Power System Oscillation Parameter Identification Method and System Based on Synchronized Phasor Data

Abstract

The present invention discloses a method and system for identifying power system oscillation parameters based on synchronized phasor data, which relates to the technical field of power system oscillation analysis. It solves the problem that the traditional MPM directly obtains the eigenvalues of the matrix pencil, resulting in large errors. The key points of its technical solution are as follows: By constructing a real Hankel matrix and solving the eigenvalues of this matrix, the fundamental wave component angular frequency that satisfies the angular frequency conjugate constraint of two modes of the fundamental frequency component and the oscillation component angular frequency that satisfies the angular frequency conjugate constraint of two modes of the oscillation component can be directly obtained. The solution is simple and the computational amount is small. Moreover, by combining the real part and the imaginary part of the synchronized phasor to construct a real Hankel matrix, the information of the synchronized phasor can be completely retained, and thus the subsynchronous oscillation parameters can be accurately identified under an ultra-short data window.

Description

Technical Field

[0001] The present invention relates to the technical field of power system oscillation analysis, and more specifically, to a method and system for identifying power system oscillation parameters based on synchronized phasor data. Background Art

[0002] In modern power systems, subsynchronous oscillation is mainly caused by the resonance between large-scale renewable energy power generation units and transmission lines. Sub-synchronous oscillation can significantly reduce the transmission capacity of the system at best, and endanger the safe operation of the system at worst, or even lead to system oscillation instability. Therefore, it is necessary to closely monitor the dynamic process of subsynchronous oscillation in the power system. The synchronized phasor measurement data provided by the wide-area measurement system and the synchronized phasor measurement terminal can effectively monitor subsynchronous oscillation events in the power system. However, the fundamental wave component, sub-synchronous component, and super-synchronous component with frequency offset from the rated frequency appear in the synchronized phasor data in the form of spectral leakage, making it difficult to accurately obtain the frequency, amplitude, and phase of each component in subsynchronous oscillation.

[0003] Previous studies have shown that the synchronized phasor data under subsynchronous oscillation is composed of a linear combination of four modes, two of which are related to the fundamental frequency component, and the other two are related to the subsynchronous oscillation component. Therefore, the matrix pencil method (MPM) is proposed to solve the subsynchronous oscillation parameters. MPM constructs a Hankel matrix to transform the modal parameter extraction problem into a matrix decomposition problem, and can directly obtain the angular frequency and coefficients of each mode, with simple solution and small computational complexity. However, this direct eigenvalue solution method ignores the angular frequency conjugate constraints of the two modes related to the fundamental wave component, and the angular frequency conjugate constraints of the two modes related to the oscillation component. Under noise conditions, the calculated eigenvalues do not satisfy the above angular frequency conjugate constraints, resulting in large identification errors for the parameters of each component. In addition, this method only considers the subsynchronous oscillation component and does not consider the super-synchronous component coupled with the subsynchronous oscillation component.

[0004] Therefore, the prior art also records that by constructing an angular frequency fitting equation and considering the angular frequency conjugate constraint in the fitting equation, the problem of angular frequency conjugate constraint of the traditional MPM is solved. However, the solution of the fitting equation deviates from the idea of MPM matrix decomposition, resulting in complex solution and large computational complexity, such as the Chinese invention patent application with the application number 202310119843.2. Therefore, how to research and design a method and system for identifying power system oscillation parameters based on synchronized phasor data that can overcome the above defects is an urgent problem for us to solve at present. Summary of the Invention

[0005] To address the deficiencies in the existing technologies, the objective of the present invention is to provide a method and system for identifying power system oscillation parameters based on synchronized phasor data. By constructing a real-domain Hankel matrix and solving its eigenvalues, the angular frequencies of the fundamental wave components that satisfy the conjugate constraints of the two modes of the fundamental frequency component and the angular frequencies of the oscillation components that satisfy the conjugate constraints of the two modes of the oscillation component can be directly obtained. The solution is simple and the computational effort is small.

[0006] The above technical objective of the present invention is achieved through the following technical solutions:

[0007] In a first aspect, a method for identifying power system oscillation parameters based on synchronized phasor data is provided, including the following steps:

[0008] S1: Establish a mathematical model of the synchronized phasors in the power system. The mathematical model of the synchronized phasors includes fundamental positive frequency components, fundamental negative frequency components, oscillation positive frequency components synthesized by sub-synchronous positive frequency components and super-synchronous negative frequency components, and oscillation negative frequency components synthesized by sub-synchronous negative frequency components and super-synchronous positive frequency components;

[0009] S2: Convert the mathematical model of the synchronized phasors into a modal model that is a linear combination of four complex exponentials and four constant parameters. The four complex exponential parameters include the positive angular frequency exponent and negative angular frequency exponent of the fundamental wave component, as well as the positive angular frequency exponent and negative angular frequency exponent of the oscillation component;

[0010] S3: Construct a first Hankel matrix based on the real part of the synchronized phasors and a second Hankel matrix based on the imaginary part of the synchronized phasors;

[0011] S4: Concatenate the first Hankel matrix and the second Hankel matrix to obtain a real-domain Hankel matrix;

[0012] S5: Solve the eigenvalues of the real-domain Hankel matrix and calculate the angular frequencies of the fundamental wave components and the angular frequencies of the oscillation components based on the eigenvalues of the real-domain Hankel matrix;

[0013] S6: Solve the four constant parameters in the modal model based on the angular frequencies of the fundamental wave components and the angular frequencies of the oscillation components;

[0014] S7: Determine the calculated values of the fundamental positive frequency components, fundamental negative frequency components, oscillation positive frequency components, and oscillation negative frequency components based on the angular frequencies of the fundamental wave components, the angular frequencies of the oscillation components, and the four constant parameters in the modal model;

[0015] S8: Determine 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 determine the frequency, amplitude, and phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component based on the calculated values of the oscillatory positive-frequency component and the oscillatory negative-frequency component.

[0016] Further, the expression of the first Hankel matrix is specifically:

[0017]

[0018] where Re(Y) is the first Hankel matrix; is the (K - L)-th synchronous phasor; K is the number of synchronous phasor data; L is a constant less than K; Re(·) is to take the real part of a complex number.

[0019] Further, the expression of the second Hankel matrix is specifically:

[0020]

[0021] where Im(Y) is the second Hankel matrix; is the (K - L)-th synchronous phasor; K is the number of synchronous phasor data; L is a constant less than K; Im(·) is to take the imaginary part of a complex number.

[0022] Further, the expression of the real-domain Hankel matrix is specifically:

[0023]

[0024] where Y' is the real-domain Hankel matrix; Re(Y) is the first Hankel matrix; Im(Y) is the second Hankel matrix.

[0025] Further, the process of solving the eigenvalues of the real-domain Hankel matrix and calculating the angular frequency of the fundamental component and the angular frequency of the oscillatory component is specifically as follows:

[0026] Split the real-domain Hankel matrix into two sub-Hankel matrices;

[0027] Construct a matrix pencil according to the two sub-Hankel matrices;

[0028] By solving the eigenvalues in the matrix pencil, obtain the positive angular frequency index and negative angular frequency index of the fundamental component and the positive angular frequency index and negative angular frequency index of the oscillatory component;

[0029] Solve for the angular frequency of the fundamental component and the angular frequency of the oscillation component based on the conjugate relationship between the positive angular frequency index and the negative angular frequency index of the fundamental component, and the conjugate relationship between the positive angular frequency index and the negative angular frequency index of the oscillation component.

[0030] Further, the expressions of the two sub-Hankel matrices are specifically as follows:

[0031]

[0032] Where, Y′ 1 is the first sub-Hankel matrix; Y′ 2 is the second sub-Hankel matrix; Y' is a real-domain Hankel matrix; L is a constant less than the number of synchronous phasor data.

[0033] Further, the expression of the matrix pencil is specifically as follows:

[0034] Y′ 2 -λY′ 1

[0035] Where, Y′ 1 is the first sub-Hankel matrix; Y′ 2 is the second sub-Hankel matrix; λ is the eigenvalue in the matrix pencil.

[0036] In a second aspect, a power system oscillation parameter identification system based on synchronous phasor data is provided, including:

[0037] A model construction module for establishing a mathematical model of synchronous phasors in a power system. The mathematical model of synchronous phasors includes a fundamental positive frequency component, a fundamental negative frequency component, an oscillation positive frequency component synthesized by a subsynchronous positive frequency component and a supersynchronous negative frequency component, and an oscillation negative frequency component synthesized by a subsynchronous negative frequency component and a supersynchronous positive frequency component;

[0038] A model conversion module for converting the mathematical model of synchronous phasors into a modal model linearly combined by 4 complex exponents and 4 constant parameters. The 4 complex exponent parameters include the positive angular frequency index and the negative angular frequency index of the fundamental component, and the positive angular frequency index and the negative angular frequency index of the oscillation component;

[0039] A matrix construction module for constructing a first Hankel matrix according to the real part of the synchronous phasor and a second Hankel matrix according to the imaginary part of the synchronous phasor;

[0040] A matrix splicing module for splicing the first Hankel matrix and the second Hankel matrix to obtain a real-domain Hankel matrix;

[0041] An eigenvalue solving module, configured to solve the eigenvalues of a real-domain Hankel matrix, and calculate the angular frequency of the fundamental wave component and the angular frequency of the oscillating component according to the eigenvalues of the real-domain Hankel matrix;

[0042] A parameter solving module, configured to solve 4 constant parameters in the modal model according to the angular frequency of the fundamental wave component and the angular frequency of the oscillating component;

[0043] A component calculation module, configured to determine the calculated values of the fundamental positive-frequency component, the fundamental negative-frequency component, the oscillating positive-frequency component, and the oscillating negative-frequency component according to the angular frequency of the fundamental wave component, the angular frequency of the oscillating component, and the 4 constant parameters in the modal model;

[0044] An oscillation identification module, configured to determine the frequency, amplitude, and phase of the fundamental wave component according to the calculated values of the fundamental positive-frequency component and the fundamental negative-frequency component, and determine the frequency, amplitude, and phase of the sub-synchronous sinusoidal component and determine the frequency, amplitude, and phase of the super-synchronous sinusoidal component according to the calculated values of the oscillating positive-frequency component and the oscillating negative-frequency component.

[0045] In a third aspect, a computer terminal is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the program, the method for identifying power system oscillation parameters based on synchronized phasor data described in any item of the first aspect is implemented.

[0046] In a fourth aspect, a computer-readable medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the method for identifying power system oscillation parameters based on synchronized phasor data described in any item of the first aspect can be implemented.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. For the method for identifying power system oscillation parameters based on synchronized phasor data provided by the present invention, by constructing a real-domain Hankel matrix and solving the eigenvalues of the matrix, the angular frequency of the fundamental wave component that satisfies the angular frequency conjugate constraint of the two modes of the fundamental frequency component and the angular frequency of the oscillating component that satisfies the angular frequency conjugate constraint of the two modes of the oscillating component can be directly obtained. The solution is simple and the calculation amount is small, solving the problem of large errors caused by directly obtaining the eigenvalues of the matrix pencil in the traditional MPM;

[0049] 2. By combining the real part and the imaginary part of the synchronized phasor to construct a real-domain Hankel matrix, the present invention can completely retain the information of the synchronized phasor, and further accurately identify the sub-synchronous oscillation parameters under an ultra-short data window. Description of the Drawings

[0050] The accompanying drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0051] Figure 1 is the flowchart in Embodiment 1 of the present invention;

[0052] Figure 2 is the system block diagram in Embodiment 2 of the present invention. Detailed implementation manners

[0053] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in combination with the embodiments and the accompanying drawings. The illustrative embodiments of the present invention and their descriptions are only used to explain the present invention and do not limit the present invention.

[0054] Embodiment 1: A method for identifying power system oscillation parameters based on synchronized phasor data, as Figure 1 shown, is specifically implemented by the following steps.

[0055] S1: Establish a mathematical model of synchronized phasors in the power system. The mathematical model of synchronized phasors includes a fundamental positive frequency component, a fundamental negative frequency component, an oscillatory positive frequency component, and an oscillatory negative frequency component; wherein, the oscillatory positive frequency component is synthesized by a sub-synchronous positive frequency component and a super-synchronous negative frequency component, and the oscillatory negative frequency component is synthesized by a sub-synchronous negative frequency component and a super-synchronous positive frequency component.

[0056] The mathematical model of power system synchronized phasors is as follows:

[0057]

[0058] Wherein,

[0059]

[0060]

[0061]

[0062] In the formula, is the k-th synchronized phasor; and are the fundamental positive frequency component and the fundamental negative frequency component respectively; and are the oscillatory positive frequency component and the oscillatory negative frequency component respectively; and are the sub-synchronous positive frequency component and the sub-synchronous negative frequency component respectively; and They are the supersynchronous positive frequency component and the supersynchronous positive frequency component respectively; * is the complex conjugate mark; N is the number of data points in the synchronous phasor calculation data window, and f N is the rated frequency of the power system, and f s is the upload frequency of the synchronous phasor data, and f 0 , x 0 , φ 0 are the frequency, amplitude and phase of the fundamental wave component of the instantaneous value respectively, and x sub , φ sub , f sub are the amplitude, phase and frequency of the subsynchronous component respectively, and x sup , φ sup , f sup are the amplitude, phase and frequency of the supersynchronous component respectively.

[0063] In specific implementation, step S1 of establishing the mathematical model of the power system synchronous phasor includes the following process:

[0064] First, establish the instantaneous signal model of the power system. This model is shown in formula (2) and includes a fundamental wave component with a possibly offset frequency, a pair of subsynchronous components and supersynchronous components with coupled frequencies.

[0065] x(t) = x 0 cos(2πf 0 t + φ 0 ) + x sub cos(2πf sub t + φ sub ) + x sup cos(2πf sup t + φ sup )(2)

[0066] In the formula, x(t) is the instantaneous signal.

[0067] Then, the synchronous phasor sequence corresponding to the instantaneous signal x(t) can be obtained by performing a discrete Fourier transform (DFT) on formula (2). Since the discrete Fourier transform is a linear transform, there is:

[0068]

[0069] In the formula, and are the synchronous phasor results corresponding to the fundamental wave component, the subsynchronous component and the supersynchronous component respectively.

[0070] From formula (1) and formula (3), and the discrete Fourier transform theory, it can be known that is composed of and in two parts. The corresponding angular frequency is The corresponding angular frequency is Without loss of generality, first assume that f 0 <f N , and determine whether the final result is f 0 <f N or f 0 >f N , that is, assume that α is the positive angular frequency and -α is the negative angular frequency.

[0071] It consists of and . Considering 0 < f sub <f N , corresponds to the positive angular frequency corresponds to the negative angular frequency Similarly,[[]] It consists of and , corresponds to the positive angular frequency corresponds to the negative angular frequency According to the above derivation, the subsynchronous positive frequency component and the supersynchronous negative frequency component are synthesized into an oscillating positive frequency component The subsynchronous negative frequency component and the supersynchronous positive frequency component are synthesized into an oscillating negative frequency component

[0072] S2: Convert the mathematical model of the synchronous phasor into a modal model composed of a linear combination of 4 complex exponentials and 4 constant parameters. The 4 complex exponential parameters include the positive angular frequency index and the negative angular frequency index of the fundamental wave component, as well as the positive angular frequency index and the negative angular frequency index of the oscillating component.

[0073] The modal model is as follows:

[0074]

[0075] Among them, λ 1 =jα; λ 2 =-jα; λ 3 =jβ; λ 4 =-jβ;

[0076] In the formula, a 1 、a 2, a 3 , a 4 is a constant parameter, and are the positive and negative angular frequency exponents of the fundamental wave component respectively, and are the positive and negative angular frequency exponents of the oscillating component respectively.

[0077] In specific implementation, in step S2, the mathematical model of the synchronized phasor is rewritten as a modal model according to formula (4). Among them, a 1 is the constant parameter of the fundamental positive frequency component, a 2 is the constant parameter of the fundamental negative frequency component, a 3 is the constant parameter of the oscillating positive frequency component, a 4 is the constant parameter of the oscillating negative frequency component, and are the positive and negative angular frequency exponents of the fundamental wave component respectively, and are the positive and negative angular frequency exponents of the oscillating component respectively. If a 1 , a 2 , a 3 , a 4 and λ 1 , λ 2 , λ 3 , λ 4 can be obtained, the frequencies, amplitudes and phases of each component can be solved, and then the identification problem of the parameters of each component can be transformed into the extraction problem of modal parameters.

[0078] The steps of the existing MPM algorithm include: First, perform truncated singular value decomposition on Y to reduce the influence of noise; Then, split the truncated singular value decomposed Y into two sub-Hankel matrices Y 1 and Y 2 ; Finally, construct the matrix pencil Y 2 -λY 1 , and by solving the eigenvalues λ of Y 1 + Y 2 , can be obtained. Then, a 1 , a 2 , a 3 , a 4 are solved by the least squares method. This method can accurately solve under ideal conditions, but under noise conditions, when directly solving the eigenvalues of Y 1 + Y 2 , the obtained and do not satisfy e jα and e-jα The conjugate relationship, and also does not satisfy e jβ and e -jβ The conjugate relationship, making it impossible to accurately solve for α and β, resulting in a relatively large parameter identification error for each component. The main reason for the above problems is that the existing MPM algorithm constructs a Hankel matrix based on synchronous phasors in the complex domain. Therefore, under the influence of measurement noise, the four eigenvalues obtained are not conjugate in pairs. If a Hankel matrix in the real domain can be constructed, theoretically, the problem of angular frequency conjugate constraint can be solved. In order to retain all the information of the complex-domain synchronous phasors while constructing a Hankel matrix in the real domain, the embodiments of the present invention combine the real part and the imaginary part of the synchronous phasors to construct a Hankel matrix in the real domain.

[0079] S3: Construct a first Hankel matrix according to the real part of the synchronous phasor, and construct a second Hankel matrix according to the imaginary part of the synchronous phasor.

[0080] In one embodiment, the expression of the first Hankel matrix is specifically:

[0081]

[0082] where Re(Y) is the first Hankel matrix; is the (K - L)-th synchronous phasor; K is the number of synchronous phasor data; L is a constant less than K; Re(·) is to take the real part of a complex number.

[0083] In addition, the expression of the second Hankel matrix is specifically:

[0084]

[0085] where Im(Y) is the second Hankel matrix; Im(·) is to take the imaginary part of a complex number.

[0086] S4: Concatenate the first Hankel matrix and the second Hankel matrix to obtain a Hankel matrix in the real domain.

[0087] The expression of the Hankel matrix in the real domain is specifically:

[0088]

[0089] where Y' is the Hankel matrix in the real domain.

[0090] S5: Solve the eigenvalues of the Hankel matrix in the real domain, and calculate the angular frequency of the fundamental component and the angular frequency of the oscillating component according to the eigenvalues of the Hankel matrix in the real domain.

[0091] In specific implementation, in step S5, first, split Y' into Y 1 ' and Y 2 ' two sub-Hankel matrices according to formula (8):

[0092]

[0093] Then, construct the matrix pencil Y′ 2 -λY′ 1 . Since the Hankel matrix is in the real number field, by solving the eigenvalues of Y 1 ' + Y′ 2 , the following can be obtained wherein, and satisfy the conjugate relationship of e jα and e -jα . Similarly, and also satisfy the conjugate relationship of e jβ and e -jβ . Furthermore, the angular frequency α of the fundamental wave component and the angular frequency β of the oscillating component can be accurately solved. Therefore, the advantages of the embodiments of the present invention are as follows: on the one hand, by constructing a real number field Hankel matrix, the problem that the angular frequencies obtained by directly calculating the eigenvalues of the matrix pencil in the existing MPM do not satisfy the conjugate constraints of ±jα and ±jβ is solved; on the other hand, by combining the real part and the imaginary part of the synchronous phasor to construct a Hankel matrix, the information of the synchronous phasor can be completely retained, effectively improving the identification accuracy of the fundamental wave parameters, subsynchronous oscillation parameters and supersynchronous, and at the same time, the solution is simple and the calculation amount is small.

[0094] S6: Solve the 4 constant parameters in the modal model according to the angular frequency of the fundamental wave component and the angular frequency of the oscillating component.

[0095] In one embodiment, step S7 solves the 4 constants in the following manner:

[0096]

[0097] S7: Determine the calculated values of the fundamental wave positive frequency component, fundamental wave negative frequency component, oscillating positive frequency component and oscillating negative frequency component according to the angular frequency of the fundamental wave component, the angular frequency of the oscillating component and the 4 constant parameters in the modal model.

[0098] S8: Determine the frequency, amplitude and phase of the fundamental wave component according to the calculated values of the fundamental wave positive frequency component and the fundamental wave negative frequency component, and determine the frequency, amplitude and phase of the subsynchronous sine component and the frequency, amplitude and phase of the supersynchronous sine component according to the calculated values of the oscillating positive frequency component and the oscillating negative frequency component.

[0099] In one embodiment, step S8 determines the frequency, amplitude, and phase of the fundamental wave component in the following manner:

[0100]

[0101]

[0102] Determine the frequency, amplitude, and phase of the subsynchronous sinusoidal component, as well as the frequency, amplitude, and phase of the supersynchronous sinusoidal component, in the following manner:

[0103]

[0104] f sup = 2f N - f sub (13)

[0105]

[0106] To verify the correctness and effectiveness of the proposed power system oscillation parameter identification method based on synchronized phasor data, a verification study was conducted using simulated PMU data with known parameters. Among them, the instantaneous value signal for generating the simulated PMU data is shown in formula (2), and the specific parameters are set as follows: The system rated frequency f N is 50 Hz, the fundamental wave amplitude x 0 and phase φ 0 are fixed and unchanged, being 100 and 0 rad respectively. The phases φ sub and φ sup of the subsynchronous / supersynchronous oscillation components in the subsynchronous oscillation are taken as 0.5 rad and 0.75 rad respectively, and the amplitudes x sub and x sup are taken as 20 and 10 respectively. To study the parameter identification accuracy characteristics of the embodiments of the present invention under the influence of noise, white noise with zero mean was added to the instantaneous value signal, and a 40 dB SNR condition was used.

[0107] The performance of the improved matrix pencil algorithm (abbreviated as "improved MPM") proposed in the embodiments of the present invention was compared with the performance of the original matrix pencil algorithm (abbreviated as "original MPM"). The comparison results are shown in Table 1. f 0 and f sub are respectively taken as 4 groups of data shown in Table 1, and both methods use a data window of 200 ms.

[0108] Table 1 Comparison of the performance of improved MPM and existing MPM

[0109]

[0110] As can be seen from Table 1, affected by noise, the relative error of parameter identification of each component by the existing MPM algorithm is relatively large. Especially in the 3rd and 4th groups of experiments, the two eigenvalues corresponding to the fundamental wave component do not satisfy the conjugate constraint, making it difficult to accurately identify the fundamental wave frequency, resulting in a large error in the identification results of the fundamental wave amplitude and other component parameters. Compared with the existing MPM algorithm, the improved MPM algorithm in this embodiment of the present invention can more accurately identify the parameters of each component.

[0111] Table 2 Comparison of calculation time consumption of three algorithms

[0112]

[0113] Table 2 shows the comparison of the single - calculation time consumption of three algorithms: the improved MPM, the original MPM, and the related technology (patent number: 202310119843.2). As can be seen from Table 2, since the improved MPM only performs matrix decomposition once, its single - calculation time consumption is relatively close to that of the original MPM. And the improved MPM has great advantages in terms of computational complexity and calculation time compared with the related technology (patent number: 202310119843.2), and can accurately identify SSO parameters with a data window in the order of hundreds of milliseconds without increasing the amount of calculation.

[0114] Embodiment 2: A power system oscillation parameter identification system based on synchronized phasor data, which is used to implement the power system oscillation parameter identification method recorded in Embodiment 1, as Figure 2 shown, includes a model construction module, a model conversion module, a matrix construction module, a matrix splicing module, a feature solving module, a parameter solving module, a component calculation module, and an oscillation identification module.

[0115] Among them, the model construction module is used to establish the mathematical model of synchronous phasors in the power system. The mathematical model of synchronous phasors includes fundamental positive frequency components, fundamental negative frequency components, oscillatory positive frequency components synthesized by sub-synchronous positive frequency components and super-synchronous negative frequency components, and oscillatory negative frequency components synthesized by sub-synchronous negative frequency components and super-synchronous positive frequency components; the model conversion module is used to convert the mathematical model of synchronous phasors into a modal model composed of a linear combination of 4 complex exponentials and 4 constant parameters. The 4 complex exponential parameters include the positive angular frequency exponent and negative angular frequency exponent of the fundamental component, as well as the positive angular frequency exponent and negative angular frequency exponent of the oscillatory component; the matrix construction module is used to construct the first Hankel matrix according to the real part of the synchronous phasor and construct the second Hankel matrix according to the imaginary part of the synchronous phasor; the matrix splicing module is used to splice the first Hankel matrix and the second Hankel matrix to obtain a real-domain Hankel matrix; the eigenvalue solving module is used to solve the eigenvalues of the real-domain Hankel matrix and calculate the angular frequency of the fundamental component and the angular frequency of the oscillatory component according to the eigenvalues of the real-domain Hankel matrix; the parameter solving module is used to solve the 4 constant parameters in the modal model according to the angular frequency of the fundamental component and the angular frequency of the oscillatory component; the component calculation module is used to determine the calculated values of the fundamental positive frequency component, fundamental negative frequency component, oscillatory positive frequency component, and oscillatory negative frequency component according to the angular frequency of the fundamental component, the angular frequency of the oscillatory component, and the 4 constant parameters in the modal model; the oscillation identification module is used to determine the frequency, amplitude, and phase of the fundamental component according to the calculated values of the fundamental positive frequency component and fundamental negative frequency component, and determine the frequency, amplitude, and phase of the sub-synchronous sine component and determine the frequency, amplitude, and phase of the super-synchronous sine component according to the calculated values of the oscillatory positive frequency component and oscillatory negative frequency component.

[0116] Working principle: In the embodiment of the present invention, by constructing a real-domain Hankel matrix and solving the eigenvalues of the matrix, the angular frequency of the fundamental component that satisfies the angular frequency conjugate constraint of the two modes of the fundamental frequency component and the angular frequency of the oscillatory component that satisfies the angular frequency conjugate constraint of the two modes of the oscillatory component can be directly obtained, solving the problem of large errors caused by directly obtaining the eigenvalues of the matrix pencil in the traditional MPM. The solution is simple and the calculation amount is small. In addition, by combining the real part and the imaginary part of the synchronous phasor to construct a real-domain Hankel matrix, the information of the synchronous phasor can be completely retained, and then the sub-synchronous oscillation parameters can be accurately identified under an ultra-short data window.

[0117] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0118] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0119] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing devices to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that realizes the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0120] These computer program instructions can also be loaded onto a computer or other programmable data processing devices, such that a series of operation steps are executed on the computer or other programmable devices to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable devices provide steps for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0121] The above specific implementation manners further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are only specific implementation manners of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for identifying power system oscillation parameters based on synchronized phasor data, characterized in that, it includes the following steps: S1: Establish a mathematical model of synchronized phasors in the power system. The mathematical model of synchronized phasors includes fundamental positive frequency components, fundamental negative frequency components, oscillation positive frequency components synthesized by sub-synchronous positive frequency components and super-synchronous negative frequency components, and oscillation negative frequency components synthesized by sub-synchronous negative frequency components and super-synchronous positive frequency components; S2: Convert the mathematical model of synchronized phasors into a modal model linearly combined by 4 complex exponentials and 4 constant parameters. The 4 complex exponential parameters include the positive angular frequency exponent and negative angular frequency exponent of the fundamental component, and the positive angular frequency exponent and negative angular frequency exponent of the oscillation component; S3: Construct a first Hankel matrix according to the real part of the synchronized phasor, and construct a second Hankel matrix according to the imaginary part of the synchronized phasor; S4: Concatenate the first Hankel matrix and the second Hankel matrix to obtain a real-domain Hankel matrix; S5: Solve the eigenvalues of the real-domain Hankel matrix, and calculate the angular frequency of the fundamental component and the angular frequency of the oscillation component according to the eigenvalues of the real-domain Hankel matrix; S6: Solve the 4 constant parameters in the modal model according to the angular frequency of the fundamental component and the angular frequency of the oscillation component; S7: Determine the calculated values of the fundamental positive frequency component, fundamental negative frequency component, oscillation positive frequency component, and oscillation negative frequency component according to the angular frequency of the fundamental component, the angular frequency of the oscillation component, and the 4 constant parameters in the modal model; S8: Determine the frequency, amplitude, and phase of the fundamental component according to the calculated values of the fundamental positive frequency component and fundamental negative frequency component, and determine the frequency, amplitude, and phase of the sub-synchronous sine component and determine the frequency, amplitude, and phase of the super-synchronous sine component according to the calculated values of the oscillation positive frequency component and oscillation negative frequency component.

2. The method for identifying power system oscillation parameters based on synchronized phasor data according to claim 1, characterized in that, the expression of the first Hankel matrix is specifically: Among them, Re(Y) is the first Hankel matrix; is the K-Lth synchronized phasor; K is the number of synchronized phasor data; L is a constant less than K; Re(·) is to take the real part of a complex number.

3. The method for identifying power system oscillation parameters based on synchronized phasor data according to claim 1, characterized in that, the expression of the second Hankel matrix is specifically: where Im(Y) is the second Hankel matrix; is the (K-L)-th synchronized phasor; K is the number of synchronized phasor data; L is a constant less than K; Im(·) is to take the imaginary part of a complex number.

4. The method for identifying power system oscillation parameters based on synchronized phasor data according to claim 1, characterized in that, the expression of the real-domain Hankel matrix is specifically: where Y' is the real-domain Hankel matrix; Re(Y) is the first Hankel matrix; Im(Y) is the second Hankel matrix.

5. The method for identifying power system oscillation parameters based on synchronized phasor data according to claim 1, characterized in that, the process of solving the eigenvalues of the real-domain Hankel matrix and calculating the angular frequency of the fundamental component and the angular frequency of the oscillation component according to the eigenvalues of the real-domain Hankel matrix is specifically: Split the real-domain Hankel matrix into two sub-Hankel matrices; Construct a matrix pencil according to the two sub-Hankel matrices; By solving the eigenvalues in the matrix pencil, the positive angular frequency exponent and negative angular frequency exponent of the fundamental wave component, as well as the positive angular frequency exponent and negative angular frequency exponent of the oscillation component, are obtained; Based on the conjugate relationship between the positive angular frequency exponent and negative angular frequency exponent of the fundamental wave component, and the conjugate relationship between the positive angular frequency exponent and negative angular frequency exponent of the oscillation component, the angular frequency of the fundamental wave component and the angular frequency of the oscillation component are solved.

6. The power system oscillation parameter identification method based on synchronized phasor data according to claim 5, characterized in that the expressions of the two sub-Hankel matrices are specifically: Among them, Y 1 ' is the first sub-Hankel matrix; Y 2 ' is the second sub-Hankel matrix; Y' is a Hankel matrix in the real number field; L is a constant less than the number of synchronized phasor data.

7. The power system oscillation parameter identification method based on synchronized phasor data according to claim 6, characterized in that the expression of the matrix pencil is specifically: Y’ 2 -λY 1 ’ where λ is the eigenvalue in the matrix pencil.

8. A power system oscillation parameter identification system based on synchronized phasor data, characterized in that it includes: a model construction module for establishing a mathematical model of synchronized phasors in a power system, and the mathematical model of synchronized phasors includes a fundamental positive frequency component, a fundamental negative frequency component, an oscillation positive frequency component synthesized by a subsynchronous positive frequency component and a supersynchronous negative frequency component, and an oscillation negative frequency component synthesized by a subsynchronous negative frequency component and a supersynchronous positive frequency component; a model conversion module for converting the mathematical model of synchronized phasors into a modal model linearly combined by 4 complex exponents and 4 constant parameters, and the 4 complex exponent parameters include the positive angular frequency exponent and negative angular frequency exponent of the fundamental wave component, as well as the positive angular frequency exponent and negative angular frequency exponent of the oscillation component; a matrix construction module for constructing a first Hankel matrix according to the real part of the synchronized phasor and constructing a second Hankel matrix according to the imaginary part of the synchronized phasor; a matrix splicing module for splicing the first Hankel matrix and the second Hankel matrix to obtain a real-domain Hankel matrix; a characteristic solving module for solving the eigenvalues of the real-domain Hankel matrix and calculating the angular frequency of the fundamental wave component and the angular frequency of the oscillation component according to the eigenvalues of the real-domain Hankel matrix; a parameter solving module for solving the 4 constant parameters in the modal model according to the angular frequency of the fundamental wave component and the angular frequency of the oscillation component; a component calculation module for determining 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 according to the angular frequency of the fundamental wave component, the angular frequency of the oscillation component, and the 4 constant parameters in the modal model; an oscillation identification module for determining the frequency, amplitude, and phase of the fundamental wave component according to the calculated values of the fundamental positive frequency component and the fundamental negative frequency component, and determining the frequency, amplitude, and phase of the subsynchronous sine component and the frequency, amplitude, and phase of the supersynchronous sine component according to the calculated values of the oscillation positive frequency component and the oscillation negative frequency component.

9. A computer terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that when the processor executes the program, it implements the power system oscillation parameter identification method based on synchronized phasor data according to any one of claims 1-7.

10. A computer-readable medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it can implement the power system oscillation parameter identification method based on synchronized phasor data according to any one of claims 1-7.

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