CN115494346A - Polynomial chaotic expansion fault positioning method and system for uncertain parameters of line - Google Patents
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Abstract
The invention discloses a polynomial chaotic expansion fault positioning method and system aiming at uncertain parameters of a line. And then obtaining a training set of a regression model through EMTR correlation coefficient criterion, and realizing the prediction of a fault interval through the regression model. According to the method, the fault interval containing the actual fault position is accurately obtained through simulation example verification, the effective positioning of the fault position is realized, and the problem that a large positioning error exists when the parameters of the power transmission line contain uncertainty in the traditional fault positioning method is solved. The method has potential engineering value in the fault location of the power transmission line.
Description
Technical Field
The invention belongs to the technical field of power transmission line fault positioning, and particularly relates to a polynomial chaotic expansion fault positioning method and system for uncertain parameters of a line.
Background
With the continuous construction of the power grid, the timely and accurate positioning of the fault position in the power transmission line has great significance for the safe and stable operation of the power grid. The application scene of the transmission line is complex, for example, in the ultra-high voltage long-distance transmission, the line crosses different regional landforms, and line parameters such as the ground clearance of an overhead line and the ground conductivity contain certain uncertainty. Therefore, a transmission line fault positioning technology considering uncertainty of line parameters is urgently needed to ensure safe and stable operation of the transmission line.
When the line parameters in the power transmission line have uncertainty, the uncertainty parameters affect the line unit length parameters, and further cause the change of key parameters such as traveling wave speed and transmission line characteristic impedance. In long-distance power transmission, the power transmission line spans different geographical features, and the characteristic wave impedance of the transmission line is inconsistent with the transmission speed of the traveling wave aiming at different soil media. In an urban power distribution network, the problem of uncertainty of the parameters also exists due to the limitation of actual engineering construction and field conditions. The traditional fault positioning technology relies on the extraction of waveform singular points, and the propagation distance is calculated by extracting wave crests and wave heads and combining the wave velocity. When a large error is introduced into key parameters such as wave velocity and the like due to uncertain line parameters, a large error is generated in a fault positioning result.
At present, in the research of the transmission line fault location technology based on Electromagnetic Time Reversal (EMTR) correlation, deterministic line parameter conditions are all based. In consideration of an application scenario of uncertain parameters in an actual power grid, a positioning error can be generated by the current positioning method based on the uncertain parameters. Related reports on line parameter uncertainty considered in transmission line fault location technology research based on electromagnetic time reversal have not been found at present.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide an electromagnetic time reversal polynomial chaos unfolding fault positioning method and system aiming at uncertainty of line parameters, so as to solve the technical problem of large positioning error existing when the parameters of a power transmission line comprise uncertainty in the conventional fault positioning method.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
the invention discloses a polynomial chaotic expansion fault positioning method aiming at uncertain parameters of a line, which comprises the following steps of:
1) Modeling the power transmission line, and determining the distribution type and the distribution interval of uncertain parameters of the line;
2) Performing quantitative analysis on uncertain parameters of the line by adopting a chaotic polynomial method, solving a transfer function from a fault point to a detection point when the power transmission line has a fault after quantization, and establishing a transfer function database considering uncertainty of the line parameters;
3) Extracting a measured signal transfer function according to a fault transient signal obtained by measuring at a detection point, and calculating a correlation coefficient between a transfer function database and the measured signal transfer function to obtain a correlation coefficient training set;
4) Establishing a regression model for the correlation coefficient training set obtained in the step 3) by adopting a regression analysis mode to obtain a fault interval containing the actual fault position.
Preferably, in step 1), the modeling of the power transmission line is to establish a power transmission line simulation model based on the determined parameters by using a transmission line solving algorithm.
Preferably, in step 2), the parameters containing uncertainty are subjected to the unfolding quantitative analysis by using a chaotic polynomial, and the specific calculation method is as follows:
in the formula, xi is a random variable, phi k (ξ) is the basis of the orthogonal polynomial, y (ξ) is the uncertainty parameter to be quantified,
for an approximation function of y (xi) after expansion using a chaotic polynomial, c k For quantizing the system of each orderNumber, P is the order of the polynomial expansion.
Further preferably, in step 2), a transfer function from a fault point to a detection point when the quantized transmission line fault occurs is solved, as follows:
in the formula, H s A transfer function corresponding to a standard random variable xi, namely a proxy model of the transfer function, is obtained through the change of the random variable xi; h k Is H s And (3) coefficients of each order of the expanded chaotic polynomial, namely transfer functions of each order after expansion.
Still further preferably, the transfer function is a function comprising a standard random variable, the type of the standard random variable being determined by the type of the probability distribution function of the line uncertainty parameter;
the value of the uncertain parameter of the original line is mapped by the standard random variable, namely, a mathematical expression of the transfer function changing along with the uncertain parameter is obtained in the transfer function proxy model.
Preferably, in step 3), the method for calculating the correlation coefficient between the transfer function database and the measured signal transfer function is as follows:
in the formula (I), the compound is shown in the specification,
for in a transfer function database
Simulated transfer function of (A)
Transfer function H measured at L from fault occurrence m (k; L); k is transmissionFunction(s)
Indexing the data;
wherein N is the recording length of the transfer function;
is the energy of the transfer function.
Further preferably, a corresponding transfer function is provided under each random variable, and a correlation coefficient calculation is performed with the actually measured fault transfer function, so that a fault position corresponding to the maximum correlation coefficient under each random variable is obtained.
Preferably, in step 4), a support vector machine is used to establish a regression analysis model:
inputting:
↓
fault location interval: [ x ] of lower limit ，x upper limit ]
And outputting the predicted fault position interval through the regression model.
The invention also discloses a system of the electromagnetic time reversal transmission line fault positioning method aiming at the uncertainty of the line parameters, which comprises the following steps:
the power transmission line modeling module is used for determining the distribution type and the distribution interval of uncertain parameters of a line;
the transfer function database construction module is used for carrying out quantitative analysis on parameters containing uncertainty, solving a transfer function from a fault point to a detection point when the power transmission line fault occurs after quantization, and establishing a transfer function database considering the uncertainty of line parameters;
a correlation coefficient training set acquisition module for extracting and acquiring a measured signal transfer function according to the fault transient signal obtained by measuring at the detection point, and calculating the correlation coefficient between the transfer function database and the measured signal transfer function to acquire a correlation coefficient training set;
and the fault section positioning module of the actual fault position is used for establishing a regression model for the correlation coefficient training set by adopting a regression analysis mode to obtain a fault section containing the actual fault position.
Compared with the prior art, the invention has the following beneficial effects:
the invention relates to an EMTR fault location interval prediction technology based on chaotic polynomial expansion, which adopts chaotic polynomial expansion to quantize line uncertainty parameters and establish a power transmission line fault model considering the line uncertainty parameters, thereby obtaining a transfer function from a line head end to a fault point when a fault occurs along the line and establishing a proxy model of the transfer function. And then obtaining a training set of a regression model through EMTR correlation coefficient criterion, and realizing the prediction of a fault interval through the regression model. According to the method, the fault interval containing the actual fault position is accurately obtained through simulation example verification, the effective positioning of the fault position is realized, and the problem that a large positioning error exists when the parameters of the power transmission line contain uncertainty in the traditional fault positioning method is solved. The method has potential engineering value in the fault location of the power transmission line.
Drawings
FIG. 1 is a schematic diagram of overhead line configuration parameters and equivalent circuits of the present invention;
FIG. 2 is a diagram of fault location errors in the presence of line height uncertainty in accordance with the present invention;
FIG. 3 is a graph of the transfer function spectrum for line height uncertainty according to the present invention; wherein (a) is the transfer function amplitude; (b) is the transfer function phase;
FIG. 4 is a graph of the correlation coefficient and predicted position as a function of a random variable ζ in the present invention; wherein (a) is the distribution curve of Max CCv (ζ); (b) is the change situation of the predicted value of the fault position along with zeta;
fig. 5 is a prediction section when there is uncertainty in the line height according to the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, 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.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Moreover, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention is described in further detail below with reference to the accompanying drawings:
the invention discloses an EMTR fault location interval prediction method based on chaotic polynomial expansion, which comprises the following steps of:
the method comprises the following steps: and establishing a power transmission line model according to the actual line parameters. And determining the distribution type and the distribution interval of the uncertain parameters according to the actual line application scene for the line parameters containing the uncertainty.
Step two: and (3) carrying out quantitative analysis on uncertainty parameters by adopting a chaotic polynomial expansion:
in the formula, xi is a random variable, phi k (xi) is the basis of the orthogonal polynomial, y (xi) is the uncertainty parameter to be quantized,
for an approximation function of y (xi) after expansion using a chaotic polynomial, c k For the quantized coefficients of the respective orders, P is the order of the polynomial expansion. Due to the orthogonal characteristic of the orthogonal polynomial, the inner product operation is simultaneously carried out on the orthogonal polynomial by two sides of the above formula, and the coefficient of each order after quantization is obtained.
And establishing a power transmission line model considering parameter uncertainty according to the quantized coefficients. In the transmission line telegraph equation:
and performing uncertain quantization on line parameters Z (omega, xi), Y (omega, xi) and response V (Z, omega, xi) and I (Z, omega, xi) containing random variables by adopting chaos polynomial expansion to obtain:
and (3) performing inner product on orthogonal polynomials at two sides of the above formula:
order to
Definition of
Rewriting the above equation into a matrix form, i.e.:
in the formula (I), the compound is shown in the specification,
the matrix is a (P + 1) × (P + 1) square matrix, the dimension P is related to the chaos polynomial expansion order, and the chaos polynomial expansion coefficient is multiplied by the alpha matrix number to generate the following result:
in the frequency domain calculation, the line subdivision interval distance and the simulation interval frequency can be set according to the information such as the actual line length, the sampling rate of the measurement system, the signal frequency and the like. Solving a transfer function proxy model from a fault point to an observation point in a frequency domain:
in the formula, H s The transfer function corresponding to the standard random variable xi is a proxy model of the transfer function, and the transfer under the uncertain parameter change can be obtained through the change of the random variable xiFunction, H k Is H s And (3) coefficients of each order of the expanded chaotic polynomial, namely transfer functions of each order after expansion.
The transfer function is a function containing a standard random variable, and the type of the standard random variable is determined by the type of a probability distribution function of a line uncertainty parameter; the value of the uncertain parameters of the original line is mapped by the standard random variable, namely, a mathematical expression of the transfer function changing along with the uncertain parameters is obtained in the transfer function proxy model.
Step three: proxy model H of transfer function s Transfer function H of line when actual measurement fault occurs m And calculating a correlation coefficient. And obtaining position information under different values of the random variable xi according to the fault position corresponding to the maximum value of the correlation coefficient.
The method for calculating the correlation coefficient between the transfer function database and the measured signal transfer function comprises the following steps:
in the formula (I), the compound is shown in the specification,
for in a transfer function database
Simulated transfer function of (A)
Transfer function H measured at L from fault occurrence m (k; L); k is a transfer function
Indexing the data;
wherein N is the recording length of the transfer function;
is the energy of the transfer function.
And each random variable has a corresponding transfer function, and correlation coefficient calculation is carried out on the transfer function and the actually measured fault transfer function, so that the fault position corresponding to the maximum correlation coefficient under each random variable can be obtained.
Step four: due to the existence of truncation errors and rounding errors in the calculation process, the maximum value of a curve of the maximum value of the correlation coefficient changing along xi does not appear to be 1. Therefore, the maximum value of the correlation number is extrapolated to the 1 direction by means of regression analysis. In this case, ξ = [0, ξ ] 0 ]Is an independent variable, ξ, of the training set 0 Is the corresponding random variable when the correlation coefficient CCv gets the maximum value:
ξ 0 ＝arg max(CCv)
the dependent variable of the training set is the position coordinate. After the training set is determined, a regression analysis model is established by adopting a support vector machine:
inputting:
↓
fault location interval: [ x ] of lower limit ，x upper limit ]
And outputting the predicted fault position interval through the regression model.
The fault location method of the present invention is described as an application example, and referring to fig. 1, the simulation model of the present invention is used for further detailed description. Take a single overhead line on the lossy ground plane in fig. 1 as an example, where: h is raised and r is radius w Earth conductivity of σ g The earth relative permittivity is epsilon g The electrical conductivity of the wire is σ w . According to the transmission line theory, the inductance L of a single-unit-length line in FIG. 1 and the DC impedance Z of a unit length w Lossy earth impedance per unit length Z g Unit length earth capacitance C, unit length earth admittance G and unit length earth admittance Y g Can be expressed as:
in the formula, gamma g Is the earth propagation constant, and the specific expression is
Assuming that the line elevations obey a uniform distribution between [10,20] m, the measured fault signal is equivalent to an elevation of 17m along the line, with height as a parameter that includes uncertainty. During simulation modeling, the transmission line height is subject to uniform distribution between [10,20] m, and 10000 random numbers are generated in the interval according to uniform distribution by adopting a Monte Carlo method and used as the transmission line height during simulation. At this time, the EMTR correlation coefficient criterion is adopted, and the positioning errors at the actual fault positions (1km, 10km,20km,30km, 40km) are shown in fig. 2, and the positioning errors increase with the increase of the fault distance.
The transmission line frame heights are uniformly distributed between [10,20] m, and the expression is as follows:
h＝15+2.89ξ
at this time, in the unit length parameter of the line, the uncertainty of the earth electric conductivity is transferred to the earth impedance and admittance per unit length:
the chaos polynomial is adopted to expand the above formula, and the expanded telegraph equation is solved to obtain the transfer function of the proxy model as shown in fig. 3. In fig. 3, the amplitude (a) and phase (b) of the transfer function at ± σ (variance) are given at the fault location of 45 km.
And (4) carrying out correlation coefficient calculation and statistics on the proxy model of the transfer function and the transfer function of the actually measured fault to obtain a curve of the maximum value of the correlation number and the variation of the predicted fault position with xi in the graph 4. As can be seen from the figure, the maximum value of the correlation coefficient maximum value curve is less than 1. Therefore, the data corresponding to the red partial curve in fig. 4 is used as a training set of the regression model to establish a fault interval prediction regression model.
Fig. 5 shows the prediction result of the regression model established in fig. 4, when the actual fault location occurs at 45km, and after the regression model is established by using the support vector machine, the obtained fault location interval is [44.84,45.13] km, where 44.84km is the lower limit of the fault prediction interval, i.e. lower limit,45.13 is the upper limit of the fault prediction interval, i.e. 45.13km, and the interval accurately contains the actual fault location.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (9)
1. A polynomial chaotic expansion fault positioning method aiming at uncertain parameters of a line is characterized by comprising the following steps:
1) Modeling the power transmission line, and determining the distribution type and the distribution interval of uncertain parameters of the line;
2) The method comprises the steps of carrying out quantitative analysis on uncertain parameters of a line by adopting a chaotic polynomial method, solving a transfer function from a fault point to a detection point when a fault of a power transmission line occurs after quantization, and establishing a transfer function database considering uncertainty of the parameters of the line;
3) Extracting a measured signal transfer function according to a fault transient signal obtained by measuring at a detection point, and calculating a correlation coefficient between a transfer function database and the measured signal transfer function to obtain a correlation coefficient training set;
4) Establishing a regression model for the correlation coefficient training set obtained in the step 3) by adopting a regression analysis mode to obtain a fault interval containing the actual fault position.
2. The electromagnetic time reversal transmission line fault location method for line parameter uncertainty according to claim 1, characterized in that in step 1), modeling the transmission line is to establish a transmission line simulation model based on the determined parameters by using a transmission line solution algorithm.
3. The electromagnetic time reversal transmission line fault location method for line parameter uncertainty according to claim 1, characterized in that in step 2), parameters containing uncertainty are quantitatively analyzed by using chaotic polynomial expansion, and a specific calculation method is as follows:
in the formula, xi is a random variable, phi k (xi) is the basis of the orthogonal polynomial, y (xi) is the uncertainty parameter to be quantized,
to adopt an approximation function of y (xi) after the chaos polynomial expansion, c k For each order of quantized coefficients, P is the order of the polynomial expansion.
4. The electromagnetic time reversal transmission line fault location method for line parameter uncertainty as recited in claim 3, wherein in step 2), a transfer function from a fault point to a detection point when the quantized transmission line fault occurs is solved as follows:
in the formula, H s The transfer function corresponding to the standard random variable xi is the proxy model of the transfer function, and the uncertain parameter variation is obtained through the variation of the random variable xiA transfer function of; h k Is H s And (3) coefficients of each order of the expanded chaotic polynomial, namely transfer functions of each order after expansion.
5. The electromagnetic time-reversal transmission line fault location method for line parameter uncertainty according to claim 4, characterized in that the transfer function is a function containing a standard random variable, the type of the standard random variable being determined by the type of the probability distribution function of the line uncertainty parameter;
the value of the uncertain parameter of the original line is mapped by the standard random variable, namely, a mathematical expression of the transfer function changing along with the uncertain parameter is obtained in the transfer function proxy model.
6. The electromagnetic time reversal transmission line fault location method for line parameter uncertainty according to claim 1, characterized in that in step 3), the correlation coefficient calculation method between the transfer function database and the measured signal transfer function is as follows:
in the formula (I), the compound is shown in the specification,
for in a transfer function database
Simulated transfer function of
Transfer function H measured at L from fault occurrence m (k; L); k is a transfer function
Indexing the data;
wherein N is the recording length of the transfer function;
is the energy of the transfer function.
7. The electromagnetic time reversal transmission line fault location method for line parameter uncertainty according to claim 6, characterized in that a corresponding transfer function exists under each random variable, correlation coefficient calculation is performed with an actually measured fault transfer function, and a fault position corresponding to a maximum correlation coefficient under each random variable is obtained.
8. The electromagnetic time reversal transmission line fault location method for line parameter uncertainty according to claim 1, characterized in that in step 4), a support vector machine is used to build a regression analysis model:
and outputting the predicted fault position interval through the regression model.
9. The system for electromagnetic time reversal transmission line fault location for line parameter uncertainty according to any of the preceding claims 1-8, comprising:
the power transmission line modeling module is used for determining the distribution type and the distribution interval of uncertain parameters of a line;
the transfer function database construction module is used for carrying out quantitative analysis on parameters containing uncertainty, solving a transfer function from a fault point to a detection point when the power transmission line fault occurs after quantization, and establishing a transfer function database considering the uncertainty of line parameters;
a correlation coefficient training set acquisition module, configured to extract a measurement signal transfer function according to a fault transient signal obtained by measurement at a detection point, and calculate a correlation coefficient between a transfer function database and the measurement signal transfer function to obtain a correlation coefficient training set;
and the fault section positioning module of the actual fault position is used for establishing a regression model for the correlation coefficient training set by adopting a regression analysis mode to obtain a fault section containing the actual fault position.
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