A transient voltage instability identification method based on Koopman operator

Abstract

The invention provides a transient voltage instability identification method based on a Koopman operator, belonging to the technical field of power systems. The method comprises the following steps: analyzing a target area, determining a key bus, and acquiring measurement data in real time through wide-area measurement; preprocessing the measurement data, determining dynamic characteristics of the preprocessed measurement data, determining whether a system fault occurs, and determining the system dynamic characteristics and the fault range by integrating all dynamic characteristics; determining the length of a Koopman operator data window based on the dynamic characteristics and the fault range, extracting the Koopman operator, and determining the dominant dynamic mode of the corresponding system in the target area; predicting the dominant dynamic mode in the time domain, judging the transient voltage instability risk of the system in the target area according to the prediction result, quickly and accurately identifying the transient voltage instability risk of a power grid, optimizing power grid operation decisions, and enhancing the power grid's ability to respond to dynamic challenges brought about by the grid connection of new energy equipment, thereby ensuring safe and stable operation of the power grid.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a transient voltage instability identification method based on a Koopman operator. Background Art

[0002] The complexity of modern power grid structure and operation characteristics has led to a sharp increase in reactive power demand for loads mainly composed of induction motors after disturbances, resulting in prominent transient voltage stability issues. The grid connection of new energy equipment has reduced the system's dynamic reactive power reserve and support capabilities. Power electronic equipment may cause new energy stations to be disconnected from the grid when their low voltage ride-through capabilities are limited, threatening the safety of the power grid. Traditional time-domain simulation methods face the challenges of modeling difficulty and large computational complexity, and are unable to meet the needs of rapid identification of complex power grids. Summary of the invention

[0003] The present invention provides a transient voltage instability identification method based on the Koopman operator. The method obtains key bus voltage data in real time through wide-area measurement, performs preprocessing to extract dynamic features, judges system faults and determines the fault range, extracts the dominant dynamic mode using the Koopman operator, and performs time domain prediction, thereby evaluating the transient voltage instability risk in the target area, quickly and accurately identifying the transient voltage instability risk of the power grid, improving the fault detection capability, optimizing the power grid operation decision-making, and enhancing the power grid's ability to respond to the dynamic challenges brought by the grid connection of new energy equipment, thereby ensuring the safe and stable operation of the power grid.

[0004] The present invention provides a transient voltage instability identification method based on Koopman operator, comprising:

[0005] Step 1: Analyze the target area, determine the key buses, and obtain the voltage amplitude measurement data of each key bus of the target area corresponding to the system in real time through wide-area measurement;

[0006] Step 2: preprocess the measurement data, determine the dynamic characteristics of the preprocessed measurement data, determine whether the system fails based on the dynamic characteristics, determine the dynamic characteristics of the system by combining all the dynamic characteristics, and then determine the scope of the fault;

[0007] Step 3: Determine the length of the Koopman operator data window based on the dynamic characteristics and the fault range, extract the Koopman operator, and then determine the dominant dynamic mode of the corresponding system in the target area;

[0008] Step 4: Perform time domain prediction on the dominant dynamic mode, and determine the transient voltage instability risk of the system in the target area according to the prediction result.

[0009] The present invention provides a transient voltage instability identification method based on the Koopman operator, analyzes the target area, determines the key bus, and obtains the voltage amplitude measurement data of each key bus of the target area corresponding to the system in real time through wide-area measurement, including:

[0010] Divide the target area according to the identification requirements, and use the topological structure diagram of the power system to analyze the connection relationship of each bus in the target area;

[0011] Based on the connection relationship, each bus is evaluated for load level, power generation capacity, and impact on the system corresponding to the target area, and all evaluation results are combined to obtain a first bus;

[0012] Performing sensitivity analysis on other buses based on the first bus, and obtaining a second bus based on the sensitivity analysis result;

[0013] The first bus and the second bus are combined to obtain a key bus, a wide area measurement device is selected based on the key bus, and voltage amplitude measurement data of each key bus is obtained according to the wide area measurement device.

[0014] The present invention provides a transient voltage instability identification method based on the Koopman operator, which pre-processes the measured data, determines the dynamic characteristics of the pre-processed measured data, determines whether the system fails based on the dynamic characteristics, and determines the dynamic characteristics of the system by integrating all dynamic characteristics, and then determines the fault range, including:

[0015] Perform timing analysis on the preprocessed measurement data, use the dynamic time warping algorithm to calculate the distance between each timing analysis result and all reference timing patterns in the reference timing pattern table, and select the reference timing pattern with the smallest distance as the best match based on the calculated warping distance;

[0016] Extracting dynamic features from the best matching reference timing pattern, and determining potential faults by comparing the timing analysis results with the dynamic features of the reference timing pattern;

[0017] According to the topological structure diagram and the potential faults, the potential fault area is locked, and at the same time, the dynamic characteristics of the system are determined by integrating all the dynamic characteristics;

[0018] The fault range of the potential fault is determined according to the dynamic characteristics and the potential fault area.

[0019] The present invention provides a transient voltage instability identification method based on the Koopman operator, which determines the length of the Koopman operator data window based on the dynamic characteristics and the fault range, extracts the Koopman operator, and further determines the dominant dynamic mode of the corresponding system in the target area, including:

[0020] Draw a dynamic characteristic curve based on the dynamic characteristics, identify the time scale of characteristic changes, record the dynamic performance of different dynamic characteristics over time, and identify the key time points that affect system behavior;

[0021] According to the characteristic change time scale, a data window is selected from the change-window table, and the length of the data window is determined according to the fault range, and the state space of the system is constructed using the data window;

[0022] Extracting window data corresponding to all sampling points in the selected data window from the measurement data, and determining a Koopman operator based on the window data;

[0023] Perform eigenvalue decomposition on the Koopman operator, and identify the dominant dynamic mode according to the decomposition result.

[0024] The present invention provides a transient voltage instability identification method based on a Koopman operator, and the Koopman operator is determined according to the window data, comprising:

[0025] constructing a numerical matrix according to the window data, constructing a first Hankel matrix and a second Hankel matrix based on a row in the numerical matrix, and constructing a proportional factor using the first Hankel matrix and the second Hankel matrix;

[0026] Reconstructing a data matrix according to the scale factor and the first Hankel matrix and the second Hankel matrix at different sampling points;

[0027] The data matrix is ​​mapped to the state space using an observation function, thereby obtaining a Koopman operator.

[0028] The present invention provides a transient voltage instability identification method based on a Koopman operator, wherein the Koopman operator is subjected to eigenvalue decomposition, and a dominant dynamic mode is identified according to the decomposition result, comprising:

[0029] Perform eigenvalue decomposition and singular value decomposition on the Koopman operator to obtain the eigenvalue, right eigenvector and left singular vector;

[0030] The dominant mode is selected according to the modulus length of the eigenvalue, the dynamic mode is constructed according to the right eigenvector corresponding to each eigenvalue, and the weight of each dynamic mode is calculated using the left singular vector;

[0031] The dominant dynamic mode of the system in the target area is obtained by integrating all the dominant modes.

[0032] The present invention provides a transient voltage instability identification method based on the Koopman operator, which performs time domain prediction on the dominant dynamic mode and determines the transient voltage instability risk of the system in the target area according to the prediction result, including:

[0033] Establishing a time domain prediction model according to the dominant dynamic mode, determining a maximum Lyapunov exponent formula according to the time domain prediction model, and calculating the maximum Lyapunov exponent;

[0034] If the calculation result is always negative, it means that there is no transient voltage instability in the system in the target area;

[0035] If the calculated result is a positive value, it means that the system will experience transient voltage instability after the fault occurs.

[0036] The present invention provides a transient voltage instability identification method based on the Koopman operator, establishing a time domain prediction model according to the dominant dynamic mode, determining a maximum Lyapunov exponent formula according to the time domain prediction model, and calculating the maximum Lyapunov exponent, including:

[0037] ,in, Represents the dynamic change of the j-th Koopman operator output by the time domain prediction model at time t; The eigenvalue of the j-th Koopman operator represented by; represents the left singular vector; represents the right eigenvector of the j-th Koopman operator; The data vector representing the sampling data of all sampling points at time t;

[0038] ,in, represents the calculation result of the maximum Lyapunov exponent; N represents the number of preset initial conditions; k=1,...,m, is the length of the finite time series, k>N; and Indicates a time interval; Represents a definer, indicating that the expression on the left is defined as the expression on the right; represents the j-th Koopman operator at time step With time step The norm of the dynamic change between ; represents the j-th Koopman operator at time step With time step The amount of dynamic change between ; m represents the number of steps from the current time step forward; represents the length of each time step; n represents the total number of time steps in the data window.

[0039] Compared with the prior art, the beneficial effects of the present application are as follows: through wide-area measurement, key bus voltage data is acquired in real time, preprocessing is performed to extract dynamic features, system faults are judged and the fault range is determined, the dominant dynamic mode is extracted using the Koopman operator, and time domain prediction is performed to evaluate the risk of transient voltage instability in the target area, quickly and accurately identify the risk of transient voltage instability in the power grid, improve fault detection capabilities, optimize power grid operation decisions, and enhance the power grid's ability to respond to dynamic challenges brought about by the connection of new energy equipment to the grid, thereby ensuring safe and stable operation of the power grid.

[0040] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description and the accompanying drawings.

[0041] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0043] Figure 1 It is a flow chart of a transient voltage instability identification method based on Koopman operator provided by an embodiment of the present invention;

[0044] Figure 2 is a schematic diagram of a Hankel matrix structure provided by an embodiment of the present invention;

[0045] Figure 3 It is a flow chart of a transient voltage instability identification method based on Koopman operator provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0047] Embodiment 1:

[0048] The embodiment of the present invention provides a transient voltage instability identification method based on Koopman operator, such as Figure 1 and Figure 3 As shown, including:

[0049] Step 1: Analyze the target area, determine the key buses, and obtain the voltage amplitude measurement data of each key bus of the target area corresponding to the system in real time through wide-area measurement;

[0050] Step 2: preprocess the measurement data, determine the dynamic characteristics of the preprocessed measurement data, determine whether the system fails based on the dynamic characteristics, determine the dynamic characteristics of the system by combining all the dynamic characteristics, and then determine the scope of the fault;

[0051] Step 3: Determine the length of the Koopman operator data window based on the dynamic characteristics and the fault range, extract the Koopman operator, and then determine the dominant dynamic mode of the corresponding system in the target area;

[0052] Step 4: Perform time domain prediction on the dominant dynamic mode, and determine the transient voltage instability risk of the system in the target area according to the prediction result.

[0053] In this embodiment, the critical bus is a bus that plays a critical role in the system, which is determined by comprehensively considering the importance of the first bus and the second bus. For example, in a certain area, bus 1 and bus 2 jointly support the main load and are therefore regarded as critical busses.

[0054] In this embodiment, the wide area measurement equipment is a device used to monitor the state of the power system in real time, and generally includes a wide area measurement unit (PMU). For example, a PMU device installed in a power grid can monitor the voltage and frequency of each bus in real time.

[0055] In this embodiment, the voltage amplitude measurement data is the voltage amplitude data of the key bus obtained from the wide area measurement equipment. For example, at a certain moment, the voltage amplitude of bus 1 is 230V, and the voltage amplitude of bus 2 is 225V.

[0056] In this embodiment, preprocessing the measured data involves cleaning and normalizing the original measured data to remove noise and abnormal values. For example, sudden noise is removed from voltage and current data, and clear time series data is obtained after smoothing.

[0057] In this embodiment, dynamic characteristics refer to the overall behavioral characteristics of the system in the time domain, which usually reflect the response mode and stability of the system under different states. These characteristics may include the frequency response, stability, oscillation mode, attenuation rate, etc. of the system. For example, in the power system, dynamic characteristics may include: the response time of the system to load changes, the ability of the system to recover to a steady state after a fault, and the transient stability of the system (such as the Lyapunov index); dynamic characteristics are the behavioral indicators of the system at a specific moment or a specific event, which are usually specific quantitative indicators extracted from time series data. These characteristics can be instantaneous, local, and are usually used to describe a specific state or behavior of the system. For example, in the power system, dynamic characteristics may include: voltage amplitude at a specific moment, instantaneous value of frequency, power fluctuation amplitude within a period of time. The difference between the two is that dynamic characteristics is a broader concept, covering the overall behavior and response pattern of the system; dynamic characteristics are specific indicators extracted from dynamic characteristics, usually quantitative descriptions of specific events or moments; dynamic characteristics are used to evaluate and analyze the overall performance and stability of the system; dynamic characteristics are used for specific fault detection and analysis, identifying potential faults by comparing dynamic characteristics with reference patterns; dynamic characteristics usually involve responses and behaviors on longer time scales; dynamic characteristics may be instantaneous or short-term behavioral manifestations.

[0058] In this embodiment, the fault range is determined based on the dynamic characteristics and the potential fault area to determine the fault range of the potential fault. For example, the fault range is locked at the load access point of bus B, which may affect multiple connected distribution lines.

[0059] In this embodiment, by performing timing analysis on the preprocessed measurement data, a dynamic time warping algorithm is used to calculate the distance to the reference timing pattern, and the pattern with the smallest distance is selected as the best match. Dynamic features are extracted from the pattern, and comparative analysis is performed to determine potential faults. The fault area is then locked in combination with the topological structure diagram.

[0060] In this embodiment, the Koopman operator is a linear operator used to analyze dynamic systems. The dynamic characteristics of a nonlinear system are studied by converting the nonlinear system into a linear form. For example, the dynamic characteristics of the system are extracted by applying the Koopman operator to the power system state data.

[0061] In this embodiment, the dominant dynamic mode is the main dynamic behavior mode of the system identified by eigenvalue decomposition. For example, after analysis, it is found that the dominant dynamic mode of the power system is the "voltage drop caused by load increase" mode.

[0062] In this embodiment, by drawing a dynamic characteristic curve, the time scale and key time points of the characteristic change are identified, and based on this, a suitable data window is selected. The window length is determined in combination with the fault range, and the state space of the system is constructed. The sampling points in the window are extracted from the measured data. The Koopman operator is determined through these data, and eigenvalue decomposition is performed to identify the dominant dynamic mode.

[0063] In this embodiment, the first and second Hankel matrices are generated based on the rows of the matrix, the scale factors are calculated using these two matrices, the data matrix is ​​reconstructed by combining the scale factors and the Hankel matrices of different sampling points, and the data matrix is ​​mapped to the state space using the observation function, thereby obtaining the Koopman operator.

[0064] In this embodiment, a time domain prediction model is established based on the dominant dynamic mode, and the calculation formula of the maximum Lyapunov exponent is determined by using the model, and calculation is performed. If the Lyapunov exponent is a negative value, it indicates that the system has not experienced transient voltage instability in the target area; if it is a positive value, it indicates that the system may experience transient voltage instability after a fault occurs.

[0065] The working principle and beneficial effects of the above technical solution are: through wide-area measurement, key bus voltage data is acquired in real time, pre-processing is performed to extract dynamic features, system faults are judged and the fault range is determined, the dominant dynamic mode is extracted using the Koopman operator, and time domain prediction is performed to evaluate the risk of transient voltage instability in the target area, quickly and accurately identify the risk of transient voltage instability in the power grid, improve fault detection capabilities, optimize power grid operation decisions, and enhance the power grid's ability to respond to dynamic challenges brought about by the connection of new energy equipment to the grid, thereby ensuring safe and stable operation of the power grid.

[0066] Embodiment 2:

[0067] The embodiment of the present invention provides a transient voltage instability identification method based on the Koopman operator, analyzes the target area, determines the key bus, and obtains the voltage amplitude measurement data of each key bus of the system corresponding to the target area in real time through wide-area measurement, including:

[0068] Divide the target area according to the identification requirements, and use the topological structure diagram of the power system to analyze the connection relationship of each bus in the target area;

[0069] Based on the connection relationship, each bus is evaluated for load level, power generation capacity, and impact on the system corresponding to the target area, and all evaluation results are combined to obtain a first bus;

[0070] Performing sensitivity analysis on other buses based on the first bus, and obtaining a second bus based on the sensitivity analysis result;

[0071] The first bus and the second bus are combined to obtain a key bus, a wide area measurement device is selected based on the key bus, and voltage amplitude measurement data of each key bus is obtained according to the wide area measurement device.

[0072] In this embodiment, the topology diagram is a diagram showing the connection relationship between various components (such as busbars, transformers, transmission lines, etc.) in the power system, for example, a power grid diagram showing different busbars and their interconnected lines.

[0073] In this embodiment, the connection relationship is the physical connection between the bus and other devices. For example, the bus A is connected to the transformer B and the load C through a transmission line.

[0074] In this embodiment, load level assessment is to analyze the load conditions of each bus in the target area to evaluate its load distribution and operating status, for example, to evaluate whether the load of a bus during peak hours is close to its rated capacity; power generation capacity assessment is to evaluate the power generation capacity and response capability of the generator in the target area, for example, to determine the maximum output power of a power plant under specific conditions; impact assessment is to analyze the impact of a specific bus fault or load change on the entire system, for example, to simulate the impact of a transmission line fault on voltage stability and current distribution.

[0075] In this embodiment, the first bus is a bus that is determined to be important in the target area according to the evaluation result. For example, in a substation, bus 1 is determined to be the first bus because it is connected to multiple important loads.

[0076] In this embodiment, sensitivity analysis is to evaluate the response of the system to changes in input parameters to identify key influencing factors, for example, analyzing the impact of a 5% load increase on the voltage level to determine which buses are most sensitive to voltage fluctuations.

[0077] In this embodiment, the second bus is a bus determined in the sensitivity analysis to be inferior to the first bus but still important. For example, in the sensitivity analysis, it is found that bus 2 has a greater response to voltage changes, so it is determined to be the second bus.

[0078] The working principle and beneficial effects of the above technical solution are: analyze the connection relationship of the busbars in the target area through the power system topology diagram, evaluate the load level and power generation capacity of each busbar, determine the first busbar based on the comprehensive evaluation results, perform sensitivity analysis on the first busbar to identify the second busbar, and finally determine the key busbar. Based on these key buses, select wide-area measurement equipment and obtain voltage amplitude data to support subsequent dynamic analysis and fault detection, improve the ability to identify key buses in the power system, optimize resource allocation, enhance real-time monitoring of the dynamic behavior of the power grid, and improve fault warning and response speed, thereby ensuring the safe and stable operation of the power grid.

[0079] Embodiment 3:

[0080] The embodiment of the present invention provides a transient voltage instability identification method based on the Koopman operator, which pre-processes the measurement data, determines the dynamic characteristics of the pre-processed measurement data, determines whether the system fails based on the dynamic characteristics, and determines the dynamic characteristics of the system by combining all dynamic characteristics, and then determines the fault range, including:

[0081] Perform timing analysis on the preprocessed measurement data, use the dynamic time warping algorithm to calculate the distance between each timing analysis result and all reference timing patterns in the reference timing pattern table, and select the reference timing pattern with the smallest distance as the best match based on the calculated warping distance;

[0082] Extracting dynamic features from the best matching reference timing pattern, and determining potential faults by comparing the timing analysis results with the dynamic features of the reference timing pattern;

[0083] According to the topological structure diagram and the potential faults, the potential fault area is locked, and at the same time, the dynamic characteristics of the system are determined by integrating all the dynamic characteristics;

[0084] The fault range of the potential fault is determined according to the dynamic characteristics and the potential fault area.

[0085] In this embodiment, the timing analysis is to perform timing analysis on the pre-processed measurement data to extract time series features, for example, to analyze the timing diagram of voltage fluctuations to identify periodic fluctuations and mutation points.

[0086] In this embodiment, the dynamic time warping algorithm uses the DTW algorithm to calculate the distance between each timing analysis result and all reference modes in the reference timing mode table. For example, the current voltage fluctuation timing result is subjected to DTW calculation with the historical normal mode to obtain the warping distance between different modes.

[0087] In this embodiment, the best matching mode is selected based on the calculated regularized distance, and the reference timing mode with the smallest distance is selected as the best match. For example, the distance between the current timing analysis result and the reference mode A is 0.2, and the distance with mode B is 0.5, so mode A is selected as the best match.

[0088] In this embodiment, comparing dynamic features is to compare the dynamic features of the timing analysis results with the dynamic features of the reference timing pattern to determine potential faults. For example, the amplitude change rate of the timing analysis results is 20 V / s, which is significantly higher than 10 V / s of mode A, indicating that a fault may exist.

[0089] In this embodiment, locking the potential fault area is to lock the fault area by combining the topological structure diagram with the potential fault information. For example, according to the fault signal location, it is determined that the fault may occur between bus B and bus C.

[0090] In this embodiment, determining the dynamic characteristics of the system is to comprehensively analyze the dynamic characteristics of the system by combining all dynamic features. For example, the dynamic characteristics of the system show that when the load surges, the voltage fluctuates greatly and the stability decreases.

[0091] The working principle and beneficial effects of the above technical solution are: by performing time series analysis on the pre-processed measurement data, using the dynamic time warping algorithm to calculate the distance to the reference time series pattern, selecting the pattern with the smallest distance as the best match, extracting dynamic features from the pattern, and performing comparative analysis to determine potential faults. The fault area is locked in combination with the topological structure diagram, and the fault range is determined by combining the dynamic features, so as to achieve rapid identification of the dynamic behavior of the power system, improve the accuracy and efficiency of fault detection, and enhance the system's ability to respond to the challenges brought by load changes and new energy access, thereby ensuring the safe and stable operation of the power grid.

[0092] Embodiment 4:

[0093] The embodiment of the present invention provides a transient voltage instability identification method based on the Koopman operator, which determines the length of the Koopman operator data window based on the dynamic characteristics and the fault range, extracts the Koopman operator, and further determines the dominant dynamic mode of the corresponding system in the target area, including:

[0094] Draw a dynamic characteristic curve based on the dynamic characteristics, identify the time scale of characteristic changes, record the dynamic performance of different dynamic characteristics over time, and identify the key time points that affect system behavior;

[0095] According to the characteristic change time scale, a data window is selected from the change-window table, and the length of the data window is determined according to the fault range, and the state space of the system is constructed using the data window;

[0096] Extracting window data corresponding to all sampling points in the selected data window from the measurement data, and determining a Koopman operator based on the window data;

[0097] Perform eigenvalue decomposition on the Koopman operator, and identify the dominant dynamic mode according to the decomposition result.

[0098] In this embodiment, the dynamic characteristic curve is a curve that describes the response characteristic changes of the system at different time points, such as the change curve of voltage, frequency or power, for example, drawing the voltage response curve of the power system after a sudden load change (such as a large-scale power consumption peak).

[0099] In this embodiment, the characteristic change time scale is the time range of the change of the system dynamic characteristics, which usually refers to the speed at which the response reaches a steady state or changes. For example, after the load changes, the system voltage reaches 90% of the steady-state value within 5 seconds, and the time scale is 5 seconds.

[0100] In this embodiment, the dynamic performance is the behavior of the system within a specific time period, including transient response, steady-state response, etc. For example, after a fault occurs, the system frequency drops sharply within 1 second and then gradually recovers within 10 seconds.

[0101] In this embodiment, the critical time point is a time node that has a significant impact on system behavior, such as the moment of fault occurrence, recovery, or important parameter change. For example, after a certain fault, the system frequency reaches the lowest point (critical time point) within 2 seconds.

[0102] In this embodiment, the system behavior refers to the response characteristics of the system under external disturbances or internal changes, such as voltage fluctuations and frequency changes of the power system when the load suddenly increases.

[0103] In this embodiment, the change-window table records the change characteristics and data of the system in different time windows. For example, the table lists the change data of voltage, frequency, power, etc. in each time window.

[0104] In this embodiment, the length of the data window determined by the fault scope is determined by selecting an appropriate data window length for analysis based on the time of the fault and the impact scope. For example, after a short circuit fault occurs, a data window of 5 seconds before and after the fault is selected for analysis.

[0105] In this embodiment, the state space is a mathematical space used to describe the system state, and is usually composed of state variables. For example, in an electric power system, the state space may include voltage, frequency, and generator speed.

[0106] The working principle and beneficial effects of the above technical solution are: by drawing dynamic characteristic curves, identifying the time scale and key time points of characteristic changes, and selecting appropriate data windows accordingly, determining the window length in combination with the fault range, constructing the state space of the system, extracting sampling points within the window from the measured data, determining the Koopman operator through these data, and performing eigenvalue decomposition to identify the dominant dynamic mode, enhance the understanding of the dynamic behavior of the power system, quickly identify key dynamic modes, optimize fault diagnosis and response strategies, and improve the stability and reliability of the system in complex environments.

[0107] Embodiment 5:

[0108] The embodiment of the present invention provides a transient voltage instability identification method based on the Koopman operator, and the Koopman operator is determined according to the window data, such as Figure 2As shown, including:

[0109] constructing a numerical matrix according to the window data, constructing a first Hankel matrix and a second Hankel matrix based on a row in the numerical matrix, and constructing a proportional factor using the first Hankel matrix and the second Hankel matrix;

[0110] Reconstructing a data matrix according to the scale factor and the first Hankel matrix and the second Hankel matrix at different sampling points;

[0111] The data matrix is ​​mapped to the state space using an observation function, thereby obtaining a Koopman operator.

[0112] In this embodiment, the numerical matrix is ​​a matrix extracted from the measurement data, and usually contains multiple variables of time series data. For example, in the power system, the numerical matrix can be a matrix containing voltage, frequency and power at different time points.

[0113] In this embodiment, the first Hankel matrix is ​​a matrix constructed by a portion of rows of the numerical matrix, and is generally used to capture the dynamic characteristics of the system. For example, if a row of the numerical matrix is ​​[V1, V2, V3, V4], the first Hankel matrix may be: .

[0114] In this embodiment, the second Hankel matrix is ​​similar to the first Hankel matrix, but is usually constructed from another part or time point of the numerical matrix. For example, assuming that the second Hankel matrix can be: .

[0115] In this embodiment, the scaling factor is a factor used to measure the relationship between the first Hankel matrix and the second Hankel matrix, and is usually obtained through matrix operations. For example, if the eigenvalues ​​of the first Hankel matrix and the second Hankel matrix are λ1 and λ2 respectively, the scaling factor can be defined as the scaling factor =λ1 / λ2.

[0116] In this embodiment, the data matrix is ​​a matrix reconstructed by combining the scale factor and the Hankel matrix, and contains more comprehensive state information. For example, the data matrix adjusted by the scale factor may be: ,in Indicates the corresponding scale factor.

[0117] In this embodiment, the observation function is a function used to map the data matrix to the state space, which is usually nonlinear. For example, assuming that the observation function is , then each element in the data matrix needs to be mapped by this function.

[0118] The working principle and beneficial effects of the above technical solution are: generating the first and second Hankel matrices based on the rows of the matrix, using these two matrices to calculate the proportional factors, reconstructing the data matrix by combining the proportional factors and the Hankel matrices of different sampling points, and using the observation function to map the data matrix to the state space to obtain the Koopman operator, thereby improving the modeling ability of the dynamic behavior of the power system, accurately extracting system characteristics, optimizing fault detection and prediction, and enhancing the stability and responsiveness of the system under complex operating conditions.

[0119] Embodiment 6:

[0120] The embodiment of the present invention provides a transient voltage instability identification method based on the Koopman operator, performing eigenvalue decomposition on the Koopman operator, and identifying a dominant dynamic mode according to the decomposition result, including:

[0121] Perform eigenvalue decomposition and singular value decomposition on the Koopman operator to obtain the eigenvalue, right eigenvector and left singular vector;

[0122] The dominant mode is selected according to the modulus length of the eigenvalue, the dynamic mode is constructed according to the right eigenvector corresponding to each eigenvalue, and the weight of each dynamic mode is calculated using the left singular vector;

[0123] The dominant dynamic mode of the system in the target area is obtained by integrating all the dominant modes.

[0124] In this embodiment, the dominant mode is in a dynamic system. The dominant mode refers to the most significant dynamic behavior in the system response and is usually identified by the modulus of the eigenvalue. For example, in an electric power system, the dominant mode may be "voltage drop caused by load increase". If the modulus of the eigenvalue corresponding to this mode is the largest, it indicates that this mode has the strongest impact on the dynamic behavior of the system.

[0125] In this embodiment, the dynamic mode refers to the behavior of the system in a specific state, which is usually constructed through the right eigenvector and reflects the time evolution characteristics of the system.

[0126] In this embodiment, the weight is the relative importance of each dynamic mode in the overall response of the system, usually calculated by the left singular vector.

[0127] In this embodiment, the integration of the dominant mode is to obtain the dominant dynamic mode of the system in the target area by integrating all the dominant modes, so as to provide a basis for system optimization and control.

[0128] The working principle and beneficial effects of the above technical solution are: perform eigenvalue decomposition and singular value decomposition on the Koopman operator to obtain eigenvalues, right eigenvectors and left singular vectors. The dominant mode is selected according to the modulus of the eigenvalue, and the dynamic mode is constructed using the corresponding right eigenvector. The weight of each dynamic mode is calculated using the left singular vector, and finally all dominant modes are integrated to identify the dominant dynamic mode of the system in the target area, enhance the stability and security of the power grid in complex environments, and meet the needs of modern power grids for rapid identification.

[0129] Embodiment 7:

[0130] The embodiment of the present invention provides a transient voltage instability identification method based on the Koopman operator, which performs time domain prediction on the dominant dynamic mode and determines the transient voltage instability risk of the system in the target area according to the prediction result, including:

[0131] Establishing a time domain prediction model according to the dominant dynamic mode, determining a maximum Lyapunov exponent formula according to the time domain prediction model, and calculating the maximum Lyapunov exponent;

[0132] If the calculation result is always negative, it means that there is no transient voltage instability in the system in the target area;

[0133] If the calculated result is a positive value, it means that the system will experience transient voltage instability after the fault occurs.

[0134] In this embodiment, the time domain prediction model is a mathematical model used to predict the future state of the system based on historical data and dynamic patterns. It is based on the dynamic behavior of the system and is usually constructed using the Koopman operator or other dynamic system theories. The input includes historical data: the historical state data of the system, such as records of changes in voltage, frequency, power, etc. over time, dynamic patterns: the dominant dynamic patterns obtained from the Koopman operator, which describe the main dynamic behavior parameters of the system: may include the system's eigenvalues, weights, etc.; the output includes future states: predicted system states, such as voltage, frequency, and power values ​​at future times; stability indicators: such as the maximum Lyapunov exponent, which is used to evaluate the stability of the system.

[0135] The working principle and beneficial effects of the above technical solution are: a time domain prediction model is established based on the dominant dynamic mode, and the calculation formula of the maximum Lyapunov exponent is determined by using the model, and calculation is performed. If the Lyapunov exponent is negative, it indicates that the system has not experienced transient voltage instability in the target area; if it is positive, it indicates that the system may have transient voltage instability after a fault occurs, thereby enhancing the safety of the power system under complex operating conditions and supporting rapid decision-making and response.

[0136] Embodiment 8:

[0137] The embodiment of the present invention provides a transient voltage instability identification method based on the Koopman operator, establishing a time domain prediction model according to the dominant dynamic mode, determining a maximum Lyapunov exponent formula according to the time domain prediction model, and calculating the maximum Lyapunov exponent, including:

[0138] ,in, Represents the dynamic change of the j-th Koopman operator output by the time domain prediction model at time t; The eigenvalue of the j-th Koopman operator represented by; represents the left singular vector; represents the right eigenvector of the j-th Koopman operator; The data vector representing the sampling data of all sampling points at time t;

[0139] ,in, represents the calculation result of the maximum Lyapunov exponent; N represents the number of preset initial conditions; k=1,...,m, is the length of the finite time series, k>N; and Indicates a time interval; Represents a definer, indicating that the expression on the left is defined as the expression on the right; represents the j-th Koopman operator at time step With time step The norm of the dynamic change between ; represents the j-th Koopman operator at time step With time step The amount of dynamic change between ; m represents the number of steps from the current time step forward; represents the length of each time step; n represents the total number of time steps in the data window.

[0140] The working principle and beneficial effects of the above technical solution are: the dynamic change of the j-th Koopman operator at time t is output by the time domain prediction model, and the norm and change of the dynamic change are calculated by combining the eigenvalue, left singular vector and right eigenvector. Using this information, the maximum Lyapunov exponent is calculated to evaluate the stability of the system under different initial conditions, so as to determine whether the transient voltage is unstable, improve the prediction ability of the dynamic behavior of the power system, timely identify potential stability risks, and optimize the dynamic response strategy for complex power grids.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A transient voltage instability identification method based on Koopman operator, characterized in that: include: Step 1: Analyze the target area, determine the key buses, and obtain the voltage amplitude measurement data of each key bus of the target area corresponding to the system in real time through wide-area measurement; Step 2: preprocess the measurement data, determine the dynamic characteristics of the preprocessed measurement data, determine whether the system fails based on the dynamic characteristics, determine the dynamic characteristics of the system by combining all the dynamic characteristics, and then determine the scope of the fault; Step 3: Determine the length of the Koopman operator data window based on the dynamic characteristics and the fault range, extract the Koopman operator, and then determine the dominant dynamic mode of the corresponding system in the target area; Step 4: Perform time domain prediction on the dominant dynamic mode, and determine the transient voltage instability risk of the system in the target area according to the prediction result.

2. The transient voltage instability identification method based on Koopman operator according to claim 1 is characterized in that: Analyze the target area, determine the key busbars, and obtain the voltage amplitude measurement data of each key busbar of the target area corresponding to the system in real time through wide-area measurement, including: Divide the target area according to the identification requirements, and use the topological structure diagram of the power system to analyze the connection relationship of each bus in the target area; Based on the connection relationship, each bus is evaluated for load level, power generation capacity, and impact on the system corresponding to the target area, and all evaluation results are combined to obtain a first bus; Performing sensitivity analysis on other buses based on the first bus, and obtaining a second bus based on the sensitivity analysis result; The first bus and the second bus are combined to obtain a key bus, a wide area measurement device is selected based on the key bus, and voltage amplitude measurement data of each key bus is obtained according to the wide area measurement device.

3. The transient voltage instability identification method based on Koopman operator according to claim 2 is characterized in that: Preprocessing the measurement data, determining the dynamic characteristics of the preprocessed measurement data, determining whether the system fails based on the dynamic characteristics, and determining the dynamic characteristics of the system by integrating all dynamic characteristics, and then determining the scope of the failure, including: Perform timing analysis on the preprocessed measurement data, use the dynamic time warping algorithm to calculate the distance between each timing analysis result and all reference timing patterns in the reference timing pattern table, and select the reference timing pattern with the smallest distance as the best match based on the calculated warping distance; Extracting dynamic features from the best matching reference timing pattern, and determining potential faults by comparing the timing analysis results with the dynamic features of the reference timing pattern; According to the topological structure diagram and the potential faults, the potential fault area is locked, and at the same time, the dynamic characteristics of the system are determined by integrating all the dynamic characteristics; The fault range of the potential fault is determined according to the dynamic characteristics and the potential fault area.

4. The transient voltage instability identification method based on Koopman operator according to claim 1 is characterized in that: The length of the Koopman operator data window is determined based on the dynamic characteristics and the fault range, and the Koopman operator is extracted to further determine the dominant dynamic mode of the corresponding system in the target area, including: Draw a dynamic characteristic curve based on the dynamic characteristics, identify the time scale of characteristic changes, record the dynamic performance of different dynamic characteristics over time, and identify the key time points that affect system behavior; According to the characteristic change time scale, a data window is selected from the change-window table, and the length of the data window is determined according to the fault range, and the state space of the system is constructed using the data window; Extracting window data corresponding to all sampling points in the selected data window from the measurement data, and determining a Koopman operator based on the window data; Perform eigenvalue decomposition on the Koopman operator, and identify the dominant dynamic mode according to the decomposition result.

5. The transient voltage instability identification method based on Koopman operator according to claim 4 is characterized in that: Determining a Koopman operator according to the window data includes: constructing a numerical matrix according to the window data, constructing a first Hankel matrix and a second Hankel matrix based on a row in the numerical matrix, and constructing a proportional factor using the first Hankel matrix and the second Hankel matrix; Reconstructing a data matrix according to the scale factor and the first Hankel matrix and the second Hankel matrix at different sampling points; The data matrix is ​​mapped to the state space using an observation function, thereby obtaining a Koopman operator.

6. The transient voltage instability identification method based on Koopman operator according to claim 4 is characterized in that: Performing eigenvalue decomposition on the Koopman operator and identifying the dominant dynamic mode according to the decomposition result includes: Perform eigenvalue decomposition and singular value decomposition on the Koopman operator to obtain the eigenvalue, right eigenvector and left singular vector; The dominant mode is selected according to the modulus length of the eigenvalue, the dynamic mode is constructed according to the right eigenvector corresponding to each eigenvalue, and the weight of each dynamic mode is calculated using the left singular vector; The dominant dynamic mode of the system in the target area is obtained by integrating all the dominant modes.

7. The transient voltage instability identification method based on Koopman operator according to claim 1 is characterized in that: The dominant dynamic mode is predicted in the time domain, and the transient voltage instability risk of the system in the target area is determined according to the prediction results, including: Establishing a time domain prediction model according to the dominant dynamic mode, determining a maximum Lyapunov exponent formula according to the time domain prediction model, and calculating the maximum Lyapunov exponent; If the calculation result is always negative, it means that there is no transient voltage instability in the system in the target area; If the calculated result is a positive value, it means that the system will experience transient voltage instability after the fault occurs.

8. The transient voltage instability identification method based on Koopman operator according to claim 6 is characterized in that: A time domain prediction model is established according to the dominant dynamic mode, a maximum Lyapunov exponent formula is determined according to the time domain prediction model, and the maximum Lyapunov exponent is calculated, including: ,in, Represents the dynamic change of the j-th Koopman operator output by the time domain prediction model at time t; The eigenvalue of the j-th Koopman operator represented by; represents the left singular vector; represents the right eigenvector of the j-th Koopman operator; The data vector representing the sampling data of all sampling points at time t; ,in, represents the calculation result of the maximum Lyapunov exponent; N represents the number of preset initial conditions; k=1,...,m, is the length of the finite time series, k>N; and Indicates a time interval; Represents a definer, indicating that the expression on the left is defined as the expression on the right; represents the j-th Koopman operator at time step With time step The norm of the dynamic change between ; represents the j-th Koopman operator at time step With time step The amount of dynamic change between ; m represents the number of steps from the current time step forward; represents the length of each time step; n represents the total number of time steps in the data window.

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