Method and device for extracting low frequency and subsynchronous oscillation parameters of power system and medium

Abstract

The application discloses a power system low-frequency and subsynchronous oscillation parameter extraction method and device and a medium, and relates to the technical field of power system automation. The method comprises the following steps: acquiring active power data of each substation, detecting and intercepting effective oscillation data through a sliding window method to generate a signal to be analyzed; performing modal decomposition on the signal to be analyzed, combining a Hilbert-Huang transform to calculate the frequency characteristics and energy of each component, so that a target modal component is screened out; constructing an extended autocorrelation matrix based on the target modal component, adaptively determining the order of an exponential decay oscillation model by singular value decomposition, and solving the fine oscillation parameters by using a parameterized spectrum estimation method; performing consistency checking on the oscillation parameters and the frequency characteristics to lock the effective modal component, and extracting the oscillation parameters of the power system according to the effective modal component. The application effectively overcomes the defects of the traditional algorithm, such as the dependence on empirical order determination and the easy generation of false modes, and significantly improves the precision and reliability of the extraction of the oscillation parameters of the power system under complex working conditions.

Description

Technical Field

[0001] This invention relates to a method, apparatus, and medium for extracting low-frequency and subsynchronous oscillation parameters in power systems, belonging to the field of power system automation technology. Background Technology

[0002] With the accelerated construction of a new power system dominated by new energy sources, the high proportion of new energy power generation and the high proportion of power electronic equipment connected to the grid have given the system a "double high" characteristic, resulting in significant changes in its dynamic characteristics. The system's equivalent inertia has decreased, its damping characteristics have weakened, and power system oscillations have become increasingly prominent, exhibiting a trend of continuously expanding frequency bands and more complex mechanisms. Among these, low-frequency oscillations and subsynchronous oscillations are core factors affecting the safe and stable operation of power systems with a high proportion of new energy. The widespread application of wide-area measurement systems provides a high-time-resolution, wide-area synchronous data foundation for oscillation monitoring and analysis. However, actual measurement data suffers from strong noise interference, significant non-stationary characteristics, and short oscillation durations, making it difficult to extract key modal parameters such as frequency, damping ratio, and amplitude of low-frequency and subsynchronous oscillations with high precision.

[0003] Existing methods for identifying power system oscillations mainly include: parametric spectrum estimation methods, which have high accuracy in low-frequency and subsynchronous oscillation analysis, but are sensitive to noise and heavily dependent on the appropriate setting of the model order, easily generating spurious modes or missing true modes, resulting in poor stability of the identification results; and mode decomposition methods, which can decompose non-stationary signals into multiple independent modal components, achieving decoupling of multimodal oscillations to some extent, and are suitable for the analysis of complex oscillation signals, but suffer from problems such as mode aliasing, endpoint effects, and unstable decomposition results, and are difficult to directly obtain key parameters such as damping ratio. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, and medium for extracting low-frequency and subsynchronous oscillation parameters in power systems. It aims to solve the technical problems in the prior art where parametric spectrum estimation methods are sensitive to noise, easily generate false modes or omit true modes, resulting in unstable identification results, and the mode decomposition methods suffer from mode aliasing and endpoint effects, making it difficult to obtain key parameters.

[0005] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution.

[0006] On one hand, the present invention provides a method for extracting low-frequency and subsynchronous oscillation parameters of power systems, including:

[0007] Acquire active power data uploaded by each substation in the wide-area measurement system;

[0008] Based on active power data, the sliding window method is used to detect the start and end of oscillations in order to extract effective oscillation data. The effective oscillation data is then preprocessed to obtain the signal to be analyzed.

[0009] Modal decomposition is performed on the signal to be analyzed to obtain multiple modal components;

[0010] Perform Hilbert-Huang transform on each modal component, calculate the frequency characteristics and energy of each modal component, and select the target modal component from multiple modal components according to preset constraints.

[0011] Based on the target modal components, an exponentially decaying oscillation model is established and an extended autocorrelation matrix is ​​constructed. By performing singular value decomposition on the extended autocorrelation matrix, the order of the exponentially decaying oscillation model is determined. The parametric spectral estimation method is then used to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target modal components.

[0012] Based on the oscillation parameters and frequency characteristics, a consistency check is performed to confirm the valid mode components from the target mode components;

[0013] The oscillation parameters of the effective modal components are extracted and used as the oscillation parameters of the current power system.

[0014] Optionally, the step of using the sliding window method to detect the start and end of oscillations in order to extract valid oscillation data includes:

[0015] The active power data is divided into multiple continuous windows by using a preset fixed window length and the variance of active power in each window is calculated.

[0016] Calculate the change in active power variance between two adjacent windows. When the change in active power variance is greater than a preset threshold, it is determined that the system oscillates. The starting sampling time of the latter window between the two adjacent windows is recorded as the oscillation start time.

[0017] When the system is in an oscillation state, when the change in the variance of active power corresponding to a consecutive preset number of windows is less than the preset threshold, the system oscillation is determined to terminate, and the starting sampling time of the first window in the consecutive preset number of windows is recorded as the oscillation termination time.

[0018] Active power data from the start of oscillation to the end of oscillation is extracted as valid oscillation data.

[0019] Optionally, the mode decomposition uses the empirical mode decomposition method to obtain multiple intrinsic mode components.

[0020] Optionally, the frequency characteristics are the average frequencies of the intrinsic modal components. The frequency characteristics and energy of each modal component are calculated, and the target modal component is selected from multiple modal components according to preset screening conditions, including:

[0021] The instantaneous frequencies of each intrinsic mode component are obtained from the Hilbert-Huang transform, and the average frequencies of each intrinsic mode component are calculated.

[0022] Calculate the energy of each intrinsic modal component:

[0023] ;

[0024] The corresponding intrinsic modal components will be selected as target modal components when the following constraints are met:

[0025] and ;

[0026] in, For the first The energy of each intrinsic mode component The moment when the oscillation begins. This is the moment when the oscillation terminates; For the first Each intrinsic mode component at time... Corresponding time-domain amplitude function For the first The average frequency corresponding to each intrinsic mode component; These are the lower and upper limits of the preset low-frequency and subsynchronous oscillation frequency ranges, respectively. This represents the total number of intrinsic modal components. This is a preset energy percentage threshold.

[0027] Optionally, the order of the exponentially decaying oscillation model can be determined by performing singular value decomposition on the extended autocorrelation matrix, including:

[0028] Singular value decomposition is performed on the extended autocorrelation matrix to extract the descending sequence of singular values;

[0029] Calculate the ratio of each singular value in the singular value sequence to the first singular value. When a singular value satisfies the following condition:

[0030] ;

[0031] Judgment No. The singular values ​​at and after the first point correspond to noise components, and the order of the exponentially decaying oscillation model is determined. for , It is a positive integer greater than 1;

[0032] in, The first singular value in the sequence One singular value; It is the first singular value with the largest amplitude in the singular value sequence; This is the preset threshold for determining the singular value of noise.

[0033] Optionally, the parameterized spectral estimation method is the Prony algorithm, which is used to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target modal components, including:

[0034] Order based on exponentially decaying oscillation model Construct a linear autoregressive equation and solve it to obtain... A discrete-time complex pole;

[0035] Based on the above Construct the Vandermonde complex matrix equation for each discrete-time complex pole and solve for the corresponding discrete-time complex pole using the least squares method. One complex amplitude;

[0036] exist Among the complex amplitudes, the complex amplitude with the largest modulus is selected, and its corresponding discrete-time complex pole is determined as the dominant pole component of the target modal component.

[0037] Based on the dominant pole components and their corresponding complex amplitudes, the oscillation parameters of the target mode components in the continuous domain are solved. The oscillation parameters include at least the fitted frequency, damping ratio, and actual amplitude.

[0038] Optionally, a consistency check is performed based on the oscillation parameters and frequency characteristics to confirm valid modal components from the target modal components, including:

[0039] For the same target modal component, extract the fitted frequency from the oscillation parameters; calculate the frequency deviation between the fitted frequency and the frequency feature.

[0040] The target modal component is retained as a valid modal component only when the frequency deviation is within a preset deviation range.

[0041] Optionally, the effective oscillation data can be preprocessed to obtain the signal to be analyzed, including:

[0042] use The criterion-based sliding window method is used to determine the valid oscillation data and remove abnormal data from the valid oscillation data;

[0043] The moving average algorithm is used to smooth and filter the effective oscillation data after removing outliers to reduce noise, thus obtaining the signal to be analyzed.

[0044] Secondly, the present invention provides a device for extracting low-frequency and subsynchronous oscillation parameters of a power system, comprising:

[0045] The data acquisition module is used to acquire active power data uploaded by each substation in the wide-area measurement system;

[0046] The effective data interception module is used to intercept effective oscillation data by using the sliding window method to detect the start and end of oscillation based on active power data, and to preprocess the effective oscillation data to obtain the signal to be analyzed.

[0047] The mode decomposition module is used to perform mode decomposition on the signal to be analyzed, obtaining multiple mode components;

[0048] The target modal component screening module is used to perform Hilbert-Huang transform on each modal component, calculate the frequency characteristics and energy of each modal component, and screen out the target modal component from multiple modal components according to preset constraints.

[0049] The adaptive order determination and parameter estimation module is used to establish an exponentially decaying oscillation model based on the target modal components and construct an extended autocorrelation matrix. By performing singular value decomposition on the extended autocorrelation matrix, the order of the exponentially decaying oscillation model is determined, and the parametric spectrum estimation method is used to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target modal components.

[0050] The consistency verification module is used to perform consistency verification based on the oscillation parameters and frequency characteristics, and to confirm the valid mode components from the target mode components;

[0051] The oscillation parameter extraction module is used to extract the oscillation parameters of the effective mode components as the oscillation parameters of the current power system.

[0052] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for extracting low-frequency and subsynchronous oscillation parameters of a power system as described in the first aspect.

[0053] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0054] This invention first acquires the active power data of each substation, and then extracts valid oscillation data by detecting the start and end of oscillations using a sliding window method. This effectively avoids a large amount of invalid data from participating in the calculation, saving computing power while ensuring computational accuracy. A two-level identification architecture of "modal decomposition and parametric spectrum estimation" is adopted. First, the complex signal to be analyzed is decoupled through modal decomposition and Hilbert-Huang transform, and target modal components are screened based on preset constraints, improving the ability of subsequent parametric spectrum estimation methods to handle complex non-stationary signals. Then, based on the screened target modal components, an extended autocorrelation matrix is ​​constructed by discretization, and the order of the exponentially decaying oscillation model is determined through singular value decomposition. This solves the technical problem of existing parametric spectrum estimation methods heavily relying on empirically set orders, which easily leads to false modes or omission of true modes. Based on this, the model is solved by combining parametric spectrum estimation, improving the accuracy and stability of high-precision extraction of low-frequency and subsynchronous oscillation parameters.

[0055] Furthermore, this invention utilizes the oscillation parameters obtained by parametric spectrum estimation to perform consistency verification with the frequency features extracted after Hilbert-Huang transform analysis. This process can eliminate pseudo-mode components caused by noise interference, thereby accurately locking in the effective mode components and ensuring the reliability of the oscillation parameter extraction results under complex and non-stationary power grid measurement conditions. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the process for extracting low-frequency and subsynchronous oscillation parameters of a power system according to an embodiment of the present invention;

[0057] Figure 2 This is a schematic diagram of the oscillation start and stop detection and effective oscillation data interception process provided in an embodiment of the present invention;

[0058] Figure 3 This is a schematic diagram of the mode decomposition and parameterized spectrum estimation fusion processing flow provided in an embodiment of the present invention;

[0059] Figure 4 A schematic diagram of a power system low-frequency and subsynchronous oscillation parameter extraction device provided in an embodiment of the present invention;

[0060] Figure 5 This is a schematic diagram of the original signal time-domain waveform provided in an embodiment of the present invention;

[0061] Figure 6 This is a schematic diagram of the original signal and the direct Prony fitting waveform provided in an embodiment of the present invention;

[0062] Figure 7 This is a schematic diagram of the time-domain waveforms of each target modal component provided in an embodiment of the present invention; wherein, Figure 7 (a) in the figure is the time-domain waveform of the target mode component one. Figure 7(b) in the diagram is the time-domain waveform of the second target mode component. Figure 7 (c) in the figure is the time-domain waveform of the target modal component three;

[0063] Figure 8 This is a schematic diagram of the target modal component and the Prony reconstructed waveform provided in an embodiment of the present invention;

[0064] Figure 9 This is a schematic diagram of the target mode component 2 and the Prony reconstructed waveform provided in an embodiment of the present invention;

[0065] Figure 10 This is a schematic diagram of the target mode component 3 and the Prony reconstructed waveform provided in an embodiment of the present invention;

[0066] Figure 11 The waveform diagram of the overall reconstructed signal and the original signal provided in the embodiment of the present invention is shown. Detailed Implementation

[0067] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0068] Example 1

[0069] This embodiment describes a method for extracting low-frequency and subsynchronous oscillation parameters in power systems. This method operates on the main station side of the power system dispatch center, and is based on... Figure 1 Specifically, it includes:

[0070] Step 1: Obtain the active power data uploaded by each substation in the wide-area measurement system;

[0071] In actual power grid systems, each power plant (substation side) is equipped with broadband measurement devices or phasor measurement units with broadband monitoring capabilities. These substation-side devices maintain the consistency of the network-wide data acquisition benchmark through GPS / BeiDou synchronized clock sources, collect basic active power data, and transmit it to the master station side through a unified power dispatch data network, serving as the data foundation for the execution of this method.

[0072] Step 2: Based on the active power data, the sliding window method is used to detect the start and end of oscillations in order to extract the effective oscillation data, and the effective oscillation data is preprocessed to obtain the signal to be analyzed;

[0073] refer to Figure 2 Using a preset fixed window length The active power data is divided into multiple continuous windows by sliding segmentation, and the variance of active power in each window is calculated.

[0074] Calculate the change in active power variance between two adjacent windows. When the change in active power variance exceeds a preset threshold... When an oscillation occurs, the system is determined to be oscillating, and the starting sampling time of the latter window among the two adjacent windows is recorded as the oscillation start time. ;

[0075] When the system is in an oscillating state, the change in active power variance corresponding to a consecutive preset number of windows is less than the preset threshold. When the system oscillation terminates, the starting sampling time of the first window in the consecutive preset number of windows is determined to be the oscillation termination time. ;

[0076] Extract the corresponding time period The active power data is used as valid oscillation data.

[0077] This step effectively avoids false triggering caused by noise fluctuations or non-oscillatory disturbances, while significantly reducing the computational burden of subsequent analysis.

[0078] Furthermore, the effective oscillation data is preprocessed to obtain the signal to be analyzed, specifically including:

[0079] use The sliding window method is used to remove outliers from valid oscillation data. This step uses a window length of [missing information]. The outlier detection criteria for the sliding window are expressed as follows:

[0080] ;

[0081] In the formula, For a moment The corresponding valid oscillation data; For the length of the window The arithmetic mean of the effective oscillation data within the sliding window; In the same The standard deviation of the effective oscillation data within a sliding window of length. If the above formula holds, then... Data deemed abnormal will be removed.

[0082] For the valid oscillating data after outlier removal, a moving average algorithm is used to smooth and filter the data to reduce noise, thus obtaining the signal to be analyzed. This step uses a window length of... Sliding window:

[0083] ;

[0084] In the formula, A discrete summation step size index specific to moving average filtering; For a moment forward interval The effective oscillation data corresponding to each sampling step size.

[0085] Step 3: Perform mode decomposition on the signal to be analyzed to obtain multiple mode components;

[0086] refer to Figure 3 This embodiment employs the empirical mode decomposition method to analyze the signal. Perform adaptive decomposition to obtain One intrinsic mode component with different time-scale characteristics and one residual term:

[0087] ;

[0088] In the formula, This represents the total number of intrinsic modal components. The first decomposition obtained One intrinsic mode component; It is the residual term after decomposition.

[0089] Step 4: Perform Hilbert-Huang transform on each modal component, calculate the frequency characteristics and energy of each modal component, and select the target modal component from multiple modal components according to the preset constraints.

[0090] Regarding the first Each intrinsic mode component Let it be the time-domain magnitude function of the transform input. The instantaneous frequencies of each eigenmode component are obtained according to the Hilbert-Huang transform. The average frequency, which serves as the frequency characteristic, is obtained by time-integrated averaging over the effective oscillation period. :

[0091] ;

[0092] Simultaneously, the energy of each intrinsic mode component is calculated. :

[0093] ;

[0094] The above mathematical symbols The general differential notation in the field of calculus, time... The corresponding integration interval is , The above is an integral operation symbol, which is a well-known mathematical expression in the fields of control, physics, and signal processing, and is not subject to any special limitations.

[0095] The corresponding intrinsic modal components will be selected as target modal components when the following constraints are met:

[0096] and ;

[0097] In the formula, , These are the lower and upper limits of the preset low-frequency and subsynchronous oscillation frequency ranges, respectively. This is a preset energy percentage threshold; To sum the indices, iterate through the subscripts.

[0098] Step 5: Based on the target mode components, establish an exponentially decaying oscillation model and construct an extended autocorrelation matrix. By performing singular value decomposition on the extended autocorrelation matrix, determine the order of the exponentially decaying oscillation model, and use the parametric spectral estimation method to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target mode components.

[0099] The parameterized spectrum estimation method is the Prony algorithm. The target modal components are discretized and sampled, with a sampling period of [missing information]. The length is obtained as Discrete time series Define the global discrete-time sampling point index as ,Will Represented as an exponentially decaying oscillation model:

[0100] ;

[0101] ;

[0102] In the formula, For characteristic pole component index; The order of the exponentially decaying oscillation model; For the first The complex amplitude of each characteristic pole component. For the first Discrete-time complex poles of a characteristic pole component. , The first The continuous-domain attenuation factor and angular frequency of each characteristic pole component.

[0103] Define the autocorrelation function of discrete samples To construct the extended autocorrelation matrix R:

[0104] ;

[0105] In the formula, For the v-th row and the i-th row of the autocorrelation matrix Column elements; The forward extension order has a maximum value of . For a discrete signal sampled with delay and its conjugate complex number.

[0106] Depend on Construction dimension Extended autocorrelation matrix .

[0107] For the extended autocorrelation matrix Perform singular value decomposition, extract the singular value sequence in descending order, and calculate the ratio of each singular value in the sequence to the first singular value. When a singular value satisfies the following condition:

[0108] ;

[0109] Judgment No. The singular values ​​at and after the first point correspond to noise components, and the order of the exponentially decaying oscillation model is determined. for ; For each integer greater than 1, there is a positive integer; in the formula, The first singular value in the sequence One singular value; It is the first singular value with the largest amplitude in the singular value sequence; This is the preset threshold for determining the singular value of noise.

[0110] According to the order of the exponentially decaying oscillation model Construct a linear autoregressive equation with the following relationship:

[0111] ;

[0112] In the formula, For the solution to be found There are linear autoregressive coefficients, and the first term... . This is the index of the current time used for linear prediction in the autoregressive equation, with a value range of [value missing]. to .

[0113] The above autoregressive relationship is expressed in matrix form and solved using the total least squares method. Construct the algebraic characteristic equation:

[0114] ;

[0115] Solving Discrete-time complex poles ,Will Discrete-time complex poles Substituting into the original exponentially decaying oscillation model, the least squares method is used to solve for the complex poles corresponding to each discrete time point. Given a complex amplitude, we obtain the Vandermonde matrix equation for the complex amplitude:

[0116] .

[0117] In the formula, Z is obtained from... Constructed A Vandermonde complex matrix of order 1; Let be the complex coefficient vector to be determined, and its i-th... The element is the th element. The complex amplitude of each characteristic pole component; It is a column vector composed of actual discrete sampling points.

[0118] In the solution Among the complex amplitudes, the complex amplitude with the largest modulus is selected, and its corresponding discrete-time complex pole is determined as the dominant pole component of the target modal component. The feature index is denoted as . Based on this dominant pole component and its corresponding complex amplitude Solve for the oscillation parameters of the target modal components in the continuous domain, including the actual amplitude. Phase angle Fitting frequency Attenuation factor Damping ratio :

[0119] ;

[0120] Step 6: Perform a consistency check based on the oscillation parameters and frequency characteristics to confirm the valid modal components from the target modal components.

[0121] For the same target modal component, extract the fitted frequency from the oscillation parameters. Calculate the fitting frequency With average frequency The frequency deviation between the two; the target modal component is retained as a valid modal component only when the frequency deviation is within the preset deviation range.

[0122] Step 7: Extract the oscillation parameters of the effective modal components as the oscillation parameters of the current power system.

[0123] The oscillation parameters of the power system are extracted, and by judging the range in which the fitted frequency falls, the oscillation type can be determined as low-frequency oscillation or subsynchronous oscillation.

[0124] Example 2

[0125] This embodiment describes a device for extracting low-frequency and subsynchronous oscillation parameters in power systems, such as... Figure 4 As shown, it includes:

[0126] The data acquisition module is used to acquire active power data uploaded by each substation in the wide-area measurement system;

[0127] The effective data interception module is used to intercept effective oscillation data by using the sliding window method to detect the start and end of oscillation based on active power data, and to preprocess the effective oscillation data to obtain the signal to be analyzed.

[0128] The mode decomposition module is used to perform mode decomposition on the signal to be analyzed, obtaining multiple mode components;

[0129] The target modal component screening module is used to perform Hilbert-Huang transform on each modal component, calculate the frequency characteristics and energy of each modal component, and screen out the target modal component from multiple modal components according to preset constraints.

[0130] The adaptive order determination and parameter estimation module is used to establish an exponentially decaying oscillation model based on the target modal components and construct an extended autocorrelation matrix. By performing singular value decomposition on the extended autocorrelation matrix, the order of the exponentially decaying oscillation model is determined, and the parametric spectrum estimation method is used to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target modal components.

[0131] The consistency verification module is used to perform consistency verification based on the oscillation parameters and frequency characteristics, and to confirm the valid mode components from the target mode components;

[0132] The oscillation parameter extraction module is used to extract the oscillation parameters of the effective mode components as the oscillation parameters of the current power system.

[0133] The specific functions of each module described above are explained in the relevant content of the method in Embodiment 1, and will not be repeated here.

[0134] Example 3

[0135] To further verify the beneficial effects of the power system low-frequency and subsynchronous oscillation parameter extraction method described in this invention, this embodiment constructs a test signal containing multiple damped oscillation modes and compares the method of this invention with the traditional identification method through simulation.

[0136] To simulate the multimodal operating conditions that actually occur in the power grid, a simulated original signal containing three damped oscillation modes is constructed. :

[0137] ;

[0138] In the formula, For simulation modal indexing; For the first The theory of simulation modes; For the first The theoretical attenuation factor for each simulation mode; For the first The theoretical center frequency of each simulation mode; For the first Phase angles of each simulation mode;

[0139] Set sampling frequency Sampling duration , .

[0140] The theoretical parameter settings for the three simulation modes are as follows, where rad is radians and Hz is hertz:

[0141] Mode 1: Theoretical center frequency 0.2Hz, theoretical attenuation factor 0.01, theoretical amplitude 1.2, theoretical damping ratio 0.796%.

[0142] The theoretical phase angle is 0.3 rad.

[0143] Mode 2: Theoretical center frequency 0.8 Hz, theoretical attenuation factor 0.015, theoretical amplitude 0.7, theoretical damping ratio 0.298%.

[0144] The theoretical phase angle is 1.1 rad.

[0145] Mode 3: Theoretical center frequency 2.0 Hz, theoretical attenuation factor 0.008, theoretical amplitude 0.5, theoretical damping ratio 0.064%.

[0146] The theoretical phase angle is 2.0 rad.

[0147] To simulate interference in a real measurement environment, the above-mentioned simulated original signal... Gaussian white noise with a standard deviation of 0.001 is superimposed to obtain the original signal (the signal to be analyzed) used for testing, and its time-domain waveform is as follows. Figure 5 As shown.

[0148] Comparative simulation analysis of the original signals:

[0149] First, without any preprocessing or mode decomposition, the traditional Prony method is directly used to identify the parameters of the original signal. Simulation results show that direct Prony analysis is highly susceptible to noise and multimodal coupling interference, resulting in extremely large errors in the extracted oscillation parameters and even the generation of severe spurious modes. The waveforms of the original signal and the directly Prony-fitted waveforms are as follows: Figure 6 As shown.

[0150] The results of direct identification using the traditional Prony method are as follows:

[0151] Mode 1 identification results: Fitted frequency 0.0000Hz, attenuation factor -20.5406, amplitude 2.0713, damping ratio 100.00%, phase angle -0.0000rad.

[0152] Mode 2 identification results: Fitted frequency 0.3101Hz, attenuation factor -0.3569, amplitude 0.9984, damping ratio 18.02%, phase angle -1.4279rad.

[0153] Mode 3 identification results: Fitted frequency 1.9342Hz, attenuation factor -0.2347, amplitude 0.5394, damping ratio 1.93%, phase -3.0850rad.

[0154] Directly using the Prony method to process multimodal and noisy raw signals results in large parameter errors and poor fitting performance.

[0155] The results of this invention are as follows:

[0156] The original signal was subjected to empirical mode decomposition and Hilbert-Huang transform according to the method described in Example 1. The time-domain waveforms of each target mode component selected are as follows: Figure 7 As shown, it includes target mode component one, target mode component two, and target mode component three. Based on each target mode component, a quadratic exponentially decaying oscillation model is performed, and the Prony method is used for parameter identification. The target mode components and their corresponding Prony reconstructed waveforms are shown below. Figure 8 , Figure 9 and Figure 10 As shown.

[0157] Mode 1 identification results: Fitted frequency 0.2009Hz, attenuation factor 0.0079, amplitude 1.2254, damping ratio 0.626%.

[0158] Phase angle 0.2354 rad;

[0159] Mode 2 identification results: Fitted frequency 0.8001Hz, attenuation factor 0.0158, amplitude 0.6617, damping ratio 0.314%, phase angle 0.6617rad;

[0160] Mode 3 identification results: Fitted frequency 2.0001Hz, attenuation factor 0.0086, amplitude 0.4921, damping ratio 0.068%, phase angle 1.9978rad.

[0161] Comparing the identification results of the traditional Prony method and the present invention, it can be seen that the traditional Prony method is completely ineffective due to noise interference, while the identification results calculated by the present invention are in high agreement with the theoretical parameters. The overall reconstructed signal is obtained by adding the reconstructed signals of all target modal components. The waveforms of the overall reconstructed signal and the original signal are shown below. Figure 11 As shown, the two are highly overlapping.

[0162] The above simulations fully demonstrate that the two-level identification architecture of "modal decomposition and parameterized spectrum estimation" adopted in this invention significantly improves the accuracy and robustness of high-precision extraction of low-frequency and subsynchronous oscillation parameters.

[0163] Example 4

[0164] Based on the same inventive concept as other embodiments, this embodiment describes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for extracting low-frequency and subsynchronous oscillation parameters of a power system as described in Embodiment 1.

[0165] In summary, this invention first acquires the active power data of each substation, and then extracts valid oscillation data by detecting the start and end of oscillations using a sliding window method. This effectively avoids a large amount of invalid data from participating in the calculation, saving computing power while ensuring computational accuracy. A two-level identification architecture of "modal decomposition and parametric spectrum estimation" is adopted. First, the complex signal to be analyzed is decoupled through modal decomposition and Hilbert-Huang transform, and target modal components are screened based on preset constraints, improving the ability of the subsequent parametric spectrum estimation method to handle complex non-stationary signals. Then, based on the screened target modal components, an extended autocorrelation matrix is ​​constructed by discretization, and the order of the exponentially decaying oscillation model is determined through singular value decomposition. This solves the technical problem that existing parametric spectrum estimation methods heavily rely on empirically set orders, leading to the generation of spurious modes or the omission of true modes. Based on this, the model is solved by combining the parametric spectrum estimation method, improving the accuracy and stability of high-precision extraction of low-frequency and subsynchronous oscillation parameters.

[0166] Furthermore, this invention utilizes the oscillation parameters obtained by parametric spectrum estimation to perform consistency verification with the frequency features extracted after Hilbert-Huang transform analysis. This process can eliminate pseudo-mode components caused by noise interference, thereby accurately locking in the effective mode components and ensuring the reliability of the oscillation parameter extraction results under complex and non-stationary power grid measurement conditions.

[0167] Furthermore, this invention utilizes the oscillation parameters obtained by parametric spectrum estimation and performs consistency verification with the frequency features extracted after Hilbert-Huang transform analysis. This process can eliminate pseudo-mode components caused by noise interference, thereby accurately locking in the effective mode components and ensuring the reliability of oscillation identification results under complex and non-stationary power grid measurement conditions.

[0168] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0169] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0170] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0171] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0172] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for extracting low-frequency and subsynchronous oscillation parameters in power systems, characterized in that, include: Acquire active power data uploaded by each substation in the wide-area measurement system; Based on active power data, the sliding window method is used to detect the start and end of oscillations in order to extract effective oscillation data. The effective oscillation data is then preprocessed to obtain the signal to be analyzed. Modal decomposition is performed on the signal to be analyzed to obtain multiple modal components; Perform Hilbert-Huang transform on each modal component, calculate the frequency characteristics and energy of each modal component, and select the target modal component from multiple modal components according to preset constraints. Based on the target modal components, an exponentially decaying oscillation model is established and an extended autocorrelation matrix is ​​constructed. By performing singular value decomposition on the extended autocorrelation matrix, the order of the exponentially decaying oscillation model is determined. The parametric spectral estimation method is then used to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target modal components. Based on the oscillation parameters and frequency characteristics, a consistency check is performed to confirm the valid mode components from the target mode components; The oscillation parameters of the effective modal components are extracted and used as the oscillation parameters of the current power system.

2. The method for extracting low-frequency and subsynchronous oscillation parameters of a power system according to claim 1, characterized in that, The method of using a sliding window to detect the start and end of oscillations in order to extract valid oscillation data includes: The active power data is divided into multiple continuous windows by using a preset fixed window length and the variance of active power in each window is calculated. Calculate the change in active power variance between two adjacent windows. When the change in active power variance is greater than a preset threshold, it is determined that the system oscillates. The starting sampling time of the latter window between the two adjacent windows is recorded as the oscillation start time. When the system is in an oscillation state, when the change in the variance of active power corresponding to a consecutive preset number of windows is less than the preset threshold, the system oscillation is determined to terminate, and the starting sampling time of the first window in the consecutive preset number of windows is recorded as the oscillation termination time. Active power data from the start of oscillation to the end of oscillation is extracted as valid oscillation data.

3. The method for extracting low-frequency and subsynchronous oscillation parameters of a power system according to claim 1, characterized in that, The mode decomposition adopts the empirical mode decomposition method, which yields multiple intrinsic mode components.

4. The method for extracting low-frequency and subsynchronous oscillation parameters of a power system according to claim 3, characterized in that, The frequency characteristics are the average frequencies of the intrinsic modal components. The frequency characteristics and energy of each modal component are calculated, and target modal components are selected from multiple modal components based on preset screening conditions, including: The instantaneous frequencies of each intrinsic mode component are obtained from the Hilbert-Huang transform, and the average frequencies of each intrinsic mode component are calculated. Calculate the energy of each intrinsic modal component: ； The corresponding intrinsic modal components will be selected as target modal components when the following constraints are met: and ; in, For the first The energy of each intrinsic mode component The moment when the oscillation begins. This is the moment when the oscillation terminates; For the first Each intrinsic mode component at time... Corresponding time-domain amplitude function For the first The average frequency corresponding to each intrinsic mode component; These are the lower and upper limits of the preset low-frequency and subsynchronous oscillation frequency ranges, respectively. This represents the total number of intrinsic modal components. This is a preset energy percentage threshold.

5. The method for extracting low-frequency and subsynchronous oscillation parameters of a power system according to claim 1, characterized in that, The order of the exponentially decaying oscillation model is determined by performing singular value decomposition on the extended autocorrelation matrix, including: Singular value decomposition is performed on the extended autocorrelation matrix to extract the descending sequence of singular values; Calculate the ratio of each singular value in the singular value sequence to the first singular value. When a singular value satisfies the following condition: ； Judgment No. The singular values ​​at and after the first point correspond to noise components, and the order of the exponentially decaying oscillation model is determined. for , It is a positive integer greater than 1; in, The first singular value in the sequence One singular value; It is the first singular value with the largest amplitude in the singular value sequence; This is the preset threshold for determining the singular value of noise.

6. The method for extracting low-frequency and subsynchronous oscillation parameters of a power system according to claim 5, characterized in that, The parameterized spectral estimation method is the Prony algorithm. It is used to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target modal components, including: Order based on the exponentially decaying oscillation model Construct a linear autoregressive equation and solve for it. A discrete-time complex pole; Based on the above Construct the Vandermonde complex matrix equation for each discrete-time complex pole and solve for the corresponding discrete-time complex pole using the least squares method. One complex amplitude; exist Among the complex amplitudes, the complex amplitude with the largest modulus is selected, and its corresponding discrete-time complex pole is determined as the dominant pole component of the target modal component. Based on the dominant pole components and their corresponding complex amplitudes, the oscillation parameters of the target mode components in the continuous domain are solved. The oscillation parameters include at least the fitted frequency, damping ratio, and actual amplitude.

7. The method for extracting low-frequency and subsynchronous oscillation parameters of a power system according to claim 1, characterized in that, Based on the oscillation parameters and frequency characteristics, a consistency check is performed to identify valid mode components from the target mode components, including: For the same target modal component, extract the fitted frequency from the oscillation parameters; calculate the frequency deviation between the fitted frequency and the frequency feature. The target modal component is retained as a valid modal component only when the frequency deviation is within a preset deviation range.

8. The method for extracting low-frequency and subsynchronous oscillation parameters of a power system according to claim 1, characterized in that, The effective oscillation data is preprocessed to obtain the signal to be analyzed, including: use The criterion-based sliding window method is used to determine the valid oscillation data and remove abnormal data from the valid oscillation data; The moving average algorithm is used to smooth and filter the effective oscillation data after removing outliers to reduce noise, thus obtaining the signal to be analyzed.

9. A device for extracting low-frequency and subsynchronous oscillation parameters in a power system, characterized in that, include: The data acquisition module is used to acquire active power data uploaded by each substation in the wide-area measurement system; The effective data interception module is used to intercept effective oscillation data by using the sliding window method to detect the start and end of oscillation based on active power data, and to preprocess the effective oscillation data to obtain the signal to be analyzed. The mode decomposition module is used to perform mode decomposition on the signal to be analyzed, obtaining multiple mode components; The target modal component screening module is used to perform Hilbert-Huang transform on each modal component, calculate the frequency characteristics and energy of each modal component, and screen out the target modal component from multiple modal components according to preset constraints. The adaptive order determination and parameter estimation module is used to establish an exponentially decaying oscillation model based on the target modal components and construct an extended autocorrelation matrix. By performing singular value decomposition on the extended autocorrelation matrix, the order of the exponentially decaying oscillation model is determined, and the parametric spectrum estimation method is used to solve the exponentially decaying oscillation model to obtain the oscillation parameters corresponding to the target modal components. The consistency verification module is used to perform consistency verification based on the oscillation parameters and frequency characteristics, and to confirm the valid mode components from the target mode components; The oscillation parameter extraction module is used to extract the oscillation parameters of the effective mode components as the oscillation parameters of the current power system.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for extracting low-frequency and subsynchronous oscillation parameters of a power system as described in any one of claims 1 to 8.

Images