CN107179439A - Electric energy gauging method based on five peak interpolations of Cosine Window FFT tri- - Google Patents
Electric energy gauging method based on five peak interpolations of Cosine Window FFT tri- Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R22/00—Arrangements for measuring time integral of electric power or current, e.g. electricity meters
- G01R22/06—Arrangements for measuring time integral of electric power or current, e.g. electricity meters by electronic methods
- G01R22/10—Arrangements for measuring time integral of electric power or current, e.g. electricity meters by electronic methods using digital techniques
Abstract
A kind of electric energy gauging method based on five peak interpolations of Cosine Window FFT tri- that the present invention is designed, its three peak interpolation correction formula based on new five Cosine Window FFT, amplitude of the frequency spectrum of FFT frequency displacement and new five cosine window functions in the maximum spectral line of fundamental wave, harmonic wave and m-Acetyl chlorophosphonazo crest frequency point and its left and right two nearest spectral lines, using fitting polynomial formulas, general amplitude, the phase and frequency interpolation correction formula of signal fundamental wave, harmonic wave and m-Acetyl chlorophosphonazo are fitted；Amplitude, the phase and frequency parameter of tested voltage signal, the fundamental wave of current signal, harmonic wave and m-Acetyl chlorophosphonazo are calculated according to general amplitude, phase and frequency interpolation correction formula；And then calculate fundamental energy, harmonic electric energy, m-Acetyl chlorophosphonazo electric energy and total electric energy.The present invention has higher accuracy in computation.
Description
Technical field
The present invention relates to digitalized electric energy field of measuring techniques, and in particular to one kind is inserted based on five peaks of Cosine Window FFT tri-
The electric energy gauging method of value.
Background technology
With the Nonlinear Dynamic electric load such as increasing electric railway, electric automobile charging pile, intelligent appliance
Come into operation, substantial amounts of electric harmonic and m-Acetyl chlorophosphonazo are generated in power supply grid.Electric harmonic, m-Acetyl chlorophosphonazo, dc-decay,
The presence of the interference components such as Voltage Drop, not only causes the distortion of power supply grid electric current, voltage waveform, has a strong impact on power supply electricity
Energy quality, jeopardizes the safe and stable operation of electric power system, even results in serious electric power accident, cause huge economic loss,
And have an effect on the accuracy of electric energy metrical.
Electric energy is the foundation that grid company, sale of electricity company etc. carry out business accounting, and can it be measured correctly, exactly,
It is directly connected to the economic benefit of power supply and demand both sides.Traditional way of energy measuring, is the definition directly according to electric energy, by electricity
Pressure is multiplied with the instantaneous sampling value of current signal, carries out time integral again to calculate the so-called full way of energy measuring of electric energy.And
The a large amount of of the Nonlinear Dynamic electric load such as electric railway, electric automobile charging pile, intelligent appliance put into operation, in power supply grid
In, power will be consumed by serving not only as load, and as harmonic source and pollution sources, it causes supply current, voltage waveform distortion
While, a large amount of harmonic waves and m-Acetyl chlorophosphonazo power etc. can be injected to power supply grid.If measuring electricity by traditional full way of energy measuring
Can, a large amount of harmonic wave interferences may be injected to power network by producing the electricity consumer of harmonic wave, but also be paid tariff less；And vast common use
Electric family not only by the interference and harm of harmonic wave, and more than pay tariff.Therefore full way of energy measuring is used, undoubtedly may band
Carry out larger electric energy metering error.
And another way of energy measuring, it is so-called fundamental energy metering method.Using it, although common electricity can be solved
The electricity consumption fairness problem of power user, you can make conventional power user be not necessarily harmonic electric energy more and pay tariff, but produce harmonic wave
Electricity consumer still only needs to pay the fundamental energy electricity charge, and it is not affected by any punishment to power supply grid injection electric harmonic pollution.
It can be seen that, whether using full way of energy measuring or using fundamental energy metering method, fail to solve to produce
The electricity consumer of harmonic source causes the problem of electric energy metrical is inaccurate to power supply grid harmonic, m-Acetyl chlorophosphonazo, let alone how
The interference such as harmonic wave that user injects to electric power system is produced by punitive measures reduced harmonic source as far as possible.
Therefore, the distortion of electric power system electric current, voltage waveform is caused for specific, typical kinematic nonlinearity load, such as
What more accurately extracts the parameters such as amplitude, the phase and frequency of fundamental wave, harmonic wave and m-Acetyl chlorophosphonazo, before accurate metering electric energy
Carry.Conventional method, is to apply window function to measured signal, carry out the computing such as Fourier transformation and interpolation amendment.Specifically
Before FFT is carried out to measured signal, its is given to apply suitable window function, to suppress because non-synchronous sampling and non-integer-period are blocked and made
Into spectrum leakage；Fourier transformation is carried out to applying the voltage of window function, current signal, to obtain the frequency spectrum that its is discrete；Again
By interpolation correction formula, error caused by fence effect is compensated.Paper " the unimodal spectral line interpolation algorithm based on approximation by polynomi-als
Application in m-Acetyl chlorophosphonazo analysis " (Xiao is first brave to wait electric power network techniques, 2008), give based on Hanning windows, Hamming windows,
The unimodal spectral line interpolation correction formula of Blackman-Harris windows, Rife-Vincent windows；" application FFT carries out power train to paper
The innovatory algorithm of system frequency analysis " (the Proceedings of the CSEEs such as Pang Hao, 2003), gives based on rectangular window, Triangle
Window, Hanning windows, Hamming windows, the double peak interpolation correction formula of Blackman windows；Paper is " based on three spectral line interpolation FFTs
Electric Power Harmonic Analysis algorithm " (the Proceedings of the CSEEs, 2012 such as ox victory lock), paper are " based on five Lai Fu-Vincent windows
Three spectral line interpolation FFT frequency analyses " (the electrical technologies such as Zhu Junwei, 2015), paper " three peaks based on Nuttall windows insert
Be worth harmonic wave Algorithm Analysis " (the electric power system protection and controls such as Zhai Ruimiao, 2015), sets forth based on Hanning windows,
Hamming windows, Blackman windows, Blackman-Harris windows, Rife-Vincent windows, three peak spectral lines of Nuttall windows are inserted
It is worth correction formula；Paper " power grid harmonic wave detection method based on four spectral line interpolation FFTs " (such as Hao Zhu protecting electrical power systems and control
System, 2014) and paper " Electric Power Harmonic Analysis based on the spectral line interpolation FFT of Nuttall windows four " (the power train blanket insurances such as Li get Min
Shield and control, 2016), it sets forth based on Triangle windows, Hanning windows, Hamming windows, Blackman, Nuttall
Four peak spectral line interpolation correction formulas of window.
In this above-mentioned four classes interpolation correction algorithm, unimodal spectral line interpolation correction formula is more complicated, the easy shadow by spectrum leakage
Ring；Double peak of spectral lines algorithm utilizes insufficient to the spectral line information contained near peak value frequency, and accuracy in computation is poor；Compose at four peaks
The accuracy in computation highest of line interpolation algorithm, but algorithm amount of calculation greatly increases, it is difficult to meet electric energy is carried out, it is in real time etc. higher
It is required that.
The content of the invention
It is an object of the invention to provide a kind of electric energy gauging method based on five peak interpolations of Cosine Window FFT tri-, the party
Method takes full advantage of the information and new five Cosine Window letters of the maximum spectral line of crest frequency point and its left and right two nearest spectral lines
Count the excellent master having, side lobe performance, it is intended to improve and ensure the degree of accuracy of electric energy metrical.
In order to solve the above technical problems, the electric energy metrical based on five peak interpolations of Cosine Window FFT tri- designed by the present invention
Method, it is characterised in that it comprises the following steps：
Step S101：Based on five peak interpolation correction formulas of Cosine Window FFT tri-, FFT frequency displacement and five Cosine Window letters
Several frequency spectrums is in fundamental wave, the maximum spectral line of harmonic wave and m-Acetyl chlorophosphonazo crest frequency point and the maximum nearest spectral line of left and right two of spectral line
Amplitude, obtains the ratio parameter β of three peak spectral line amplitudes formula；
Step S102：Fitting of a polynomial is carried out to the ratio parameter β of three peak spectral line amplitudes, fitted based on five Cosine Windows
The universal frequency correction factor α of the peak spectral line interpolations of FFT tri- formula；
Step S103：According to the amplitude correction formula of measured signal, general amplitude correction coefficient g (α) public affairs are fitted
Formula；
Step S104：According to general amplitude correction coefficient g (α) and universal frequency correction factor α, general amplitude is obtained
Correction formula, phase only pupil filter formula and frequency correction formula；
Step S2：According to the general amplitude, phase and frequency correction formula, tested voltage and current signal is calculated
Fundamental wave, the amplitude of harmonic wave and m-Acetyl chlorophosphonazo composition, phase and frequency parameter；
Step S3：According to the fundamental wave of the tested voltage and current signal, the amplitude of harmonic wave and m-Acetyl chlorophosphonazo, phase and frequency
Parameter, calculates fundamental energy, harmonic electric energy, m-Acetyl chlorophosphonazo electric energy and total electric energy respectively.
The step S2 specifically includes following steps：
Step S201：Apply five cosine window functions respectively to voltage, current signal and carry out FFT, to obtain
State the frequency spectrum that voltage, current signal apply new five cosine window functions；
Step S202：Using peak detection technology, detect respectively the fundamental wave of tested voltage and current signal, harmonic wave and
The amplitude of m-Acetyl chlorophosphonazo peak point maximum spectral line and the maximum nearest spectral line of left and right two of spectral line；
Step S203：Using the ratio parameter formula of three peak spectral line amplitudes, the base of voltage and current signal is calculated respectively
The ratio parameter β of three peak spectral line amplitudes at ripple, harmonic wave and m-Acetyl chlorophosphonazo peak point value；
Step S204：According to three peak breadth of spectral lines at the fundamental wave of voltage and current signal, harmonic wave and m-Acetyl chlorophosphonazo peak point
It is worth ratio parameter β value, and substitutes into the universal frequency correction factor α fitted formula, and then calculates tested voltage and electricity
Flow the value of the frequency correction factor α at fundamental wave, harmonic wave and the m-Acetyl chlorophosphonazo peak point of signal；
Step S205：According to the frequency correction factor α calculated value, the general amplitude correction system fitted is substituted into
Number g (α) formula, obtains the amplitude correction coefficient g at fundamental wave, harmonic wave and the m-Acetyl chlorophosphonazo peak point of tested voltage and current signal
The value of (α)；
Step S206：By the gained frequency correction factor α and amplitude correction coefficient g (α) value, bring into respectively general
Amplitude, phase and frequency interpolation correction formula, interpolation amendment go out the fundamental wave, harmonic wave and m-Acetyl chlorophosphonazo of tested voltage and current signal
The parameters such as amplitude, phase and frequency.
The calculation formula of the frequency correction factor α is：
β -0.10716678 β of α=1.388888883+0.01652129·β5-0.00300526·β7, wherein, β is
The ratio parameter of three peak spectral line amplitudes.
The calculation formula of the amplitude correction coefficient g (α) is：
G (α)=2.03174603+0.36840261 α2+0.03539348·α4+0.00246968·α6,
Wherein, α is frequency correction factor.
The general amplitude correction formula is A=(y1+2y2+y3)·g(α)/N；
Wherein, y2For the maximum spectral line kth of spectrum curve peak point1The amplitude of bar spectral line, y1And y3Respectively spectrum curve peak
The value point maximum left and right two nearest spectral lines of spectral line are kth2Bar and kth3The amplitude of bar spectral line, N is sampled data length.
The present invention takes full advantage of excellent master, the side lobe performance that five cosine window functions have, and windowing FFT frequency spectrum exists
The information of the maximum spectral line of fundamental wave, harmonic wave and m-Acetyl chlorophosphonazo crest frequency point and its left and right two nearest spectral lines, with higher calculating
The degree of accuracy.Although three peak spectral line interpolation correction algorithms do not take into full account the comprehensive information of the symmetrical spectral line of peak value frequency, its
Comprehensive advantage in terms of accuracy in computation and calculating speed is obvious.
Brief description of the drawings
Fig. 1 is that the power network fundamental frequency of one embodiment of the invention is more than or less than peak point maximum spectrum in the case of 50Hz
The schematic diagram of line and its left and right two nearest spectral lines.Wherein, (a) is the schematic diagram that power network fundamental frequency is more than 50Hz, and (b) is
Power network fundamental frequency is less than 50Hz schematic diagram.
Fig. 2 is the spectral characteristic of new five cosine window functions, it is seen that it has preferably main lobe, side lobe performance.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail：
Five Cosine Windows in the electric energy gauging method based on five peak interpolations of Cosine Window FFT tri- designed by the present invention
The peak interpolation correction formulas of FFT tri- include：
Hanning window function whan (n) time-domain expression：
In formula：N is the length of window function.Quadravalence involution is carried out to Hanning window functions, its time-domain expression w (n) is：
Its coefficient meets condition it can be seen from the time-domain expression of the window function：
In formula, αmFor the coefficient of the window function, and coefficient number M is 5, therefore the window function belongs to a kind of new five cosine
Window function.Its frequency-domain expression is specially：
Wherein, WR(ω) is the discrete spectrum function of rectangular window, and its expression formula is：
When | W (ω) |, it is necessary to meet following relation when=0：
When d=± 1, correspondence | W (ω) | two zero points nearest apart from origin, therefore, its main lobe width isSide lobe peak is -74.6dB, and side lobe attenuation speed reaches 75dB/otc, i.e., it has preferable master, side lobe performance,
ω represents angular frequency, and d is the integer for meeting inequality establishment.
General frequency correction factors formula α is represented by：
β -0.10716678 β of α=1.388888883+0.01652129·β5-0.00300526·β7(1)
General amplitude correction coefficient formula g (α) is represented by：
G (α)=2.03174603+0.36840261 α2+0.03539348·α4+0.00246968·α6(2)
General amplitude correction formula has：
A=(y1+2y2+y3)·g(α)/N (3)
General phase only pupil filter formula is：
General frequency correction formula has：
f0=k0Δ f=(k1-1+α)fs/N (5)
In formula：k0For the spectral line of fundamental wave；k1For the maximum spectral line at fundamental wave spectral line；Δ f is spectral resolution； fsFor sampling
Frequency；N is signal length；For signal spectrum.
Derivation：
Assuming that the measured signal containing multiple harmonic (m-Acetyl chlorophosphonazo), with sample frequency fsAfter being sampled, discrete sequence is obtained
Arrange x (n)：
Wherein, m represents overtone order；M is maximum overtone order；AmAnd θmThe amplitude and phase of m subharmonic are represented respectively
Position；f0Represent fundamental frequency.
Formula (6) is used instead Euler's formula to be expressed as：
The forms of time and space of new five cosine window functions is w (n), and its discrete spectrum isThen after x (n) adding windows
FFT expression formulas be:
Wherein, n be it is discrete use point, W to be Fourier transformation e indexes for frequency spectrum, the e of window function, j is Fourier transformation
The factor；
If ignoring negative frequency-mf0Locate the secondary lobe influence of spectral peak, in positive frequency mf0Neighbouring continuous frequency spectrum function is：
F is the spectral frequencies of Fourier transformation；
Formula (9) is sampled, the expression formula that can obtain its discrete Fourier transform is：
Wherein, Δ f=fs/ N, is discrete frequency interval；N is sampled data length, and k is the spectral line of frequency spectrum.
With fundamental frequency f0=k0Exemplified by Δ f.Because mains frequency has fluctuation, and it is generally not accurate 50Hz, such as
This, is sampled with fixed frequency to measured signal, will occur fence effect, i.e. the Frequency point of its highest discrete spectral line,
It is difficult to the exactly frequency of spectrum curve peak value, that is, k0It is generally not integer.If spectrum curve peak point maximum spectral line and its
Left and right two nearest spectral lines are respectively kth1Bar, kth2Bar and kth3Bar spectral line.If α=k0-k1, due to k2=k1-1≤k1≤k3
=k1+ 1, α ∈ [- 0.5,0.5], k2-k0=-1- α, k3-k0=1- α, corresponding to amplitude is respectively As shown in Figure 1.Make three peak spectral line amplitude ratios
Aspect ratio β=y3-y1/y2, then have：
According to fitting of a polynomial regression formulas polyfit (β, α, 7), inverse function α=f is obtained-1(β), you can obtain general
Frequency correction factor α formula, see formula (1).
By following formula
y1+2y2+y3=0.5A (| W [2 π (- α -1)/N] |+2 | W [2 π (- α)/N] |+| W [2 π (- α+1)/N] |)
The correction formula of amplitude is obtained, i.e.,
Order
G (α)=2N/ (| W [2 π (- α -1)/N] |+2 | W [2 π (- α)/N] |+| W [2 π (- α+1)/N] |),
Approximation by polynomi-als is carried out by polyfit (α, g (α), 7) program, amplitude correction coefficient g (α) formula can be obtained,
See formula (2).Bring formula (2) into formula (12), then obtain general amplitude correction formula, see formula (3).
It can be seen that by formula (3), the actual fundamental wave peak value of measured signal is to utilize the maximum spectral line of peak point and its left and right two
What the weighted amendment of amplitude of nearest spectral line was obtained, therefore the algorithm is referred to as three peak interpolation correction algorithms.
Electric energy calculation formula
There are amplitude, the amendment type of phase and frequency of the actual fundametal compoment of measured signal, so that it may sufficiently accurately calculate
Go out the fundamental wave of tested actual signal, the amplitude of each harmonic and m-Acetyl chlorophosphonazo component, phase and frequency, and then just can be accurate enough
Ground calculates fundamental wave, each harmonic and m-Acetyl chlorophosphonazo electric energy.From orthogonality of trigonometric function, different integers time voltage, electric current
Harmonic component does not produce active energy, therefore the electric energy calculating formula of fundamental wave, harmonic wave, m-Acetyl chlorophosphonazo is：
In formula, WnFor n-th harmonic or the active energy of m-Acetyl chlorophosphonazo, when n takes 1, W1For fundamental energy；When n is taken more than 1
Integer when, WnFor harmonic electric energy；When the negated integers of n, WnFor m-Acetyl chlorophosphonazo electric energy；Un、InRespectively voltage signal, electric current are believed
Number n-th harmonic or m-Acetyl chlorophosphonazo amplitude, when n takes 1 be fundamental voltage amplitude；αn、βnRespectively voltage signal, current signal
The initial phase of n-th harmonic or m-Acetyl chlorophosphonazo, is fundamental phase when n takes 1；T is line voltage, the primitive period of electric current；When h is
Between window number, according to IEC61000-4-7 standards, typically take 10 primitive periods.
Electric energy is emulated
Power supply grid voltage, current simulations model are as shown in table 1, wherein containing multiple harmonic composition, being specially
Wherein, f0 is fundamental frequency, is fluctuated generally between 49.7Hz~50.3Hz, and sample frequency fs=4000Hz is pressed
According to IEC61000-4-7 standards, the spectrum analysis time window of harmonic measure is 200ms, U by Uniform provisionskIt is humorous for kth time voltage
The amplitude of ripple；For the phase of kth time voltage harmonic, IkFor the amplitude of kth primary current harmonic wave；For kth primary current harmonic wave
Phase.
The voltage of table 1, the fundamental wave of current signal and harmonic parameters
Wherein,Unit：Degree, V units：Volt, A units：Ampere；
Hanning windows, Hamming windows, Blackman windows, Blackman-Harris windows and new five is respectively adopted
Cosine Window is based on three peak interpolation algorithms and carries out electric energy metrical simulation calculation, and the length of window function elects as at 800 points, and fundamental frequency takes
50.1Hz, simulation result is given in table 2.
The simulation result of the electric energy of table 2
Electric energy metrical algorithm based on the new peak interpolation amendments of five Cosine Window FFT tri- it can be seen from simulation result
Accuracy in computation, compared to high one of other four kinds of algorithms or even more than two orders of magnitude；Meanwhile, even-order harmonic electric energy it is accurate
Degree is also obviously improved, this explanation, the electric energy metrical proposed by the present invention based on the new peak interpolation amendments of five Cosine Window FFT tri-
Algorithm has higher accuracy in computation really.
In addition, the electric energy gauging method based on the new peak interpolation amendments of five Cosine Window FFT tri- of the embodiment of the present invention
Other compositions and effect, are known to those skilled in the art, and to reduce redundancy, repeat no more.
The content that this specification is not described in detail belongs to prior art known to professional and technical personnel in the field.
Claims (5)
1. a kind of electric energy gauging method based on five peak interpolations of Cosine Window FFT tri-, it is characterised in that it comprises the following steps：
Step S101：Based on five peak interpolation correction formulas of Cosine Window FFT tri-, FFT frequency displacement and five cosine window functions
Frequency spectrum fundamental wave, the maximum spectral line of harmonic wave and m-Acetyl chlorophosphonazo crest frequency point and the maximum nearest spectral line of left and right two of spectral line amplitude,
Obtain the ratio parameter β of three peak spectral line amplitudes formula；
Step S102：Fitting of a polynomial is carried out to the ratio parameter β of three peak spectral line amplitudes, fitted based on five Cosine Window FFT
The universal frequency correction factor α of three peak spectral line interpolations formula；
Step S103：According to the amplitude correction formula of measured signal, general amplitude correction coefficient g (α) formula is fitted；
Step S104：According to general amplitude correction coefficient g (α) and universal frequency correction factor α, general amplitude correction is obtained
Formula, phase only pupil filter formula and frequency correction formula；
Step S2：According to the general amplitude, phase and frequency correction formula, the base of tested voltage and current signal is calculated
Ripple, the amplitude of harmonic wave and m-Acetyl chlorophosphonazo composition, phase and frequency parameter；
Step S3：According to the fundamental wave of the tested voltage and current signal, the amplitude of harmonic wave and m-Acetyl chlorophosphonazo, phase and frequency ginseng
Amount, calculates fundamental energy, harmonic electric energy, m-Acetyl chlorophosphonazo electric energy and total electric energy respectively.
2. the electric energy gauging method according to claim 1 based on five peak interpolations of Cosine Window FFT tri-, it is characterised in that：
The step S2 specifically includes following steps：
Step S201：Apply five cosine window functions respectively to voltage, current signal and carry out FFT, to obtain the electricity
Pressure, current signal apply the frequency spectrum of new five cosine window functions；
Step S202：Using peak detection technology, the fundamental wave of tested voltage and current signal, harmonic wave and humorous are detected respectively
The amplitude of crest value point maximum spectral line and the maximum nearest spectral line of left and right two of spectral line；
Step S203：Using the ratio parameter formula of three peak spectral line amplitudes, the fundamental wave, humorous of voltage and current signal is calculated respectively
The ratio parameter β of three peak spectral line amplitudes at ripple and m-Acetyl chlorophosphonazo peak point value；
Step S204：According to three peak spectral line Amplitude Rations at the fundamental wave of voltage and current signal, harmonic wave and m-Acetyl chlorophosphonazo peak point
Value parameter β value, and the universal frequency correction factor α fitted formula is substituted into, and then calculate tested voltage and current letter
Number fundamental wave, harmonic wave and m-Acetyl chlorophosphonazo peak point at frequency correction factor α value；
Step S205：According to the frequency correction factor α calculated value, the general amplitude correction coefficient g fitted is substituted into
The formula of (α), obtains the amplitude correction coefficient g (α) at fundamental wave, harmonic wave and the m-Acetyl chlorophosphonazo peak point of tested voltage and current signal
Value；
Step S206：By the gained frequency correction factor α and amplitude correction coefficient g (α) value, general width is brought into respectively
Value, phase and frequency interpolation correction formula, interpolation amendment go out the width of the fundamental wave, harmonic wave and m-Acetyl chlorophosphonazo of tested voltage and current signal
The parameters such as value, phase and frequency.
3. the electric energy gauging method according to claim 2 based on five peak interpolations of Cosine Window FFT tri-, it is characterised in that：
The calculation formula of the frequency correction factor α is：
β -0.10716678 β of α=1.388888883+0.01652129·β5-0.00300526·β7, wherein, β is three peaks
The ratio parameter of spectral line amplitude.
4. the electric energy gauging method according to claim 3 based on five peak interpolations of Cosine Window FFT tri-, it is characterised in that：
The calculation formula of the amplitude correction coefficient g (α) is：
G (α)=2.03174603+0.36840261 α2+0.03539348·α4+0.00246968·α6, wherein, α is frequency
Correction factor.
5. the electric energy gauging method according to claim 3 based on five peak interpolations of Cosine Window FFT tri-, it is characterised in that：
The general amplitude correction formula is A=(y1+2y2+y3)·g(α)/N；
Wherein, y2For the maximum spectral line kth of spectrum curve peak point1The amplitude of bar spectral line, y1And y3Respectively spectrum curve peak point
The maximum left and right two nearest spectral lines of spectral line are kth2Bar and kth3The amplitude of bar spectral line, N is sampled data length.
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| CN109709390A (en) * | 2018-12-19 | 2019-05-03 | 深圳市中电电力技术股份有限公司 | A kind of three-phase high-precision harmonic electric energy meter |
| CN109709390B (en) * | 2018-12-19 | 2021-10-01 | 深圳市中电电力技术股份有限公司 | Three-phase high-precision harmonic electric energy meter |
| CN110095650A (en) * | 2019-05-05 | 2019-08-06 | 三峡大学 | The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows |
| CN110954746A (en) * | 2019-11-27 | 2020-04-03 | 云南电网有限责任公司电力科学研究院 | Six-interpolation FFT algorithm based on four-term Nuttall cosine window |
| CN112287290A (en) * | 2020-09-25 | 2021-01-29 | 国网天津市电力公司营销服务中心 | Segmented FFT analysis method for load dynamic power signal characteristics of power distribution network |
| CN115825557A (en) * | 2022-11-25 | 2023-03-21 | 国网四川省电力公司映秀湾水力发电总厂 | Generalized harmonic analysis method, device and medium based on harmonic component zero setting |
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