CN111913034A - Power oscillation detection method based on high-order cumulant and ESPRIT algorithm - Google Patents
Power oscillation detection method based on high-order cumulant and ESPRIT algorithm Download PDFInfo
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Abstract
The invention discloses a power oscillation detection method based on high-order cumulant and an ESPRIT algorithm, which introduces the high-order cumulant, can shield the interference of white Gaussian noise and colored noise to signals, and can retain effective information related to oscillation in the signals. In order to eliminate the influence of measurement data noise on power oscillation detection and make up the defects of the existing method, the signals need to be subjected to correlation preprocessing, then high-order cumulant is used for replacing the original signals, and finally ESPRIT identification is carried out. The method has simple operation steps and high operation speed, thereby having better application prospect.
Description
Technical Field
The invention belongs to the field of oscillation detection of power systems, and particularly relates to a power oscillation detection method.
Background
With the continuous expansion of the scale of the power grid, the access of a new energy power generation system and the occurrence of the interconnection situation of the regional power grid, power oscillation accidents in the system are more frequent, and the safe and stable operation of the power grid is seriously threatened. The power oscillation of the power system is timely and accurately detected, effective oscillation information can be provided for scheduling, measures can be taken to suppress and eliminate the power oscillation in time, and the stable operation of the power system is guaranteed, so that the method has important significance.
The current common power oscillation analysis methods can be divided into two major categories, one is a linear analysis method, and the other is a signal analysis method based on measured data. The linear analysis method can obtain abundant oscillation information, but has high dependence on a system model and can cause the problem of dimension disaster when the power grid scale is large. Therefore, the linear analysis method is only suitable for mechanism type research and post-accident analysis.
The signal analysis method based on the measured data mainly comprises a Prony algorithm, a Hilbert-Huang transform algorithm, wavelet transform, an Empirical Mode Decomposition (EMD) algorithm, a subspace decomposition algorithm and the like. These signal analysis methods have characteristics and are improved in the aspect of operation speed, but the effect is not good in the aspect of gaussian noise suppression, so that the accuracy of the oscillation detection result cannot be guaranteed. In order to obtain power oscillation information of a power system accurately in time, it is necessary to improve the noise suppression aspect of the detection method.
Therefore, it is necessary to determine a power oscillation method which can be applied online and can eliminate the influence of gaussian noise.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a power oscillation detection method based on high-order cumulant and an ESPRIT algorithm, which can accurately detect power oscillation information generated in a system under the interference of Gaussian noise.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a power oscillation detection method based on high-order cumulant and ESPRIT algorithm comprises the following steps:
(1) updating electrical signal data sampled by a Phasor Measurement Unit (PMU) in the system;
(2) performing signal preprocessing on the sampled electrical signal data;
(3) calculating the fourth-order cumulant of the preprocessed signal;
(4) substituting the fourth-order cumulant of the signal for the original signal data;
(5) performing power oscillation identification on the data obtained in the step (4) by using an ESPRIT algorithm;
(6) judging whether power oscillation occurs according to the identification result, and if the power oscillation occurs, outputting oscillation information to a dispatching center; and (4) if the power oscillation does not occur, returning to the step (1).
Further, in the step (2), the signal preprocessing comprises identification, elimination, correction and filtering of abnormal data; the abnormal data refers to erroneous data points that apparently do not follow the data trend due to measurement deviation.
Further, the anomalous data is identified by:
where, i is 7,8iAs the original data, it is the original data,
the interpolated data is obtained;
the first 6 data points were verified as normal data points,
the point-by-point calculation is carried out according to the time sequence by the two formulas
The abnormal data is satisfied with the following formula:
in order to avoid the step signal being rejected as abnormal data, when the dots of the above formula continuously appear more than 5 times, it is considered that y isk,yk+1,...yk+5All are normal data if y is determinedk,yk+1,...yk+5And if the abnormal data are abnormal data, removing the abnormal data, correcting the abnormal data by using a Lagrange interpolation method, and finally filtering the data after the abnormal data are processed by adopting a Butterworth filter.
Further, in step (3), for a zero-mean k-order stationary random process { x (k) }, k ≧ 3, the n-order cumulant of the process is a function of n-1 independent arguments, then the n-order cumulant of the process, cnxThe definition is as follows:
cnx(τ1,…,τn-1)＝cum{x(n),x(n+τ1),…,x(n+τn-1)}
wherein, tau1,...,τn-1And (4) determining the hysteresis quantity, wherein cum represents the accumulation operation, and when the value of n is 4, the fourth-order accumulation quantity is obtained.
Further, in step (5), an ESPRIT algorithm based on the least square method is adopted, a matrix is constructed by a dimensionality reduction subspace matrix of the original signal, and the frequency omega of each periodic component in the signal is estimated by using the matrix psipAnd attenuation coefficient sigmap：
Wherein, U1，U2Is a reduced dimensional subspace matrix of the original signal, the superscript H denotes the conjugate transpose, λpIs a characteristic value of Ψ, TsIs the sampling time;
and obtaining the amplitude and initial phase information of the signal by using a least square method based on the frequency and the attenuation coefficient of each periodic component in the signal.
Adopt the beneficial effect that above-mentioned technical scheme brought:
the method can effectively shield the interference of Gaussian noise in various scenes, and accurately detect the power oscillation information including low-frequency oscillation and subsynchronous oscillation in the system. The method has simple operation steps and high operation speed, thereby having better application prospect.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a waveform diagram of a noise-containing signal and a fitting signal in example 1;
FIG. 3 is a waveform diagram of a noise-containing signal and a fitting signal of example 2;
FIG. 4 is a waveform diagram of the noise-containing signal and the fitting signal of example 3.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention provides a power oscillation detection method based on high-order cumulant and an ESPRIT algorithm, which comprises the following steps as shown in figure 1:
s1: updating electrical signal data sampled by a Phasor Measurement Unit (PMU) in the system;
s2: preprocessing the acquired data by signals;
s3: calculating the fourth-order cumulant of the preprocessed signal;
s4: replacing the fourth-order accumulated quantity of the signals obtained in the step S3 with the original signal data;
s5: performing power oscillation identification on the data output in the step S4 by using an Estimation of Signal Parameter of Rotation Invariant Technology (ESPRIT) algorithm;
s6: judging whether power oscillation occurs according to the identification result: if oscillation occurs, outputting oscillation information to a dispatching center; if no oscillation occurs, the process returns to step S1 to continue the detection.
In this embodiment, preferably, in the step S2, the signal preprocessing includes identification, elimination, correction of abnormal data, and filtering of data; the abnormal data refers to erroneous data points that apparently do not follow the data trend due to measurement deviation.
In this embodiment, a seven-point second-order algorithm forward difference formula is adopted to identify abnormal data, and the formulas of the identification algorithm are shown in formulas (1) and (2):
wherein, i is 7,8iAs the original data, it is the original data,
is interpolated data. Checking that the first 6 points are normal points, and calculating point by point according to time sequence by using the two expressionsFor abnormal data, it
If the value is larger than the normal value, it is considered that the abnormal data satisfies the formula (3).
In order to avoid the step signal being rejected as abnormal data, when the point satisfying the equation (3) appears more than 5 times in succession, it is considered that y isk,yk+1,...yk+5All are normal values. If y is determinedk,yk+1,...yk+5And if the data are abnormal data, removing the abnormal data and correcting the abnormal data by using a Lagrange interpolation method.
The data after the anomalous data processing is then filtered using a butterworth filter. Firstly, the sampling frequency of the filter is set as the sampling frequency f of the WAMSsSampling period TsIs the inverse of the sampling frequency. The performance index of the digital filter is then determined: maximum attenuation of passbandpMinimum attenuation of stop bandsPassband cut-off frequency omegapAnd stop band cut-off frequency omegas. According to the impulse response invariant method, the analog angular frequency omega and the digital angular frequency omega have a linear relation, so that the band-pass cut-off frequency omega of the analog filter can be obtainedpAnd Ωs。
The Butterworth low-pass filter magnitude squared function is:
where K is the order of the filter, ΩcIs attenuating the frequencyAccording to the index, the following can be obtained:
in the present embodiment, it is preferable that, in the above-described step S3, the fourth-Order accumulation amount belongs to a high-Order accumulation amount (HOC), and is a third-Order and above statistic. For a zero-mean k-order stationary random process { x (k) } (k ≧ 3), the n-order cumulant of the process is a function of n-1 independent arguments, then the n-order cumulant of the process, cnxThe definition is shown as the following formula:
cnx(τ1,…,τn-1)＝cum{x(n),x(n+τ1),…,x(n+τn-1)} (6)
in the formula1,...,τn-1For the lag, it can be generated directly with a statistic generating function, and cum represents the accumulation operation. When n is 4, the fourth-order cumulant can be obtained.
In the present embodiment, it is preferable that in the above step S5, an ESPRIT algorithm based on a least square method is adopted. The basic principle of the ESPRIT algorithm is as follows.
Firstly, according to the pre-processed actually measured data sequence x0，x1，...，xN-1Constructing a Hankel matrix X as shown in formula (7):
wherein M + L-1 ═ N. The covariance matrix of the calculated data is R XXT。
And solving the eigenvalue and the eigenvector of the covariance matrix R, performing descending order arrangement on the eigenvalue, and obtaining the corresponding eigenvector V. It can be decomposed into signal subspaces VsSum noise subspace VnI.e. V ═ Vs，Vn]。VsThe column vector of (b) is the eigenvector corresponding to the largest P eigenvalues of the covariance matrix R (P is the number of complex sinusoidal components in the sampled signal). Will VsDelete line 1, mostObtaining a dimensionality reduction signal subspace V after the last line1，V2. There is a unique invertible transformation matrix T such that V1＝V2And T, setting U as an original signal, and obtaining a dimensionality reduction subspace U of the original signal in the same way1，U2Satisfying formula (8):
U1＝V1T,U2＝V2T,U2＝U1Ψ (8)
u in formula (8)1，U2Is a known quantity decomposed from the data matrix, so a matrix shown in equation (10) can be constructed and the signal estimated according to the calculation of equation (11):
wherein λ ispIs a characteristic value of Ψ, TsIs the sampling time. Frequency of each periodic component is ωpAttenuation coefficient of σp. And obtaining information such as amplitude, initial phase and the like by using a least square method based on the frequency and attenuation coefficient of each component in the signal.
Fig. 2 to 4 show three examples to demonstrate the effectiveness and accuracy of the process of the present invention. Wherein, the arithmetic example 1 is an artificially constructed oscillation signal, and the expression is as follows;
TABLE 1
Table 1 shows the comparison of the identification results of the method used in the present invention and the ESPRIT algorithm performed directly on the original power system signal under equation 1. By means of fig. 2 and table 1, HOC-ESPRIT is more accurate than using the ESPRIT method directly. In addition, the operation time required after the addition of the high-order cumulant link is far shorter than that of the ESPRIT method directly used.
Example 2 is a case of subsynchronous oscillation occurring in a wind power delivery system model of a doubly-fed induction wind turbine.
TABLE 2
Table 2 shows the comparison of the identification results of the method used in the present invention and the ESPRIT algorithm directly performed on the original power system signal in example 2. Through fig. 3 and table 2, it can be found that the influence of gaussian noise cannot be eliminated by directly using the ESPRIT method, the HOC-ESPRIT accuracy is higher, and the operation speed is faster.
Example 3 is a case where a two-zone system generates inter-zone low frequency oscillation.
TABLE 3
Table 3 shows the comparison of the identification results of the method used in the present invention and the ESPRIT algorithm directly performed on the original power system signal in example 3. Since the inter-region oscillation mode is single, it can be seen from fig. 4 and table 3 that the effect of gaussian noise cannot be excluded by directly using the ESPRIT method, and the HOC-ESPRIT method can more accurately and rapidly detect the inter-region low-frequency oscillation mode.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.
Claims (5)
1. A power oscillation detection method based on high-order cumulant and ESPRIT algorithm is characterized by comprising the following steps:
(1) updating electrical signal data sampled by a Phasor Measurement Unit (PMU) in the system;
(2) performing signal preprocessing on the sampled electrical signal data;
(3) calculating the fourth-order cumulant of the preprocessed signal;
(4) substituting the fourth-order cumulant of the signal for the original signal data;
(5) performing power oscillation identification on the data obtained in the step (4) by using an ESPRIT algorithm;
(6) judging whether power oscillation occurs according to the identification result, and if the power oscillation occurs, outputting oscillation information to a dispatching center; and (4) if the power oscillation does not occur, returning to the step (1).
2. The method for detecting power oscillation based on high-order cumulant and ESPRIT algorithm as claimed in claim 1, wherein in step (2), the signal pre-processing comprises identification, elimination, correction and filtering of abnormal data; the abnormal data refers to erroneous data points that apparently do not follow the data trend due to measurement deviation.
3. The method of claim 2, wherein the abnormal data is identified by the following equation:
where, i is 7,8, …, N is data length, y isiAs the original data, it is the original data,
the interpolated data is obtained;
the first 6 data points were verified as normal data points,
the point-by-point calculation is carried out according to the time sequence by the two formulas
The abnormal data is satisfied with the following formula:
in order to avoid the step signal being rejected as abnormal data, when the dots of the above formula continuously appear more than 5 times, it is considered that y isk,yk+1,...yk+5All are normal data if y is determinedk,yk+1,...yk+5And if the abnormal data are abnormal data, removing the abnormal data, correcting the abnormal data by using a Lagrange interpolation method, and finally filtering the data after the abnormal data are processed by adopting a Butterworth filter.
4. The method for detecting power oscillation according to claim 1, wherein in step (3), for a zero-mean k-order stationary random process { x (k) }, k ≧ 3, the n-order cumulant of the process is a function of n-1 independent arguments, then the n-order cumulant of the process, c, isnxThe definition is as follows:
cnx(τ1,···,τn-1)＝cum{x(n),x(n+τ1),···,x(n+τn-1)}
wherein, tau1,…,τn-1And (4) determining the hysteresis quantity, wherein cum represents the accumulation operation, and when the value of n is 4, the fourth-order accumulation quantity is obtained.
5. The method for detecting power oscillation based on high-order cumulant and ESPRIT algorithm as claimed in claim 1, wherein in step (5), the ESPRIT algorithm based on least square method is adopted, and the power oscillation is detected by the originalConstructing a matrix by using the signal dimensionality reduction subspace matrix, and estimating the frequency omega of each periodic component in the signal by using the matrix psipAnd attenuation coefficient sigmap：
Wherein, U1，U2Is a reduced dimensional subspace matrix of the original signal, the superscript H denotes the conjugate transpose, λpIs a characteristic value of Ψ, TsIs the sampling time;
and obtaining the amplitude and initial phase information of the signal by using a least square method based on the frequency and the attenuation coefficient of each periodic component in the signal.
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