CN109274107B - Low-frequency oscillation signal parameter identification method considering singular values - Google Patents

Low-frequency oscillation signal parameter identification method considering singular values Download PDF

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CN109274107B
CN109274107B CN201811306935.7A CN201811306935A CN109274107B CN 109274107 B CN109274107 B CN 109274107B CN 201811306935 A CN201811306935 A CN 201811306935A CN 109274107 B CN109274107 B CN 109274107B
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CN109274107A (en
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王�义
孙永辉
翟苏巍
武小鹏
吕欣欣
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Hohai University HHU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Abstract

The invention discloses a method for identifying low-frequency oscillation signal parameters considering singular values, which can effectively detect the singular values existing in measurement, innovation sequences and model structures, avoids the problem of divergence under the condition of the singular values of the traditional Kalman filtering by reducing the weight of the singular values, improves the robustness of the identification method, and can realize the accurate identification of the low-frequency oscillation signal parameters of a power system under the condition of the singular values.

Description

Low-frequency oscillation signal parameter identification method considering singular values
Technical Field
The invention relates to a method for identifying parameters of a low-frequency oscillation signal model considering singular values, and belongs to the technical field of signal analysis and parameter identification.
Background
The safety and stability problems of the power system are closely related to the low-frequency oscillation signals, and the low-frequency oscillation signals contain the operation situation information of the power system. Therefore, how to extract the information represented by the low-frequency oscillation signal through a monitoring and analyzing means and take appropriate measures timely is of great significance for ensuring the safe operation of the power system.
In recent years, many scholars have conducted intensive and extensive research on the identification of low-frequency oscillation signal modes and model parameter identification of power systems. Aiming at the problem of parameter identification of a low-frequency oscillation signal model, a plurality of effective methods are provided, which mainly comprise Fast Fourier Transform (FFT), wavelet algorithm, Prony algorithm, Extended Kalman Filter (EKF) and the like. The precision of the FFT parameter identification method is limited by a data window, and the damping characteristic of the oscillation signal cannot be effectively reflected; the low-frequency oscillation signal parameter identification method based on the wavelet algorithm can embody the time-varying characteristic of a signal, but has the problem that the wavelet basis is difficult to select; the Prony algorithm is simple and convenient, but is sensitive to noise. The EKF method has the characteristics of online identification, low memory occupation of calculation, high efficiency and wide application. However, it should be noted that none of the above methods considers singular values caused by impulse noise, and accurate identification of the low frequency oscillation signal parameters cannot be achieved in such a case.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects of the existing method and improve the robustness and identification precision of the low-frequency oscillation signal model parameter identification method, the invention designs the low-frequency oscillation signal parameter identification model considering singular values and the parameter identification method thereof.
The technical scheme adopted by the invention is as follows: a low-frequency oscillation signal parameter identification model considering singular values is used for establishing a state space model of which the state variable components comprise parameters to be estimated of a low-frequency oscillation signal model of an electric system;
the low-frequency oscillation signal of the power system consists of N exponentially decaying oscillation wave signals:
Figure GDA0003231274400000011
in the formula, λi,wi,δi,φiRespectively, amplitude, frequency, attenuation factor, initial phase; n (t) is a zero mean white noise;
the 4N state variables are defined as follows:
Figure GDA0003231274400000021
Figure GDA0003231274400000022
x4i-1,k＝wi (4)
x4i,k＝δi (5)
in the formula, the index i represents the i-th damped oscillation wave signal constituting the low-frequency oscillation signal, k represents the time, fsRepresenting the sampling frequency, the state component at the time k +1 is obtained according to the formula:
Figure GDA0003231274400000023
Figure GDA0003231274400000024
x4i-1,k+1＝x4i-1,k+ω4i-1,k (8)
x4i,k+1＝x4i,k+ω4i,k (9)
in the formula, ω4i-j,k(i-1 … N, j-0 … 3) k is time mean zero and covariance matrix W iskWhite gaussian noise of (1);
the output equation of the measured values is:
Figure GDA0003231274400000025
in the formula eta2i-1＝cos(φi)，η2i＝-sin(φi)，nkIs mean zero and covariance matrix is RkWhite gaussian noise.
The invention also provides a parameter identification method based on the parameter identification model, which comprises the following steps:
s1: acquiring a state space model containing model parameters in the state variable component;
s2: initial value of parameter estimation at time when initial k is 0
Figure GDA0003231274400000026
Parameter estimationError covariance sigma0|0Covariance matrix W satisfied by noisekAnd RkInitial values are respectively W0And R0Identifying the maximum time S by the parameter;
s3: calculating a predicted value of a parameter at time k
Figure GDA0003231274400000027
Figure GDA0003231274400000028
Wherein f (-) corresponds to a nonlinear system function in the state equation of the low-frequency oscillation signal,
Figure GDA0003231274400000029
representing the estimated value of the k-1 time parameter;
s4: calculating parameter prediction error covariance sigma at time kk|k-1The calculation formula is as follows:
Figure GDA0003231274400000031
in the formula (I), the compound is shown in the specification,
Figure GDA0003231274400000032
represents the function f (-) in
Figure GDA0003231274400000033
The Jacobian matrix, ∑k-1|k-1Is the estimation error covariance at time k-1;
s5: combining parameter prediction values
Figure GDA0003231274400000034
And the measured value zkEstablishing a linear batch processing regression model, and increasing the measurement redundancy of the low-frequency oscillation signal parameter identification:
Figure GDA0003231274400000035
in the formula (I), the compound is shown in the specification,
Figure GDA0003231274400000036
Hkrepresents the measurement output matrix at the time k, I is the identity matrix, xkRepresenting the true value of the k time parameter, ek～N(0,Rk) To conform to the Gaussian distributed systematic noise sequence, δk|k-1For predicting a parameter
Figure GDA0003231274400000037
And the actual value x of the parameterkA difference of (d);
Figure GDA0003231274400000038
the satisfied covariance matrix is
Figure GDA0003231274400000039
LkWherein the compound can be obtained by Coriolis decomposition;
s6: calculating the projection values of the data points h in all possible vectors u by using a robust projection statistical method to detect the linear regression model in the step (5)
Figure GDA00032312744000000310
The singular value of (a);
Figure GDA00032312744000000311
in the formula, PSiTo represent
Figure GDA00032312744000000312
Projection value corresponding to the ith row marked (. smallcircle.)TRepresenting the matrix transpose, medk(. to) for the median value calculation, a decision threshold d is set, if PSi 2＞d2Then judging the behavior singular value and according to the behavior singular valueReducing the corresponding weight of the line measurement value
Figure GDA00032312744000000313
Namely, it is
Figure GDA00032312744000000314
S7: performing white-whitening treatment on the linear regression model in S5:
yk＝Akxk+ηk (18)
in the formula (I), the compound is shown in the specification,
Figure GDA00032312744000000315
s8: the initial weight matrix of the iterative least square is
Figure GDA00032312744000000316
Wherein q (r)si)＝ψ(rsi)/rsiThe function denoted by ψ (·) is:
Figure GDA0003231274400000041
wherein c is a threshold value and r is a parametersiThe calculation method is
Figure GDA0003231274400000042
s＝1.4826·medi|rt(i)|，
Figure GDA0003231274400000043
In the formula, yk(i) Line i, a, representing the measured value at time kiIs an output matrix AkRow i;
s9: solving S7 by using an iterative least square method to obtain a low-frequency oscillation parameter identification result;
s10: calculating the estimation error covariance (Sigma) at time kk|k：
Figure GDA0003231274400000044
In the formula (I), the compound is shown in the specification,
Figure GDA0003231274400000045
s11: and (5) performing low-frequency oscillation model parameter identification according to the time sequence, stopping iteration when k +1 is larger than S, and outputting a parameter identification result.
The iterative least square method in the step S9 comprises the following calculation method:
Figure GDA0003231274400000046
in the formula
Figure GDA0003231274400000047
For the v-th least square optimization iteration result at time k, Q(v)Is the least squares weight matrix of the v-th iteration.
Has the advantages that: compared with the prior art, the method provided by the invention has the advantages that the influence caused by singular values is avoided and the parameter identification effect of the low-frequency oscillation signal model is effectively improved by detecting the singular values, reducing the weight and the like and optimizing by using an iterative least square method.
Drawings
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
FIG. 2 is a diagram of an embodiment of a low frequency oscillating input signal including singular values;
FIG. 3 shows the result of identifying parameters of an embodiment of a low frequency oscillation input signal by using an EKF method;
FIG. 4 shows the result of parameter identification of low frequency oscillation input signal according to an embodiment of the present invention;
FIG. 5 shows the absolute error result of the parameter identification of the low frequency oscillation signal according to the embodiment of the present invention.
Detailed Description
The invention is further illustrated below with reference to the figures and examples.
Low-frequency oscillation modal parameter identification modeling
The low-frequency oscillation signal of the power system consists of a plurality of exponentially decaying oscillation wave signals, namely:
Figure GDA0003231274400000051
in the formula, λi,wi,δi,φiRespectively, amplitude, frequency, attenuation factor, initial phase; n (t) is a zero mean white noise.
Considering a low-frequency oscillation signal of a power system composed of N exponentially decaying oscillation wave signals, 4N state variables are defined as follows:
Figure GDA0003231274400000052
Figure GDA0003231274400000053
x4i-1,k＝wi (4)
x4i,k＝δi (5)
in the formula, the index i represents the i-th damped oscillation wave signal constituting the low-frequency oscillation signal, k represents the time, fsRepresenting the sampling frequency, the state component at time k +1 is further derived according to the above equation:
Figure GDA0003231274400000054
Figure GDA0003231274400000055
x4i-1,k+1＝x4i-1,k+ω4i-1,k (8)
x4i,k+1＝x4i,k+ω4i,k (9)
in the formula of omega4i-j,k(i-1 … N, j-0 … 3) k is time mean zero and covariance matrix W iskWhite gaussian noise.
The output equation of the measured values is:
Figure GDA0003231274400000056
in the formula eta2i-1＝cos(φi)，η2i＝-sin(φi)，nkIs mean zero and covariance matrix is RkWhite gaussian noise.
At this point, a state space model containing parameters to be estimated of the low-frequency oscillation signal model of the power system in the state variable component is established.
As shown in fig. 1, the method of the present invention for identifying parameters of a low frequency oscillation signal model of an embodiment includes the following steps:
s1: acquiring a state space model containing model parameters in the state variable component;
s2: initializing initial values of the identification method of the low-frequency oscillation model parameters, such as the initial value of parameter estimation at the moment when k is 0
Figure GDA0003231274400000061
Parameter estimation error covariance ∑0|0The covariance matrix of noise WkAnd RkAre each W0And R0Identifying the maximum time S by the parameter;
s3: calculating a predicted value of a parameter at time k
Figure GDA0003231274400000062
The calculation formula is as follows:
Figure GDA0003231274400000063
in the formula (I), the compound is shown in the specification,
Figure GDA0003231274400000064
the non-linear system function in the state equation of the low-frequency oscillation signal corresponding to the f (-) represents the estimated value of the parameter at the time t-1 as follows
Figure GDA0003231274400000065
Figure GDA0003231274400000066
x4i-1,k+1＝x4i-1,k+ω4i-1,k
x4i,k+1＝x4i,k+ω4i,k
In the formula, ω4i-j,k(i-1 … N, j-0 … 3) k is zero time mean and covariance WkWhite gaussian noise of (1);
s4: calculating parameter prediction error covariance sigma at time kk|k-1The calculation formula is as follows:
Figure GDA0003231274400000067
in the formula (I), the compound is shown in the specification,
Figure GDA0003231274400000068
represents the function f (-) in
Figure GDA0003231274400000069
The Jacobian matrix, ∑k-1|k-1Is the estimation error covariance at time k-1;
s5: combining parameter prediction values
Figure GDA00032312744000000610
And the measured value zkEstablishing a linear batch regression model to increase the measurement redundancy of the parameter identification of the low-frequency oscillation signal: the specific form is as follows:
Figure GDA00032312744000000611
in the formula HkRepresents the measurement output matrix at the time k, I is the identity matrix, xkRepresenting the true value of the k time parameter, ek～N(0,Rk) To conform to the Gaussian distributed systematic noise sequence, δk|k-1For predicting a parameter
Figure GDA00032312744000000612
And the actual value x of the parameterkThe difference value. The expression can be further expressed correspondingly as
Figure GDA0003231274400000071
In the formula (I), the compound is shown in the specification,
Figure GDA0003231274400000072
Hkrepresents the measurement output matrix at the time k, I is the identity matrix, xkRepresenting the true value of the k time parameter, ek～N(0,Rk) To conform to the Gaussian distributed systematic noise sequence, δk|k-1Is the true value of the parameter
Figure GDA0003231274400000073
And the predicted value xkA difference of (d);
Figure GDA0003231274400000074
the satisfied covariance matrix is
Figure GDA0003231274400000075
LkWherein the compound can be obtained by Coriolis decomposition.
S6: using robust projection statistical method to find out all possible data points hThe projected value of the vector u is used to detect the linear regression model in S5
Figure GDA0003231274400000076
The principle of the singular value of (a) is as follows:
Figure GDA0003231274400000077
in the formula, PSiTo represent
Figure GDA0003231274400000078
Projection value corresponding to the ith row marked (. smallcircle.)TRepresenting the matrix transpose, medk(. cndot.) is the operation of finding the median. Setting the decision threshold d to 1.5, if
Figure GDA0003231274400000079
Then the singular value of the behavior is determined, and in order to overcome the influence of the singular value of the behavior on the parameter estimation, the corresponding weight of the measured value of the behavior needs to be reduced
Figure GDA00032312744000000710
Namely, it is
Figure GDA00032312744000000711
S7: performing white-whitening treatment on the linear regression model in S5, and multiplying the two ends simultaneously
Figure GDA00032312744000000712
Namely, it is
Figure GDA00032312744000000713
Further finishing, expressed in the following form
yk＝Akxk+ηk (18)
In the formula
Figure GDA00032312744000000714
S8: iterative least squares initial weight matrix
Figure GDA00032312744000000715
Wherein q (r)si)＝ψ(rsi)/rsiThe function denoted by ψ (·) is:
Figure GDA00032312744000000716
c is a threshold (typically 1.5) and r is a parametersiThe calculation method comprises the following steps:
Figure GDA00032312744000000717
s＝1.4826·medi|rk(i)|，
Figure GDA00032312744000000718
in the formula yk(i) Line i, a, representing the measured value at time kiIs an output matrix AkRow i.
S9: solving the equation in the step (7) by using an iterative least square method to obtain the low-frequency oscillation parameter identification, wherein the calculation method comprises the following steps
Figure GDA0003231274400000081
In the formula
Figure GDA0003231274400000082
For the v-th least square optimization iteration result at time k, Q(v)Is the least squares weight matrix of the v-th iteration.
S10: calculating the estimation error covariance (Sigma) at time kk|kThe calculation formula is as follows
Figure GDA0003231274400000083
In the formula
Figure GDA0003231274400000084
S11: and (5) performing low-frequency oscillation model parameter identification according to the steps (3) to (10) according to the time sequence, stopping iteration when k +1 is larger than S, and outputting a parameter identification result.
Example (b):
in order to verify the effectiveness and the practicability of the method, the following common test example for parameter identification and analysis of the low-frequency oscillation model of the power system is adopted, and the mathematical expression of the low-frequency oscillation signal is as follows:
y1(t)＝e-0.012t sin(0.5t)+n t 0≤t≤400
the real frequency w of the low-frequency oscillation signal is 0.5, the real damping factor δ is 0.012, and the sampling time t is k (k is 1,2 … 400), ntIs gaussian white noise. When the method is used for identifying the parameters of the low-frequency oscillation model, the maximum identification iteration time S is set to 400, and the initial value of the parameter identification is set to 400
Figure GDA0003231274400000085
The initial values of the covariance matrix satisfied by the parameter estimation covariance matrix, the system noise and the measurement noise are respectively as follows:
Figure GDA0003231274400000086
R0＝10-5
it is assumed that the measured value of the low-frequency oscillation signal is affected by impulse noise at time t-30 and 36 (i.e., the low-frequency oscillation input signal of the embodiment, as shown in fig. 2), that is:
n30＝-10，n36＝-10。
the model parameter identification analysis is performed on the low-frequency oscillation test signal containing the singular value in fig. 2, and the mode parameter identification is performed by respectively adopting the EKF (the required related parameter value is the same as the initial parameter value of the method of the invention) and the method of the invention. The result of identifying the low frequency oscillation signal parameters of the embodiment by the EKF method is shown in FIG. 3, and the result of identifying the low frequency oscillation signal parameters of the embodiment by the method of the present invention is shown in FIG. 4. FIG. 5 further shows the absolute error between the parameter identification result and the actual parameter value. As can be seen from fig. 3 and 4, in the case of singular values, the EKF method cannot converge to the true values, and the identification result is meaningless; the method provided by the invention can effectively inhibit the influence caused by singular values, and realize accurate identification of low-frequency oscillation signal parameters, which shows that the method has stronger robustness compared with the EKF method. As can be further seen from the parameter identification error in FIG. 5, the method of the present invention has high identification accuracy and convergence performance.
Based on the analysis of the parameter identification result, the method for identifying the low-frequency oscillation signal model parameters considering the singular value can effectively inhibit and weaken the identification error brought by the singular value, and has stronger robustness.

Claims (2)

1. A method for identifying parameters of low-frequency oscillation signals considering singular values is characterized by comprising the following steps: the method comprises the following steps:
s1: establishing a state space model containing parameters to be estimated of the low-frequency oscillation signal model of the power system in state variable components;
the low-frequency oscillation signal of the power system consists of N exponentially decaying oscillation wave signals:
Figure FDA0003147192150000011
in the formula, λi,wi,δi,φiRespectively, amplitude, frequency, attenuation factor, initial phase; n (t) is a zero mean white noise;
the 4N state variables are defined as follows:
Figure FDA0003147192150000012
Figure FDA0003147192150000013
x4i-1,k＝wi (4)
x4i,k＝δi (5)
in the formula, the index i represents the i-th damped oscillation wave signal constituting the low-frequency oscillation signal, k represents the time, fsRepresenting the sampling frequency, the state component at the time k +1 is obtained according to the formula:
Figure FDA0003147192150000014
Figure FDA0003147192150000015
x4i-1,k+1＝x4i-1,k+ω4i-1,k (8)
x4i,k+1＝x4i,k+ω4i,k (9)
in the formula, ω4i-j,k(i-1 … N, j-0 … 3) denotes that the time-mean of k is zero and the covariance matrix is WkWhite gaussian noise of (1);
the output equation of the measured values is:
Figure FDA0003147192150000016
in the formula eta2i-1＝cos(φi)，η2i＝-sin(φi)，nkIs mean zero and covariance matrix is RkWhite gaussian noise of (1);
s2: initial value of parameter estimation at time when initial k is 0
Figure FDA0003147192150000021
Parameter estimation error covariance ∑0|0Covariance matrix W satisfied by noisekAnd RkInitial values are respectively W0And R0Identifying the maximum time S by the parameter;
s3: calculating a predicted value of a parameter at time k
Figure FDA0003147192150000022
Figure FDA0003147192150000023
Wherein f (-) corresponds to a nonlinear system function in the state equation of the low-frequency oscillation signal,
Figure FDA0003147192150000024
representing the estimated value of the k-1 time parameter;
s4: calculating parameter prediction error covariance sigma at time kk|k-1The calculation formula is as follows:
Figure FDA0003147192150000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003147192150000026
represents the function f (-) in
Figure FDA0003147192150000027
The Jacobian matrix, ∑k-1|k-1Is the estimation error covariance at time k-1;
s5: combining parameter prediction values
Figure FDA0003147192150000028
And the measured value zkEstablishing a linear batch processing regression model, and increasing the measurement redundancy of the low-frequency oscillation signal parameter identification:
Figure FDA0003147192150000029
in the formula (I), the compound is shown in the specification,
Figure FDA00031471921500000210
Hkrepresents the measurement output matrix at the time k, I is the identity matrix, xkRepresenting the true value of the k time parameter, ek～N(0,Rk) To conform to the Gaussian distributed systematic noise sequence, δk|k-1For predicting a parameter
Figure FDA00031471921500000211
And the actual value x of the parameterkA difference of (d);
Figure FDA00031471921500000212
the satisfied covariance matrix is
Figure FDA00031471921500000213
LkWherein the compound can be obtained by Coriolis decomposition;
s6: calculating the projection values of the data points h in all possible vectors u by using a robust projection statistical method to detect the linear regression model in the step (5)
Figure FDA00031471921500000214
The singular value of (a);
Figure FDA00031471921500000215
in the formula, PSiTo represent
Figure FDA00031471921500000216
Projection value corresponding to the ith row marked (. smallcircle.)TRepresentation matrixTransposition, medk(. to) for the median value calculation, a decision threshold d is set, if PSi 2＞d 2Then, the singular value of the behavior is determined, and the corresponding weight of the measured value of the row is reduced according to the singular value of the behavior
Figure FDA0003147192150000031
Namely, it is
Figure FDA0003147192150000032
S7: performing white-whitening treatment on the linear regression model in S5:
yk＝Akxk+ηk (18)
in the formula (I), the compound is shown in the specification,
Figure FDA0003147192150000033
s8: the initial weight matrix of the iterative least square is
Figure FDA0003147192150000034
Wherein q (r)si)＝ψ(rsi)/rsiThe function denoted by ψ (·) is:
Figure FDA0003147192150000035
wherein c is a threshold value and r is a parametersiThe calculation method is
Figure FDA0003147192150000036
s＝1.4826·medi|rt(i)|，
Figure FDA0003147192150000037
In the formula, yk(i) Line i, a, representing the measured value at time kiIs an output matrix AkRow i;
s9: solving S7 by using an iterative least square method to obtain a low-frequency oscillation parameter identification result;
s10: calculating the estimation error covariance (Sigma) at time kk|k：
Figure FDA0003147192150000038
In the formula (I), the compound is shown in the specification,
Figure FDA0003147192150000039
s11: and (5) performing low-frequency oscillation model parameter identification according to the time sequence, stopping iteration when k +1 is larger than S, and outputting a parameter identification result.
2. The method according to claim 1, wherein the method for identifying the parameters of the low-frequency oscillation signal includes: the iterative least square method in the step S9 comprises the following calculation method:
Figure FDA00031471921500000310
in the formula
Figure FDA00031471921500000311
For the v-th least square optimization iteration result at time k, Q(v)Is the least squares weight matrix of the v-th iteration.
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