CN110083891A - A kind of calculation method of the plesiochronous linear correction factor of DFT amplitude - Google Patents
A kind of calculation method of the plesiochronous linear correction factor of DFT amplitude Download PDFInfo
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- CN110083891A CN110083891A CN201910285042.7A CN201910285042A CN110083891A CN 110083891 A CN110083891 A CN 110083891A CN 201910285042 A CN201910285042 A CN 201910285042A CN 110083891 A CN110083891 A CN 110083891A
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- 238000004458 analytical method Methods 0.000 claims abstract description 28
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Abstract
The present invention relates to a kind of frequency analysis technology, specially a kind of calculation method of the plesiochronous linear correction factor of DFT amplitude；Including using the linear correction formula of plesiochronous DFTWhen the frequency analysis amplitude of synchronism DFT is linearly corrected, linear correction factor M and βiCalculating step are as follows: step 1: Δ u is spaced 0.1 value Δ μ in [- 30,30] rangei, and according to formulaAnd A1(Δ u)=Generate L=601 group A1kData, and be recorded asForm；Step 2 determines positive integer M=10；Step 3: according to Δ μiArray Δ is generated with M；Step 4: according to formula B=(ΔTΔ)‑1ΔTA solves B；Step 5: seeking mean square deviationStep 6: increase M value one by one to 20, repeating the above steps three to five and records corresponding G and B；Step 7: making G the smallest M and βiThe linear correction factor of amplitude of as plesiochronous DFT.
Description
Technical field
The present invention relates to a kind of frequency analysis technology, specially a kind of calculating of the plesiochronous linear correction factor of DFT amplitude
Method.
Background technique
Frequency analysis technology is answered in various fields such as electric energy quality monitoring, electronic product production testing, electric appliances monitorings
It is the important technical for carrying out power system monitor, quality inspection, monitoring of tools with extensive.Frequency analysis is most widely used at present
Technology be discrete Fourier transform (DFT) and Fast Fourier Transform (FFT) (FFT).Quasi-synchronous sampling technique is mutually tied with DFT technique
The frequency analysis technology of conjunction can be improved the precision of frequency analysis, formula are as follows:
In formula: k is the number (such as fundamental wave k=1,3 subharmonic k=3) for needing the harmonic wave obtained；Sin and cos are respectively
Sine and cosine functions；And ak and bk are respectively the real and imaginary parts of k subharmonic；AkFor amplitude；N is the number of iterations；W=nN；
γiFor a weighting coefficient；For the sum of all weighting coefficients；F (i) is the ith sample value of analysis waveform；N
For sampling number in the period.
An iteration coefficient gammaiIt is determined by integration method, ideal period sampled point N and the number of iterations n, was specifically derived
Journey is referring to document [some problem [J] electrical measurement and instrument in the application of Dai Xianzhong quasi-synchro sampling, 1988, (2): 2-7].
In engineer application, frequency analysis always carry out the sampling of finite point be difficult to stricti jurise synchronize adopt
Sample.In this way, when the plesiochronous DFT of application carries out frequency analysis, will exist the leakage of the long range as caused by truncation effect and
The short range leakage as caused by fence effect, so that analysis result precision is not high or even insincere.
Fig. 1 gives the Error Graph for carrying out frequency analysis for any given example using plesiochronous DFT.It can be with from figure
It was found that the harmonic amplitude of plesiochronous DFT algorithm misses by a mile, it is substantially insincere.
The harmonic amplitude error of plesiochronous DFT algorithm is larger when in order to solve the problems, such as signal frequency deviation, can be using linear
Modified method is modified harmonic amplitude, and specific method is: using the linear correction formula of plesiochronous DFT
The frequency analysis amplitude of synchronism DFT is linearly corrected.
Summary of the invention
The present invention provides a kind of calculation method of plesiochronous linear correction factor of DFT amplitude, to determine the width of plesiochronous DFT
It is worth linear correction factor M and βi.The analysis that ideal correction factor can effectively reduce plesiochronous DFT frequency analysis technology misses
Difference obtains high-precision frequency analysis as a result, raw to improve electric energy quality monitoring, electronic product based on frequency analysis theory
Produce the quality of the fields instrument and equipments such as inspection, electric appliances monitoring and the validity of state judgement.
The technical solution of the present invention is as follows: a kind of calculation method of the plesiochronous linear correction factor of DFT amplitude, including use standard
The synchronous linear correction formula of DFTWhen the frequency analysis amplitude of synchronism DFT is linearly corrected, line
Property correction factor M and βiCalculating step are as follows:
Step 1: Δ μ is spaced 0.1 value Δ μ in [- 30,30] rangei, and according to formula
WithGenerate L=601 group A1kData, and be recorded as
Form；
Step 2: determining positive integer M=10；
Step 3: according to Δ μiArray Δ is generated with M；
Step 4: according to formula B=(ΔTΔ)-1ΔTA solves B；
Step 5: seeking mean square deviation
Step 6: increase M value one by one to 20, three to five are repeated the above steps, and record corresponding G and B；
Step 7: making G the smallest M and βiThe linear correction factor of amplitude of as plesiochronous DFT.
Preferably, the plesiochronous DFT harmonic analysis method described in it are as follows:
WithIn formula: k is overtone order；AkFor the amplitude of k subharmonic；N is sampling number in the period；N is
The number of iterations；W=nN；F (j) is j-th of sampled data；γjFor quasi-synchro sampling an iteration coefficient, by integration method, n and
N is determined；For the sum of all an iteration coefficients, Q=(N+1) when complexification rectangular integration methodn。
Preferably, the Δ μ described in it is signal frequency deviation rate, it is description signal frequency relative to ideal frequency degrees of offset
Physical quantity, is defined as: Δ μ=Nf1/fs- 1, in formula: f1For signal frequency；fsFor sample frequency.
The calculation method of the plesiochronous linear correction factor of DFT amplitude of the invention has the advantages that the present invention obtains
Analysis precision is increased to 10-7Grade；It is low that method of the present invention fundamentally solves plesiochronous DFT harmonic amplitude analysis precision
The problem of, without carrying out complicated inverting and amendment, algorithm is simple；Existing instrument and equipment, skill are improved using the present invention
It is feasible in art, and does not need to increase any hardware spending and can make to analyze result and can be improved to 10-7Grade；This method
Amplitude is linearly repaired when can equally be well applied to carry out plesiochronous DFT using muiltiple-trapezoid integration method, iterative Simpson integration method
The calculating of positive coefficient is not limited in complexification rectangular integration method.
Detailed description of the invention
Fig. 1 is the harmonic amplitude analytical error figure of plesiochronous DFT.
Fig. 2 is harmonic amplitude analytical error figure of the invention.
Specific embodiment
As shown, the linear correction factor calculation method of plesiochronous DFT amplitude of the invention includes 7 calculating steps:
Step 1: Δ μ is spaced 0.1 value Δ μ in [- 30,30] rangei, and according to formula
With
Generate L=601 group A1kData, and be recorded as
Form；
Step 2: determining positive integer M=10；
Step 3: according to Δ μiArray Δ is generated with M；
Step 4: according to formula B=(ΔTΔ)-1ΔTA
It solvesStep 5: seeking mean square deviation
Step 6: increase M value one by one to 20, the step 3 that repeats the above steps to step 5, and record corresponding G and B；Step
Rapid seven, make G the smallest M and βiThe linear correction factor of amplitude of as plesiochronous DFT.When integral way is complexification rectangular integration side
Method, the linear correction factor M and β of amplitude that the above method is calculated when the number of iterations n=4~8iAre as follows:
Using the calculation method of the above-mentioned plesiochronous linear correction factor of DFT amplitude, high-precision harmonic wave width can be obtained
Value analysis result.The analysis example such as given for Fig. 1, the analysis precision that the present invention obtains are increased to 10-7Grade (figure
2)；Fundamentally solve the problems, such as that plesiochronous DFT harmonic amplitude analysis precision is low, without carrying out the anti-of complexity
It drills and corrects, algorithm is simple；Existing instrument and equipment is improved using the present invention, is technically feasible, and does not need to increase
Any hardware spending can be such that analysis result can be improved to 10-7Grade；This method is similarly also applied for trapezoidal using complexification
Integration method, iterative Simpson integration method carry out the calculating of amplitude linear correction factor when plesiochronous DFT, are not limited in multiple
Change rectangular integration method.
It is enlightenment with the above-mentioned desirable embodiment according to invention, through the above description, relevant staff is complete
Can without departing from the scope of the technological thought of the present invention', carry out various changes and amendments, this invention it is technical
Range is not limited to the contents of the specification, it is necessary to which the technical scope thereof is determined according to the scope of the claim.
Claims (3)
1. a kind of calculation method of the plesiochronous linear correction factor of DFT amplitude, it is characterised in that: including using plesiochronous DFT line
Property correction formulaWhen the frequency analysis amplitude of synchronism DFT is linearly corrected, linear correction factor
M and βiCalculating step are as follows:
Step 1: Δ μ is spaced 0.1 value Δ μ in [- 30,30] rangei, and according to formula
WithGenerate L=601 group A1kData, and be recorded as's
Form；
Step 2: determining positive integer M=10；
Step 3: according to Δ μiArray Δ is generated with M；
Step 4: according to formula B=(ΔTΔ)-1ΔTA solves B；
Step 5: seeking mean square deviation
Step 6: increase M value one by one to 20, repeating the above steps three to five and records corresponding G and B；
Step 7: making G the smallest M and βiThe linear correction factor of amplitude of as plesiochronous DFT.
2. the calculation method of the plesiochronous linear correction factor of DFT amplitude according to claim 1, it is characterised in that: its institute
The plesiochronous DFT harmonic analysis method stated are as follows:
WithIn formula: k is overtone order；AkFor the amplitude of k subharmonic；N is sampling number in the period；N is iteration
Number；W=nN；F (j) is j-th of sampled data；γjFor quasi-synchro sampling an iteration coefficient, determined by integration method, n and N
It is fixed；For the sum of all an iteration coefficients, Q=(N+1) when complexification rectangular integration methodn。
3. the calculation method of the plesiochronous linear correction factor of DFT amplitude according to claim 1, it is characterised in that: its institute
The Δ μ stated is signal frequency deviation rate, is the physical quantity for describing signal frequency relative to ideal frequency degrees of offset, is defined as: Δ μ
=Nf1/fSIn -1 formula: f1For signal frequency；fSFor sample frequency.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112526209A (en) * | 2020-10-20 | 2021-03-19 | 江苏宝亨新电气有限公司 | Synchronous phasor measurement method for power system |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109142866A (en) * | 2015-05-19 | 2019-01-04 | 江苏理工学院 | A kind of humorous phase angle analysis method based on linear correction algorithm |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109142866A (en) * | 2015-05-19 | 2019-01-04 | 江苏理工学院 | A kind of humorous phase angle analysis method based on linear correction algorithm |
Non-Patent Citations (1)
| Title |
|---|
| ZHONGJUN FU等: "A Linear-Correction Algorithm for Quasi-Synchronous DFT", 《MATHEMATICAL PROBLEMS IN ENGINEERING》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112526209A (en) * | 2020-10-20 | 2021-03-19 | 江苏宝亨新电气有限公司 | Synchronous phasor measurement method for power system |
| CN112526209B (en) * | 2020-10-20 | 2023-09-19 | 江苏宝亨新电气有限公司 | Synchronous phasor measurement method for power system |
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Application publication date: 20190802 |