Gaussian process regression are set by combining harmonic mechanism as follows:
after the parameter dimension of the harmonic general uncertainty model is reduced from m dimension to d dimension by using partial correlation, the corresponding parameter vector AhAlso decrease to d dimension, denoted as Wh＝[zh,1,zh,2,...,zh,d]Thus, formula (2) can be expressed as follows:
Ih＝WhXd+Ch (3)
taking the formula (3) as a mean function of the Gaussian process; when the covariance function is selected, in order to fully reflect the influence degree of different variables on harmonic characteristics, different parameters are assigned to each variable, so that the following function is selected as the covariance function:
Figure FDA0002996051000000021
in the formula ximIs a variable vector xiThe m-th variable, xjmIs a variable vector xjThe mth variable in (1); sigmafIs the signal variance; sigmamThe variance scale represents the influence capability of different variables.
7. The Gaussian process regression-based harmonic source general uncertainty modeling method as claimed in claim 6, wherein the harmonic source general uncertainty model parameters are solved by a maximum likelihood method, and the harmonic source general uncertainty model is obtained by the following implementation manner:
model parameter set θ ═ { σ ═ σf；σm；Wh；ChThe parameter is identified by a maximum likelihood method; the negative log-likelihood function of the conditional probability of the training set samples is L (θ) — logp (y | x, θ), which is made to bias the hyper-parameter θ, and thenMinimizing the partial derivative by a conjugate gradient method to obtain an optimal hyperparameter; the negative log-likelihood function L (θ) and the partial derivative with respect to the hyper-parameter θ can be represented by:
Figure FDA0002996051000000022
Figure FDA0002996051000000023
wherein
Figure FDA0002996051000000024
α＝C-1y；
Identifying a hyper-parameter θ ═ σ of the modelf；σm；Wh；ChAfter that, the variable x can be predicted by using equations (7) and (8)*Predicted result y of*Mean of gaussian distribution of
Figure FDA0002996051000000025
Sum variance cov (y)*)；
Figure FDA0002996051000000031
Figure FDA0002996051000000032
8. The Gaussian process regression-based harmonic source general uncertainty modeling method as claimed in claim 3, characterized in that the online update strategy of the harmonic general uncertainty model is implemented as follows:
two indexes to be used are introduced: hit rate and coefficient of variation; the hit rate represents the proportion of the actual harmonic current value falling in the selected confidence interval, the accuracy of the prediction result is reflected, and if m points of the N prediction results in one prediction fall in the selected confidence interval, the hit rate of the prediction is as follows:
Figure FDA0002996051000000033
the variation coefficient reflects the discrete degree of the prediction result, if the variation coefficient of a certain prediction result is more than 15%, the discrete degree of the data is considered to be too large, the prediction result is abnormal, and the prediction interval is considered to be not hit; let the coefficient of variation be defined as follows:
Figure FDA0002996051000000034
in the formula
Figure FDA0002996051000000035
And
Figure FDA0002996051000000037
respectively the mean value and the standard deviation of the nth prediction result;
online harmonic generic uncertainty model
Figure FDA0002996051000000036
The specific steps of updating the strategy are as follows:
1) building a general uncertainty model of a harmonic source by using offline data or historical data;
2) setting a monitoring scale data point number D and a hit rate threshold value t;
3) inputting real-time monitoring data into a harmonic source universal uncertainty model constructed by using offline data or historical data by taking the D as a rolling analysis window, comparing and analyzing the actually-measured harmonic current and the harmonic current distribution predicted by the model, and calculating the hit rate and the variation coefficient;
4) in a certain period of time with the data length of D, if the hit rate is greater than t, the harmonic source general uncertainty model is not updated, and the next analysis window is entered; if the hit rate is smaller than the threshold value t, the load is considered to be abnormally operated or changed for a long time at the moment, and the stored D monitoring data are used for updating the general uncertainty model of the harmonic source;
and circulating the steps 3) -4).
9. A computer-readable storage medium, having stored thereon computer program instructions executable by a processor, the computer program instructions, when executed by the processor, being capable of carrying out the method steps of claims 1-8.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114236235A (en) * 2021-12-17 2022-03-25 福州大学 Local unobservable system harmonic source positioning method adopting similar feature matching
CN117081082A (en) * 2023-10-17 2023-11-17 国网上海市电力公司 Active power distribution network operation situation sensing method and system based on Gaussian process regression
CN117748507A (en) * 2024-02-06 2024-03-22 四川大学 Distribution network harmonic access uncertainty assessment method based on Gaussian regression model
CN117748507B (en) * 2024-02-06 2024-05-03 四川大学 Distribution network harmonic access uncertainty assessment method based on Gaussian regression model

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7755360B1 (en) * 2005-10-24 2010-07-13 Seektech, Inc. Portable locator system with jamming reduction
CN105790261A (en) * 2016-03-29 2016-07-20 全球能源互联网研究院 Random harmonic flow calculation method
US20170061305A1 (en) * 2015-08-28 2017-03-02 Jiangnan University Fuzzy curve analysis based soft sensor modeling method using time difference Gaussian process regression
CN109815934A (en) * 2019-02-12 2019-05-28 西华大学 A kind of multiple dimensioned OGLPE feature extracting method applied to fault of converter
CN111274701A (en) * 2020-01-20 2020-06-12 福州大学 Harmonic source affine modeling method adopting interval monitoring data dimension reduction regression

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7755360B1 (en) * 2005-10-24 2010-07-13 Seektech, Inc. Portable locator system with jamming reduction
US20170061305A1 (en) * 2015-08-28 2017-03-02 Jiangnan University Fuzzy curve analysis based soft sensor modeling method using time difference Gaussian process regression
CN105790261A (en) * 2016-03-29 2016-07-20 全球能源互联网研究院 Random harmonic flow calculation method
CN109815934A (en) * 2019-02-12 2019-05-28 西华大学 A kind of multiple dimensioned OGLPE feature extracting method applied to fault of converter
CN111274701A (en) * 2020-01-20 2020-06-12 福州大学 Harmonic source affine modeling method adopting interval monitoring data dimension reduction regression

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
张逸 等: "基于高斯过程回归的谐波源不确定性通用模型", 《中国电机工程学报》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114236235A (en) * 2021-12-17 2022-03-25 福州大学 Local unobservable system harmonic source positioning method adopting similar feature matching
CN114236235B (en) * 2021-12-17 2024-02-06 福州大学 Harmonic source positioning method for local unobservable system by adopting similar feature matching
CN117081082A (en) * 2023-10-17 2023-11-17 国网上海市电力公司 Active power distribution network operation situation sensing method and system based on Gaussian process regression
CN117081082B (en) * 2023-10-17 2024-01-23 国网上海市电力公司 Active power distribution network operation situation sensing method and system based on Gaussian process regression
CN117748507A (en) * 2024-02-06 2024-03-22 四川大学 Distribution network harmonic access uncertainty assessment method based on Gaussian regression model
CN117748507B (en) * 2024-02-06 2024-05-03 四川大学 Distribution network harmonic access uncertainty assessment method based on Gaussian regression model

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