Power system oscillation parameter identification method and device based on improved matrix pencil algorithm

Abstract

The application provides a power system oscillation parameter identification method and device based on an improved matrix pencil algorithm, wherein the method comprises the following steps: converting a mathematical model of power system synchronous phasor into a modal model composed of four complex exponents and four constant parameter linear combinations; establishing a Hankel matrix according to the synchronous phasor data, and decomposing the Hankel matrix into multiple sub-Hankel matrices; constructing a matrix pencil according to every adjacent two sub-Hankel matrices, and solving characteristic polynomial coefficients of the matrix pencil; and establishing a characteristic polynomial equation of positive / negative angular frequency exponents of a fundamental component and an oscillation component based on the characteristic polynomial coefficients of the matrix pencil, so that the fundamental component angular frequency and the oscillation component angular frequency which are closest to the matrix pencil eigenvalues can be obtained while satisfying the conjugate constraints between the angular frequencies of the two modalities of the fundamental component and the conjugate constraints between the angular frequencies of the two modalities of the oscillation component, and the identification precision of the fundamental parameter, the subsynchronous oscillation parameter and the supersynchronous parameter is effectively improved.

Description

Technical Field

[0001] This invention relates to the field of wide-area monitoring and subsynchronous oscillation technology for power systems, and particularly to a method and apparatus for identifying power system oscillation parameters based on an improved matrix bundle algorithm. Background Technology

[0002] In modern power systems, subsynchronous oscillations are mainly caused by resonance between large-scale renewable energy generation units and transmission lines. Subsynchronous oscillations can significantly reduce system transmission capacity, jeopardize system safety, and even lead to system instability. Therefore, close monitoring of the dynamic process of subsynchronous oscillations in power systems is necessary. While wide-area measurement systems and synchronization phasor measurement terminals can effectively monitor subsynchronous oscillation events in power systems, the fundamental, subsynchronous, and supersynchronous components (frequency deviations from the rated frequency) appear in the synchronization phasor data through spectral leakage, making it difficult to accurately obtain the frequency, amplitude, and phase of each component in the subsynchronous oscillation.

[0003] Previous studies have shown that the phasor data under subsynchronous oscillation consists of a linear combination of four modes, two of which are related to the fundamental frequency component and the other two to the subsynchronous oscillation component. Therefore, some scholars have proposed using the Matrix Bundle Mode Extraction (MPM) algorithm to solve for the subsynchronous oscillation parameters and employing truncated singular value decomposition to improve the reliability of identification. The main idea of ​​the MPM algorithm is to construct a matrix bundle using two adjacent Hankel matrices and extract modes by solving the eigenvalues ​​of the matrix bundle. However, this method of directly solving for eigenvalues ​​ignores the conjugate constraints between the angular frequencies of the two modes related to the fundamental frequency component and the two modes related to the subsynchronous oscillation component. Under noisy conditions, the calculated eigenvalues ​​do not satisfy these two conjugate constraints due to noise, resulting in large errors in the mode parameters and consequently, large errors in the parameter identification of each component. Furthermore, this method only considers the subsynchronous oscillation component and does not consider the supersynchronous component coupled to it. Summary of the Invention

[0004] The embodiments of the present invention provide a method and apparatus for identifying power system oscillation parameters based on an improved matrix beam algorithm, which is used to solve the problems existing in the prior art.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] A power system oscillation parameter identification method based on an improved matrix bundle algorithm includes: S1 models the power system synchronization phasor as a mathematical model consisting of a fundamental positive frequency component, a fundamental negative frequency component, an oscillating positive frequency component, and an oscillating negative frequency component; wherein, the oscillating positive frequency component is synthesized from the subsynchronous positive frequency component and the supersynchronous negative frequency component, and the oscillating negative frequency component is synthesized from the subsynchronous negative frequency component and the supersynchronous positive frequency component. S2 transforms the mathematical model of the power system synchronization phasor into a modal model consisting of a linear combination of four complex exponents and four constant parameters; the four complex exponents include: the positive and negative angular frequency exponents of the fundamental component, and the positive and negative angular frequency exponents of the oscillation component. S3. Based on the synchronization phasor data, a Hankel matrix is ​​established, and the Hankel matrix is ​​decomposed into multiple sub-Hankel matrices; S4 Constructs a matrix bundle based on each pair of adjacent sub-Hankel matrices and solves for the coefficients of the characteristic polynomial of the matrix bundle; S5 Based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the fundamental component, establish the characteristic polynomial equations for the positive and negative angular frequency indices of the fundamental component; based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the oscillation component, establish the characteristic polynomial equations for the positive and negative angular frequency indices of the oscillation component. S6 Based on the numerical solution method, the characteristic polynomial equations of the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component are solved respectively. The angular frequency of the fundamental component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the fundamental component is obtained, as well as the angular frequency of the oscillating component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the oscillating component. S7 Based on the angular frequencies of the fundamental component and the oscillation component obtained in step S6, solve for the four constant parameters in the modal model. S8 Based on the angular frequency of the fundamental component and the angular frequency of the oscillation component, as well as the four constant parameters in the modal model obtained in step S7, the calculated values ​​of the fundamental positive frequency component, the fundamental negative frequency component, the oscillation positive frequency component, and the oscillation negative frequency component are obtained by calculation. S9 Based on the calculated values ​​of the fundamental positive frequency component and the fundamental negative frequency component, the frequency, amplitude, and phase of the fundamental component are obtained through calculation; based on the calculated values ​​of the oscillation positive frequency component and the oscillation negative frequency component, the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the calculated values ​​of the supersynchronous sinusoidal component, are obtained through calculation.

[0007] Preferably, step S1 includes: Through (1) Establish an instantaneous signal model for the power system; where, It is an instantaneous signal; Through (2) For instantaneous signals Corresponding synchronization phasor sequence Perform a discrete Fourier transform; Based on equation (2), through equation (3) A mathematical model of the synchronous phasors of the power system is established; among which, , , , , , , In the formula, For the first One synchronous phasor; and These are the fundamental positive frequency component and the fundamental negative frequency component, respectively. and These are the positive frequency component and the negative frequency component of the oscillation, respectively. and These are the positive and negative frequency components of the subsynchronization, respectively. and These are the positive and negative frequency components of supersynchronization, respectively. For complex conjugate notation; To calculate the number of data points in the data window for phasor synchronization, The rated frequency of the power system To synchronize the phasor data upload frequency, , , These represent the frequency, amplitude, and phase of the fundamental component at instantaneous values. , , These represent the amplitude, phase, and frequency of the subsynchronous component, respectively. , , These represent the amplitude, phase, and frequency of the supersynchronous component, respectively.

[0008] Preferably, step S2 includes: The mathematical model of the power system synchronization phasor is transformed to obtain the modal model consisting of a linear combination of four complex exponents and four constant parameters. (4) in, ; , , , , , , ; These are constant parameters for the fundamental positive frequency component. For the constant parameters of the fundamental negative frequency component, For the constant parameters of the positive frequency component of the oscillation, For the constant parameters of the negative frequency component of the oscillation, and These are the positive and negative angular frequency indices of the fundamental component, respectively. and These are the positive and negative angular frequency indices of the oscillation component, respectively.

[0009] Preferably, step S3 includes: Through (5) Establish the Hankel matrix; where, For synchronous phasors; Through (6) The Hankel matrix is ​​decomposed into multiple sub-Hankel matrices; where, For Hankel matrix, The number of synchronized phasor data. Less than constant, The number of sub-Hankel matrices. , … This is the sub-Hankel matrix.

[0010] Preferably, step S4 includes: Through (7) Construct a matrix bundle.

[0011] Preferably, step S5 includes: Through (8) Establish the characteristic polynomial equation for the positive angular frequency index of the fundamental component; where, , , , , The coefficients of the characteristic polynomial of the matrix bundle, is the positive angle frequency index of the fundamental component. The residuals of the characteristic polynomial equation for the positive angular frequency exponent of the fundamental component are indicated by superscripts (1), (2), ..., ( ). p -1) Corresponds to different matrix bundles; Through (9) Establish the characteristic polynomial equation for the negative angular frequency exponent of the fundamental component; where, The negative angular frequency index of the fundamental component. The residual of the characteristic polynomial equation for the negative angular frequency exponent of the fundamental component; Through (10) Establish the characteristic polynomial equation for the positive angular frequency exponent of the oscillating component; where, The positive angle frequency index of the oscillating component is given. The residual of the characteristic polynomial equation for the positive angular frequency exponent of the oscillating component; Through (11) Establish the characteristic polynomial equation for the negative angular frequency exponent of the oscillating component; where, The negative angular frequency index of the oscillating component. The residual of the characteristic polynomial equation for the negative angular frequency exponent of the oscillating component is given.

[0012] Preferably, step S6 includes: Through (12) Solve the characteristic polynomial equations for the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component, respectively.

[0013] Preferably, step S7 includes: Through (13) Solve for the four constant parameters in the modal model.

[0014] Preferably, step S9 includes: Through (14) (15) Calculate the frequency, amplitude, and phase of the fundamental component; Through (16) (17) (18) Obtain the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the frequency, amplitude, and phase of the supersynchronous sinusoidal component.

[0015] Secondly, the present invention provides a power system oscillation parameter identification device based on an improved matrix beam algorithm, comprising: The oscillation parameter identification module is used for: The power system synchronization phasor is modeled as a mathematical model consisting of a fundamental positive frequency component, a fundamental negative frequency component, an oscillating positive frequency component, and an oscillating negative frequency component; wherein, the oscillating positive frequency component is synthesized from the subsynchronous positive frequency component and the supersynchronous negative frequency component, and the oscillating negative frequency component is synthesized from the subsynchronous negative frequency component and the supersynchronous positive frequency component. The mathematical model of the power system synchronization phasor is transformed into a modal model consisting of a linear combination of four complex exponents and four constant parameters. The four complex exponents include the positive and negative angular frequency exponents of the fundamental component, and the positive and negative angular frequency exponents of the oscillation component. A Hankel matrix is ​​constructed based on the synchronization phasor data, and the Hankel matrix is ​​decomposed into multiple sub-Hankel matrices; Construct a matrix bundle based on each pair of adjacent sub-Hankel matrices, and solve for the coefficients of the characteristic polynomial of the matrix bundle; Based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the fundamental component, the characteristic polynomial equations for the positive and negative angular frequency indices of the fundamental component are established; based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the oscillation component, the characteristic polynomial equations for the positive and negative angular frequency indices of the oscillation component are established. Based on the numerical solution method, the characteristic polynomial equations of the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component are solved respectively. The angular frequencies of the fundamental component that minimize the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the fundamental component are obtained, as well as the angular frequencies of the oscillating component that minimize the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the oscillating component. Based on the angular frequencies of the fundamental component and the oscillation component obtained from the solution, the four constant parameters in the modal model are solved. Based on the angular frequencies of the fundamental component and the oscillation component, as well as the four constant parameters in the modal model obtained by performing the above step 7, the calculated values ​​of the fundamental positive frequency component, the fundamental negative frequency component, the oscillation positive frequency component, and the oscillation negative frequency component are obtained by calculation. Based on the calculated values ​​of the fundamental positive frequency component and the fundamental negative frequency component, the frequency, amplitude, and phase of the fundamental component are obtained through calculation; based on the calculated values ​​of the oscillation positive frequency component and the oscillation negative frequency component, the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the frequency, amplitude, and phase of the supersynchronous sinusoidal component, are obtained through calculation. The display module is used to output the calculated frequency, amplitude, and phase of the fundamental component; and the calculated values ​​of the frequency, amplitude, and phase of the positive oscillation frequency component, the negative oscillation frequency component, the subsynchronous sinusoidal component, and the supersynchronous sinusoidal component.

[0016] As can be seen from the technical solutions provided by the embodiments of the present invention above, the power system oscillation parameter identification method and apparatus based on the improved matrix bundle algorithm provided by the present invention includes: converting the mathematical model of the power system synchronization phasor into a modal model composed of a linear combination of four complex exponents and four constant parameters; establishing a Hankel matrix based on the synchronization phasor data and decomposing the Hankel matrix into multiple sub-Hankel matrices; constructing a matrix bundle based on each pair of adjacent sub-Hankel matrices and solving for the characteristic polynomial coefficients of the matrix bundle; establishing characteristic polynomial equations for the positive / negative angular frequency exponents of the fundamental component and the oscillation component based on the characteristic polynomial coefficients of the matrix bundle, which can obtain the fundamental component angular frequency and the oscillation component angular frequency that satisfy both the conjugate constraints between the two modes of the fundamental component and the conjugate constraints between the two modes of the oscillation component, and are closest to the eigenvalues ​​of the matrix bundle, thus effectively improving the identification accuracy of the fundamental parameters, subsynchronous oscillation parameters and supersynchronous oscillation parameters.

[0017] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 The flowchart of the power system oscillation parameter identification method based on the improved matrix beam algorithm provided by the present invention is shown below. Figure 2 The logic block diagram of the power system oscillation parameter identification device based on the improved matrix beam algorithm provided by the present invention is shown in the figure.

[0020] In the picture: 201. Oscillation Parameter Identification Module 202. Display Module. Detailed Implementation

[0021] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0022] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0023] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0024] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0025] See Figure 1 This invention provides a method for identifying power system oscillation parameters based on an improved matrix beam algorithm, comprising: S1 models the power system synchronization phasor as a mathematical model consisting of a fundamental positive frequency component, a fundamental negative frequency component, an oscillating positive frequency component, and an oscillating negative frequency component; wherein, the oscillating positive frequency component is synthesized from the subsynchronous positive frequency component and the supersynchronous negative frequency component, and the oscillating negative frequency component is synthesized from the subsynchronous negative frequency component and the supersynchronous positive frequency component. S2 transforms the mathematical model of the power system synchronization phasor into a modal model consisting of a linear combination of four complex exponents and four constant parameters; the four complex exponents include: the positive and negative angular frequency exponents of the fundamental component, and the positive and negative angular frequency exponents of the oscillation component. S3 establishes a Hankel matrix based on the synchronization phasor data and decomposes the Hankel matrix into multiple sub-Hankel matrices; S4 Constructs a matrix bundle based on each pair of adjacent sub-Hankel matrices and solves for the coefficients of the characteristic polynomial of the matrix bundle; S5 Based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the fundamental component, establish the characteristic polynomial equations for the positive and negative angular frequency indices of the fundamental component; based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the oscillation component, establish the characteristic polynomial equations for the positive and negative angular frequency indices of the oscillation component. S6 Based on the numerical solution method, the characteristic polynomial equations of the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component are solved respectively. The angular frequency of the fundamental component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the fundamental component is obtained, as well as the angular frequency of the oscillating component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the oscillating component. S7 Based on the angular frequencies of the fundamental component and the oscillation component obtained in step S6, solve for the four constant parameters in the modal model. S8 Based on the angular frequency of the fundamental component and the angular frequency of the oscillation component, as well as the four constant parameters in the modal model obtained in step S7, the calculated values ​​of the fundamental positive frequency component, the fundamental negative frequency component, the oscillation positive frequency component, and the oscillation negative frequency component are obtained by calculation. S9 Based on the calculated values ​​of the fundamental positive frequency component and the fundamental negative frequency component, the frequency, amplitude, and phase of the fundamental component are obtained through calculation; based on the calculated values ​​of the oscillation positive frequency component and the oscillation negative frequency component, the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the calculated values ​​of the supersynchronous sinusoidal component, are obtained through calculation.

[0026] In the embodiments provided by the present invention, the specific process of step S1 is as follows.

[0027] First, an instantaneous signal model of the power system is established, as shown in formula (1), which includes a fundamental component with a possible frequency shift, a pair of frequency-coupled subsynchronous components and supersynchronous components.

[0028] (1)

[0029] In the formula, It is an instantaneous signal.

[0030] Then, instantaneous signal Corresponding synchronization phasor sequence This can be obtained by performing a Discrete Fourier Transform (DFT) on equation (2). Since the Discrete Fourier Transform is a linear transform, we have: (2) In the formula, , and The results are the synchronization phasor results for the fundamental component, subsynchronous component, and supersynchronous component, respectively.

[0031] Then, a mathematical model of the power system synchronization phasors is established according to equation (2). The mathematical model of the power system synchronization phasors is as follows: (3) in, ; ; ; ; ; ; ; In the formula, For the first One synchronous phasor; and These are the fundamental positive frequency component and the fundamental negative frequency component, respectively. and These are the positive frequency component and the negative frequency component of the oscillation, respectively. and These are the positive and negative frequency components of the subsynchronization, respectively. and These are the positive and negative frequency components of supersynchronization, respectively. For complex conjugate notation; To calculate the number of data points in the data window for phasor synchronization, The rated frequency of the power system To synchronize the phasor data upload frequency, , , These represent the frequency, amplitude, and phase of the fundamental component at instantaneous values. , , These represent the amplitude, phase, and frequency of the subsynchronous component, respectively. , , These represent the amplitude, phase, and frequency of the supersynchronous component, respectively.

[0032] From the above formulas (2) and (3), and from the theory of discrete Fourier transform, it can be seen that... Depend on and It consists of two parts. The corresponding angular frequency is , The corresponding angular frequency is We can make the following assumptions without losing generality. The final result is determined based on subsequent calculations. or , that is, assuming It is a positive angle frequency. It is a negative angular frequency.

[0033] Depend on and It consists of two parts, taking into account , Corresponding positive angle frequency , Corresponding negative angular frequency Similarly, Depend on and It consists of two parts. Corresponding positive angle frequency , Corresponding negative angular frequency Based on the above derivation, the subsynchronous positive frequency component... and supersynchronous negative frequency components Synthesized into positive frequency components of oscillation The subsynchronous negative frequency component and supersynchronous positive frequency components Synthesized into oscillating negative frequency components .

[0034] Step S2 is to rewrite the mathematical model of the synchronization phasor into a modal model consisting of a linear combination of four complex exponents and four constant parameters. The four complex exponent parameters include: the positive and negative angular frequency exponents of the fundamental component, and the positive and negative angular frequency exponents of the oscillation component. The modal model is as follows: (4) in, ; ; ; ; ; ; ; ; In the formula, , , , are constant parameters. and These are the positive and negative angular frequency indices of the fundamental component, respectively. and These are the positive and negative angular frequency indices of the oscillation component, respectively.

[0035] In specific implementation, in step S2, the mathematical model of the synchronization phasor is rewritten into a modal model according to formula (4), where, These are constant parameters for the fundamental positive frequency component. For the constant parameters of the fundamental negative frequency component, For the constant parameters of the positive frequency component of the oscillation, For the constant parameters of the negative frequency component of the oscillation, and These are the positive and negative angular frequency indices of the fundamental component, respectively. and Let be the positive and negative angular frequency indices of the oscillation component, respectively. If we can calculate... , , , and , , , This allows us to solve for the frequency, amplitude, and phase of each component, thus transforming the identification of component parameters into the extraction of modal parameters.

[0036] The steps of existing MPM algorithms include: First, for Perform truncated singular value decomposition to reduce the impact of noise; then, the truncated singular value decomposition results... Split into and Two sub-Hankel matrices; finally, construct the matrix bundle. By solving Eigenvalues You can get , , , Then, the solution is obtained using the least squares method. , , , This method can solve accurately under ideal conditions, but the solution error is large under noise conditions. This is because truncated singular value decomposition can only eliminate smaller singular values ​​that are related to noise, while the noise in the larger singular values ​​that are retained cannot be eliminated. and The two sub-Hankel matrices still contain noise, which can be solved directly. When eigenvalues ​​are obtained, they are affected by noise. and Not satisfied and The conjugate relationship, and Also not satisfied and The conjugate relationship cannot be accurately solved. and This results in a large error in the parameter identification of each component.

[0037] According to the theory of MPM, in the eigenvalues Equal to any When (m=1,2,3,4), It is a reduced-rank matrix, at this time The determinant of is equal to 0, that is This expression is equivalent to ,Will Expanding by the characteristic polynomial yields: (5) In the formula, , , , , These are the coefficients of the characteristic polynomial.

[0038] Under ideal conditions, solve eigenvalues Because the constraint condition of pairwise conjugate among the four eigenvalues ​​was not considered when calculating the eigenvalues, under the influence of noise, eigenvalues Not satisfied and , and A pairwise conjugate relationship, and, will the correct , , , Substituting into formula (5), the value of the characteristic polynomial is not equal to zero, but approaches zero. Therefore, this embodiment of the invention proposes to... and Substitute the values ​​into formula (5) to establish the characteristic polynomial equation, and then find the polynomial equation whose residuals are minimized. and will and Substitute the values ​​into formula (5) to establish the characteristic polynomial equation, and then find the polynomial equation whose residuals are minimized. The result obtained in this way , , , It satisfies the pairwise conjugate constraint and is closest to the eigenvalues ​​of the matrix bundle, thus effectively improving the identification accuracy of each component parameter under noise conditions.

[0039] S3 is to build a Hankel matrix based on the synchronization phasor data and decompose the Hankel matrix into multiple sub-Hankel matrices.

[0040] In one embodiment, in step S3, the Hankel matrix is ​​as follows: (6) In the formula, For synchronous phasors; The sub-Hankel matrix is ​​as follows: (7) In the formula, For Hankel matrix, The number of synchronized phasor data. Less than constant, The number of sub-Hankel matrices. , … This is the sub-Hankel matrix.

[0041] S4 constructs a matrix bundle based on each pair of adjacent sub-Hankel matrices and solves for the characteristic polynomial coefficients of the matrix bundle.

[0042] In one embodiment, in step S4, the matrix bundle is as follows: (8) In the formula, , … These are the eigenvalues ​​of each matrix bundle.

[0043] In practical implementation, existing MPM algorithms will Split into and Construct a matrix bundle from two sub-Hankel matrices. Only one set of characteristic polynomial coefficients can be solved. In this embodiment of the invention, step S3 first... The matrix is ​​subjected to truncated singular value decomposition, retaining the first 4 singular values. Then, the singular value decomposition is performed using formulas (6) and (7). Split into , … Multiple sub-Hankel matrices are used. In step S4, the matrix bundles of each pair of adjacent sub-Hankel matrices are constructed according to formula (8). This allows for the solution of multiple sets of eigenvalue polynomial coefficients between each pair of adjacent sub-Hankel matrices. Under noise conditions, the corresponding eigenvalue polynomial coefficients of different matrix bundles are not the same. In this embodiment of the invention, the eigenvalue polynomial coefficients of the set of eigenvalue polynomial coefficients that are less affected by noise are selected for solution. and This can further improve the accuracy of identifying the parameters of each component.

[0044] Step S5 involves establishing the characteristic polynomial equations for the positive and negative angular frequency indices of the fundamental component based on the characteristic polynomial coefficients, the positive and negative angular frequency indices of the fundamental component; and establishing the characteristic polynomial equations for the positive and negative angular frequency indices of the oscillation component based on the characteristic polynomial coefficients, the positive and negative angular frequency indices of the oscillation component.

[0045] Specifically, the characteristic polynomial equation for the positive angular frequency index of the fundamental component is established as follows: (9) In the formula, , , , , The coefficients of the characteristic polynomial of the matrix bundle, is the positive angle frequency index of the fundamental component. The residuals of the characteristic polynomial equation for the positive angular frequency exponent of the fundamental component are indicated by superscripts (1), (2), ..., ( ). p -1) Corresponds to different matrix bundles.

[0046] The characteristic polynomial equation for the negative angular frequency index of the fundamental component is established as follows: (10) In the formula, The negative angular frequency index of the fundamental component. The residual of the characteristic polynomial equation for the negative angular frequency exponent of the fundamental component is given.

[0047] The characteristic polynomial equation of the positive angle frequency exponent of the oscillating component is established as follows: (11) In the formula, The positive angle frequency index of the oscillating component is given. The residual is the characteristic polynomial equation of the positive angular frequency exponent of the oscillating component.

[0048] The characteristic polynomial equation of the negative angular frequency exponent of the oscillating component is established as follows: (12) In the formula, The negative angular frequency index of the oscillating component. The residual of the characteristic polynomial equation for the negative angular frequency exponent of the oscillating component is given.

[0049] In the specific implementation process, in step S5, Substituting the coefficients of multiple sets of eigenvalue polynomials into formula (5), we establish the characteristic polynomial equation (9) of the positive angular frequency index of the fundamental component. Substituting multiple sets of eigenvalue polynomial coefficients into formula (5), we establish the characteristic polynomial equation (10) for the negative angular frequency index of the fundamental component; Substituting the coefficients of multiple eigenvalue polynomials into formula (5), we establish the characteristic polynomial equation (11) of the negative angular frequency exponent of the oscillating component. Substitute the coefficients of multiple eigenvalue polynomials into formula (5) to establish the characteristic polynomial equation (12) of the negative angular frequency exponent of the oscillating component.

[0050] Step S6 is based on numerical methods to find the angular frequency of the fundamental component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency indices of the fundamental component; and to find the angular frequency of the oscillating component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency indices of the oscillating component.

[0051] In practice, in step S6, the angular frequency of the fundamental component and the angular frequency of the oscillation component can be solved according to formula (13): (13) Step S7 involves solving for the four constant parameters in the modal model based on the angular frequencies of the fundamental component and the oscillation component obtained from the solution.

[0052] In a preferred embodiment, step S7 solves for the four constants as follows: (14) Step S8 is to determine the calculated values ​​of the fundamental positive frequency component, the fundamental negative frequency component, the oscillation positive frequency component, and the oscillation negative frequency component based on the angular frequency of the fundamental component, the angular frequency of the oscillation component, and the four constant parameters in the modal model.

[0053] Step S9 determines the frequency, amplitude, and phase of the fundamental component based on the calculated values ​​of the fundamental positive frequency component and the fundamental negative frequency component; and determines the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the frequency, amplitude, and phase of the supersynchronous sinusoidal component, based on the calculated values ​​of the oscillation positive frequency component and the oscillation negative frequency component.

[0054] In a preferred embodiment, step S10 determines the frequency, amplitude, and phase of the fundamental component in the following manner; (15) (16) The frequency, amplitude, and phase of the subsynchronous sinusoidal component, and the frequency, amplitude, and phase of the supersynchronous sinusoidal component, are determined as follows: (17) (18) (19).

[0055] The present invention also provides an embodiment to exemplarily demonstrate the correctness and effectiveness of the method provided by the present invention. A verification study was conducted using simulated PMU data with known parameters. The instantaneous value signal for generating the simulated PMU data is shown in formula (2), and the specific parameters are set as follows: system rated frequency... The fundamental frequency is 50 Hz. and phase The phases of the subsynchronous / supersynchronous oscillation components in the subsynchronous oscillation are fixed at 100 and 0 rad respectively. and Take amplitudes of 0.5 rad and 0.75 rad respectively. and To study the parameter identification accuracy characteristics of the embodiments of the present invention under the influence of noise, zero-mean white noise was added to the instantaneous value signal, and a signal-to-noise ratio (SNR) of 40dB was used, with values ​​of 20 and 10 respectively.

[0056] The performance of the improved matrix beam algorithm proposed in this invention embodiment is compared with that of existing matrix beam algorithms. The comparison results are shown in Table 1. and Take the four sets of data shown in Table 1 respectively, and use a data window of 200ms for both methods.

[0057] Table 1 Performance Comparison between Improved MPM and Existing MPM

[0058] As shown in Table 1, due to the influence of noise, the existing MPM algorithm has a relatively large error in identifying the parameters of each component. In particular, in the third and fourth groups of experiments, the two eigenvalues ​​corresponding to the fundamental component have the same sign, which does not satisfy the conjugate constraint and makes it difficult to accurately identify the fundamental frequency. As a result, the identification results of the fundamental amplitude and other component parameters are unusable. Compared with the existing MPM algorithm, the improved MPM algorithm of this embodiment can identify the parameters of each component more accurately.

[0059] Secondly, the present invention provides a power system oscillation parameter identification device based on an improved matrix beam algorithm, such as... Figure 2 As shown, it includes: Oscillation parameter identification module 201 is used for: The power system synchronization phasor is modeled as a mathematical model consisting of a fundamental positive frequency component, a fundamental negative frequency component, an oscillating positive frequency component, and an oscillating negative frequency component; wherein, the oscillating positive frequency component is synthesized from the subsynchronous positive frequency component and the supersynchronous negative frequency component, and the oscillating negative frequency component is synthesized from the subsynchronous negative frequency component and the supersynchronous positive frequency component. The mathematical model of the power system synchronization phasor is transformed into a modal model consisting of a linear combination of four complex exponents and four constant parameters. The four complex exponents include the positive and negative angular frequency exponents of the fundamental component, and the positive and negative angular frequency exponents of the oscillation component. A Hankel matrix is ​​constructed based on the synchronization phasor data, and the Hankel matrix is ​​decomposed into multiple sub-Hankel matrices; Construct a matrix bundle based on each pair of adjacent sub-Hankel matrices, and solve for the coefficients of the characteristic polynomial of the matrix bundle; Based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the fundamental component, the characteristic polynomial equations for the positive and negative angular frequency indices of the fundamental component are established; based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the oscillation component, the characteristic polynomial equations for the positive and negative angular frequency indices of the oscillation component are established. Based on the numerical solution method, the characteristic polynomial equations of the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component are solved respectively. The angular frequencies of the fundamental component that minimize the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the fundamental component are obtained, as well as the angular frequencies of the oscillating component that minimize the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the oscillating component. Based on the angular frequencies of the fundamental component and the oscillation component obtained from the solution, the four constant parameters in the modal model are solved. Based on the angular frequencies of the fundamental component and the oscillation component, as well as the four constant parameters in the modal model obtained by performing the above step 7, the calculated values ​​of the fundamental positive frequency component, the fundamental negative frequency component, the oscillation positive frequency component, and the oscillation negative frequency component are obtained by calculation. Based on the calculated values ​​of the fundamental positive frequency component and the fundamental negative frequency component, the frequency, amplitude, and phase of the fundamental component are obtained through calculation; based on the calculated values ​​of the oscillation positive frequency component and the oscillation negative frequency component, the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the frequency, amplitude, and phase of the supersynchronous sinusoidal component, are obtained through calculation. Display module 202 is used to output the calculated frequency, amplitude and phase of the fundamental component; and the calculated values ​​of the frequency, amplitude and phase of the positive frequency component, negative frequency component, subsynchronous sinusoidal component, and supersynchronous sinusoidal component.

[0060] In summary, the present invention provides a method and apparatus for identifying power system oscillation parameters based on an improved matrix bundle algorithm. The method includes: converting the mathematical model of the power system synchronization phasor into a modal model composed of a linear combination of four complex exponents and four constant parameters; establishing a Hankel matrix based on the synchronization phasor data and decomposing the Hankel matrix into multiple sub-Hankel matrices; constructing a matrix bundle based on each pair of adjacent sub-Hankel matrices and solving for the characteristic polynomial coefficients of the matrix bundle; and establishing characteristic polynomial equations for the positive / negative angular frequency exponents of the fundamental component and the oscillation component based on the characteristic polynomial coefficients of the matrix bundle. This yields fundamental component angular frequencies and oscillation component angular frequencies that satisfy both the conjugate constraints between the two modes of the fundamental component and the conjugate constraints between the two modes of the oscillation component, and are closest to the eigenvalues ​​of the matrix bundle, effectively improving the identification accuracy of fundamental parameters, subsynchronous oscillation parameters, and supersynchronous oscillation parameters.

[0061] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0062] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0063] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0064] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for identifying power system oscillation parameters based on an improved matrix bundle algorithm, characterized in that, include: S1 models the power system synchronization phasor as a mathematical model consisting of a fundamental positive frequency component, a fundamental negative frequency component, an oscillating positive frequency component, and an oscillating negative frequency component; wherein, the oscillating positive frequency component is synthesized from the subsynchronous positive frequency component and the supersynchronous negative frequency component, and the oscillating negative frequency component is synthesized from the subsynchronous negative frequency component and the supersynchronous positive frequency component. S2 transforms the mathematical model of the power system synchronization phasor into a modal model consisting of a linear combination of four complex exponents and four constant parameters; the four complex exponents include: the positive and negative angular frequency exponents of the fundamental component, and the positive and negative angular frequency exponents of the oscillation component. S3. Based on the synchronization phasor data, a Hankel matrix is ​​established, and the Hankel matrix is ​​decomposed into multiple sub-Hankel matrices; S4 Constructs a matrix bundle based on each pair of adjacent sub-Hankel matrices and solves for the coefficients of the characteristic polynomial of the matrix bundle; S5 Based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the fundamental component, establish the characteristic polynomial equations for the positive and negative angular frequency indices of the fundamental component; based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the oscillation component, establish the characteristic polynomial equations for the positive and negative angular frequency indices of the oscillation component. S6 Based on the numerical solution method, the characteristic polynomial equations of the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component are solved respectively. The angular frequency of the fundamental component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the fundamental component is obtained, as well as the angular frequency of the oscillating component that minimizes the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the oscillating component. S7 Based on the angular frequencies of the fundamental component and the oscillation component obtained in step S6, solve for the four constant parameters in the modal model. S8 Based on the angular frequency of the fundamental component and the angular frequency of the oscillation component, as well as the four constant parameters in the modal model obtained in step S7, the calculated values ​​of the fundamental positive frequency component, the fundamental negative frequency component, the oscillation positive frequency component, and the oscillation negative frequency component are obtained by calculation. S9 Based on the calculated values ​​of the fundamental positive frequency component and the fundamental negative frequency component, the frequency, amplitude, and phase of the fundamental component are obtained through calculation; based on the calculated values ​​of the oscillation positive frequency component and the oscillation negative frequency component, the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the calculated values ​​of the supersynchronous sinusoidal component, are obtained through calculation.

2. The method according to claim 1, characterized in that, Step S1 includes: Through （1） Establish an instantaneous signal model for the power system; where, It is an instantaneous signal; Through （2） For instantaneous signals Corresponding synchronization phasor sequence Perform a discrete Fourier transform; Based on equation (2), through equation （3） A mathematical model of the synchronous phasors of the power system is established; among which, , , , , , , In the formula, For the first One synchronous phasor; and These are the fundamental positive frequency component and the fundamental negative frequency component, respectively. and These are the positive frequency component and the negative frequency component of the oscillation, respectively. and These are the positive and negative frequency components of the subsynchronization, respectively. and These are the positive and negative frequency components of supersynchronization, respectively. For complex conjugate notation; To calculate the number of data points in the data window for phasor synchronization, The rated frequency of the power system To synchronize the phasor data upload frequency, , , These represent the frequency, amplitude, and phase of the fundamental component at instantaneous values. , , These represent the amplitude, phase, and frequency of the subsynchronous component, respectively. , , These represent the amplitude, phase, and frequency of the supersynchronous component, respectively.

3. The method according to claim 2, characterized in that, Step S2 includes: The mathematical model of the power system synchronization phasor is transformed to obtain the modal model consisting of a linear combination of four complex exponents and four constant parameters. （4） in, ; , , , , , , ; These are constant parameters for the fundamental positive frequency component. For the constant parameters of the fundamental negative frequency component, For the constant parameters of the positive frequency component of the oscillation, For the constant parameters of the negative frequency component of the oscillation, and These are the positive and negative angular frequency indices of the fundamental component, respectively. and These are the positive and negative angular frequency indices of the oscillation component, respectively.

4. The method according to claim 3, characterized in that, Step S3 includes: Through （5） Establish the Hankel matrix; where, For synchronous phasors; Through （6） The Hankel matrix is ​​decomposed into multiple sub-Hankel matrices; where, For Hankel matrix, The number of synchronized phasor data. Less than The constant, The number of sub-Hankel matrices. , … This is the sub-Hankel matrix.

5. The method according to claim 4, characterized in that, Step S4 includes: Through （7） Construct a matrix bundle.

6. The method according to claim 5, characterized in that, Step S5 includes: Through （8） Establish the characteristic polynomial equation for the positive angular frequency index of the fundamental component; where, , , , , The coefficients of the characteristic polynomial of the matrix bundle, is the positive angle frequency index of the fundamental component. The residuals of the characteristic polynomial equation for the positive angular frequency exponent of the fundamental component are indicated by superscripts (1), (2), ..., ( ). p -1) Corresponds to different matrix bundles; Through （9） Establish the characteristic polynomial equation for the negative angular frequency exponent of the fundamental component; where, The negative angular frequency index of the fundamental component. The residual of the characteristic polynomial equation for the negative angular frequency exponent of the fundamental component; Through （10） Establish the characteristic polynomial equation for the positive angular frequency exponent of the oscillating component; where, The positive angle frequency index of the oscillating component is given. The residual of the characteristic polynomial equation for the positive angular frequency exponent of the oscillating component; Through （11） Establish the characteristic polynomial equation for the negative angular frequency exponent of the oscillating component; where, The negative angular frequency index of the oscillating component. The residual of the characteristic polynomial equation for the negative angular frequency exponent of the oscillating component is given.

7. The method according to claim 6, characterized in that, Step S6 includes: Through （12） Solve the characteristic polynomial equations for the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component, respectively.

8. The method according to claim 7, characterized in that, Step S7 includes: Through （13） Solve for the four constant parameters in the modal model.

9. The method according to claim 8, characterized in that, Step S9 includes: Through （14） （15） Calculate the frequency, amplitude, and phase of the fundamental component; Through （16） （17） （18） Obtain the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the frequency, amplitude, and phase of the supersynchronous sinusoidal component.

10. A power system oscillation parameter identification device based on an improved matrix beam algorithm, characterized in that, include: The oscillation parameter identification module is used for: The power system synchronization phasor is modeled as a mathematical model consisting of a fundamental positive frequency component, a fundamental negative frequency component, an oscillating positive frequency component, and an oscillating negative frequency component; wherein, the oscillating positive frequency component is synthesized from the subsynchronous positive frequency component and the supersynchronous negative frequency component, and the oscillating negative frequency component is synthesized from the subsynchronous negative frequency component and the supersynchronous positive frequency component. The mathematical model of the power system synchronization phasor is transformed into a modal model consisting of a linear combination of four complex exponents and four constant parameters. The four complex exponents include the positive and negative angular frequency exponents of the fundamental component, and the positive and negative angular frequency exponents of the oscillation component. A Hankel matrix is ​​constructed based on the synchronization phasor data, and the Hankel matrix is ​​decomposed into multiple sub-Hankel matrices; Construct a matrix bundle based on each pair of adjacent sub-Hankel matrices, and solve for the coefficients of the characteristic polynomial of the matrix bundle; Based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the fundamental component, the characteristic polynomial equations for the positive and negative angular frequency indices of the fundamental component are established; based on the coefficients of the characteristic polynomial, the positive and negative angular frequency indices of the oscillation component, the characteristic polynomial equations for the positive and negative angular frequency indices of the oscillation component are established. Based on the numerical solution method, the characteristic polynomial equations of the positive angular frequency exponent of the fundamental component, the negative angular frequency exponent of the fundamental component, the positive angular frequency exponent of the oscillating component, and the negative angular frequency exponent of the oscillating component are solved respectively. The angular frequencies of the fundamental component that minimize the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the fundamental component are obtained, as well as the angular frequencies of the oscillating component that minimize the sum of the residuals of the characteristic polynomial equations of the positive and negative angular frequency exponents of the oscillating component. Based on the angular frequencies of the fundamental component and the oscillation component obtained from the solution, the four constant parameters in the modal model are solved. Based on the angular frequencies of the fundamental component and the oscillation component, as well as the four constant parameters in the modal model obtained by performing the above step 7, the calculated values ​​of the fundamental positive frequency component, the fundamental negative frequency component, the oscillation positive frequency component, and the oscillation negative frequency component are obtained by calculation. Based on the calculated values ​​of the fundamental positive frequency component and the fundamental negative frequency component, the frequency, amplitude, and phase of the fundamental component are obtained through calculation; based on the calculated values ​​of the oscillation positive frequency component and the oscillation negative frequency component, the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the frequency, amplitude, and phase of the supersynchronous sinusoidal component, are obtained through calculation. The display module is used to output the calculated frequency, amplitude, and phase of the fundamental component; and the calculated values ​​of the frequency, amplitude, and phase of the positive oscillation frequency component, the negative oscillation frequency component, the subsynchronous sinusoidal component, and the supersynchronous sinusoidal component.

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