CN113517686B - Low-frequency oscillation analysis method based on Givens orthogonal similarity transformation - Google Patents
Low-frequency oscillation analysis method based on Givens orthogonal similarity transformation Download PDFInfo
- Publication number
- CN113517686B CN113517686B CN202110488277.3A CN202110488277A CN113517686B CN 113517686 B CN113517686 B CN 113517686B CN 202110488277 A CN202110488277 A CN 202110488277A CN 113517686 B CN113517686 B CN 113517686B
- Authority
- CN
- China
- Prior art keywords
- matrix
- transformation
- low
- frequency oscillation
- givens
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/002—Flicker reduction, e.g. compensation of flicker introduced by non-linear load
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
Landscapes
- Physics & Mathematics (AREA)
- Nonlinear Science (AREA)
- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Complex Calculations (AREA)
Abstract
The invention discloses a low-frequency oscillation analysis method based on Givens orthogonal similarity transformation, which comprises the following steps: reading an oscillation signal, and determining the number of sampling points and sampling intervals of an input signal; solving the differential equation coefficient of the low-frequency oscillation Prony algorithm autoregressive model, forming a Hessenberg matrix corresponding to a high-order equation according to the differential equation coefficient, and recording the Hessenberg matrix as a matrix H; solving the eigenvalue of the matrix H through a double QR algorithm based on Givens similarity transformation; solving attenuation factors and frequencies of all main modes of low-frequency oscillation according to the eigenvalue of the matrix H; and forming a Jacobian matrix according to the characteristic roots, and solving the amplitude and phase angle of each main mode of the low-frequency oscillation by using a least square method. The invention applies double QR transformation based on Givens orthogonal similarity transformation during analysis and calculation, thereby greatly reducing the calculated amount and improving the calculation efficiency of low-frequency oscillation analysis of the power system.
Description
Technical Field
The invention relates to the technical field of power system automation, in particular to a low-frequency oscillation analysis method based on Givens orthogonal similarity transformation.
Background
With the increasing expansion of the interconnected region of the power grid and the increasing complexity of the structure and the model of the power system, the stability and the low-frequency oscillation of the power grid become more serious. The low-frequency oscillation is a primary problem threatening the stable operation of the power system and limiting the transmission capability of the interconnected power grid, and even causing the collapse of the power grid in severe cases, so that the analysis and control of the low-frequency oscillation become one of the important subjects of the power system stability research. The low-frequency oscillation frequency range of the power system is generally 0.2-2.5 Hz, the Prony algorithm can directly extract the amplitude, the phase, the frequency and the attenuation factor of the oscillation signal, and the method is the most widely applied method for identifying the current low-frequency oscillation mode. The algorithm belongs to a time domain method for modal parameter identification, and essentially adopts the mathematics of fitting an equally-spaced sampling signal by using a group of multi-order linear combinations of exponential terms and directly calculating the information of amplitude, phase, frequency, damping factor and the like of the signal. When the oscillation mode is multi-step and the sampling rate increases, the amount of computation to identify the oscillation amplitude and phase out increases exponentially.
In the current low-frequency oscillation Prony algorithm of the power system, after solving a regular equation of an Autoregressive (AR) model to obtain a difference equation coefficient, the problem of solving a real coefficient characteristic polynomial to obtain a root is solved, which corresponds to a characteristic value of a Hessenberg matrix, and a QR algorithm is usually adopted to solve by using a householder orthogonal similarity transformation. The Hessenberg matrix formed in the Prony algorithm is a highly sparse matrix, the sparse matrix is usually changed into a full matrix through householder transformation, the calculation amount of solution is increased, and the number of sampling points in the Prony algorithm sampling is usually far greater than the actual order of the system. The QR algorithm based on householder transformation solves the characteristic value of the Hessenberg matrix with high dimensionality and high sparsity, greatly increases the calculation time consumption, and is difficult to meet the real-time analysis requirement of a power grid, so that a proper orthogonal transformation matrix is selected, and the method plays a significant role in improving the efficiency of low-frequency oscillation analysis of a power system.
Disclosure of Invention
The invention provides a low-frequency oscillation analysis method based on Givens orthogonal similarity transformation, which aims to: the calculation efficiency of the low-frequency oscillation Prony analysis of the power system is improved.
The technical scheme of the invention is as follows:
a low-frequency oscillation analysis method based on GivenS orthogonal similarity transformation comprises the following steps:
s1: reading an oscillation signal, and determining the number of sampling points and sampling intervals of an input signal;
s2: solving the differential equation coefficient of the low-frequency oscillation Prony algorithm autoregressive model, forming a Hessenberg matrix corresponding to a high-order equation according to the differential equation coefficient, and recording the Hessenberg matrix as a matrix H;
s3: solving the eigenvalue of the matrix H through a double QR algorithm based on Givens similarity transformation;
s4: solving attenuation factors and frequencies of all main modes of low-frequency oscillation according to the eigenvalue of the matrix H;
s5: and forming a Jacobian matrix according to the characteristic values, and solving the amplitude and phase angle of each main mode of low-frequency oscillation by using a least square method.
As a further improvement of the method, the step S3 specifically includes the following steps:
s31: taking the matrix H as a current matrix A;
s32: finding out the position of the first zero element of the reciprocal of the secondary diagonal of the current matrix A to obtain the last diagonal block-irreducible quasi-triangular matrix C of the current matrix, wherein the matrix C is a lower right corner sub-matrix of the current matrix formed by all elements of the lower sides of the row partition lines and the right sides of the column partition lines by using the rows and the columns of the zero elements;
s33: judging the order of the diagonal block-irreducible quasi-triangular matrix C, if the order of the matrix C is 1 or 2, solving the eigenvalue of the matrix C, shrinking the current matrix A, returning to the step S32, otherwise, executing the step S34;
s34: performing double QR transformation based on Givens orthogonal similarity transformation on the current matrix A to obtain a quasi-triangular matrix B;
s35: and (4) taking the quasi-triangular matrix B as a new current matrix A, turning to step S32, and performing circular iterative operation until the order of the current matrix A is shrunk to zero, namely all eigenvalues of the matrix H are solved.
As a further improvement of the method, in step S34, the step of performing Givens orthogonal similarity transformation-based dual QR transformation on the current matrix a to obtain a quasi-triangular matrix B includes:
s341: determining an orthogonal transformation matrix G 0 And performing similarity transformation on the matrix A:
the orthogonal transformation matrix G 0 For melting
The first column is an upper triangle,
a dual QR transform matrix for matrix a to quasi-triangular matrix B:
B＝Q T AQ
where Q is an orthogonal matrix, origin shifted by μ 1 And mu 2 Is the eigenvalue of the sub-matrix of 2 x 2 order in the lower right corner of A;
s342: continuing to form a plurality of new similarity transformation matrixes by using Givens transformation
G 1 ，G 2 ，…，G i ，…，G n-2
By n-2 Givens transformations
Change matrix B 1 A quasi-triangular matrix B;
the relationship between the similarity transformation matrices is: q T ＝G n-2 …G 1 G 0 。
As a further improvement of the method, the orthogonal transformation matrix G of step S341 0 The determination method comprises the following steps:
first, the lower right hand corner second order sub-matrix of matrix A
Has a characteristic value of mu 1 And mu 2 Let δ be μ 1 +μ 2 ，ρ＝μ 1 μ 2 Then there is
Matrix array
Only the first three elements of (1) are non-zero, let this column be X 0 ＝(p 0 ，q 0 ，r 0 ，0，...，0) T X is obtained from the following formula 0 Non-zero elements of (a):
second, transform the matrix G using Givens 01 Through G 01 X 0 Erasure elementElement q 0 Is mixing X 0 Is changed to X' 0 ；
The transformation matrix G 01 Is composed of
Wherein
The calculation result is X' 0 ＝(p 1 ，0，r 0 ，0，...，0) T ；
Thirdly, transforming the matrix G by using Givens 02 Through G 02 X′ 0 Elimination of element r 0 (ii) a The transformation matrix G 02 Is composed of
Wherein
The transformation matrix G 01 And a transformation matrix G 02 The relationship between them is: g 0 ＝G 02 G 01 。
As a further improvement of the method, the method for calculating the attenuation factor and the frequency of each main mode of low-frequency oscillation in step S4 includes:
wherein z is i The characteristic root of the high-order equation corresponding to the characteristic value of the matrix H.
Compared with the prior art, the invention has the following beneficial effects: compared with householder transformation, the method applies double QR transformation based on Givens orthogonal similarity transformation in the Prony analysis and calculation, increases fewer non-zero injection elements in the transformation process, greatly reduces the calculated amount, improves the calculation efficiency of the Prony analysis of the low-frequency oscillation of the power system, and further improves the practicability of the low-frequency oscillation analysis of the power system.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings:
as shown in fig. 1, a Givens orthogonal similarity transformation-based low-frequency oscillation analysis method includes the following steps:
s1: and reading the oscillation signal, and determining the number of sampling points and the sampling interval of the input signal.
S2: and solving the coefficient of a differential equation of the low-frequency oscillation Prony algorithm autoregressive model, forming a corresponding high-order equation Hessenberg matrix according to the coefficient of the differential equation, and recording the matrix as a matrix H.
The concrete solving steps are as follows:
the Prony algorithm is directed to a signal identification method of sampling data at equal intervals, a model of the signal can be represented as a set of decaying sinusoidal components, and estimation values of sampling signals x (0), x (1), … and x (n-1) can be expressed as
Wherein, b i ，z i Assume complex, i.e.:
in the formula, A i Is the amplitude; alpha is alpha i Is an attenuation factor; f. of i Is the frequency; Δ t is the sampling interval.
To find the fitting parameters, the sum of squares of errors is minimized
A complex least squares problem can be solved, i.e., solved.
Namely, the linear difference equation of the constant coefficients is set as:
if z is to be i Viewed as the root of a linear constant coefficient difference equation, then z i Satisfy the characteristic equation
Then
The fitting to x (n) is a homogeneous solution of a constant coefficient linear difference equation, and the estimation error is set as e (n), that is
Substituting (5) into (3) to obtain
Wherein
A is obtained by solving the formula (5) i 、θ i 、α i 、f i Is estimated. Solving the AR model from the output signals generated by an Autoregressive (AR) model excited by the formula (5) x (n) which can be regarded as the noise E (n)The regular equation can obtain the coefficient a of the difference equation i . The least squares estimation for the (6) parameters is such that
And minimum.
According to formula (6) having (x), (n) with x n Is shown)
Consider equation (6) as a cost function with a variable as a
To minimize it, let
Then there is
Corresponding to a minimum error energy of
Definition of
Obtaining a normal equation form of the coefficient a in the Prony algorithm according to (10) and (11):
to obtain
For brevity, this is: r.a ═ R
Where the elements of the matrix R are calculated as follows:
wherein i, j is 1, 2, …, p
While
Where i is 1, 2, …, p.
The coefficient a of the difference equation is obtained from the above i Then substituting the formula to obtain z by polynomial root finding i
That is to say
As can be seen from the knowledge of linear algebra,
can be seen as an eigenpolynomial of some real matrix, and therefore the eigenroot z of the high-order equation is solved i The problem of (i ═ 1, 2., p) becomes the problem of finding all eigenvalues of the matrix. It can be verified that the matrix corresponding to the characteristic polynomial is the upper Hessenberg matrix
S3: since the matrix H is an upper Hessenberg matrix, all eigenvalues can be directly obtained by the dual QR algorithm.
The general steps of the real matrix double QR algorithm, the double QR conversion from the matrix A to the matrix B, and the calculation process is summarized as
B＝Q T AQ (20)
Where A and B are both real matrices, Q is an orthogonal matrix, and the origin is shifted by mu 1 And mu 2 Is the eigenvalue of the sub-matrix of order 2 × 2 in the lower right corner of a.
Obviously, the key to the transformation is how to solve the orthogonal matrix Q. Because the essence of QR decomposition is a real matrix
Is an upper triangle:
and Q T Can take the product of n-1 orthogonal matrices
Q T ＝G n-2 …G 1 G 0
Matrix G 0 ，G 1 ，…，G n-2 Have the effect of multiplying them to the left
Then, the first n-1 columns are sequentially arranged as upper triangles. Therefore, the number of the first and second electrodes is increased,orthogonal similarity transformation B ═ Q T AQ can be decomposed into n-1 orthogonal similarity transforms
That is to say, QR decomposition
And similarity transformation B ═ Q T AQ can be performed simultaneously without the need to find the matrix Q.
In this embodiment, the eigenvalue of the matrix H is solved by a dual QR algorithm based on Givens similarity transformation, and the specific steps are as follows:
s31: taking the matrix H as the current matrix A.
S32: and finding out the position of the zero element which is the first zero element of the last diagonal of the current matrix A to obtain the final diagonal block-irreducible quasi-triangular matrix C of the current matrix, wherein the matrix C is a sub-matrix at the lower right corner of the current matrix formed by all elements of the row and column parting lines where the zero element is located, the lower sides of the row parting lines and the right sides of the column parting lines.
S33: and judging the order of the diagonal block-irreducible quasi-triangular matrix C, if the order of the matrix C is 1 or 2, solving the eigenvalue of the matrix C, shrinking the current matrix A (the shrunk matrix is the upper left corner sub-matrix corresponding to the lower right corner sub-matrix in the step S32), returning to the step S32, and otherwise, executing the step S34.
S34: performing double QR transformation based on Givens orthogonal similarity transformation on the current matrix A to obtain a quasi-triangular matrix B, which comprises the following steps:
s341: determining an orthogonal transformation matrix G 0 And performing similarity transformation on the matrix A:
the orthogonal transformation matrix G 0 For melting
The first column is an upper triangle.
The orthogonal transformation matrix G 0 The determination method comprises the following steps:
first, the lower right hand corner second order sub-matrix of matrix A
Has a characteristic value of mu 1 And mu 2 Let δ be μ 1 +μ 2 ，ρ＝μ 1 μ 2 Then there is
Since A is a quasi-triangular matrix, the matrix
Only the first three elements of (1) are non-zero, let this column be X 0 ＝(p 0 ，q 0 ，r 0 0, 0.., 0) T, X is obtained from the following formula 0 Non-zero elements of (a):
second, transform the matrix G using Givens 01 Through G 01 X 0 Elimination of element q 0 Is mixing X 0 Is changed to X' 0 ；
The transformation matrix G 01 Is composed of
Wherein
I n-2 Is an n-2 order identity matrix, matrix G 01 Wherein the elements not shown represent zero elements, and the calculation result is X' 0 ＝(p 1 ，0，r 0 ，0，...，0)T；
Thirdly, transforming the matrix G by using Givens 02 Through G 02 X′ 0 Elimination of element r 0 ；
The transformation matrix G 02 Is composed of
Wherein
The transformation matrix G 01 And a transformation matrix G 02 The relationship between them is: g 0 ＝G 02 G 01 By G 0 The result of the similarity transformation performed on the alignment triangle array A is
Where elements not indicated in the matrix represent zero elements, x represents non-zero elements, and … represents elements similar to the preceding matrix elements (zero or non-zero elements).
The right side position of the secondary diagonal is 0 element after Givens is multiplied by right, the position is 0, the multiplication operation of the position element is reduced in the transformation process, and the calculation iteration times are very large under the condition that the matrix dimension is very large, so that the calculation amount is greatly reduced.
It can be seen that the current matrix B 1 Still not a Hessenberg matrix (quasi-triangular matrix), quantization matrix B 1 The quasi-triangular matrix B is calculated by using n-2 Givens transformations, as detailed in step S342.
S342: continuing to form a new similarity transformation matrix G by using Givens transformation 1 ，G 2 ，…，G i ，…，G n-2 By n-2 Givens transformations
Change matrix B 1 A quasi-triangular matrix B; the relationship between the similarity transformation matrices is: q T ＝G n-2 …G 1 G 0 。
The above-mentioned elementary orthogonal matrix G i (i-1, 2.., n-2) has the same meaning as G 0 Similar simple equations.
For matrix B 1 If B is ordered 1 Is first column of (1) is X 1 Then matrix G 1 Should make the linear transformation G 1 X 1 Elimination of X 1 Element q of (1) 1 And r 1 In the visible, see G 1 Equation of (c) and block diagonal form and G 0 And the like. Successively transformed according to the respective similarity transformation matrices, in general, B i And B 1 Similarly, there are only three non-zero elements below the minor diagonal (two in column i, one in column i + 1)
If the ith column is X i ＝(×，×，...，p i ，q i ，r i ，0，...，0) T Parameter p thereof i 、q i 、r i (i-0, 1.., n-2) from the corresponding matrix B i The ith column of (1):
when i is n-2, there are
Transforming matrix G with Givens i The purpose of which is to convert by pair X i Is linearly transformed G i X i Post-elimination of element q therein i And r i The conversion steps are divided into two steps:
first, transform the matrix G using Givens i1 Through G i1 X i Elimination of element q 0 Is mixing X i Is changed to X' i ；
The transformation matrix G i1 Is composed of
Wherein
The result of the calculation is X i1 ＝(p i1 ，0，r i ，0，...，0) T 。
Second, transform the matrix G using Givens i2 Through G i2 X′ i Elimination of element r i ；
The transformation matrix G i2 Is composed of
Wherein
The transformation matrix G i1 And a transformation matrix G i2 The relationship between them is: g i ＝G i2 G i1 。
S35: and (4) taking the quasi-triangular matrix B as a new current matrix A, turning to the step S32, and performing loop iteration operation until the order of the current matrix A is shrunk to zero, namely all eigenvalues of the matrix H are solved.
S4: and solving the attenuation factor and the frequency of each main mode of the low-frequency oscillation according to the eigenvalue of the matrix H, wherein the calculation formula is as follows:
wherein z is i The characteristic root of the high-order equation corresponding to the characteristic value of the matrix H.
S5: and forming a Jacobian matrix according to the characteristic roots, and solving the amplitude and phase angle of each main mode of the low-frequency oscillation by using a least square method.
In summary, in the Givens orthogonal similarity transformation-based power system low-frequency oscillation Prony algorithm, fitting a sampling value is a homogeneous solution of a constant coefficient linear difference equation, and under the condition that the coefficient of the difference equation is known, the root can be solved according to the characteristic equation of the difference equation, namely, the characteristic value of a Hessenberg matrix formed by the coefficients of the difference equation is solved. In actual sampling, the number of sampling points is usually much larger than the actual order of the system, and under the condition of unclear system models, in order to make the sample matrix contain the comprehensive characteristics of signals as much as possible, the dimension of the sample matrix takes the maximum value, and the initial order is generally selected to be half of the number of sampling points, namely N/2, so that the dimension of the Hessenberg matrix is larger.
Method for repeatedly utilizing similarity transformation GAG in double QR algorithm T Usually, the left multiplication is to realize the elimination operation of non-zero elements under the secondary diagonal through Givens orthogonal transformation, when the elements above the diagonal of the matrix a are a full matrix or a matrix with higher packing density, the calculation amount is relatively small by utilizing householder transformation, but a Hessenberg matrix formed by difference equation coefficients in a Prony algorithm has the characteristic of high sparseness, the original corresponding row and column can be changed into the full matrix after the householder transformation, on one hand, the Givens transformation increases relatively few non-zero injection elements in the transformation process, one element is less in each calculation, and when the calculation times are increased by explosion, the correspondingly reduced calculation amount is very considerable. On the other hand, the programming is simple without calculation3 × 3 matrix of householder transforms.
Through practical verification of a low-frequency oscillation signal of a certain power grid, the sampling frequency is 20hz, the number of sampling points is 200, the order is 100, a Hessenberg matrix is 100 multiplied by 100, the characteristic value multiplication and addition operation is 6189681 times by adopting a double QR algorithm based on Householder transformation, the characteristic value multiplication and addition operation frequency is 4933812 by adopting the method, the operation efficiency is improved by 21%, the floating point multiplication and addition operation frequency is reduced, the calculation efficiency is improved, and the practicability of low-frequency oscillation analysis of the power system is further improved.
Claims (2)
1. A low-frequency oscillation analysis method based on Givens orthogonal similarity transformation is characterized in that: the method comprises the following steps:
s1: reading an oscillation signal, and determining the number of sampling points and sampling intervals of an input signal;
s2: solving the differential equation coefficient of the low-frequency oscillation Prony algorithm autoregressive model, forming a Hessenberg matrix corresponding to a high-order equation according to the differential equation coefficient, and recording the Hessenberg matrix as a matrix H;
s3: solving the eigenvalue of the matrix H through a double QR algorithm based on Givens orthogonal similarity transformation;
s4: solving attenuation factors and frequencies of all main modes of low-frequency oscillation according to the eigenvalue of the matrix H;
s5: forming a Jacobian matrix according to the characteristic values, and solving the amplitude and phase angle of each main mode of low-frequency oscillation by using a least square method;
step S3 specifically includes the following steps:
s31: taking the matrix H as a current matrix A;
s32: finding out the position of the first zero element of the next diagonal of the current matrix A to obtain the last diagonal block of the current matrix, namely an irreducible quasi-triangular matrix C, wherein the matrix C is a sub-matrix of the lower right corner of the current matrix formed by all elements on the lower sides of row partition lines and the right sides of column partition lines, and the row and column partition lines where the zero element is located;
s33: judging the order of the diagonal block-irreducible quasi-triangular matrix C, if the order of the matrix C is 1 or 2, solving the eigenvalue of the matrix C, shrinking the current matrix A, returning to the step S32, otherwise, executing the step S34;
s34: performing double QR transformation based on Givens orthogonal similarity transformation on the current matrix A to obtain a quasi-triangular matrix B;
s35: taking the quasi-triangular matrix B as a new current matrix A, turning to the step S32, and performing loop iteration operation until the order of the current matrix A is shrunk to zero, namely all eigenvalues of the matrix H are solved;
step S34, the step of obtaining the quasi-triangular matrix B by performing Givens orthogonal similarity transformation-based double QR transformation on the current matrix a includes:
s341: determining a similarity transformation matrix G 0 And performing similarity transformation on the matrix A:
the similarity transformation matrix G 0 For melting
The first column is an upper triangle,
a dual QR transform matrix for matrix a to quasi-triangular matrix B:
B＝Q T AQ
where Q is an orthogonal matrix, R is an upper triangular matrix, I is an identity matrix, origin shift μ 1 And mu 2 Is the eigenvalue of the sub-matrix of 2 × 2 order in the lower right corner of a;
s342: continuing to form a plurality of new similarity transformation matrixes G by utilizing Givens transformation 1 ，G 2 ，…，G i ，…，G n-2
By n-2 Givens transformations
Change matrix B 1 A quasi-triangular matrix B;
the relationship between the similarity transformation matrices is: q T ＝G n-2 …G 1 G 0 ；
Step S341 the similarity transformation matrix G 0 The determination method comprises the following steps:
first, the lower right hand corner second order sub-matrix of matrix A
Has a characteristic value of mu 1 And mu 2 Let δ be μ 1 +μ 2 ，ρ＝μ 1 μ 2 Then there is
Matrix array
Only the first three elements of (1) are non-zero, let this column be X 0 ＝(p 0 ,q 0 ,r 0 ,0,…,0) T X is obtained from the following formula 0 Non-zero elements of (a):
second, transform the matrix G using Givens 01 Through G 01 X 0 Elimination of element q 0 Is mixing X 0 Is changed to X' 0 ；
The transformation matrix G 01 Is composed of
Wherein, I n-2 Is an n-2 order identity matrix;
the calculation result is X' 0 ＝(p 1 ,0,r 0 ,0,…,0) T ；
Thirdly, transforming the matrix G by using Givens 02 Through G 02 X′ 0 Elimination of element r 0 ；
The transformation matrix G 02 Is composed of
Wherein, I n-3 Is an n-3 order identity matrix;
the transformation matrix G 01 And a transformation matrix G 02 The relationship between them is: g 0 ＝G 02 G 01 。
2. A Givens orthogonal similarity transformation-based low-frequency oscillation analysis method as claimed in claim 1, wherein: step S4 is a method for calculating the attenuation factor and the frequency of each main mode of the low-frequency oscillation, including:
wherein z is i Being a matrix HAnd delta t is a sampling interval of the characteristic root of the high-order equation corresponding to the characteristic value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110488277.3A CN113517686B (en) | 2021-05-06 | 2021-05-06 | Low-frequency oscillation analysis method based on Givens orthogonal similarity transformation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110488277.3A CN113517686B (en) | 2021-05-06 | 2021-05-06 | Low-frequency oscillation analysis method based on Givens orthogonal similarity transformation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113517686A CN113517686A (en) | 2021-10-19 |
| CN113517686B true CN113517686B (en) | 2022-09-20 |
Family
ID=78064071
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110488277.3A Active CN113517686B (en) | 2021-05-06 | 2021-05-06 | Low-frequency oscillation analysis method based on Givens orthogonal similarity transformation |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113517686B (en) |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010028469A (en) * | 2008-07-18 | 2010-02-04 | Kyoto Univ | Receiving device and receiving method |
| WO2010135745A1 (en) * | 2009-05-22 | 2010-11-25 | Maxlinear, Inc. | Signal processing block for a receiver in wireless communication |
| CN104091092A (en) * | 2014-07-29 | 2014-10-08 | 上海交通大学 | Feature value analysis system for small-interference stability of large-scale power system |
| CN105740209A (en) * | 2016-01-28 | 2016-07-06 | 大连海事大学 | Givens iteration based Prony analysis method for low frequency oscillation |
| CN106526359A (en) * | 2016-10-21 | 2017-03-22 | 国网新疆电力公司电力科学研究院 | Prony algorithm and ill-conditioned data analysis-based power grid low-frequency oscillation on-line detection algorithm |
| CN106845010A (en) * | 2017-02-16 | 2017-06-13 | 西南交通大学 | Based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony |
| CN112749369A (en) * | 2021-01-19 | 2021-05-04 | 东方电子股份有限公司 | Power system state estimation method based on Givens orthogonal transformation |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103630742B (en) * | 2013-12-16 | 2015-09-30 | 国家电网公司 | A kind of acquisition methods of dynamic signal parameter |
-
2021
- 2021-05-06 CN CN202110488277.3A patent/CN113517686B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2010028469A (en) * | 2008-07-18 | 2010-02-04 | Kyoto Univ | Receiving device and receiving method |
| WO2010135745A1 (en) * | 2009-05-22 | 2010-11-25 | Maxlinear, Inc. | Signal processing block for a receiver in wireless communication |
| CN104091092A (en) * | 2014-07-29 | 2014-10-08 | 上海交通大学 | Feature value analysis system for small-interference stability of large-scale power system |
| CN105740209A (en) * | 2016-01-28 | 2016-07-06 | 大连海事大学 | Givens iteration based Prony analysis method for low frequency oscillation |
| CN106526359A (en) * | 2016-10-21 | 2017-03-22 | 国网新疆电力公司电力科学研究院 | Prony algorithm and ill-conditioned data analysis-based power grid low-frequency oscillation on-line detection algorithm |
| CN106845010A (en) * | 2017-02-16 | 2017-06-13 | 西南交通大学 | Based on the low-frequency oscillation dominant pattern discrimination method for improving SVD noise reductions and Prony |
| CN112749369A (en) * | 2021-01-19 | 2021-05-04 | 东方电子股份有限公司 | Power system state estimation method based on Givens orthogonal transformation |
Non-Patent Citations (1)
| Title |
|---|
| 基于改进Prony法的电力***低频振荡快衰分量辨识;牟建伟等;《电气工程学报》;机械工业信息研究院;20181231;第13卷(第12期);第36-40页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113517686A (en) | 2021-10-19 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Cheng et al. | Exponential convergence and H‐c multiquadric collocation method for partial differential equations | |
| Collins | Renormalization: an introduction to renormalization, the renormalization group and the operator-product expansion | |
| Faßbender | Symplectic methods for the symplectic eigenproblem | |
| Dale et al. | Spatial autocorrelation and statistical tests: some solutions | |
| Batselier et al. | Computing low-rank approximations of large-scale matrices with the tensor network randomized SVD | |
| Kibangou et al. | Tensor analysis-based model structure determination and parameter estimation for block-oriented nonlinear systems | |
| Anton et al. | Weak symplectic schemes for stochastic Hamiltonian equations | |
| Kouri et al. | Inverse scattering theory: Renormalization of the Lippmann-Schwinger equation for acoustic scattering in one dimension | |
| CN113517686B (en) | Low-frequency oscillation analysis method based on Givens orthogonal similarity transformation | |
| Buzzard | Efficient basis change for sparse‐grid interpolating polynomials with application to T‐cell sensitivity analysis | |
| Carroll | Adding filters to improve reservoir computer performance | |
| Aryani et al. | A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process | |
| Shim et al. | Non-crossing quantile regression via doubly penalized kernel machine | |
| Merdan et al. | Solving of some random partial differential equations by using differential transformation method and laplace-padé method | |
| Bailey et al. | Experimental mathematics: recent developments and future outlook | |
| Rincón et al. | Wavelet-RKHS-based functional statistical classification | |
| He et al. | Large‐scale super‐Gaussian sources separation using Fast‐ICA with rational nonlinearities | |
| Bar‐Yoseph et al. | An efficient L2 Galerkin finite element method for multi‐dimensional non‐linear hyperbolic systems | |
| Nguyen et al. | A deep learning approach for solving Poisson’s equations | |
| Usevich | Decomposing multivariate polynomials with structured low-rank matrix completion | |
| CN114548400A (en) | Rapid flexible full-pure embedded neural network wide area optimization training method | |
| Rontogiannis et al. | An adaptive LS algorithm based on orthogonal Householder transformations | |
| Bostan et al. | Algebraic diagonals and walks | |
| Benner et al. | GR decompositions and their relations to Cholesky‐like factorizations | |
| Yaghouti et al. | Choosing the best value of shape parameter in radial basis functions by Leave-P-Out Cross Validation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |