CN106932642A - Electric Power Harmonic Analysis method - Google Patents
Electric Power Harmonic Analysis method Download PDFInfo
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- CN106932642A CN106932642A CN201710146296.1A CN201710146296A CN106932642A CN 106932642 A CN106932642 A CN 106932642A CN 201710146296 A CN201710146296 A CN 201710146296A CN 106932642 A CN106932642 A CN 106932642A
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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- G01R23/16—Spectrum analysis; Fourier analysis
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Abstract
The invention discloses a kind of Electric Power Harmonic Analysis method, including obtain input voltage actual cycle sampling number；Calculate translational movement needed for each sampled point；Calculate total translational movement needed for the interpolation point；Corresponding actual samples point value is obtained using the integer part of total translational movement as side-play amount, quadratic interpolation is carried out according to three sampled values and the fractional part of total translational movement that obtain and is obtained the corresponding interpolated data of the interpolation point；Repeat the above steps up to processed points reach total points, so as to obtain brand-new interpolating sequence；The interpolating sequence of the voltage and current for storing again is analyzed and calculates electric harmonic parameter.The frequency analysis error that the spectral leakage of FFT causes when the inventive method effectively inhibits non-synchronous sampling；The phase-locked loop circuit of complexity in Hardware synchronous sampling is eliminated, is finely adjusted without to the ADC sampling intervals, thus applicable surface is extremely wide；Decay of the interpolation to each harmonic amplitude is effectively reduced, the frequency analysis degree of accuracy and operation efficiency is greatly improved.
Description
Technical field
The invention belongs to electric automatization field, and in particular to a kind of Electric Power Harmonic Analysis method.
Background technology
With developing rapidly for Power Electronic Technique, such as photo-voltaic power supply, wind-powered electricity generation, electric arc furnaces, electric railway and rolling mill
Deng widely using for load, nonlinear-load gradually increases in the proportion of power network.What current nonlinear-load was caused in power network
Harmonic pollution problems are increasingly highlighted, and electric administrative department is also increasingly improved to the attention rate of harmonic meter metering accuracy.It is domestic in
Issue in 2014 implements harmonic meter standard《GB/T17215.302-2013 state type harmonic wave active electric energy meters》, harmonic meter is entered
Gone it is unified and standard so that it is more effective in power network, more reasonably play a role.
Current most widely used harmonic analysis method is fft algorithm, it is known that be intended to obtain accurately and reliably
Analysis result, it is necessary to solve the FFT spectrum leakage problem that non-synchronous sampling causes, non-synchronous sampling shows as sample frequency with electricity
Net fundamental frequency it is asynchronous.The one periodic sampling points of the signal of fft algorithm requirement simultaneously are 2 integer power.Generally,
Power network fundamental frequency fluctuation range very little, generally within ± 0.5Hz；But under some powerful nonlinear-loads, power network
Frequency fluctuation scope is larger, up to several hertz.In harmonic meter standard GB/T/T 17215.302-2013, it is desirable to which frequency changes
Within ± 2%, the harmonic electric energy metering error knots modification of high-precision 1 grade of harmonic meter is less than ± 0.5% to variable, if so
Realize that harmonic electric energy metering must take into consideration the influence that frequency fluctuation brings using fft algorithm.
The method for reducing non-synchronous sampling errors at present mainly has window function and interpolation algorithm and the major class of synchronous sampling technique two.
Time domain adds the Cosine Window can to efficiently reduce spectrum leakage, and frequency spectrum interpolation is carried out to FFT result in frequency domain can reduce fence effect
The error that should cause, but adding window and the data operation quantity of frequency spectrum interpolation treatment are big, and including solving sublinear equation high, division fortune
The treatment such as calculation, spectral line peak value searching, it is high to cpu performance requirement, it is not suitable for meter platform.Synchronous sampling technique has hardware synchronization
Two kinds of sampling and synchronous sampling by software.Hardware synchronous sampling is to realize tracking of the sample frequency to fundamental frequency using phaselocked loop,
But need to carry out input signal LPF and filter direct current harmony wave component beyond power frequency, phaselocked loop when sample frequency is higher
Divider ratio is larger, and phase-locking frequency multiplication circuit design difficulty is larger, and the technology can be used only in based on Approach by inchmeal (SAR) and can
On the ADC sampled by hardware trigger, some other kinds of ADC such as sigma-delta ADC cannot using the technology, its sampling interval without
Method is finely tuned.Synchronous sampling by software is the frequency input signal obtained according to measurement, by timer or other programmable delay moulds
Block is finely adjusted to the ADC sampling intervals, so as to realize frequency-tracking.The algorithm also can be used only on SAR ADC, high-resolution,
The sigma-delta ADC of high integration and low cost starts overlong time, it is impossible to use the technology, and in high accuracy electric energy metered system
Analog sampling generally need using sigma-delta ADC.Therefore, the non-synchronous sampling of sigma-delta ADC and its in electric energy metrical application
It is current urgent problem that middle use FFT carries out frequency analysis.
The content of the invention
It is an object of the invention to provide a kind of high-precision Electric Power Harmonic Analysis method.
This Electric Power Harmonic Analysis method that the present invention is provided, comprises the following steps：
S1. the actual periodic sampling points of input voltage are obtained；
S2. calculate each and adopt according to the actual periodic sampling points obtained in step S1 and the analysis points being previously set
Translational movement needed for sampling point；
S3. the total translational movement needed for the sequence number according to interpolation point and each translational movement put calculate the interpolation point, while obtaining
Take the integer part and fractional part of total translational movement；
The integer part of the total translational movement that S4. will be obtained in step S3 obtains corresponding actual samples point as side-play amount
Value, and quadratic interpolation is carried out according to the fractional part of the total translational movement obtained in three sampled values and step S3 for obtaining, obtain
The corresponding interpolated data of the interpolation point；
S5. repeat step S3~S4 always counts up to processed points reach, so as to obtain brand-new interpolating sequence；It is sharp again
It is analyzed with the interpolating sequence of the voltage and current stored in step S4, according to Analysis result calculation electric harmonic parameter.
Described in step S2 calculate each sampled point required for translational movement, specially counted using equation below
Calculate：
Δ=(M-N)/N
In formula, Δ is the translational movement of each sampled point；M is actual periodic sampling points；N is the analysis site being previously set
Number.
The total translational movement needed for calculating current interpolation point described in step S3 simultaneously obtains its integer part and fractional part,
Specially calculated using equation below：
Δn=n Δs
P=[Δsn]=[n Δs]
Q=Δsn- p=n Δs-p
In formula, n is the sequence number of interpolation point, and span is 0~N-1；ΔnTotal translational movement for needed for current interpolation point；p
It is the integer part of total translational movement, [Δn] represent to ΔnRound；Q is the fractional part of total translational movement.
The integer part of the total translational movement that will be obtained in step S3 described in step S4 obtains corresponding as side-play amount
Total translational movement integer part p in actual samples point value, specially the sequence number n and step S3 according to current interpolation point from voltage and
In current sample value sequence search input block starting point after n+p, n+p+1 and n+p+2 point sampled value.
Quadratic interpolation described in step S4 is Lagrange quadratic interpolations.
The fractional part of three sampled values that the basis described in step S4 is obtained and the total translational movement obtained in step S3
Carry out quadratic interpolation and obtain the corresponding interpolated data of the interpolation point, specially calculated using following formula：
u'n=(q-1) (q-2)/2un+p-q(q-2)·un+p+1+q(q-1)/2·un+p+2
i'n=(q-1) (q-2)/2in+p-q(q-2)·in+p+1+q(q-1)/2·in+p+2
In formula, n is the sequence number of interpolation point, and span is 0~N-1；P is the integer part of total translational movement；Q is total translation
The fractional part of amount；un+p、un+p+1And un+p+2And in+p、in+p+1And in+p+2The voltage and current data block starting being respectively input into
The sampling point value of the n-th+p, n+p+1 and n+p+2 point after point；u′nWith i 'nIt is the nth point data after interpolation.
The interpolating sequence of the voltage and current to storing described in step S5 is analyzed, specially the voltage to storing
Interpolating sequence with electric current carries out fft analysis.
Electric harmonic parameter described in step S5 includes each harmonic voltage, individual harmonic current and total harmonic wave wattful power
Rate.
This Electric Power Harmonic Analysis method that the present invention is provided, by using resampling technique, by periodic sampling points
Needed for not the crude sampling sequence of 2 exponential is converted to fft algorithm 2 exponential point, even if under non-synchronous sampling
Can obtain complete cycle and suitable for the data sequence of FFT, the spectral leakage of FFT is drawn when this effectively inhibits non-synchronous sampling
The frequency analysis error for rising；The inventive method eliminates the lock phase of complexity in Hardware synchronous sampling using the realization of pure software algorithm
Loop circuit, is finely adjusted without to the ADC sampling intervals, thus be applicable not only to SAR ADC also allow for be difficult to modification ADC weeks
Normally fft algorithm is used in the electric energy metrical application of the sigma-delta ADC in phase property sampling interval；Further, since using Lagrange
Quadratic interpolattion realizes resampling, compared with linear interpolation method, effectively reduces decay of the interpolation to each harmonic amplitude, carries significantly
Higher harmonics accuracy of analysis, and there is operation efficiency higher compared with Interpolating Window FFT Algorithm.
Brief description of the drawings
Fig. 1 is the general principle block diagram of the inventive method.
Fig. 2 is flow chart of the method for the present invention.
Fig. 3 is the Lagrange quadratic interpolation example schematic diagrams in the inventive method.
Precision result schematic diagram when Fig. 4 is in the inventive method using linear interpolation.
Precision result schematic diagram when Fig. 5 is in the inventive method using Lagrange quadratic interpolations.
Specific embodiment
It is as shown in Figure 1 general principle block diagram of the invention：Present invention is primarily based on Lagrange interpolation and FFT resamplings
Technology.First with sigma-delta ADC collection voltages and electric current, discrete voltage sample value and current sample value sequence is obtained, and
Calculate the periodic quantity of voltage；Then the cycle according to voltage enter row interpolation resampling to voltage and current；Then fft algorithm is passed through
Frequency analysis is carried out to the voltage and current data sequence after interpolation；Harmonic voltage, harmonic wave are calculated finally according to fft analysis result
The harmonic wave measuring index such as electric current, total harmonic wave be active.
It is illustrated in figure 2 flow chart of the method for the present invention：This Electric Power Harmonic Analysis method that the present invention is provided, including such as
Lower step：
S1. the actual periodic sampling points of input voltage are obtained；
S2. calculate each and adopt according to the actual periodic sampling points obtained in step S1 and the analysis points being previously set
Translational movement needed for sampling point, is specially calculated using equation below：
Δ=(M-N)/N
In formula, Δ is the translational movement of each sampled point；M is actual periodic sampling points；N is the analysis site being previously set
Number；
S3. the total translational movement needed for the sequence number according to interpolation point and each translational movement put calculate the interpolation point, while obtaining
The integer part and fractional part of total translational movement are taken, is specially calculated using equation below：
Δn=n Δs
P=[Δsn]=[n Δs]
Q=Δsn- p=n Δs-p
In formula, n is the sequence number of interpolation point, and span is 0~N-1；ΔnTotal translational movement for needed for current interpolation point；p
It is the integer part of total translational movement, [Δn] represent to ΔnRound；Q is the fractional part of total translational movement；
The integer part of the total translational movement that S4. will be obtained in step S3 obtains corresponding actual samples point as side-play amount
Value, and quadratic interpolation is carried out according to the fractional part of the total translational movement obtained in three sampled values and step S3 for obtaining, obtain
The corresponding interpolated data of the interpolation point；
Total translational movement integer part p in sequence number n and step S3 first according to current interpolation point is adopted from voltage and current
In sample sequence search input block starting point after n+p, n+p+1 and n+p+2 point sampled value；Following formula meter is used again
Calculation obtains the corresponding interpolated data of the interpolation point：
u'n=(q-1) (q-2)/2un+p-q(q-2)·un+p+1+q(q-1)/2·un+p+2
i'n=(q-1) (q-2)/2in+p-q(q-2)·in+p+1+q(q-1)/2·in+p+2
In formula, n is the sequence number of interpolation point, and span is 0~N-1；P is the integer part of total translational movement；Q is total translation
The fractional part of amount；un+p、un+p+1And un+p+2And in+p、in+p+1And in+p+2The voltage and current data block starting being respectively input into
The sampling point value of the n-th+p, n+p+1 and n+p+2 point after point；u′nWith i 'nIt is the nth point data after interpolation；
S5. repeat step S3~S4 always counts up to processed points reach, so as to obtain brand-new interpolating sequence；It is sharp again
Fft analysis are carried out with the interpolating sequence of the voltage and current stored in step S4, each harmonic is included according to Analysis result calculation
The electric harmonic parameters such as voltage, individual harmonic current and total harmonic wave active power.
The present invention realizes that sample-synchronousization are processed by Lagrange polynomial interopolations and resampling technique.Polynomial interopolation
It is that row interpolation is clicked through by the multinomial data-oriented discrete to a group, finds a multinomial that can pass through these data points
Function, so that the method for building new data point, wherein simplest method is to use Lagrange interpolation polynomial.Given data
Point is measured from by ADC, and new data point is obtained by software interpolation calculation.Assuming that there is r+1 discrete data point (x0,y0),(x1,
y1),....,(xr,yr), then the general formulae of Lagrange interpolation polynomial is：
Wherein, r is polynomial exponent number, LiX () is Lagrangian fundamental polynomials, its expression formula is：
Knowable to above formula, fundamental polynomials LiX () has the property that：
Obviously, according to LiX the attribute of (), interpolation polynomial y=L (x) passes through this r+1 data point；
R=2 is made, then obtains Lagrangian quadratic interpolation multinomial, it passes through 3 consecutive number strong points and calculates unknown at x
Value y, it is as follows：
Wherein LiX () is basic Lagrange quadratic polynomial.
It is illustrated in figure 3 the Lagrange quadratic interpolation example schematic diagrams in the inventive method：Lagrange quadratic interpolations
It is the polynomial interopolation that exponent number r is 2, compared with linear interpolation, the interpolation method has good calculating performance and precision, especially
Real-time high-efficiency suitable for electric energy metrical application calculates the current waveform larger with the distortion factor under nonlinear-load.In figure 3, lead to
The step of crossing execution embodiment a and b, we have obtained 3 consecutive number strong points (n+p, un+p)、(n+p+1,un+p+1) and (n+p+
2,un+p+2) and interpolation point position be n+p+q, three point data and x=n+p+q are substituted into (10) formula and abbreviation, then obtain n+p+q
The unknown-value u' at placenComputing formula.3 data points are ADC sampled value solid marks in figure, by inserting for these data points
Value function is dotted line parabola.Identical process is repeated using multiple new consecutive number strong points to can obtain complete cycle and be applicable
In the data sequence of FFT.
The points that the present invention chooses fft algorithm are N=256, and the time window width of fft analysis is 1 cycle, i.e. frequency spectrum point
Resolution is fundamental frequency.Due to the Lagrangian quadratic interpolation method tool of the ratio between interpolation input point and FFT points Ns between 2~3
There are good calculating performance and precision, therefore present invention selection ADC sample frequencys fsIt is 25.6kHz, i.e., one when fundamental frequency is 50Hz
Individual periodic sampling points are 512.
The present invention is emulated using MATLAB softwares to the harmonic wave algorithm for being provided, and checking is carried out using the inventive method
The frequency analysis influence that especially degree of accuracy of higher hamonic wave analysis and fundamental frequency fluctuate to harmonic wave algorithm.Set up the emulation of algorithm
Model is as follows：
(1) data sequence of single harmonic component is superimposed using following formula generation fundamental wave：
Wherein, fsIt is sample frequency, fs=25.6kHz；finBe fundamental frequency, its in the range of 47.5~52.5Hz with
0.5Hz incremental variations, to verify influence of the fundamental frequency fluctuation to harmonic wave algorithm；A1WithIt is fundamental voltage amplitude and phase, AhWithIt is h subharmonic amplitude and phase, Ah=0.1A1,H is overtone order, in the range from 2~63；K is data sequence
Row number；
(2) above-mentioned data sequence carried out respectively using the inventive method linear interpolation (error is as shown in Figure 4) and
Lagrange quadratic interpolations (error is as shown in Figure 5)；
(3) the N point datas sequence for being obtained to interpolation carries out fft analysis, calculates the corresponding amplitude of each harmonic and phase value；
(4) by the calculated value of each harmonic amplitude and phase and original value AhWithIt is compared, calculates what interpolation caused
Harmonic error；
As shown in Figure 4 and Figure 5, it is that the present invention carries out software emulation according to above simulation model, two for obtaining kind interpolation side
Under the conditions of different fundamental frequencies, each harmonic component amplitude deviates the characteristic of original value to method.Be not difficult to find out from figure, superposition 2~
63 subharmonic and fundamental frequency are changed under the simulated conditions of 52.5Hz from 47.5Hz, and the present invention is based on Lagrange quadratic interpolations
Harmonic analysis method error within 0.65%, its ratio of precision using linear interpolation it is high nearly 10 times.
Claims (8)
1. a kind of Electric Power Harmonic Analysis method, comprises the following steps：
S1. the actual periodic sampling points of input voltage are obtained；
S2. each sampled point is calculated according to the actual periodic sampling points obtained in step S1 and the analysis points being previously set
Required translational movement；
S3. the total translational movement needed for the translational movement of the sequence number according to interpolation point and each point calculates the interpolation point, while obtain should
The integer part and fractional part of total translational movement；
The integer part of the total translational movement that S4. will be obtained in step S3 obtains corresponding actual samples point value as side-play amount, and
Fractional part according to the total translational movement obtained in three sampled values and step S3 for obtaining carries out quadratic interpolation, obtains the interpolation
The corresponding interpolated data of point；
S5. repeat step S3~S4 always counts up to processed points reach, so as to obtain brand-new interpolating sequence；Recycle step
The interpolating sequence of the voltage and current stored in rapid S4 is analyzed, according to Analysis result calculation electric harmonic parameter.
2. Electric Power Harmonic Analysis method according to claim 1, it is characterised in that calculating described in step S2 each adopt
Translational movement required for sampling point, is specially calculated using equation below：
Δ=(M-N)/N
In formula, Δ is the translational movement of each sampled point；M is actual periodic sampling points；N is the analysis points being previously set.
3. Electric Power Harmonic Analysis method according to claim 1, it is characterised in that the calculating described in step S3 is currently inserted
Total translational movement needed for value point simultaneously obtains its integer part and fractional part, is specially calculated using equation below：
Δn=n Δs
P=[Δsn]=[n Δs]
Q=Δsn- p=n Δs-p
In formula, n is the sequence number of interpolation point, and span is 0~N-1；ΔnTotal translational movement for needed for current interpolation point；P is total
The integer part of translational movement, [Δn] represent to ΔnRound；Q is the fractional part of total translational movement.
4. Electric Power Harmonic Analysis method according to claim 1, it is characterised in that described in step S4 by step S3
The integer part of the total translational movement for obtaining obtains corresponding actual samples point value as side-play amount, specially according to current interpolation point
Sequence number n and step S3 in total translational movement integer part p search input block from voltage and current sample value sequence
The sampled value of n+p, n+p+1 and n+p+2 point after initial point.
5. according to the Electric Power Harmonic Analysis method that one of Claims 1 to 4 is described, it is characterised in that secondary described in step S4
Interpolation is Lagrange quadratic interpolations.
6. Electric Power Harmonic Analysis method according to claim 5, it is characterised in that what the basis described in step S4 was obtained
The fractional part of the total translational movement obtained in three sampled values and step S3 carry out quadratic interpolation obtain the interpolation point it is corresponding insert
Value Data, is specially calculated using following formula：
u'n=(q-1) (q-2)/2un+p-q(q-2)·un+p+1+q(q-1)/2·un+p+2
i'n=(q-1) (q-2)/2in+p-q(q-2)·in+p+1+q(q-1)/2·in+p+2
In formula, n is the sequence number of interpolation point, and span is 0~N-1；P is the integer part of total translational movement；Q is total translational movement
Fractional part；un+p、un+p+1And un+p+2And in+p、in+p+1And in+p+2The voltage and current data block starting point being respectively input into it
The sampling point value of the n-th+p, n+p+1 and n+p+2 point afterwards；u′nWith i 'nIt is the nth point data after interpolation.
7. Electric Power Harmonic Analysis method according to claim 5, it is characterised in that described in step S5 to the electricity that stores
The interpolating sequence of pressure and electric current is analyzed, and the interpolating sequence of the specially voltage and current to storing carries out fft analysis.
8. Electric Power Harmonic Analysis method according to claim 7, it is characterised in that the electric harmonic ginseng described in step S5
Number includes each harmonic voltage, individual harmonic current and total harmonic wave active power.
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| CN109959825A (en) * | 2017-12-26 | 2019-07-02 | 东南大学 | A kind of non-linear voltage-controlled attenuator fitted calibration method based on Lagrange's interpolation |
| CN110687350A (en) * | 2019-09-12 | 2020-01-14 | 江苏大学 | Power grid voltage and current harmonic analysis method and system |
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| CN110687350A (en) * | 2019-09-12 | 2020-01-14 | 江苏大学 | Power grid voltage and current harmonic analysis method and system |
| CN110879311A (en) * | 2019-12-02 | 2020-03-13 | 北京四方继保自动化股份有限公司 | Method for calculating power of power grid |
| CN111525510A (en) * | 2020-05-06 | 2020-08-11 | 中国大唐集团科学技术研究院有限公司华东电力试验研究院 | Excitation inrush current evaluation method and device based on Lagrange interpolation method |
| CN113671245A (en) * | 2021-08-18 | 2021-11-19 | 国网陕西省电力公司电力科学研究院 | Digital interface with built-in time domain integration function and time domain next-time voltage acquisition method |
| CN115598416A (en) * | 2022-09-16 | 2023-01-13 | 珠海多创科技有限公司（Cn） | Method and system for processing station area sampling signal, storage medium and computer equipment |
| CN115598416B (en) * | 2022-09-16 | 2024-01-30 | 珠海多创科技有限公司 | Processing method, system, storage medium and computer equipment for area sampling signal |
| CN117169590A (en) * | 2023-08-15 | 2023-12-05 | 嘉兴市科讯电子有限公司 | Power harmonic analysis method and device based on software variable sampling rate |
| CN117169590B (en) * | 2023-08-15 | 2024-03-29 | 嘉兴市科讯电子有限公司 | Power harmonic analysis method and device based on software variable sampling rate |
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