CN110932755A - Distributed low-voltage distribution network line parameter estimation method based on recursive least square method - Google Patents
Distributed low-voltage distribution network line parameter estimation method based on recursive least square method Download PDFInfo
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Abstract
The invention discloses a distributed low-voltage distribution network line parameter estimation method based on a recursive least square method, which comprises the following steps: firstly, numbering power line sections and nodes according to a low-voltage distribution network topology, and establishing an equation set according to a kirchhoff voltage law and a kirchhoff current law; secondly, cleaning abnormal data of the measured data acquired by the centralized meter reading system or the intelligent electric meter by a low-pass filtering processing method; thirdly, performing mathematical modeling on the line parameter estimation according to a least square method, designing recursive least square estimation parameters, and designing a line impedance parameter estimation algorithm by adopting the recursive least square method; and fourthly, carrying out reliability analysis on the line parameter estimation result by adopting kernel estimation and point estimation.
Description
Technical Field
The invention relates to a distributed low-voltage distribution network line parameter estimation method based on a recursive least square method, and belongs to the field of distribution network state estimation.
Background
With the rapid development of the times, the low-voltage distribution network has numerous branches, complex structure and quick change, and brings great challenges to the safe and stable operation of the distribution network. On one hand, line aging is caused by the increase of the service time of the line, the corrosion of a severe natural environment and other reasons, and line parameters are greatly changed due to the influence of construction, transformation, accidents and the like; on the other hand, in the case of a low-voltage distribution network with large and complex branches, line parameters are still in the monitoring blank, and huge manpower and material resources are needed for additionally installing a measuring device.
The PMU is high in cost and is mainly arranged at outgoing lines of 500kV transformer substations and important power plants, so that a low-voltage distribution network line is generally not provided with a PMU synchronous measuring device, and a large amount of measured data based on a centralized meter reading system or a household intelligent electric meter can be obtained in the low-voltage distribution network. The least square method is used as a non-statistical parameter estimation method, and in a random environment, probability statistical information of the measured data does not need to be known, but an obtained estimation result has better statistical property, so that the method has better tolerance capability. Therefore, how to utilize the existing measurement data and establish a simple, practical and accurate line parameter estimation method aiming at the line parameter characteristics of the low-voltage distribution network has strong practical significance for improving the analysis and operation level of the distribution network.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems and the defects in the prior art, the invention provides a distributed low-voltage distribution network line parameter estimation method based on a recursive least square method, which can simply and accurately estimate the low-voltage distribution network line parameters.
The technical scheme is as follows: a distributed low-voltage distribution network line parameter estimation method based on a recursive least square method is characterized by comprising the following steps:
firstly, numbering power line sections and nodes according to a low-voltage distribution network topology, and establishing an equation set according to a kirchhoff voltage law and a kirchhoff current law;
secondly, cleaning abnormal data of the measured data acquired by the centralized meter reading system or the intelligent electric meter by a low-pass filtering processing method;
thirdly, performing mathematical modeling on the line impedance parameter estimation according to a least square method, designing recursive least square estimation parameters, and designing a line impedance parameter estimation algorithm by adopting the recursive least square method;
and fourthly, carrying out reliability analysis on the line parameter estimation result by adopting kernel estimation and point estimation.
Preferably, in the first step, the secondary side of the low-voltage distribution network transformer is taken as a first node, the other nodes of the distribution network are numbered in sequence, an equation set is established according to KVL and KCL, the equation set is rewritten into a matrix form, and finally a state estimation equation of the low-voltage distribution network topology is obtained through the property of matrix elementary transformation.
Preferably, in the second step, a low-pass filtering algorithm is used to filter abnormal data in the input data:
where x represents the input data, y represents the filtered data, s represents the laplacian operator,
the cut-off frequency is indicated.
Preferably, in the third step, the line parameters of the low-voltage distribution network are regarded as unchanged, and the effective values of the voltage and the current obtained by the centralized meter reading system are substituted into a least square recursion equation for calculation.
Preferably, in the fourth step, a kernel density estimation and point estimation method is adopted to obtain probability density distribution, a confidence interval, expectation and variance of the line parameter estimation result, and then reliability analysis is performed on the line parameter estimation result.
Preferably, in the fourth step, a gaussian kernel function is used to perform reliability analysis on the result, and the probability density function of the line parameter estimation result can be obtained through gaussian kernel density estimation and then obtained through gaussian kernel density estimation
Obtaining a value containing a true value of a parameterpConfidence of 1-
The confidence interval of (c).
Preferably, in the fourth step, the point estimation method uses moment estimation, without assuming its data distribution,
in the formula (I), the compound is shown in the specification,
and
respectively as low-voltage distribution network line parameter estimation result samples
The expectation and the variance of the signals to be measured,
represents the total number of samples.
Has the advantages that: compared with the prior art, the distributed low-voltage distribution network line parameter estimation method based on the recursive least square method can realize distributed real-time calculation of line impedance parameters, has real-time performance, and can eliminate the problem that the two sampling data of the least square method are the same when the load changes slightly, so that the problem is solved.
Drawings
Fig. 1 is a schematic diagram illustrating a principle of analyzing a topology of a low-voltage distribution network according to an embodiment of the present invention.
FIG. 2 is a flow chart of an embodiment of the present invention.
FIG. 3 is a schematic diagram of a recursive least squares calculation.
Detailed Description
The invention is further elucidated with reference to the drawings and the embodiments.
As shown in fig. 1 to 3, the present embodiment provides a distributed low-voltage distribution network line parameter estimation method based on a recursive least square method, which is used for a low-voltage ac distribution network, and the specific method includes the following steps:
firstly, numbering power line sections and nodes according to a low-voltage distribution network topology, and establishing an equation set according to a Kirchhoff Voltage Law (KVL) and a Kirchhoff Current Law (KCL);
as shown in fig. 1, the topology of the low-voltage distribution network in this example is read, and the nodes are numbered 1 to 10, whereu gRepresenting the voltage on the secondary side of the distribution network transformer,xthe parameters of the line are represented by,u 2…u 4,u 6…u 10which is indicative of the voltage at each node,i 3,i 4,i 6…i 10each of the load currents is represented individually,i 12represents the line current;
taking node 10 as an example, modeling is performed according to KVL and KCL:
the parameters marked by the dotted lines in the attached figure 1 are measured and the above formula is rewritten as follows:
throughnThe secondary measurement can be obtainednThe system of equations:
writing the above formula into matrix form
Namely, it is
Matrix arrayHAndyare all measured values.
And secondly, reading N groups of measured data from the centralized meter reading system, and processing abnormal data. The abnormal data can influence the calculation precision of the least square method, and the basic idea of abnormal data cleaning is to filter the abnormal data in the input data by adopting a low-pass filtering algorithm:
x represents input data, y represents filtered data, s represents the laplacian operator,
the cut-off frequency is indicated.
Thirdly, performing mathematical modeling on the line parameter estimation according to a least square method, designing recursive least square estimation parameters, and designing a line impedance parameter estimation algorithm by adopting the recursive least square method;
according to the line parameter estimation method based on the recursive least square method, line impedance parameters are estimated according to sampling data, low-voltage distribution network line parameters are considered to be slow in change, and the low-voltage distribution network is short in line and basically has pure resistance characteristics, so that the low-voltage distribution network can be approximated to a pure resistance network, voltage and current effective values obtained by a centralized meter reading system can be substituted into a state estimation equation for calculation, and a synchronous measurement device such as a PMU (phasor measurement unit) is not needed.
A schematic diagram of calculation by the recursive least square method is shown in fig. 3, and impedance parameter estimation can be performed according to the recursive least square method:
wherein I represents an identity matrix and R is a measured noise covariance matrix, which may beaI，aFor the adjustable coefficient, 0.1 can be generally adopted for adjusting the convergence rate.
And fourthly, obtaining a large amount of power distribution network measurement data according to the centralized meter reading system, and further obtaining a large amount of line parameter estimation results of the multiple-time discontinuities, so that probability density distribution, confidence intervals, expectation, variance and the like of the line parameter estimation results are obtained by adopting a kernel density estimation and point estimation method in the step, and reliability analysis is carried out on the line parameter estimation results.
The kernel density estimation does not need prior knowledge about data distribution, namely, no hypothesis is made on the data distribution, the method is a method for researching data distribution characteristics directly from sample data, and the result is subjected to reliability analysis by adopting a Gaussian kernel function in the step. The probability density function of a large number of line parameter estimation results can be obtained through Gaussian kernel density estimation and then
Obtaining a value containing a true value of a parameterpHas a confidence of
A confidence interval.
In addition, the low-voltage distribution network line parameter estimation result is generally a single result, and the point estimation is a method for estimating an overall parameter by using sample statistics, and comprises moment estimation, maximum likelihood estimation and the like. The moment estimation adopted in the step does not need to assume the data distribution, and has the characteristics of unbiasedness, effectiveness, consistency and the like.
In the formula (I), the compound is shown in the specification,
and
respectively as a distribution network line parameter estimation result sample
The expectation and the variance of the signals to be measured,
represents the total number of samples.
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.
Claims (7)
1. A distributed low-voltage distribution network line parameter estimation method based on a recursive least square method is characterized by comprising the following steps:
firstly, numbering power line sections and nodes according to a low-voltage distribution network topology, and establishing an equation set according to a kirchhoff voltage law and a kirchhoff current law;
secondly, cleaning abnormal data of the measured data acquired by the centralized meter reading system or the intelligent electric meter by a low-pass filtering processing method;
thirdly, performing mathematical modeling on the line impedance parameter estimation according to a least square method, designing recursive least square estimation parameters, and designing a line impedance parameter estimation algorithm by adopting the recursive least square method;
and fourthly, carrying out reliability analysis on the line parameter estimation result by adopting kernel estimation and point estimation.
2. The distributed low-voltage distribution network line parameter estimation method based on the recursive least square method according to claim 1, characterized in that in the first step, the secondary side of the low-voltage distribution network transformer is taken as a first node, the other nodes of the distribution network are numbered in sequence, an equation set is established according to KVL and KCL and is rewritten into a matrix form, and finally, a state estimation equation of the low-voltage distribution network topology is obtained through the property of matrix elementary transformation.
3. The distributed low voltage distribution network line parameter estimation method based on recursive least squares according to claim 2, characterized in that in the second step, the abnormal data in the input data will be filtered with a low pass filtering algorithm:
where x represents the input data, y represents the filtered data, s represents the laplacian operator,
the cut-off frequency is indicated.
4. The distributed low-voltage distribution network line parameter estimation method based on the recursive least square method according to claim 3, wherein in the third step, the low-voltage distribution network line parameters are regarded as unchanged, and the effective values of the voltage and the current obtained by the centralized meter reading system are substituted into a least square recursive equation for calculation.
5. The distributed low-voltage distribution network line parameter estimation method based on the recursive least square method according to claim 4, characterized in that in the fourth step, a kernel density estimation and point estimation method is adopted to obtain a probability density distribution, a confidence interval, an expectation and a variance of a line parameter estimation result, and then a reliability analysis is performed on the line parameter estimation result.
6. The distributed low-voltage distribution network line parameter estimation method based on the recursive least square method as claimed in claim 5, wherein in the fourth step, a Gaussian kernel function is adopted to perform reliability analysis on the result, the probability density function of the line parameter estimation result can be obtained through Gaussian kernel density estimation, and then the probability density function is obtained through the Gaussian kernel density estimation
Obtaining a value containing a true value of a parameterpConfidence of 1-
The confidence interval of (c).
7. The distributed low voltage distribution network line parameter estimation method based on recursive least squares method according to claim 6, characterized in that in the fourth step, the point estimation method uses moment estimation without assuming its data distribution,
in the formula (I), the compound is shown in the specification,
and
respectively as low-voltage distribution network line parameter estimation result samples
The expectation and the variance of the signals to be measured,
represents the total number of samples.
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