CN113884969B - Error threshold determining method for detecting power quality monitoring device by using fractal dimension - Google Patents
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Abstract
The invention belongs to the technical field of equipment detection, and particularly relates to an error threshold determining method for detecting an electric energy quality monitoring device by using a fractal dimension. The invention provides an error threshold determining method for detecting an electric energy quality monitoring device by using a fractal dimension, which is used for detecting the electric energy quality monitoring device by using the fractal dimension, has higher detection precision for data loss and low time setting precision, and reversely deduces the error threshold for detecting the electric energy quality monitoring device by using the fractal dimension according to the maximum measurement error of the electric energy quality monitoring device in a point-to-point method, has higher detection precision, and is proved by experiments, the error threshold determined by the method can effectively judge the measurement error of the electric energy quality monitoring device, and can accurately judge whether the electric energy quality monitoring device is qualified when harmonic waves become large.
Description
Technical Field
The invention belongs to the technical field of equipment detection, and particularly relates to an error threshold determining method for detecting an electric energy quality monitoring device by using a fractal dimension.
Background
At present, the accuracy of the power quality monitoring device is tested by adopting a point-to-point method, but the point-to-point method has the defects of strict and accurate time setting requirement and low judgment accuracy. The maximum allowable error requirements for the harmonic voltages specified in national standard GB/T19862-2016 are shown in Table 1.
TABLE 1 maximum allowable error for Point-to-Point comparison
The point-to-point comparison method is characterized in that the monitoring device is considered to be qualified as long as the error between the monitoring device and the high-precision power quality measuring device is controlled within 5 percent. The problem with this approach is that it is possible to monitor the device at 1%U N The following are acceptable but above 1%U N If the test is failed, the monitoring device is judged to be failed after the harmonic wave is increased.
For example, assume that the monitoring device detects U h =4v, high precision power quality measuring device measures U hN =54V, nominal voltage 110kV, at which time U hN ＜1％U N And U is h -U hN The = -50V is within the maximum allowable error, so the monitoring device is judged to be acceptable. But howeverIt is likely that the monitoring device is judged to be out of order after the harmonic wave becomes large. The fractal dimension algorithm can solve the above problem of the point-to-point method, but an effective determination method is not provided for determining an error threshold value for determining whether the detected power quality monitoring device is normal by using the fractal dimension detection.
Disclosure of Invention
In order to solve the problems, the invention provides an error threshold determining method for detecting a power quality monitoring device by using a fractal dimension, which comprises the following specific technical scheme:
the method for determining the error threshold of the power quality monitoring device by using the fractal dimension comprises the following steps:
s1: simulating an inaccurate critical state of the detected power quality monitoring device according to the maximum error threshold value of the point-to-point method;
s2: randomly intercepting harmonic voltage data monitored by a tested power quality monitoring device and a high-precision power quality monitoring device for testing, and respectively calculating fractal dimensions by using a structural function method;
s3: and calculating the maximum error value of the fractal dimension, and taking the 95% probability value of all the maximum errors as the final error threshold value of the device for detecting the electric energy quality by using the fractal dimension.
Preferably, the step S1 specifically includes: and adding randomly obtained noise into the harmonic voltage signal monitored by the power quality monitoring device to be tested according to the maximum error threshold value of 5% of the point-to-point method so as to simulate an inaccurate critical state when the power quality monitoring device to be tested monitors.
Preferably, the noise is 5% of the harmonic voltage signal monitored by the power quality monitoring device, that is, each point is added or subtracted with 5% of the value of the harmonic voltage signal monitored by the power quality monitoring device at the point, the value of each point of the generated new signal is 95% or 105% of the value of the original signal, and each point is at the edge conforming to the error range so as to simulate the limit condition monitored by the power quality monitoring device.
Preferably, the specific adding method of the noise is as follows:
for each point, generating a random number which is between 0 and 1 and obeys uniform distribution, when the generated random number is smaller than 0.5, the signal size of the corresponding point becomes 105% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be measured at the point, and when the generated random number is larger than or equal to 0.5, the signal size of the corresponding point becomes 95% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be measured at the point. The calculation formula is as follows:
wherein R-U n (0, 1), i=1, 2, …, n, S is a harmonic voltage signal obtained by monitoring by the power quality monitoring device to be tested, S * The method is a new signal obtained by adding noise to the harmonic voltage signal monitored by the monitored power quality monitoring device, the new signal is used for simulating the harmonic voltage signal monitored by the monitored power quality monitoring device in an inaccurate critical state, and R represents an n-dimensional random number which is uniformly distributed from 0 to 1.
Preferably, the structural function method is calculated as follows:
the structural function s (t) of the discrete signal y (i) is:
s(t)＝<[y(x+t)-y(x)] 2 〉＝ct 4-2D ； (1)
wherein t represents the number of intervals of data points; s (t) is a function of t; x is the abscissa on the curve; y (x) is the ordinate corresponding to the coordinate x;<[y(x+t)-y(x)] 2 >an arithmetic mean value representing the difference square; c is a constant;
calculating corresponding s (t) for a plurality of t to obtain a scaleless interval of the binodal curve lgt-lgs (t), calculating the slope of the scaleless interval to obtain the fractal dimension, and converting the fractal dimension D with the slope alpha into the following relationship:
preferably, the first order difference is carried out on the binodal curve lgt-lgs (t), the binodal curve lgt-lgs (t) obtained by a structural function method is calculated by adopting a fuzzy C-means algorithm to obtain a final scale-free interval, and the fractal dimension curve is obtained by adopting a least square method to fit the scale-free interval.
Preferably, the fuzzy C-means algorithm is specifically:
known data sample x= { X 1 ,x 2 ,…,x n Fuzzy classification matrix a= [ a ] ij ] c×n And cluster center c= [ C ] 1 ,c 2 ,…,c c ] T The fuzzy C-means algorithm can be expressed as:
wherein: c is the number of clustering centers; n is the number of samples; m is a weighted index; a, a ij And d ij The membership degree and Euclidean distance of the jth data point to the ith clustering center are respectively determined.
Preferably, the method further comprises the step of removing coarse errors in the data of the double logarithmic curve after the first order difference; reclassifying the retained data, and removing part of miscellaneous points; and selecting an interval with smaller scattered point fluctuation and positive fitting slope in the fitting result as a finally obtained scale-free interval.
Preferably, the method for discriminating the coarse errors is to perform least square fitting on the clustering results respectively, and the data set with larger fitting error is the coarse error.
The beneficial effects of the invention are as follows: the invention provides an error threshold determining method for detecting an electric energy quality monitoring device by using a fractal dimension, which is used for detecting the electric energy quality monitoring device by using the fractal dimension, has higher detection precision for data loss and low time setting precision, and reversely deduces the error threshold for detecting the electric energy quality monitoring device by using the fractal dimension according to the maximum measurement error of the electric energy quality monitoring device in a point-to-point method, has higher detection precision, and is proved by experiments, the error threshold determined by the method can effectively judge the measurement error of the electric energy quality monitoring device, and can accurately judge whether the electric energy quality monitoring device is qualified when harmonic waves become large.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. Like elements or portions are generally identified by like reference numerals throughout the several figures. In the drawings, elements or portions thereof are not necessarily drawn to scale.
FIG. 1 is a block diagram of an in-situ verification of a power quality monitoring device;
fig. 2 is a schematic diagram of an on-site verification of a power quality monitoring device.
FIG. 3 is a fractal dimension maximum error;
fig. 4 shows the 5 th harmonic of a 220kV sarin 110kV north stone Sha Xian 193 circuit breaker in an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. 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.
It should be understood that the terms "comprises" and "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
The method for determining the error threshold of the power quality monitoring device by using the fractal dimension comprises the following steps:
s1: and simulating an inaccurate critical state when the power quality monitoring device to be tested monitors according to the maximum error threshold value of the point-to-point method. The method comprises the following steps: and adding randomly obtained noise into the harmonic voltage signal monitored by the power quality monitoring device to be tested according to the maximum error threshold value of 5% of the point-to-point method so as to simulate an inaccurate critical state when the power quality monitoring device to be tested monitors.
The noise is 5% of the harmonic voltage signal monitored by the power quality monitoring device to be tested, namely each point is added or subtracted by 5% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be tested, the value of each point of the generated new signal is 95% or 105% of the value of the original signal, and each point is positioned at the edge conforming to the error range so as to simulate the limit condition monitored by the power quality monitoring device to be tested.
The specific adding method of the noise is as follows:
for each point, generating a random number which is between 0 and 1 and obeys uniform distribution, when the generated random number is smaller than 0.5, the signal size of the corresponding point becomes 105% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be measured at the point, and when the generated random number is larger than or equal to 0.5, the signal size of the corresponding point becomes 95% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be measured at the point. The calculation formula is as follows:
wherein R-U n (0, 1), i=1, 2, …, n, S is a harmonic voltage signal obtained by monitoring by the power quality monitoring device to be tested, S * The method is a new signal obtained by adding noise to the harmonic voltage signal monitored by the monitored power quality monitoring device, the new signal is used for simulating the harmonic voltage signal monitored by the monitored power quality monitoring device in an inaccurate critical state, and R represents an n-dimensional random number which is uniformly distributed from 0 to 1.
S2: the measured power quality monitoring device and the high-precision power quality monitoring device are connected according to fig. 1, and the two devices start to measure after time synchronization according to fig. 2. And randomly intercepting harmonic voltage data monitored by the power quality monitoring device to be tested and the high-precision power quality monitoring device to test, and respectively calculating fractal dimensions of the harmonic voltage data by using a structural function method.
The fractal dimension calculation by the structural function method is specifically as follows:
the structural function method regards all points on the discrete signal curve as a time series with fractal features, and the structural function s (t) of the discrete signal y (i) is:
s(t)＝<[y(x+t)-y(x)] 2 >＝ct 4-2D ； (2)
wherein t represents the number of intervals of data points; s (t) is a function of t; x is the abscissa on the curve; y (x) is the ordinate corresponding to the coordinate x;<[y(x+t)-y(x)] 2 >an arithmetic mean value representing the difference square; c is a constant;
calculating corresponding s (t) for a plurality of t to obtain a scaleless interval of the binodal curve lgt-lgs (t), calculating the slope of the scaleless interval to obtain a fractal dimension, and converting the slope alpha, D and the slope alpha of the scaleless interval into the following relationship:
the non-scale interval is a relatively straight line segment on the double-logarithmic curve, and the slope of the line segment is approximately constant, so that the first-order difference is carried out on the double-logarithmic curve, and the line segment is characterized in that the fluctuation is tiny in the non-scale interval and larger outside the non-scale interval. The double logarithmic curves after the first order difference can be clustered according to the characteristics, and a fuzzy C-means algorithm is selected for clustering.
The fuzzy C-means is a clustering algorithm based on an objective function, the fuzzy theory is used for analyzing and modeling data, the clustering center and the classification matrix are continuously corrected until the data meets the termination criterion, the uncertainty description of the class of the data is obtained, the class of the data is obtained according to the membership degree, and the fuzzy C-means is an improved algorithm for K-means. And carrying out first-order difference on the double logarithmic curve lgt-lgs (t), calculating the double logarithmic curve lgt-lgs (t) obtained by a structural function method by adopting a fuzzy C-means algorithm to obtain a final scale-free interval, and fitting the scale-free interval by adopting a least square method to obtain a fractal dimension curve. The fuzzy C-means algorithm is specifically:
known data sample x= { X 1 ,x 2 ,…,x n Fuzzy classification matrix a= [ a ] ij ] c×n And cluster center c= [ C ] 1 ,c 2 ,…,c c ] T The fuzzy C-means algorithm can be expressed as:
wherein: c is the number of clustering centers; n is the number of samples; m is a weighted index; a, a ij And d ij The membership degree and Euclidean distance of the jth data point to the ith clustering center are respectively determined.
The double logarithmic curve after the first order difference is divided into two types, wherein one type is coarse errors in data, and the coarse errors are removed. The method for judging the coarse errors is to perform least square fitting on the clustering results respectively, and the data set with larger fitting error is the coarse errors. The range of intervals obtained by one classification may not be accurate enough, so that the retained data needs to be classified again, and part of miscellaneous points are removed to obtain a more accurate scale-free interval. And (3) respectively carrying out least square fitting on the clustering results, wherein the rough error is removed, the difference of the second clustering result in the fitting error is not too large, and problems are inevitably caused by taking the fitting error as a discrimination standard, so that a section with small scattered point fluctuation and positive fitting slope in the fitting result is selected as a finally obtained scale-free section.
S3: and calculating the maximum error value of the fractal dimension, and taking the 95% probability value of all the maximum errors as the final error threshold value of the device for detecting the electric energy quality by using the fractal dimension.
The fractal dimension calculation method is used for measuring harmonic waves and identifying device abnormality, new indexes for measuring harmonic wave errors, the calculation method and the maximum allowable error requirement are provided, and whether the electric energy quality monitoring device is abnormal can be accurately judged when the harmonic wave content is small. When the signal fractal dimension error exceeds the maximum allowable error, the power quality monitoring device can be considered to be incapable of monitoring the out-of-standard signal, and is inaccurate, and a large amount of experimental simulation is needed for finding the proper maximum allowable error.
The maximum fractal dimension allowable error is most reasonable to find under the limit condition of the power quality monitoring device, and the invention provides a simulation experiment for the power quality monitoring device under the limit condition. For harmonic and inter-harmonic signals, the allowable error limit value of the point-to-point comparison method to the device under the national standard is 5%. By the error limit value, an inaccurate critical state of the power quality monitoring device can be correspondingly simulated, and the fractal dimension error maximum value of simulated test data and actual data in the critical state can be regarded as the maximum allowable error.
And (3) selecting harmonic data from the hundred-color wind power plant and the ida wind power plant, intercepting 1200 harmonic data for testing, respectively carrying out multiple tests under different harmonic frequencies from 2 to 19, calculating harmonic voltage data monitored by the tested electric energy quality monitoring device and the high-precision electric energy quality monitoring device by using a structural function method for testing, respectively calculating fractal dimensions by using the structural function method, and finally obtaining an error result shown in figure 3.
In the experiment, the original signal selected should meet the condition of 'low harmonic content', 1%U is used when the error of harmonic voltage is calculated according to GB/T19862-2016 N As a boundary for the division of different formulas, will be less than 1%U N The harmonic wave with smaller content is considered, and the selected (inter) harmonic wave data meets the condition in the experiment for solving the maximum error.
In the process of calculating the fractal dimension, the situation that the fractal dimension is larger than 2 may occur, because the signal does not have fractal characteristics, the greatest fractal characteristic is self-similarity, that is, the self-similarity of a system means that the characteristics of a certain structure or process are similar from different spatial scales or time scales, or the local property or local structure of a certain system or structure is similar to the whole. The fractal dimension calculation method is obtained by the slope of a scale-free interval, namely the scale invariance of the fractal is utilized, the characteristic is that a local area is selected on the fractal, the local area is amplified, and the obtained amplified image shows the morphological characteristic of the original image.
For data with abrupt points, the local structure is different from the whole so that the fractal characteristics are not possessed, while for data similar to white noise, we consider Brownian motion to produce fluctuating voltages in a circuit, while the existing literature formula derives that the fractal dimension of Brownian motion is 2, from which it is explained whether harmonic voltage data similar to white noise has fractal characteristics is unknown, but the fractal dimension does exist in a situation slightly exceeding 2, and when the dimension thereof is set to 2 by using a W-M fractal function, the final result is also an image similar to white noise. For convenience of judgment, these data are rejected regardless of the case where the fractal dimension is greater than 2.
In order to find the threshold, the statistical characteristic value 95% probability value is analyzed and whether harmonic test inaccuracy occurs is judged. The sampled points are arranged in order from big to small, the maximum value of 5% is removed, and the maximum value in the rest is the 95% probability value. The national standard GB/T14549-93 'electric energy quality public Power grid harmonic' prescribes a 95% probability value as a standard for evaluating the severity of harmonic pollution. By analogy with this approach, the 95% probability value for all maximum errors is 5.0170%, thus setting the threshold to 5%. When the harmonic fractal dimension error exceeds 5%, the detected power quality monitoring device can be determined to be inaccurate. The maximum allowable error results are shown in table 5.
Table 5 maximum allowable error results
Wherein U is hN For harmonic voltage measured by high-precision electric energy quality measuring device, U h For harmonic voltage measured by the power quality monitoring device, U N At nominal voltage, D hN Fractal dimension, D, of harmonic voltage measured for high-precision power quality measurement device h Is electric energyFractal dimension of harmonic voltage measured by the quantity monitoring device.
Harmonic voltage is more than or equal to 1%U N And<1％U N in both cases the error calculation is consistent, when U hN <1％U N In the time-course of which the first and second contact surfaces,
if at U hN <1％U N While still adopting the formulaAnd the maximum allowable absolute value error is 5%, then
The above-mentioned formula meets U hN <1％U N And the maximum allowable error of the corresponding calculation formula. The maximum allowable error is therefore consistent in both cases in the national standard.
Therefore, the calculation method of the maximum error result in table 1 in this embodiment meets the national standard.
The 5 th harmonic data from a 220kV sand forest transformer 110kV North stone Sha Xian 193 breaker is selected as experimental data, one data is recorded every three seconds, the sampling time is 3 hours 0 minutes to 3 hours 10 minutes, 200 data sampling points are taken as measurement results of a high-precision power quality monitoring device, and the measurement results are shown as curve 2 in fig. 4. The selected data is added to gaussian noise to simulate the measured data of the power quality monitoring device under test, and the scalar snr specifies the signal to noise ratio per sample in dB, and 23dB of the added data is used to simulate the data of the power quality monitoring device under test, as shown by curve 1 in fig. 4.
The maximum error is 0.08551%, the minimum error is 0.00001499%, and more than 95% of the requirements of national standards are met, but as seen from fig. 4, the result of the monitoring device is greatly different from that of the high-precision power quality measuring device, and the phenomenon that the measured power quality monitoring device is judged to be unqualified after harmonic wave is possibly increased.
The result of the detected power quality monitoring device and the result of the high-precision power quality measuring device are enlarged by five times, less than 95% of points meet the national standard requirement, the minimum error is 3.52%, the maximum error reaches 25.41%, and the detected power quality monitoring device can be considered to be inaccurate.
If the fractal dimension method is adopted, the fractal dimension of the curve of the monitoring device is 1.988, the fractal dimension of the curve measured by the high-precision power quality measuring device is 1.772, the relative error is 12.20%, and the maximum allowable error is exceeded, and the relative error of the two devices exceeds the error threshold, so that the measured power quality monitoring device is considered to be abnormal, and the device needs to be replaced.
Those of ordinary skill in the art will appreciate that the elements of the examples described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the elements of the examples have been described generally in terms of functionality in the foregoing description to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In the embodiments provided in this application, it should be understood that the division of units is merely a logic function division, and there may be other manners of division in practical implementation, for example, multiple units may be combined into one unit, one unit may be split into multiple units, or some features may be omitted.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention, and are intended to be included within the scope of the appended claims and description.
Claims (7)
1. The method for determining the error threshold of the power quality monitoring device by using the fractal dimension is characterized by comprising the following steps of: the method comprises the following steps:
s1: simulating an inaccurate critical state of the detected power quality monitoring device according to the maximum error threshold value of the point-to-point method;
s2: randomly intercepting harmonic voltage signals monitored by the power quality monitoring device to be tested and the high-precision power quality monitoring device to be tested, and respectively calculating fractal dimensions monitored by the power quality monitoring device to be tested and the high-precision power quality monitoring device by using a structural function method; the calculation process of the structural function method is as follows:
the structural function s (t) of the discrete signal y (i) is:
s(t)＝<[y(x+t)-y(x)] 2 >＝kt 4-2D ； (1)
wherein t represents the number of intervals of data points; s (t) is a function of t; x is the abscissa on the curve; y (x) is the ordinate corresponding to the coordinate x;<[y(x+t)-y(x)] 2 >an arithmetic mean value representing the difference square; k is a constant;
calculating corresponding s (t) for a plurality of t to obtain a scaleless interval of the binodal curve lgt-lgs (t), calculating the slope of the scaleless interval to obtain a fractal dimension, wherein the slope of the scaleless interval is alpha, and the conversion relation between the fractal dimension D and the slope alpha is as follows:
performing first-order difference on a double-logarithmic curve lgt-lgs (t), calculating a double-logarithmic curve lgt-lgs (t) obtained by a structural function method by adopting a fuzzy C-means algorithm to obtain a final scale-free interval, and fitting the scale-free interval by adopting a least square method to obtain a fractal dimension curve;
s3: and calculating the maximum error value of the fractal dimension, and taking the 95% probability value of all the maximum error values as the final error threshold value of the electric energy quality monitoring device by using the fractal dimension.
2. The method for determining an error threshold for detecting a power quality monitoring device using a fractal dimension according to claim 1, wherein:
the step S1 specifically comprises the following steps: and adding randomly obtained noise into the harmonic voltage signal monitored by the power quality monitoring device to be tested according to 5% of the maximum error threshold value of the point-to-point method so as to simulate an inaccurate critical state when the power quality monitoring device to be tested monitors.
3. The method for determining an error threshold for detecting a power quality monitoring device using a fractal dimension according to claim 2, wherein:
the noise is 5% of the harmonic voltage signal monitored by the power quality monitoring device to be tested, namely each point is added or subtracted by 5% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be tested, the value of each point of the generated new signal is 95% or 105% of the value of the original signal, and each point is positioned at the edge conforming to the error range so as to simulate the limit condition monitored by the power quality monitoring device to be tested.
4. The error threshold determination method for detecting a power quality monitoring device using a fractal dimension according to claim 3, wherein:
the specific adding method of the noise comprises the following steps:
for each point, generating a random number which is between 0 and 1 and is subjected to uniform distribution, when the generated random number is smaller than 0.5, changing the signal size of the corresponding point into 105% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be tested, and when the generated random number is greater than or equal to 0.5, changing the signal size of the corresponding point into 95% of the value of the harmonic voltage signal monitored by the power quality monitoring device to be tested; the calculation formula is as follows:
wherein R-U n (0, 1), i=1, 2, …, n, S is a harmonic voltage signal obtained by monitoring by the power quality monitoring device to be tested, S * The method is a new signal obtained by adding noise to the harmonic voltage signal monitored by the monitored power quality monitoring device, the new signal is used for simulating the harmonic voltage signal monitored by the monitored power quality monitoring device in an inaccurate critical state, and R represents an n-dimensional random number which is uniformly distributed from 0 to 1.
5. The method for determining an error threshold for detecting a power quality monitoring device using a fractal dimension according to claim 1, wherein:
the fuzzy C-means algorithm specifically comprises the following steps:
known data sample x= { X 1 ,x 2 ,…,x n Fuzzy classification matrix a= [ a ] ij ] c×n And cluster center c= [ C ] 1 ,c 2 ,…,c c ] T The fuzzy C-means algorithm is expressed as:
wherein: c is the number of clustering centers; n is the number of samples; m is a weighted index; a, a ij And d ij The membership degree and Euclidean distance of the jth data point to the ith clustering center are respectively determined.
6. The method for determining an error threshold for detecting a power quality monitoring device using a fractal dimension according to claim 1, wherein: the method also comprises the steps of removing coarse errors in the data of the double logarithmic curve after the first order difference; reclassifying the retained data, and removing part of miscellaneous points; and selecting an interval with smaller scattered point fluctuation and positive fitting slope in the fitting result as a finally obtained scale-free interval.
7. The method for determining an error threshold for detecting a power quality monitoring device using a fractal dimension according to claim 6, wherein: the method for judging the coarse errors is to perform least square fitting on the clustering results respectively, and the data set with larger fitting error is the coarse errors.
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