CN104578115A - Electric system low frequency oscillation mode identification method based on correlation functions - Google Patents
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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
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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
- H02J3/002—Flicker reduction, e.g. compensation of flicker introduced by non-linear load
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Abstract
The invention discloses an electric system low frequency oscillation mode identification method based on correlation functions. The method includes the following steps that firstly, a section of an active power signal of a circuit having high observability for a low frequency oscillation mode under the circumstance that no large disturbance exists in an electric system is read and serves as a signal to be analyzed, and a sampling time interval Ts is determined; secondly, the read active power signal is preprocessed to obtain a corresponding power fluctuation signal; thirdly, a self-correlation function of the power fluctuation signal is solved, and a system free oscillation signal is obtained; fourthly, based on an extended Prony method, mode identification is carried out on the free oscillation signal to obtain a low frequency oscillation mode frequency and a damping ratio. The electric system low frequency oscillation mode identification method has the advantages that the method is only based on random response signals, operation is simple, the calculation amount is small, and identification accuracy is good.
Description
Technical Field
The invention relates to the technical field of analysis and control of power systems, in particular to a correlation function-based low-frequency oscillation mode identification method for a power system.
Background
The low-frequency oscillation is an inherent phenomenon of an alternating current interconnection system, and the low-frequency oscillation problem is more prominent due to the improvement of the interconnection degree of a power system, the enlargement of the interconnection scale and the large use of a quick excitation system in the power system. At present, the problem of low-frequency oscillation seriously threatens the stability of a power system and limits the electric energy transmission capability of an interconnected power grid. The accurate control of the low-frequency oscillation mode of the system has important significance on the safe and stable operation of the power system.
The low-frequency oscillation mode analysis based on the measured data can overcome the defect that the model analysis cannot follow the change of the system structure and parameters, and has higher practicability. The low frequency oscillation pattern recognition method based on the measurement signal is classified according to the type of the input signal and may be classified into a method based on a transient oscillation signal and a method based on a random response signal. Transient oscillation signals refer to free oscillation responses of a system subjected to obvious disturbance and can be fitted by linear combination of a series of complex exponential functions; the random response signal refers to a response excited by new energy power generation and random fluctuation of a load under the condition that the system normally operates, and is a full response of the system under random excitation, and generally cannot be fitted by linear combination of complex exponential functions directly, so that the method based on the transient oscillation signal cannot be directly applied to random response signals to identify low-frequency oscillation modes. The transient oscillation signal data volume is small in an actual power grid, the random response signal caused by power generation and load fluctuation exists in the system almost at the moment, the random response signal is easy to obtain, and the low-frequency oscillation mode identification result based on the random response signal can better reflect the small disturbance stability of the system under the condition of normal operation of the system.
In the method for identifying the low-frequency oscillation mode based on the random response signal, a subspace method needs to measure an input signal of a system, and the input signal in an actual power system cannot be measured, so that the application of the method is limited; the random subspace method needs to carry out singular value decomposition on a huge matrix, and has large calculation amount and complex algorithm; the method based on the ARMA model is difficult to accurately identify the damping ratio; the random decrement technology is combined with the Prony method, and the estimation of the random decrement technology on the free oscillation signal is rough, so that the identification of the Prony on the damping ratio is not accurate enough.
Therefore, in the prior art, the required input signal of the power system is not measurable, the calculation amount is large, or the method is not accurate enough for identifying the damping ratio.
Disclosure of Invention
The invention aims to solve the technical problem of providing a correlation function-based low-frequency oscillation mode identification method for a power system, which is based on random response signals output by the power system only, has simple and reliable algorithm and higher damping ratio identification accuracy.
The technical scheme adopted by the invention for solving the problems is as follows:
a method for identifying a low-frequency oscillation mode of a power system based on a correlation function comprises the following steps:
step A: reading the line active power signal with high observability to the low-frequency oscillation mode under the condition of no large disturbance of a section of power system as a signal to be analyzed and determining the sampling time intervalT s ；
And B: preprocessing the read active power signal to obtain a corresponding power fluctuation signal;
and C: solving an autocorrelation function of the power fluctuation signal to obtain a system free oscillation signal;
step D: and based on an extended Prony method, carrying out mode identification on the free oscillation signal to obtain the frequency and the damping ratio of a low-frequency oscillation mode.
The invention directly utilizes the system random response signal excited by power generation and load fluctuation under the normal operation condition of the power grid, does not depend on the free oscillation signal of a large disturbance excitation system, does not need to measure the input signal of the power system, has small calculated amount and good identification accuracy, is beneficial to accurately mastering the damping characteristic of the system under the normal operation condition of the power grid, lays a foundation for inhibiting the generation of weak damping or negative damping low-frequency oscillation and improving the power angle stability of the power grid, and effectively solves the technical problems of the existing power system low-frequency oscillation mode identification method based on the random response signal that the input signal of the system needs to be measured, the calculated amount is large or the identification accuracy of the damping ratio is not good.
Further, the step B: the specific operation steps of preprocessing the read active power signal to obtain a corresponding power fluctuation signal are as follows:
and eliminating abnormal data from the read line active power signal through data preprocessing, filling missing data with the previous normal data when the data are missing, and obtaining a modified active power sequencePAnd then removing the trend term by using a method of subtracting a least square fitting polynomial to obtain the data length ofNPower fluctuation signal deltaP. The invention uses the line active power signal under the normal operation condition of the power systemPAs the signal to be analysed, hence the signalPWithout a large mutation and the outlier is characterized by a far-off from normal, the outlier can be determined according to the following conditions.
If the condition is satisfied, the first stepiThe point is determined to be an abnormal data point,padding with the previous normal data; if the condition is not satisfied, the point is considered to be a normal data point.
Further, obtaining the corrected active power sequencePAnd then removing the trend term by using a method of subtracting a least square fitting polynomial to obtain the data length ofNPower fluctuation signal deltaPThe specific operation steps are as follows:
b1: is constructed in a length ofNAt a time interval ofT s Time series ofT；
；
B2: constructing a matrix A;
；
wherein,mis the order of the fitting polynomial;
b3: calculating coefficients of fitting polynomialb；
；
Wherein, the upper labelTRepresenting the transpose, coefficient, of the solving matrix；
B4: determining a power fluctuation signal DeltaP，
。
Further, the step C: signaling the power fluctuationNumber deltaPObtaining an autocorrelation function of lengthLFree-running response signal ofR(k)(k=0，1,……L-1)；
Wherein:Nas power fluctuation signal deltaPThe length of the data.
Further, the step D: based on an extended Prony parameter estimation method, carrying out mode identification on the free oscillation response signal, and identifying the frequency and the damping ratio of a low-frequency oscillation mode, wherein the specific operation steps are as follows:
d1: using said free-running signalRData in (1)R(0)，R(1)，……，R(L-1) Computing sample functionsr(i, j)：
Wherein,Lfor the free-running response data length,p e in order to expand the order of the order,p e the size is taken asL/2；
D2: constructing an extended matrixR e ：
；
D3: for the spreading matrixR e Singular value decomposition is carried out:
wherein,Hrepresents a conjugate transpose;Uis a matrixR e A matrix composed of the left singular vectors of (a);Vis a matrixR e A matrix composed of right singular vectors of (a); sigma is diagonal matrix, diagonal elements are matrixR e Singular value of，，…，；
D4: according to a matrixR e Singular value determination order ofpAnd constructing a matrixV 1 、 V 2 ：
Comparing elements in a diagonal matrix sigmaFind out to satisfyIs smallest integer ofiOrder of signalp=i(ii) a And constructing a matrixV 1 、 V 2 ：
，
；
D5: coefficient of calculationa 1 、a 2 、…、a p ：
Wherein,a= [a 1 ,a 2 , …,a p ]T；
d6: solving the root of the following polynomial
；
D7: calculating the frequency of a low frequency oscillation modef i Damping ratio ofd i ，(i=1,2, …,p)
；
Wherein:T s for the sampling interval, arctan is an arctangent function, ln is taken from the natural logarithm, Re denotes taking the real part of the complex number, and Im denotes taking the imaginary part of the complex number.
In conclusion, the beneficial effects of the invention are as follows:
the method comprises the steps of firstly reading a line active power signal with high observability on a low-frequency oscillation mode under the condition that a section of power system has no large disturbance as a signal to be analyzed, and determining a sampling time intervalT s (ii) a Then preprocessing the read active power signal to obtain a corresponding power fluctuation signal; then, solving an autocorrelation function of the power fluctuation signal to obtain a system free oscillation signal; and finally, based on an extended Prony method, carrying out mode identification on the free oscillation response signal, and identifying the technical scheme of the frequency and the damping ratio of the low-frequency oscillation mode, namely, directly utilizing the system random response signal excited by power generation and load fluctuation under the normal operation condition of the power grid, and not depending on the free oscillation signal of a large-disturbance excitation systemThe method has the advantages of small size, good identification accuracy, contribution to accurately mastering the damping characteristic of the system in the normal operation state of the power grid, laying a foundation for inhibiting weak damping or negative damping low-frequency oscillation and improving the power angle stability of the power grid, and effectively solving the technical problems of large calculated amount, complex algorithm or poor identification accuracy of the damping ratio of the input signal of the system to be measured in the conventional random response signal-based power system low-frequency oscillation mode identification method. The method for identifying the low-frequency oscillation mode under the normal operation condition of the power system is based on the random response signal output by the power system, the algorithm is simple and reliable, and the damping ratio identification accuracy is high.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a schematic diagram of an IEEE16 machine 68 node test system.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples.
Example (b):
as shown in fig. 1, a method for identifying a low-frequency oscillation mode of a power system based on a correlation function includes the following steps:
step A: reading the line active power signal with high observability to the low-frequency oscillation mode under the condition of no large disturbance of a section of power system as a signal to be analyzed and determining the sampling time intervalT s ；
The fact that the power grid has no large disturbance means that no short-circuit fault occurs in the power grid or the running state of a large-capacity unit is switched. The essence of the low-frequency oscillation is the phase between the power angles of the generatorFor oscillation, the oscillation is obviously shown in the oscillation of active power on a line, so that engineering is used to identify a low-frequency oscillation mode from line active power data, and selecting a line active power signal with higher observability to the low-frequency oscillation mode as a signal to be analyzed is a premise for accurately identifying the low-frequency oscillation mode, while the observability of the line active power signal to the mode is obtained according to model analysis or long-term operation experience of a power system, and is common knowledge in the field. The simulation step size in this embodiment is 0.01 second, soT s Take 0.01 seconds.
And B: preprocessing the read active power signal to obtain a corresponding power fluctuation signal;
and C: solving an autocorrelation function of the power fluctuation signal to obtain a system free oscillation signal;
step D: and based on an extended Prony method, carrying out mode identification on the free oscillation signal to obtain the frequency and the damping ratio of a low-frequency oscillation mode.
And B, the step of: the specific operation steps of preprocessing the read active power signal to obtain a corresponding power fluctuation signal are as follows:
and eliminating abnormal data from the read line active power signal through data preprocessing, estimating missing data, namely filling the missing data with the previous normal data when the data are missing to obtain a modified active power sequencePAnd then removing the trend term by using a method of subtracting a least square fitting polynomial to obtain the data length ofNPower fluctuation signal deltaP. The invention uses the line active power signal under the normal operation condition of the power systemPAs the signal to be analysed, hence the signalPWithout a large mutation and the outlier is characterized by a far-off from normal, the outlier can be determined according to the following conditions.
（1）
If the condition is satisfied, the first stepiJudging the points as abnormal data points, and filling the abnormal data points with the previous normal data; if the condition is not satisfied, the point is considered to be a normal data point.
Obtaining the corrected active power sequencePDetermining a sampling time intervalT s Then, a method of subtracting a least square fitting polynomial is used for removing a trend term to obtain the data length ofNPower fluctuation signal deltaPThe specific operation steps are as follows:
b1: is constructed in a length ofNAt a time interval ofT s Time series ofT；
；（2）
B2: construction matrixA；
；（3）
Wherein,mis the order of the fitting polynomial;
b3: calculating coefficients of fitting polynomialb；
；
Wherein, the upper labelTRepresenting the transpose, coefficient, of the solving matrixTheoretically, inmThe larger the value of (A), the more thoroughly the trend term is removed, butmThe larger the calculation amount is, the larger the order number in practical applicationmTaking the number as 5;
b4: determining powerFluctuation signal deltaP，
。
And C, performing the step of: the power fluctuation signal deltaPObtaining an autocorrelation function of lengthLFree-running response signal ofR(k)(k=0,1,……L-1)；
（4）
Wherein:Nas power fluctuation signal deltaPData length of (2), in the present embodimentNThe number of data samples in 10 minutes is taken,Lthe length of the free-running oscillation signal is shown in this embodimentLThe number of data samples in 10 seconds is taken as:
（5）
the step D: based on an extended Prony parameter estimation method, carrying out mode identification on the free oscillation response signal, and identifying the frequency and the damping ratio of a low-frequency oscillation mode, wherein the specific operation steps are as follows:
d1: using said free-running signalRData in (1)R(0)，R(1)，……，R(L-1) calculating a sample functionr(i, j)：
（6）
Wherein,Lfor the free-running response data length,p e in order to expand the order of the order,p e the size is taken asL/2；
D2: constructing an extended matrixR e ：
（7）
D3: for the spreading matrixR e Singular value decomposition is carried out:
（8）
wherein,Hrepresents a conjugate transpose;Uis a matrixR e A matrix composed of the left singular vectors of (a);Vis a matrixR e A matrix composed of right singular vectors of (a); sigma is diagonal matrix, diagonal elements are matrixR e Singular value of，，…，；
D4: according to a matrixR e Singular value determination order ofpAnd constructing a matrixV 1 、 V 2 ：
Comparing elements in a diagonal matrix sigmaFind out to satisfyIs smallest integer ofiOrder of signalp=i(ii) a And constructing a matrixV 1 、 V 2 ：
（9）
（10）
D5: coefficient of calculationa 1 、a 2 、…、a p ：
（11）
Wherein,a= [a 1 ,a 2 , …,a p ]T。
d6: solving the root of the following polynomial
（12）
D7: calculating the frequency of a low frequency oscillation modef i Damping ratio ofd i ，(i=1,2, …,p)
（13）
Wherein:T s for the sampling interval, arctan is an arctangent function, ln is taken from the natural logarithm, Re denotes taking the real part of the complex number, and Im denotes taking the imaginary part of the complex number.
The method is used for extracting free oscillation signals from system full response signals based on an autocorrelation function, and is applied to aspects of mechanical fault diagnosis, structural vibration mode identification and the like. The core of the technology is that the autocorrelation function of the full response of the linear system under the white noise excitation has the same form expression with the free response function of the system, and the free oscillation signal of the system is approximately estimated by solving the autocorrelation function.
The scheme in the embodiment of the present application is introduced through simulation experiments as follows:
the scheme in the embodiment of the application is subjected to simulation verification by adopting an IEEE16 machine 68 node test system, and the system is mainly divided into 5 regions, namely, a region 1 (G1-G9), a region 2 (G10-G13), a region 3 (G14), a region 4 (G15) and a region 5 (G16) as shown in FIG. 2. Through the eigenvalue analysis of the state matrix after the system linearization, 4 dominant oscillation modes exist in the system, as shown in table 1, table 1 is the true value of the low-frequency oscillation mode between 16 machine 68 node system areas, wherein the damping ratio of the modes can be changed by adjusting the PSS parameters of the generator. Mode 1 is where region 1-2 oscillates relative to region 3-5, mode 2 is where region 1-4 oscillates relative to region 5, mode 3 is where region 1 oscillates relative to region 2, and mode 4 is where region 3 and region 5 oscillate relative to region 4. Lines 1-47, lines 68-50, lines 8-9 and lines 67-42 are selected to monitor mode 1, mode 2, mode 3 and mode 4, respectively, for active power.
In order to simulate small-amplitude random disturbance in an actual power system, a random small-amplitude disturbance power signal with the load point amplitude of 0.5% is injected into a main load node of a 16-machine 68 node system, the power disturbance signal is subjected to Gaussian distribution, and the simulation time is 10 minutes. In order to eliminate the contingency of the identification result caused by single power fluctuation, Monte Carlo thought simulation is adopted, 100 times of simulation experiments are carried out, the method in the application is tested from the perspective of probability statistics, and a table 2 shows the identification result of the method in the application.
TABLE 1
TABLE 2
Therefore, the identification result is compared with the real value, the method is adopted to process the random response signal, the average value of the frequency and the damping ratio obtained by multiple experiments is close to the theoretical value, the frequency average value error of each mode is less than 1%, the damping ratio average value error is less than 10%, and the standard deviation of the frequency and the damping ratio is small, so that the method can accurately identify the low-frequency oscillation mode from the random response signal of the power system.
In summary, the invention adopts the method of firstly reading the line active power signal with higher observability to the low-frequency oscillation mode under the condition that a section of the power system has no large disturbance as the signal to be analyzed and determining the sampling time intervalT s (ii) a Then preprocessing the read active power signal to obtain a corresponding power fluctuation signal; solving an autocorrelation function of the power fluctuation signal to obtain a system free oscillation signal; and finally, based on an extended Prony method, carrying out mode identification on the free oscillation signal, and identifying the technical scheme of the low-frequency oscillation mode frequency and the damping ratio, namely, directly utilizing the system random response signal excited by load fluctuation under the normal operation condition of the power grid, and not depending on the free oscillation signal of a large-disturbance excitation system.
As described above, the present invention can be preferably realized.
Claims (5)
1. A method for identifying a low-frequency oscillation mode of a power system based on a correlation function is characterized by comprising the following steps:
step A: reading the line active power signal with high observability to the low-frequency oscillation mode under the condition of no large disturbance of a section of power system as a signal to be analyzed and determining the sampling time intervalT s ；
And B: preprocessing the read active power signal to obtain a corresponding power fluctuation signal;
and C: solving an autocorrelation function of the power fluctuation signal to obtain a system free oscillation signal;
step D: and based on an extended Prony method, carrying out mode identification on the free oscillation signal to obtain the frequency and the damping ratio of a low-frequency oscillation mode.
2. The method for identifying the low-frequency oscillation mode of the power system based on the correlation function of claim 1, wherein the step B: the specific operation steps of preprocessing the read active power signal to obtain a corresponding power fluctuation signal are as follows:
and eliminating abnormal data from the read line active power signal through data preprocessing, filling missing data with the previous normal data when the data are missing, and obtaining a modified active power sequencePAnd then removing the trend term by using a method of subtracting a least square fitting polynomial to obtain the data length ofNPower fluctuation signal deltaP。
3. The method for identifying the low-frequency oscillation mode of the power system based on the correlation function of claim 1, wherein the step C: the power fluctuation signal deltaPObtaining an autocorrelation function of lengthLFree-running response signal ofR(k)(k=0,1,……L-1)；
Wherein:Nas power fluctuation signal deltaPThe length of the data.
4. The method for identifying the low-frequency oscillation mode of the power system based on the correlation function of claim 1, wherein the step D: based on an extended Prony parameter estimation method, carrying out mode identification on the free oscillation response signal, and identifying the frequency and the damping ratio of a low-frequency oscillation mode, wherein the specific operation steps are as follows:
D1: using said free-running signalRData in (1)R(0)，R(1)，……，R(L-1) Computing sample functionsr(i, j)：
Wherein,Lfor the free-running response data length,p e in order to expand the order of the order,p e the size is taken asL/2；
D2: constructing an extended matrixR e ：
；
D3: for the spreading matrixR e Singular value decomposition is carried out:
wherein,Hrepresents a conjugate transpose;Uis a matrixR e A matrix composed of the left singular vectors of (a);Vis a matrixR e A matrix composed of right singular vectors of (a); sigma is diagonal matrix, diagonal elements are matrixR e Singular value of，，…，；
D4: according to a matrixR e Singular value determination order ofpAnd constructing a matrixV 1 、 V 2 ：
Comparing elements in a diagonal matrix sigmaFind out to satisfyIs smallest integer ofiOrder of signalp=i(ii) a And constructing a matrixV 1 、 V 2 ：
，
；
D5: coefficient of calculationa 1 、a 2 、…、a p ：
Wherein,a= [a 1 ,a 2 ,…,a p ]T；
d6: solving the root of the following polynomial
；
D7: calculating the frequency of a low frequency oscillation modef i Damping ratio ofd i ，(i=1,2, …,p)
；
Wherein:T s for the sampling interval, arctan is negative or positiveAnd a tangent function, wherein ln is a natural logarithm, Re represents a real part of a complex number, and Im represents an imaginary part of the complex number.
5. The correlation function-based power system low-frequency oscillation mode identification method as claimed in claim 2, wherein the corrected active power sequence is obtainedPAnd then removing the trend term by using a method of subtracting a least square fitting polynomial to obtain the data length ofNPower fluctuation signal deltaPThe specific operation steps are as follows:
b1: is constructed in a length ofNAt a time interval ofT s Time series ofT；
；
B2: constructing a matrix A;
；
wherein,mis the order of the fitting polynomial;
b3: calculating coefficients of fitting polynomialb；
；
Wherein, the upper labelTRepresenting the transpose, coefficient, of the solving matrix；
B4: determining a power fluctuation signal DeltaP，
。
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