A method and system for extracting a low-frequency oscillation characteristic signal of a power system

Abstract

The application discloses a kind of power system low-frequency oscillation characteristic signal extraction methods, comprising: the electrical variation data of acquisition each generator outlet is preprocessed;Through complementary ensemble empirical mode decomposition, variation data is decomposed, and noise component is filtered out;SPA smoothing algorithm is used to process the electrical variation signal after denoising;Prony method is used to decompose the signal after smoothing, and the amplitude and phase of each frequency component are extracted;The application has more excellent noise suppression capability and signal fidelity, can effectively solve the problem of modal aliasing, can adaptively identify and filter out various noise components, and shows good adaptability to noise interference under different operating conditions of power system;SPA smoothing algorithm reduces the error introduced by complementary ensemble empirical mode decomposition while effectively retaining the key features of low-frequency oscillation;Combined with Prony method, the characteristic parameters of the oscillation signal can be accurately extracted in a strong noise environment, providing a reliable data basis for low-frequency oscillation source identification.

Description

Technical Field

[0001] This invention relates to a method for extracting low-frequency oscillation characteristic signals in power systems, belonging to the field of power system relay protection technology. Background Technology

[0002] Low-frequency power oscillations are power oscillations occurring in power systems within the frequency range of 0.1–2.5 Hz after disturbance. Their main characteristics include a persistently fluctuating generator relative power angle. Based on damping characteristics, they can be classified into three types: negatively damped oscillations with divergent properties, weakly damped oscillations with continuous oscillations, and strongly damped oscillations with rapid decay. Negatively damped oscillations cause continuous divergence in power signals, posing a serious threat to system stability; weakly damped oscillations lead to continuous power fluctuations, affecting the safe operation of the power grid. These oscillations reduce the reliability and stability of the power network, potentially causing power supply disruptions. Given the potential threat of low-frequency oscillations to power grid security, accurate and timely monitoring and modal identification are crucial for understanding the system's dynamic characteristics and developing suppression strategies. To this end, researchers have developed a series of signal analysis methods based on wide-area measurement systems.

[0003] Currently, in the field of low-frequency oscillation mode identification in power systems, although methods such as the matrix bundle method, fast Fourier transform, and Hilbert-Huang transform are all used, each has its limitations: the matrix bundle method is not adaptable to nonlinear data in the early stages of large disturbances; the fast Fourier transform requires the signal to contain only a single dominant mode; and the Hilbert-Huang transform is plagued by endpoint effects and mode aliasing. In contrast, the Prony algorithm, due to its ability to directly extract characteristic parameters such as amplitude, phase, frequency, and damping of oscillation signals, has been applied to actual system fault analysis, demonstrating unique value. However, a significant drawback of this method is its high sensitivity to noise, which makes it difficult to reliably construct the signal matrix required for wide-area monitoring from noisy measured data. Therefore, implementing effective pre-filtering is a key prerequisite for improving the practicality and robustness of the Prony algorithm and meeting the requirements of wide-area measurement systems. Summary of the Invention

[0004] The technical problem to be solved by the present invention is that the prior art contains only a single dominant mode, is affected by endpoint effects and mode aliasing, and is highly sensitive to noise.

[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 oscillation characteristic signals in a power system, comprising:

[0007] Obtain electrical change data for each generator outlet;

[0008] The electrical change data is preprocessed;

[0009] The electrical variation data is decomposed using complementary set empirical mode decomposition to filter out noise components;

[0010] The SPA smoothing algorithm is used to process the denoised electrical change signal to obtain a smooth signal;

[0011] The smoothed signal was decomposed using the Prony method to extract the amplitude and phase of each modal frequency component, providing key feature data for subsequent low-frequency oscillation identification.

[0012] A three-stage cascaded filtering process was constructed, consisting of complementary set empirical mode decomposition, SPA smoothing algorithm, and Prony method. By complementing each other's algorithmic advantages, a synergistic enhancement effect is achieved, resulting in superior noise suppression and signal fidelity compared to single feature signal extraction methods.

[0013] The electrical change data includes changes in active power, reactive power, generator voltage, and generator frequency.

[0014] The formula for calculating the change in active power at the generator outlet is as follows:

[0015]

[0016] in, For generator outlet The change in active power at any given time. For generator outlet Real-time active power data collected at any given moment. This refers to the active power output at the generator's outlet under stable operating conditions.

[0017] The formula for calculating the change in reactive power at the generator outlet is as follows:

[0018]

[0019] in, For generator outlet The change in reactive power at any given time. For generator outlet Real-time reactive power data at any given moment. This refers to the reactive power output of the generator under stable operating conditions.

[0020] The formula for calculating the generator voltage change is as follows:

[0021]

[0022] in, For the first generator The change in voltage at any given time. For the first generator Real-time voltage acquisition value at any given moment. For the first Voltage value of the generator under stable operating conditions;

[0023] The formula for calculating the generator frequency change is as follows:

[0024]

[0025]

[0026] in, For real-time rotational speed, The number of rotor pole pairs, For frequency, For the first generator The change in frequency at any given time For the first generator Real-time frequency data acquisition value at any given moment. For the first Frequency value of the generator under stable operating conditions.

[0027] The preprocessing includes normalizing the electrical change data using the following formula:

[0028]

[0029]

[0030]

[0031]

[0032] in, Rated apparent power, The rated voltage of the unit. The rated frequency of the unit, For generator outlet The change in active power at any given time. For generator outlet The change in reactive power at any given time. For the first generator The change in voltage at any given time. For the first generator The change in frequency at any given time This represents the normalized change in active power. This represents the normalized change in reactive power. This represents the normalized change in unit voltage. This represents the normalized change in unit frequency.

[0033] The complete feature signal extraction method provided by this invention has high computational efficiency and adaptive parameter adjustment, and can be directly integrated into existing wide-area measurement systems, providing effective technical support for real-time monitoring and analysis of low-frequency oscillations in power systems.

[0034] The decomposition of the electrical variation data through complementary set empirical mode decomposition includes:

[0035] Determine the total number of decompositions and generate a pair of white noise sequences with equal amplitude and opposite signs. The expressions for the positive and negative noise signals are as follows:

[0036]

[0037]

[0038] in, The original input signal, This is the noise amplitude coefficient. For the first The positive noise signal of this experiment For the first Positive and negative noise-added signals from this experiment For the first The white noise sequence generated in this experiment;

[0039] The positive and negative noise signals are added to the original signal respectively to obtain two new signals to be decomposed;

[0040] Perform EMD decomposition on the two signals to be decomposed respectively to obtain two sets of IMF components and residuals. The EMD decomposition formula is as follows:

[0041]

[0042]

[0043] in, For the first The positive signal of the second test One eigenmode function For the first The negative signal in the second test One eigenmode function For the first The residual of the positive signal in the second experiment, For the first The residual of the negative signal in the second experiment for The total number of floors;

[0044] Repeat the above steps multiple times. Based on the noise identification criterion, filter out the noise-dominant IMFs from all IMF components of the same order, and retain only the signal-dominant IMFs for averaging. The ensemble averaging formula is as follows:

[0045]

[0046]

[0047] in, For the final One eigenmode function For the final residual term, For the first The positive signal of the second test One eigenmode function For the first The negative signal in the second test One eigenmode function For the first The residual of the positive signal in the second experiment, For the first The residual of the negative signal in the second trial;

[0048] The IMF components and residuals obtained after output averaging are shown below. The final result of CEEMD decomposition of the original signal is as follows:

[0049]

[0050] in, For the final One eigenmode function For the final residual term, for The total number of floors.

[0051] The improved complementary set empirical mode decomposition method adopted effectively solves the mode aliasing problem through positive and negative noise pair cancellation strategy. It can adaptively identify and filter out various noise components and shows good adaptability to noise interference under different operating conditions of power system.

[0052] The process of processing the denoised electrical change signal using the SPA smoothing algorithm includes:

[0053] Based on the low-frequency oscillation characteristics, an odd window width and polynomial order are selected. The polynomial model expression for the low-frequency oscillation signal is as follows:

[0054]

[0055] in, The low-frequency oscillation signal component within the window. For polynomial coefficients, For local indexes within a window;

[0056] Using the center of the window as a local index, a coefficient template matrix for the associated oscillation signal is generated based on the polynomial model. The expression for the coefficient template matrix is ​​as follows:

[0057]

[0058] in, For the length of the data window, The order of the polynomial;

[0059] A normal equation is established using the least squares method. After solving for the coefficients, the first row is extracted as a fixed smoothing weight for adaptive oscillation denoising. The formula is as follows:

[0060]

[0061] in, For the coefficient template matrix, This is the vector of polynomial coefficients;

[0062] The weights are used as a convolution kernel and slid along the oscillating signal. A weighted average is then taken to obtain the smoothed value at each position, preserving the key oscillation features. The signal smoothing formula is as follows:

[0063]

[0064] in, For the first The smoothed oscillation signal value at each position, These are the elements of the weight coefficient vector. For the first The original low-frequency oscillation signal value at each location, The signal length;

[0065] The system uses mirror expansion to supplement the beginning and end data, and combines weights to calculate the boundary smoothing value.

[0066] The SPA smoothing algorithm effectively preserves the key features of low-frequency oscillations while reducing the error introduced by complementary set empirical mode decomposition, thus solving the contradiction between feature distortion and noise residue in traditional denoising methods.

[0067] The process of decomposing the smoothed signal using the Prony method to extract the amplitude and phase of each modal frequency component includes:

[0068] An augmented Hankel matrix containing a data matrix and observation vectors is constructed using the smoothed signal. The expression for the data matrix is ​​as follows:

[0069]

[0070] in, This represents the total number of sampling points. The smoothed signal sequence, This is a preset model order;

[0071] The expression for the observation vector is as follows:

[0072]

[0073] The augmented matrix expression is as follows:

[0074]

[0075] in, For data matrix, For observation vectors;

[0076] Singular value decomposition is performed on the augmented matrix, and the signal subspace and noise subspace are distinguished by the magnitude of the singular values. The singular value decomposition formula is as follows:

[0077]

[0078] in, The left singular vector matrix represents the time structure of the signal. The right singular vector matrix represents the frequency structure of the signal. It is a singular value matrix, representing the energy magnitude of each component;

[0079] Analyze the singular value spectrum and select the number of significant singular values ​​as the actual order of the signal. The formula for determining the actual order of the signal is as follows:

[0080]

[0081] in, Let be the singular values ​​of the singular value matrix, arranged in descending order. The true order of the signal. A threshold is used to distinguish between signals and noise;

[0082] Using the noise subspace vector, the linear prediction coefficients are solved by the overall least squares method, as shown in the following formula:

[0083]

[0084] in, These are the estimated values ​​of the prediction coefficients. These are the basis vectors that are related to the columns of the data matrix and also fall within the noise subspace. It contains basis vectors that are related to the observation vector and also fall within the noise subspace;

[0085] Solve for the characteristic polynomial formed by the prediction coefficients, and calculate the frequency and attenuation factor from the magnitude and phase of the roots. The formula for calculating the characteristic polynomial is as follows:

[0086]

[0087] in, To extract the first from the least squares solution One predictive coefficient, is the root of the characteristic equation;

[0088] The formulas for calculating the frequency and attenuation factor are as follows:

[0089]

[0090]

[0091] in, For the first The attenuation factor of each component, For the first The oscillation frequency of each component;

[0092] Substituting the obtained poles into the original model, the amplitude and initial phase of each modal frequency component are finally determined by least squares fitting, as shown in the following formula:

[0093]

[0094]

[0095] in, The smoothed signal vector, For complex amplitude vectors, For the first The amplitude of each component, For the first The initial phase of each component.

[0096] By combining the pre-filtered signal with the Prony method, the amplitude, phase, frequency and damping of the oscillation signal can be accurately extracted in a noisy environment, providing a reliable data basis for the identification of low-frequency oscillation sources.

[0097] In a second aspect, the present invention provides a device for extracting low-frequency oscillation characteristic signals of a power system, comprising:

[0098] The signal change acquisition module is used to acquire electrical change data at each generator outlet and preprocess the electrical change data.

[0099] The noise filtering and signal reconstruction module is used to decompose the electrical change data and filter out noise components.

[0100] The signal smoothing and optimization module is used to process the denoised electrical change signals;

[0101] The oscillation mode extraction module is used to decompose the smoothed signal and extract the amplitude and phase of each mode frequency component.

[0102] Thirdly, the present invention provides a computer system, comprising:

[0103] Memory, used to store computer programs;

[0104] A processor is used to execute the computer program to implement the steps of the method for extracting low-frequency oscillation characteristic signals of a power system.

[0105] Fourthly, the present invention provides a computer program product, including computer instructions, characterized in that, when the computer instructions are executed by a processor, they implement the steps of the method for extracting low-frequency oscillation characteristic signals of a power system.

[0106] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0107] This invention constructs a three-stage cascaded filtering process, achieving a synergistic enhancement effect through complementary algorithmic advantages, resulting in superior noise suppression and signal fidelity. The improved complementary set empirical mode decomposition method employs a positive and negative noise pair cancellation strategy to effectively solve the mode aliasing problem, adaptively identifying and filtering out various noise components, and demonstrating good adaptability to noise interference under different power system operating conditions. The SPA smoothing algorithm effectively preserves the key characteristics of low-frequency oscillations while reducing the errors introduced by the complementary set empirical mode decomposition. The pre-filtered signal, combined with the Prony method, can accurately extract characteristic parameters such as amplitude, phase, frequency, and damping of the oscillation signal in strong noise environments, providing a reliable data foundation for the identification of low-frequency oscillation sources. Attached Figure Description

[0108] Figure 1 This is a schematic diagram of the method for extracting low-frequency oscillation characteristic signals of a power system as shown in Embodiment 1 of the present invention;

[0109] Figure 2 This is an example image of all the signal IMFs shown in Embodiment 1 of the present invention;

[0110] Figure 3 This is an example image of all noisy IMFs shown in Embodiment 1 of the present invention;

[0111] Figure 4This is a schematic diagram of the complete set empirical mode decomposition results shown in Embodiment 1 of the present invention;

[0112] Figure 5 This is a schematic diagram of the SPA smoothing result of the complementary set empirical mode decomposition denoised signal shown in Embodiment 1 of the present invention;

[0113] Figure 6 This is a schematic diagram of the Prony analysis results after traditional EMD decomposition and denoising, as shown in Embodiment 1 of the present invention.

[0114] Figure 7 This is a schematic diagram of the Prony analysis results after complementary set empirical mode decomposition and SPA smoothing and denoising, as shown in Embodiment 1 of the present invention. Detailed Implementation

[0115] 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.

[0116] Example 1

[0117] This embodiment introduces a method for extracting low-frequency oscillation characteristic signals in power systems, including:

[0118] Obtain electrical change data for each generator outlet;

[0119] Preprocess the electrical change data;

[0120] Electrical variation data are decomposed using complementary set empirical mode decomposition to filter out noise components;

[0121] The SPA smoothing algorithm is used to process the denoised electrical change signal to obtain a smooth signal;

[0122] The Prony method is used to decompose the smoothed signal and extract the amplitude and phase of each modal frequency component, providing key feature data for subsequent low-frequency oscillation identification.

[0123] Electrical change data include changes in active power, reactive power, generator voltage, and generator frequency.

[0124] The formula for calculating the change in active power at the generator outlet is as follows:

[0125]

[0126] in, For generator outlet The change in active power at any given time. For generator outlet Real-time active power data collected at any given moment. This refers to the active power output at the generator's outlet under stable operating conditions.

[0127] The formula for calculating the change in reactive power at the generator outlet is as follows:

[0128]

[0129] in, For generator outlet The change in reactive power at any given time. For generator outlet Real-time reactive power data at any given moment. This refers to the reactive power output of the generator under stable operating conditions.

[0130] The formula for calculating generator voltage change is as follows:

[0131]

[0132] in, For the first generator The change in voltage at any given time. For the first generator Real-time voltage acquisition value at any given moment. For the first Voltage value of the generator under stable operating conditions;

[0133] The formula for calculating the generator frequency change is as follows:

[0134]

[0135]

[0136] in, For real-time rotational speed, The number of rotor pole pairs, For frequency, For the first generator The change in frequency at any given time For the first generator Real-time frequency data acquisition value at any given moment. For the first Frequency value of the generator under stable operating conditions.

[0137] Preprocessing includes normalizing the electrical change data, using the following formula:

[0138]

[0139]

[0140]

[0141]

[0142] in, Rated apparent power, The rated voltage of the unit. The rated frequency of the unit, For generator outlet The change in active power at any given time. For generator outlet The change in reactive power at any given time. For the first generator The change in voltage at any given time. For the first generator The change in frequency at any given time This represents the normalized change in active power. This represents the normalized change in reactive power. This represents the normalized change in unit voltage. This represents the normalized change in unit frequency.

[0143] The decomposition of electrical variation data through complementary set empirical mode decomposition includes:

[0144] Determine the total number of decompositions and generate a pair of white noise sequences with equal amplitude and opposite signs. The expressions for the positive and negative noise signals are as follows:

[0145]

[0146]

[0147] in, The original input signal, This is the noise amplitude coefficient. For the first The positive noise signal of this experiment For the first Positive and negative noise-added signals from this experiment For the first The white noise sequence generated in this experiment;

[0148] The positive and negative noise signals are added to the original signal respectively to obtain two new signals to be decomposed;

[0149] Perform EMD decomposition on the two signals to be decomposed, and obtain two sets of IMF components and residuals. The EMD decomposition formula is as follows:

[0150]

[0151]

[0152] in, For the first The positive signal of the second test One eigenmode function For the first The negative signal in the second test One eigenmode function For the first The residual of the positive signal in the second experiment, For the first The residual of the negative signal in the second experiment for The total number of floors;

[0153] Repeat the above steps multiple times. Based on the noise identification criterion, filter out the noise-dominant IMFs from all IMF components of the same order, and retain only the signal-dominant IMFs for averaging. The ensemble averaging formula is as follows:

[0154]

[0155]

[0156] in, For the final One eigenmode function For the final residual term, For the first The positive signal of the second test One eigenmode function For the first The negative signal in the second test One eigenmode function For the first The residual of the positive signal in the second experiment, For the first The residual of the negative signal in the second trial;

[0157] The IMF components and residuals obtained after output averaging are shown below. The final result of CEEMD decomposition of the original signal is as follows:

[0158]

[0159] in, For the final One eigenmode function For the final residual term, for The total number of floors.

[0160] Specifically, noise amplitude coefficient The value is usually between 0.1 and 0.3.

[0161] Specifically, such as Figure 2 The image data of the noisy IMF components shown indicates that the filtered components exhibit typical noise characteristics: violent high-frequency oscillations in the time domain, chaotic amplitude variations, and a lack of obvious periodic patterns. The complementary ensemble empirical mode decomposition algorithm performs batch screening and discrimination of each order of IMF components through preset noise identification thresholds (including statistical indicators such as correlation coefficient and energy ratio), ensuring that only the signal-dominant IMF components are retained for subsequent processing.

[0162] Specifically, such as Figure 3 The signal IMF components exhibit characteristics distinctly different from the noise IMF: these components possess clear structural features, smooth oscillation modes, and regular amplitude variations. By applying an arithmetic mean to the IMFs of the same order retained in multiple rounds of decomposition, the interference of random noise is effectively suppressed, while the physical characteristics and modal properties of the original signal are fully preserved. The final output average IMF components and residuals constitute the final result of complementary set empirical mode decomposition. Figure 4 As shown in the reconstruction results, the correlation coefficient between the standard reconstructed signal and the original signal reaches 0.9996, verifying the effectiveness of the processing procedure.

[0163] The SPA smoothing algorithm is used to process the denoised electrical variation signal, including:

[0164] Based on the low-frequency oscillation characteristics, an odd window width and polynomial order are selected. The polynomial model expression for the low-frequency oscillation signal is as follows:

[0165]

[0166] in, The low-frequency oscillation signal component within the window. For polynomial coefficients, For local indexes within a window;

[0167] Using the center of the window as a local index, a coefficient template matrix for the associated oscillating signal is generated based on the polynomial model. The expression for the coefficient template matrix is ​​as follows:

[0168]

[0169] in, For the length of the data window, The order of the polynomial;

[0170] A normal equation is established using the least squares method. After solving for the coefficients, the first row is extracted as a fixed smoothing weight for adaptive oscillation denoising. The formula is as follows:

[0171]

[0172] in, For the coefficient template matrix, This is the vector of polynomial coefficients;

[0173] The weights are used as a convolution kernel and slid along the oscillating signal. A weighted average is then taken to obtain the smoothed value at each position, preserving the key oscillation features. The signal smoothing formula is as follows:

[0174]

[0175] in, For the first The smoothed oscillation signal value at each position, These are the elements of the weight coefficient vector. For the first The original low-frequency oscillation signal value at each location, The signal length;

[0176] The system uses mirror expansion to supplement the beginning and end data, and combines weights to calculate the boundary smoothing value.

[0177] Specifically, zero padding can also be used to fill in the beginning and end of the data.

[0178] Specifically, local index within the window The range is arrive .

[0179] Specifically, the polynomial coefficient vector The first column is the fixed smoothing weight.

[0180] Specifically, such as Figure 4 As shown, although the signal reconstructed by complementary set empirical mode decomposition maintains a very high similarity to the original signal overall (correlation coefficient reaches 0.9996), at local time points (such as... Figure 4 There are still obvious amplitude abrupt change points around 23 seconds and 25 seconds.

[0181] Specifically, such as Figure 5As shown, after processing with the SPA method, local abrupt changes in the signal are effectively suppressed, and the waveform becomes smoother. This process is mathematically equivalent to a low-pass filter, which filters out physically meaningless high-frequency noise introduced by the reconstruction, while preserving the valuable low-frequency oscillation modes in the original signal to the greatest extent possible. A smoother signal provides a cleaner input for the Prony algorithm, enabling it to more accurately and stably identify and extract the dominant fundamental, harmonic, and other core frequency components of the signal.

[0182] The Prony method is used to decompose the smoothed signal and extract the amplitude and phase of each modal frequency component, including:

[0183] An augmented Hankel matrix containing the data matrix and observation vectors is constructed using the smoothed signal. The expression for the data matrix is ​​as follows:

[0184]

[0185] in, This represents the total number of sampling points. The smoothed signal sequence, This is a preset model order;

[0186] The expression for the observation vector is as follows:

[0187]

[0188] The augmented matrix expression is as follows:

[0189]

[0190] in, For data matrix, For observation vectors;

[0191] Singular value decomposition is performed on the augmented matrix to distinguish the signal subspace from the noise subspace by the magnitude of the singular values. The singular value decomposition formula is as follows:

[0192]

[0193] in, The left singular vector matrix represents the time structure of the signal. The right singular vector matrix represents the frequency structure of the signal. It is a singular value matrix, representing the energy magnitude of each component;

[0194] Analyze the singular value spectrum and select the number of significant singular values ​​as the actual order of the signal. The formula for determining the actual order of the signal is as follows:

[0195]

[0196] in, Let be the singular values ​​of the singular value matrix, arranged in descending order. The true order of the signal. A threshold is used to distinguish between signals and noise;

[0197] Using the noise subspace vector, the linear prediction coefficients are solved by the overall least squares method, as shown in the following formula:

[0198]

[0199] in, These are the estimated values ​​of the prediction coefficients. These are the basis vectors that are related to the columns of the data matrix and also fall within the noise subspace. It contains basis vectors that are related to the observation vector and also fall within the noise subspace;

[0200] Solve for the characteristic polynomial formed by the prediction coefficients, and calculate the frequency and attenuation factor from the magnitude and phase of the roots. The formula for calculating the characteristic polynomial is as follows:

[0201]

[0202] in, To extract the first from the least squares solution One predictive coefficient, is the root of the characteristic equation;

[0203] The formulas for calculating frequency and attenuation factor are as follows:

[0204]

[0205]

[0206] in, For the first The attenuation factor of each component, For the first The oscillation frequency of each component;

[0207] Substituting the obtained poles into the original model, the amplitude and initial phase of each modal frequency component are finally determined by least squares fitting, as shown in the following formula:

[0208]

[0209]

[0210] in, The smoothed signal vector, For complex amplitude vectors, For the first The amplitude of each component, For the first The initial phase of each component.

[0211] Specifically, determining the threshold It is usually taken as 0.01-0.05.

[0212] Specifically, such as Figure 6 , Figure 7 As shown, after preprocessing by the method of this invention, the modal parameters obtained from Prony analysis are more concentrated in the state space, effectively suppressing spurious modes. Simultaneously, the consistency between the reconstructed signal and the original signal is significantly improved, with the correlation coefficient increasing to 0.9996. The comparative results fully demonstrate the significant advantages of the CEEMD-SPA joint denoising strategy in purifying the input signal and improving the accuracy and reliability of Prony analysis.

[0213] Example 2

[0214] Based on the same inventive concept as Embodiment 1, this embodiment introduces a device for extracting low-frequency oscillation characteristic signals in a power system, comprising:

[0215] The signal change acquisition module is used to acquire electrical change data from each generator outlet and preprocess the electrical change data.

[0216] The noise filtering and signal reconstruction module is used to decompose electrical change data and filter out noise components;

[0217] The signal smoothing and optimization module is used to process the denoised electrical change signals;

[0218] The oscillation mode extraction module is used to decompose the smoothed signal and extract the amplitude and phase of each mode frequency component.

[0219] Example 3

[0220] Based on the same inventive concept as Embodiment 1, this embodiment introduces a computer system, including:

[0221] Memory, used to store computer programs;

[0222] A processor is used to execute computer programs to implement a method for extracting low-frequency oscillation characteristic signals from a power system.

[0223] Example 4

[0224] Based on the same inventive concept as Embodiment 1, this embodiment introduces a computer program product, including computer instructions, characterized in that the steps of a method for extracting low-frequency oscillation characteristic signals of a power system are implemented when the computer instructions are executed by a processor.

[0225] In summary, this invention collects the active power, reactive power, voltage, and frequency changes at each generator outlet, performs normalization preprocessing on these changes, and then decomposes the preprocessed signal through a three-stage cascade filtering process. Based on noise identification criteria, the noise-dominant IMF component is filtered out, and the signal-dominant IMF component is retained and ensemble-averaged to eliminate noise influence. Next, a polynomial model and fixed smoothing weights are used to perform moving average processing on the signal to reduce local errors. Finally, the smoothed signal is decomposed, and the actual order of the signal is determined by constructing an augmented Hankel matrix and singular value decomposition. The overall least squares method is used to solve for the linear prediction coefficients, and finally, the modal parameters such as amplitude, phase, frequency, and damping ratio of each modal frequency component are extracted. This invention can effectively suppress noise interference, significantly improve the accuracy and stability of Prony analysis, and has good adaptability to low-frequency oscillation signals under different operating conditions of power systems, providing a reliable technical means for the accurate identification of low-frequency oscillation sources.

Claims

1. A method for extracting low-frequency oscillation characteristic signals in a power system, characterized in that, include: Obtain electrical change data for each generator outlet; The electrical change data is preprocessed; The electrical variation data is decomposed using complementary set empirical mode decomposition to filter out noise components; The SPA smoothing algorithm is used to process the denoised electrical change signal to obtain a smooth signal; The smoothed signal was decomposed using the Prony method to extract the amplitude and phase of each modal frequency component, providing key feature data for subsequent low-frequency oscillation identification.

2. The method for extracting low-frequency oscillation characteristic signals in power systems according to claim 1, characterized in that, The electrical change data includes changes in active power, reactive power, generator voltage, and generator frequency.

3. The method for extracting low-frequency oscillation characteristic signals in power systems according to claim 1, characterized in that, The formula for calculating the change in active power at the generator outlet is as follows: in, For generator outlet The change in active power at any given time. For generator outlet Real-time active power data collected at any given moment. This refers to the active power output at the generator's outlet under stable operating conditions. The formula for calculating the change in reactive power at the generator outlet is as follows: in, For generator outlet The change in reactive power at any given time. For generator outlet Real-time reactive power data at any given moment. This refers to the reactive power output of the generator under stable operating conditions. The formula for calculating the generator voltage change is as follows: in, For the first generator The change in voltage at any given time. For the first generator Real-time voltage acquisition value at any given time. For the first Voltage value of the generator under stable operating conditions; The formula for calculating the generator frequency change is as follows: in, For real-time rotational speed, The number of rotor pole pairs, For frequency, For the first generator The change in frequency at any given time For the first generator Real-time frequency data acquisition value at any given moment. For the first Frequency value of the generator under stable operating conditions.

4. The method for extracting low-frequency oscillation characteristic signals in a power system according to claim 1, characterized in that, The preprocessing includes normalizing the electrical change data using the following formula: in, Rated apparent power, The rated voltage of the unit. The rated frequency of the unit, For generator outlet The change in active power at any given time. For generator outlet The change in reactive power at any given time. For the first generator The change in voltage at any given time. For the first generator The change in frequency at any given time This represents the normalized change in active power. This represents the normalized change in reactive power. This represents the normalized change in unit voltage. This represents the normalized change in unit frequency.

5. The method for extracting low-frequency oscillation characteristic signals in a power system according to claim 1, characterized in that, The decomposition of the electrical variation data through complementary set empirical mode decomposition includes: Determine the total number of decompositions and generate a pair of white noise sequences with equal amplitude and opposite signs. The expressions for the positive and negative noise signals are as follows: in, The original input signal, This is the noise amplitude coefficient. For the first The positive noise signal of this experiment For the first Positive and negative noise-added signals from this experiment For the first The white noise sequence generated in this experiment; The positive and negative noise signals are added to the original signal respectively to obtain two new signals to be decomposed; Perform EMD decomposition on the two signals to be decomposed respectively to obtain two sets of IMF components and residuals. The EMD decomposition formula is as follows: in, For the first The positive signal of the second test One eigenmode function For the first The negative signal in the second test One eigenmode function For the first The residual of the positive signal in the second experiment, For the first The residual of the negative signal in the second experiment for The total number of floors; Repeat the above steps multiple times. Based on the noise identification criterion, filter out the noise-dominant IMFs from all IMF components of the same order, and retain only the signal-dominant IMFs for averaging. The ensemble averaging formula is as follows: in, For the final One eigenmode function For the final residual term, For the first The positive signal of the second test One eigenmode function For the first The negative signal in the second test One eigenmode function For the first The residual of the positive signal in the second experiment, For the first The residual of the negative signal in the second trial; The IMF components and residuals obtained after output averaging are shown below. The final result of CEEMD decomposition of the original signal is as follows: in, For the final One eigenmode function For the final residual term, for The total number of floors.

6. The method for extracting low-frequency oscillation characteristic signals in a power system according to claim 1, characterized in that, The process of processing the denoised electrical change signal using the SPA smoothing algorithm includes: Based on the low-frequency oscillation characteristics, an odd window width and polynomial order are selected. The polynomial model expression for the low-frequency oscillation signal is as follows: in, The low-frequency oscillation signal component within the window. For polynomial coefficients, For local indexes within a window; Using the center of the window as a local index, a coefficient template matrix for the associated oscillation signal is generated based on the polynomial model. The expression for the coefficient template matrix is ​​as follows: in, For the length of the data window, The order of the polynomial; A normal equation is established using the least squares method. After solving for the coefficients, the first row is extracted as a fixed smoothing weight for adaptive oscillation denoising. The formula is as follows: in, For the coefficient template matrix, This is the vector of polynomial coefficients; The weights are used as a convolution kernel and slid along the oscillating signal. A weighted average is then taken to obtain the smoothed value at each position, preserving the key oscillation features. The signal smoothing formula is as follows: in, For the first The smoothed oscillation signal value at each position, These are the elements of the weight coefficient vector. For the first The original low-frequency oscillation signal value at each location, The signal length; The system uses mirror expansion to supplement the beginning and end data, and combines weights to calculate the boundary smoothing value.

7. The method for extracting low-frequency oscillation characteristic signals in a power system according to claim 1, characterized in that, The process of decomposing the smoothed signal using the Prony method to extract the amplitude and phase of each modal frequency component includes: An augmented Hankel matrix containing a data matrix and observation vectors is constructed using the smoothed signal. The expression for the data matrix is ​​as follows: in, This represents the total number of sampling points. The smoothed signal sequence, This is a preset model order; The expression for the observation vector is as follows: The augmented matrix expression is as follows: in, For data matrix, For observation vectors; Singular value decomposition is performed on the augmented matrix, and the signal subspace and noise subspace are distinguished by the magnitude of the singular values. The singular value decomposition formula is as follows: in, The left singular vector matrix represents the time structure of the signal. The right singular vector matrix represents the frequency structure of the signal. It is a singular value matrix, representing the energy magnitude of each component; Analyze the singular value spectrum and select the number of significant singular values ​​as the actual order of the signal. The formula for determining the actual order of the signal is as follows: in, Let be the singular values ​​of the singular value matrix, arranged in descending order. The true order of the signal. A threshold is used to distinguish between signals and noise; Using the noise subspace vector, the linear prediction coefficients are solved by the overall least squares method, as shown in the following formula: in, These are the estimated values ​​of the prediction coefficients. These are the basis vectors that are related to the columns of the data matrix and also fall within the noise subspace. It contains basis vectors that are related to the observation vector and also fall within the noise subspace; Solve for the characteristic polynomial formed by the prediction coefficients, and calculate the frequency and attenuation factor from the magnitude and phase of the roots. The formula for calculating the characteristic polynomial is as follows: in, To extract the first from the least squares solution One predictive coefficient, is the root of the characteristic equation; The formulas for calculating the frequency and attenuation factor are as follows: in, For the first The attenuation factor of each component, For the first The oscillation frequency of each component; Substituting the obtained poles into the original model, the amplitude and initial phase of each modal frequency component are finally determined by least squares fitting, as shown in the following formula: in, The smoothed signal vector, For complex amplitude vectors, For the first The amplitude of each component, For the first The initial phase of each component.

8. A device for extracting low-frequency oscillation characteristic signals in a power system, characterized in that, include: The signal change acquisition module is used to acquire electrical change data at each generator outlet and preprocess the electrical change data. The noise filtering and signal reconstruction module is used to decompose the electrical change data and filter out noise components. The signal smoothing and optimization module is used to process the denoised electrical change signals; The oscillation mode extraction module is used to decompose the smoothed signal and extract the amplitude and phase of each mode frequency component.

9. A computer system, characterized in that, include: Memory, used to store computer programs; A processor is configured to execute the computer program to implement the steps of the method for extracting low-frequency oscillation characteristic signals of a power system as described in any one of claims 1 to 7.

10. A computer program product comprising computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method for extracting low-frequency oscillation characteristic signals of a power system as described in any one of claims 1 to 7.

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