Subsynchronous oscillation identification detection method and system based on multi-compression improved spline chirp transformation

Abstract

The invention relates to a subsynchronous oscillation identification detection method and system based on multiple compression improved spline chirp transformation, and belongs to the field of power system oscillation detection. The method comprises the following steps: firstly, collecting a current signal and a voltage signal output from a power system, then converting the time-domain current signal and the voltage signal into a time-frequency domain by utilizing improved spline chirp transformation, and extracting and mapping an improved spline chirp transformation result to a new time-frequency spectrum by adopting multiple compression transformation; and reconstructing the obtained time-frequency spectrum information, and carrying out identification estimation on oscillation parameters in a new time-frequency spectrum by adopting a matrix pencil algorithm so as to obtain parameters of the next synchronous oscillation signal in different modals. According to the method, subsynchronous oscillation signal modal extraction and parameter estimation can be realized in a high-noise environment, subsynchronous oscillation occurring in a system can be automatically detected, and efficient and accurate time-frequency feature extraction requirements can be comprehensively met.

Description

Technical Field

[0001] The invention belongs to the field of power system oscillation detection, and in particular relates to a subsynchronous oscillation identification and detection method and system based on multiple compression improved spline chirp transform. Background Art

[0002] The access of a high proportion of renewable energy and the widespread application of power electronic equipment have formed a "double high" development trend, bringing unprecedented challenges to the dynamic behavior and stability characteristics of traditional power systems. SSO in the power system is an unstable phenomenon that occurs quickly and spreads over a wide range, which may cause equipment damage and system instability. The existence of the SSO problem will seriously affect the system's transmission capacity and new energy consumption, and may even cause overall system instability. Therefore, the development of effective SSO detection technology that can accurately identify the subsynchronous component parameters of voltage and current and dynamically monitor the generation and propagation of SSO has very important theoretical significance and application value, and it is imperative to effectively suppress it.

[0003] With the widespread application of wide area measurement systems (WAMS) and phasor measurement units (PMU) in power systems, WAMS and PMU have become effective platforms for SSO monitoring in most transmission networks and power plants. WAMS and PMU can provide fundamental synchrophasor data with high reporting rate and wide area synchronization, which greatly facilitates the dynamic online monitoring of power grids. When SSO occurs, the voltage and power data of the power grid or generator recorded by WAMS and PMU usually contain harmonic signals other than the 50Hz fundamental. Since these signals usually contain noise, the analysis method should have high modal resolution and noise immunity for SSO detection.

[0004] The time-frequency spectrum analysis (TFA) method combines the advantages of the time domain and the frequency domain, providing a detailed view of the frequency characteristics of the signal changing over time, and is particularly suitable for the analysis of non-stationary signals. In order to obtain a better time-frequency distribution, Mann et al. proposed the chirp transform (CT). CT obtains a linear chirp basis that adapts to the speed of instantaneous frequency changes by selecting corresponding parameters. Yang et al. improved on the basis of traditional CT and proposed the spline chirp transform (SCT). SCT obtains the parameters of the spline kernel by spline approximation, thereby improving the time-frequency resolution. In order to improve the time-frequency concentration, many scholars have proposed various combined methods. For example, Liu Jingliang et al. proposed a structural instantaneous frequency identification method based on synchronous squeezing wavelet transform. Yu et al. proposed the synchronous extraction transform (SET). SET improves the time-frequency analysis effect by extracting the energy that best matches the instantaneous frequency and eliminating the rest of the energy. At the same time, Yu et al. proposed the multiple squeezing transform (MSST) combined with STFT. The MSST algorithm squeezes the energy to the time-frequency ridge according to the specified frequency range, and achieves the effect of improving the energy concentration through multiple squeezing.

[0005] Existing time-frequency analysis methods still have shortcomings in the trade-off between time-frequency resolution and energy concentration, energy leakage suppression, computational complexity, adaptability to complex nonlinear signals, and robustness in low signal-to-noise ratio environments, making it difficult to fully meet the needs of efficient and accurate time-frequency feature extraction. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention proposes a subsynchronous oscillation identification and detection method and system based on multiple compressed improved spline chirp transform, the purpose of which is to automatically detect subsynchronous oscillations occurring in the system in a high noise environment.

[0007] The technical solution of the present invention is: a subsynchronous oscillation identification and detection method based on multiple compression improved spline chirp transform, comprising the following steps:

[0008] Step 1: Collect the voltage signal and current signal output by the power system and perform Taylor expansion;

[0009] Step 2, calculating the time-frequency spectrum of the improved spline chirp transform of the voltage signal and the current signal after Taylor expansion;

[0010] Step 3: Using a multiple compression algorithm, the exchange result of the time-frequency spectrum of the improved spline chirp is extracted and mapped to a new time-frequency spectrum and the signal is reconstructed;

[0011] Step 4: Use the matrix bundle algorithm to calculate the parameter value of the mode to which the extracted signal belongs after signal reconstruction.

[0012] Specifically, the reference model of the voltage signal and current signal collected in step 1 is q(t);

[0013]

[0014] In the formula, t is the time variable, φ 0 (t) is the phase at the expansion point, A(m) is the amplitude function, and Taylor expansion is used for formula (1):

[0015]

[0016] Where A(t) is the amplitude function after Taylor expansion, u is the integral variable, φ′(t) is the derivative of the phase, and φ(t) is the phase of the signal after Taylor expansion. Therefore, the unified model of the voltage signal and current signal after Taylor expansion is x(t):

[0017]

[0018] Specifically, the specific steps of step 2 are:

[0019] Improved spline chirp transform ISCT for calculating the unified current-voltage model x(t) after Taylor expansion s Time spectrum of:

[0020]

[0021] In the formula, λ 1 , 2 is the parameter to be optimized, σ is the Gaussian window function, ω is the frequency, t is the time variable, t 0 is the time value at the expansion point, α is the spline interpolation kernel function coefficient, is the signal analytical expression, specifically

[0022]

[0023] Where n is the total number of interpolation coefficients, α k is the discrete spline interpolation kernel function coefficient, γ i The coefficients satisfy the following conditions:

[0024]

[0025] In the formula, γ i is the i-th interpolation coefficient, γ i+1 is the i+1th interpolation coefficient, is the kth interpolation kernel function coefficient under the i+1th interpolation coefficient, t i is the discretized i-th time series value, t i+1 is the i+1th time series value after discretization. According to the energy concentration principle, the objective function and constraint conditions for the parameter calculation to be optimized are:

[0026]

[0027] In the formula, argmax represents the objective function, Sc represents the constraint condition, K is the proportional coefficient, K = 10, L is the width of the window function, L = 1000, Ts is the sampling period, N is the signal length, T is the signal duration, ω max For the maximum frequency limit, take the inverse of half the sampling frequency, ω min For the minimum frequency limit, take twice the Nyquist sampling rate, and solve formula (7) through the optimization algorithm to obtain the two parameter values ​​of the window function.

[0028] Specifically, the specific steps of step three are:

[0029] The instantaneous frequency of any point on the time-frequency spectrum of the improved spline chirp transform is calculated as:

[0030]

[0031] In the formula, ISCT is the derivative with respect to time t. s The first compression transformation is performed:

[0032]

[0033] In the formula, δ() is the Dirichlet function, η is the frequency corresponding to a certain time τ, IMSSCT [1] (τ,η) indicates the first compression transformation. is the compression transformation coefficient of x(t) at the time-frequency point (τ,η);

[0034] Then use formula (9) to perform the compression transformation again, and get the secondary compression transformation as follows:

[0035]

[0036] In the formula, is the secondary compression transformation coefficient of x(t) at the time-frequency point (τ, η). Similarly, the time-frequency mapping result obtained by formula (10) is used to perform b compression transformations to complete the multiple compression transformations on the new mapped time-frequency spectrum:

[0037]

[0038] In the formula, is the b-time compression transform coefficient of x(t) at the time-frequency point (τ,η), IMSSCT [b] (τ, η) is the b-th transformation result, IMSSCT [b-1] (τ, η) is the result of the b-1th transformation;

[0039] Adaptive Mode Extraction:

[0040] For electrical signals, the amplitude distribution information at each position of the time-frequency spectrum is obtained through the time-frequency mapping of IMSSCT, and the frequency bandwidth of each signal component is obtained from the time-frequency window. The amplitude distribution of the model component of each window at time t is determined by the calculation result of formula (7), so the time-frequency window is processed as follows:

[0041]

[0042] Where, IMSSCT tn (t n ,η) is the IMSSCT value in the nth window, ε represents the selected threshold, which is determined by the accuracy requirement of signal reconstruction, G g (t n , ω) is the window function after determining the optimized parameters;

[0043] For the electrical signal containing subsynchronous oscillation information, find the highest amplitude position index in the time-frequency window as the starting point, and then retrieve the G g (t n ,ω 0 -Δ) or G g (t n ,ω 0 +Δ), △ is the instantaneous frequency bandwidth, record the corresponding frequency bandwidth estimation, and detect the frequency bandwidth corresponding to the next instantaneous frequency based on the amplitude in the time-frequency window. So we have:

[0044]

[0045] In the formula, ω k is the kth instantaneous frequency, φ′ k (t n )’s instantaneous frequency of the kth mode;

[0046] The signal on the new time-frequency spectrum is reconstructed as follows:

[0047]

[0048] Where σ is the value of the window function at 0, IMSSCT [b] is the improved spline chirp transform value after compression b times, To reconstruct the signal.

[0049] Specifically, the specific steps of step four are:

[0050] Constructing the Hankel matrix

[0051]

[0052] Where P is the number of rows in the matrix, J is the number of columns in the matrix, and the Hankel matrix is ​​decomposed into submatrices H 1 and H 2 :

[0053]

[0054] In the formula, H 1 It can be further decomposed into:

[0055] H 1 =ΓΛΨ (17)

[0056] Where Γ is the left singular vector, A is the diagonal singular value, and Ψ is the right singular vector:

[0057]

[0058] In the formula, diag([β 1 , β 2, ..., β M ]) indicates that the main diagonal elements are β 1 , β 2 , ..., β M The M-order diagonal matrix, similarly, H 2 It can also be decomposed into:

[0059] H 2 =Γ∑ΛΨ (19)

[0060] Where ∑ is the eigenvalue matrix:

[0061] ∑=diag([z 1 , z 2 , …, z M ]) (20)

[0062] So the eigenvalue z i By calculation get, is the matrix H 1 The pseudo-inverse matrix of is solved by the least squares method:

[0063]

[0064] In the formula, z i is the eigenvalue, β i is a singular value, ζ i is the damping coefficient, A i is the amplitude, φ i is the phase, △t is the length of the window function, Re() represents taking the real part of the complex number, and Im() represents removing the imaginary part of the complex number.

[0065] A subsynchronous oscillation identification and detection system based on multiple compressed improved spline chirp transform includes the following modules:

[0066] Signal preprocessing module: collects the voltage signal and current signal output by the power system and performs Taylor expansion preprocessing, and inputs the preprocessed signal data into the calculation module;

[0067] Calculation module: used to calculate the time-frequency spectrum of the improved spline chirp transform of the preprocessed signal data, extract and map the exchange results of the time-frequency spectrum of the improved spline chirp to the new time-frequency spectrum using a multiple compression algorithm, and input it into the signal reconstruction module;

[0068] Signal reconstruction module: detects the number of modes in the transformed time-frequency signal and reconstructs it into a time domain signal, which is input into the parameter estimation module;

[0069] Parameter estimation module: Matrix bundle algorithm is used to calculate the parameter value of the mode to which the extracted signal belongs after signal reconstruction.

[0070] A computer-readable storage medium stores a subsynchronous oscillation identification and detection program based on multiple compressed improved spline chirp transforms. When the subsynchronous oscillation identification and detection program based on multiple compressed improved spline chirp transforms is loaded and executed, the subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transforms is implemented.

[0071] The beneficial effects of the present invention are as follows: the present invention can realize the mode extraction and parameter estimation of subsynchronous oscillation signals in a high noise environment, and by optimizing the time-frequency transformation strategy, improve the extraction accuracy and energy concentration of instantaneous frequency, thereby effectively suppressing the energy leakage problem. At the same time, the use of an adaptive parameter control mechanism enables the method to more accurately characterize complex nonlinear instantaneous frequency changes and improve the ability to analyze multi-component signals. In addition, the present invention can automatically detect subsynchronous oscillations occurring in the system, thereby fully meeting the needs of efficient and accurate time-frequency feature extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The present invention will be further described below in conjunction with the accompanying drawings.

[0073] Figure 1 A specific flow chart of the method in a specific embodiment of the present invention;

[0074] Figure 2 It is a diagram of the signal under test under the simulated sub-synchronous oscillation test signal;

[0075] Figure 3 It is a detection diagram of the sub-synchronous oscillation signal result of STFT under the simulated sub-synchronous oscillation test signal;

[0076] Figure 4 It is a detection diagram of the sub-synchronous oscillation signal result of SCT under the simulated sub-synchronous oscillation test signal;

[0077] Figure 5 This is a subsynchronous oscillation signal result detection diagram of IMSSCT under the simulated subsynchronous oscillation test signal;

[0078] Figure 6 This is a comparison diagram between the reconstructed signal diagram and the original signal diagram of the subsynchronous oscillation signal result of IMSSCT under the simulated subsynchronous oscillation test signal. DETAILED DESCRIPTION

[0079] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] Example 1: Figure 1 As shown, a subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transform includes the following steps:

[0081] S1, collecting the voltage signal and current signal output by the power system and performing Taylor expansion;

[0082] The reference model of the collected voltage and current signals is q(t);

[0083]

[0084] In the formula, t is the time variable, φ 0 (t) is the phase at the expansion point, A(m) is the amplitude function, and Taylor expansion is used for formula (1):

[0085]

[0086] Where A(t) is the amplitude function after Taylor expansion, u is the integral variable, φ′(t) is the derivative of the phase, and φ(t) is the phase of the signal after Taylor expansion. Therefore, the unified model of the voltage signal and current signal after Taylor expansion is x(t):

[0087]

[0088] S2. Calculate the time-frequency spectrum of the improved spline chirp transform of the voltage signal and the current signal after Taylor expansion. The specific steps are:

[0089] Improved spline chirp transform ISCT for calculating the unified current-voltage model x(t) after Taylor expansion s Time spectrum of:

[0090]

[0091] In the formula, λ 1 , 2 is the parameter to be optimized, which is used to adapt to the instantaneous frequency change and improve the time-frequency aggregation. σ is the Gaussian window function, ω is the frequency, t is the time variable, and t 0 is the time value at the expansion point, α is the spline interpolation kernel function coefficient, is the signal analysis expression, specifically:

[0092]

[0093] Where n is the total number of interpolation coefficients, α k is the discrete spline interpolation kernel function coefficient, γ i The coefficients satisfy the following conditions:

[0094]

[0095] In the formula, γ i is the i-th interpolation coefficient, γ i+1 is the i+1th interpolation coefficient, is the kth interpolation kernel function coefficient under the i+1th interpolation coefficient, t i is the discretized i-th time series value, t i+1 is the i+1th time series value after discretization. According to the energy concentration principle, the objective function and constraint conditions for the parameter calculation to be optimized are:

[0096]

[0097] In the formula, argmax represents the objective function, Sc represents the constraint condition, K is the proportional coefficient, K = 10, L is the width of the window function, L = 1000, Ts is the sampling period, N is the signal length, T is the signal duration, ω max For the maximum frequency limit, take the inverse of half the sampling frequency, ω min For the minimum frequency limit, take twice the Nyquist sampling rate, and solve formula (7) through the optimization algorithm to obtain the two parameter values ​​of the window function.

[0098] S3, using a multiple compression algorithm to extract and map the exchange result of the time-frequency spectrum of the improved spline chirp to a new time-frequency spectrum and reconstruct the signal, the specific steps are:

[0099] The instantaneous frequency of any point on the time-frequency spectrum of the improved spline chirp transform is calculated as:

[0100]

[0101] In the formula, ISCT is the derivative with respect to time t. s The first compression transformation is performed:

[0102]

[0103] In the formula, δ() is the Dirichlet function, η is the frequency corresponding to a certain time τ, IMSSCT [1] (τ,η) indicates the first compression transformation. is the compression transformation coefficient of x(t) at the time-frequency point (τ,η);

[0104] Then use formula (9) to perform the compression transformation again, and get the secondary compression transformation as follows:

[0105]

[0106] In the formula, is the secondary compression transformation coefficient of x(t) at the time-frequency point (τ, η). Similarly, the time-frequency mapping result obtained by formula (10) is used to perform b compression transformations to complete the multiple compression transformations on the new mapped time-frequency spectrum:

[0107]

[0108] In the formula, is the b-time compression transform coefficient of x(t) at the time-frequency point (τ,η), IMSSCT [b] (τ, η) is the b-th transformation result, IMSSCT [b-1] (τ, η) is the b-1th transformation result;

[0109] Adaptive Mode Extraction:

[0110] For electrical signals, the amplitude distribution information at each position of the time-frequency spectrum is obtained through the time-frequency mapping of IMSSCT, and the frequency bandwidth of each signal component is obtained from the time-frequency window. The amplitude distribution of the model component of each window at time t is determined by the calculation result of formula (7), so the time-frequency window is processed as follows:

[0111]

[0112] Where, IMSSCT tn (t n , η) is the IMSSCT value in the nth window, ε represents the selected threshold, which is determined by the accuracy requirement of signal reconstruction, G g (t n , ω) is the window function after determining the optimized parameters;

[0113] For the electrical signal containing subsynchronous oscillation information, find the highest amplitude position index in the time-frequency window as the starting point, and then retrieve the G g (t n ,ω 0 -Δ) or G g (t n ,ω 0 +Δ), △ is the instantaneous frequency bandwidth, record the corresponding frequency bandwidth estimation, and detect the frequency bandwidth corresponding to the next instantaneous frequency based on the amplitude in the time-frequency window. So we have:

[0114]

[0115] In the formula, ω k is the kth instantaneous frequency, φ′ k (t n )’s instantaneous frequency of the kth mode;

[0116] The signal on the new time-frequency spectrum is reconstructed as follows:

[0117]

[0118] Where σ is the value of the window function at 0, IMSSCT [b] is the improved spline chirp transform value after compression b times, To reconstruct the signal.

[0119] S4. Calculate the parameter value of the mode to which the extracted signal belongs after signal reconstruction using the matrix bundle algorithm. The specific steps are:

[0120] Constructing the Hankel matrix

[0121]

[0122] Where P is the number of rows in the matrix, J is the number of columns in the matrix, and the Hankel matrix is ​​decomposed into submatrices H 1 and H 2 :

[0123]

[0124] In the formula, H 1 It can be further decomposed into:

[0125] H 1 =ΓAΨ (17)

[0126] Where Γ is the left singular vector, Λ is the diagonal singular value, and Ψ is the right singular vector:

[0127]

[0128] In the formula, diag([β 1 , β 2 , ..., β M ]) indicates that the main diagonal elements are β 1 , β 2 , ..., β M The M-order diagonal matrix, similarly, H 2 It can also be decomposed into:

[0129] H 2 =Γ∑AΨ (19)

[0130] Where ∑ is the eigenvalue matrix:

[0131] ∑=diag([z 1 , z 2 , …, z M ]) (20)

[0132] So the eigenvalue z i By calculation get, is the matrix H 1 The pseudo-inverse matrix of is solved by the least squares method:

[0133]

[0134] In the formula, z i is the eigenvalue, β i is a singular value, ζ i is the damping coefficient, A i is the amplitude, φ i is the phase, △t is the length of the window function, Re() represents taking the real part of the complex number, and Im() represents removing the imaginary part of the complex number.

[0135] A subsynchronous oscillation identification and detection method system, used to implement the subsynchronous oscillation identification and detection method, includes the following modules:

[0136] Signal preprocessing module: collects the voltage signal and current signal output by the power system and performs Taylor expansion preprocessing, and inputs the preprocessed signal data into the calculation module;

[0137] Calculation module: used to calculate the time-frequency spectrum of the improved spline chirp transform of the preprocessed signal data, extract and map the exchange results of the time-frequency spectrum of the improved spline chirp to the new time-frequency spectrum using a multiple compression algorithm, and input it into the signal reconstruction module;

[0138] Signal reconstruction module: detects the number of modes in the transformed time-frequency signal and reconstructs it into a time domain signal, which is input into the parameter estimation module;

[0139] Parameter estimation module: Matrix bundle algorithm is used to calculate the parameter value of the mode to which the extracted signal belongs after signal reconstruction.

[0140] A computer-readable storage medium stores a subsynchronous oscillation identification and detection program based on multiple compressed improved spline chirp transforms. When the subsynchronous oscillation identification and detection program based on multiple compressed improved spline chirp transforms is loaded and executed, the subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transforms is implemented.

[0141] In order to facilitate those skilled in the art to understand the technical content of the invention, the invention is further explained below in conjunction with the accompanying drawings. The invention performs parameter identification of subsynchronous oscillation on the subsynchronous oscillation test signal shown in Table 1, and the simulation results are as follows: Figure 2 shown.

[0142] Table 1

[0143]

[0144] The subsynchronous oscillation is caused by interference occurring at 0.5s and then cleared after 0.1s. Then, STFT, SCT and IMSSCT are performed on the signal. Figure 3 is the STFT image, Figure 4 is the SCT image, Figure 5 It is the IMSSCT image. It can be seen from the three figures that the modes after the occurrence of SSO are concentrated on three frequencies. Figure 3 The curve obtained by STFT is blurred. Figure 4 Although the results obtained by SCT are more obvious, the energy concentration is not high. Figure 5 The results obtained by IMSSCT clearly show the time-frequency curve results of the three modes; in addition, at the two ends of the generation and end of the oscillation component, the IMSSCT time-frequency analysis is more concentrated in the image than the other three algorithms.

[0145] In addition, in order to verify the signal reconstruction capability of PMSST, the original signal is compared with the reconstructed signal obtained by PMSST. Figure 5 The results shown in the figure use the root mean square error (RMSE) to quantitatively evaluate the reconstruction performance, namely:

[0146]

[0147] In the formula, s is the original input signal, To reconstruct the measured value of the signal, |||| 2 Indicates the second norm. Figure 6 It can be seen that PMSST has good signal reconstruction ability and can reconstruct the signal s(t) well. The RMSE of the signal after IMSSCT processing is 2.5076×10 -5 , indicating that PMSST can reconstruct the signal well. The results of parameter estimation of the reconstructed signal are shown in Table 2.

[0148] Table 2

[0149]

[0150]

[0151] It can be seen that the method used in the present invention can effectively detect noisy subsynchronous oscillation signals.

[0152] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transform, characterized in that: The following steps are involved: Step 1: Collect the voltage signal and current signal output by the power system and perform Taylor expansion; Step 2, calculating the time-frequency spectrum of the improved spline chirp transform of the voltage signal and the current signal after Taylor expansion; Step 3: Using a multiple compression algorithm, the exchange result of the time-frequency spectrum of the improved spline chirp is extracted and mapped to a new time-frequency spectrum and the signal is reconstructed; Step 4: Use the matrix bundle algorithm to calculate the parameter value of the mode to which the extracted signal belongs after signal reconstruction.

2. The subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transform according to claim 1, characterized in that: The reference model of the voltage signal and current signal collected in step 1 is q(t); In the formula, t is the time variable, φ0(t) is the phase at the expansion point, and A(m) is the amplitude function. Using Taylor expansion for formula (1), we have: Where A(t) is the amplitude function after Taylor expansion, u is the integral variable, φ′(t) is the derivative of the phase, and φ(t) is the phase of the signal after Taylor expansion. Therefore, the unified model of the voltage signal and current signal after Taylor expansion is x(t):

3. The subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transform according to claim 1, characterized in that: The specific steps of step 2 are: Improved spline chirp transform ISCT for calculating the unified current-voltage model x(t) after Taylor expansion s Time spectrum of: In the formula, λ1 and λ2 are the parameters to be optimized, σ is the Gaussian window function, ω is the frequency, t is the time variable, t0 is the time value at the expansion point, and α is the spline interpolation kernel function coefficient. is the signal analysis expression, specifically: Where n is the total number of interpolation coefficients, α k is the discrete spline interpolation kernel function coefficient, γ i The coefficients satisfy the following conditions: In the formula, γ i is the i-th interpolation coefficient, γ i+1 is the i+1th interpolation coefficient, is the kth interpolation kernel function coefficient under the i+1th interpolation coefficient, t i is the discretized i-th time series value, t i+1 is the i+1th time series value after discretization. According to the energy concentration principle, the objective function and constraint conditions for the parameter calculation to be optimized are: In the formula, argmax represents the objective function, Sc represents the constraint condition, K is the proportional coefficient, L is the width of the window function, Ts is the sampling period, N is the signal length, T is the signal duration, ω max For the maximum frequency limit, take the inverse of half the sampling frequency, ω min For the minimum frequency limit, take twice the Nyquist sampling rate, and solve formula (7) through the optimization algorithm to obtain the two parameter values ​​of the window function.

4. The subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transform according to claim 3 is characterized in that: The specific steps of step three are: The instantaneous frequency of any point on the time-frequency spectrum of the improved spline chirp transform is calculated as: In the formula, ISCT is the derivative with respect to time t. s The first compression transformation is performed: In the formula, δ() is the Dirichlet function, η is the frequency corresponding to a certain time τ, IMSSCT [1] (τ,η) indicates the first compression transformation. is the compression transformation coefficient of x(t) at the time-frequency point (τ,η); Then use formula (9) to perform the compression transformation again, and get the secondary compression transformation as follows: In the formula, is the secondary compression transformation coefficient of x(t) at the time-frequency point (τ, η). Similarly, the time-frequency mapping result obtained by formula (10) is used to perform b compression transformations to complete the multiple compression transformations on the new mapped time-frequency spectrum: In the formula, is the b-time compression transform coefficient of x(t) at the time-frequency point (τ,η), IMSSCT [b] (τ, η) is the b-th transformation result, IMSSCT [b-1] (τ, η) is the result of the b-1th transformation; Adaptive Mode Extraction: For electrical signals, the amplitude distribution information at each position of the time-frequency spectrum is obtained through the time-frequency mapping of IMSSCT, and the frequency bandwidth of each signal component is obtained from the time-frequency window. The amplitude distribution of the model component of each window at time t is determined by the calculation result of formula (7), so the time-frequency window is processed as follows: Where, IMSSCT tn (t n , η) is the IMSSCT value in the nth window, ε represents the selected threshold, G g (t n , ω) is the window function after determining the optimized parameters; For the electrical signal containing subsynchronous oscillation information, find the highest amplitude position index in the time-frequency window as the starting point, and then retrieve the G g (t n ,ω0-Δ) or G g (t n , ω0+Δ), Δ is the instantaneous frequency bandwidth, record the corresponding frequency bandwidth estimation, and detect the frequency bandwidth corresponding to the next instantaneous frequency based on the amplitude in the time-frequency window. So: In the formula, ω k is the kth instantaneous frequency, φ′ k (t n )’s instantaneous frequency of the kth mode; The signal on the new time-frequency spectrum is reconstructed as follows: Where σ is the value of the window function at 0, IMSSCT [b] is the improved spline chirp transform value after compression b times, To reconstruct the signal.

5. The subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transform according to claim 3, characterized in that: The specific steps of step 4 are: Constructing the Hankel matrix Where P is the number of rows of the matrix, J is the number of columns of the matrix, and the Hankel matrix is ​​decomposed into sub-matrices H1 and H2: In the formula, H1 is further decomposed into: H1=ΓΛΨ(17) Where Γ is the left singular vector, Λ is the diagonal singular value, and Ψ is the right singular vector: In the formula, diag([β1, β2,...,β M ]) indicates that the main diagonal elements are β1, β2, ..., β M The M-order diagonal matrix of , similarly, H2 is decomposed into: H2=Γ∑ΛΨ (19) Where ∑ is the eigenvalue matrix: ∑=diag([z1,z2,…,z M ]) (20) Therefore, the eigenvalue zi is calculated by get, is the pseudo-inverse matrix of matrix H1, which can be solved by the least squares method: In the formula, z i is the eigenvalue, β i is a singular value, ζ i is the damping coefficient, A i is the amplitude, φ i is the phase, Δt is the length of the window function, Re() represents taking the real part of the complex number, and Im() represents removing the imaginary part of the complex number.

6. A subsynchronous oscillation identification and detection system based on multiple compressed improved spline chirp transform, characterized in that: Includes the following modules: Signal preprocessing module: collects the voltage signal and current signal output by the power system and performs Taylor expansion preprocessing, and inputs the preprocessed signal data into the calculation module; Calculation module: used to calculate the time-frequency spectrum of the improved spline chirp transform of the preprocessed signal data, extract and map the exchange results of the time-frequency spectrum of the improved spline chirp to the new time-frequency spectrum using a multiple compression algorithm, and input it into the signal reconstruction module; Signal reconstruction module: detects the number of modes in the transformed time-frequency signal and reconstructs it into a time domain signal, which is input into the parameter estimation module; Parameter estimation module: Matrix bundle algorithm is used to calculate the parameter value of the mode to which the extracted signal belongs after signal reconstruction.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a subsynchronous oscillation identification and detection program based on multiple compressed improved spline chirp transforms. When the subsynchronous oscillation identification and detection program based on multiple compressed improved spline chirp transforms is loaded and executed, the subsynchronous oscillation identification and detection method based on multiple compressed improved spline chirp transforms as described in any one of claims 1 to 6 is implemented.

Images