Data-driven participation factor calculation method

Abstract

The invention belongs to the technical field of dynamic analysis of a power system, and particularly relates to a data-driven participation factor calculation method, which directly extracts modal information from dynamic response data of the power system based on dynamic mode decomposition, avoids the dependence of a traditional method on a mathematical model of the power system, remarkably reduces the calculation complexity and improves the calculation efficiency. The method is suitable for real-time analysis of a large-scale power system; through combination of singular value decomposition and DMD, high-dimensional data of an electric power system is subjected to dimension reduction processing, low-dimensional modal information is extracted, calculation efficiency and analysis precision are improved, participation factors are redefined, dynamic characteristics of time-space evolution of the electric power system are combined, the modal participation degree can be more comprehensively quantified, and the dynamic performance of the electric power system is improved. And the dominant mode and the key node in the power system can be accurately identified. The method is high in adaptability, can process dynamic behaviors of a nonlinear power system, is suitable for various operation states, and provides powerful support for dynamic stability analysis and real-time monitoring of the power system.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system dynamic analysis, and in particular relates to a data-driven participation factor calculation method, a participation factor extraction method based on dynamic mode decomposition (DMD), which is used for modal analysis and participation factor calculation of power system dynamic behavior. Background Art

[0002] As the scale of power systems continues to expand and a high proportion of renewable energy is connected to the grid, the dynamic characteristics of power systems are becoming increasingly complex. How to extract effective features from power system dynamic response data and realize power system fault detection remains a challenging problem. Traditional modal analysis methods, such as wavelet transform and variational modal decomposition, have been widely used in power system dynamic analysis. However, these methods usually rely on experience in the selection of thresholds and are prone to problems such as modal aliasing and noise sensitivity, making them difficult to adapt to the needs of modern power system analysis. In addition, traditional participation factor calculation methods are usually based on the state matrix of the power system. The calculation process is complex and time-consuming, making it difficult to quickly apply them in large-scale power systems.

[0003] Dynamic mode decomposition (DMD), a data-driven method, can extract modal information from power system dynamic response data, extract low-dimensional dynamic patterns from high-dimensional data, and reveal the inherent evolution of the power system, providing new insights into power system disturbance analysis. Furthermore, while DMD has been widely used in fields such as fluid mechanics, its application in power system dynamic analysis is relatively limited. Therefore, a DMD-based participation factor extraction method is urgently needed to simplify the analysis of power system dynamic behavior and improve computational efficiency. Summary of the Invention

[0004] In order to solve the increasingly complex dynamic characteristics of the power system mentioned in the above background technology, traditional modal analysis methods usually rely on experience in the selection of thresholds, and are prone to problems such as modal aliasing and noise sensitivity, and the calculation process is complex and time-consuming. Technical problems, the present invention provides a data-driven participation factor calculation method for simplifying the modal analysis and participation factor calculation of the dynamic behavior of the power system, improving calculation efficiency, and adapting to the real-time analysis needs of modern power systems.

[0005] The technical solution provided by the present invention is as follows: a data-driven participation factor calculation method, the method comprising the following steps: Step 1: Construct the Hankel matrix using the dynamic response data of the power system; The acquired dynamic response data of the power system is used as input, and the following Hankel matrix is ​​constructed with the dynamic response data of the discrete power system: (1); In formula (1): express At the sampling point Sampling data at Indicates the A vector of all observable sample values ​​at a given moment; Step 2: perform linear mapping approximation on the discrete sampled measurement data; Discrete sampled measurement data can be approximately represented by a linear mapping as follows: (2); In formula (2): It is a high-order complex matrix that can capture the dynamic change characteristics inherent in the measurement information. Its eigenvalues ​​and eigenvectors contain the dynamic oscillation information of the power system. Get the Krylov subspace sequence, expressed as (3); (4); (5); From formulas (3)-(5), we can get: (6); Step 3: Use DMD decomposition to extract low-dimensional modal information; Through the original data matrix Orthogonal projection decomposition of : (7); In formula (7): Represents A low-dimensional approximation matrix with similar features but with irrelevant features discarded; is a matrix The left singular vector matrix of the singular value decomposition (SVD) is as follows: (8); In formula (8): Matrix U and Matrix V are the left and right singular value vectors, respectively, and both are unitary matrices; is a diagonal matrix of singular values; Combining the above formula, we can get the low-dimensional approximate matrix of the power system: The calculation formula is (9) ; For low-dimensional approximation matrices Perform eigenvalue decomposition: (10); In formula (10): is the eigenvalue matrix, is the non-zero eigenvalue corresponding to the oscillation mode, is the eigenvector matrix, , represents the mode in the low-dimensional space, is the number of oscillation modes; From the above conclusions: (11); Step 4: Establish the oscillation mode matrix and amplitude coefficient matrix; According to the SVD definition of the data matrix: (12); (13); (14); In formula (12), is the oscillation mode matrix, each column Indicates the relative oscillation trend of a certain oscillation mode in the power system and reflects the spatial distribution characteristics of the power system under different modes; In formula (14), is the time-dependent amplitude coefficient matrix, describing the evolution of the amplitude of each mode over time; Step 5: Extract the oscillation mode participation factor; Estimated data series , which can be expressed as: (15); Formula (15) decomposes the dynamic behavior of the power system into the superposition of multiple modes, each of which is represented by its spatial characteristics. , time characteristics and amplitude evolution Each dynamic mode is weighted by the product of each Ritz mode value and the corresponding energy extracted from each time-varying mode. (16); Define the state-mode relationship: (17); In formula (17), Provides a measure of the mode's participation in the power system state; The participation factor matrix is ​​established, which is calculated by summing the row vectors of the above formula and is used to associate the power system state and mode: (18); (19); in, It is the participation factor, which is directly related to the spatial distribution and temporal characteristics of the mode. It can describe the contribution of the mode at both the local and global levels.

[0006] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least: Based on the dynamic mode decomposition (DMD) method, the present invention extracts modal information directly from the dynamic response data of the power system, avoiding the traditional method's reliance on the mathematical model of the power system, significantly reducing the computational complexity, and being suitable for real-time analysis of large-scale power systems. Through the combination of singular value decomposition and DMD, the high-dimensional data of the power system is reduced in dimensionality, and low-dimensional modal information is extracted, improving computational efficiency and analysis accuracy. In addition, the present invention proposes a new participation factor definition method that, combined with the dynamic characteristics of the power system's evolution over time and space, can more comprehensively quantify the degree of modal participation and accurately identify the dominant modes and key nodes in the power system. This method is highly adaptable, capable of handling the dynamic behavior of nonlinear power systems, and applicable to a variety of operating states. It provides strong support for dynamic stability analysis and real-time monitoring of power systems and has high practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0008] Figure 1 This is a flow chart of a data-driven participation factor calculation method in an embodiment of the present invention; Figure 2 The measuring device in the embodiment of the present invention collects the transient zero-sequence current of each line as the dynamic response data time curve of the 10kV resonant grounding power system; Figure 3 This is a graph showing the participation factor calculation results of a data-driven participation factor calculation method of the present invention. DETAILED DESCRIPTION

[0009] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0010] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as an "exemplary" in the present invention should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of the word "exemplary" is intended to present concepts in a concrete manner. Furthermore, in the embodiments of the present invention, "and / or" can mean both or either of the two.

[0011] In the embodiments of the present invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, when the distinction is not emphasized, the meanings they convey are the same. The terms "of," "corresponding," and "corresponding" may sometimes be used interchangeably. It should be noted that, when the distinction is not emphasized, the meanings they convey are the same.

[0012] In the embodiments of the present invention, sometimes a subscript such as W1 may be written as a non-subscript such as W1. When the difference is not emphasized, the meanings to be expressed are the same.

[0013] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0014] Figure 1 This is a flow chart of a data-driven participation factor calculation method in an example of the present invention. The embodiment of the present invention provides a data-driven participation factor calculation method. Figure 1 , including the following steps, and the following steps are performed in sequence, Step 1: Use the dynamic response data of the power system to construct the Hankel matrix. The specific process is as follows: Dynamic mode decomposition algorithm: Obtain dynamic response data of the power system based on time domain simulation or PMU measurement: (20); In formula (20), The dynamic response of the power system The sampling value at the moment, is the sampling interval.

[0015] The following Hankel matrix is ​​constructed based on the dynamic response data of the discrete power system: (1); In formula (1): express At the sampling point Sampling data at Indicates the A vector of all observable sample values ​​at a given moment; Step 2: Perform linear mapping approximation on the discrete sampled measurement data. The specific process is as follows: Discrete sampled measurement data can be approximately represented by a linear mapping as follows: (2); In formula (2): It is a high-order complex matrix that can capture the dynamic change characteristics inherent in the measurement information. Its eigenvalues ​​and eigenvectors contain the dynamic oscillation information of the power system. Get the Krylov subspace sequence, expressed as (3); (4); (5); From formulas (3)-(5), we can get: (6); Step 3: Use DMD decomposition to extract low-dimensional modal information. The specific process is as follows: Through the original data matrix Orthogonal projection decomposition of : (7); In formula (7): Represents A low-dimensional approximation matrix with similar features but with irrelevant features discarded; is a matrix The left singular vector matrix of the singular value decomposition (SVD) is as follows: (8); In formula (8): Matrix U and Matrix V are the left and right singular value vectors, respectively, and both are unitary matrices; is a diagonal matrix of singular values; Combining the above formula, we can get the low-dimensional approximate matrix of the power system: The calculation formula is (9) ; For low-dimensional approximation matrices Perform eigenvalue decomposition: (10); In formula (10): is the eigenvalue matrix, is the non-zero eigenvalue corresponding to the oscillation mode, is the eigenvector matrix, , represents the mode in the low-dimensional space, is the number of oscillation modes; From the above conclusions: (11); Step 4: Establish the oscillation mode matrix and amplitude coefficient matrix. The specific process is as follows: According to the SVD definition of the data matrix: (12); (13); (14); In formula (12), is the oscillation mode matrix, each column Indicates the relative oscillation trend of a certain oscillation mode in the power system and reflects the spatial distribution characteristics of the power system under different modes; In formula (14), is the time-dependent amplitude coefficient matrix, describing the evolution of the amplitude of each mode over time; Step 5: Extract the oscillation mode participation factor; Estimated data series , which can be expressed as: (15); Formula (15) decomposes the dynamic behavior of the power system into the superposition of multiple modes, each of which is represented by its spatial characteristics. , time characteristics and amplitude evolution Each dynamic mode is weighted by the product of each Ritz mode value and the corresponding energy extracted from each time-varying mode. (16); Estimating the relationship between power system states and modes is a key step in understanding the contribution of each mode to the overall power system dynamics. Traditional methods use the participation factor to evaluate this relationship by multiplying the right and left eigenvectors. This method has the advantage of being independent of the units and dimensions of the state variables, providing a robust analytical tool for the relationship between power system states and modes. However, in this paper, we propose a new participation definition method that directly incorporates the dynamic characteristics of the power system's evolution over time and space, thereby more comprehensively quantifying the degree of modal participation.

[0016] From this, we define the state-mode relationship: (17); In formula (17), Provides a measure of the mode's participation in the power system state; The participation factor matrix is ​​established, which is calculated by summing the row vectors of the above formula and is used to associate the power system state and mode: (18); (19); in, It is the participation factor, which is directly related to the spatial distribution and temporal characteristics of the mode. It can describe the contribution of the mode at both the local and global levels.

[0017] The data-driven participation factor calculation method proposed in this paper extracts participation factors based on dynamic mode decomposition. This method extracts modal information from the power system in a data-driven manner. Based on the extracted modal information and participation factors, it analyzes the dynamic behavior of the power system, identifies the dominant modes and key nodes in the power system, and provides a basis for dynamic stability analysis and control of the power system. This method avoids the reliance on mathematical models of the power system found in traditional methods, simplifies the calculation process, and improves computational efficiency. Compared with traditional methods, this method has higher practical application value and can meet the real-time analysis requirements of modern power systems.

[0018] The present invention is described in further detail below in conjunction with examples: The accuracy of the extracted participation factors is verified on a 10kV resonant grounded power system simulation model built by PSCAD / EMTDC electromagnetic simulation software. The model includes 5 lines. Assuming that a single-phase grounding fault occurs on line L3, the fault transition resistance is 10Ω, the fault initial phase angle is 90°, the model sampling frequency is 20kHz, and the fundamental frequency is 50Hz. The transient zero-sequence current of each line is collected by measuring equipment as the dynamic response data input of the 10kV resonant grounded power system. The dynamic response data of the 10kV resonant grounded power system is as follows: Figure 2 The data-driven participation factor calculation method proposed in this application is used to identify the dynamic response data of the 10kV resonant grounded power system, and the obtained participation factors and the participation degrees of each modal participation factor are shown in the figure. like Figure 3 shown.

[0019] In the above example, the two sets of dominant oscillation frequencies identified by the DMD method are 50.15Hz and 370.56Hz, which are basically consistent with the dominant oscillation frequencies of the power system identified by FFT, 49.94Hz and 374.53Hz. Figure 3It can be seen that mode 3 has a significantly higher degree of participation in the overall power system than other modes. According to the participation formula introduced in the theory of this invention, mode 3 has a greater dynamic impact on power system faults. This is consistent with the energy concentration of the fault characteristic signal at a specific frequency and on a specific line. This mode can be used as a dominant characteristic mode to identify fault lines. At the same time, the adaptability analysis of the algorithm proposed in this invention was carried out under different setting conditions. The results are shown in Table 1. Table 1 Extraction effect of participating factors by the method of the present invention Fault line transition resistance Signal-to-noise ratio Fault distance Initial phase angle <![CDATA[P ki ]]> Extract results L1 20 0 3 30° <![CDATA[[ 200.80 51.98 54.85 70.41 35.59]]]> correct L1 20 0 8 30° <![CDATA[[ 193.17 53.16 50.84 66.48 34.09]]]> correct L2 10 5 15 0° <![CDATA[[30.15 199.14 32.36 48.87 21.64]]]> correct L2 10 20 15 0° <![CDATA[[54.26 172.25 55.67 81.26 37.17]]]> correct L4 500 0 5 30° <![CDATA[[30.51 37.55 40.43 99.11 26.76]]]> correct L4 2000 0 5 30° <![CDATA[[16.61 18.10 19.31 40.01 12.76]]]> correct L5 15 5 10 30° <![CDATA[[29.30 30.15 30.49 36.71 1 61.27 ]]]> correct L5 15 5 10 60° <![CDATA[[19.07 20.12 20.99 25.27 1 34.79 ]]]> correct

[0020] The above analyses all validate the modal information extracted using the DMD method, calculate the participation factor of the power system, analyze the dynamic behavior of the power system based on the participation factor calculation results, identify the dominant modes and key nodes in the power system, and provide a basis for dynamic stability analysis and control of the power system. This method also demonstrates good robustness. The above examples demonstrate the feasibility and effectiveness of the present method in analyzing the dynamic behavior of power systems.

[0021] The software program involved in the present invention is compiled based on mobile communication, network and computer processing technologies, and the software program involved in the present invention is a technology familiar to those skilled in the art.

[0022] The above embodiments can be implemented in whole or in part via software, hardware (e.g., circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions or computer programs. When loaded or executed on a computer, the processes or functions described in accordance with the embodiments of the present invention are fully or partially performed. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0023] It should be understood that the term "and / or" as used herein simply describes a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B together, or B alone. A and B can be singular or plural. Furthermore, the character " / " as used herein generally indicates an "or" relationship between the associated objects, but it may also indicate an "and / or" relationship. For specific understanding, please refer to the context.

[0024] In this disclosure, "at least one" means one or more, and "plurality" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, "at least one of a, b, or c" can mean: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or plural.

[0025] It should be understood that in various embodiments of the present invention, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0026] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0027] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described equipment, devices and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0028] In the several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interface, indirect coupling or communication connection of the device or unit, which can be electrical, mechanical or other forms.

[0029] The units described as separate components may or may not be physically separate, and 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 these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0030] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0031] If the functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or the portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media that can store program code, such as USB flash drives, mobile hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0032] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person 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 based on the scope of protection of the claims.

Claims

1. A data-driven participation factor calculation method, characterized in that: The following steps are involved: Step 1: Construct the Hankel matrix using the dynamic response data of the power system; The acquired dynamic response data of the power system is used as input, and a matrix is ​​constructed using the dynamic response data of the discrete power system; Step 2: perform linear mapping approximation on the discrete sampled measurement data; Step 3: Use DMD decomposition to extract low-dimensional modal information; Step 4: Establish the oscillation mode matrix and amplitude coefficient matrix; Step 5: Extract oscillation mode participation factors: Decompose the dynamic behavior of the power system into a superposition of multiple modes, each of which is determined by its spatial characteristics, temporal characteristics, and amplitude evolution; define a state-mode relationship to represent the measure of the mode's participation in the power system state; A participation factor matrix is ​​established to associate the power system state and mode. The participation factor is directly related to the spatial distribution and temporal characteristics of the mode, and can describe the contribution of the mode at both the local and global levels.

2. A data-driven participation factor calculation method according to claim 1, characterized in that: In step 1, the acquired dynamic response data of the power system is used as input, and the following Hankel matrix is ​​constructed using the dynamic response data of the discrete power system: （1）； In formula (1): express At the sampling point Sampling data at Indicates the A vector of all observable sample values ​​at a given moment.

3. A data-driven participation factor calculation method according to claim 2, characterized in that: In step 2, the discrete sampled measurement data can be approximately represented by a linear mapping as follows: （2）； In formula (2): It is a high-order complex matrix that can capture the dynamic change characteristics inherent in the measurement information. Its eigenvalues ​​and eigenvectors contain the dynamic oscillation information of the power system. Get the Krylov subspace sequence, expressed as （3）； （4）； （5）； From formulas (3)-(5), we can get: （6）。 4. A data-driven participation factor calculation method according to claim 3, characterized in that: In step 3, DMD decomposition is used to extract low-dimensional modal information: Through the original data matrix Orthogonal projection decomposition of : （7）； In formula (7): Represents A low-dimensional approximation matrix with similar features but with irrelevant features discarded; is a matrix The left singular vector matrix of the singular value decomposition (SVD) is as follows: （8）； In formula (8): Matrix U and Matrix V are the left and right singular value vectors, respectively, and both are unitary matrices; is a diagonal matrix of singular values; Combining the above formula, we can get the low-dimensional approximate matrix of the power system: The calculation formula is （9） ； For low-dimensional approximation matrices Perform eigenvalue decomposition: （10）； In formula (10): is the eigenvalue matrix, is the non-zero eigenvalue corresponding to the oscillation mode, is the eigenvector matrix, , represents the mode in the low-dimensional space, is the number of oscillation modes; From the above conclusions: （11）。 5. A data-driven participation factor calculation method according to claim 4, characterized in that: In step 4, the process of establishing the oscillation mode matrix and amplitude coefficient matrix is ​​as follows: According to the SVD definition of the data matrix: （12）； （13）； （14）； In formula (12), is the oscillation mode matrix, each column Indicates the relative oscillation trend of a certain oscillation mode in the power system and reflects the spatial distribution characteristics of the power system under different modes; In formula (14), is the time-dependent amplitude coefficient matrix that describes the evolution of the amplitude of each mode with time.

6. A data-driven participation factor calculation method according to claim 5, characterized in that: In step 5, the process of extracting the oscillation mode participation factor is as follows: Estimated data series , which can be expressed as: （15）； Formula (15) decomposes the dynamic behavior of the power system into the superposition of multiple modes, each of which is represented by its spatial characteristics. , time characteristics and amplitude evolution Each dynamic mode is weighted by the product of each Ritz mode value and the corresponding energy extracted from each time-varying mode. (16); Define the state-mode relationship: （17）； In formula (17), Provides a measure of the mode's participation in the power system state; The participation factor matrix is ​​established, which is calculated by summing the row vectors of the above formula and is used to associate the power system state and mode: （18）； （19）； in, It is the participation factor, which is directly related to the spatial distribution and temporal characteristics of the mode. It can describe the contribution of the mode at both the local and global levels.

7. A data-driven participation factor calculation method according to claim 1, characterized in that: In step 1, the dynamic response data of the power system is obtained through time domain simulation or PMU.

8. A data-driven participation factor calculation method according to claim 7, characterized in that: Obtain dynamic response data of the power system based on time domain simulation or PMU measurement: （20）； In formula (20), The dynamic response of the power system The sampling value at the moment, is the sampling interval.

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