CN109446643B - Method for establishing household appliance load harmonic model based on measured data - Google Patents

Method for establishing household appliance load harmonic model based on measured data Download PDF

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CN109446643B
CN109446643B CN201811258954.7A CN201811258954A CN109446643B CN 109446643 B CN109446643 B CN 109446643B CN 201811258954 A CN201811258954 A CN 201811258954A CN 109446643 B CN109446643 B CN 109446643B
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孙媛媛
谢香敏
张凌菡
李树荣
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Abstract

The invention discloses a method for establishing a load harmonic model of a household appliance based on measured data, which comprises the following steps: acquiring actually measured voltage and current data of a household appliance load, and carrying out Fourier analysis on the measured data to obtain phasor values of each subharmonic of the voltage and the current; establishing a cross frequency admittance matrix harmonic model of the household appliance load; and taking the obtained phasor values of the harmonics of the voltage and the current as input, and calculating cross frequency admittance matrix model parameters based on a generalized linear complex partial least square method to obtain a cross frequency admittance harmonic model of the household appliance. The invention has the beneficial effects that: the method can be accurate and rapid on the basis of not knowing the internal circuit structure and parameters of the household load, is simple and practical, and has great significance for ensuring accurate analysis and evaluation of the harmonic generation condition of the power distribution network.

Description

Method for establishing household appliance load harmonic model based on measured data
Technical Field
The invention belongs to the field of load harmonic modeling, and particularly relates to a method for establishing a load harmonic model of a household appliance based on measured data.
Background
In the current electric power system, the electricity consumption of residents accounts for more than 30% of the total electric energy consumption, and along with the development of the intelligent power distribution network, the proportion of the electricity consumption of residents is continuously increased. However, due to the fact that a large number of power electronic devices exist in the household load, harmonic current distortion of most household appliances is very serious, the total distortion rate of some current harmonics even exceeds 100%, and measured data show that the total required distortion rate of harmonic current on certain resident power distribution feeders can reach 12%, so that the resident load becomes a very important harmonic source. The generated harmonic wave can cause a series of problems of increased harmonic loss in a residential distribution network, overload of a transformer and a neutral wire, increased probability of failure of electronic equipment and the like. Therefore, in order to accurately evaluate and analyze the influence of a large number of accesses of household loads on the civil power distribution network and correspondingly provide appropriate treatment measures to improve the power quality, it is very necessary to establish an accurate harmonic model for the household loads.
At present, harmonic modeling methods related to loads of household appliances can be divided into methods based on equivalent circuit analysis and modeling methods based on measured data. The equivalent circuit analysis based approach requires knowing the equivalent circuit of the household appliance load and the specific values of the circuit parameters. In practice, however, the power supply circuit for many household appliance loads is complex in structure, it is difficult to obtain a simplified equivalent circuit thereof, and the parameters of the circuit are not constant or difficult to estimate. The modeling method based on the measured data only needs to actually measure the load to obtain the voltage and current data of the load. In the past, a constant current source model is usually adopted to calculate the harmonic current of the household appliance load, but the constant current source model simplifies the influence of the power supply voltage on the harmonic current of the load, so that the calculated harmonic current does not change along with the power supply voltage, and therefore, the harmonic load sensitive to the power supply voltage can generate larger errors. Therefore, harmonic modeling is carried out on the household appliance load by using the cross frequency admittance matrix model, however, in the process of solving the parameters of the cross frequency admittance matrix model by using the ordinary least square method, the problem of matrix morbidity occurs in the calculation process, so that the solved model parameters are inaccurate, and the modeling precision is influenced.
Disclosure of Invention
In order to solve the problems, the invention provides a method for establishing a household appliance load harmonic model based on measured data, which can accurately evaluate the influence of a large amount of household load access on a domestic power distribution network and effectively improve the power quality of the power distribution network.
In order to achieve the purpose, the invention adopts the following technical scheme:
in one or more embodiments, a method for establishing a harmonic model of a load of a household appliance based on measured data is disclosed, which includes:
(1) acquiring actually measured voltage and current data of a household appliance load, and carrying out Fourier analysis on the measured data to obtain phasor values of each subharmonic of the voltage and the current;
(2) establishing a cross frequency admittance matrix harmonic model of the household appliance load;
(3) and (2) taking the phasor values of the harmonics of the voltage and the current obtained in the step (1) as input, and calculating cross frequency admittance matrix model parameters based on a generalized linear complex partial least square method to obtain a cross frequency admittance harmonic model of the household appliance.
Further, the method for acquiring the actually measured voltage and current data of the household appliance load specifically comprises the following steps:
an experiment measuring platform is established, the supply voltage of a household load is the actual power grid voltage, and the supply voltage u of the household load is measured through a voltage clamp and a current clampMAnd the actual current iMAnd acquiring actually measured power supply voltage and actual current data through the data acquisition device.
Further, establishing a cross frequency admittance matrix harmonic model of the household appliance load, specifically:
Figure BDA0001843443440000021
wherein the content of the first and second substances,
Figure BDA0001843443440000022
characterizing the ith harmonic current phasor value;
Figure BDA0001843443440000023
characterizing a jth harmonic voltage magnitude; y isijCharacterizing the degree of contribution of the jth harmonic voltage to the ith harmonic current, i being 1, 3, …, H; j ═ 1, 3, …, K; the highest harmonic order of voltage and current is selected as H and K, respectively.
Further, expanding a cross frequency admittance matrix harmonic model of the household appliance load;
converting the expanded cross-frequency admittance matrix harmonic model of the household appliance load into a compact form, wherein the compact form is that a dependent variable matrix I is equal to the product of an independent variable matrix U and a cross-frequency admittance matrix Y;
respectively amplifying the independent variable matrix U and the dependent variable matrix I, extracting the maximum relevant variable through an iteration method, and extracting the main component based on a generalized linear complex partial least square method to obtain the estimated values of the independent variable matrix U and the dependent variable matrix I;
and calculating to obtain a cross frequency admittance matrix.
Further, the method expands a harmonic model of a cross frequency admittance matrix of the load of the household appliance, and specifically comprises the following steps:
Figure BDA0001843443440000024
in the formula (I), the compound is shown in the specification,
Figure BDA0001843443440000025
an ith harmonic current phasor value representing an nth set of measurement data,
Figure BDA0001843443440000026
a j-th harmonic voltage magnitude value representing an nth set of measurement data.
Further, the independent variable matrix U and the dependent variable matrix I are respectively augmented byU＝[U,U*]，I＝[I,I*]In which the upper label (·)*Taking conjugate operation;
extracting the maximum relevant variable through an iteration method, specifically:
Figure BDA0001843443440000031
wherein the content of the first and second substances,t mis thatUAndIthe m-th principal component phasor of (a),p mandq mare respectivelyUAndIt is the corresponding principal component matrix, and P and Q are the corresponding load matrices.U MAndI Mis thatUAndIm represents the maximum principal component number, determined by cross-checking.
Further, extracting principal components based on a generalized linear complex partial least square method, wherein the specific process is as follows:
for independent variable matrix U and dependent variable matrixI is respectively augmented to obtain initial input matrixes ofU 1＝[U,U*]，I 1＝[I,I*]，U1＝U,I1I ═ I; the upper label (·)*Taking conjugate operation;
let i be 1, …, M;
when i is 1, the matrix is obtained
Figure BDA0001843443440000032
The eigenvector w corresponding to the maximum eigenvalue1；
The first principal component vector t is obtained1And its augmented vectort 1Respectively is as follows:
Figure BDA0001843443440000033
and (3) obtaining a load vector corresponding to the first principal component vector:
Figure BDA0001843443440000034
an input matrix when i is 2 is obtained according to the principal component vector and the load vector is
Figure BDA0001843443440000035
Repeating the steps, and extracting M principal component vectors, wherein the size of M is determined by a cross-checking method.
Further, the estimated values of the independent variable matrix and the dependent variable matrix are respectively
Figure BDA0001843443440000036
And
Figure BDA0001843443440000037
further expressed as:
Figure BDA0001843443440000038
wherein e is-j2θRepresents a phase angle rotation operator, can
Figure BDA0001843443440000039
Is converted into
Figure BDA00018434434400000310
Superscript (·)*Taking conjugate operation; the matrices M and N are specifically:
Figure BDA00018434434400000311
wherein the content of the first and second substances,
Figure BDA00018434434400000312
further, a cross-frequency admittance matrix is obtained by calculation, specifically:
Y＝(M+N×e-j2θ)。
compared with the prior art, the invention has the beneficial effects that:
aiming at the load of the household electrical appliance, the method for calculating the cross frequency admittance matrix model parameters by using the generalized linear complex-partial least square method has the advantages of accuracy, rapidness, simplicity and practicality on the basis of not knowing the internal circuit structure and parameters of the household electrical appliance, and has great significance for ensuring accurate analysis and evaluation of the generation condition of the harmonic wave of the power distribution network.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of a method for creating a harmonic model of a household appliance load based on measured data;
FIG. 2 is a circuit diagram of an experimental platform for experimental measurements;
FIG. 3(a) is a graph of current waveforms and a graph of a comparison of frequency spectra for a compact fluorescent lamp based on the method of the present invention, calculated based on the ordinary least squares method, and the actual current waveforms;
FIG. 3(b) is a graph of current waveform and a comparison of frequency spectrum for an electric bicycle charger based on the method of the present invention, calculated based on the ordinary least squares method, and the actual current waveform;
FIG. 3(c) is a graph of current waveforms and a comparison of frequency spectra for a desktop computer based on the method of the present invention, based on the common least squares calculation and the actual current waveforms.
Detailed Description
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.
Example one
In one or more embodiments, a method for establishing a harmonic model of a load of a household appliance based on measured data is disclosed, which comprises the following specific steps:
1. and establishing an experimental measurement platform to obtain the actually measured voltage and current data of the household appliance load.
As shown in fig. 2, an experimental measurement platform is established, in order to consider the influence of the voltage in the actual power grid on the load of the household appliance, the supply voltage of the household load is the actual power grid voltage, and the supply voltage u is measured by a voltage clamp and a current clampMAnd the actual current iMAnd acquiring actual voltage and current data by combining a data acquisition board and data acquisition software LABVIEW, and then performing Fourier analysis on the acquired data to acquire a voltage phasor value and a current phasor value.
2. And establishing a cross frequency admittance matrix harmonic model of the household appliance load.
Aiming at the load of the household appliance, a cross frequency admittance matrix harmonic model is established, and the specific expression is as follows:
Figure BDA0001843443440000051
wherein the elements
Figure BDA0001843443440000052
Characterizing the ith harmonic current phasor value;
Figure BDA0001843443440000053
characterizing a jth harmonic voltage magnitude; y isijCharacterizing the degree of contribution of the jth harmonic voltage to the ith harmonic current, i being 1, 3, …, H; j ═ 1, 3, …, K; the highest harmonic order of voltage and current is selected as H and K, respectively.
In order to calculate the parameters of the harmonic model of the cross-frequency admittance matrix by using the measured voltage and current phasor values, equation (1) needs to be extended as follows:
Figure BDA0001843443440000054
in the formula
Figure BDA0001843443440000055
An ith harmonic current phasor value representing an nth set of measurement data,
Figure BDA00018434434400000514
a j-th harmonic voltage magnitude value representing an nth set of measurement data.
The compact form of equation (2) is:
I＝YU(3)
wherein
Figure BDA00018434434400000513
In the form of a matrix of independent variables,
Figure BDA00018434434400000512
in the form of a matrix of dependent variables,
Figure BDA00018434434400000511
is a cross-frequency admittance matrix.
3. And calculating the harmonic model parameters of the cross frequency admittance matrix based on the generalized linear complex partial least square method.
The independent variable matrix U and the dependent variable matrix I obtained in the formula (3) in the step (3) are respectively augmented to obtain the augmented matrixes thereof, namelyU＝[U,U*]，I＝[I,I*]In which the upper label (·)*To take conjugate operation. Extracting the most relevant variable by an iterative method, as shown in formula (4):
Figure BDA00018434434400000510
whereint mIs thatUAndIthe m-th principal component phasor of (a),p mandq mare respectivelyUAndIt is the corresponding principal component matrix, and P and Q are the corresponding load matrices.U MAndI Mis thatUAndIwherein M represents the maximum principal component number, as determined by cross-checking.
Extracting principal components based on generalized linear complex partial least square method, firstly, respectively amplifying independent variable matrix U and dependent variable matrix I to obtain initial input matrix ofU 1＝[U,U*]，I 1＝[I,I*]，U1＝U,I1I, wherein (·)*Taking conjugate operation; when i is 1, the matrix is obtained
Figure BDA0001843443440000061
The eigenvector w corresponding to the maximum eigenvalue1Wherein Eigmax{. represents the eigenvector operation taking the maximum eigenvalue; then, the first principal component vector and its augmentation vector are obtained
Figure BDA0001843443440000062
Then, the load vector corresponding to the first principal component vector is obtained
Figure BDA0001843443440000063
Finally, the input matrix when i is 2 can be obtained through the principal component vector and the load vector as
Figure BDA0001843443440000064
Repeating the previous cycle steps, M principal component vectors can be extracted, where the magnitude of M can be determined by cross-checking.
The method for extracting the principal components based on the generalized linear complex partial least square method comprises the following steps:
1) initialization:U 1＝[U,U*],I 1＝[I,I*],U1＝U,I1＝I
2) and (3) circulation: suppose i is 1, …, M
3)
Figure BDA0001843443440000065
4)
Figure BDA0001843443440000066
5)
Figure BDA0001843443440000067
6)
Figure BDA0001843443440000068
7) Store wi,ti,p iAndq i
8) end the cycle
The upper label (·)+In a broad sense inverse, e.g. to t1Taking the generalized inverse can be written as
Figure BDA0001843443440000069
Based on the above steps of extracting principal components, estimated values of independent variable matrix and dependent variable matrix can be obtained, respectively
Figure BDA00018434434400000610
And
Figure BDA00018434434400000611
can be further expressed as:
Figure BDA00018434434400000612
wherein e-j2θRepresents a phase angle rotation operator, can
Figure BDA00018434434400000613
Is converted into
Figure BDA00018434434400000614
The matrices M and N can be calculated:
Figure BDA0001843443440000071
wherein
Figure BDA0001843443440000072
Therefore, the cross-frequency admittance matrix calculated by the generalized linear complex partial least square method is:
Y＝(M+N×e-j2θ) (7)
in order to verify the calculation method provided by the invention, a common least square method is adopted as a comparative calculation method, the power supply voltage of each household load is the actual power grid voltage, and the household loads shown in the following table are verified in an experiment:
Figure BDA0001843443440000073
the following table shows the error between the amplitude and phase angle of each harmonic current of the model reconstructed current and the actual current of the above three household loads:
Figure BDA0001843443440000074
the results of the calculation and actual measurement results of the three household loads by the method of the present invention and the comparison of the ordinary least square method are shown in fig. 3(a) - (c), and it can be known from the results in the figures that the current waveform diagram for the harmonic modeling of the household loads based on the method of the present invention substantially matches the current waveform diagram of the actual results, and the error is substantially kept within 10%, while the current waveform obtained by the harmonic modeling based on the ordinary least square method has a larger deviation from the actual current waveform, and the error is substantially more than 30%.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (5)

1. A method for establishing a household appliance load harmonic model based on measured data is characterized by comprising the following steps:
(1) acquiring actually measured voltage and current data of a household appliance load, and carrying out Fourier analysis on the measured data to obtain phasor values of each subharmonic of the voltage and the current;
(2) establishing a cross frequency admittance matrix harmonic model of the household appliance load,
(3) taking phasor values of each harmonic of the voltage and the current obtained in the step (1) as input, and calculating cross frequency admittance matrix model parameters based on a generalized linear complex partial least square method to obtain a cross frequency admittance harmonic model of the household appliance;
expanding a cross frequency admittance matrix harmonic model of the household appliance load;
converting the expanded cross-frequency admittance matrix harmonic model of the household appliance load into a compact form, wherein the compact form is that a dependent variable matrix I is equal to the product of an independent variable matrix U and a cross-frequency admittance matrix Y;
respectively amplifying the independent variable matrix U and the dependent variable matrix I, extracting the maximum relevant variable through an iteration method, and extracting the main component based on a generalized linear complex partial least square method to obtain the estimated values of the independent variable matrix U and the dependent variable matrix I;
calculating to obtain a cross frequency admittance matrix;
wherein the estimated values of the independent variable matrix and the dependent variable matrix are respectively
Figure FDF0000009776120000011
And
Figure FDF0000009776120000012
further expressed as:
Figure FDF0000009776120000013
wherein e is-j2θRepresents a phase angle rotation operator, can
Figure FDF0000009776120000014
Is converted into
Figure FDF0000009776120000015
Superscript (·)*Taking conjugate operation; the matrices M and N are specifically:
Figure FDF0000009776120000016
wherein the content of the first and second substances,
Figure FDF0000009776120000017
the cross frequency admittance matrix obtained by calculation is specifically as follows:
Y＝(M+N×e-j2θ)。
2. the method for creating a harmonic model of a household appliance load based on measured data according to claim 1, wherein the method for obtaining measured voltage and current data of a household appliance load comprises:
an experiment measuring platform is established, the supply voltage of a household load is the actual power grid voltage, and the supply voltage u of the household load is measured through a voltage clamp and a current clampMAnd the actual current iMAnd acquiring actually measured power supply voltage and actual current data through the data acquisition device.
3. The method for building a harmonic model of a household appliance load based on measured data according to claim 1, wherein the harmonic model of a cross-frequency admittance matrix of the household appliance load is expanded, specifically:
Figure FDF0000009776120000021
in the formula (I), the compound is shown in the specification,
Figure FDF0000009776120000022
an ith harmonic current phasor value representing an nth set of measurement data,
Figure FDF0000009776120000023
a j-th harmonic voltage magnitude value representing an nth set of measurement data.
4. The method of claim 1, wherein the independent variable matrix U and the dependent variable matrix I are augmented separately and respectively as followsU＝[U,U*]，I＝[I,I*]In which the upper label (·)*Taking conjugate operation;
extracting the maximum relevant variable through an iteration method, specifically:
Figure FDF0000009776120000024
wherein the content of the first and second substances,t mis thatUAndIthe m-th principal component phasor of (a),p mandq mare respectivelyUAndIt is the corresponding principal component matrix, P and Q are the corresponding load matrices;U MandI Mis thatUAndIm represents the maximum principal component number, determined by cross-checking.
5. The method for establishing the household appliance load harmonic model based on the measured data as claimed in claim 4, characterized in that the principal components are extracted based on a generalized linear complex partial least squares method, the specific process is as follows:
the independent variable matrix U and the dependent variable matrix I are respectively augmented to obtain initial input matrices ofU 1＝[U,U*]，I 1＝[I,I*]，U1＝U,I1I ═ I; the upper label (·)*Taking conjugate operation;
let i be 1, …, M;
when i is 1, the matrix is obtained
Figure FDF0000009776120000025
The eigenvector w corresponding to the maximum eigenvalue1；
The first principal component vector t is obtained1And its augmented vectort 1Respectively is as follows: t is t1＝U1w1,
Figure FDF0000009776120000026
And (3) obtaining a load vector corresponding to the first principal component vector:
Figure FDF0000009776120000027
an input matrix when i is 2 is obtained according to the principal component vector and the load vector is
Figure FDF0000009776120000028
Repeating the steps, and extracting M principal component vectors, wherein the size of M is determined by a cross-checking method.
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