CN109683016A - A kind of harmonic amplitude analysis method - Google Patents
A kind of harmonic amplitude analysis method Download PDFInfo
- Publication number
- CN109683016A CN109683016A CN201910048391.7A CN201910048391A CN109683016A CN 109683016 A CN109683016 A CN 109683016A CN 201910048391 A CN201910048391 A CN 201910048391A CN 109683016 A CN109683016 A CN 109683016A
- Authority
- CN
- China
- Prior art keywords
- harmonic
- analysis
- formula
- frequency
- plesiochronous
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
Landscapes
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- General Physics & Mathematics (AREA)
- Measuring Frequencies, Analyzing Spectra (AREA)
Abstract
The present invention relates to high-precision harmonic amplitude analysis methods, in particular to a kind of harmonic amplitude analysis method that realization is improved on the basis of a kind of plesiochronous DFT to obtain high-precision frequency analysis result to be efficiently modified the analytical error of plesiochronous DFT frequency analysis technology；The following steps are included: Step 1: equidistant W+2 sampling number of sampling { f (i), i=0,1 ..., w+1 }；Step 2: applying plesiochronous DFT formula since sampled point i=0, analyzes W+1 data and obtain fundamental informationWithStep 3: obtaining fundamental information from sampled point i=1 using plesiochronous W+1 data of DFT formula analysisWithStep 4: calculating the frequency drift μ of signal using formula；Step 5: obtaining each harmonic information using plesiochronous W+1 data of DFT formula analysis since sampled point i=0WithStep 6: calculating the amplitude of each harmonic using formula；Step 7: linearly correcting the amplitude of each harmonic using formula.
Description
Technical field
The present invention relates to the high-precision harmonic amplitude analysis methods that realization is improved on the basis of a kind of plesiochronous DFT, specifically
Refer to a kind of harmonic amplitude analysis 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 positive respectively
String and cosine function；And ak and bk are respectively the real and imaginary parts of k subharmonic；N is the number of iterations；W is determined by integration method, is adopted
When with muiltiple-trapezoid integration method, W=nN；γiFor a weighting coefficient；For the sum of all weighting coefficients；
F (i) is the ith sample value of analysis waveform；N is sampling number in the period.
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.
Summary of the invention
For above-mentioned deficiency in the prior art, the present invention provides a kind of high-precision harmonic wave of harmonic amplitude analysis method point
Analysis method, to be efficiently modified the analytical error of plesiochronous DFT frequency analysis technology, obtain high-precision frequency analysis as a result, from
And the fields instrument such as electric energy quality monitoring, electronic product production testing, the electric appliances monitoring of raising based on frequency analysis theory
The validity of quality and the state judgement of equipment.
To realize the above technical purpose, the technical scheme is that a kind of harmonic amplitude analysis method, including following step
It is rapid:
Step 1: equidistant W+2 sample point data of sampling { f (i), i=0,1 ..., w+1 }；
Step 2: applying plesiochronous DFT formula since sampled point i=0
W+1 data of analysis obtain fundamental informationWith
Step 3: obtaining fundamental information from sampled point i=1 using plesiochronous W+1 data of DFT formula analysis
With
Step 4: using formula:Calculate the frequency drift μ of signal；
Step 5: obtaining each harmonic information using plesiochronous W+1 data of DFT formula analysis since sampled point i=0With
Step 6: using formulaCalculate the amplitude of each harmonic；
Step 7: using formulaThe amplitude of linear amendment each harmonic.
Preferably, M and β under different the number of iterations niValue is
Preferably, equal interval sampling is according to the cycle T and frequency f of the ideal signal for carrying out frequency analysis, at one
Sample N point in period, i.e. sample frequency is fs=Nf, and N >=64.
Preferably, W=nN；Then according to sample frequency fs=Nf, W+2 sample point data sequence { f (i), i are obtained
=0,1 ..., w+1 }, n >=3 finally carry out frequency analysis to the data sequence.
Preferably,For the sum of all weighting coefficients.
It is had the advantages that using harmonic amplitude analysis method of the present invention
(1) high-precision harmonic amplitude analyzes result.The analysis example such as given for Fig. 1, the analysis that the present invention obtains
Precision is increased to 10-7Grade (Fig. 2).
(2) method of the present invention fundamentally solves the problems, such as that plesiochronous DFT harmonic amplitude analysis precision is low, and
Without carrying out complicated inverting and amendment, algorithm is simple.
(3) relative to plesiochronous DFT, frequency analysis technology of the present invention only needs to increase a sampled point and just solves
Plesiochronous DFT analytical error big problem, it is easy to accomplish.
(4) existing instrument and equipment is improved using the present invention, be technically feasible, and do not need to increase any hard
Part expense can make analysis result can be improved 10-7 grades.
(5) this method is similarly also applied for carrying out successive ignition rather than the frequency analysis process of an iteration, at this time only
Needing an iteration to resolve into successive ignition realization can.
As an iteration with successive ignition is substantially, only when calculating, successive ignition carries out decoupled method, and
An iteration is that the process of successive ignition is merged into iteration coefficient γiIn once calculate complete, so the present invention it is equally applicable
In successive ignition process.
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
Below with reference to the given attached drawing of the present invention and specific example, the present invention is further explained, it should be understood that these embodiments
It is only illustrative of the invention and is not intended to limit the scope of the invention, based on the embodiment of the present invention, ordinary skill people
Member's every other embodiment obtained under the premise of no creative work.Belong to protection scope of the present invention.
In the specific implementation, a kind of high-precision harmonic amplitude analysis method of the invention, comprising the following steps:
Firstly, W+2 sampled point of equal interval sampling, with obtain analyzed signal discrete series f (i), i=0,1 ...,
w+1}.Wherein, W=nN.
Equal interval sampling refers to: according to the frequency for the ideal signal for carrying out frequency analysis, (such as power frequency component frequency f is
50Hz, period 20mS) determine sample frequency fS=Nf, it is equably sampled in one cycle under the action of sample frequency fS
N point.Generally, periodic sampling point N=64 or more than can obtain preferable frequency analysis as a result, and the number of iterations n=3~5
Comparatively ideal frequency analysis result can be obtained.
Integration method has muiltiple-trapezoid integration method, complexification rectangular integration method, Simpson's method etc. a variety of, can basis
Actual conditions are selected.
Secondly, applying plesiochronous DFT formula since sampled point i=0
W+1 data of analysis obtain fundamental informationWith
Again, fundamental information is obtained from sampled point i=1 using plesiochronous W+1 data of DFT formula analysisWith
Again, using formula:Calculate the frequency drift μ of signal；
Again, each harmonic information is obtained using plesiochronous W+1 data of DFT formula analysis since sampled point i=0With
Then, using formulaCalculate the amplitude of each harmonic；
Finally, using formulaThe amplitude of linear amendment each harmonic.
Equal interval sampling is the cycle T and frequency f (such as power frequency component frequency f according to the ideal signal for carrying out frequency analysis
For 50Hz, period 20mS), N point is sampled in one cycle, i.e. sample frequency is fs=Nf, and N >=64.
Described W+2 sample point data of sampling refers to W=nN.Then according to sample frequency fs=Nf, sampled point is obtained
Data sequence { f (i), i=0,1 ..., w+1 }, n >=3 finally carry out frequency analysis to the data sequence.
An iteration coefficient gammaiIt is determined by integration method, ideal period sampled point N and the number of iterations n, specific derivation process
Referring to document [some problem [J] electrical measurement and instrument in the application of Dai Xianzhong quasi-synchro sampling, 1988, (2): 2-7.].
For the sum of all weighting coefficients.
The drift μ of signal frequency is the fixation according to sampling number N in neighbouring sample point fundamental wave phase angle difference and ideal period
Relationship and obtain, the drift μ of signal frequency can also be used for amendment fundamental wave and higher hamonic wave frequency f1 and higher hamonic wave frequency
Rate fk (fk=k μ fs/N)。
The present invention and its embodiments have been described above, description is not limiting, it is shown in the drawings also only
It is one of embodiments of the present invention, actual structure is not limited to this.All in all if the ordinary skill people of this field
Member is enlightened by it, without departing from the spirit of the invention, is not inventively designed similar to the technical solution
Frame mode and embodiment, be within the scope of protection of the invention.
Claims (5)
1. a kind of harmonic amplitude analysis method, it is characterised in that: the following steps are included:
Step 1: equidistant W+2 sample point data of sampling { f (i), i=0,1 ..., w+1 }；
Step 2: applying plesiochronous DFT formula since sampled point i=0
W+1 data of analysis obtain fundamental informationWith
Step 3: obtaining fundamental information from sampled point i=1 using plesiochronous W+1 data of DFT formula analysisWith
Step 4: using formula:Calculate the frequency drift μ of signal；
Step 5: obtaining each harmonic information using plesiochronous W+1 data of DFT formula analysis since sampled point i=0With
Step 6: using formulaCalculate the amplitude of each harmonic；
Step 7: using formulaThe amplitude of linear amendment each harmonic.
2. harmonic amplitude analysis method according to claim 1, it is characterised in that: M and β under different the number of iterations niValue
For
3. harmonic amplitude analysis method according to claim 1, it is characterised in that: equal interval sampling is according to progress harmonic wave
The cycle T and frequency f of the ideal signal of analysis sample N point in one cycle, i.e. sample frequency is fs=Nf, and N >=64.
4. harmonic analysis method according to claim 1 or 2, it is characterised in that: W=nN；Then according to sample frequency fs
=Nf obtains W+2 sample point data sequence
{ f (i), i=0,1 ..., w+1 }, n >=3 finally carry out frequency analysis to the data sequence.
5. a kind of harmonic amplitude analysis method according to claim 1, it is characterised in that:Add to be all
The sum of weight coefficient.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910048391.7A CN109683016A (en) | 2019-01-18 | 2019-01-18 | A kind of harmonic amplitude analysis method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910048391.7A CN109683016A (en) | 2019-01-18 | 2019-01-18 | A kind of harmonic amplitude analysis method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN109683016A true CN109683016A (en) | 2019-04-26 |
Family
ID=66192398
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910048391.7A Pending CN109683016A (en) | 2019-01-18 | 2019-01-18 | A kind of harmonic amplitude analysis method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109683016A (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2007124732A (en) * | 2005-10-25 | 2007-05-17 | Mitsubishi Electric Corp | Power converter |
| KR20100075225A (en) * | 2008-12-24 | 2010-07-02 | 충북대학교 산학협력단 | Apparatus and method for detecting/tracing time-varying harmonic in the power system |
| CN103439566A (en) * | 2011-10-21 | 2013-12-11 | 常州顺创电气科技有限公司 | Operating method of MOA resistive current tester with relatively high precision |
| CN104849551A (en) * | 2015-05-19 | 2015-08-19 | 江苏理工学院 | Harmonic phase angle analysis method |
| CN106526312A (en) * | 2016-10-10 | 2017-03-22 | 清华大学 | Electric energy metering method based on R-V(III) window FFT double-peak interpolation |
| CN108037361A (en) * | 2017-12-05 | 2018-05-15 | 南京福致通电气自动化有限公司 | A kind of high-precision harmonic parameters method of estimation based on sliding window DFT |
-
2019
- 2019-01-18 CN CN201910048391.7A patent/CN109683016A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2007124732A (en) * | 2005-10-25 | 2007-05-17 | Mitsubishi Electric Corp | Power converter |
| KR20100075225A (en) * | 2008-12-24 | 2010-07-02 | 충북대학교 산학협력단 | Apparatus and method for detecting/tracing time-varying harmonic in the power system |
| CN103439566A (en) * | 2011-10-21 | 2013-12-11 | 常州顺创电气科技有限公司 | Operating method of MOA resistive current tester with relatively high precision |
| CN104849551A (en) * | 2015-05-19 | 2015-08-19 | 江苏理工学院 | Harmonic phase angle analysis method |
| CN109030942A (en) * | 2015-05-19 | 2018-12-18 | 江苏理工学院 | Humorous phase angle analysis method |
| 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 |
| CN106526312A (en) * | 2016-10-10 | 2017-03-22 | 清华大学 | Electric energy metering method based on R-V(III) window FFT double-peak interpolation |
| CN108037361A (en) * | 2017-12-05 | 2018-05-15 | 南京福致通电气自动化有限公司 | A kind of high-precision harmonic parameters method of estimation based on sliding window DFT |
Non-Patent Citations (2)
| Title |
|---|
| ZHONGJUN FU: "A Linear-Correction Algorithm for Quasi-Synchronous DFT", 《MATHEMATICAL PROBLEMS IN ENGINEERING》 * |
| 夏雯 等: "电力系统谐波分析方法综述", 《通信电源技术》 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN103454494B (en) | A kind of high-precision harmonic analysis method | |
| CN101701984B (en) | Fundamental wave and harmonic wave detecting method based on three-coefficient Nuttall windowed interpolation FFT | |
| Yao et al. | Fast S-transform for time-varying voltage flicker analysis | |
| CN102508026B (en) | Harmonic wave analysis method for electric energy quality harmonic wave analyzer | |
| CN111984920B (en) | Subsynchronous/supersynchronous harmonic parameter identification method, subsynchronous/supersynchronous harmonic parameter identification device, subsynchronous/supersynchronous harmonic parameter identification equipment and medium | |
| CN103064010B (en) | Parameter estimation method for artificial circuit fault component based on Hilbert-Huang transforming (HHT) | |
| Chanda et al. | A wavelet multiresolution-based analysis for location of the point of strike of a lightning overvoltage on a transmission line | |
| CN105675126A (en) | Novel method for detecting sound pressure of multi-frequency multi-source complex stable sound field | |
| CN109239463B (en) | Dielectric loss measurement method based on linear correction algorithm | |
| CN109521273B (en) | Synchronous phasor measurement method, system and device | |
| CN101718816A (en) | Fundamental wave and harmonic wave detection method based on four-item coefficient Nuttall window interpolation FFT | |
| CN104849551B (en) | A kind of humorous phase angle analysis method | |
| CN104849530B (en) | A kind of measuring method of MOA resistive current first harmonics | |
| CN109683016A (en) | A kind of harmonic amplitude analysis method | |
| CN110083891A (en) | A kind of calculation method of the plesiochronous linear correction factor of DFT amplitude | |
| CN103983852B (en) | Harmonic analysis method of power quality harmonic analyzer | |
| CN103604989A (en) | Harmonic wave analysis method of power-quality harmonic wave analyzer | |
| CN103592512A (en) | Harmonic analysis method of power quality harmonic analyzer | |
| Khodaparast et al. | Real time phasor estimation based on recursive prony with several channels of one pmu | |
| CN103576120A (en) | Calibration and self-healing algorithm for third-harmonic component quasi-synchronous information transmission | |
| CN103969507B (en) | A kind of electric energy quality harmonic analyzes method | |
| Liu et al. | Data-driven approach for generating tricomponent nonstationary non-gaussian thunderstorm wind records using continuous wavelet transforms and S-transform | |
| Li et al. | A generic flicker measurement method based on feature sequence reconstruction | |
| CN106980043A (en) | A kind of improvement phase difference correction method based on Hanning window | |
| Dedovic et al. | Identification on Dominant Oscillation Based on EMD and Prony’s Method Approach |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20190426 |
|
| RJ01 | Rejection of invention patent application after publication |