CN117630487A - System harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm - Google Patents
System harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm Download PDFInfo
- Publication number
- CN117630487A CN117630487A CN202311386585.0A CN202311386585A CN117630487A CN 117630487 A CN117630487 A CN 117630487A CN 202311386585 A CN202311386585 A CN 202311386585A CN 117630487 A CN117630487 A CN 117630487A
- Authority
- CN
- China
- Prior art keywords
- harmonic
- point
- impedance
- harmonic impedance
- points
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 126
- 230000011218 segmentation Effects 0.000 title claims abstract description 48
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 37
- 238000004364 calculation method Methods 0.000 claims abstract description 29
- 230000008859 change Effects 0.000 claims abstract description 24
- 230000002159 abnormal effect Effects 0.000 claims abstract description 19
- 238000012216 screening Methods 0.000 claims abstract description 17
- 239000011159 matrix material Substances 0.000 claims description 15
- 230000008569 process Effects 0.000 claims description 14
- 238000012360 testing method Methods 0.000 claims description 12
- 238000005070 sampling Methods 0.000 claims description 8
- 238000007689 inspection Methods 0.000 claims description 4
- 238000000342 Monte Carlo simulation Methods 0.000 claims description 3
- 238000001514 detection method Methods 0.000 claims description 3
- 238000001914 filtration Methods 0.000 claims description 3
- 238000005259 measurement Methods 0.000 claims description 3
- 230000009191 jumping Effects 0.000 claims description 2
- 230000035772 mutation Effects 0.000 abstract description 12
- 238000004088 simulation Methods 0.000 abstract description 8
- 230000000694 effects Effects 0.000 abstract description 6
- 230000002411 adverse Effects 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 4
- 238000012417 linear regression Methods 0.000 description 4
- 238000004458 analytical method Methods 0.000 description 3
- 230000008878 coupling Effects 0.000 description 2
- 238000010168 coupling process Methods 0.000 description 2
- 238000005859 coupling reaction Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000005192 partition Methods 0.000 description 2
- 241000669618 Nothes Species 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 239000003990 capacitor Substances 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000002452 interceptive effect Effects 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 238000013450 outlier detection Methods 0.000 description 1
- 230000001172 regenerating effect Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000012106 screening analysis Methods 0.000 description 1
- 230000001360 synchronised effect Effects 0.000 description 1
- 230000007704 transition Effects 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/40—Arrangements for reducing harmonics
Landscapes
- Measurement Of Resistance Or Impedance (AREA)
Abstract
According to the system harmonic impedance estimation method based on the LOF screening-heuristic segmentation algorithm, firstly, pearson correlation coefficient is used for screening to obtain data with strong correlation between harmonic voltage and current amplitude, and then an LOF method is used for eliminating abnormal values in the data, so that the influence of background harmonic fluctuation and the abnormal values on an impedance estimation result is reduced; then, a heuristic segmentation algorithm is used for checking the harmonic impedance mutation points of the system, so that the real-time estimation of the harmonic impedance is realized, and the calculation error is reduced; and finally, calculating the harmonic impedance of the system by using a complex domain robust regression method, so that errors caused by the fact that the real part and the imaginary part of the harmonic data vector are calculated separately by using a traditional robust regression method can be effectively eliminated. Simulation and experimental results show that the method is effective and correct, and the method provided by the invention can reduce adverse effects on impedance calculation caused by background harmonic voltage fluctuation and system harmonic impedance change, and has a wider application range.
Description
Technical Field
The invention relates to the technical field of electric power harmonic impedance calculation, in particular to a system harmonic impedance estimation method based on an LOF screening-heuristic segmentation algorithm.
Background
With the rapid development of power electronics technology, the number of harmonic sources of a power system is increased sharply based on large-scale distributed power grid connection mainly of photovoltaic and wind power, and the injected harmonic has new characteristics of uncertainty, fluctuation, intermittence and the like, so that new challenges are brought to analysis of harmonic problems of the power system. In order to accurately divide the harmonic responsibilities, effectively manage the harmonic pollution, it is necessary to effectively evaluate the harmonic emission levels at the system side and the user side at the point of common coupling (point of common coupling, PCC).
The premise of the harmonic emission level evaluation is to accurately evaluate the system harmonic impedance. The existing harmonic impedance calculation methods are mainly divided into an 'intervention type' method and a 'non-intervention type', wherein the 'intervention type' method needs to inject disturbance into a system or change a network topology structure of the system to estimate the harmonic impedance of the system, but the method can have adverse effects on the normal operation of the system. The non-intervention method is to calculate the harmonic impedance by using the load or the natural disturbance of the system and the measurable parameters under the condition of not interfering the normal operation of the system, and the method has no influence on the normal operation of the system and is widely adopted. The existing method comprises the following steps: fluctuation amount method, linear regression method, independent component method, covariance method, etc.
Non-intrusive methods are susceptible to background harmonic fluctuations and abrupt changes in system harmonic impedance. For the problem of background harmonic fluctuation, the current common solution is to obtain data segment calculation with strong correlation of harmonic voltage and harmonic current at PCC through data screening. The change of the operation mode of the power system, the change of the switching capacitor bank or the reactive compensation mode and the like are all main reasons for the change of the harmonic impedance of the system, so that the research on the abrupt change of the harmonic impedance of the system is less at present, and if the abrupt change of the impedance is not considered and calculated by using a traditional method, the real-time performance of an estimation result is poor and the error is larger.
Therefore, the invention provides a new harmonic impedance estimation method based on an LOF screening-heuristic segmentation algorithm, which comprises the steps of firstly screening and obtaining data with strong correlation between harmonic voltage and current amplitude by using a Pearson correlation coefficient, and then removing abnormal values in the data by using the LOF method, so as to reduce the influence of background harmonic fluctuation and the abnormal values on an impedance estimation result. And then, the system harmonic impedance abrupt change points are checked by using a heuristic segmentation algorithm, so that the real-time estimation of the harmonic impedance is realized and the calculation error is reduced. The system harmonic impedance is then calculated using a complex domain robust regression method. Simulation and experimental results show that the method provided by the invention has the effectiveness and correctness, and provides a new thought for the problem of harmonic impedance estimation under the scenes of background harmonic fluctuation and impedance mutation.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a system harmonic impedance estimation method based on an LOF screening-heuristic segmentation algorithm, which can well reduce the influence of background harmonic fluctuation and abnormal values on an impedance estimation result, can detect an impedance abrupt change time point, realizes real-time estimation of harmonic impedance, has a wider application range, and solves the problems in the background art.
In order to achieve the above purpose, the present invention provides the following technical solutions: a system harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm comprises the following steps:
s1, screening out a period with smaller background harmonic fluctuation based on a Pearson correlation coefficient, and removing abnormal values in harmonic data by using an LOF method;
s2, detecting and segmenting a time point when the harmonic impedance of the system is suddenly changed based on a heuristic segmentation algorithm;
s3, estimating the harmonic impedance of the system based on a complex domain robust regression method.
Preferably, in step S1, the filtering out the period with smaller background harmonic fluctuation based on the Pearson correlation coefficient, and removing the outlier in the harmonic data by using the LOF method specifically includes: sliding window is arranged, and harmonic voltage is calculated in sliding modeAnd current amplitude->Correlation coefficient of subsequence, screening R>0.9, and eliminating harmonic data outliers according to the data point density condition by using a LOF method.
Preferably, the step S1 specifically includes:
and->The calculation formula of the Pearson correlation coefficient is as follows
Wherein:and->Is the ith harmonic voltage and current data; m is the sampling window width, namely the number of harmonic voltage and current data in the concerned time period; />And->The average value of the harmonic voltage and the current of the corresponding sampling window is obtained; r is E (-1, 1).
After screening out a harmonic data subsequence with relatively stable background harmonic, an LOF method is used for eliminating abnormal values possibly existing in the data.
Preferably, the LOF method specifically includes:
(1) d (p, o) represents the distance between p and o.
(2) Kth distance (k-distance)
The kth distance d from the point p k (p), defined as: d, d k (p) =d (p, o), satisfying the following two conditions.
a) At least k points o 'excluding p are included in the set, so that d (p, o')isless than or equal to d (p, o);
b) There are at most k-1 points o 'in the set that do not include p, such that d (p, o') < d (p, o).
In short, p is taken as a center of a circle and radiates outwards until the kth adjacent point is covered.
(3) Kth distance neighborhood
Kth distance neighborhood N of data point p k (p) pointing to a set of all points within the kth distance of p, including points at the kth distance. It can be seen that N k (p)|≥k。
(4) Kth reachable distance
reach_dist k (o,p)＝max{d k (o),d(o,p)} (13)
The kth reachable distance of data point o to data point p is defined as the greater of the kth distance of point o and the distance of point o to point p.
(5) Local reachable density
The kth local reachable density of data point p, i.e., the inverse of the average kth reachable distance from point p to all points within the kth distance neighborhood of point p. The density of the point p is represented, and the higher the density of the point p and surrounding points is, the smaller the reachable distance of each point is, and the larger the lrd value is; the lower the concentration of the point p with the surrounding points, the larger the reachable distance of the points is the actual distance between the two points, and the larger the lrd value is.
(6) Local outlier factor
The kth local outlier factor of the data point p, meaning N of the point p k (p) comparing the average local reachable density of all points in the neighborhood with the local reachable density of point p, the greater the ratio is 1, indicating that the less the density of p points is than the density of points around it, p points being outliers; the smaller this ratio is than 1, indicating that the density of p-points is greater than that of its surrounding points, p-points being normal points.
Preferably, the step S2 specifically includes:
coarse estimates of system harmonic impedance are calculated using the principle of the ratio method to segment the data points. When the background harmonic is relatively stable, the number of harmonic sample data is assumed to be P, and each harmonic data point isA coarse estimate of the system harmonic impedance can be approximated by the following equation.
Calculating harmonic impedance rough estimation values of all adjacent two data points through a formula (5), then using a heuristic segmentation algorithm (BG algorithm) to test system harmonic impedance mutation points, setting a time sequence consisting of N system harmonic impedance rough estimation values calculated by the formula (5) as x (t), sliding and selecting a segmentation point i from the left side to the right side of the sequence, and calculating the average value mu of the left side and the right side of each segmentation point 1 (i) Sum mu 2 (i) Standard deviation s 1 (i) Sum s 2 (i) Merging deviation S of i points D (i) Is that
Wherein N is 1 ,N 2 Points of the subsequences on the left and right sides of the i point are respectively indicated.
The statistical value T (i) of the T test is used to quantify the mean difference of the subsequences on the left and right sides of the partition point i, as follows.
Repeating the calculation process for each point in the harmonic impedance time sequence x (T) to obtain a detection statistical value sequence T (T) corresponding to the sequence x (T), wherein the larger the T is, the larger the average value phase difference between the sub-sequences at the left and right sides of the division point is. Then calculate the maximum value T in T (T) max Statistical significance of P (T) max )。
P(T max )＝Prob(T≤T max ) (19)
Wherein P (T) max ) Indicating that T value is less than or equal to T in the random process max Is a probability of (2).
In general P (T) max ) Can be approximated as
Wherein the variables are test formulas obtained by Monte Carlo simulation, eta=4.19 lnN-11.54, delta=0.40, N is the length of time series x (t), v=N-2,as an incomplete beta function, the expression is
In harmonic impedance discontinuity inspection, a threshold value P is set 0 If P (T) max )≥P 0 The harmonic impedance sequence x (t) is split into two sub-sequences with different mean values at the point, otherwise, the sub-sequences are not split.
Similarly, the above steps are repeated for the new sub-sequence after segmentation, if the sub-sequence has P (T max )≥P 0 And the average value difference degree between the subsequence and the subsequence adjacent to the left and right meets the conditions, if the subsequence is divided, otherwise, the subsequence is not divided. Repeating the steps until the length of all the subsequences is less than or equal to l 0 (l 0 Is the smallest segmentation scale) is not segmented any more. Through the operation, the harmonic impedance sequence x (t) can be divided into a plurality of subsequences with different average values, and the dividing point is the time point when the harmonic impedance of the system is suddenly changed. Generally, l 0 ≥25,P 0 ∈[0.5,0.95]。
Preferably, the step S3 specifically includes:
if the measurement error of the harmonic data is considered, the harmonic impedance linear equation can be expressed as
Where ε is a complex error term.
By screening and abrupt checking a certain group of harmonic voltage and current data after segmentation, it can be obtained by the formula (12)
Writing it in matrix form
Y＝βX+ε (24)
In the method, in the process of the invention,
in the formula, the symbol "Θ" means "written as".
To obtain a complex domain robust regression model, first, looking at a complex least squares basic principle, the complex error square sum minimum relationship is as follows, namely, the complex error square sum minimum relationship satisfies
Element X in complex vector matrix X k (k=1, 2) is rewritten as real and imaginary parts, i.e.Then Q is converted to about->And->Is a function of (i.e.)
According to the extremum principle in the differential science, the solution obtained by the following formula (16) is the complex least square solution of the complex vector matrix X.
The objective function of complex-domain robust regression can be expressed as
Wherein omega is i Is a weight coefficient.
There are many ways to construct weights, and the present invention chooses to use the Huber method to define weights.
Diagonalizing the weights calculated in equation (27), i.e
Wherein, c h Is constant, typically 1.345; u (u) i Is a normalized residual.
u i ＝ε i /s (31)
s＝mid(ε)/0.6745 (32)
mid(ε)＝Middle|ε i -Middle(ε)| (33)
Wherein s is the residual scale; middle (epsilon) is the median of the elements in vector epsilon.
The basic steps of complex domain robust regression calculation are as follows:
1) Firstly, calculating to obtain a parameter vector by using a complex least square method
Wherein: k is the iteration number, the symbol' "is the transpose of the matrix, the symbol" -1 "is the inversion of the matrix and the symbol" - "is the complex conjugate.
In the method, in the process of the invention,
2) Calculating to obtain complex residual error vector epsilon (k) The normalized residual vector u is calculated by the formulas (20), (21), (22) (k) ；
3) The weight vector omega is calculated by using the Huber method and is converted into a diagonal matrix W * ；
4) Calculating the estimated value of complex domain robust regression, namely
5) Comparing the current estimation result with the last one, ifSatisfy |X k+1 -X k |<Mu condition (mu is check accuracy, generally set to 10 -5 ) And ending the iterative process, otherwise, jumping to the second loop until convergence.
The beneficial effects of the invention are as follows: the invention uses Pearson correlation coefficient to screen and obtain the data with strong correlation between the harmonic voltage and the current amplitude, and then eliminates the abnormal value in the data by using the LOF method, thereby reducing the influence of background harmonic fluctuation and the abnormal value on the impedance estimation result; the invention uses heuristic segmentation algorithm to test the harmonic impedance mutation points of the system, thereby realizing the real-time estimation of the harmonic impedance and reducing the calculation error; the invention uses the complex domain robust regression method to calculate the system harmonic impedance, and can effectively eliminate errors caused by the fact that the traditional robust regression method separately calculates the real part and the imaginary part of the harmonic data vector. The method provided by the invention can reduce adverse effects on impedance calculation caused by background harmonic voltage fluctuation and system harmonic impedance change, and has better precision and wider application range compared with a general linear regression method.
Drawings
FIG. 1 is a flow chart of a system harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm in the method of the present invention;
FIG. 2 is a diagram of a Norton equivalent circuit in the method of the present invention;
FIG. 3 is a schematic diagram of the 5 th distance of data point p in the LOF method in the method of the present invention;
FIG. 4 shows the data points p and o in the LOF method of the present invention 1 ,o 2 Is a schematic diagram of the reachable distance of (a);
FIG. 5 is an equivalent model of abrupt impedance transitions in the method of the present invention;
FIG. 6 is an IEEE14 node system equivalent model of an embodiment of the invention;
FIG. 7 is a plot of harmonic data at the PCC, FIG. 7 (a) is harmonic voltage magnitude and phase angle data, and FIG. 7 (b) is harmonic current magnitude and phase angle data, according to an embodiment of the present invention;
FIG. 8 is a plot of harmonic voltage versus current amplitude scatter in an embodiment of the invention;
FIG. 9 is a plot of harmonic voltage versus current amplitude for a filter using Pearson correlation coefficients in an embodiment of the invention;
FIG. 10 is a plot of harmonic voltage versus current amplitude scatter after outliers are removed by LOF in an embodiment of the present invention;
FIG. 11 is a graph of the result of identifying impedance discontinuities by a heuristic segmentation algorithm in an embodiment of the present invention;
fig. 12 shows the error contrast of the methods according to the embodiment of the present invention, fig. 12 (a) shows the amplitude error contrast, and fig. 12 (b) shows the phase angle error contrast.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
The invention provides a system harmonic impedance estimation method based on an LOF screening-heuristic segmentation algorithm. Firstly, data with strong correlation between harmonic voltage and current amplitude is obtained by using Pearson correlation coefficient screening, and then abnormal values in the data are removed by using an LOF method, so that the influence of background harmonic fluctuation and the abnormal values on impedance estimation results is reduced. And then, the system harmonic impedance abrupt change points are checked by using a heuristic segmentation algorithm, so that the real-time estimation of the harmonic impedance is realized and the calculation error is reduced. And finally, calculating the harmonic impedance of the system by using a complex domain robust regression method, so that errors caused by the fact that the real part and the imaginary part of the harmonic data vector are calculated separately by using a traditional robust regression method can be effectively eliminated. Simulation and experimental results show the effectiveness and correctness of the method, and a new idea is provided for the problem of harmonic impedance estimation under the scenes of background harmonic fluctuation and impedance mutation.
The harmonic impedance calculation method taking background harmonic voltage fluctuation and impedance change into consideration, as shown in fig. 1, comprises the following steps:
s1, screening out a period with smaller background harmonic fluctuation based on a Pearson correlation coefficient, and removing abnormal values in harmonic data by using an LOF method;
s2, detecting and segmenting a time point when the harmonic impedance of the system is suddenly changed based on a heuristic segmentation algorithm;
s3, estimating the harmonic impedance of the system based on a complex domain robust regression method.
The system harmonic impedance estimation method based on the LOF screening-heuristic segmentation algorithm can accurately estimate the system harmonic impedance under the conditions of background harmonic fluctuation and impedance mutation.
Further, step1 includes: sliding window is arranged, and harmonic voltage is calculated in sliding modeAnd current amplitude->Correlation coefficient of subsequence, screening R>0.9, and eliminating harmonic data outliers according to the data point density condition by using a LOF method.
In a specific embodiment, in the system harmonic impedance estimation method Step1 based on the LOF screening-heuristic segmentation algorithm of the present invention, the basic principle of screening harmonic data by using Pearson correlation coefficients includes:
because the power system is complex and difficult to directly analyze and calculate, the power system is divided into a system side and a user side by using a Norton equivalent circuit, and the harmonic impedance of the system is estimated by measuring harmonic voltage and current data at the PCC. The equivalent model is shown in fig. 2.
From the Norton equivalent circuit of FIG. 2, the following relation can be obtained
Wherein:the h-order harmonic voltage at the PCC; />H-harmonic current at PCC; />The harmonic impedance of the system is h times; />The current is the h-th background harmonic current; />Is the h-th order background harmonic voltage.
As can be seen from equation (23), the system harmonic impedance is calculated over a period of timeRemain unchanged and background harmonic voltage +>When relatively stable, harmonic voltage at PCC +.>And harmonic current->And obtaining the system harmonic impedance value by linear regression.
As can be seen from the noon equivalent circuit model and the equation (23), when the system side background harmonic voltage and the user side harmonic current are in different fluctuation degrees, the harmonic voltage and the harmonic current at the PCC will have the following four conditions.
1) Background harmonic voltageUser harmonic current->No fluctuation occurs, at this time, the amplitude of the harmonic voltage at the PCCAnd harmonic current amplitude->Constant, the system harmonic impedance cannot be calculated.
2) Only user harmonic currentWave motion occurs, and background harmonic voltage +>Keep constant at this point +.>And (3) withShows a strong positive correlation to +.>Is in abscissa, & lt + & gt>A positive correlation straight line is presented for the data point distribution on the ordinate, the slope of the straight line is +.>Intercept is->At this time, the harmonic impedance of the computing system is +.>Most ideal time period.
3) Only the followingBackground harmonic voltageWave motion occurs, and user harmonic current +>Keep constant at this point +.>And (3) withShows a strong negative correlation to +.>Is in abscissa, & lt + & gt>The data point distribution on the ordinate shows a negative correlation line with a slope of +.>Intercept is->
4) Background harmonic voltageHarmonic current +.>At the same time wave motion, if->Dominant fluctuations, from 3) it is known that the slope of the line is close to +.>If->Dominant fluctuations, from 2) it is known that the slope of the line is close to +.>If the fluctuation conditions of the two are equivalent, the two are +>And->There is no correlation and the distribution is more disordered.
In the actual operation of the power system, the background harmonic voltageHarmonic current +.>Is a random process, and the harmonic data acquired during the time period of interest may include one or more of the above, but onlyAnd->The system harmonic impedance calculated when the strong positive correlation is shown is accurate, so how to screen data to obtain the data segment of the situation is the key to accurately calculate the system harmonic impedance.
The Pearson correlation coefficient R concept in probability statistics is introduced to quantify the harmonic voltage amplitude at PCCAnd harmonic current amplitude->Correlation of (2), therebyAnd screening to obtain a data segment with relatively stable background harmonic. />And->The calculation formula of the Pearson correlation coefficient is as follows
Wherein:and->Is the ith harmonic voltage and current data; m is the sampling window width, namely the number of harmonic voltage and current data in the concerned time period; />And->The average value of the harmonic voltage and the current of the corresponding sampling window is obtained; r is E (-1, 1).
In a specific embodiment, in the system harmonic impedance estimation method Step1 based on the LOF screening-heuristic segmentation algorithm, the basic principle of eliminating abnormal values of harmonic data by using the LOF method includes:
the local outlier (Local Outlier Factor, LOF) method is an outlier detection algorithm based on density, and the core idea is that the outlier of each data is calculated according to the density degree of the neighborhood of the data points, the outlier can quantify the outlier degree of the data points, then a threshold value is set, and the data with the outlier being larger than the threshold value is the outlier. The basic principle of the LOF method will now be described as follows.
Relevant definition of LOF method
(1) d (p, o) represents the distance between p and o.
(2) Kth distance (k-distance)
The kth distance d from the point p k (p), defined as: d, d k (p) =d (p, o), satisfying the following two conditions.
a) At least k points o 'excluding p are included in the set, so that d (p, o')isless than or equal to d (p, o);
b) There are at most k-1 points o 'in the set that do not include p, such that d (p, o') < d (p, o).
In short, p is taken as a center of a circle and radiates outwards until the kth adjacent point is covered. Fig. 3 is the 5 th distance of p.
(3) Kth distance neighborhood
Kth distance neighborhood N of data point p k (p) pointing to a set of all points within the kth distance of p, including points at the kth distance. It can be seen that N k (p)|≥k。
(4) Kth reachable distance
reach_dist k (o,p)＝max{d k (o),d(o,p)} (2)
The kth reachable distance of data point o to data point p is defined as the greater of the kth distance of point o and the distance of point o to point p. O, as shown in FIG. 4 1 The 5 th reachable distance to p is d (o 1 ,p)，o 2 The 5 th reachable distance to p is d 5 (o 2 )。
(5) Local reachable density
The kth local reachable density of data point p, i.e., the inverse of the average kth reachable distance from point p to all points within the kth distance neighborhood of point p. The density of the point p is represented, and the higher the density of the point p and surrounding points is, the smaller the reachable distance of each point is, and the larger the lrd value is; the lower the concentration of the point p with the surrounding points, the larger the actual distance between the two points with larger reachable distance of the points, and the larger the lrd value.
(6) Local outlier factor
The kth local outlier factor of the data point p, meaning N of the point p k (p) comparing the average local reachable density of all points in the neighborhood with the local reachable density of point p, the greater the ratio is 1, indicating that the less the density of p points is than the density of points around it, p points being outliers; the smaller this ratio is than 1, indicating that the density of p-points is greater than that of its surrounding points, p-points being normal points.
In a specific embodiment, in the system harmonic impedance estimation method Step2 based on the LOF screening-heuristic segmentation algorithm, the basic principle of verifying the harmonic impedance mutation point by using the heuristic segmentation algorithm comprises the following steps:
the precondition for calculating the harmonic impedance by using the regression method is that the harmonic impedance does not change suddenly, but under the actual running condition of the power system, the harmonic impedance of the system changes suddenly due to the running mode change of the system, the load increase and decrease or the reactive compensation device switching. Therefore, analysis of harmonic impedance discontinuity problems is required.
The harmonic impedance mutation occurs at a certain time point and remains relatively stable for a period of time due to the reasons, so that the law of the harmonic impedance mutation of the system can be simplified to be shown in fig. 5, and the law of the harmonic impedance mutation is shown as t at the time point 1 ,t 2 ,…,t n-1 The harmonic impedance is abrupt at time, and is (t) i ,t i+1 ) The harmonic impedance in (i=1, 2, …, n-1) does not change suddenly, so that the regression method can be used to estimate the system harmonic impedance value in the time period, but the key of the problem is to identify the point of time when the impedance changes suddenly.
Coarse estimates of system harmonic impedance are calculated using the principle of the ratio method to segment the data points. When the background harmonic is relatively stable, the number of harmonic sample data is assumed to be P, and each harmonic data point isThen tie upA coarse estimate of the system harmonic impedance may be approximated by the following equation.
Calculating harmonic impedance rough estimation values of all adjacent two data points through a formula (5), then using a heuristic segmentation algorithm (BG algorithm) to test system harmonic impedance mutation points, setting a time sequence consisting of N system harmonic impedance rough estimation values calculated by the formula (5) as x (t), sliding and selecting a segmentation point i from the left side to the right side of the sequence, and calculating the average value mu of the left side and the right side of each segmentation point 1 (i) Sum mu 2 (i) Standard deviation s 1 (i) Sum s 2 (i) Merging deviation S of i points D (i) Is that
Wherein N is 1 ,N 2 Points of the subsequences on the left and right sides of the i point are respectively indicated.
The statistical value T (i) of the T test is used to quantify the mean difference of the subsequences on the left and right sides of the partition point i, as follows.
Repeating the calculation process for each point in the harmonic impedance time sequence x (T) to obtain a detection statistical value sequence T (T) corresponding to the sequence x (T), wherein the larger the T is, the larger the average value phase difference between the sub-sequences at the left and right sides of the division point is. Then calculate the maximum value T in T (T) max Statistical significance of P (T) max )。
P(T max )＝Prob(T≤T max ) (8)
Wherein P (T) max ) Indicating that T value is less than or equal to T in the random process max Is a probability of (2).
In general P (T) max ) Can be approximated as
Wherein the variables are test formulas obtained by Monte Carlo simulation, eta=4.19 lnN-11.54, delta=0.40, N is the length of time series x (t), v=N-2,as an incomplete beta function, the expression is
In harmonic impedance discontinuity inspection, a threshold value P is set 0 If P (T) max )≥P 0 The harmonic impedance sequence x (t) is split at this point into two sub-sequences with mutually different means, otherwise it is not split.
Similarly, the above steps are repeated for the new sub-sequence after segmentation, if the sub-sequence has P (T max )≥P 0 And the average value difference degree between the subsequence and the subsequence adjacent to the left and right meets the conditions, if the subsequence is divided, otherwise, the subsequence is not divided. Repeating the steps until the length of all the subsequences is less than or equal to l 0 (l 0 Is the smallest segmentation scale) is not segmented any more. Through the operation, the harmonic impedance sequence x (t) can be divided into a plurality of subsequences with different average values, and the dividing point is the time point when the harmonic impedance of the system is suddenly changed. Generally, l 0 ≥25,P 0 ∈[0.5,0.95]。
In a specific embodiment, in the system harmonic impedance estimation method Step3 based on the LOF screening-heuristic segmentation algorithm, the basic principle of estimating the system harmonic impedance by using the complex domain robust regression method includes:
if the measurement error of the harmonic data is considered, the harmonic impedance linear equation can be expressed as
Where ε is a complex error term.
By screening and abrupt checking a certain group of harmonic voltage and current data after segmentation, it can be obtained by the formula (12)
Writing it in matrix form
Y＝βX+ε (13)
In the method, in the process of the invention,
in the formula, the symbol "Θ" means "written as".
To obtain a complex domain robust regression model, first, looking at a complex least squares basic principle, the complex error square sum minimum relationship is as follows, namely, the complex error square sum minimum relationship satisfies
Element X in complex vector matrix X k (k=1, 2) is rewritten as real and imaginary parts, i.e.Then Q is converted to about->And->Is a function of (i.e.)
According to the extremum principle in the differential science, the solution obtained by the following formula (16) is the complex least square solution of the complex vector matrix X.
Next, the detailed derivation of equation (14) is performed
In the method, in the process of the invention,representing the conjugate of the complex vector.
Q versus real partDeviation determination guide
Finishing the item shifting of (25)
Similarly, Q is the imaginary partDeviation determination guide
Finishing (27) to obtain
Combining and finishing formula (26) and formula (28)
Due toTherefore, formula (29) is
Will be expressed as a matrix form, i.e
Complex least squares solution with respect to system harmonic impedance and background harmonic voltage X is therefore
The objective function of complex-domain robust regression can be expressed as
Wherein omega is i Is a weight coefficient.
There are many ways to construct weights, and the present invention chooses to use the Huber method to define weights.
Diagonalizing the weights calculated in equation (27), i.e
Wherein, c h Is constant, typically 1.345; u (u) i Is a normalized residual.
u i ＝ε i /s (20)
s＝mid(ε)/0.6745 (21)
mid(ε)＝Middle|ε i -Middle(ε)| (22)
Wherein s is the residual scale; middle (epsilon) is the median of the elements in vector epsilon.
The basic steps of complex-domain robust regression calculation are as follows.
1) Firstly, calculating to obtain a parameter vector by using a complex least square method
2) Calculating to obtain complex residual error vector epsilon (k) The normalized residual vector u is calculated by the formulas (20), (21), (22) (k) 。u (k) Is a matrix, i.e. u i K is the number of iterations.
3) The weight vector omega is calculated by using the Huber method and is converted into a diagonal matrix W * . Omega being the weighting element omega i Is a set of (3).
4) Calculating the estimated value of complex domain robust regression, namely
5) Comparing the current estimation result with the last one, if meeting the requirement of |X k+1 -X k |<Mu condition (mu is check accuracy, generally set to 10 -5 ) The iteration process is ended, noThe process jumps to step two until convergence.
Example 2
The technical effects of the present invention will be described below by way of a specific example. Taking fifth harmonic as an example, the standard IEEE14 node system shown in fig. 6 is selected for simulation analysis, and the effectiveness of the method provided by the invention is verified.
The rated voltage of the test system is 500kV, and the test system consists of two generators, three phase adjusters, fourteen bus nodes, fifteen power transmission lines and three transformers. When the simulation model is built, the parameters of each element and load are set according to the standard parameters of the IEEE14 system, and the harmonic impedance of the system under the condition of normal operation of the power system is measured.
For a complex electric power system, since an appropriate study object needs to be selected, bus 11 is taken as a concerned bus, HL connected by the bus is taken as a load side harmonic source, and a system side harmonic source load is connected through bus 6. Therefore, the bus 11 can be regarded as a PCC point, HL as a user side harmonic source, and the rest of the load excluding the user side is equivalent to the system side, and the simulation calculation is performed by the method herein to estimate the equivalent impedance of the system side.
In order to simulate the system harmonic impedance change caused by the change of the operation mode, the switching of the reactive device and the increase and decrease of the load under the actual operation condition, the experiment is carried out in three parts, and the first part measures the harmonic impedance under the normal operation condition of the system; the second part measures the harmonic impedance in the case of a synchronous camera on the cut-out busbar 6; the third part measures the harmonic impedance in the case of reducing the bus 6 harmonic source load HS impedance. The simulation duration is 48s, each part is 16s, harmonic data at the concerned bus 11 is obtained through FFT conversion every 0.02s, and 2400 sampling points are taken in total.
Fig. 7 is a plot of the harmonic current amplitude and the harmonic voltage amplitude on the abscissa and the ordinate, which is obtained by performing the screening analysis after obtaining the harmonic data by the data of 0 to 16s obtained by the FFT, as shown in fig. 8. As can be seen from fig. 8, there is a positive correlation between the harmonic voltage amplitude and the harmonic current amplitude, but the correlation is not obvious due to the influence of the background harmonic fluctuation, and the sliding screening is performed on the harmonic data through Pearson correlation coefficient, and the data segment with R >0.9 is reserved, and the relation between the two after screening is shown in fig. 9.
As can be seen from fig. 9, the positive correlation between the amplitude of the harmonic voltage and the amplitude of the harmonic current after the filtering by the Pearson correlation coefficient is stronger, and the data segment with relatively stable background harmonic is effectively filtered, so that the filtered data can be used for calculating the harmonic impedance of the system. However, scattered discrete points still exist in the screened data, and the discrete points influence the determination of an initial fitting straight line of a complex domain robust regression method used later, so that the final calculation result of harmonic impedance is influenced.
The method is used for eliminating scattered abnormal points according to the density condition of harmonic data points, so that the robustness of a complex domain robust regression equation is improved, and a harmonic voltage amplitude and harmonic current amplitude scatter diagram after the abnormal points are eliminated according to the LOF method is shown in fig. 10. As can be seen from fig. 10, the LOF can effectively reject abnormal values in the harmonic data, and the remaining data points can be better fitted into a straight line, that is, a regression equation corresponding to the harmonic impedance, so that the calculated harmonic impedance value can be more accurate.
The influence of the background harmonic wave fluctuation and the abnormal value on the result can be effectively reduced through data screening, and then the time point of sudden change of the system harmonic impedance is needed to be identified through a heuristic segmentation algorithm for segmentation calculation. The recognition results are shown in fig. 11 below. As can be seen from fig. 11, the system harmonic impedance abrupt change occurs at sampling points 926 and 2203, corresponding to the set 16s and 32s abrupt change time, so the heuristic segmentation algorithm proposed herein can effectively detect the system harmonic impedance abrupt change time point. After the mutation points are detected, the segmentation calculation is carried out, and the harmonic impedance value is estimated by a complex domain robust regression method, and the result is shown in the following table 1.
TABLE 1
In order to illustrate that the method provided by the invention can improve the calculation precision of the harmonic impedance of the system, the complex least square method and the traditional robust regression method are respectively used for comparison with the method provided by the invention, and the impedance estimation error is shown in the following figure 12. As can be seen from fig. 12, the complex least square method is influenced by the outlier, so that the calculated harmonic impedance error is larger, while the conventional robust regression and the method provided by the invention can reduce the outlier influence, so as to obtain a more accurate calculation result, but the conventional robust regression separately calculates the real part and the imaginary part of the system harmonic impedance, so that the calculation result is not the least square solution of the original equation, so that the calculation error is larger than the method provided by the invention, so that the system harmonic impedance estimation method based on the LOF screening-heuristic segmentation algorithm provided by the invention has better precision and wider application range compared with the general linear regression method.
The invention provides a harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance change, which is suitable for impedance calculation of a single harmonic source and a plurality of harmonic sources. According to simulation results, when the background harmonic voltage fluctuates, the cross correlation coefficient of the proposed time sequence cluster can align the harmonic voltage and the current in a translation way and screen out the data segment meeting the conditions, and compared with the traditional pearson correlation coefficient method, the error can be reduced better. When the system impedance changes, the proposed Pettitt method based on binary segmentation can effectively screen out the time point when the harmonic impedance changes suddenly, and the effect is better than that of a general inspection method. When there are multiple outliers, the regenerative weight least squares method is more robust than other methods. Therefore, the method provided by the invention can reduce adverse effects on impedance calculation caused by background harmonic voltage fluctuation and system harmonic impedance change, and has a wider application range.
Although the present invention has been described with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described, or equivalents may be substituted for elements thereof, and any modifications, equivalents, improvements and changes may be made without departing from the spirit and principles of the present invention.
Claims (5)
1. A system harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm is characterized by comprising the following steps:
s1, screening out a period with smaller background harmonic fluctuation based on a Pearson correlation coefficient, and removing abnormal values in harmonic data by using an LOF method;
s2, detecting and segmenting a time point when the harmonic impedance of the system is suddenly changed based on a heuristic segmentation algorithm;
s3, estimating the harmonic impedance of the system based on a complex domain robust regression method.
2. The system harmonic impedance estimation method based on the LOF screening-heuristic segmentation algorithm as set forth in claim 1, wherein: in step S1, the filtering out the period with smaller background harmonic fluctuation based on the Pearson correlation coefficient, and removing the abnormal value in the harmonic data by using the LOF method specifically includes: sliding window is arranged, and harmonic voltage is calculated in sliding modeAnd current amplitude->Pearson correlation coefficient of subsequence, R is selected>0.9, and eliminating harmonic data outliers according to the data point density condition by using a LOF method.
3. The system harmonic impedance estimation method based on the LOF screening-heuristic segmentation algorithm as set forth in claim 2, wherein: the harmonic voltageAnd current amplitude->Pearson correlation of subsequencesThe numerical formula is:
wherein:and->Is the ith harmonic voltage and current data; m is the sampling window width; />And->The average value of the harmonic voltage and the current of the corresponding sampling window is obtained; r epsilon (-1, 1);
the LOF method specifically comprises the following steps:
(1) Definition d (p, o) represents the distance between p and o;
(2) Kth distance: the kth distance d from the point p k (p), defined as: d, d k (p) =d (p, o), and satisfies the following two conditions:
a) At least k points o 'excluding p are included in the set, so that d (p, o')isless than or equal to d (p, o);
b) At most k-1 points o 'not including p in the set, such that d (p, o') < d (p, o);
(3) The kth distance neighborhood: kth distance neighborhood N of data point p k (p) pointing to a set of all points within the kth distance of p, including the point at the kth distance, knowing |N k (p)|≥k；
(4) Kth reachable distance:
reach_dist k (o,p)＝max{d k (o),d(o,p)} (2)
the kth reachable distance from data point o to data point p is defined as the greater of the kth distance from point o and the distance from point o to point p;
(5) Local reachable density:
the kth local reachable density of the data point p, namely the reciprocal of the average kth reachable distance from all points in the kth distance neighborhood of the point p to the point p, represents the density condition of the point p, and the higher the density of the point p and surrounding points is, the smaller the reachable distance of each point is, and the larger the lrd value is; the lower the concentration of the point p and the surrounding points is, the larger the reachable distance between the points is, and the larger the lrd value is;
(6) Local outlier factor:
the kth local outlier of data point p, i.e., N, of point p k (p) comparing the average local reachable density of all points in the neighborhood with the local reachable density of point p, the ratio being greater than 1, indicating that the density of p points is less than the density of points around it, the p points being outliers; this ratio is less than 1, indicating that the density of p-dots is greater than the density of its surrounding dots, p-dots being normal dots.
4. The system harmonic impedance estimation method based on the LOF screening-heuristic segmentation algorithm as set forth in claim 1, wherein: the step S2 specifically includes:
s21, calculating to obtain a rough estimation value of the system harmonic impedance by using a ratio method principle to segment data points; when the background harmonic wave is relatively stable, the number of harmonic wave sample data is set as P, and each harmonic wave data point isThe rough estimate of the system harmonic impedance is approximated by:
calculating harmonic impedance rough estimation values of all adjacent two data points through a formula (5), and then using a heuristic segmentation algorithm to test harmonic impedance abrupt change points of the system;
s22, setting a time sequence consisting of N system harmonic impedance rough estimation values calculated by the formula (5) as x (t), sliding from the left side to the right side of the sequence to select a division point i, and calculating the average value mu of the left side and the right side of each division point 1 (i) Sum mu 2 (i) Standard deviation s 1 (i) Sum s 2 (i) Merging deviation S of i points D (i) Is that
Wherein N is 1 ,N 2 Points of the subsequences on the left side and the right side of the point i are respectively represented;
s23, using a statistical value T (i) of T test to quantify the mean value difference of the subsequences at the left and right sides of the division point i, wherein the formula is as follows:
repeating the calculation process for each point in the harmonic impedance time sequence x (T) to obtain a detection statistical value sequence T (T) corresponding to the sequence x (T), wherein the larger the T is, the larger the average value phase difference between the sub-sequences at the left and right sides of the division point is;
then calculate the maximum value T in T (T) max Statistical significance of P (T) max )：
P(T max )＝Prob(T≤T max ) (8)
Wherein P (T) max ) Indicating that T value is less than or equal to T in the random process max Probability of (2);
P(T max ) Can be approximated as:
wherein the variables are test formulas obtained by Monte Carlo simulation, eta=4.19 ln N-11.54, delta=0.40, N is the length of time series x (t), v=N-2,as an incomplete beta function, the expression is:
in harmonic impedance discontinuity inspection, a threshold value P is set 0 If P (T) max )≥P 0 Dividing the harmonic impedance sequence x (t) into two sub-sequences with different average values at the point, otherwise, not dividing the sub-sequences;
s24, repeating the steps for the new sub-sequence after segmentation, if the sub-sequence has P (T max )≥P 0 The sub-sequences are segmented if the average difference degree between the sub-sequences and the left and right adjacent sub-sequences meets the conditions, otherwise, the sub-sequences are not segmented;
repeating the steps until the length of all the subsequences is less than or equal to l 0 When it is no longer divided, l 0 Is the minimum dividing ruler; through the operation, the harmonic impedance sequence x (t) can be divided into a plurality of subsequences with different average values, and the division point is the time point when the harmonic impedance of the system is suddenly changed.
5. The system harmonic impedance estimation method based on the LOF screening-heuristic segmentation algorithm as set forth in claim 1, wherein: the robust regression method based on the complex domain estimates the harmonic impedance of the system, and specifically comprises the following steps:
taking into account the measurement error of the harmonic data, the harmonic impedance linear equation is expressed as
Wherein ε is a complex error term;
based on a complex least square basic principle, obtaining an objective function of complex domain robust regression;
estimating the system harmonic impedance by using a complex domain robust regression method, wherein the complex domain robust regression calculation comprises the following basic steps:
1) Firstly, calculating to obtain a parameter vector by using a complex least square method
Wherein: k is the iteration number, the symbol' "is the transpose of the matrix, symbol" -1 "is the inversion of the matrix and symbol" - "is the complex conjugate;
in the method, in the process of the invention,
2) Calculating to obtain complex residual error vector epsilon (k) The normalized residual vector u is calculated by the following formula (k) ；
u i ＝ε i /s
s＝mid(ε)/0.6745
mid(ε)＝Middle|ε i -Middle(ε)|
Wherein s is the residual scale; middle (epsilon) is the median of the elements in vector epsilon;
3) The weight vector omega is calculated by using the Huber method and is converted into a diagonal matrix W * ；
4) Calculating the estimated value of complex domain robust regression, namely
5) If meeting |X k+1 -X k |<Mu condition, iterative processEnding, outputting the harmonic impedance of the system; otherwise, jumping to the loop of the step 2) until convergence.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311386585.0A CN117630487A (en) | 2023-10-25 | 2023-10-25 | System harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311386585.0A CN117630487A (en) | 2023-10-25 | 2023-10-25 | System harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN117630487A true CN117630487A (en) | 2024-03-01 |
Family
ID=90026020
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311386585.0A Pending CN117630487A (en) | 2023-10-25 | 2023-10-25 | System harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117630487A (en) |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109033499A (en) * | 2018-06-07 | 2018-12-18 | 南京航空航天大学 | A kind of aero-engine method for predicting residual useful life of multistage consistency check |
| CN110850164A (en) * | 2019-10-25 | 2020-02-28 | 华北电力大学 | Multi-harmonic responsibility division method considering background harmonic voltage fluctuation and impedance change |
| CN111693773A (en) * | 2020-04-29 | 2020-09-22 | 国网江苏省电力有限公司电力科学研究院 | Harmonic source responsibility division method based on mutual approximation entropy data screening |
| CN112083461A (en) * | 2020-07-20 | 2020-12-15 | 西安电子科技大学 | RTK cycle slip testing method based on BG algorithm |
| CN115563477A (en) * | 2022-12-02 | 2023-01-03 | 南方电网数字电网研究院有限公司 | Harmonic data identification method and device, computer equipment and storage medium |
| CN116008665A (en) * | 2022-12-21 | 2023-04-25 | 云南电网有限责任公司文山供电局 | Harmonic impedance estimation method for power system |
| CN116226604A (en) * | 2023-03-28 | 2023-06-06 | 长安大学 | Method, device and equipment for diagnosing and measuring overall variation degree of hydrologic sequence |
| CN116243108A (en) * | 2023-03-16 | 2023-06-09 | 国网江苏省电力有限公司南通市通州区供电分公司 | Distribution network fault point positioning method, system, equipment and medium |
| CN116467556A (en) * | 2023-03-28 | 2023-07-21 | 四川大学 | Harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation |
-
2023
- 2023-10-25 CN CN202311386585.0A patent/CN117630487A/en active Pending
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109033499A (en) * | 2018-06-07 | 2018-12-18 | 南京航空航天大学 | A kind of aero-engine method for predicting residual useful life of multistage consistency check |
| CN110850164A (en) * | 2019-10-25 | 2020-02-28 | 华北电力大学 | Multi-harmonic responsibility division method considering background harmonic voltage fluctuation and impedance change |
| CN111693773A (en) * | 2020-04-29 | 2020-09-22 | 国网江苏省电力有限公司电力科学研究院 | Harmonic source responsibility division method based on mutual approximation entropy data screening |
| CN112083461A (en) * | 2020-07-20 | 2020-12-15 | 西安电子科技大学 | RTK cycle slip testing method based on BG algorithm |
| CN115563477A (en) * | 2022-12-02 | 2023-01-03 | 南方电网数字电网研究院有限公司 | Harmonic data identification method and device, computer equipment and storage medium |
| CN116008665A (en) * | 2022-12-21 | 2023-04-25 | 云南电网有限责任公司文山供电局 | Harmonic impedance estimation method for power system |
| CN116243108A (en) * | 2023-03-16 | 2023-06-09 | 国网江苏省电力有限公司南通市通州区供电分公司 | Distribution network fault point positioning method, system, equipment and medium |
| CN116226604A (en) * | 2023-03-28 | 2023-06-06 | 长安大学 | Method, device and equipment for diagnosing and measuring overall variation degree of hydrologic sequence |
| CN116467556A (en) * | 2023-03-28 | 2023-07-21 | 四川大学 | Harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation |
Non-Patent Citations (2)
| Title |
|---|
| 文雯;刘文哲;肖祥武;向春波;谢小鹏;姜鑫;: "基于大数据和并行随机森林算法火电机组供电煤耗计算模型", 热力发电, no. 09, 10 September 2018 (2018-09-10) * |
| 贾秀芳: "基于复数域稳健回归的多谐波源污染责任量化方法", 《太阳能学报》, 28 May 2019 (2019-05-28), pages 1 - 7 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| He et al. | Fault detection and classification in EHV transmission line based on wavelet singular entropy | |
| CN106443285B (en) | Multiple-harmonic-source harmonic responsibility quantitative analysis method based on total least square method | |
| CN107565553A (en) | A kind of power distribution network robust dynamic state estimator method based on UKF | |
| CN106971076B (en) | A kind of water quality of river monitoring data sequential encryption method | |
| CN116467556B (en) | Harmonic impedance calculation method considering background harmonic voltage fluctuation and impedance variation | |
| CN113687433B (en) | Bi-LSTM-based magnetotelluric signal denoising method and system | |
| CN116362398A (en) | Power load prediction method based on modal decomposition and reconstruction and LSTM-MLR hybrid model | |
| CN111541255B (en) | Low-frequency oscillation mode identification method and system based on dynamic system | |
| Li et al. | Grid-constrained data cleansing method for enhanced bus load forecasting | |
| CN106972949A (en) | A kind of fractional order network system situation method of estimation based on adaptive equalization technology | |
| CN112149296B (en) | Method for judging stability type of hydrologic time sequence | |
| Zhang et al. | Robust adaptive Unscented Kalman Filter with gross error detection and identification for power system forecasting-aided state estimation | |
| CN107204616B (en) | Power system random state estimation method based on self-adaptive sparse pseudo-spectral method | |
| CN117630487A (en) | System harmonic impedance estimation method based on LOF screening-heuristic segmentation algorithm | |
| Whalen et al. | An evaluation of the self-determined probability-weighted moment method for estimating extreme wind speeds | |
| CN115204404B (en) | Method and device for inhibiting errors in fermi subsystem measurement | |
| Ma et al. | Online assessment of failure probability for smart meters based on SARIMA-LTFRLS | |
| CN106529805B (en) | Generator importance-based power generation system reliability evaluation method | |
| CN107732940B (en) | Power system stabilizer parameter optimization test method based on ADPSS | |
| CN116298670A (en) | Intelligent fault positioning method and system suitable for multi-branch distribution line | |
| CN115032458A (en) | Harmonic impedance estimation method based on power grid system and computer storage medium | |
| CN115293090A (en) | Multi-harmonic source responsibility quantification method based on reconstruction data processing | |
| CN107576866A (en) | It is a kind of to approach sparse reconstruct and the method for distinguishing multiple harmonic sources of interior point method based on smooth | |
| Acurio et al. | Design and Implementation of a Machine Learning State Estimation Model for Unobservable Microgrids | |
| CN113537821A (en) | Rapid assessment method and system for state of power system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |