CN103941091A - Power system HHT harmonious wave detection method based on improved EMD end point effect - Google Patents
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Abstract
The invention relates to the field of detection of harmonious waves in power systems, in particular to a power system HHT harmonious wave detection method based on improved EMD end point effect. The method comprises the steps of selecting end points and extreme point as reference variables and comparing the relation of the end points and extreme point according to a signal boundary distorting phenomenon occurred in the EMD decomposition course, adopting a mirror image extension method to improve the end point effect, utilizing an improved mirror image method to perform EMD decomposition on the power system harmonious waves so as to obtain all of intrinsic mode function (IMF), utilizing Hilbert conversion to perform decomposition on the power system harmonious waves subjected to the EMD decomposition so as to obtain signal time-frequency characteristics. The power system HHT harmonious wave detection method facilities rapid detection of harmonious wave composition of the power system harmonious waves, accordingly improves the power system harmonious wave recognition capability and is suitable for power systems and relevant departments and used for power system harmonious wave detection.
Description
Technical Field
The invention relates to the field of harmonic detection of a power system, in particular to a HHT (Hilbert-Huang transform) harmonic detection method of the power system based on an improved EMD (empirical mode decomposition) end effect.
Background
The harmonic wave of the power system is one of important indexes of power quality, and the existence of the harmonic wave directly influences the normal power utilization of power users. The detection of the harmonic wave of the power system is the basis for processing the harmonic wave problem of the power system, and the harmonic wave of the power system must be detected in order to ensure high-quality power supply.
At present, the common harmonic detection methods for the power system mainly include an analog filter method, a harmonic detection method based on instantaneous reactive power, a harmonic detection method based on fourier transform, a harmonic detection method based on wavelet transform, and the like. The analog filter circuit is easy to realize and low in cost, but is easily influenced by the environment, and the detection precision cannot be guaranteed; the harmonic detection method based on the reactive power theory can accurately detect the harmonic, the detection circuit is simple, but when the low-pass filter is used for extracting the direct-current component, the delay of one power supply period is generated; the Fast Fourier Transform (FFT) -based detection method has the advantages that the harmonic frequency to be eliminated can be selected, and the defects of longer time delay and poorer real-time performance are overcome; although wavelet transformation can perform multi-resolution decomposition on signals under different scales, the essence of wavelet transformation is a theory based on basis function expansion, signal analysis depends on selection of basis functions to a great extent, and for a specific problem, selection of an optimal basis is not followed by a determined rule, so that analysis is not ideal and is only suitable for transient and non-stationary signals.
The Hilbert-Huang (HHT) algorithm was proposed by the American Cornish Cornishica albuginea (Norden E.Huang) in 1998, is a novel time-frequency analysis method, overcomes the defects of the original time-frequency analysis method, is suitable for processing nonlinear non-stationary signals, and is widely applied to various fields after being proposed. HHT Algorithm first useEmpirical mode decompositionThe method (EMD) obtains a limited number of Intrinsic Mode Functions (IMF), and then uses Hilbert transform sumInstantaneous frequencyThe method obtains a time domain spectrum of the signal. However, there are defects and shortcomings in boundary processing, modal mixing and curve fitting, which affect the analysis effect of HHT, and need to optimize and modify itAnd then. Therefore, after various power system harmonic detection methods are comprehensively compared, the invention adopts the HHT algorithm to detect the power system harmonic, and selects the boundary processing as the starting point on the basis of the original algorithm to improve the EMD end effect. The method is applied to the harmonic detection of the power system, has important significance on the research and popularization of Hilbert-Huang transform, and is beneficial exploration combined with the harmonic detection of the power system.
Disclosure of Invention
The invention aims to provide a power system HHT harmonic detection method based on an improved EMD endpoint effect, which is beneficial to improving the detection of power system harmonics so as to improve the harmonic identification capability.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for detecting HHT harmonic wave of a power system based on improved EMD endpoint effect comprises the following steps of improving the endpoint effect by adopting a mirror image continuation method, carrying out EMD decomposition on the harmonic wave of the power system by utilizing the improved mirror image method, and decomposing the harmonic wave of the power system after EMD decomposition by utilizing Hilbert transform to obtain the time-frequency characteristic of the harmonic wave signal, wherein the method comprises the following specific steps:
step S1: selecting extreme points and end points as parameter variables, defining k as iteration number of the intrinsic mode function, k =0,1,2, n, m is the order of the intrinsic mode function, m =1,2,3, n, selecting the harmonic signal of the power system after filteringCarrying out analysis;
step S2: let the residual componentIf, ifIf the function is a monotone function, outputting the result, otherwise, turning to the step S3;
step S3: to harmonic of electric power systemPerforming analysis by first obtaining a time series of maximum pointsTime series of minimum pointsLeft end point valueAnd a right endpoint valueThen, determining the placement positions of the left mirror surface and the right mirror surface by adopting a mirror surface selection principle; wherein,andrepresenting a time-sequential sequence of occurrence of the extreme points in the harmonic signal data of the entire power system,i=0,1,2,···n；
step S4: carrying out mirror extension on harmonic signals of the power system by using the placed mirror surface, and respectively extending a period at the left end part and the right end part according to a mirror surface selection principle;
step S5: respectively carrying out mirror image extension on the left and right end parts of the harmonic signals of the power system for one period, enveloping the harmonic signals according to a cubic spline interpolation method to obtain upper and lower envelope lines which are respectively marked asAnd(ii) a Taking the mean value of envelopeAnd calculating the mean value of the envelope curveHarmonic signals with electric power systemDifference of (2)；
Step S6: to pairMaking IMF decision ifThe following conditions are satisfied:
(1) the number of extreme and zero crossing points should be equal or at most one different;
(2) the mean value of the envelope lines formed by respectively connecting the local maximum value and the local minimum value is zero at any point, namely the signals are locally symmetrical about a time axis;
then will beAs harmonic signals of power systemsOtherwise will be the first IMF component ofAs a new harmonic signal of the power system, go to step S3 and repeat k times to obtainBy usingTo determine whether each screening result satisfies the IMF condition:
in the formula,is a pair ofRepetition ofThe component of the second order of magnitude,the value range of (A) is usually 0.2-0.3;satisfy the requirement ofWhen required, willThe IMF component of the first order, which is the harmonic signal of the power system, is described asWill beFrom harmonic signals of the power systemThe residual component is obtained by separation:
in the formula,is the remaining component after the first order IMF component is decomposed;
step S7: will be provided withAs new harmonic signals of power systemsRepeating steps S3-S6 until the final remaining componentsBeing a constant or a monotonic function, the result of EMD decomposition of the harmonic signal of the power system can then be expressed as:
in the above formula, the first and second carbon atoms are,the method comprises the steps of obtaining IMF components after EMD decomposition of harmonic waves of a power system is completed, wherein m is an IMF component order;
step S8: after EMD decomposition is completed, time-frequency analysis is carried out on power system harmonic waves, firstly, Hilbert transformation is carried out on any one-order IMF component obtained by EMD decomposition, and then:
in the above formula, the first and second carbon atoms are,is thatHilbert transform;
step S9: definition ofAnalytic signal of (2):
in the formula,is thatThe analytic signal of (1);
step S10: and solving the instantaneous amplitude, the instantaneous phase and the instantaneous frequency of the IMF component according to the analytic signal:
in the above formula, the first and second carbon atoms are,、andrespectively representing instantaneous amplitude, instantaneous phase and instantaneous frequency; up to this point, the steps S9-S10
Solving instantaneous power, instantaneous phase and instantaneous frequency of any first order inherent mode function;
step S11: after the instantaneous power, the instantaneous phase and the instantaneous frequency are solved, the Hilbert spectrum is continuously solved; omitting the residual componentAnd define the Hilbert spectrum, written as:
in the above formula, the first and second carbon atoms are,；
step S12: the Hilbert marginal spectrum is further solved and recorded as:
the Hilbert margin spectrum provides the total amplitude and energy distributed over each frequency value, which represents the cumulative amplitude or energy over the entire data sequence in the form of probabilities; to this end, detection analysis is performed on power system harmonic signals using HHTs that improve the EMD endpoint effect.
In the embodiment of the present invention, in step S3, the mirror selection principle is specifically as follows,
comparing the left extreme point with the left end point to determine the placement position of the left mirror surface, and comparing the right extreme point with the right end point to determine the placement position of the right mirror surface; then the process of the first step is carried out,
left end mirror time sequence:
at initial increment of harmonic signal:
when the harmonic signal is initially decreased:
right mirror time series:
at the end of the harmonic signal increment:
when the harmonic signal end is decreased:
in the formula,、respectively a left end mirror surface time sequence and a right end mirror surface time sequence, when the left end mirror surface time sequence and the right end mirror surface time sequence are 1 or n, the mirror surface is placed at a left end point or a right end point,、、andrespectively representing a left maximum, a left minimum, a right maximum and a right minimum of the signal sequence.
In the embodiment of the present invention, in step S4, the minimum value and the maximum value time series after the mirror extensionRespectively as follows:
in the formula,andrespectively a left minimum value, a left maximum value, a right minimum value and a right maximum value time sequence after continuation,the time sequence after the extension of the original extreme point is obtained;
minimum and maximum sequences after mirror extension:
in the formula,respectively a left minimum value, a left maximum value, a right minimum value and a right maximum value after continuation,the extended sequence for the original extreme point.
Compared with the prior art, the invention has the following beneficial effects:
1. the phenomenon of end point 'flying wing' is effectively inhibited, and a signal curve is completely enveloped;
2. the harmonic signals can be accurately and adaptively separated, redundant IMF components are not generated, and the precision is greatly improved.
Drawings
FIG. 1 is a flow chart of the operation of an embodiment of the present invention.
Fig. 2 is a graph of the effect of the envelope of the signal before the mirror image method is improved and a graph of the effect of the difference between the original signal and the mean values of the upper and lower envelopes.
Fig. 3 is a diagram showing the effect of EMD decomposition on the harmonics of the power system before the mirror image method is improved.
FIG. 4 is a graph of instantaneous frequency and instantaneous amplitude found for power system harmonics before the mirror image method is modified.
Fig. 5 is a Hilbert spectrum obtained by solving for power system harmonics before the mirror image method is improved.
Fig. 6 is a Hilbert margin spectrum obtained by solving for power system harmonics before the mirror image method is improved.
Fig. 7 is a graph of the effect of the envelope of the signal after the mirror image method is improved and a graph of the effect of the difference between the original signal and the mean values of the upper and lower envelopes.
Fig. 8 is a diagram showing the effect of performing EMD decomposition on the harmonics of the power system after the mirror image method is improved.
FIG. 9 is the instantaneous frequency and instantaneous amplitude found for power system harmonics after the mirror image method has been modified.
Fig. 10 is a Hilbert spectrum obtained by solving for power system harmonics after the mirror image method is modified.
Fig. 11 is a Hilbert margin spectrum obtained by solving for power system harmonics after the mirror image method is improved.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The invention relates to a power system HHT harmonic detection method based on an improved EMD endpoint effect, which adopts a mirror image continuation method to improve the endpoint effect, utilizes the improved mirror image method to carry out EMD decomposition on power system harmonics, and utilizes Hilbert transform to decompose the power system harmonics after EMD decomposition to obtain the time-frequency characteristics of harmonic signals;
the method for detecting HHT harmonic wave of power system is described with reference to FIG. 1, and is used for detecting harmonic wave signal of power systemUsing before and after improvementThe effect diagram obtained by performing simulation by the subsequent mirror image method is shown in the attached figures 2-11, and the method specifically comprises the following steps:
step 1: selecting extreme points and end points as parameter variables, defining k as iteration number of the intrinsic mode function, k =0,1,2, n, m is the order of the intrinsic mode function, m =1,2,3, n, selecting the harmonic signal of the power system after filteringAnd (6) carrying out analysis.
Step 2: let the residual componentIf, ifIf the function is a monotone function, outputting the result, otherwise, turning to the step 3.
And step 3: to harmonic of electric power systemPerforming analysis by first obtaining a time series of maximum pointsTime series of minimum pointsLeft end point valueAnd a right endpoint valueComparing the left extreme point with the left end point to determine the placement of the left mirror, and comparing the right extreme point with the right end point to determine the placement of the right mirror, whereinAndrepresenting the time sequence of the appearance of the extreme points in the harmonic signal data of the whole power system respectively、、Andrepresenting the left maximum, the left minimum, the right maximum and the minimum of the signal sequence, and the mirror selection principle can be detailed as follows:
left end mirror time sequence:
at initial increment of harmonic signal:
when the harmonic signal is initially decreased:
right mirror time series:
at the end of the harmonic signal increment:
when the harmonic signal end is decreased:
in the formula,、the time sequence of the left end mirror surface and the time sequence of the right end mirror surface are respectively, and when the time sequence of the left end mirror surface and the time sequence of the right end mirror surface is 1 or n, the mirror surface is placed at the left end point or the right end point.
And 4, step 4: and carrying out mirror image continuation on the harmonic signals of the power system by using the placed mirror surface. The left end part and the right end part respectively extend a period according to a mirror selection principle, and a minimum value time sequence and a maximum value time sequence after the mirror extensionRespectively as follows:
in the formula,andrespectively a left minimum value, a left maximum value, a right minimum value and a right maximum value time sequence after continuation,for the time sequence after the extension of the original extreme point, the minimum value and the maximum value sequence after the mirror image extension:
in the formula,for the sequence of minima and maxima after the mirror extension,respectively a left minimum value, a left maximum value, a right minimum value and a right maximum value after continuation,the extended sequence for the original extreme point.
And 5: respectively extending the left and right parts of the mirror image for one period to obtain harmonic signals of the power system, enveloping the harmonic signals according to a cubic spline interpolation method to obtain upper and lower envelope lines, and respectively recording the upper and lower envelope lines asAnd. Taking the mean value of envelopeAnd calculating the mean value of the envelope curveHarmonic signals with electric power systemDifference of (2)。
Step 6, the pairMaking IMF decision ifThe following conditions are satisfied:
(1) the number of extreme and zero crossing points should be equal or at most one different;
(2) the mean value of the envelope lines formed by respectively connecting the local maximum value and the local minimum value is zero at any point, namely the signals are locally symmetrical about a time axis;
then will beAs harmonic signals of power systemsOtherwise will be the first IMF component ofTurning to step 3 as a new harmonic signal of the power system, and repeating the step k times to obtainBy usingTo determine whether each screening result satisfies the IMF condition:
in the formula,is a pair ofRepetition ofThe component of the second order of magnitude,the value range of (A) is usually 0.2-0.3.Satisfy the requirement ofWhen required, willThe IMF component of the first order, which is the harmonic signal of the power system, is described asWill beFrom
Harmonic signals of power systemSeparating to obtain the residual component:
in the formula,is the remaining component after the first order IMF component is decomposed.
And 7: will be provided withAs new harmonic signals of power systemsRepeating steps 3-6 until the final remaining componentsIs a constant or is a monotonic function. The EMD decomposition result of the power system harmonic signal can then be expressed as:
in the above formula, the first and second carbon atoms are,and m is an IMF order, namely an IMF component after EMD decomposition of the harmonic waves of the power system is completed.
And 8: and after EMD decomposition is completed, performing time-frequency analysis on the harmonic waves of the power system. First, for any item obtained by EMD decomposition
The first-order IMF component is Hilbert transformed, then:
in the above formula, the first and second carbon atoms are,is thatHilbert transform.
And step 9: statorYi (Chinese character)Analytic signal of (2):
in the formula,is thatTo resolve the signal.
Step 10: and solving the instantaneous amplitude, the instantaneous phase and the instantaneous frequency of the IMF component according to the analytic signal:
in the above formula, the first and second carbon atoms are,、andrespectively representing instantaneous amplitudeInstantaneous phase and instantaneous frequency. To this end, the instantaneous power, instantaneous phase and instantaneous frequency of any first order natural mode function can be determined by steps 9-10.
Step 11: after the instantaneous power, the instantaneous phase and the instantaneous frequency are solved, the Hilbert spectrum is continuously solved, and residual components are omittedAnd define the Hilbert spectrum, written as:
in the above formula, the first and second carbon atoms are,。
step 12: the Hilbert marginal spectrum is further solved and recorded as:
the Hilbert marginal spectrum provides the total amplitude and energy distributed over each frequency value, which represents the cumulative amplitude or energy over the entire data sequence in the form of probabilities, to which detection analysis is done for power system harmonic signals using HHT to improve EMD end-point effects.
FIGS. 2-11 are graphs showing the effect of simulation by using the mirror image method before and after the improvement: wherein, fig. 2 is a signal envelope effect diagram before the image method is improved and an effect diagram of a difference between an original signal and upper and lower envelope means, fig. 3 is an effect diagram of EMD decomposition of a power system harmonic before the image method is improved, fig. 4 is an instantaneous frequency and instantaneous amplitude obtained for the power system harmonic before the image method is improved, fig. 5 is a Hilbert spectrum obtained by solving the power system harmonic before the image method is improved, fig. 6 is a Hilbert marginal spectrum obtained by solving the power system harmonic before the image method is improved, fig. 7 is a signal envelope effect diagram after the image method is improved and an effect diagram of a difference between the original signal and the upper and lower envelope means, fig. 8 is an effect diagram of EMD decomposition of the power system harmonic after the image method is improved, fig. 9 is an instantaneous frequency and instantaneous amplitude obtained for the power system harmonic after the image method is improved, fig. 10 is a Hilbert spectrum obtained by solving the power system harmonics after the mirror image method is improved, and fig. 11 is a Hilbert marginal spectrum obtained by solving the power system harmonics after the mirror image method is improved.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (3)
1. A power system HHT harmonic detection method based on improved EMD endpoint effect is characterized in that: the method comprises the following steps of improving an endpoint effect by adopting a mirror image continuation method, carrying out EMD decomposition on the harmonic wave of the power system by utilizing the improved mirror image method, and decomposing the harmonic wave of the power system after EMD decomposition by utilizing Hilbert transform to obtain the time-frequency characteristic of the harmonic wave signal, wherein the method specifically comprises the following steps:
step S1: selecting extreme points and end points as parameter variables, defining k as iteration times of the inherent modal function, k =0,1,2, n, m is the order of the inherent modal function, m =1,2,3N, selecting the filtered harmonic signal of the power systemCarrying out analysis;
step S2: let the residual componentIf, ifIf the function is a monotone function, outputting the result, otherwise, turning to the step S3;
step S3: to harmonic of electric power systemPerforming analysis by first obtaining a time series of maximum pointsTime series of minimum pointsLeft end point valueAnd a right endpoint valueThen, determining the placement positions of the left mirror surface and the right mirror surface by adopting a mirror surface selection principle; wherein,andrepresenting a time-sequential sequence of occurrence of the extreme points in the harmonic signal data of the entire power system,i=0,1,2,···n；
step S4: carrying out mirror extension on harmonic signals of the power system by using the placed mirror surface, and respectively extending a period at the left end part and the right end part according to a mirror surface selection principle;
step S5: respectively carrying out mirror image extension on the left and right end parts of the harmonic signals of the power system for one period, enveloping the harmonic signals according to a cubic spline interpolation method to obtain upper and lower envelope lines which are respectively marked asAnd(ii) a Taking the mean value of envelopeAnd calculating the mean value of the envelope curveHarmonic signals with electric power systemDifference of (2)；
Step S6: to pairMaking IMF decision ifThe following conditions are satisfied:
(1) the number of extreme and zero crossing points should be equal or at most one different;
(2) the mean value of the envelope lines formed by respectively connecting the local maximum value and the local minimum value is zero at any point, namely the signals are locally symmetrical about a time axis;
then will beAs harmonic signals of power systemsOtherwise will be the first IMF component ofAs a new harmonic signal of the power system, go to step S3 and repeat k times to obtainBy usingTo determine whether each screening result satisfies the IMF condition:
in the formula,is a pair ofThe resulting component was repeated k-1 times,the value range of (A) is usually 0.2-0.3;satisfy the requirement ofWhen required, willThe IMF component of the first order, which is the harmonic signal of the power system, is described asWill beFrom harmonic signals of the power systemThe residual component is obtained by separation:
in the formula,is the remaining component after the first order IMF component is decomposed;
step S7: will be provided withAs new harmonic signals of power systemsRepeating steps S3-S6 until the final remaining componentsBeing a constant or a monotonic function, the result of EMD decomposition of the harmonic signal of the power system can then be expressed as:
in the above formula, the first and second carbon atoms are,the method comprises the steps of obtaining IMF components after EMD decomposition of harmonic waves of a power system is completed, wherein m is an IMF component order;
step S8: after EMD decomposition is completed, time-frequency analysis is carried out on power system harmonic waves, firstly, Hilbert transformation is carried out on any one-order IMF component obtained by EMD decomposition, and then:
in the above formula, the first and second carbon atoms are,is thatHilbert transform;
step S9: definition ofAnalytic signal of (2):
in the formula,is thatThe analytic signal of (1);
step S10: and solving the instantaneous amplitude, the instantaneous phase and the instantaneous frequency of the IMF component according to the analytic signal:
in the above formula, the first and second carbon atoms are,、andrespectively representing instantaneous amplitude, instantaneous phase and instantaneous frequency; up to this point, the steps S9-S10
Solving instantaneous power, instantaneous phase and instantaneous frequency of any first order inherent mode function;
step S11: after the instantaneous power, the instantaneous phase and the instantaneous frequency are solved, the Hilbert spectrum is continuously solved; omitting the residual componentAnd define the Hilbert spectrum, written as:
in the above formula, the first and second carbon atoms are,；
step S12: the Hilbert marginal spectrum is further solved and recorded as:
the Hilbert margin spectrum provides the total amplitude and energy distributed over each frequency value, which represents the cumulative amplitude or energy over the entire data sequence in the form of probabilities; to this end, detection analysis is performed on power system harmonic signals using HHTs that improve the EMD endpoint effect.
2. The power system HHT harmonic detection method based on improved EMD end-point effect according to claim 1, wherein: in step S3, the mirror selection principle is specifically as follows,
comparing the left extreme point with the left end point to determine the placement position of the left mirror surface, and comparing the right extreme point with the right end point to determine the placement position of the right mirror surface; then the process of the first step is carried out,
left end mirror time sequence:
at initial increment of harmonic signal:
when the harmonic signal is initially decreased:
right mirror time series:
at the end of the harmonic signal increment:
when the harmonic signal end is decreased:
in the formula,、respectively a left end mirror surface time sequence and a right end mirror surface time sequence, when the left end mirror surface time sequence and the right end mirror surface time sequence are 1 or n, the mirror surface is placed at a left end point or a right end point,、、andrespectively representing a left maximum, a left minimum, a right maximum and a right minimum of the signal sequence.
3. The power system HHT harmonic detection method based on improved EMD end-point effect according to claim 2, wherein: in step S4, the minimum and maximum time series after the mirror extensionRespectively as follows:
in the formula,andrespectively a left minimum value, a left maximum value, a right minimum value and a right maximum value time sequence after continuation,the time sequence after the extension of the original extreme point is obtained;
minimum and maximum sequences after mirror extension:
in the formula,respectively a left minimum value, a left maximum value, a right minimum value and a right maximum value after continuation,the extended sequence for the original extreme point.
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