CN102539915B - Method for accurately calculating power harmonic wave parameters through adopting time delay Fourier transform frequency measurement method - Google Patents

Method for accurately calculating power harmonic wave parameters through adopting time delay Fourier transform frequency measurement method Download PDF

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CN102539915B
CN102539915B CN 201210002074 CN201210002074A CN102539915B CN 102539915 B CN102539915 B CN 102539915B CN 201210002074 CN201210002074 CN 201210002074 CN 201210002074 A CN201210002074 A CN 201210002074A CN 102539915 B CN102539915 B CN 102539915B
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formula
harmonic
window function
frequency
fft
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CN102539915A (en
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唐轶
方永丽
谷露
孙瑜欣
于正华
李建华
陈雷
渐伟
张跃
尹远
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China University of Mining and Technology CUMT
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Abstract

The invention provides a method for accurately calculating power harmonic wave parameters through adopting a time delay Fourier transform frequency measurement method, and belongs to a method for automatically monitoring an analytical instrument and an automatic monitoring device used for voltage and current waveform distortion of various power networks. The method includes the following steps: firstly, truncating sampled power harmonic wave signals through adopting a symmetrical window function; performing fast Fourier transform (FFT for short) for the truncated signals; truncating sampled power signals of the same length through adopting the same symmetrical window function at a time delay L point of the sampled power harmonic wave signals, and performing FFT for the truncated signals; accurately calculating out the fundamental wave and the frequency of each harmonic wave as per the phase difference of angle of the FFT performed for two times; calculating out the fundamental wave and the correction factor of each harmonic wave through adopting the method of interpolation in the frequency domain of the dissymmetrical window function; and finally, calculating out the amplitude value and the phase position of each power harmonic wave. The method provided by the invention has remarkable advantage with respect to the time spent in calculation as compared with other windowed FFT interpolation correction and analysis methods, best suits the DSP with hardware FFT, and is a practical algorithm.

Description

Time delay Fourier transform Measuring Frequency Method accurate Calculation electric harmonic parametric technique
Technical field
The present invention relates to a kind of analytical instrument and automatic monitoring method of automated watch-keeping facility, particularly a kind of time delay Fourier transform Measuring Frequency Method accurate Calculation electric harmonic parametric technique for various line voltages and current waveform distortion.
Background technology
Along with the development of Power Electronic Technique and device, the application of nonlinear-load in electric system is more and more extensive, and Harmonious Waves in Power Systems is polluted day by day serious, and harmonic wave has become the subject matter that affects the quality of power supply.The high precision of harmonic component parameter is estimated will be conducive to the assessment of the quality of power supply and take corresponding necessary control measures.
Fast fourier transform (FFT) is the most efficiently instrument of frequency analysis.But the prerequisite of FFT Accurate Analysis frequency spectrum is to guarantee blocking synchronized sampling and the complete cycle of signal.The actual electric network frequency fluctuates near power frequency usually, therefore causes non-synchronous sampling and non-integer cycle to block, and this will produce between spectrum leakage and spectrum and disturb, and makes analysis of spectrum produce error.Address the above problem two kinds of schemes: a kind of technical scheme is that the PHASE-LOCKED LOOP PLL TECHNIQUE by hardware or software solves synchronized sampling and number of cycles is blocked problem; Because mains frequency is not steady state value, and the phaselocked loop response needs the time, thereby can not guarantee the Complete Synchronization sampling.Another kind of technical scheme is mainly to concentrate on main lobe by the selection spectrum energy, and the window function that the secondary lobe spectrum energy is little and amplitude attenuation is fast is to reduce disturbing the i.e. long scope leakage of frequency spectrum between spectrum; By revising in Frequency domain interpolation value or two line shape fitting, reducing fence effect, and then improve the harmonic wave estimated accuracy.Adopt the windowed interpolation method all effectively to improve the precision that harmonic wave is estimated, but along with the order of interpolation fair curve fitting function increases and harmonic wave contains increasing of number of times, calculated amount rolled up when the harmonic wave estimated accuracy improved.
Summary of the invention
The objective of the invention is to provide a kind of time delay Fourier transform Measuring Frequency Method accurate Calculation electric harmonic parametric technique, be to line voltage and the analysis of current waveform distortion and the method for the automatic monitoring calculation of electric harmonic parameter, be used for analytical instrument and the automated watch-keeping facility of various line voltages and current waveform distortion.
The object of the present invention is achieved like this: the method step is as follows:
Step a. take the sampling period as T sThe analyzed electric power signal of sampling is that voltage or current signal get: x (n), according to the measuring accuracy requirement, select suitable gravity center of symmetric window function w (n) n ∈ [0, N-1] to block the electric power signal that has been sampled and get: x w(n)=and x (n) w (n) n ∈ [0, N-1], N is the data truncation length of window function, and to truncated signal x w(n) carry out fast fourier transform (be called for short: FFT):
k∈[0,N-1];
Described gravity center of symmetric window function is: the Chinese is peaceful, hamming, Bu Laike, Lai Fu or Nuttall;
Multifrequency electric power (voltage or electric current) harmonic signal can be expressed as follows:
In the formula: p ∈ [1, P], p is overtone order, is positive integer; P is higher harmonics number of times; A pIt is p subharmonic amplitude; f 1Be the electric power signal fundamental frequency; It is p subharmonic initial phase angle;
Behind sampling discretization, get Serial No.:
Ts is the sampling period in the formula; X (n) is added gravity center of symmetric window function w (n) n ∈ [0, N-1] block calling sequence x w(n)=and x (n) w (n), to x w(n) carry out fast fourier transform (be called for short: FFT):
Step b. uses " step a " used same window function w (m) m ∈ [0, M-1] to block to sampled data x (n) time delay L point again: x w(m)=x (n) w (m) m ∈ [0, M-1], M=N, carry out too FFT and get:
l∈[0,M-1]
Wherein, the L value must satisfy formula 1 condition:
L-aQ ± 1≤0.5 formula 1
In the formula 1: Q is the sampling number of a primitive period; A is natural number; And, if data length allows, should suitably increase the L value;
L sampled point of time-delay in time domain, and with same window function w (m), block x (n) with same data length M=N and get x w(m)=x (n) w (m), [m ∈ 0, M-1], and carry out again the FFT conversion and get:
k∈[0,M-1];
Step c calculates the frequency of first-harmonic and each harmonic with formula 2:
Formula 2
In the formula 2: p is overtone order; f 1It is fundamental frequency; k pAnd l pBe respectively X w(k) and X wThe peak value spectral line of p subharmonic (l);
Be X w(k) and X w(l) at the phase differential of the peak value spectral line at p subharmonic place; With Be respectively X w(k) and X w(l) at the peak value spectral line k at p subharmonic place pAnd l pPhase place;
Steps d. the first-harmonic that calculates according to " step c " and the frequency values of each harmonic calculate the digital angular frequency k of the peak value spectral line at p subharmonic place with formula 3 pThe real figure angular frequency of Δ ω and p rd harmonic signal p=2 π pf 1T sValue of delta ω p,
δ ω p=k pΔ ω-2 π pf 1T sFormula 3
δ in the formula 3 ω pδ for timing sampling, the non-integer-period discrete spectrum after blocking ω p, | δ ω p|≤0.5 Δ ω, Δ ω=2 π/N;
Use again δ ω pIn used Frequency domain interpolation value of blocking the gravity center of symmetric window function of analyzing data, Hanning window function discrete spectrum, try to achieve the correction coefficient of first-harmonic and each harmonic by formula 4:
β p=1/W (δ ω P) formula 4
W (δ in the formula 4 ω p) used gravity center of symmetric window function is at ω=δ ω pThe amplitude at place;
Step e. calculates respectively the amplitude A of first-harmonic and each harmonic with formula 5 and formula 6 pAnd phase place
Ax=β pX w(k p) formula 5
Formula 6.
Because With By X w(k p) and X w(l p) imaginary part and real part calculate respectively and X w(k p) and X w(l p) imaginary part and the computational accuracy of real part all to be subjected to the impact of " disturbing between spectrum ", therefore, window function pair With Computational accuracy direct impact is arranged, carrying out " step a " and " step b " when selecting window function, need " according to the measuring accuracy requirement, selecting suitable gravity center of symmetric window function " guarantee measuring accuracy; Only consider that from measuring accuracy select the little and fast window function of decaying (such as the Nattall window function) of secondary lobe amplitude, this will be conducive to improve measuring accuracy as far as possible.
Beneficial effect, owing to adopted such scheme, at first block the electric harmonic signal of having sampled with gravity center of symmetric window function, and truncated signal carried out fast fourier transform (be called for short FFT), then the electric harmonic signal time delay L point of having sampled is blocked the sampling electric power signal of equal length with same gravity center of symmetric window function again, also carry out FFT.Accurately calculate the frequency of first-harmonic and each harmonic according to the phase angle of 2 FFT, and then the method that is used in gravity center of symmetric window function Frequency domain interpolation value calculates the correction coefficient of first-harmonic and each harmonic, last, calculate amplitude and the phase place of each time electric harmonic.
Utilize digital signal " time delay " in time domain, through in frequency domain, forming the character of " phase shift " behind the Fourier transform, accurately calculate the frequency of electric harmonic by 2 FFT, and then calculate again amplitude and the phase place of electric power each harmonic by the method for gravity center of symmetric window function Frequency domain interpolation value.Than other FFT correcting algorithm, computation amount of the present invention is particularly suitable for having on the DSP signal processor of FFT hardware and uses, and is reaching purpose of the present invention.
Advantage: the present invention and other existing various windowing FFT interpolation correction analytical methods are calculating consuming time having a clear superiority in, being suitable for most having the DSP digital signal processor of hardware FFT, is a kind of method of electric harmonic high precision computation of great practical value.
Description of drawings
Discrete spectrum figure after Fig. 1 timing sampling, non-integer-period block.
Fig. 2 Hanning window function discrete spectrum figure.
Calculated rate graph of errors under Fig. 3 Different L value condition.
Embodiment
Embodiment 1: directly with voltage divider or from the voltage transformer pt secondary side obtain electrical network bus voltage signal, obtain current signal from Current Transmit, send to the signal sampling entrance through behind the suitable signal condition.
Concrete steps are as follows:
Step a. take the sampling period as T sThe analyzed electric power signal of sampling is that voltage or current signal get: x (n), according to the measuring accuracy requirement, select suitable gravity center of symmetric window function w (n) n ∈ [0, N-1] to block the electric power signal that has been sampled and get: x w(n)=and x (n) w (n) n ∈ [0, N-1], N is the data truncation length of window function, and to truncated signal x w(n) carry out fast fourier transform (be called for short: FFT):
k∈[0,N-1]。
Described gravity center of symmetric window function is: the Chinese is peaceful, hamming, Bu Laike, Lai Fu or Nuttall;
Multifrequency electric power (voltage or electric current) harmonic signal can be expressed as follows:
In the formula: p ∈ [1, P], p is overtone order, is positive integer; P is higher harmonics number of times; A pIt is p subharmonic amplitude; f 1Be the electric power signal fundamental frequency; It is p subharmonic initial phase angle.
Behind sampling discretization, get Serial No.:
Ts is the sampling period in the formula.X (n) is added gravity center of symmetric window function w (n) n ∈ [0, N-1] block calling sequence x w(n)=and x (n) w (n), to x w(n) carry out fast fourier transform (be called for short: FFT):
Step b. uses " step a " used same window function w (m) m ∈ [0, M-1] to block to sampled data x (n) time delay L point again: x w(m)=x (n) w (m) m ∈ [0, M-1], M=N, carry out too FFT and get:
l∈[0,M-1]
Wherein, the L value must satisfy formula 1 condition:
L-aQ ± 1≤0.5 formula 1
In the formula 1: Q is the sampling number (may be non-integer) of a primitive period; A is natural number.And, if data length allows, should suitably increase the L value;
L sampled point of time-delay in time domain, and with same window function w (m), block x (n) with same data length M=N and get x w(m)=x (n) w (m), [m ∈ 0, M-1], and carry out again the FFT conversion and get:
k∈[0,M-1];
Step c calculates the frequency of first-harmonic and each harmonic with formula 2:
Formula 2
In the formula 2: p is overtone order; f 1It is fundamental frequency; k pAnd l pBe respectively X w(k) and X wThe peak value spectral line of p subharmonic (l); Be X w(k) and X w(l) at the phase differential of the peak value spectral line at p subharmonic place. With Be respectively X w(k) and X w(l) at the peak value spectral line k at p subharmonic place pAnd l pPhase place;
If k pBar and l pThe bar spectral line is respectively the peak value spectral line of twice FFT conversion p subharmonic, and then according to " time delay " character of Fourier conversion, the phase differential of twice FFT conversion should be-2 π pf 1LT s, that is:
In the formula: Be X w(k) and X w(l) at the phase differential of the peak value spectral line at p subharmonic place; With Be respectively X w(k) and X w(l) at the peak value spectral line k at p subharmonic place pAnd l pPhase place.Do you consider N=M when simplifying following formula? 1, that is:
N-1=M-1=N then gets formula 2:
Analysis mode 2 is because x (n) and x (m) be the same signal cutout of same frequency being sampled with same window function identical data length, then k p=l pAs seen, harmonic frequency pf 1Measuring error with Error be directly proportional, be inversely proportional to L.Because Along with the variation of L take 2 π as the cycle, therefore, when L just in time was the sampling number of first-harmonic one-period, namely (wherein: Q was the sampling number (may be non-integer) of a primitive period to L=aQ; A is natural number) time, At this moment there is not theoretical measuring error.If energy synchronized sampling, complete cycle block, then just can obtain L=aQ.Because the frequency of electrical network is vicissitudinous, actual measurement is difficult to accomplish block synchronized sampling and complete cycle.Measuring method proposed by the invention is applicable to equal interval sampling, therefore, formula 2 survey frequencies must be brought measuring error, for reducing measuring error, carry out must satisfying formula 1 when " step b " selects L, namely should get L-aQ ± 1≤0.5, and, under the condition that data length allows, suitably increase the L value.
Steps d. the first-harmonic that calculates according to " step c " and the frequency values of each harmonic calculate the digital angular frequency k of the peak value spectral line at p subharmonic place with formula 3 pThe real figure angular frequency of Δ ω and p rd harmonic signal p=2 π pf 1T sValue of delta ω p,
δ ω p=k pΔ ω-2 π pf 1T sFormula 3
In the formula 3: | δ ω p|≤0.5 Δ ω, such as Fig. 1, Δ ω=2 π/N.
Use again δ ω pIn the Frequency domain interpolation value of gravity center of symmetric window function, try to achieve the correction coefficient of first-harmonic and each harmonic by formula 4:
β p=1/W (δ ω p) formula 4
W (δ in the formula 4 ω p) used gravity center of symmetric window function is at ω=δ ω pThe amplitude at place;
If δ ω pDigital angular frequency k for the peak value spectral line at p subharmonic place pThe real figure angular frequency of Δ ω and p rd harmonic signal p=2 π pf 1T sDifference, that is: δ ω p=k pΔ ω-2 π pf 1T sFormula 3
Establish again β p=A P/ X w(k p) be the correction coefficient of first-harmonic and each harmonic, A pAmplitude for the p subharmonic.Because
Then: β p = A p X w ( k p ) = A p W ( k p Δω + δ ωp - ω p ) A p W ( k p Δω - ω p ) = W ( 0 ) W ( - δ ωp ) = 1 W ( δ ωp )
Step e. calculates respectively the amplitude A of first-harmonic and each harmonic with formula 5 and formula 6 pAnd phase place
A PpX w(k p) formula 5
Formula 6
By β p=A p/ X w(k p) can get the amplitude of P subharmonic: A ppX w(k p) formula 5
By Can get the phase place of p subharmonic:
Formula 6;
In fact, because With By X w(k p) and X w(l p) imaginary part and real part calculate respectively and X w(k p) and X w(l p) imaginary part and the computational accuracy of real part all to be subjected to the impact of " disturbing between spectrum ", therefore, window function pair With Computational accuracy direct impact is arranged, therefore, carrying out " step a " and " step b " when selecting window function, need " according to the measuring accuracy requirement, selecting suitable gravity center of symmetric window function " guarantee measuring accuracy.Only consider that from measuring accuracy select the little and fast window function of decaying (such as the Nattall window function) of secondary lobe amplitude, this will be conducive to improve measuring accuracy as far as possible.

Claims (1)

1. time delay Fourier transform frequency measurement comes accurate Calculation electric harmonic parametric technique, and it is characterized in that: the method step is as follows:
Step a. is with sampling period T sThe analyzed electric harmonic signal of sampling is that voltage or current signal get: x (n),
In the formula: p ∈ [1, P], p is overtone order, is positive integer; P is higher harmonics number of times; A pIt is p subharmonic amplitude; f 1Be the electric power signal fundamental frequency; It is p subharmonic initial phase angle;
According to the measuring accuracy requirement, select suitable gravity center of symmetric window function w (n) n ∈ [0, N-1] to block the electric harmonic signal that has been sampled and get: x w(n)=and x (n) w (n) n ∈ [0, N-1], N is the data truncation length of window function, and to truncated signal x w(n) carry out fast fourier transform (be called for short: FFT):
Described gravity center of symmetric window function is: the Chinese is peaceful, hamming, Bu Laike, Lai Fu or Nuttall;
Step b. uses " step a " used same window function w (m) m ∈ [0, M-1] to block x (n) with same data length M=N to time delay L sampled point of sampled data x (n) again:
x w(m)=and x (n) w (m), carry out too FFT and get:
Wherein, the L value must satisfy formula 1 condition:
L-aQ ± 1≤0.5 formula 1
In the formula 1: Q is the sampling number of a primitive period; A is natural number; And, if data length allows, should suitably increase the L value;
Step c calculates the frequency of first-harmonic and each harmonic with formula 2:
Formula 2
In the formula 2: p is overtone order; f 1It is fundamental frequency; k pAnd l pBe respectively X w(k) and X wThe peak value spectral line of p subharmonic (l); Be X w(k) and X w(l) at the phase differential of the peak value spectral line at p subharmonic place; With Be respectively X w(k) and X w(l) at the peak value spectral line k at p subharmonic place pAnd l pPhase place;
Steps d. the first-harmonic that calculates according to " step c " and the frequency values of each harmonic calculate the digital angular frequency k of the peak value spectral line at p subharmonic place with formula 3 pThe real figure angular frequency of Δ ω and p rd harmonic signal p=2 π pf 1T sValue of delta ω p,
δ ω p=k pΔ ω-2 π pf 1T sFormula 3
δ in the formula 3 ω pδ for timing sampling, the non-integer-period discrete spectrum after blocking ω p, | δ ω p|≤0.5 Δ ω, Δ ω=2 π/N;
Use again δ ω pIn the Frequency domain interpolation value of described gravity center of symmetric window function, the gravity center of symmetric window function discrete spectrum, try to achieve the correction coefficient of first-harmonic and each harmonic by formula 4:
β p=1/W (δ ω p) formula 4
W (δ in the formula 4 ω p) be that used gravity center of symmetric window function is at ω=δ ω pThe amplitude at place;
Step e. calculates respectively the amplitude A of first-harmonic and each harmonic with formula 5 and formula 6 pAnd phase place
A ppX w(k p) formula 5
Formula 6.
CN 201210002074 2012-01-06 2012-01-06 Method for accurately calculating power harmonic wave parameters through adopting time delay Fourier transform frequency measurement method Expired - Fee Related CN102539915B (en)

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