CN113468474B - Power grid frequency estimation method based on root Mini-Norm - Google Patents

Power grid frequency estimation method based on root Mini-Norm Download PDF

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CN113468474B
CN113468474B CN202111035426.7A CN202111035426A CN113468474B CN 113468474 B CN113468474 B CN 113468474B CN 202111035426 A CN202111035426 A CN 202111035426A CN 113468474 B CN113468474 B CN 113468474B
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power grid
vector
norm
frequency estimation
mini
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CN113468474A (en
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罗耀强
张珍凤
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Nanjing Estable Electric Power Technology Co ltd
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Abstract

The invention discloses a power grid frequency estimation method based on a root Mini-norm.A complex exponential model of sampled data is designed aiming at steady-state power grid sampled data of an additive Gaussian noise background, then asymptotic unbiased autocorrelation processing is carried out on the sampled data, then the data after autocorrelation processing is decomposed into a multidimensional signal subspace and a multidimensional noise subspace by adopting an MUSIC algorithm in spectrum decomposition, then the multidimensional noise subspace is mapped into a one-dimensional vector, and finally, a polynomial root solving method is adopted aiming at the characteristics that the power grid center frequency is one and the corresponding complex exponential model is two, so that the power grid center frequency is calculated; according to the method, the Mini-Norm method is utilized to map the multidimensional matrix operation into the one-dimensional vector operation, so that the calculated amount is reduced, the power grid frequency estimation performance of the multidimensional noise subspace can be achieved, and the calculated amount can be reduced; the method not only considers the performance precision of the power grid frequency estimation, but also reduces the requirement on calculated amount.

Description

Power grid frequency estimation method based on root Mini-Norm
Technical Field
The invention relates to a power grid frequency estimation method based on a root Mini-Norm, which is used for estimating the frequency of a power system and belongs to the technical field of operation and control of the power system.
Background
With the wide application of nonlinear loads such as power electronic semiconductor devices and the like in a power grid, a large amount of higher harmonics are injected into a power system, so that the voltage and current waveforms of the power grid are distorted, and serious influence is brought to the accurate measurement and harmonic analysis of the power grid frequency. The frequency is the most basic parameter for the operation of the power system, and accurate and rapid frequency estimation has important application value for the operation, monitoring and control of the power system.
At present, a frequency estimation method of a power system mainly uses Fast Fourier Transform (FFT), and performs two-point or three-point interpolation on a spectral line to obtain a frequency estimation value of a signal. The classic FFT transform belongs to the frequency domain method, which has a high requirement on the requirement of the sample data volume.
Music (multiple Signal classification), a class of spatial spectrum estimation algorithms, is characterized by using covariance matrix (Rx) of received data to perform feature decomposition, separating Signal subspace and noise subspace, using orthogonality of Signal direction vector and noise subspace to form spatial scanning spectrum, and performing global search spectrum peak, thereby implementing parameter estimation of Signal. However, the classical MUSIC algorithm is computationally intensive.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a power grid frequency estimation method based on a root Mini-Norm, which not only retains the estimation precision of the spectrum estimation method on the power grid frequency, but also reduces the operation amount compared with the classical MUSIC algorithm.
In order to solve the technical problem, the power grid frequency estimation method based on the root Mini-Norm is characterized in that a complex exponential model of sampled data is designed aiming at steady-state power grid sampled data of an additive Gaussian noise background, then asymptotic unbiased autocorrelation processing is carried out on the sampled data, then the data after autocorrelation processing is decomposed into a multidimensional signal subspace and a multidimensional noise subspace by adopting a MUSIC algorithm in spectrum decomposition, then the multidimensional noise subspace is mapped into a one-dimensional vector, and finally a polynomial root solving method is adopted aiming at the characteristics that the power grid center frequency is one and the corresponding complex exponential model is two, so that the power grid center frequency is calculated.
The Mini-Norm algorithm belongs to a time domain method. The time domain method can greatly reduce the requirement for the amount of sampled data relative to the frequency domain method. The time domain method utilizes an Euler formula and Hilbert transformation to transform a sinusoidal signal into a complex exponential sinusoidal signal, then utilizes the uniqueness of spectral decomposition, can intuitively and quickly estimate the frequency of a power grid, and theoretically, the estimation precision can reach the lower boundary of Clarmero.
Specifically, the power grid frequency estimation method based on the root Mini-Norm comprises the following steps:
step 1: selecting a section of sine signal sampling sequence sampled at equal intervals
Figure 302105DEST_PATH_IMAGE001
Wherein, in the step (A),
Figure 219246DEST_PATH_IMAGE002
represents a vector of a sequence of samples representing the sequence of samples,
Figure 687398DEST_PATH_IMAGE003
represents the first
Figure 82608DEST_PATH_IMAGE004
The number of sequential samples of the data is,
Figure 896980DEST_PATH_IMAGE005
，
Figure 657125DEST_PATH_IMAGE006
representing the total number of sampled data;
step 2: to the sampling sequence vector
Figure 924159DEST_PATH_IMAGE002
Performing asymptotic unbiased autocorrelation operation to obtain autocorrelation vector
Figure 123059DEST_PATH_IMAGE007
，
Figure 978888DEST_PATH_IMAGE008
The expression of (a) is:
Figure 972252DEST_PATH_IMAGE009
wherein the content of the first and second substances,
Figure 664265DEST_PATH_IMAGE010
representative pair
Figure 401276DEST_PATH_IMAGE011
The conjugation is taken out and the reaction is carried out,
Figure 924662DEST_PATH_IMAGE012
，
Figure 31203DEST_PATH_IMAGE013
representing the number of autocorrelation vectors;
and step 3: according to a given autocorrelation vector
Figure 272828DEST_PATH_IMAGE014
Will be
Figure 547952DEST_PATH_IMAGE014
Rewriting is in the form of Toeplitz matrix, set to
Figure 129106DEST_PATH_IMAGE015
(ii) a To pair
Figure 464272DEST_PATH_IMAGE015
Singular value decomposition is carried out, and the expression is as follows:
Figure 193194DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure 255697DEST_PATH_IMAGE017
、
Figure 753674DEST_PATH_IMAGE018
and
Figure 525321DEST_PATH_IMAGE019
respectively corresponding to a left singular vector, a singular value and a right singular vector of the signal subspace;
Figure 616905DEST_PATH_IMAGE020
、
Figure 499410DEST_PATH_IMAGE021
and
Figure 851894DEST_PATH_IMAGE022
respectively corresponding to a right singular vector, a singular value and a right singular vector of the noise subspace;
and 4, step 4: for step 3
Figure 279595DEST_PATH_IMAGE020
Mapping to Mini-Norm form: for a complex exponential type grid frequency estimation,
Figure 717530DEST_PATH_IMAGE020
is composed of
Figure 279093DEST_PATH_IMAGE023
Dimension matrix, let
Figure 751662DEST_PATH_IMAGE024
Is composed of
Figure 865112DEST_PATH_IMAGE020
The Mini-Norm form (1), wherein,
Figure 774031DEST_PATH_IMAGE025
the expression of (a) is:
Figure 998339DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure 997519DEST_PATH_IMAGE027
，
Figure 281870DEST_PATH_IMAGE028
，
Figure 694396DEST_PATH_IMAGE029
is that
Figure 410811DEST_PATH_IMAGE030
The transpose of (a) is performed,
Figure 592393DEST_PATH_IMAGE031
；
and 5: let us say that in step 4
Figure 782066DEST_PATH_IMAGE032
According to
Figure 619572DEST_PATH_IMAGE033
Establishing a polynomial expression:
Figure 185683DEST_PATH_IMAGE034
solving a polynomial by
Figure 487351DEST_PATH_IMAGE035
The mode is a positive value closest to 1, and the grid frequency estimation value is
Figure 34876DEST_PATH_IMAGE036
Is that
Figure 421995DEST_PATH_IMAGE037
(ii) a Wherein the content of the first and second substances,
Figure 791796DEST_PATH_IMAGE038
representative pair
Figure 620075DEST_PATH_IMAGE035
Taking the imaginary part of the signal to be processed,
Figure 417130DEST_PATH_IMAGE039
representative pair
Figure 25966DEST_PATH_IMAGE035
Taking a real part of the signal,
Figure 887874DEST_PATH_IMAGE040
represents the function of the inverse tangent of the line,
Figure 898555DEST_PATH_IMAGE041
representing a sequence of acquired samples
Figure 804194DEST_PATH_IMAGE042
The sampling frequency of the time.
Under the background of power grid frequency estimation based on the existing MUSIC spectrum estimation, according to the dividing mode of a signal subspace and a noise subspace of the power grid frequency estimation in the MUSIC spectrum estimation method, the power grid frequency estimation calculation amount based on the multidimensional noise subspace method is in direct proportion to the dimension of the subspace. And the multidimensional noise subspace is converted into a one-dimensional vector, so that the power grid frequency estimation performance of the multidimensional noise subspace can be achieved, and the calculated amount can be reduced.
The invention utilizes the Mini-Norm method to map the multidimensional matrix operation into the one-dimensional vector operation, thereby reducing the calculated amount, achieving the power grid frequency estimation performance of the multidimensional noise subspace and reducing the calculated amount. Compared with the prior art, the method not only considers the power grid frequency estimation performance precision, but also reduces the requirement on calculated amount.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a method for estimating grid frequency based on root Mini-Norm.
Fig. 2 shows a sample sequence with a signal-to-noise ratio of 10 dB.
FIG. 3 is a graph of the mean estimate of the grid frequency for signal-to-noise ratios from 0dB to 20 dB.
Fig. 4 is a plot of the power grid frequency estimated variance from 0dB to 20dB signal-to-noise ratio.
Detailed Description
In the power grid frequency estimation method based on the root Mini-Norm according to the embodiment, as shown in fig. 1 to 4, for steady-state power grid sampling data of a section of additive gaussian noise background, a complex exponential model of the sampling data is designed, then, the sampling data is subjected to asymptotic and unbiased autocorrelation processing, then, the data subjected to autocorrelation processing is decomposed into a multidimensional signal subspace and a multidimensional noise subspace by using a MUSIC classification algorithm in spectrum decomposition, the multidimensional noise subspace is mapped into a one-dimensional vector, and finally, for the characteristic that the power grid center frequency is one and the corresponding complex exponential model is two, a polynomial root-finding method is adopted to calculate the power grid center frequency.
As shown in fig. 1, the method specifically comprises the following steps:
step 1: selecting a section of power grid voltage signal sampling sequence sampled at equal intervals
Order sampling sequence
Figure 900326DEST_PATH_IMAGE001
Wherein, in the step (A),
Figure 611930DEST_PATH_IMAGE002
represents a vector of a sequence of samples representing the sequence of samples,
Figure 664069DEST_PATH_IMAGE043
represents the first
Figure 802926DEST_PATH_IMAGE004
The number of sequential samples of the data is,
Figure 386354DEST_PATH_IMAGE006
representing the total number of sample data.
Step 2: obtaining a self-correlation vector
Order to
Figure 573753DEST_PATH_IMAGE007
In order to be a vector of the auto-correlation,
Figure 559026DEST_PATH_IMAGE044
the expression of (a) is:
Figure 868785DEST_PATH_IMAGE045
wherein, in the step (A),
Figure 627925DEST_PATH_IMAGE046
representative pair
Figure 681331DEST_PATH_IMAGE011
And (4) taking conjugation.
And step 3: for the autocorrelation vector
Figure 521111DEST_PATH_IMAGE047
Performing singular value decomposition in the form of Toeplitz matrix
Order to
Figure 939454DEST_PATH_IMAGE015
Is an autocorrelation vector
Figure 231896DEST_PATH_IMAGE047
In the form of Toeplitz matrix. To pair
Figure 88993DEST_PATH_IMAGE015
Singular value decomposition is carried out, and the expression is as follows:
Figure 970230DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure 621791DEST_PATH_IMAGE017
、
Figure 667108DEST_PATH_IMAGE048
and
Figure 548793DEST_PATH_IMAGE049
respectively corresponding to a left singular vector, a singular value and a right singular vector of the signal subspace;
Figure 636835DEST_PATH_IMAGE020
、
Figure 903868DEST_PATH_IMAGE021
and
Figure 791184DEST_PATH_IMAGE022
corresponding to the right singular vector, singular value and right singular vector of the noise subspace, respectively.
And 4, step 4: mapping noise subspaces to Mini-Norm form
For a complex exponential type grid frequency estimation,
Figure 194483DEST_PATH_IMAGE020
is composed of
Figure 453426DEST_PATH_IMAGE050
Dimension matrix, let
Figure 145439DEST_PATH_IMAGE051
Is composed of
Figure 882451DEST_PATH_IMAGE020
The Mini-Norm form (1), wherein,
Figure 405836DEST_PATH_IMAGE052
the expression of (a) is:
Figure 22631DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure 998677DEST_PATH_IMAGE027
，
Figure 539380DEST_PATH_IMAGE028
，
Figure 120534DEST_PATH_IMAGE029
is that
Figure 455701DEST_PATH_IMAGE030
The transpose of (a) is performed,
Figure 184622DEST_PATH_IMAGE031
。
and 5: solving the polynomial to obtain the estimated value of the frequency
According to
Figure 951852DEST_PATH_IMAGE053
Establishing a polynomial expression:
Figure 449830DEST_PATH_IMAGE034
solving a polynomial by
Figure 955897DEST_PATH_IMAGE035
The mode is a positive value closest to 1, and the grid frequency estimation value is
Figure 109798DEST_PATH_IMAGE036
Is that
Figure 992303DEST_PATH_IMAGE054
. Wherein the content of the first and second substances,
Figure 531738DEST_PATH_IMAGE038
representative pair
Figure 474286DEST_PATH_IMAGE035
Taking the imaginary part of the signal to be processed,
Figure 912221DEST_PATH_IMAGE039
representative pair
Figure 270521DEST_PATH_IMAGE035
Taking a real part of the signal,
Figure 743091DEST_PATH_IMAGE040
represents the function of the inverse tangent of the line,
Figure 590961DEST_PATH_IMAGE041
representing a sequence of acquired samples
Figure 204607DEST_PATH_IMAGE042
The sampling frequency of the time.
Step 6: simulation result
The invention aims at power grid frequency estimation method simulation based on a root Mini-Norm. In the simulation, the assumption is made
Figure 428915DEST_PATH_IMAGE055
,
Figure 755991DEST_PATH_IMAGE056
，
Figure 978025DEST_PATH_IMAGE057
. A sample sequence at a signal-to-noise ratio of 10dB, as shown in fig. 2. From fig. 3 and 4, it can be seen that the power grid frequency estimation performance based on the root Mini-Norm is substantially consistent with the estimation performance of the MUSIC method.
According to the simulation result, the data are decomposed into the multi-dimensional signal subspace and the multi-dimensional noise subspace by adopting the MUSIC algorithm in the spectrum decomposition, then the multi-dimensional noise subspace is mapped into the one-dimensional vector, and finally, the power grid center frequency is calculated by adopting a polynomial root-finding method according to the characteristic that the power grid center frequency is one and the corresponding complex exponential model is two. The method can not only achieve the power grid frequency estimation performance of the multidimensional noise subspace, but also reduce the calculated amount.
The above embodiments do not limit the present invention in any way, and all technical solutions obtained by means of equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims (1)

1. A power grid frequency estimation method based on a root Mini-Norm is characterized by comprising the following steps: aiming at steady-state power grid sampling data of an additive Gaussian noise background, designing a complex index model of the sampling data, then performing asymptotic unbiased autocorrelation processing on the sampling data, then decomposing the data after autocorrelation processing into a multi-dimensional signal subspace and a multi-dimensional noise subspace by adopting an MUSIC algorithm in spectrum decomposition, mapping the multi-dimensional noise subspace into a one-dimensional vector, and finally calculating the power grid center frequency by adopting a polynomial root-solving method aiming at the characteristics that the power grid center frequency is one and the corresponding complex index model is two; which comprises the following steps:
step 1: selecting a section of sine signal sampling sequence sampled at equal intervals
Figure DEST_PATH_IMAGE001
Wherein, in the step (A),
Figure 157788DEST_PATH_IMAGE002
represents a vector of a sequence of samples representing the sequence of samples,
Figure DEST_PATH_IMAGE003
represents the first
Figure 887977DEST_PATH_IMAGE004
The number of sequential samples of the data is,
Figure DEST_PATH_IMAGE005
，
Figure 730031DEST_PATH_IMAGE006
representing the total number of sampled data;
step 2: to the sampling sequence vector
Figure 125241DEST_PATH_IMAGE002
Performing asymptotic unbiased autocorrelation operation to obtain autocorrelation vector
Figure DEST_PATH_IMAGE007
，
Figure 254127DEST_PATH_IMAGE008
The expression of (a) is:
Figure DEST_PATH_IMAGE009
wherein the content of the first and second substances,
Figure 138906DEST_PATH_IMAGE010
representative pair
Figure DEST_PATH_IMAGE011
The conjugation is taken out and the reaction is carried out,
Figure 405940DEST_PATH_IMAGE012
，
Figure DEST_PATH_IMAGE013
representing the number of autocorrelation vectors;
and step 3: according to a given autocorrelation vector
Figure 417889DEST_PATH_IMAGE014
Will be
Figure 86768DEST_PATH_IMAGE014
Rewriting is in the form of Toeplitz matrix, set to
Figure DEST_PATH_IMAGE015
(ii) a To pair
Figure 142449DEST_PATH_IMAGE015
Singular value decomposition is carried out, and the expression is as follows:
Figure 896778DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE017
、
Figure 945374DEST_PATH_IMAGE018
and
Figure DEST_PATH_IMAGE019
respectively corresponding to a left singular vector, a singular value and a right singular vector of the signal subspace;
Figure 531076DEST_PATH_IMAGE020
、
Figure DEST_PATH_IMAGE021
and
Figure 773970DEST_PATH_IMAGE022
respectively corresponding to a right singular vector, a singular value and a right singular vector of the noise subspace;
and 4, step 4: for step 3
Figure 15595DEST_PATH_IMAGE020
Mapping to Mini-Norm form: for a complex exponential type grid frequency estimation,
Figure 290719DEST_PATH_IMAGE020
is composed of
Figure DEST_PATH_IMAGE023
Dimension matrix, let
Figure 996507DEST_PATH_IMAGE024
Is composed of
Figure 657906DEST_PATH_IMAGE020
The Mini-Norm form (1), wherein,
Figure DEST_PATH_IMAGE025
the expression of (a) is:
Figure 386828DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE027
，
Figure 527959DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE029
is that
Figure 838986DEST_PATH_IMAGE030
The transpose of (a) is performed,
Figure DEST_PATH_IMAGE031
；
and 5: let us say that in step 4
Figure 672950DEST_PATH_IMAGE032
According to
Figure DEST_PATH_IMAGE033
Establishing a polynomial expression:
Figure 623588DEST_PATH_IMAGE034
solving a polynomial by
Figure DEST_PATH_IMAGE035
The mode is a positive value closest to 1, and the grid frequency estimation value is
Figure 817678DEST_PATH_IMAGE036
Is that
Figure DEST_PATH_IMAGE037
(ii) a Wherein the content of the first and second substances,
Figure 232479DEST_PATH_IMAGE038
representative pair
Figure 175027DEST_PATH_IMAGE035
Taking the imaginary part of the signal to be processed,
Figure DEST_PATH_IMAGE039
representative pair
Figure 426011DEST_PATH_IMAGE035
Taking a real part of the signal,
Figure 846628DEST_PATH_IMAGE040
represents the function of the inverse tangent of the line,
Figure DEST_PATH_IMAGE041
representing a sequence of acquired samples
Figure 381514DEST_PATH_IMAGE042
The sampling frequency of the time.
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WO2021087728A1 (en) * 2019-11-05 2021-05-14 Alibaba Group Holding Limited Differential directional sensor system
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