CN115577251A - Method, system and terminal for detecting non-stationary subsynchronous oscillation signal - Google Patents

Method, system and terminal for detecting non-stationary subsynchronous oscillation signal Download PDF

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CN115577251A
CN115577251A CN202211271848.9A CN202211271848A CN115577251A CN 115577251 A CN115577251 A CN 115577251A CN 202211271848 A CN202211271848 A CN 202211271848A CN 115577251 A CN115577251 A CN 115577251A
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张琳
李青峰
吴熙
李叶
宋美艺
陈曦
任双雪
曹苗
张钊
陈全杰
刘虹
刘善通
卫璐
王怡洁
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Southeast University
Economic and Technological Research Institute of State Grid Shaanxi Electric Power Co Ltd
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Abstract

The invention discloses a method, a system and a terminal for detecting a non-stationary subsynchronous oscillation signal, which belong to the field of oscillation detection of electric power systems 2 M 4 The self-adaptive reset threshold value adjusting method of the estimator is used for self-adaptively adjusting the reset threshold value under different noise environments. When the self-reset criterion is effective, the EKF parameters are initialized and the signals are continuously detected, so that the real-time monitoring of the noise-containing non-stationary SSO signals is realized. Finally, the effectiveness of the proposed method is verified through simulation analysis.

Description

Method, system and terminal for detecting non-stationary subsynchronous oscillation signal
Technical Field
The invention relates to the field of oscillation detection of power systems, in particular to a method, a system and a terminal for detecting non-stationary subsynchronous oscillation signals.
Background
The new energy grid-connected power system SSO has the non-stationary characteristic of time-varying frequency and amplitude, and SSO signals in an actual system usually contain a large amount of noise, so that online identification is difficult. Currently, the conventional SSO identification methods can be roughly classified into two types: synchrophasor-based methods and waveform-based methods. The synchrophasor-based method measures the SSO parameters through the spectral leakage component of the synchrophasor, and a complex algorithm is required to eliminate the influence of the fundamental frequency signal on the SSO component measurement. In addition, the method requires an observation window length of more than 2 seconds, and cannot capture the mode of rapid change of the SSO. Waveform-based methods, on the other hand, are mainly based on DFT and Prony. Classical DFT suffers from the problems of the fence effect and spectral leakage and relies on a long observation window to improve resolution. Prony is a high-precision SSO identification method, but it lacks time-varying tracking ability. In addition, when the SSO signal is disturbed by noise, the accuracy of Prony identification is greatly affected.
Kalman Filtering (KF) has been widely used for on-line synchrophasor estimation, which can accurately estimate the amplitude, phase, and frequency of a signal under noise in a recursive manner. Recently, KF has also been applied to SSO detection. However, KF will face filter divergence problems when SSO frequencies are mutated. Furthermore, KF-based methods require the frequency of the SSO to be acquired in advance. There is a method to combine KF with a reset criterion to solve the above problem, but this method does not provide a threshold selection criterion in the reset criterion, and in the case of different signal to noise ratios of the detected signals, the reset threshold cannot be adaptively selected for different noise environments, so that the detection performance of the algorithm will be affected, and the adaptivity is not high.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a non-stationary subsynchronous oscillation signal detection method, aiming at accurately detecting non-stationary SSO information generated in a system under the Gaussian noise interference.
The purpose of the invention can be realized by the following technical scheme:
a non-stationary subsynchronous oscillation signal detection method comprises the following steps:
preprocessing signal data, calculating signal parameters of the preprocessed signal data through four-state EKF (extended Kalman Filter) and reconstructing the signal to obtain an SSO (Single side offset) signal fitting at the current moment, and calculating a residual ratio e rati o：
Figure BDA0003895075480000011
In the formula e k Is kT s The residual error of the time of day,
Figure BDA0003895075480000012
is an estimate of the SSO signal;
by using M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold r e ：
Figure BDA0003895075480000021
Wherein SNR is signal-to-noise ratio;
when satisfying the condition e ratio Greater than r e Then the error covariance matrix P in the four-state EKF is calculated k Reset to nI 4×4 And updates the initial frequency value.
Further, the residual ratio e ratio Based on residual error e k And (3) calculating:
kT s residual error e of time k Is represented as follows:
Figure BDA0003895075480000022
wherein, y k Is a quantity measurement; e.g. of a cylinder k The variance of (c) can be approximated by:
Figure BDA0003895075480000023
wherein m is the window length, and k is greater than or equal to 1<m, then m is replaced by k; SSO signal estimation
Figure BDA0003895075480000024
The variance of (c) can be calculated by:
Figure BDA0003895075480000025
the residual ratio e ratio Satisfies the following conditions:
Figure BDA0003895075480000026
further, the adoption of M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold r e The method specifically comprises the following steps:
after four-state EKF calculation, if the formulas (9) to (12) are satisfied, e ratio Can be approximated by formula (13):
Figure BDA0003895075480000027
Figure BDA0003895075480000028
Figure BDA0003895075480000029
Figure BDA00038950754800000210
Figure BDA00038950754800000211
then the value y is measured k SNR of (d) can be calculated by:
Figure BDA00038950754800000212
according to formula (13) and formula (14), e ratio Can be further expressed as:
Figure BDA0003895075480000031
when the filter diverges, the fitted SSO signal will deviate significantly from the true value and satisfy
Figure BDA0003895075480000032
Then, the following inequality holds:
Figure BDA0003895075480000033
e k ＞v k (17)
Figure BDA0003895075480000034
according to e ratio Greater than r e The following inequalities hold true for the conditions of (1), (15), (16), and (18):
Figure BDA0003895075480000035
combining equation (15) and equation (19), the threshold can be calculated by:
Figure BDA0003895075480000036
then according to equation (20) y can be measured k Determining the threshold r at SNR of e 。
Further, with M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold comprising the steps of:
let M 2 Denotes y k Second order moment of (c):
Figure BDA0003895075480000037
let M 4 Denotes y k Fourth order moment of (d):
Figure BDA0003895075480000038
defining the signal power as S and the noise power as N; m 2 Can be moved from belowThe formula is given as:
M 2 ＝S+N (23)
and, M 4 Can be given by:
M 4 ＝k x S 2 +6SN+k v N 2 (24)
wherein k is x And k v Signal kurtosis and noise kurtosis, respectively;
solving equations (23) and (24) for S and N yields:
Figure BDA0003895075480000039
Figure BDA00038950754800000310
form (a) a
Figure BDA0003895075480000041
And
Figure BDA0003895075480000042
the estimated amount of the ratio of (A)/(B) is expressed as M 2 M 4 Estimating quantity; for zero mean sinusoidal signals, k x =1.5, for noise, k v =3, therefore:
Figure BDA0003895075480000043
the second and fourth moments are estimated from the time average of the measured signal, satisfying equations (28) and (29):
Figure BDA0003895075480000044
Figure BDA0003895075480000045
measured signaly k The estimated SNR of (d) is:
Figure BDA0003895075480000046
in view of the SNR estimation bias, an additional term Δ is introduced in equation (20), as shown below, to make the threshold adjustment more reliable:
Figure BDA0003895075480000047
as mentioned above, the threshold r e The adaptive adjustment can be performed by using the equations (27) to (31).
Further, if e is satisfied ratio Greater than r e And the time interval between resets is greater than time interval T Δ Is reset, the error covariance matrix P in the four state EKF is obtained k Reset to nI 4×4 Updating the initial frequency value, re-initializing the initialized signal data, calculating signal parameters through four-state EKF (extended Kalman filter) and reconstructing the signal to obtain an SSO (Single satellite) signal fitting at the current moment;
otherwise, the initialized signal data is directly reinitialized, signal parameters are calculated through the four-state EKF, signal reconstruction is carried out, and the SSO signal fitting at the current moment is obtained.
Further, the additional term Δ is set to 2.5.
Further, it is characterized in that the SSO signal and each parameter of the SSO signal can be obtained by the equations (1) to (4):
Figure BDA0003895075480000048
Figure BDA0003895075480000049
f S (kT s )＝f S0 +x 3 (k) (3)
α S (kT s )＝-x 4 (k) (4)
in the formula
Figure BDA0003895075480000051
Is an SSO signal that the EKF fits with a state vector,
Figure BDA0003895075480000052
is an estimate of the SSO signal, x 1 (k)、x 2 (k)、x 3 (k) And x 4 (k) Four state variables of EKF; f. of S0 Is the initial value of the frequency.
In a second aspect, the present invention further provides a system for detecting a non-stationary subsynchronous oscillation signal, including:
the signal preprocessing module: preprocessing the signal data, and inputting the preprocessed signal data into a fitting module;
a fitting module: performing signal parameter calculation on the initialized signal data through the four-state EKF, performing signal reconstruction, and outputting an SSO signal fitted at the current moment;
a calculation module: for calculating the residual ratio e ratio And by M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold r e ；
The self-reset judging module: based on e ratio And r e Determining whether to reset the error covariance matrix P k And an initial value of frequency;
when satisfying the condition e ratio Greater than r e And the time interval between resets is greater than time interval T Δ Then reset is performed to set the error covariance matrix P in the four state EKF k Reset to nI 4×4 Updating the initial frequency value, and inputting the initialized signal data into the signal processing module again for processing; otherwise, the initialized signal data is directly input into the signal processing module for processing.
In a third aspect, the present invention further provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, where the memory stores the computer program capable of running on the processor, and when the processor loads and executes the computer program, the method for detecting a non-stationary subsynchronous oscillation signal according to any of the foregoing methods is used.
In a fourth aspect, the present invention further provides a computer-readable storage medium, in which a computer program is stored, and when the computer program is loaded and executed by a processor, the method for detecting a non-stationary subsynchronous oscillation signal is adopted.
The invention has the beneficial effects that:
put forward a method based on M 2 M 4 The threshold adjusting method of the estimator can automatically determine the threshold of the reset criterion in the environments with different signal-to-noise ratios, ensure the effectiveness of the reset criterion in different scenes and enable the self-reset EKF method to be more adaptive.
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The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a flow diagram illustrating a method according to an embodiment of the present invention;
FIG. 2 is a signal plot of scene 1 under test;
fig. 3 is a diagram of self-reset EKF reconstructed SSO results for scenario 1;
FIG. 4 is a diagram of SSO parameter identification results of scenario 1;
FIG. 5 is a signal plot of scene 2 under test;
FIG. 6 is a graph of SSO results from self-resetting EKF reconstruction for scenario 2;
FIG. 7 is a diagram of SSO parameter identification results of scenario 2.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The specific embodiment discloses a method for detecting a non-stationary subsynchronous oscillation signal by improving adaptive resetting of an EKF, and a specific flow chart of the method is shown in FIG. 1, and the method comprises the following steps:
s1: carrying out initialization setting on the parameters;
s2: obtaining a three-phase measured value, carrying out DQ conversion and removing a direct current component;
s3: if the discrete time k is smaller than the ratio T between the reset time interval and the sampling time interval Δ /T s Step S4 is entered; otherwise, the process proceeds to step S5.
S4: obtaining the most suitable initial frequency value f by using parallel EKF S0 Then adding 1 to the discrete time and returning to the step S2;
s5: calculating signal parameters by utilizing the four-state EKF and reconstructing signals;
s6: calculating a residual ratio e ratio ；
S7: by means of M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and calculates the adaptive reset threshold r based thereon e ；
S8: if e ratio Greater than r e And the time interval between resets is greater than T Δ The process advances to step S9; otherwise, go to step S10;
s9: the error covariance matrix P k Reset to nI 4×4 And updating the initial frequency value;
s10: outputting a calculation result of the k moment obtained in the step S5, and then adding 1 to the discrete moment;
s11: if the signal detection is finished, the process is finished; otherwise, the process goes to step S2.
In said step S1, the following parameters are initialized:
Figure BDA0003895075480000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003895075480000062
is the initial value of the state vector; p 1 Is P k Represents a covariance matrix of state vector estimation errors. I is 4×4 Is a 4 x 4 identity matrix, n is a large integer, and n is set to 100 in the present invention. Q and R are respectively the covariance matrix of the process noise equation and the noise covariance of the measurement equation, and the two values are kept unchanged in the invention. m is the window length, which should be at least larger than the corresponding number of oscillation periods. For example, if the sampling interval T s Is 0.001s, then m should be greater than 1/(f) Smin T s ) =200, wherein f Smin Is the minimum SSO frequency, f Smin ＝5Hz。T Δ The minimum time interval between two resets is used for preventing unnecessary resets in the iteration convergence of the extended Kalman filter.
In step S2, the signal obtained by converting the three-phase measurement signal into DQ is represented by the transient signal x in the DQ axis dq (t) consists of fundamental and time-varying SSO components, which can be modeled as:
Figure BDA0003895075480000071
in the formula (I), the compound is shown in the specification,
Figure BDA0003895075480000072
and
Figure BDA0003895075480000073
the fundamental component and the SSO component, respectively. It is noted that
Figure BDA0003895075480000074
Below the DQ axis is a dc bias. The SSO component is focused on in the invention, so that the DC bias needs to be removed firstly
Figure BDA0003895075480000075
The time-varying SSO component in equation (2) can be expressed as:
Figure BDA0003895075480000076
in the formula, A S (t)、f S (t) and phi S Respectively, a time-varying amplitude, a time-varying frequency, and an initial phase of the SSO component. Alpha is alpha S Is the damping factor for SSO.
In said step S4, the invention applies a set of EKFs (without adaptive reset) to obtain a relatively accurate initial frequency value f S0 . Since the SSO frequency range is typically 5Hz to 45Hz (sync frequency 50 Hz) or 55Hz (sync frequency 60 Hz), the initial frequencies of the EKFs are set to 5Hz, 10Hz, 15Hz, \ 8230;, 45Hz (or 55 Hz), respectively. Wherein all EKFs can be run in parallel, which does not increase the computational burden. Parallel EKF selection-to-residual ratio expectation E (E) ratio ) The smallest corresponding frequency is the most suitable frequency. The adaptive reset method and the most appropriate initial frequency are then applied to the EKF.
In said step S5, at a fixed sampling interval T s Measuring the signal, the continuous-time model at the kth sampling point in (3) can be expressed as:
Figure BDA0003895075480000077
at 2 pi f S (k) For rotating the reference frame, the above signals can be rewritten as:
Figure BDA0003895075480000078
Figure BDA0003895075480000079
and
Figure BDA00038950754800000710
in-phase component and quadrature component, respectively, from a state variable x 1 And x 2 And (4) showing. The subsynchronous frequency offset is determined by a third state variable x 3 And (4) showing. Negative number-alpha of damping factor S By a fourth state variable x 4 And (4) showing. Then, the formula (5) mayTo write the following four-state signal model:
Figure BDA00038950754800000711
the SSO signal is calculated with the following formula:
Figure BDA0003895075480000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003895075480000082
is an SSO signal that the EKF fits with a state vector,
Figure BDA0003895075480000083
is an estimate of the SSO signal. The amplitude, frequency and damping factor of the SSO signal are calculated from the state estimate using the following equation:
Figure BDA0003895075480000084
f S (kT s )＝f S0 +x 3 (k) (9)
α S (kT s )＝-x 4 (k) (10)
in the formula, x 1 (k)、x 2 (k)、x 3 (k) And x 4 (k) Four state variables for EKF; f. of S0 Is the initial value of the frequency.
In step S6, kT is determined for EKF with Gaussian process s Residual error e of time k Is represented as follows:
Figure BDA0003895075480000085
wherein, y k Is a measurement of quantity. e.g. of the type k The variance of (d) can be approximated by:
Figure BDA0003895075480000086
wherein m is the window length, and k is greater than or equal to 1<m, then m is replaced by k. SSO signal estimation
Figure BDA0003895075480000087
The variance of (c) can be calculated by:
Figure BDA0003895075480000088
the self-reset criterion is defined as follows:
Figure BDA0003895075480000089
in the formula, r e Is a self-resetting threshold. e.g. of a cylinder ratio The error between the estimated value and the true value is reflected as a residual ratio.
In step S7, the four-state EKF is calculated as follows:
Figure BDA00038950754800000810
Figure BDA00038950754800000811
Figure BDA00038950754800000812
Figure BDA00038950754800000813
wherein v is k Representing the noise in the EKF measurement equation.
Thus, e ratio Can approximateComprises the following steps:
Figure BDA0003895075480000091
note the measured value y k Signal-to-noise ratio (SNR) of (d) can be calculated by:
Figure BDA0003895075480000092
according to formulae (19) and (20), e ratio Can be expressed as:
Figure BDA0003895075480000093
according to equation (21), e is the estimated SSO signal exactly matches the true value ratio Size and y of k Is directly related. When the filter diverges, the estimated SSO signal will deviate significantly from the true value, and usually have
Figure BDA0003895075480000094
Then, the following inequality holds:
Figure BDA0003895075480000095
e k ＞v k (23)
Figure BDA0003895075480000096
from equations (14), (21), (22), and (24), it is apparent that the following inequalities hold:
Figure BDA0003895075480000097
in consideration of equation (21) and equation (25), the threshold value may be calculated by the following equation:
Figure BDA0003895075480000098
according to equation (26), y can be measured in the estimation k Determining the threshold r at SNR of e . Then, M is added 2 M 4 The estimator is applied to SNR estimation.
Let M 2 Denotes y k Second order moment of (c):
Figure BDA0003895075480000099
let M be 4 Denotes y k Fourth order moment of (d):
Figure BDA00038950754800000910
the signal power is defined as S and the noise power as N. Thus, M 2 Can be given by:
M 2 ＝S+N (29)
and, M 4 Can be given by:
M 4 ＝k x S 2 +6SN+k v N 2 (30)
wherein k is x And k v Signal kurtosis and noise kurtosis, respectively.
Solving equations (29) and (30) for S and N yields:
Figure BDA0003895075480000101
Figure BDA0003895075480000102
form (a) a
Figure BDA0003895075480000103
And
Figure BDA0003895075480000104
the estimated quantity of the ratio of (A) to (B) is denoted as M 2 M 4 And (5) estimating the quantity. For zero mean sinusoidal signals, k x =1.5, for noise, k v =3, therefore:
Figure BDA0003895075480000105
in practical applications, the second and fourth moments are estimated from the time average of the measured signals:
Figure BDA0003895075480000106
Figure BDA0003895075480000107
measured signal y k The estimated SNR of (d) is:
Figure BDA0003895075480000108
an additional term Δ is introduced in equation (26) to make the threshold adjustment more reliable, taking into account the SNR estimation bias, as follows:
Figure BDA0003895075480000109
as mentioned above, the threshold r e The adaptive adjustment can be performed by using the expressions (33) to (37). In equation (37), the present invention sets the additional term Δ to 2.5 through experimental tests.
In step S8, since the EKF is an iterative algorithm, the deviation between the estimated value and the true value may be relatively large during the convergence process, and equation (8) may be satisfied and result in a continuous reset. To be made intoAvoiding unnecessary resets, each reset requiring a time interval T Δ Waiting for the algorithm to converge before allowing the next reset.
In step S9, it is considered that the SSO component undergoes a nonlinear change such as a frequency change, and the EKF loses its traceability. At this time, the error covariance matrix P k Needs to be reset to nI 4×4 (n = 100), and the initial value f of the frequency in the EKF S0 Needs to be updated to the time (k-1) T s The estimated frequency.
Fig. 2 to 4 and fig. 5 to 7 show examples in two scenarios to prove the effectiveness and accuracy of the process proposed by the present invention. An artificially constructed non-stationary SSO signal, expressed as formula (32):
Figure BDA0003895075480000111
in the formula, n (t) is white noise. The whole simulation time length is 20s and is divided into four time periods. In period 1 (0-5 s), the signal frequency is 10Hz, the amplitude is 10, and the attenuation coefficient is-0.05. In period 2 (5-10 s), the frequency became 15Hz and the amplitude was constant at 12.8. In periods 3 (10-15 s) and 4 (15-20 s), the frequency becomes 20Hz and 15Hz, respectively, keeping the amplitude constant at 12.8.
In scenario 1, the signal to noise ratio is set to 30dB, the sampling frequency is 1000Hz Δ The window length m was set to 300 at 0.3s, and the results of the simulation using 100 monte carlo method are shown in fig. 2 to 4.
In scenario 2, the signal to noise ratio is set to 10dB, the sampling frequency is 1000Hz Δ The window length m was set to 300 at 0.3s, and the results of the simulation using 100 monte carlo method are shown in fig. 5 to 7.
It can be seen that the method used in the present invention can effectively detect noisy non-stationary SSO signals.
The embodiment of the application discloses a non-stationary subsynchronous oscillation signal detection system, which comprises the following modules:
the signal processing module: initializing the signal data, and inputting the initialized signal data into a fitting module;
a fitting module: performing signal parameter calculation and signal reconstruction on the initialized signal data through the four-state EKF, and outputting an SSO signal fitted at the current moment;
a calculation module: for calculating the residual ratio e ratio And by M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold r e ；
The self-reset judging module: based on e ratio And r e Determining whether to reset the error covariance matrix P k And a frequency threshold;
when satisfying the condition e ratio Greater than r e And the time interval between resets is greater than time interval T Δ Then reset is performed to set the error covariance matrix P in the four state EKF k Reset to nI 4×4 Updating the initial frequency value, and inputting the initialized signal data into the signal processing module again for processing; otherwise, the initialized signal data is directly input into the signal processing module for processing.
The embodiment of the application also discloses a terminal device, which comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein when the processor executes the computer program, any one of the non-stationary subsynchronous oscillation signal detection methods in the embodiments is adopted.
The terminal device may adopt a computer device such as a desktop computer, a notebook computer, or a cloud server, and includes but is not limited to a processor and a memory, for example, the terminal device may further include an input/output device, a network access device, a bus, and the like.
The processor may be a Central Processing Unit (CPU), and of course, according to an actual use situation, other general processors, digital Signal Processors (DSPs), application specific integrated circuits (AS ics), ready-made programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, and the like may also be used, and the general processor may be a microprocessor or any conventional processor, and the application is not limited thereto.
The memory may be an internal storage unit of the terminal device, for example, a hard disk or a memory of the terminal device, or an external storage device of the terminal device, for example, a plug-in hard disk, a smart card memory (SMC), a secure digital card (SD) or a flash memory card (FC) equipped on the terminal device, and the memory may also be a combination of the internal storage unit of the terminal device and the external storage device, and the memory is used for storing a computer program and other programs and data required by the terminal device, and the memory may also be used for temporarily storing data that has been output or will be output, which is not limited in this application.
According to the terminal device, any one of the X in the above embodiments is stored in a memory of the terminal device, and is loaded and executed on a processor of the terminal device, so that the terminal device is convenient to use.
The embodiment of the application further discloses a computer readable storage medium, and the computer readable storage medium stores a computer program, wherein when the computer program is executed by a processor, any one of the non-stationary subsynchronous oscillation signal detection methods in the embodiments is adopted.
The computer program may be stored in a computer readable medium, the computer program includes computer program code, the computer program code may be in a source code form, an object code form, an executable file or some intermediate form, and the like, the computer readable medium includes any entity or device capable of carrying the computer program code, a recording medium, a usb disk, a removable hard disk, a magnetic disk, an optical disk, a computer memory, a Read Only Memory (ROM), a Random Access Memory (RAM), an electrical carrier signal, a telecommunication signal, a software distribution medium, and the like, and the computer readable medium includes but is not limited to the above components.
The method for detecting a non-stationary subsynchronous oscillation signal in any of the above embodiments is stored in a computer-readable storage medium through the computer-readable storage medium, and is loaded and executed on a processor, so as to facilitate storage and application of the method.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.

Claims (10)

1. A method for detecting a non-stationary subsynchronous oscillation signal, comprising:
preprocessing signal data, calculating signal parameters of the preprocessed signal data through four-state EKF (extended Kalman Filter) and reconstructing the signal to obtain an SSO (Single Strand offset) signal fitted at the current moment, and calculating a residual ratio e ratio ：
Figure FDA0003895075470000011
In the formula e k Is kT s The residual error of the time of day,
Figure FDA0003895075470000012
is an estimate of the SSO signal;
by using M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold r e ：
Figure FDA0003895075470000013
Wherein SNR is signal-to-noise ratio;
when satisfying if e ratio Greater than r e Then the error covariance matrix P in the four-state EKF is determined k Reset to nI 4×4 And updates the initial frequency value.
2. Non-stationary subsynchronous oscillation signal detection as in claim 1Method, characterized by a residual ratio e ratio Based on residual error e k And (3) calculating:
kT s residual error e of time k Is represented as follows:
Figure FDA0003895075470000014
wherein, y k Is a quantity measurement; e.g. of the type k The variance of (c) can be approximated by:
Figure FDA0003895075470000015
wherein m is the window length, and k is greater than or equal to 1<m, then m is replaced by k; SSO signal estimation
Figure FDA0003895075470000016
The variance of (d) can be calculated by:
Figure FDA0003895075470000017
the residual ratio e ratio Satisfies the following conditions:
Figure FDA0003895075470000018
3. the method of claim 2, wherein said employing M is performed by a computer system 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold r e The method specifically comprises the following steps:
after four-state EKF calculation, if the formulas (9) to (12) are satisfied, e ratio Can be approximated by formula (13):
Figure FDA0003895075470000019
Figure FDA00038950754700000110
Figure FDA00038950754700000111
Figure FDA0003895075470000021
Figure FDA0003895075470000022
then the value y is measured k SNR of (d) can be calculated by:
Figure FDA0003895075470000023
according to formula (13) and formula (14), e ratio Can be further expressed as:
Figure FDA0003895075470000024
when the filter diverges, the fitted SSO signal will deviate significantly from the true value and satisfy
Figure FDA0003895075470000025
Then, the following inequality holds:
Figure FDA0003895075470000026
e k ＞v k (17)
Figure FDA0003895075470000027
according to e ratio Greater than r e The following inequalities hold true for the conditions of (1), (15), (16), and (18):
Figure FDA0003895075470000028
combining equation (15) and equation (19), the threshold can be calculated by:
Figure FDA0003895075470000029
then according to equation (20) y can be measured k Determining the threshold r at SNR of e 。
4. The method of claim 3, wherein M is used 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold comprising the steps of:
let M 2 Denotes y k Second order moment of (c):
Figure FDA00038950754700000210
let M 4 Denotes y k Fourth order moment of (d):
Figure FDA00038950754700000211
the signal power is defined as S, and the noise power is defined as N; m 2 Can be given by:
M 2 ＝S+N (23)
and, M 4 Can be given by:
M 4 ＝k x S 2 +6SN+k v N 2 (24)
wherein k is x And k v Signal kurtosis and noise kurtosis, respectively;
solving equations (23) and (24) for S and N yields:
Figure FDA0003895075470000031
Figure FDA0003895075470000032
form a
Figure FDA0003895075470000033
And with
Figure FDA0003895075470000034
The estimated quantity of the ratio of (A) to (B) is denoted as M 2 M 4 Estimating quantity; for zero mean sinusoidal signals, k x =1.5, for noise, k v =3, therefore:
Figure FDA0003895075470000035
the second and fourth moments are estimated from the time average of the measured signal, satisfying equations (28) and (29):
Figure FDA0003895075470000036
Figure FDA0003895075470000037
measured signal y k The estimated SNR of (d) is:
Figure FDA0003895075470000038
in view of the SNR estimation bias, an additional term Δ is introduced in equation (20), as shown below, to make the threshold adjustment more reliable:
Figure FDA0003895075470000039
as mentioned above, the threshold r e The adaptive adjustment can be performed by using the equations (27) to (31).
5. The method as claimed in claim 1, wherein if e is satisfied ratio Greater than r e And the time interval between resets is greater than time interval T Δ Is reset, the error covariance matrix P in the four state EKF is formed k Reset to nI 4×4 Updating the initial frequency value, re-initializing the initialized signal data, calculating signal parameters through four-state EKF, and reconstructing signals to obtain SSO signals fitted at the current moment;
otherwise, the initialized signal data is directly reinitialized, signal parameters are calculated through the four-state EKF, signal reconstruction is carried out, and the SSO signal fitting at the current moment is obtained.
6. The method of claim 4, wherein the addition term Δ is set to 2.5.
7. The method for detecting a non-stationary subsynchronous oscillation signal according to claim 1, wherein the parameters of the SSO signal and the SSO signal are obtained by equations (1) to (4):
Figure FDA0003895075470000041
Figure FDA0003895075470000042
f S (kT s )＝f S0 +x 3 (k) (3)
α S (kT s )＝-x 4 (k) (4)
in the formula
Figure FDA0003895075470000043
Is an SSO signal that the EKF fits with a state vector,
Figure FDA0003895075470000044
is an estimate of the SSO signal, x 1 (k)、x 2 (k)、x 3 (k) And x 4 (k) Four state variables of EKF; f. of S0 Is the initial value of the frequency.
8. A non-stationary subsynchronous oscillation signal detection system, comprising:
the signal preprocessing module: preprocessing the signal data, and inputting the preprocessed signal data into a fitting module;
a fitting module: performing signal parameter calculation on the initialized signal data through the four-state EKF, performing signal reconstruction, and outputting an SSO signal fitted at the current moment;
a calculation module: for calculating the residual ratio e ratio And by M 2 M 4 The estimator calculates the signal-to-noise ratio of the signal and establishes an adaptive reset threshold r e ；
The self-reset judging module: based on e ratio And r e Determining whether to reset the error covariance matrix P k And a frequency threshold;
when satisfying the condition e ratio Greater than r e And the time interval between resets is greater than time interval T Δ Then reset is performed to set the error covariance matrix P in the four state EKF k Reset to nI 4×4 Updating the initial frequency value, and inputting the initialized signal data into the signal processing module again for processing; otherwise, the initialized signal data is directly input into the signal processing module for processing.
9. A terminal device comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the memory stores the computer program capable of running on the processor, and the processor loads and executes the computer program, and the method for detecting a non-stationary subsynchronous oscillation signal according to any one of claims 1 to 7 is used.
10. A computer-readable storage medium, in which a computer program is stored, which, when loaded and executed by a processor, implements a method for non-stationary subsynchronous oscillation signal detection according to any one of claims 1 to 7.
CN202211271848.9A 2022-10-18 2022-10-18 Method, system and terminal for detecting non-stationary subsynchronous oscillation signal Pending CN115577251A (en)

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