CN106932642B - Electric Power Harmonic Analysis method - Google Patents
Electric Power Harmonic Analysis method Download PDFInfo
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- CN106932642B CN106932642B CN201710146296.1A CN201710146296A CN106932642B CN 106932642 B CN106932642 B CN 106932642B CN 201710146296 A CN201710146296 A CN 201710146296A CN 106932642 B CN106932642 B CN 106932642B
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- 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
Abstract
The invention discloses a kind of Electric Power Harmonic Analysis methods, including obtain input voltage actual cycle sampling number；Translational movement needed for calculating 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 offset, quadratic interpolation is carried out according to three obtained sampled value and the fractional part of total translational movement and obtains the corresponding interpolated data of the interpolation point；It repeats the above steps until processed points reach total points, to obtain completely new interpolating sequence；Electric harmonic parameter is analyzed and calculated to the interpolating sequence of the voltage and current stored again.Frequency analysis error caused by the spectral leakage of FFT when the method for the present invention effectively inhibits non-synchronous sampling；Phase-locked loop circuit complicated in Hardware synchronous sampling is eliminated, is finely adjusted without to the ADC sampling interval, thus applicable surface is extremely wide；Decaying of the interpolation to each harmonic amplitude is effectively reduced, frequency analysis accuracy and operation efficiency are greatly improved.
Description
Technical field
The invention belongs to electric automatization fields, and in particular to a kind of Electric Power Harmonic Analysis method.
Background technique
With the rapid development of power electronic technique, such as photo-voltaic power supply, wind-powered electricity generation, electric arc furnaces, electric railway and rolling mill
Equal loads are widely used, and nonlinear-load is gradually increased in the specific gravity of power grid.Caused by nonlinear-load is in power grid at present
Harmonic pollution problems are increasingly prominent, and electric administrative department also increasingly improves the attention rate of harmonic meter metering accuracy.The country in
Publication in 2014 implements harmonic meter standard " GB/T17215.302-2013 state type harmonic wave active electric energy meter ", to harmonic meter into
Gone it is unified and standard so that it is more effective in power grid, more reasonably plays a role.
Current most widely used harmonic analysis method is fft algorithm, it is known that be intended to obtain accurately and reliably
As a result, FFT spectrum leakage problem caused by non-synchronous sampling must be solved, non-synchronous sampling shows as sample frequency and electricity for analysis
Net fundamental frequency it is asynchronous.Fft algorithm requires the integer power that the periodic sampling points of signal are 2 simultaneously.Under normal circumstances,
Power grid fundamental frequency fluctuation range very little, usually within ± 0.5Hz；But under certain powerful nonlinear-loads, power grid
Frequency fluctuation range is larger, up to several hertz.In harmonic meter standard GB/T/T 17215.302-2013, it is desirable that frequency changes
For variable within ± 2%, the harmonic electric energy metering error knots modification of high-precision 1 grade of harmonic meter is less than ± 0.5%, so if
Realize that harmonic electric energy metering must be taken into consideration frequency fluctuation bring and influence using fft algorithm.
The method for reducing non-synchronous sampling errors at present mainly has window function and interpolation algorithm and synchronous sampling technique two major classes.?
Time domain adds Cosine Window that spectrum leakage can be effectively reduced, and carrying out frequency spectrum interpolation to FFT result in frequency domain can reduce fence effect
Caused error is answered, but adding window and the data operation quantity of frequency spectrum interpolation processing are big, and including solving high sublinear equation, division fortune
The processing such as calculation, spectral line peak value searching requires height to cpu performance, is not suitable for meter platform.Synchronous sampling technique has hardware synchronization
It samples and two kinds of synchronous sampling by software.Hardware synchronous sampling is that tracking of the sample frequency to fundamental frequency is realized using phaselocked loop,
But it needs to filter out input signal progress low-pass filtering the direct current and harmonic components other than 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 ADC by hardware trigger sampling, certain other kinds of ADC such as sigma-delta ADC is not available the technology, the sampling interval without
Method fine tuning.Synchronous sampling by software is the frequency input signal obtained according to measurement, passes through timer or other programmable delay moulds
Block is finely adjusted the ADC sampling interval, 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, is not available the technology, and in high-precision electric energy metered system
Analog sampling it is usually necessary to use sigma-delta ADC.Therefore, the non-synchronous sampling of sigma-delta ADC and its in electrical energy measurement application
It is current urgent problem that middle use FFT, which carries out frequency analysis,.
Summary of the invention
The purpose of the present invention is to provide a kind of high-precision Electric Power Harmonic Analysis methods.
This Electric Power Harmonic Analysis method provided by the invention, includes the following steps:
S1. the actual periodic sampling points of input voltage are obtained；
S2. actual periodic sampling points and the analysis points being previously set according to obtained in step S1 are calculated and are each adopted
Translational movement needed for sampling point；
S3. total translational movement needed for calculating the interpolation point according to the translational movement of the serial number of interpolation point and each point, is obtained simultaneously
Take the integer part and fractional part of total translational movement；
S4. corresponding actual samples point is obtained using the integer part of total translational movement obtained in step S3 as offset
Value, and the fractional part of total translational movement according to obtained in three obtained sampled value and step S3 carries out quadratic interpolation, obtains
The corresponding interpolated data of the interpolation point；
S5. step S3~S4 is repeated until processed points reach total points, to obtain completely new interpolating sequence；It is sharp again
It is analyzed with the interpolating sequence of the voltage and current stored in step S4, calculates electric harmonic parameter based on the analysis results.
Translational movement required for each sampled point of calculating described in step S2 is specially counted using following formula
It calculates:
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.
Total translational movement needed for calculating current interpolation point described in step S3 simultaneously obtains its integer part and fractional part,
Specially calculated using following formula:
Δn=n Δ
P=[Δn]=[n Δ]
Q=Δn- p=n Δ-p
In formula, n is the serial number of interpolation point, and value range is 0~N-1；ΔnFor total translational movement needed for current interpolation point；p
For the integer part of total translational movement, [Δn] indicate to ΔnIt is rounded；Q is the fractional part of total translational movement.
It is corresponding using the integer part of total translational movement obtained in step S3 as offset acquisition described in step S4
Actual samples point value, specially according to total translational movement integer part p in the serial number n and step S3 of 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 interpolation.
The fractional part of total translational movement according to obtained in three obtained sampled value and step S3 described in step S4
It carries out quadratic interpolation and obtains 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 serial number of interpolation point, and value range 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 respectively inputted
The sampling point value of n-th+p, n+p+1 and n+p+2 point after point；u′nWith i 'nFor the nth point data after interpolation.
The interpolating sequence of the voltage and current of storage is analyzed described in step S5, specially to the voltage of storage
Fft analysis is carried out with the interpolating sequence of electric current.
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 provided by the invention is counted a periodic sampling by using resampling technique
Not the crude sampling sequence of 2 exponential is converted to needed for fft algorithm 2 exponential point, even if under non-synchronous sampling
Complete cycle can be obtained and be 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 risen；The method of the present invention is realized using pure software algorithm, eliminates locking phase complicated in Hardware synchronous sampling
Loop circuit is finely adjusted without to the ADC sampling interval, thus is applicable not only to SAR ADC and is also convenient for being difficult to modify ADC weeks
Normal use fft algorithm in the electrical energy measurement application of the sigma-delta ADC in phase property sampling interval；Further, since using Lagrange
Quadratic interpolattion realizes that resampling effectively reduces decaying of the interpolation to each harmonic amplitude, mention significantly compared with linear interpolation method
Higher harmonics accuracy of analysis, and there is higher operation efficiency compared with Interpolating Window FFT Algorithm.
Detailed description of the invention
Fig. 1 is the basic principle block diagram of the method for the present invention.
Fig. 2 is flow chart of the method for the present invention.
Fig. 3 is the Lagrange quadratic interpolation example schematic diagram in the method for the present invention.
Fig. 4 is precision result schematic diagram when using linear interpolation in the method for the present invention.
Fig. 5 is precision result schematic diagram when using Lagrange quadratic interpolation in the method for the present invention.
Specific embodiment
As shown in Figure 1 be basic principle block diagram of the invention: present invention is primarily based on Lagrange interpolation and FFT resampling
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 interpolation resampling is carried out to voltage and current according to the period of voltage；Then pass through fft algorithm
Frequency analysis is carried out to the voltage and current data sequence after interpolation；Harmonic voltage, harmonic wave are finally calculated according to fft analysis result
The harmonic waves measuring indexs 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 provided by the invention, including such as
Lower step:
S1. the actual periodic sampling points of input voltage are obtained；
S2. actual periodic sampling points and the analysis points being previously set according to obtained in step S1 are calculated and are each adopted
Translational movement needed for sampling point is specially calculated using following formula:
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. total translational movement needed for calculating the interpolation point according to the translational movement of the serial number of interpolation point and each point, is obtained simultaneously
The integer part and fractional part of total translational movement are taken, is specially calculated using following formula:
Δn=n Δ
P=[Δn]=[n Δ]
Q=Δn- p=n Δ-p
In formula, n is the serial number of interpolation point, and value range is 0~N-1；ΔnFor total translational movement needed for current interpolation point；p
For the integer part of total translational movement, [Δn] indicate to ΔnIt is rounded；Q is the fractional part of total translational movement；
S4. corresponding actual samples point is obtained using the integer part of total translational movement obtained in step S3 as offset
Value, and the fractional part of total translational movement according to obtained in three obtained sampled value and step S3 carries out quadratic interpolation, obtains
The corresponding interpolated data of the interpolation point；
It is adopted first according to total translational movement integer part p in the serial number n and step S3 of current interpolation point 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 serial number of interpolation point, and value range 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 respectively inputted
The sampling point value of n-th+p, n+p+1 and n+p+2 point after point；u′nWith i 'nFor the nth point data after interpolation；
S5. step S3~S4 is repeated until processed points reach total points, to obtain completely new interpolating sequence；It is sharp again
Fft analysis is carried out with the interpolating sequence of the voltage and current stored in step S4, calculating based on the analysis results includes each harmonic
The electric harmonics parameters such as voltage, individual harmonic current and total harmonic wave active power.
The present invention realizes sample-synchronousization processing by Lagrange polynomial interopolation and resampling technique.Polynomial interopolation
It is that row interpolation is clicked through to one group of discrete data-oriented by multinomial, finding one can multinomial Jing Guo these data points
Function, thus the method for constructing new data point, wherein simplest method is using 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 are as follows:
Wherein, r is polynomial order, LiIt (x) is Lagrangian fundamental polynomials, expression formula are as follows:
From above formula it is found that fundamental polynomials Li(x) it has the property that
Obviously, according to Li(x) attribute, interpolation polynomial y=L (x) pass through this r+1 data point；
R=2 is enabled, then obtains Lagrangian quadratic interpolation multinomial, is calculated by 3 consecutive number strong points unknown at x
Value y, as follows:
Wherein LiIt (x) is basic Lagrangian quadratic polynomial.
The Lagrange quadratic interpolation example schematic diagram being illustrated in figure 3 in the method for the present invention: Lagrange quadratic interpolation
The polynomial interopolation for being 2 for order r, compared with linear interpolation, which has good calculated performance and precision, especially
Real-time high-efficiency suitable for electrical energy measurement application calculates and the biggish current waveform of the distortion factor under nonlinear-load.In Fig. 3, lead to
The step a and b for executing embodiment are crossed, 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 placenCalculation formula.3 data points, that is, ADC sampled value solid marks in figure, by inserting for these data points
Value function is dotted line parabola.Complete cycle can be obtained using multiple new identical processes of consecutive number strong points repetition and be applicable in
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 was 1 period, 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 N between 2~3
There are good calculated performance and precision, therefore the present invention selects ADC sample frequency fsFor 25.6kHz, i.e., one when fundamental frequency is 50Hz
A periodic sampling points are 512.
The present invention emulates provided harmonic wave algorithm using MATLAB software, and verifying is carried out using the method for the present invention
The frequency analysis especially accuracy of higher hamonic wave analysis and fundamental frequency fluctuate the influence to harmonic wave algorithm.Establish the emulation of algorithm
Model is as follows:
(1) data sequence of fundamental wave superposition single harmonic component is generated using following formula:
Wherein, fsFor sample frequency, fs=25.6kHz；finFor fundamental frequency, within the scope of 47.5~52.5Hz with
0.5Hz incremental variations, to verify influence of the fundamental frequency fluctuation to harmonic wave algorithm；A1WithFor fundamental voltage amplitude and phase, AhWithFor h subharmonic amplitude and phase, Ah=0.1A1,H is overtone order, in the range of 2~63；K is data sequence
Row number；
(2) using the method for the present invention above-mentioned data sequence is carried out respectively linear interpolation (error is as shown in Figure 4) and
Lagrange quadratic interpolation (error is as shown in Figure 5)；
(3) fft analysis is carried out to the N point data sequence that interpolation obtains, 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, caused by calculating interpolation
Harmonic error；
As shown in Figure 4 and Figure 5, software emulation, two kinds of obtained interpolation sides are carried out according to the above simulation model for the present invention
For method under the conditions of different fundamental frequencies, each harmonic component amplitude deviates the characteristic of original value.From figure it is not difficult to find out that, superposition 2~
63 subharmonic and fundamental frequency are changed to from 47.5Hz under the simulated conditions of 52.5Hz, and the present invention is based on Lagrange quadratic interpolations
Harmonic analysis method error within 0.65%, ratio of precision is nearly 10 times high using linear interpolation.
Claims (7)
1. a kind of Electric Power Harmonic Analysis method, includes the following steps:
S1. the actual periodic sampling points of input voltage are obtained；
S2. actual periodic sampling points and the analysis points being previously set according to obtained in step S1 calculate each sampled point
Required translational movement；
S3. total translational movement needed for calculating the interpolation point according to the translational movement of the serial number of interpolation point and each point, while obtaining should
The integer part and fractional part of total translational movement；
S4. corresponding actual samples point value is obtained using the integer part of total translational movement obtained in step S3 as offset, and
The fractional part of total translational movement according to obtained in three obtained sampled value and step S3 carries out quadratic interpolation, obtains the interpolation
The corresponding interpolated data of 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 serial number of interpolation point, and value range 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 respectively inputted it
The sampling point value of n-th+p, n+p+1 and n+p+2 point afterwards；u′nWith i 'nFor the nth point data after interpolation；
S5. step S3~S4 is repeated until processed points reach total points, to obtain completely new interpolating sequence；It recycles
To the interpolating sequence of voltage and current analyzed, calculate electric harmonic parameter based on the analysis results.
2. Electric Power Harmonic Analysis method according to claim 1, it is characterised in that calculating described in step S2 is each adopted
Translational movement required for sampling point is specially calculated using following formula:
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 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 following formula:
Δn=n Δ
P=[Δn]=[n Δ]
Q=Δn- p=n Δ-p
In formula, n is the serial number of interpolation point, and value range is 0~N-1；ΔnFor total translational movement needed for current interpolation point；P is total
The integer part of translational movement, [Δn] indicate to ΔnIt is rounded；Q is the fractional part of total translational movement.
4. Electric Power Harmonic Analysis method according to claim 1, it is characterised in that will be in step S3 described in step S4
The integer part of obtained total translational movement obtains corresponding actual samples point value as offset, specially according to current interpolation point
Serial number n and step S3 in total translational movement integer part p from voltage and current sample value sequence search input block
The sampled value of n+p, n+p+1 and n+p+2 point after initial point.
5. Electric Power Harmonic Analysis method described according to claim 1~one of 4, it is characterised in that secondary described in step S4
Interpolation is Lagrange quadratic interpolation.
6. Electric Power Harmonic Analysis method according to claim 5, it is characterised in that utilization described in step S5 obtains
The interpolating sequence of voltage and current is analyzed, and specially carries out fft analysis to the interpolating sequence of obtained voltage and current.
7. Electric Power Harmonic Analysis method according to claim 6, it is characterised in that the ginseng of electric harmonic described in step S5
Number includes each harmonic voltage, individual harmonic current and total harmonic wave active power.
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| CN109959825B (en) * | 2017-12-26 | 2023-07-21 | 东南大学 | Nonlinear voltage-controlled attenuator fitting calibration method based on Lagrange interpolation method |
| 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 |
| CN111525510B (en) * | 2020-05-06 | 2021-11-26 | 中国大唐集团科学技术研究总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 |
| 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 |
| 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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