CN103034757A - Wind farm time-frequency domain modeling method based on empirical mode decomposition (EMD) - Google Patents

Wind farm time-frequency domain modeling method based on empirical mode decomposition (EMD) Download PDF

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CN103034757A
CN103034757A CN2012105076737A CN201210507673A CN103034757A CN 103034757 A CN103034757 A CN 103034757A CN 2012105076737 A CN2012105076737 A CN 2012105076737A CN 201210507673 A CN201210507673 A CN 201210507673A CN 103034757 A CN103034757 A CN 103034757A
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唐西胜
胡枭
苗福丰
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State Grid Corp of China SGCC
North China Electric Power Research Institute Co Ltd
Institute of Electrical Engineering of CAS
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Abstract

The invention relates to a wind farm time-frequency domain modeling method based on empirical mode decomposition (EMD). The method comprises the steps that obtained measured data of wind farm power is processed through EMD into a plurality of intrinsic mode functions (IMF) after being subjected to normalized filtering processing, hilbert transform is carried out on the IMFs respectively to generate corresponding time-frequency spectra, then the time-frequency spectra are respectively fitted, the fitting results are respectively subjected to hilbert transform to obtain time domain expressions, and the time domain expressions are summed to obtain a wind farm analytical model containing various fluctuation characteristics. According to the modeling method disclosed by the invention, the analytical model established in a time-frequency domain modeling means contains the typical fluctuation characteristic information of the wind farm, and the model is used for simulating the impact analysis of wind farm fluctuation with nonstationary randomness on network voltage and frequency.

Description

Wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition
Technical field
The present invention relates to wind farm grid-connected impact analysis technical field, be specifically related to comprise the foundation of the wind energy turbine set reliable model of fluctuation information.
Background technology
Empirical mode decomposition (Empirical Mode Decomposition, be EMD) be the ingredient of HHT(Hilbert-HuangTransform), delivered a kind of method for the treatment of non-stationary signal that proposes in " TheEmpi rical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationaryTime Series Analysis " in 1998 by people such as Norden E.Huang and Steven R.Long.The effect of EMD is that non-stationary signal is decomposed into some intrinsic mode function IMF(intrinsic Mode Function that satisfy Hilbert transform), these IMF are carried out Hilbert transform, can access the distribution situation of signal transient frequency.EMD has complete adaptivity, can come self-adaptation to produce " base " according to concrete signal, and the IMF that is namely produced by " screening " process does not need to preset basis function, and this is the advantage place of EMD just also.
Wind farm grid-connected impact analysis is that following wind energy turbine set realizes necessity work that extensive high infiltration is incorporated into the power networks.Given this impact analysis of being incorporated into the power networks mainly relies on simulation study, is prerequisite so set up reliable wind energy turbine set model, and this requires the wind energy turbine set model must be able to comprise wind energy turbine set with the power swing characteristic of non-stationary randomness.And present wind energy turbine set modeling approach mainly is based on the wind energy turbine set equivalent model of equivalent wind speed, and its basic ideas are to come an equivalent wind energy turbine set with separate unit or several Fans, and the input wind speed of blower fan then substitutes with equivalent wind speed.This wherein comprises two key issues, and the one, the computing method of equivalent wind speed, another is the correction of fan parameter.Because the complicacy of wind energy turbine set self structure comprises structural information and is difficult to set up at interior accurate physical model, this Equivalent Modeling thinking provides a kind of shortcut.Yet, because the existence of the inner inertia of wind energy turbine set and smoothing effect, input between wind speed and the output power and be difficult to find accurately corresponding relation, cause the wave characteristic that equivalent model can not the reproducing output power.This is extremely disadvantageous for wind farm grid-connected impact analysis.
Summary of the invention
The objective of the invention is to set up the wind energy turbine set model that comprises the output-power fluctuation characteristic information, be used for wind farm grid-connected lower impact analysis to electrical network.
The present invention adopts the Hilbert transform method, the intrinsic mode function IMF signal that has the different frequency interval behind empirical mode decomposition (EMD) is carried out Time-frequency Spectrum Analysis, simulate the less smooth curve of residual error, and obtain time-domain expression via anti-Hilbert transform, i.e. wind energy turbine set analytic model.
The wind energy turbine set time-frequency domain modeling method concrete steps that the present invention is based on empirical mode decomposition (EMD) are as follows:
1. the output power data Pwind_i (t) of every unit in the collection wind energy turbine set sums up the output power Pwind_i (t) of every unit in the wind energy turbine set that collects, and tries to achieve the wind energy turbine set gross output
Figure BDA00002511004800021
The wind energy turbine set gross output
Figure BDA00002511004800022
Be every unit blower fan output power Pwind_i (t) sum in the wind energy turbine set, namely
Figure BDA00002511004800023
Wherein t is the time.
To the wind energy turbine set gross output
Figure BDA00002511004800024
Carry out normalized, choose the total specified output power Pe of wind energy turbine set (t) as base value.
Data after the normalization are carried out Fourier transform, generate frequency spectrum, observe spectral characteristic, the frequency distribution of the data after the estimation normalization, and carry out filtering by lowpass digital filter, the noise spot that the elimination error is larger, the data that obtain are designated as P (t), and P (t) is carried out following processing as the Power Output for Wind Power Field data.
2. Power Output for Wind Power Field P (t) is carried out empirical mode decomposition (EMD) and process, P (t) is decomposed into n intrinsic mode function c 1(t), c 2(t) ... c n(t) and remaining component rn (t), that is:
P ( t ) = Σ j = 1 n e j ( t ) + r n ( t ) - - - ( 1 )
C in the formula 1(t), c 2(t) ... c n(t) can think the fluctuation characteristic function of the filtered data of Power Output for Wind Power Field normalization, rn (t) can think the trend function of the filtered data of Power Output for Wind Power Field normalization.
3. respectively to intrinsic mode function c 1(t), c 2(t) ... c n(t) do Hilbert transform, generate time-frequency spectrum, concrete steps are:
C n ( t ) = 1 π ∫ - ∞ + ∞ C n ( τ ) t - τ d τ - - ( 2 )
C in the formula n(t) be c n(t) Hilbert function
Its contravariant is changed to:
C n ( t ) = 1 π ∫ - ∞ + ∞ C n ( τ ) τ - t dτ - - - ( 3 )
Obtain analytic signal:
Z(t)=c n(t)+iC n(t)=a(t)e iθ(t)(4)
A in the formula (t) is instantaneous amplitude, a ( t ) = [ c n ( t ) 2 + C n ( t ) 2 ] 1 2 - - - ( 5 )
θ (t) is phase place, θ ( t ) = arctan C n ( t ) c n ( t ) - - - ( 6 )
Instantaneous frequency f (t) is calculated as follows:
f ( t ) = 1 2 π dθ ( t ) dt - - - ( 7 )
Process successively intrinsic mode function c1 (t) by above-mentioned steps, c2 (t) ..., cn (t) can obtain respectively the time-frequency spectrum f1 (t) of described intrinsic mode function, f2 (t) ..., fn (t).
4. respectively to f1 (t), f2 (t) ..., fn (t) carries out match, namely obtains their fitting function.Then directly in time domain, carry out match for remaining component rn (t).
5. respectively anti-Hilbert transform is carried out in these time-frequency domain matched curves that obtain in the step 4), can be obtained the analytical expression in the corresponding time domain.Concrete grammar is:
Can obtain θ according to formula (8) n(t) expression formula is as follows:
θ n(t)=2π∫f n(t)dt(8)
With formula (8) and formula (2), formula (6) simultaneous, namely can solve expression formula cn (t).According to said method can solve successively c1 (t), c2 (t) ..., cn (t) is the analytical expression in the time domain.
6. with c1 (t), c2 (t) ..., cn (t) and R n(t) time-domain expression sums up, and sums up with the expression formula of remaining component, namely obtains the analytical expression of wind energy turbine set model.
In above-mentioned formula and the expression formula, t represents the time.
Can directly as in the power source access electric system simulation model, by gathering and analytic system voltage, frequency change, can analyze the wind energy turbine set fluctuation to the impact of line voltage, frequency by the wind energy turbine set interpretive model that above-mentioned steps is set up out.
The present invention's advantage compared with prior art is:
(1) modeling of the present invention foothold is measured data, by the method for digital signal processing, sets up the wind energy turbine set model that can be used in Computer Simulation.Than existing equivalent modeling method, modeling method of the present invention is not subjected to the interference of the interior labyrinth of wind energy turbine set and various enchancement factors, can be good at the various typical fluctuation characteristic of reproducing Power Output for Wind Power Field, be used for wind farm grid-connected lower impact analysis to line voltage, frequency, have higher reliability.
(2) the present invention also improves the spectrum analysis of Power Output for Wind Power Field.Mostly existing spectrum analysis is to be based upon directly processes original signal, and the spectral frequencies that obtains distributes wide in range and complicated.The present invention is by the EMD method, and the original signal that will include the complex frequency composition is decomposed into some signals with separate frequency bands, more clearly observation and analysis wind energy turbine set fluctuation characteristic.
Description of drawings
Fig. 1 is the overview flow chart of modeling method of the present invention;
Fig. 2 is empirical mode decomposition (EMD) process flow diagram;
Fig. 3 is the match process flow diagram based on the Hilbert transform frequency spectrum;
Fig. 4 is Power Output for Wind Power Field (gaining merit) time domain waveform figure;
Fig. 5 is the time domain waveform figure behind the empirical mode decomposition that carries out 9 times with Power Output for Wind Power Field P (t);
Fig. 6 is for carrying out each component c1-c9 among Fig. 5 the time-frequency domain oscillogram after the Hilbert transform;
Fig. 7 is high, normal, basic frequency range each several part oscillogram;
Fig. 8 is system frequency variation diagram after the original wind power access;
Fig. 9 is system frequency variation diagram after the access of empirical mode decomposition HFS;
Figure 10 is system frequency variation diagram after the access of empirical mode decomposition intermediate-frequency section;
Figure 11 is that EMD decomposes the rear system frequency variation diagram of low frequency part access.
Embodiment
The invention will be further described below in conjunction with the drawings and specific embodiments.
The concrete steps of modeling method of the present invention are as follows:
1. active power of wind power field data acquisition
Gather the output power Pwind_i (t) of every the unit of wind energy turbine set in certain wind field, and sum up, acquired results is this wind energy turbine set gross output
Figure BDA00002511004800041
That is:
P win d j ( t ) = Σ i = 1 n P win d i ( t ) - - - ( 1 )
2. normalized
Choosing the total specified output power Pe of this wind energy turbine set (t) is base value, to what obtain in the step 1
Figure BDA00002511004800043
Carry out normalized, obtain data P or ( t ) = P wind _ f ( f ) P e ( t ) .
3. data filtering is processed
The discrete series P that step 2 is obtained Or(t) by numerical method generating power spectrum, observe P Or(t) frequency distribution situation is chosen rational lowpass digital filter to P Or(t) carry out filtering, the noise spot that the elimination error is larger, the data that obtain are designated as P (t), with the Power Output for Wind Power Field of P (t) as subsequent treatment, as shown in Figure 4.
4. carry out empirical mode decomposition (EMD)
As shown in Figure 2, P is carried out empirical mode decomposition, Power Output for Wind Power Field P (t) is decomposed into n intrinsic mode function c 1(t), c 2(t) ... c n(t) and remaining component r n(t).Concrete steps are as follows:
According to the definition of intrinsic mode function, use m kExpression asks k average to obtain mP (t) to signal P (t), and the difference of signal P (t) and mP (t) is defined as intrinsic mode function component c 1, that is:
c 1=P(t)-mP(t)
Obtain c 1After, with P (t)-c 1Decompose again as pending signal, can obtain the 2nd intrinsic mode function component c 2, the rest may be inferred to the n time, obtains n intrinsic mode function component Cn, and the decomposition expression formula of the intrinsic mode function of its each time is:
c 2 = P ( t ) - c 1 - m [ P ( t ) - c 1 ] = mp ( t ) - m 2 P ( t ) c 2 = P ( t ) - c 2 - c 2 - m [ P ( t ) - c 1 - c 2 ] = m 2 P ( t ) - m 2 P ( t ) · · · c n = m n - 1 P ( t ) - m n P ( t )
Can stop to decompose satisfy the condition of predesignating when decomposition result after.Finally can obtain the result:
P ( t ) = Σ i = 1 n c i + r n
The concrete steps of empirical mode decomposition (EMD) method are as follows:
(1) signal waveform of observation Power Output for Wind Power Field P (t), estimated frequency distributes, and from Local modulus maxima and the minimum point that replaces continuously, fits to respectively coenvelope and lower envelope with 3 battens.Coenvelope and lower envelope are averaged, obtain the average m of coenvelope and lower envelope 1Definition component h 1Be signal P (t) and average m 1Difference, that is:
P(t)-m 1=h 1
(2) owing to some problems occur in 3 spline-fittings: produce the new existing numerical point of extreme point, translation and amplification and two ends Near The Extreme Point and produce larger swing etc., need to repeat to process according to step described in (1).In the 2nd time is processed, component h 1As pending data, so:
h 1-m 11=h 11
If result is dissatisfied, can continue to process, until the k time is processed h kBecome an intrinsic mode function component, that is:
h 2(k-2)-m 2k=h 2k
With h 2kBe defined as:
c 1=h 1k
c 2It is exactly required intrinsic mode function component.
Must determine a criterion that stops to process to re-treatment, this criterion may be selected to be following standard deviation e SD, that is:
e SD = Σ t = 0 T [ | h 2 ( k - 1 ) ( t ) - h 2 k ( t ) | 2 h 2 ( k - 1 ) 2 ( t ) ]
e SDRepresentative value can be set between 0.2~0.3.
(3) from original signal P (t), isolate intrinsic mode function component c 2After, have:
P(t)-c 1=r 2
The r1 that obtains is the data after original power data P (t) weeds out fluctuation c1.
With r 1Carry out re-treatment as new data by method described in the step (2):
r 1-c 2=r 2
In like manner, r2 is the data after r1 weeds out fluctuation c2, can think that also r2 is the data after original power data P (t) weeds out fluctuation c1 and c2.
So continue to process, have:
r 2 - c 3 = r 3 r 2 - c 4 = r 4 · · · r n - 1 - c n = r n
Above result is combined, namely obtains:
P ( t ) = Σ k = 1 n c k + r n
So, just original signal P (t) is resolved into n intrinsic mode function component c k(k=1,2 ..., n), and 1 residual components r nC wherein 1(t), c 2(t) ... c n(t) can think the fluctuation characteristic function of Power Output for Wind Power Field P (t), rn (t) can think the trend function of Power Output for Wind Power Field P (t).Empirical mode decomposition only need to be known extreme point, does not need to know average or zero reference value, because the zero reference value to each intrinsic mode function component obtains in processing procedure.
The condition that stops at last having following 2 kinds: 1. intrinsic mode function component c nOr residual components r nBecome than the predetermined value hour of regulation; 2. r nBecome monotonic quantity, therefrom or else can process drawing the intrinsic mode function component.For the function P (t) that contains trend term, r nIt is exactly the trend term among the P (t).Among the embodiment P (t) is carried out empirical mode decomposition nine times, each the IMF component after the processing and rn are as shown in Figure 5.
5. generation time-frequency spectrum
Respectively to intrinsic mode function c 1(t), c 2(t) ... c n(t) and rn (t) do Hilbert transform and generate time-frequency spectrum, concrete steps are:
C n ( t ) = 1 π ∫ - ∞ + ∞ C n ( τ ) t - τ d τ - - ( 2 )
Its contravariant is changed to:
C n ( t ) = 1 π ∫ - ∞ + ∞ C n ( τ ) τ - t dτ - - - ( 3 )
Obtain analytic signal:
Z(t)=c n(t)+iC n(t)=a(t)e iθ(t)(4)
A in the formula (t) is instantaneous amplitude, a ( t ) = [ c n ( t ) 2 + C n ( t ) 2 ] 1 2 - - - ( 5 )
θ (t) is phase place, θ ( t ) = arctan C n ( t ) c n ( t ) - - - ( 6 )
Instantaneous frequency is calculated as follows:
f ( t ) = 1 2 π dθ ( t ) dt - - - ( 7 )
In the formula, C n(t) be c n(t) Hilbert function.
Process successively c1 (t) by above-mentioned steps, c2 (t) ..., cn (t) can obtain respectively their time-frequency spectrum f1 (t), f2 (t) ..., fn (t).The time-frequency spectrum of Fig. 6 for nine intrinsic mode functions (IMF) in the step 5 being carried out generate after the Hilbert transform.According to each intrinsic mode function (IMF) component energy proportion, in conjunction with instantaneous frequency, as shown in Figure 3, it can be divided into high, medium and low 3 frequency ranges.F1 is referred to as high band between 1Hz-2Hz; F2-f7 is referred to as Mid Frequency between 0.02-1Hz; F8, f9 is lower than 0.02Hz, is referred to as low-frequency range.The waveform of each several part and energy proportion are as shown in Figure 7.
6. time-frequency spectrum match
Respectively to f1 (t), f2 (t) ..., fn (t) carries out match, namely obtains their fitting function.
7. return time domain
Anti-Hilbert transform is carried out in these time-frequency domain matched curves that respectively step 5) obtained, and can obtain corresponding time-domain expression.Concrete grammar is:
Can obtain θ according to formula (7) n(t) expression formula is as follows:
θ n(t)=2π∫f n(t)dt(8)
With formula (8) and formula (2), formula (6) simultaneous, namely can solve expression formula cn (t).According to said method can solve successively c1 (t), c2 (t) ..., cn (t) is the time domain analytical expression.With c1 (t), c2 (t) ..., cn (t) and r (t) sum up, and acquired results is the analytic model of wind energy turbine set.
In above-mentioned formula and the expression formula, t represents the time.
To be accessed in the electric system simulation model as power source by the wind energy turbine set model that above-mentioned steps is set up out, obtain system frequency and change as shown in Figure 8.The situation of change of system frequency when Fig. 9 ~ Figure 11 is respectively in high frequency, intermediate frequency and the low frequency component access electric system.Can clearly differentiate each frequency component to the difference of effect on power system by situation shown in the figure, prove practicality of the present invention.

Claims (7)

1. wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition is characterized in that described modeling method concrete steps are as follows:
1) the output power Pwind_i (t) with every unit in the wind energy turbine set that collects sums up, and obtains the wind energy turbine set gross output, to the wind energy turbine set gross output
Figure FDA00002511004700011
Carry out normalized, and carry out low-pass filtering, in the above-mentioned expression formula, t is the time;
2) data after processing are carried out empirical mode decomposition, generate a plurality of intrinsic mode function components and remaining component;
3) respectively to step 2) the intrinsic mode function component that obtains carries out Hilbert transform, obtains its corresponding time-frequency spectrum;
The time-frequency spectrum of the intrinsic mode function that 4) respectively step 3) is obtained is carried out match, obtains corresponding fitting function; Then directly in time domain, carry out match for remaining component;
The time-frequency domain fitting function of the intrinsic mode function that 5) respectively step 4) is obtained carries out anti-Hilbert transform, obtains the analytical expression in the time domain;
6) expression formula in the described time domain that step 5) is obtained sums up, and sums up with the expression formula of remaining component, namely obtains the analytical expression of wind energy turbine set model.
2. the wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition according to claim 1 is characterized in that, in the described step 1), chooses the total specified output power Pe of wind energy turbine set (t) as normalized base value, to the wind energy turbine set gross output
Figure FDA00002511004700012
Carry out normalized, in the above-mentioned expression formula, t is the time; The data that obtain after the normalized are carried out Fourier transform generate frequency spectrum, estimate the frequency distribution of the data after the normalization, and the data after the normalization are carried out low-pass filtering, the unreasonable data point that elimination causes because of measuring error.
3. the wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition according to claim 1 is characterized in that described step 2) specific as follows:
With P(t) represent through the filtered data of normalization, the filtered data of normalization are carried out obtaining after empirical mode decomposition is processed:
P ( t ) = Σ j = 1 n e j ( t ) + r n ( t ) - - - ( 1 )
C wherein j(t) j intrinsic mode function component IMF of expression signal j, r n(t) the remaining function component after the expression signal decomposes through n time; J intrinsic mode function component IMF jBe distributed in different frequency range and by from high to low order row, i.e. f C2>f C2>f C2>...>f Cn, having realized that namely the time-frequency domain of signal separates, in the above-mentioned expression formula, t is the time.
4. the wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition according to claim 1 is characterized in that, in the described step 3), and the intrinsic mode function c that obtains 1(t), c 2(t) ... c n(t) think the fluctuation characteristic function of the filtered data of Power Output for Wind Power Field normalization, respectively to intrinsic mode function c 1(t), c 2(t) ... c n(t) carry out Hilbert transform, generate time-frequency spectrum, concrete steps are:
C n ( t ) = 1 π ∫ - ∞ + ∞ C n ( τ ) t - τ d τ - - ( 2 )
C in the formula n(t) be c n(t) Hilbert function
Its contravariant is changed to:
C n ( t ) = 1 π ∫ - ∞ + ∞ C n ( τ ) τ - t dτ - - - ( 3 )
Obtain analytic signal:
Z(t)=c n(t)+iC n(t)=a(t)e iθ(t)(4)
A in the formula (t) is instantaneous amplitude, a ( t ) = [ c n ( t ) 2 + C n ( t ) 2 ] 1 2 - - - ( 5 )
θ (t) is phase place, θ ( t ) = arctan C n ( t ) c n ( t ) - - - ( 6 )
Instantaneous frequency f (t) is calculated as follows:
f ( t ) = 1 2 π dθ ( t ) dt - - - ( 7 )
Process successively intrinsic mode function c1 (t) by above-mentioned steps, c2 (t) ..., cn (t), can obtain respectively the time-frequency spectrum f1 (t) of described intrinsic mode function, f2 (t) ... fn (t), in above-mentioned formula and the expression formula, t is the time.
5. the wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition according to claim 1, it is characterized in that, the time-frequency spectrum f1 (t) of the intrinsic mode function that described step 4) obtains step 3), f2 (t) ..., fn (t) carries out match, obtain intrinsic mode function c1 (t), c2 (t) ..., the fitting function of cn (t); Then directly carry out match for remaining component rn (t) in time domain and obtain fitting function, in the above-mentioned expression formula, t is the time.
6. the wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition according to claim 1 is characterized in that described step 5) is specially:
Obtain θ according to formula (7) n(t) expression formula is as follows:
θ n(t)=2π∫f n(t)dt(8)
With formula (8) and formula (2), formula (6) simultaneous, solve expression formula cn (t); According to said method solve successively c1 (t), c2 (t) ..., cn (t) is the analytical expression in the time domain, and in the above-mentioned expression formula, t is the time.
7. the wind energy turbine set time-frequency domain modeling method based on empirical mode decomposition according to claim 1, it is characterized in that, in the described step 6), the analytical expression that intrinsic modal components fitting result and remaining component fitting result is added and obtain the wind energy turbine set model: X (t)=c1 (t)+c2 (t)+... + cn (t)+R (t), in the above-mentioned expression formula, t is the time.
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