Disturbance source positioning method based on dynamic mode decomposition

Abstract

The invention relates to a disturbance source positioning method based on dynamic mode decomposition, which belongs to the technical field of power system operation and analysis and comprises the following steps of: accurately extracting oscillation mode characteristics of a system by performing matrix decomposition on actually measured data; furthermore, a participation factor analysis model fusing time-space characteristics is constructed, and the spatial distribution characteristics and the time evolution characteristics of the modal are comprehensively considered, so that accurate positioning of the oscillation source is realized. Compared with a traditional method, the method has the advantages of no dependence on a detailed system model, high positioning precision and the like, is realized completely based on measurement data calculation, avoids complex system modeling, and has relatively high practical application value and popularization potential.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system operation and analysis, and in particular relates to a disturbance source locating technology based on a dynamic mode decomposition method, which is used for identifying and locating forced disturbance sources in a power system. Background Art

[0002] In recent years, the integration of renewable energy, the development of communication technology, and smart grids have increased the complexity of power systems, resulting in frequent and diverse system disturbances. Accurately identifying and locating disturbance sources in power systems is crucial to ensuring stable system operation. Oscillations in power systems are primarily categorized as natural oscillations, which stem from the inherent characteristics of the system itself, and forced oscillations, which are caused by the continuous injection of energy from external disturbance sources. While mature solutions exist for natural oscillations, forced oscillations, due to their propagation characteristics and location complexity, have become the primary focus of this research. Disturbance source location primarily relies on analysis of data collected by synchronized phasor measurement units (PMUs), but traditional methods often struggle to accurately distinguish between disturbance sources and disturbance responses when faced with complex disturbances.

[0003] Therefore, developing a new method that can effectively identify and accurately locate disturbance sources in power systems is of great significance. Dynamic mode decomposition (DMD), an emerging data-driven analysis method, can extract key dynamic features from high-dimensional time series data without relying on physical system models. Therefore, researching a disturbance source location method based on DMD is of great significance for improving power grid security and optimizing control strategies.

[0004] In summary, in view of the shortcomings of existing technologies, it is urgent to develop a high-precision, low-computational complexity disturbance source identification and location method to effectively deal with the increasingly complex forced oscillation problems in power systems and improve the stable operation level of the system. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a disturbance source locating method based on dynamic pattern decomposition, which is used to solve the existing technical problems of low disturbance source identification accuracy, high algorithm complexity, and difficulty in adapting to the ever-changing forms of modern power systems.

[0006] A disturbance source location method based on dynamic mode decomposition includes the following steps, which are performed in sequence: Step 1: Collect power system oscillation data, including active power P, bus voltage V, and frequency f, through synchronized phasor measurement units (PMUs) distributed at generator locations. Step 2: Using power system oscillation data as input, a dynamic mode decomposition model is constructed; Step 3: Perform FFT spectrum analysis on the oscillation mode to identify the main oscillation frequency of the power system. According to the characteristics of the modal phase trajectory, it can be divided into natural oscillation and forced oscillation. Step 4: Calculate the participation factor. Use the participation factor to quantify the oscillation mode in time and space dimensions, and identify the generator unit with a high participation factor value as the oscillation source.

[0007] The dynamic mode decomposition model described in step 2 is: , Where, U is the left singular vector matrix, Y is the eigenvector matrix, is the right singular vector matrix, is the oscillation mode matrix, each column Represents the spatial distribution characteristics of a certain oscillation mode of the system; is the time-dependent amplitude coefficient matrix, m is the number of oscillation modes, For modal j The eigenvalue of .

[0008] The calculation method of the participation factor in step 4 is: ① Calculate the modal time-varying energy: , Where, For modal j The characteristic value of k is the time step; Initial state In the j projection onto a modality; ② Construct participation factors: , Where, is the element in the right eigenvector matrix, corresponding to the mode j In the state variable i The spatial component on .

[0009] The above-mentioned design scheme achieves the following beneficial effects: a method for locating disturbance sources based on dynamic mode decomposition accurately extracts the system's oscillation modal characteristics by performing matrix decomposition on measured data. Furthermore, a participating factor analysis model integrating spatiotemporal characteristics is constructed to comprehensively consider the spatial distribution and temporal evolution characteristics of the modalities, enabling precise localization of the oscillation source. Compared with traditional methods, this method offers advantages such as high positioning accuracy without relying on detailed system models. Furthermore, this method is completely based on measured data, avoiding complex system modeling, and thus possesses high practical application value and potential for widespread adoption. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The present invention will be further described below with reference to the accompanying drawings and specific embodiments: Figure 1 The figure is a schematic block diagram of the flow of a disturbance source location method based on dynamic mode decomposition according to the present invention.

[0011] Figure 2 This is a topology diagram of the WECC 179 node system in a specific implementation manner of the present invention.

[0012] Figure 3 This is a phase trajectory diagram of the forced oscillation mode in a specific embodiment of the present invention.

[0013] Figure 4 This is a heat diagram of the participation factors of each oscillation mode of the generator in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0014] A method for locating forced oscillation disturbance sources based on dynamic mode decomposition, such as Figure 1 As shown: The following steps are included: Step 1. Data preparation: Synchronize electrical data (including active power P , bus voltage V ,frequency f ) can be generated from oscillation data captured by PMUs distributed at different generator locations.

[0015] Step 2: Using wide-area measurement data under power system oscillation conditions as input, a dynamic mode decomposition model is constructed: ① The measurement data matrix X It is divided into two parts: The measurement vector representing the previous N-1 moments of the system state; Represents the measurement vector at the next N-1 moments. The relationship between the two can be expressed as:

[0016] in, A It is a high-order complex matrix that can capture the inherent dynamic change characteristics of the measurement information. Its eigenvalues ​​and eigenvectors contain the dynamic oscillation information of the system. r is the residual matrix.

[0017] ② Process the matrix through singular value decomposition (SVD) X 1 :

[0018] in, U is the left singular vector matrix; Σ is the singular value matrix; is the right singular vector matrix.U and V are all unitary matrices.

[0019] ③ Construct a low-order approximate matrix F :

[0020] in, F is the system dynamics matrix after dimensionality reduction, F The eigenvalues ​​and eigenvectors contain the main oscillation information of the system.

[0021] ④ Calculation F The eigenvalues ​​and eigenvectors of :

[0022] in, Λ is the eigenvalue matrix, Y is the eigenvector matrix ⑤ Finally, construct the dynamic mode expression of the system:

[0023] in: is the oscillation mode matrix, each column Represents the spatial distribution characteristics of a certain oscillation mode of the system; is the time-dependent amplitude coefficient matrix, m is the number of oscillation modes.

[0024] Step 3: Oscillation characteristics analysis: FFT spectrum analysis is performed on the extracted oscillation modes to identify the main oscillation frequencies in the system. The phase trajectory characteristics of each mode are analyzed to distinguish between natural and forced oscillations. Forced oscillation modes exhibit a standard circular closed trajectory, while natural oscillation modes exhibit a spiral inward-converging phase trajectory. Forced oscillation modes are relevant to disturbance source location and are therefore used as the analysis target for subsequent oscillation source location.

[0025] Step 4: Calculate participation factor; ① Calculate the modal time-varying energy:

[0026] Among them: For modal j The characteristic value of k represents the time step; Initial state In the j Projection on a modality.

[0027] ② Construct participation factors:

[0028] in, is the element in the right eigenvector matrix, corresponding to the mode j In the state variable i The spatial component on .

[0029] By calculating the participation factor, the combined impact of each mode on the system's different state variables can be accurately quantified in both time and space, providing a theoretical basis for oscillation source location. However, its accuracy depends heavily on the quality and integrity of the measurement data. In actual power systems, factors such as measurement noise, missing data, and system parameter uncertainty can affect the accuracy of the participation factor calculation. Therefore, in its application, it is necessary to combine prior knowledge of the system with various auxiliary methods for cross-validation to ensure the reliability of oscillation source location.

[0030] Step 5: Locate the oscillation source; By analyzing the participation factor distribution of each generator in the forced oscillation mode, the generator unit with the highest participation factor value is identified as the oscillation source. Using a heat map, the participation factor distribution of each generator in the forced oscillation mode can be visually displayed, accurately locating the source of the system's forced oscillation, thus completing the oscillation source location.

[0031] The present invention utilizes the constructed dynamic mode decomposition and participation factor analysis model to obtain the forced oscillation modal characteristics and the location of the oscillation source. This step is to fully utilize the measurement data to analyze the oscillation characteristics, with the aim of avoiding system modeling and realizing data-driven forced oscillation mode extraction and precise positioning of the oscillation source.

[0032] Below in conjunction with embodiment, the present invention is described in further detail: like Figure 2 The WECC 179-node system shown in the figure has a forced oscillation source located at generator 79, which uses the GENROU model, while the remaining generators use the GENCLS model. The damping parameters of all generators in the system are D The values ​​are all 4, but the D value of generator 79 is 0, and all loads adopt the constant MVA model. The forced oscillation signal is injected into the excitation system of generator 79 in the form of a 0.89 Hz sinusoidal signal.

[0033] Under the condition of forced oscillation of the system, the response of each node shows obvious oscillation fluctuation characteristics. In order to accurately locate the oscillation source, the dynamic mode decomposition technology is first used to extract the system oscillation mode, and then Figure 3 As shown in the figure, the forced oscillation mode is determined to be mode 4 through phase trajectory analysis. Finally, the participation factor of each node in this mode is calculated to locate the oscillation source. The calculation results are shown in the figure. Figure 4 shown.

[0034] The feasibility and effectiveness of the method of the present invention in locating the oscillation source of the power system were further verified by the precise positioning results of the forced oscillation source of generator No. 79.

[0035] according to Figure 4 It can be seen from the oscillation source positioning results shown that the method proposed in the present invention can accurately identify the location of the forced oscillation source and provide effective support for system oscillation suppression and stable control.

Claims

1. A disturbance source localization method based on dynamic mode decomposition, characterized by: The following steps are included: And the following steps are carried out in sequence: Step 1: Collect power system oscillation data, including active power P, bus voltage V, and frequency f, through synchronized phasor measurement units (PMUs) distributed at generator locations. Step 2: Using power system oscillation data as input, a dynamic mode decomposition model is constructed; Step 3: Perform FFT spectrum analysis on the oscillation mode to identify the main oscillation frequency of the power system. According to the characteristics of the modal phase trajectory, it can be divided into natural oscillation and forced oscillation. Step 4: Calculate the participation factor. Use the participation factor to quantify the oscillation mode in time and space dimensions, and identify the generator unit with a high participation factor value as the oscillation source.

2. The method for locating disturbance sources based on dynamic mode decomposition according to claim 1, wherein: The dynamic mode decomposition model described in step 2 is: ， Where, U is the left singular vector matrix, Y is the eigenvector matrix, is the right singular vector matrix, is the oscillation mode matrix, each column Represents the spatial distribution characteristics of a certain oscillation mode of the system; is the time-dependent amplitude coefficient matrix, m is the number of oscillation modes, For modal j The eigenvalue of .

3. The method for locating disturbance sources based on dynamic mode decomposition according to claim 1, wherein: The calculation method of the participation factor in step 4 is: ① Calculate the modal time-varying energy: ， Where, For modal j The characteristic value of k is the time step; Initial state In the j projection onto a modality; ② Construct participation factors: ， Where, is the element in the right eigenvector matrix, corresponding to the mode j In the state variable i The spatial component on .

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