CN113884969A - Error threshold value determination method for power quality monitoring device by utilizing fractal dimension detection - Google Patents
Error threshold value determination method for power quality monitoring device by utilizing fractal dimension detection Download PDFInfo
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Abstract
The invention belongs to the technical field of equipment detection, and particularly relates to a method for determining an error threshold of a power quality monitoring device by utilizing fractal dimension detection. The invention provides a method for determining an error threshold of a power quality monitoring device by utilizing fractal dimension, which has higher detection precision for data loss and low time synchronization precision by utilizing the power quality monitoring device by utilizing the fractal dimension, and reversely deduces the error threshold of the power quality monitoring device by utilizing the fractal dimension according to the maximum measurement error of the power quality monitoring device in a point-to-point method, so that the method has higher detection precision.
Description
Technical Field
The invention belongs to the technical field of equipment detection, and particularly relates to a method for determining an error threshold of a power quality monitoring device by utilizing fractal dimension detection.
Background
At present, a point-to-point method is adopted to test the precision of the power quality monitoring device, but the point-to-point method has the defects of strict and accurate time setting requirement and low judgment precision. The maximum allowable error requirement of the harmonic voltage specified in the national standard GB/T19862-2016 is shown in Table 1.
TABLE 1 maximum allowable error of Point-to-Point alignment
The idea of the point-to-point comparison method is that the monitoring device is qualified as long as the error between the monitoring device and the high-precision power quality measuring device is controlled within 5%. The problem with this approach is that it is possible to monitor the device at 1% UNThe following are acceptable, but at greater than 1% UNThe harmonic waves are unqualified, and the phenomenon that the monitoring device is judged to be unqualified after the harmonic waves are increased is completely possible.
For example, assume that the monitoring device detects Uh4V, U is measured by a high-precision electric energy quality measuring devicehN54V, nominal 110kV, UhN＜1％UNAnd U ish-UhN-50V is within the maximum allowable error, so the monitoring device is judged to be qualified. But instead of the other end of the tube
After the harmonic waves are likely to become large, the monitoring device is judged to be unqualified. The fractal dimension algorithm can solve the problems of the point-to-point method, but an effective error threshold value for determining whether the fractal dimension detection is adopted to judge whether the detected electric energy quality monitoring device is normal is not providedAnd determining a method.
Disclosure of Invention
In order to solve the problems, the invention provides an error threshold value determining method for detecting a power quality monitoring device by utilizing fractal dimension, which has the following specific technical scheme:
the method for determining the error threshold of the power quality monitoring device by utilizing fractal dimension detection comprises the following steps:
s1: simulating an inaccurate critical state when the monitored energy quality monitoring device monitors according to the maximum error threshold of the point-to-point method;
s2: randomly intercepting harmonic voltage data monitored by a monitored electric energy quality monitoring device and a high-precision electric energy 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 power quality monitoring device by using the fractal dimension.
Preferably, the step S1 is specifically: according to the maximum error threshold value of 5% of the point-to-point method, randomly obtained noise is added into a harmonic voltage signal obtained by monitoring of the measured electric energy quality monitoring device so as to simulate an inaccurate critical state when the measured electric energy quality monitoring device monitors.
Preferably, the noise is 5% of the harmonic voltage signal monitored by the measured electric energy quality monitoring device, that is, each point adds or subtracts 5% of the value of the harmonic voltage signal monitored by the measured electric energy quality monitoring device at the point, the value of each point of the generated new signal is 95% or 105% of the original signal, and each point is at the edge meeting the error range, so as to simulate the limit condition monitored by the measured electric energy quality monitoring device.
Preferably, the specific adding method of the noise is as follows:
and generating a random number which is between 0 and 1 and is subjected to uniform distribution for each point, wherein when the generated random number is less than 0.5, the signal size of the corresponding point is changed into 105% of the value of the harmonic voltage signal monitored by the electric energy quality monitoring device at the point, and when the generated random number is more than or equal to 0.5, the signal size of the corresponding point is changed into 95% of the value of the harmonic voltage signal monitored by the electric energy quality monitoring device at the point. The calculation formula is as follows:
wherein, R to Un(0,1), i is 1,2, …, n, S is harmonic voltage signal monitored by the device for monitoring the quality of the measured electric energy, S*The harmonic voltage signal obtained by monitoring the measured electric energy quality monitoring device is simulated by adding noise to the harmonic voltage signal obtained by monitoring the measured electric energy quality monitoring device under an inaccurate critical state, and R represents an n-dimensional random number obeying 0-1 uniform distribution.
Preferably, the calculation process of the structural function method is as follows:
the structure function s (t) of the discrete signal y (i) is:
s(t)＝<[y(x+t)-y(x)]2〉＝ct4-2D； (1)
wherein t represents the number of intervals of the data points; s (t) is a function of t; x is the abscissa on the curve; y (x) is a vertical coordinate corresponding to the coordinate x;<[y(x+t)-y(x)]2>an arithmetic mean representing the difference square; c is a constant;
calculating corresponding s (t) aiming at a plurality of t to obtain a scale-free interval of a log-log curve lgt-lgs (t), calculating the slope of the scale-free interval to obtain a fractal dimension, wherein the slope alpha of the scale-free interval is the conversion relation between the fractal dimension D and the slope alpha:
preferably, the first-order difference is carried out on the log-log curve lgt-lgs (t), the fuzzy C-means algorithm is adopted to calculate the log-log curve lgt-lgs (t) obtained by the structural function method to obtain a final scale-free interval, and the least square method is adopted to fit the scale-free interval to obtain the fractal dimension curve.
Preferably, the fuzzy C-means algorithm is specifically:
known data sample X ═ X1,x2,…,xnThe fuzzy classification matrix a ═ a }ij]c×nAnd the clustering center C ═ C1,c2,…,cc]TThe fuzzy C-means algorithm can be expressed as:
in the formula: c is the number of clustering centers; n is the number of samples; m is a weighting index; a isijAnd dijRespectively the membership and Euclidean distance of the jth data point to the ith clustering center.
Preferably, the method further comprises the step of removing gross errors in the data of the log-log curve after the first-order difference; classifying the reserved data again, and removing part of miscellaneous points; and selecting an interval with small scatter fluctuation and positive fitting slope in the fitting result as a finally obtained scale-free interval.
Preferably, the coarse error is determined by performing least square fitting on the clustering results respectively, and the data set with larger fitting error is the coarse error.
The invention has the beneficial effects that: the invention provides a method for determining an error threshold of a power quality monitoring device by utilizing fractal dimension, which has higher detection precision for data loss and low time synchronization precision by utilizing the power quality monitoring device by utilizing the fractal dimension, and reversely deduces the error threshold of the power quality monitoring device by utilizing the fractal dimension according to the maximum measurement error of the power quality monitoring device in a point-to-point method, so that the method has higher detection precision.
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In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings that are needed in the detailed description of the invention or the prior art will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 is a block diagram of a power quality monitoring device for field verification;
fig. 2 is a schematic diagram of on-site calibration of the power quality monitoring device.
FIG. 3 is a diagram of maximum error of fractal dimension;
fig. 4 shows the 5 th harmonic of a 220kV sarin-110 kV north stone sand line 193 breaker in an embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It will be understood that the terms "comprises" and/or "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 herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention 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 this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
The method for determining the error threshold of the power quality monitoring device by utilizing fractal dimension detection comprises the following steps:
s1: and simulating an inaccurate critical state when the monitored energy quality monitoring device monitors according to the maximum error threshold of the point-to-point method. The method specifically comprises the following steps: according to the maximum error threshold value of 5% of the point-to-point method, randomly obtained noise is added into a harmonic voltage signal obtained by monitoring of the measured electric energy quality monitoring device so as to simulate an inaccurate critical state when the measured electric energy quality monitoring device monitors.
The noise is 5% of the harmonic voltage signal monitored by the monitored electric energy quality monitoring device, namely, each point is added with or subtracted from 5% of the value of the harmonic voltage signal monitored by the monitored electric energy quality monitoring device, the value of each point of the generated new signal is 95% or 105% of the original signal, and each point is at the edge meeting the error range so as to simulate the limit condition monitored by the monitored electric energy quality monitoring device.
The specific adding method of the noise comprises the following steps:
and generating a random number which is between 0 and 1 and is subjected to uniform distribution for each point, wherein when the generated random number is less than 0.5, the signal size of the corresponding point is changed into 105% of the value of the harmonic voltage signal monitored by the electric energy quality monitoring device at the point, and when the generated random number is more than or equal to 0.5, the signal size of the corresponding point is changed into 95% of the value of the harmonic voltage signal monitored by the electric energy quality monitoring device at the point. The calculation formula is as follows:
wherein, R to Un(0,1), i is 1,2, …, n, S is harmonic voltage signal monitored by the device for monitoring the quality of the measured electric energy, S*Is a new signal obtained by adding noise to a harmonic voltage signal obtained by monitoring of a monitored electric energy quality monitoring device, is used for simulating the harmonic voltage signal obtained by monitoring the monitored electric energy quality monitoring device in an inaccurate critical state, and R represents obedience0 to 1 evenly distributed n-dimensional random numbers.
S2: according to the figure 1, a device for monitoring the quality of the measured electric energy and a device for monitoring the quality of the high-precision electric energy are connected, and the two devices start to measure after time synchronization according to the figure 2. And randomly intercepting the harmonic voltage data monitored by the monitored electric energy quality monitoring device and the high-precision electric energy quality monitoring device for testing, and respectively calculating the fractal dimension by using a structural function method.
The fractal dimension calculated by the structure function method is specifically as follows:
the structure function method regards all points on the discrete signal curve as a time sequence with fractal characteristics, and the structure function s (t) of the discrete signal y (i) is as follows:
s(t)＝<[y(x+t)-y(x)]2>＝ct4-2D； (2)
wherein t represents the number of intervals of the data points; s (t) is a function of t; x is the abscissa on the curve; y (x) is a vertical coordinate corresponding to the coordinate x;<[y(x+t)-y(x)]2>an arithmetic mean representing the difference square; c is a constant;
calculating corresponding s (t) aiming at a plurality of t to obtain a scale-free interval of a log-log curve lgt-lgs (t), calculating the slope of the scale-free interval to obtain a fractal dimension, wherein the conversion relation between the slope alpha of the scale-free interval, D and the slope alpha is as follows:
the scale-free interval is a straight line segment on the log-log curve, and the slope of the line segment is approximately constant, so that the first-order difference is carried out on the log-log curve, and the scale-free interval is characterized in that the fluctuation is small in the scale-free interval and large outside the scale-free interval. According to the characteristic, the dual-logarithm curve after the first-order difference is clustered, and a fuzzy C-means algorithm is selected for clustering.
The fuzzy C mean value is a clustering algorithm based on a target function, data are analyzed and modeled by using a fuzzy theory, a clustering center and a classification matrix are continuously corrected to meet a termination criterion, uncertainty description of data categories is obtained, the categories of the data are obtained according to membership degrees, and the fuzzy C mean value is an improved algorithm for K-means. And (3) carrying out first-order difference on the log-log curve lgt-lgs (t), calculating the log-log 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 specifically comprises the following steps:
known data sample X ═ X1,x2,…,xnThe fuzzy classification matrix a ═ a }ij]c×nAnd the clustering center C ═ C1,c2,…,cc]TThe fuzzy C-means algorithm can be expressed as:
in the formula: c is the number of clustering centers; n is the number of samples; m is a weighting index; a isijAnd dijRespectively the membership and Euclidean distance of the jth data point to the ith clustering center.
The log-log curves after the first-order difference are divided into two types, one type is a coarse error in the data, and the coarse error needs to be eliminated. The method for judging the gross errors is to respectively carry out least square fitting on the clustering results, and the data set with larger fitting errors is the gross errors. The range of the interval obtained by the primary classification may not be accurate enough, so that the retained data needs to be classified again, and part of the miscellaneous points are removed to obtain a more accurate scale-free interval. And performing least square fitting on the clustering results respectively, wherein coarse errors are removed, the difference of the second clustering result on the fitting errors is not too large, and some problems are caused by only taking the fitting errors as a discrimination standard, so that an interval with small scattered point fluctuation and positive fitting slope in the fitting results is selected as a finally obtained scale-free interval.
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 power quality monitoring device by using the fractal dimension.
The fractal dimension calculation method is used for measuring harmonic waves and identifying device abnormality, new indexes and calculation methods for measuring harmonic wave errors and requirements for maximum allowable errors are provided, and whether the power quality monitoring device is abnormal or not can be accurately judged when the harmonic wave content rate is low. When the fractal dimension error of the signal exceeds the maximum allowable error, the power quality monitoring device can be determined to be inaccurate because the signal which exceeds the standard cannot be monitored, and a large amount of experimental simulation is needed when the proper maximum allowable error is found.
The maximum fractal dimension allowed error is found to be most reasonable under the limit condition of the electric energy quality monitoring device, and the invention provides a simulation experiment of the electric energy 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, the critical state of inaccuracy of the power quality monitoring device can be correspondingly simulated, and the maximum value of the fractal dimension error of the simulated test data and the actual data in the state can be regarded as the maximum allowable error.
Selecting harmonic data from a Bai and Itoa wind power plant, intercepting 1200 pieces of harmonic data for testing, wherein the harmonic times are from 2 to 19, respectively performing multiple tests under different harmonic times, calculating harmonic voltage data monitored by a measured electric energy quality monitoring device and a high-precision electric energy quality monitoring device by using a structure function method for testing, respectively calculating fractal dimensions by using the structure function method, and finally obtaining an error result as shown in figure 3.
In the experiment, the selected original signal should satisfy the condition of small harmonic content, and the error of the harmonic voltage calculated by GB/T19862-2016 is 1% UNAs a boundary for different formulaic divisions, so will be less than 1% UNThe harmonic with a small content is considered, and in an experiment for solving the maximum error, the selected (inter) harmonic data all meet the condition.
The case that the fractal dimension is larger than 2 may occur in the process of calculating the fractal dimension, because the signal does not have fractal characteristics, and the characteristic of the fractal 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 limited nature 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 means that a local area is selected on the fractal optionally, the local area is amplified, and the obtained amplified image shows the morphological characteristics of the original image.
For data with catastrophe points, the local structure is different from the whole and therefore does not have fractal characteristics, for data similar to white noise, the fact that the Brownian motion generates fluctuating voltage in a circuit is considered, and the fractal dimension of the Brownian motion is deduced to be 2 by a literature formula is explained in the aspect that whether harmonic voltage data similar to the white noise has fractal characteristics is unknown, but the fractal dimension can be slightly more than 2, and when the fractal dimension is set to be 2 by using a W-M fractal function, the final result is also an image similar to the white noise. For convenience of judgment, the data are removed without considering the situation that the fractal dimension is larger than 2.
In order to find out the threshold value, the 95% probability value of the statistical characteristic value is analyzed and whether the harmonic test is inaccurate or not is judged. And (4) arranging the sampled points in the descending order, removing the maximum value of 5%, and obtaining the maximum value of the rest as the 95% probability value. The national standard GB/T14549-93 'harmonic of electric energy quality public power grid' provides that 95% probability value is used as the standard for evaluating the severity of harmonic pollution. Analogy to this approach, the 95% probability value for all maximum errors is 5.0170%, thus setting the threshold to 5%. When the error of the harmonic fractal dimension exceeds 5%, the device for monitoring the quality of the measured electric energy can be determined to be inaccurate. The maximum allowable error results are shown in table 5.
TABLE 5 maximum allowable error results
Wherein, UhNHarmonic voltage, U, measured by high-precision electric energy quality measuring deviceshHarmonic voltage, U, measured for a power quality monitoring deviceNIs a nominal voltage, DhNFractal dimension, D, of harmonic voltage measured by high-precision electric energy quality measuring apparatushThe fractal dimension of the harmonic voltage measured by the power quality monitoring device.
Harmonic voltage is more than or equal to 1 percent UNAnd<1％UNin both cases, the error calculation is consistent when U ishN<1％UNWhen the temperature of the water is higher than the set temperature,
if at UhN<1％UNWhile still using the formula
And the maximum allowable absolute value error is 5%, then
The above formula satisfies UhN<1％UNThe 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 of the maximum error result in table 1 in this embodiment is in accordance with the national standard.
5-time harmonic data of a 220kV Shalin transform 110kV northern gravel sand line 193 circuit breaker is selected as experimental data, one data is recorded every three seconds, the sampling time is 3 hours and 0 minutes to 3 hours and 10 minutes, 200 data sampling points are totally used as the measurement result of the high-precision electric energy quality monitoring device, and the measurement result is shown as a curve 2 in fig. 4. The measured data of the measured electrical energy quality monitoring device is simulated by adding Gaussian noise to the selected data, scalar snr specifies the ratio of the signal to the noise of each sampling point in dB, and the data of the measured electrical energy quality monitoring device is simulated by adding 23dB, as shown in curve 1 in FIG. 4.
The maximum error is 0.08551%, the minimum error is 0.00001499%, and the point exceeding 95% meets the national standard requirements, but as seen from fig. 4, the result of the monitoring device is greatly different from the result of the high-precision electric energy quality measuring device, and after the harmonic wave is increased, the measured electric energy quality monitoring device is judged to be unqualified.
The result of the measured electric energy quality monitoring device and the result of the high-precision electric energy quality measuring device are enlarged by five times, the point less than 95 percent meets the requirements of national standards, the minimum error is 3.52 percent, the maximum error reaches 25.41 percent, and the measured electric energy quality monitoring device can be determined to be inaccurate.
If a 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 electric energy quality measuring device is 1.772, the relative error is 12.20 percent and exceeds the maximum allowable error, and the relative error of the two devices exceeds the error threshold, so that the detected electric energy quality monitoring device is considered to be abnormal and 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 components of the examples have been described above generally in terms of their functionality in order to clearly illustrate the 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 implementation. 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 the present application, it should be understood that the division of the unit is only one division of logical functions, and other division manners may be used in actual 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 used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the present invention, and they should be construed as being included in the following claims and description.
Claims (9)
1. The method for determining the error threshold of the power quality monitoring device by utilizing fractal dimension is characterized by comprising the following steps of: the method comprises the following steps:
s1: simulating an inaccurate critical state when the monitored energy quality monitoring device monitors according to the maximum error threshold of the point-to-point method;
s2: randomly intercepting harmonic voltage data monitored by a monitored electric energy quality monitoring device and a high-precision electric energy 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 power quality monitoring device by using the fractal dimension.
2. The method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 1, wherein:
the step S1 specifically includes: according to the maximum error threshold value of 5% of the point-to-point method, randomly obtained noise is added into a harmonic voltage signal obtained by monitoring of the measured electric energy quality monitoring device so as to simulate an inaccurate critical state when the measured electric energy quality monitoring device monitors.
3. The method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 2, wherein:
the noise is 5% of the harmonic voltage signal monitored by the monitored electric energy quality monitoring device, namely, each point is added with or subtracted from 5% of the value of the harmonic voltage signal monitored by the monitored electric energy quality monitoring device, the value of each point of the generated new signal is 95% or 105% of the original signal, and each point is at the edge meeting the error range so as to simulate the limit condition monitored by the monitored electric energy quality monitoring device.
4. The method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 3, wherein:
the specific adding method of the noise comprises the following steps:
and generating a random number which is between 0 and 1 and is subjected to uniform distribution for each point, wherein when the generated random number is less than 0.5, the signal size of the corresponding point is changed into 105% of the value of the harmonic voltage signal monitored by the electric energy quality monitoring device at the point, and when the generated random number is more than or equal to 0.5, the signal size of the corresponding point is changed into 95% of the value of the harmonic voltage signal monitored by the electric energy quality monitoring device at the point. The calculation formula is as follows:
wherein, R to Un(0,1), i is 1,2, …, n, S is harmonic voltage signal monitored by the device for monitoring the quality of the measured electric energy, S*The harmonic voltage signal obtained by monitoring the measured electric energy quality monitoring device is simulated by adding noise to the harmonic voltage signal obtained by monitoring the measured electric energy quality monitoring device under an inaccurate critical state, and R represents an n-dimensional random number obeying 0-1 uniform distribution.
5. The method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 1, wherein: the calculation process of the structure function method is as follows:
the structure function s (t) of the discrete signal y (i) is:
s(t)＝<[y(x+t)-y(x)]2>＝ct4-2D； (1)
wherein t represents the number of intervals of the data points; s (t) is a function of t; x is the abscissa on the curve; y (x) is a vertical coordinate corresponding to the coordinate x;<[y(x+t)-y(x)]2>an arithmetic mean representing the difference square; c is a constant;
calculating corresponding s (t) aiming at a plurality of t to obtain a scale-free interval of a log-log curve lgt-lgs (t), calculating the slope of the scale-free interval to obtain a fractal dimension, wherein the slope alpha of the scale-free interval is the conversion relation between the fractal dimension D and the slope alpha:
6. the method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 5, wherein: and (3) carrying out first-order difference on the log-log curve lgt-lgs (t), calculating the log-log 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.
7. The method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 6, wherein:
the fuzzy C-means algorithm specifically comprises the following steps:
known data sample X ═ X1,x2,…,xnThe fuzzy classification matrix a ═ a }ij]c×nAnd the clustering center C ═ C1,c2,…,cc]TThe fuzzy C-means algorithm can be expressed as:
in the formula: c is the number of clustering centers; n is the number of samples; m is a weighting index; a isijAnd dijRespectively the membership and Euclidean distance of the jth data point to the ith clustering center.
8. The method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 6, wherein: removing gross errors in the data of the log-log curves after the first-order difference; classifying the reserved data again, and removing part of miscellaneous points; and selecting an interval with small scatter fluctuation and positive fitting slope in the fitting result as a finally obtained scale-free interval.
9. The method for determining the error threshold of the power quality monitoring device by using fractal dimension as claimed in claim 6, wherein: the method for judging the gross errors is to respectively carry out least square fitting on the clustering results, and the data set with larger fitting errors is the gross errors.
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