CN103941091A - Power system HHT harmonious wave detection method based on improved EMD end point effect - Google Patents

Abstract

The invention relates to the field of harmonic detection in electric power systems, in particular to an HHT harmonic detection method in electric power systems based on improved EMD endpoint effects. Aiming at the phenomenon of signal boundary distortion in the process of EMD decomposition, this method compares the relationship between endpoints and extreme points by selecting endpoints and extreme points as reference variables, and uses the method of mirror extension to improve the effect of endpoints. The improved image method decomposes the harmonics of the power system by EMD to obtain all the intrinsic mode functions (IMF), and uses the Hilbert transform to decompose the harmonics of the power system after EMD decomposition to obtain the time-frequency characteristics of the signal. This method is beneficial to quickly detect the harmonic composition in the harmonics of the power system, thereby improving the harmonic identification ability of the power system, and is suitable for relevant departments such as the power system for the harmonic detection of the power system.

Description

Power System HHT Harmonic Detection Method Based on Improved EMD Endpoint Effect

technical field

The invention relates to the field of harmonic detection in electric power systems, in particular to an HHT harmonic detection method in electric power systems based on improved EMD endpoint effects.

Background technique

Power system harmonics are one of the important indicators of power quality, and the existence of harmonics directly affects the normal power consumption of power users. The detection of power system harmonics is the basis for dealing with power system harmonics. In order to ensure high-quality power supply, it is necessary to detect power system harmonics.

At present, the commonly used harmonic detection methods in power systems mainly include analog filter method, harmonic detection method based on instantaneous reactive power, harmonic detection method based on Fourier transform, and harmonic detection method based on wavelet transform. method. The analog filter circuit is easy to implement and low in cost, but it is easily affected by the environment, and the detection accuracy cannot be guaranteed; the harmonic detection method based on reactive power theory can accurately detect harmonics, and the detection circuit is relatively simple, but the low-pass filter is used to extract When there is a DC component, there will be a delay of a power cycle; the advantage of the fast Fourier transform (FFT) detection method is that the harmonic order to be eliminated can be selected, but the disadvantage is that the delay is long and the real-time performance is slightly poor; although the wavelet transform The signal can be decomposed into multi-resolution at different scales, but the essence of wavelet transform is a theory based on the expansion of basis functions. Signal analysis largely depends on the selection of basis functions, and for a specific problem, the optimal basis There is no definite rule to follow for the selection, which makes the analysis not ideal, and is only suitable for transient and non-stationary signals.

The Hilbert-Huang (HHT) algorithm was proposed by Norden E. Huang, a Chinese-American in 1998. This algorithm is a new type of time-frequency analysis method, which solves the shortcomings of the original time-frequency analysis method. It is suitable for the processing of nonlinear and non-stationary signals, and has been widely used in various fields since it was proposed. The HHT algorithm first uses the empirical mode decomposition method (EMD) to obtain a limited number of intrinsic mode functions (IMF for short), and then uses the Hilbert transform and the instantaneous frequency method to obtain the time domain spectrum of the signal. However, there are still defects and deficiencies in boundary processing, mode mixing and curve fitting, which affect the analysis effect of HHT, and need to be optimized and improved. Therefore, the present invention adopts the HHT algorithm to detect the harmonics of the power system after comprehensively comparing various methods for detecting the harmonics of the power system, and on the basis of the original algorithm, selects the boundary processing as the starting point, and conducts the EMD endpoint effect Improve. And it is applied to the harmonic detection of the power system, which is not only of great significance to the research and promotion of the Hilbert-Huang transform, but also a beneficial exploration combined with the harmonic detection of the power system.

Contents of the invention

The purpose of the present invention is to provide a power system HHT harmonic detection method based on the improved EMD endpoint effect, which is conducive to improving the detection of power system harmonics, thereby improving the ability of harmonic identification.

In order to achieve the above object, the technical solution of the present invention is: a power system HHT harmonic detection method based on the improved EMD endpoint effect, using the method of mirror extension to improve the endpoint effect, and using the improved mirror image method to detect the harmonic of the power system The wave is decomposed by EMD, and the time-frequency characteristics of the harmonic signal are obtained by using the Hilbert transform to decompose the harmonics of the power system after EMD decomposition. The specific steps are as follows:

Step S1: Select extreme points and endpoints as parameter variables, define k as the number of iterations of the intrinsic mode function, k=0,1,2,...n; m is the order of the intrinsic mode function, m=1, 2,3···n; select the harmonic signal of the power system after filtering to analyze;

Step S2: Let the remaining components ,if is a monotone function, then output the result, otherwise go to step S3;

Step S3: Harmonics of the power system For analysis, first obtain the time series of maximum points , time series of minimum points , left endpoint value and the right endpoint value , and then use the mirror selection principle to determine the placement positions of the left mirror and the right mirror; among them, and Indicates the chronological sequence of extreme points appearing in the harmonic signal data of the entire power system, i =0,1,2,...n;

Step S4: Use the placed mirror to perform mirror extension on the harmonic signal of the power system, and the left and right ends are respectively extended for one cycle according to the principle of mirror selection;

Step S5: Envelope the harmonic signals of the power system after the left and right ends have been mirrored and extended for one period respectively according to the cubic spline interpolation method to obtain the upper and lower envelopes, which are denoted as and ; Take the mean value of the envelope , and calculate the mean value of the envelope and power system harmonic signals the difference ;

Step S6: Yes Carry out IMF judgment, if Meet the following conditions:

(1) The number of extreme points and zero-crossing points should be equal or at most one difference;

(2) The mean value of the envelope formed by connecting its local maximum and local minimum is zero at any point, that is, the signal is locally symmetrical about the time axis;

then will Harmonic signal of power system The first IMF component of , otherwise it will be As a new power system harmonic signal, go to step S3 and repeat k times to get ,use value to determine whether each screening result meets the IMF condition:

In the formula, for right repeat The amount of time obtained, The value range of is usually 0.2~0.3; satisfy When requested, the As the first-order IMF component of the power system harmonic signal, denoted as ,Will Harmonic signals from power systems Separated from to get the remaining components:

In the formula, is the remaining component after decomposing the first-order IMF component;

Step S7: put As a new power system harmonic signal , repeat steps S3-S6 until the final remaining component is a constant or a monotonic function, so the EMD decomposition result of the power system harmonic signal can be expressed as:

In the above formula, is the IMF component after the power system harmonic EMD decomposition is completed, and m is the order of the IMF component;

Step S8: After the EMD decomposition is completed, time-frequency analysis is performed on the harmonics of the power system. First, the Hilbert transform is performed on any first-order IMF component obtained from the EMD decomposition, then:

In the above formula, yes Hilbert transform;

Step S9: Define The parsed signal:

In the formula, that is analysis signal;

Step S10: Solve the instantaneous amplitude, instantaneous phase and instantaneous frequency of the IMF component according to the analytical signal:

In the above formula, , and represent the instantaneous amplitude, instantaneous phase and instantaneous frequency respectively; so far, by steps S9-S10

Calculate the instantaneous power, instantaneous phase and instantaneous frequency of any first-order intrinsic mode function;

Step S11: After calculating the instantaneous power, instantaneous phase and instantaneous frequency, continue to solve the Hilbert spectrum; omit the remaining components , and define the Hilbert spectrum, denoted as:

In the above formula, ;

Step S12: Further solve the Hilbert marginal spectrum, denoted as:

The Hilbert marginal spectrum provides the total amplitude and energy distributed on each frequency value, which expresses the cumulative amplitude or energy on the entire data sequence in the form of probability; so far, the HHT of the improved EMD endpoint effect is used for power system harmonic signals Complete assay analysis.

In the embodiment of the present invention, in step S3, the mirror surface selection principle is specifically as follows,

Compare the left extreme point with the left endpoint value to determine the placement position of the left mirror, and compare the right extreme point with the right endpoint value to determine the placement position of the right mirror; then,

Left end mirror time series:

When the harmonic signal is initially incremented:

When the harmonic signal initially decreases:

Right-hand mirror time series:

When increasing at the end of the harmonic signal:

When the end of the harmonic signal decreases:

In the formula, , are the left end mirror time series and the right end mirror time series respectively, when the left and right end mirror time series are 1 or n, it means that the mirror is placed at the left end or right end, , , and Represents the left maximum, left minimum, right maximum and right minimum of the signal sequence, respectively.

In the embodiment of the present invention, in step S4, the minimum value and maximum value time series after mirror extension They are:

In the formula, and are the time series of left minimum, left maximum, right minimum and right maximum, respectively, after continuation, is the time series after the extension of the original extremum point;

The sequence of minima and maxima after mirror continuation:

In the formula, are respectively the extended left minimum value, left maximum value, right minimum value and right maximum value sequence, is the sequence after the extension of the original extremum point.

Compared with the prior art, the present invention has the following beneficial effects:

1. The "flying wing" phenomenon at the endpoint has been effectively suppressed, and the signal curve has obtained a complete envelope;

2. Harmonic signals can be accurately and adaptively separated, and there is no redundant IMF component, and the accuracy has been greatly improved.

Description of drawings

Fig. 1 is the work flowchart of the embodiment of the present invention.

Figure 2 is an effect diagram of the signal envelope before the mirror method is improved and an effect diagram of the difference between the original signal and the mean value of the upper and lower envelopes.

Figure 3 is an effect diagram of EMD decomposition of power system harmonics before the improvement of the image method.

Figure 4 is the instantaneous frequency and instantaneous amplitude obtained for power system harmonics before the improvement of the image method.

Figure 5 is the Hilbert spectrum obtained by solving the harmonics of the power system before the image method is improved.

Figure 6 is the Hilbert marginal spectrum obtained by solving the harmonics of the power system before the improvement of the image method.

Fig. 7 is an effect diagram of the signal envelope after the mirror method is improved and an effect diagram of the difference between the original signal and the mean value of the upper and lower envelopes.

Figure 8 is an effect diagram of EMD decomposition of power system harmonics after the mirror image method is improved.

Figure 9 shows the instantaneous frequency and instantaneous amplitude obtained for power system harmonics after the image method is improved.

Figure 10 is the Hilbert spectrum obtained by solving the harmonics of the power system after the image method is improved.

Figure 11 is the Hilbert marginal spectrum obtained by solving the harmonics of the power system after the image method is improved.

Detailed ways

The technical solution of the present invention will be specifically described below in conjunction with the accompanying drawings.

The invention is a power system HHT harmonic detection method based on the improved EMD endpoint effect. The endpoint effect is improved by the method of image continuation, and the EMD decomposition of the power system harmonic is carried out by using the improved image method, and the Hilbert transformation is used. The time-frequency characteristics of the harmonic signal are obtained by decomposing the harmonics of the power system after EMD decomposition;

The power system HHT harmonic detection method is described in conjunction with Figure 1, and the power system harmonic signal Use the pre-improved and improved mirroring method to simulate the effect diagram shown in Figure 2-11, specifically follow the steps below:

Step 1: Select extreme points and endpoints as parameter variables, define k as the number of iterations of the intrinsic mode function, k=0,1,2,...n; m is the order of the intrinsic mode function, m=1, 2,3···n; select the harmonic signal of the power system after filtering for analysis.

Step 2: Make the remaining components ,if is a monotone function, then output the result, otherwise go to step 3.

Step 3: For Power System Harmonics For analysis, first obtain the time series of maximum points , time series of minimum points , left endpoint value and the right endpoint value , and compare the extreme point on the left with the value of the left endpoint to determine the placement of the left mirror, and compare the extreme point on the right with the value of the right endpoint to determine the placement of the right mirror, where and Indicates the chronological sequence of extreme points appearing in the harmonic signal data of the entire power system, respectively using , , and Represents the left maximum value, left minimum value, right maximum value and minimum value of the signal sequence, and the mirror selection principle can be refined as follows:

Left end mirror time series:

When the harmonic signal is initially incremented:

When the harmonic signal initially decreases:

Right-hand mirror time series:

When increasing at the end of the harmonic signal:

When the end of the harmonic signal decreases:

In the formula, , They are the left end mirror time series and the right end mirror time series respectively. When the left and right end mirror time series are 1 or n, it means that the mirror is placed at the left end or right end.

Step 4: Use the placed mirror to mirror and extend the harmonic signal of the power system. The left and right ends are respectively extended for one cycle according to the principle of mirror surface selection, and the time series of minimum and maximum values after mirror extension They are:

In the formula, and are the time series of left minimum, left maximum, right minimum and right maximum, respectively, after continuation, is the time series after the continuation of the original extreme point, and the minimum and maximum value series after the mirror continuation:

In the formula, is the sequence of minima and maxima after mirror extension, are respectively the extended left minimum value, left maximum value, right minimum value and right maximum value sequence, is the sequence after the extension of the original extremum point.

Step 5: Envelope the harmonic signal of the power system after the left and right ends of the mirror image have been extended for one period respectively according to the cubic spline interpolation method to obtain the upper and lower envelopes, which are denoted as and . Take the mean of the envelope , and calculate the mean value of the envelope and power system harmonic signals the difference .

Step 6: Right Carry out IMF judgment, if Meet the following conditions:

(1) The number of extreme points and zero-crossing points should be equal or at most one difference;

(2) The mean value of the envelope formed by connecting its local maximum and local minimum is zero at any point, that is, the signal is locally symmetrical about the time axis;

then will Harmonic signal of power system The first IMF component of , otherwise it will be As the new power system harmonic signal, go to step 3 and repeat k times to get ,use value to determine whether each screening result meets the IMF condition:

In the formula, for right repeat The amount of time obtained, The value range of is usually 0.2~0.3. satisfy When requested, the As the first-order IMF component of the power system harmonic signal, denoted as ,Will from

Power system harmonic signal Separated from and get the remaining components:

In the formula, is the remaining component after decomposing the first-order IMF component.

Step 7: Put As a new power system harmonic signal , repeat steps 3-6 until the final remaining components be a constant or a monotonic function. So the EMD decomposition result of the power system harmonic signal can be expressed as:

In the above formula, is the IMF component after the power system harmonic EMD decomposition is completed, and m is the IMF order.

Step 8: After the EMD decomposition is completed, time-frequency analysis is performed on the power system harmonics. First, any EMD decomposition obtained

It means that the first-order IMF component is subjected to Hilbert transformation, then:

In the above formula, yes The Hilbert transform.

Step 9: Define The parsed signal:

In the formula, that is analysis signal.

Step 10: Solve for the instantaneous amplitude, instantaneous phase, and instantaneous frequency of the IMF component from the analytical signal:

In the above formula, , and represent the instantaneous amplitude, instantaneous phase, and instantaneous frequency, respectively. So far, the instantaneous power, instantaneous phase and instantaneous frequency of any first-order intrinsic mode function can be obtained from steps 9-10.

Step 11: After calculating the instantaneous power, instantaneous phase and instantaneous frequency, continue to solve the Hilbert spectrum, omitting the remaining components , and define the Hilbert spectrum, denoted as:

In the above formula, .

Step 12: Further solve the Hilbert marginal spectrum, denoted as:

The Hilbert marginal spectrum provides the total amplitude and energy distributed on each frequency value, which expresses the cumulative amplitude or energy on the entire data sequence in the form of probability. So far, the HHT of the improved EMD endpoint effect is used for the harmonic signal of the power system Complete assay analysis.

Accompanying drawing 2-11 is the effect diagram obtained by simulation using the mirror method before and after improvement: Among them, Fig. 2 is the effect diagram of the signal envelope before the mirror method is improved and the effect of the difference between the original signal and the mean value of the upper and lower envelopes Fig. 3 is the effect diagram of EMD decomposition of power system harmonics before the mirror method is improved, Fig. 4 is the instantaneous frequency and instantaneous amplitude of the power system harmonics before the mirror method is improved, and Fig. 5 is the mirror image method The Hilbert spectrum obtained by solving the harmonics of the power system before the improvement is made. Figure 6 is the Hilbert marginal spectrum obtained by solving the harmonics of the power system before the improvement of the mirror method. Figure 7 is the signal envelope after the mirror method is improved and the original The effect diagram of the difference between the signal and the mean value of the upper and lower envelopes. Figure 8 is the effect diagram of the EMD decomposition of the power system harmonics after the mirror method is improved. Figure 9 is the instantaneous power system harmonics obtained after the mirror method is improved. Frequency and instantaneous amplitude, Figure 10 is the Hilbert spectrum obtained by solving the power system harmonics after the mirror method is improved, and Figure 11 is the Hilbert marginal spectrum obtained by solving the power system harmonics after the mirror method is improved.

The above are the preferred embodiments of the present invention, and all changes made according to the technical solution of the present invention, when the functional effect produced does not exceed the scope of the technical solution of the present invention, all belong to the protection scope of the present invention. the

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.