Weak Sub-synchronous Oscillation Identification Method Based on Machine Learning and Kalman Filter

Abstract

The present invention discloses a method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering, which relates to the technical field of power system stability and control, and includes two parts: a neural network model and a Kalman filtering model. The neural network model is responsible for extracting the pre-estimated oscillation frequency of each subsynchronous oscillation component from the original oscillation signal. The Kalman filtering model uses the output result of the machine learning model as the initial parameter value to extract the corresponding subsynchronous oscillation component from the total original signal. Based on the output result, oscillation parameters such as the frequency, amplitude, and damping ratio of each subsynchronous oscillation component of the subsynchronous oscillation signal are calculated according to the numerical calculation formula. It has excellent noise resistance, solves the problem that traditional Kalman filtering methods are difficult to be directly applied to subsynchronous oscillation identification, has better model interpretability than conventional machine learning algorithms, and has better real-time performance than traditional methods, meeting the requirements of actual engineering applications.

Description

Technical Field

[0001] The present invention relates to the technical field of power system stability and control, specifically a method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering. Background Art

[0002] Weak subsynchronous oscillation signals are easily submerged in noise, making identification difficult and relying on algorithms with excellent anti-noise performance for identification. In addition, if the identification results are to be used for subsequent risk perception, the algorithm requires a very high processing speed to meet the real-time requirements.

[0003] Traditional FT algorithms, such as the fast Fourier transform FFT, discrete Fourier transform DFT, etc., have the advantages of simplicity and speed in subsynchronous oscillation identification, but are prone to frequency leakage and fence effects, and require prior noise processing of the original signal waveform, with poor anti-noise performance; modal decomposition algorithms have high detection accuracy and good anti-noise performance, but have a heavy computational burden and cannot guarantee real-time performance; the Kalman filter KF algorithm has the advantages of high accuracy, good anti-noise performance, high real-time performance, etc., but if used in the task of subsynchronous oscillation identification, it is necessary to obtain the prior knowledge of "SSO frequency", and the acquisition difficulty is relatively large.

[0004] Compared with traditional SSO identification algorithms, artificial intelligence methods do not need to establish a mathematical model for specific problems, and the trained models are very simple and convenient to use, with many advantages such as easy use, good anti-noise performance, high real-time performance, etc.; however, the application of artificial intelligence methods in the field of subsynchronous oscillation identification is less, mainly limited by the non-interpretability of artificial intelligence models; artificial intelligence models rely on a large amount of data to train the models, completely shielding the internal details, resulting in the reliability of the models not being guaranteed. When the identification results are incorrect, it is impossible to find the root cause of the model problems and it is difficult to achieve fault tracing. Therefore, artificial intelligence methods are difficult to be directly used in the task of subsynchronous oscillation identification in power systems with extremely high reliability requirements. And the traditional Kalman filter algorithm requires the known oscillation frequency when applied to subsynchronous oscillation identification. Therefore, a method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering is proposed now. Summary of the Invention

[0005] To solve the deficiencies mentioned in the above background art, the purpose of the present invention is to provide a method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering.

[0006] The purpose of the present invention can be achieved through the following technical solutions: A method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering, the method comprising the following steps:

[0007] Step 1: Send the input signal into the machine learning model. The machine learning model pre-estimates the subsynchronous oscillation frequency during oscillation and obtains the output result, and then sends the output result to the Kalman filter;

[0008] Step 2: Establish a Kalman filter for each subsynchronous component. The Kalman filter uses the received output result as the parameter input, and calculates each subsynchronous component using the Kalman filtering algorithm to obtain the amplitude, damping ratio, and frequency of each subsynchronous component.

[0009] Further, the machine learning model consists of one normalization layer, two long short-term memory artificial neural network layers, and three fully connected network layers. The input signal is the original subsynchronous oscillation signal, and the output result is the pre-estimated frequency of each subsynchronous component.

[0010] Further, the Kalman filter model uses the output result of the machine learning model as the initial parameter to decompose the corresponding subsynchronous oscillation component from the original waveform.

[0011] Further, the implementation process of the Kalman filter model includes a priori estimation stage and posteriori estimation stage. The state estimation matrix at each moment in the a priori estimation stage or posteriori estimation stage contains 4 component values: the x1 component of the oscillation, the x2 component of the oscillation, the angular velocity deviation, and the damping ratio.

[0012] Further, the a priori estimation stage includes two time update equations, and the two time update equations are as follows:

[0013]

[0014]

[0015] In the formula, represents the a priori state estimation matrix at time k, represents the posteriori state estimation matrix at time k - 1, A represents the state transition matrix, u k-1 represents the control quantity of the system at time k - 1, and B represents the transformation matrix that converts the control quantity into the state quantity; represents the a priori estimation covariance matrix at time k, P k-1 represents the posteriori estimation covariance matrix at time k - 1, and Q represents the process excitation noise covariance.

[0016] Further, the posteriori estimation stage includes three state update equations, and the three state update equations are as follows:

[0017]

[0018]

[0019]

[0020] Wherein, K k represents the filtering gain matrix at time k, also known as the Kalman filtering gain, represents the prior estimation covariance matrix at time k, and H k represents the observation conversion matrix from the state variable to the observed value at time k, and R represents the measurement noise covariance; represents the posterior state estimation matrix at time k, and z k represents the actual measured value at time k; P k represents the posterior estimation covariance matrix at time k.

[0021] Further, the observation conversion matrix depends on the pre-estimated frequency of the corresponding subsynchronous component output by the machine learning model and the prior state estimation matrix at the current moment; assuming that the prior state estimation matrix at time k is [x k1 , x k2 , x k3 , x k4 T , and the corresponding timestamp at time k is t k , then the calculation method of the observation conversion matrix H k at time k is as follows:

[0022] H k = [h k1 , h k2 , h k3 , h k4

[0023]

[0024]

[0025]

[0026]

[0027] Wherein, f is the pre-estimated frequency of the SSO component, that is, the result output by the machine learning model, and h k1 , h k2 , h k3 , h k4 are the four components of the observation conversion matrix H k at time k.

[0028] Further, according to the posterior state estimation matrix at the final moment, the amplitude, frequency, and damping ratio of the corresponding subsynchronous oscillation component can be calculated. Assuming that the posterior state estimation matrix at the final moment is [x1, x2, x3, x4] T , the calculation method is as follows: ​​

[0029]

[0030] f sso = f - x3 / 2π

[0031] ζ = x4

[0032] where A is the amplitude of the subsynchronous component, f sso is the final frequency of the subsynchronous component, and ζ is the damping ratio of the subsynchronous component.

[0033] Advantages of the present invention:

[0034] During the use of the present invention, the input signal is sent into the machine learning model. The machine learning model pre - estimates the subsynchronous oscillation frequency during oscillation and obtains the output result, and then sends the output result to the Kalman filter; a Kalman filter is established for each subsynchronous component. The Kalman filter uses the received output result as the parameter input and calculates the subsynchronous component using the Kalman filtering algorithm to obtain the amplitude, damping ratio, and frequency of each subsynchronous component; the present invention is based on the machine learning algorithm and the Kalman filtering algorithm, and has excellent anti - noise performance and real - time performance at the same time. Moreover, it is not necessary to construct a mathematical model for specific problems, and directly obtains the subsynchronous component frequency quickly, ensuring the rapidity and convenience of obtaining the weak subsynchronous oscillation frequency under low signal - to - noise ratio; and using the Kalman filter algorithm on the basis of the machine learning model improves the interpretability of the model. At the same time, the Kalman filter algorithm can further correct and precise the SSO frequency estimated by the machine learning model, ensuring the reliability of the model. Description of the Drawings

[0035] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings;

[0036] Figure 1 is the flow chart of the present invention. Detailed Embodiments

[0037] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0038] Such as Figure 1As shown, a method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering, the method comprising the following steps:

[0039] Step 1: Send the input signal into the machine learning model. The machine learning model pre-estimates the subsynchronous oscillation frequency during oscillation and obtains an output result, and sends the output result to the Kalman filter;

[0040] Step 2: Establish a Kalman filter for each subsynchronous component. The Kalman filter uses the received output result as a parameter input, and calculates each subsynchronous component using the Kalman filtering algorithm to obtain the amplitude, damping ratio, and frequency of each subsynchronous component.

[0041] It should be noted that the machine learning model consists of one normalization layer, two long short-term memory artificial neural network layers, and three fully connected network layers. The input signal is the original subsynchronous oscillation signal, and the output result is the pre-estimated frequency of each subsynchronous component.

[0042] It should be noted that the Kalman filter model uses the output result of the machine learning model as the initial parameter to decompose the corresponding subsynchronous oscillation component from the original waveform.

[0043] It should be noted that the implementation process of the Kalman filter model includes a prior estimation stage and a posterior estimation stage. The state estimation matrix at each moment in the prior estimation stage or the posterior estimation stage contains 4 component values: the x1 component of the oscillation, the x2 component of the oscillation, the angular velocity deviation, and the damping ratio.

[0044] It should be noted that the prior estimation stage includes two time update equations, and the two time update equations are as follows:

[0045]

[0046]

[0047] In the formula, represents the prior state estimation matrix at time k, represents the posterior state estimation matrix at time k-1, A represents the state transition matrix, u k-1 represents the control quantity of the system at time k-1, and B represents the transformation matrix that converts the control quantity into a state quantity; represents the prior estimation covariance matrix at time k, P k-1 represents the posterior estimation covariance matrix at time k-1, and Q represents the process excitation noise covariance.

[0048] It should be noted that the posterior estimation stage includes three state update equations, and the three state update equations are as follows:

[0049]

[0050]

[0051]

[0052] In the formula, K k represents the filtering gain matrix at time k, also known as the Kalman filtering gain, represents the prior estimation covariance matrix at time k, H k represents the observation transformation matrix from the state variable to the observed value at time k, and R represents the measurement noise covariance; represents the posterior state estimation matrix at time k, z k represents the actual measured value at time k; P k represents the posterior estimation covariance matrix at time k.

[0053] It should be noted that the observation transformation matrix depends on the pre-estimated frequency of the corresponding subsynchronous component output by the machine learning model and the prior state estimation matrix at the current moment; assume that the prior state estimation matrix at time k is [x k1 , x k2 , x k3 , x k4 T , and the corresponding timestamp at time k is t k , then the calculation method of the observation transformation matrix H k at time k is as follows:

[0054] H k =[h k1 , h k2 , h k3 , h k4

[0055]

[0056]

[0057]

[0058]

[0059] In the formula, f is the pre-estimated frequency of the SSO component, that is, the result output by the machine learning model, and h k1 , h k2 , h k3 , h k4 are the four components of the observation transformation matrix H k at time k.

[0060] ​​It should be noted that according to the posterior state estimation matrix at the final moment, the amplitude, frequency, and damping ratio of the corresponding subsynchronous oscillation component can be calculated. Let the posterior state estimation matrix at the final moment be [x1, x2, x3, x4]. T , and the calculation method is as follows:

[0061]

[0062] f sso = f - x3 / 2π

[0063] ζ = x4

[0064] In the formula, A is the amplitude of the subsynchronous component, f sso is the final frequency of the subsynchronous component, and ζ is the damping ratio of the subsynchronous component.

[0065] It should be further noted that in the specific implementation process, the simulation data generated by the following formula is used for experiments:

[0066]

[0067] In the formula, x(t) represents the oscillatory simulation observation value at time t, P represents the number of subsynchronous oscillation components, represents the sum of the simulation observation values of each subsynchronous oscillation component, where a p represents the amplitude of the p-th subsynchronous component, represents the phase value of the p-th subsynchronous component, σp represents the damping ratio of the p-th subsynchronous component, ωp represents the angular frequency of the p-th subsynchronous component, T s represents the sampling frequency, j is the unit of the imaginary part of a complex number, that is, the square root of -1; w(t) represents the noise interference at time t.

[0068] The experimental data to be measured is constructed using the following parameters:

[0069] Set the original waveform to be identified to contain two subsynchronous components. The frequency, amplitude, damping ratio, and angular phase value of the first subsynchronous component are: 25 Hz, 3, -1, 10; the frequency, amplitude, damping ratio, and angular phase value of the second subsynchronous component are: 35 Hz, 2.8, -1, 20; Gaussian noise with a signal-to-noise ratio of 20 dB is used to interfere with the waveform. The sample sampling frequency is set to 1000 Hz, and the time span is 1 s.

[0070] First, the machine learning model part needs to be trained. The training set consists of 600 groups of simulation data randomly generated within the specified parameter range, and the labels are the corresponding parameters of the simulation data. The machine learning model consists of one normalization layer, two LSTM layers, and three fully connected layers. Each LSTM layer contains 1000 neurons. The hyperparameter settings of the three fully connected layers are 1000*500, 500*128, and 128*8 respectively. The mean squared error loss is used as the loss function, and the Adam stochastic optimization method is used as the training optimizer. The learning rate of the optimizer is set to 0.001. The constructed training set is used to train the machine learning model, and the number of training epochs is set to 100. After the training is completed, the trained machine learning model is saved.

[0071] Furthermore, set the initial parameters of the Kalman filter model. The parameter settings of the state transition matrix A, the initial covariance matrix P0, the initial state estimation matrix x0, the process excitation noise covariance Q, and the measurement noise covariance R are as follows:

[0072]

[0073] x0 = [0 0 0 0] T

[0074] Q = 0

[0075] R = 0.5

[0076] It should be noted that for the test and evaluation of the waveform to be measured, the trained machine learning model is loaded to identify the original waveform. The frequency identification results of each synchronous component are taken as the input of the Kalman filter model corresponding to each oscillation component. The parameters are calculated using the posterior state estimation matrix at the final moment of the output of the Kalman filter model of each oscillation component, and the following are obtained: the frequencies, amplitudes, and damping ratios of subsynchronous component 1 are 24.730833 Hz, 3.155087, and -0.979432 respectively; the frequencies, amplitudes, and damping ratios of subsynchronous component 1 are 34.824087 Hz, 2.738075, and -1.068182 respectively.

[0077] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art of this industry should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. A method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering, characterized in that The method includes the following steps: Step 1: Send the input signal into the machine learning model. The machine learning model pre-estimates the subsynchronous oscillation frequency during oscillation and obtains the output result, and sends the output result to the Kalman filter; The Kalman filter model uses the output result of the machine learning model as the initial parameter to decompose the corresponding subsynchronous oscillation component from the original waveform; The implementation process of the Kalman filter model includes a priori estimation stage and posteriori estimation stage. The state estimation matrix at each moment in the a priori estimation stage or posteriori estimation stage includes 4 component values: the x1 component of the oscillation, the x2 component of the oscillation, the angular velocity deviation, and the damping ratio; Step 2: Establish a Kalman filter for each subsynchronous component. The Kalman filter uses the received output result as the parameter input, and calculates each subsynchronous component using the Kalman filtering algorithm to obtain the amplitude, damping ratio, and frequency of each subsynchronous component.

2. The method for identifying weak subsynchronous oscillation based on machine learning and Kalman filtering according to claim 1, wherein The machine learning model consists of one normalization layer, two long short-term memory artificial neural network layers, and three fully connected network layers. The input signal is the original subsynchronous oscillation signal, and the output result is the pre-estimated frequency of each subsynchronous component.

3. The method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering according to claim 1, characterized in that, The a priori estimation stage includes two time update equations, and the two time update equations are as follows: wherein, represents the prior state estimation matrix at time k, represents the posterior state estimation matrix at time k-1, A represents the state transition matrix, and u k-1 represents the control quantity of the system at time k-1, and B represents the transformation matrix that converts the control quantity into the state quantity; represents the prior estimation covariance matrix at time k, and P k-1 represents the posterior estimation covariance matrix at time k-1, and Q represents the process excitation noise covariance.

4. The method for identifying weak subsynchronous oscillations based on machine learning and Kalman filtering according to claim 1, characterized in that The posteriori estimation stage includes three state update equations, and the three state update equations are as follows: where, K k represents the filtering gain matrix at time k, also known as the Kalman filter gain, represents the prior estimate covariance matrix at time k, H k represents the observation transformation matrix from the state variable to the observed value at time k, and R represents the measurement noise covariance; represents the posterior state estimate matrix at time k, z k represents the actual measured value at time k; P k represents the posterior estimate covariance matrix at time k.

5. The method for identifying weak subsynchronous oscillation based on machine learning and Kalman filtering according to claim 4, wherein The observation conversion matrix depends on the corresponding sub-synchronous component pre-estimated frequency output by the machine learning model and the prior state estimation matrix at the current moment; assume that the prior state estimation matrix at time k is [x k1 , x k2 , x k3 , x k4 T , and the corresponding timestamp at time k is t k , then the calculation method of the observation conversion matrix H k at time k is as follows:​ H k = [h k1 , h k2 , h k3 , h k4 ​ where f is the pre-estimated frequency of the SSO component, that is, the result output by the machine learning model, and h k1 , h k2 , h k3 , h k4 are the four components of the observation conversion matrix H k at time k.

6. The method for identifying weak subsynchronous oscillation based on machine learning and Kalman filtering according to claim 5, characterized in that The amplitude, frequency, and damping ratio of the corresponding subsynchronous oscillation component can be calculated based on the posterior state estimation matrix at the final moment. Let the posterior state estimation matrix at the final moment be [x1, x2, x3, x4] T , and the calculation method is as follows: f sso = f - x3 / 2π ζ = x4 where A is the amplitude of the subsynchronous component, f sso is the final frequency of the subsynchronous component, and ζ is the damping ratio of the subsynchronous component.

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