CN103163372A

CN103163372A - Method for analyzing harmonics of power system by adopting Hilbert-Huang transform (HHT)

Info

Publication number: CN103163372A
Application number: CN2013100992271A
Authority: CN
Inventors: 李育灵; 郭芳霞; 张涛; 张璨; 文福拴; 王俊红; 王建军; 刘焕磊; 陈建军; 安成万; 魏子琪; 弓晓亮
Original assignee: CHANGZHI POWER SUPPLY BRANCH OF SHANXI ELECTRIC POWER Corp; State Grid Corp of China SGCC
Current assignee: CHANGZHI POWER SUPPLY BRANCH OF SHANXI ELECTRIC POWER Corp; State Grid Corp of China SGCC
Priority date: 2013-03-26
Filing date: 2013-03-26
Publication date: 2013-06-19
Anticipated expiration: 2033-03-26
Also published as: CN103163372B

Abstract

The invention discloses a method for analyzing harmonics of a power system by adopting Hilbert-Huang transform (HHT), and belongs to the technical field of power quality analysis of power systems. According to the technical scheme, the capable of obtaining integral mode function components of an original signal by adopting HHT comprises the following steps of: obtaining each mode function component of the original signal of a power signal by adopting HHT, judging whether mode mixing exists or not, separating the mode-mixed part of the original signal of the power signal from the original signal, sequentially performing Fourier transform and filtration on an analysis signal, performing HHT on the filtered signal to obtain each mode function component of the analysis signal, and integrating mode function components without mode mixing and each mode function component of the analysis signal to obtain the integral mode function components of the original signal. The method is applied to an electric power sector.

Description

Adopt the harmonic analysis in power system method of HHT

Technical field

The present invention adopts the harmonic analysis in power system method of HHT, belongs to the electric power quality analysis technical field.

Background technology

The people such as Huang have proposed a kind of brand-new time series signal analytical approach in 1998---HHT (Hilbert-Huang Transform), the method is to take Fourier transform as the linearity on basis and an important breakthrough of stable state analysis of spectrum, is the analytical approach for the nonlinear and nonstationary signal.

HHT comprises two processes: at first by empirical mode decomposition (empirical mode decomposition, EMD) signal decomposition is become limited intrinsic mode function (intrinsic mode function, IMF) then component carries out the Hilbert conversion to IMF and obtains instantaneous frequency and instantaneous amplitude; EMD is the core process of HHT, because only have carrying out the Hilbert conversion through the IMF after EMD, the instantaneous frequency that obtains and instantaneous amplitude just have physical significance.

There is the problem of mode aliasing in EMD in the application of reality, when 2 in the signal frequencies that form components were in 2 frequencys multiplication, EMD can't disassemble it; In " The use of a masking signal to improve empirical mode decomposition " that DEERING R and KAISER J F deliver, masking signal EMD method has been proposed, but it is larger that two parameters of structure masking signal are chosen difficulty, affected the further popularization of the method; In " Two techniques to enhance empirical mode decomposition for power quality applications " that SENROY N and SURYANARAYANAN S deliver, frequency heterodyne EMD method has been proposed, but error and the boundary effect of decomposing due to EMD can produce pseudo-mode component in low-frequency range, these pseudo-mode components will overturn and be high fdrequency component after the frequency heterodyne, mix and indistinguishable with true high fdrequency component; Therefore, on the existing methods basis, rationally adopting HHT accurate analysis electric system each harmonic is focus and the difficult point of research at present.

Summary of the invention

The present invention overcomes the deficiency that prior art exists, and technical matters to be solved is: provide a kind of and can obtain by HHT the method for each complete mode function component of original signal.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: adopt the harmonic analysis in power system method of HHT, comprise the following steps:

The first step: adopt HHT to obtain each mode function component of original signal to electric power signal, judge whether to occur the mode aliasing, if the mode aliasing occurs, enter second step;

Second step: separate from original signal mode aliasing part occurs in the electric power signal original signal, obtain analytic signal, then entered for the 3rd step;

The 3rd step: analytic signal is carried out Fourier transform and filtering successively, then entered for the 4th step;

The 4th step: adopt HHT to obtain each mode function component of analytic signal to filtered signal, then entered for the 5th step;

The 5th step: each mode function component of analytic signal that the mode function component of mode aliasing does not occur and obtain in the 4th step in the first step is integrated, obtained each complete mode function component of original signal.

In the above-mentioned first step, judge whether to occur the mode aliasing by the HHT instantaneous frequency.

In above-mentioned the 3rd step, analytic signal is carried out the harmonic component that Fourier transform determines to be positioned at 2 frequencys multiplication, the harmonic component that will be positioned at two frequencys multiplication by high-pass filtering and low-pass filtering is separated.

The beneficial effect that the present invention compared with prior art has is: a kind of harmonic analysis in power system method that the invention provides HHT of employing, judge whether to occur the mode aliasing by the HHT instantaneous frequency, the signal Fourier transform of mode aliasing part is determined to be positioned at the harmonic component of 2 frequencys multiplication, by the high pass low-pass filtering, alias component is separated afterwards, solved the mode Aliasing Problem of conventional EMD; Partly integrate obtaining each mode function component after filtering and before aliasing not occuring, thereby obtain complete each harmonic and corresponding frequency and the amplitude of original signal; Can effectively overcome the HHT that causes due to the mode aliasing and analyze inaccurate problem, method is succinct, and accuracy is high.

Description of drawings

The present invention will be further described in detail below in conjunction with accompanying drawing:

Fig. 1 adopts HHT to detect the flow process of harmonic wave;

Fig. 2 is the conventional EMD method decomposition result of signal;

Fig. 3 is the instantaneous frequency of each IMF;

Fig. 4 is the Fourier spectrum analysis of X (t);

Fig. 5 is EMD decomposition result after filtering;

Fig. 6 is the instantaneous frequency of each IMF after filtering HHT;

Fig. 7 is the instantaneous amplitude of each IMF after filtering HHT;

Embodiment

The present invention adopts the harmonic analysis in power system method of HHT, comprises the following steps:

The particular content of HHT method is as follows:

One, empirical mode decomposition

Empirical mode decomposition is the intrinsic mode function component of different scale feature with signal decomposition, and these natural mode of vibration components satisfy following two conditions:

1, the number of the number of extreme point and zero crossing equates or differs at most 1:

The mean value of the envelope up and down that is made of maximum value and minimal value 2, at any time, is 0.

Arbitrary signal S( t), its step that is decomposed into each intrinsic mode function component is as follows:

1, all local maximum point are done cubic spline interpolation, form the coenvelope line:

2, all local minimum point are done cubic spline interpolation, form the lower envelope line;

3, calculate the mean value curve of up and down envelope M ₁, signal S( t) with M ₁Difference be first part P ₁:

P ₁= S( t)- M ₁ (1)

If 4 P ₁Satisfy two conditions of IMF, it is first IMF, otherwise it is obtained to step 3 as original signal repeating step 1 P ₁₁:

P ₁₁= P ₁- M ₁₁ (2)

In formula: M ₁₁For P ₁The average of envelope up and down.

5, repeat screening until the kInferior P _{1
k}Satisfy two conditions of IMF

P _{1
k}= P _{1(1-
k)}- M _{1
k} (3)

Can utilize in actual computation V _DValue judge whether each the selection result is IMF:

(4)

In formula: rBe the number of signal point of comprising after sampling, usually V _DValue is 0.2 ~ 0.3.

6, order C ₁= P _{1
k}, C ₁Be first IMF, it has comprised short period component in original signal.Will C ₁From S( t) in separate:

R ₁= S( t)- C ₁ (5)

7, will R ₁Repeat above step as original signal nInferior, but picked up signal S( t) nIndividual IMF

R ₂= R ₁- C ₂

R _n= R _n-1- C _n (6)

8, when R _nIn the time of can not therefrom decompositing IMF again for monotonic quantity, decomposable process finishes.Can obtain:

(7)

Two, Hilbert conversion

Each IMF that obtains through EMD is carried out the Hilbert conversion, C ₁( t) the Hilbert formal definition be:

Figure 2013100992271100002DEST_PATH_IMAGE003

(8)

The structure analytic signal:

(9)

The amplitude function is:

Figure 2013100992271100002DEST_PATH_IMAGE005

(10)

Instantaneous phase is:

(11)

Instantaneous frequency is:

Figure 2013100992271100002DEST_PATH_IMAGE007

(12)

Adopt the trend of harmonic detection method of power of HHT as follows:

1, EMD mode aliasing judging quota adopts HHT analytic system harmonic wave;

If do not exist the mode aliasing can directly obtain required each harmonic information, if need further to take measures to address this problem but the mode aliasing occurs, and at present only decompose by EMD each IMF figure intuitive judgment that obtains for the judge whether the mode aliasing occurs, lack quantizating index, a kind of index whether the mode aliasing occurs of passing judgment on by the HHT instantaneous frequency has been proposed, definition frequency drop here:

(13)

In formula: f _lWith f _r-mBe respectively in HHT instantaneous frequency figure lIndividual and r- mIndividual Frequency point.Because there is boundary effect in EMD, so removed the part point on border when asking maximin in formula (13).

d _f< d _set (14)

In formula: d _setBe setting threshold, be made as 50Hz when detecting Harmonious Waves in Power Systems here.When the instantaneous frequency of certain intrinsic mode function component does not satisfy formula (14), judge to have the mode aliasing, need take measures to eliminate.

2, based on the EMD of high pass low-pass filtering

In the country's quality of power supply standard clear limit value of each harmonic, system harmonics detects needs accurate analysis to go out each harmonic, and then whether qualified judge the harmonic wave indices; The 50Hz that is spaced apart based on the adjacent each harmonic of power frequency, some subharmonic that comprises in sampled signal probably is positioned at 2 frequencys multiplication, directly adopt EMD can't decomposite these harmonic waves, so adopt the HHT method need to solve the problem that EMD can't decompose signal in 2 frequencys multiplication if the harmonic wave of electric system detects.

Utilize Fourier transform can determine harmonic component in signal, high-frequency signal and the low frequency signal that then can adopt the high pass low-pass filtering will be positioned at 2 frequencys multiplication are separated respectively, adopt afterwards the EMD method that the signal of separating is decomposed.

Suppose the signal of mode aliasing occurs X( t) harmonic component determined after Fourier transform has f _a, f _bWith f _c( f _a＜ f _b＜ f _c), wherein f _c/ f _b＜2, f _b / f _a2; Due to f _bWith f _cFrequency be positioned at 2 frequencys multiplication, so the mode aliasing has occured when adopting EMD; Adopt the high pass low-pass filtering to obtain following two signals:

X _H( t)= F _H( X( t))

X _L( t)= F _L( X( t)) (15)

In formula: F _H() and F _L() is respectively high-pass filtering and low-pass filtering, and frequency is f _cComponent be positioned at X _H( t) in, frequency is f _aWith f _bComponent be positioned at X _L( t) in, can adopt the EMD method afterwards and the mode aliasing can not occur.

As shown in Figure 1, this embodiment adopts the step of HHT detection Harmonious Waves in Power Systems as follows:

1, adopt HHT to obtain the time-frequency figure of each modal components of signal to signal;

2, calculate the frequency drop of each modal components, find the mode function component that begins to occur the mode aliasing;

3, remove generation mode aliasing each component before from original signal, obtain analytic signal;

4, to the analytic signal Fourier transform, and the component that is positioned at 2 frequencys multiplication is carried out respectively high pass and low-pass filtering;

5, adopt HHT to obtain each modal components figure and instantaneous frequency figure and instantaneous amplitude figure to filtered signal;

6, the component that the mode aliasing does not occur in the component in step 5 and step 2 is integrated, obtained each mode function component of complete signal.

Suppose signal S (t)=10sin (2 π 50t)+5sin (2 π 100t)+4sin (2 π 150t)+6sin (2 π 350t), utilize conventional EMD method that original signal s (t) is decomposed, obtain the result of each IMF as shown in Figure 2, the instantaneous frequency figure of IMF as shown in Figure 3.

As can be seen from Figure 2: the mode aliasing has occured in IMF2, and this is intuitively to see from the EMD decomposition result; Can be obtained the frequency drop of the first two IMF: df1=28Hz by Fig. 3; Df2=84H can be judged since second IMF by formula (14) and the mode aliasing occurs.Remove IMF1 and namely obtain analytic signal X (t) from original signal S (t), X (t) is carried out the Fourier transform result as shown in Figure 4.

Comprised as can be seen from Figure 4 150Hz, 100Hz and three components of 50Hz in X (t), 150Hz and 100Hz and 100Hz and 50Hz are positioned at 2 frequencys multiplication, and this has also explained the reason of IMF generation mode aliasing in Fig. 2; Adopt the EMD method to decompose according to the result of Fig. 4 after to X (t) high pass low-pass filtering, then with Fig. 2 in the mode aliasing do not occur component integrate, result is as shown in Figure 5; The instantaneous frequency of each IMF and instantaneous amplitude are respectively as shown in Figure 6 and Figure 7; Can find out from Fig. 5 to Fig. 7 the problem that adopts method of the present invention to efficiently solve the mode aliasing, resulting result is consistent with original signal S (t).

Claims

1. adopt the harmonic analysis in power system method of HHT, it is characterized in that: comprise the following steps:

2. the harmonic analysis in power system method of employing HHT according to claim 1, is characterized in that: in the above-mentioned first step, judge whether to occur the mode aliasing by the HHT instantaneous frequency.

3. the harmonic analysis in power system method of employing according to claim 2 HHT, it is characterized in that: in above-mentioned the 3rd step, analytic signal is carried out the harmonic component that Fourier transform determines to be positioned at 2 frequencys multiplication, and the harmonic component that will be positioned at two frequencys multiplication by high-pass filtering and low-pass filtering is separated.