CN104142424B - A kind of method of accurate measurement non-sinusoidal voltage signal and system thereof - Google Patents

Abstract

The present invention provides method and the system thereof of a kind of accurate measurement non-sinusoidal voltage signal, and the method comprising the steps of: according to the sampled value of nonsinusoidal wave to be measured, determines the magnitude of voltage of n staircase waveform step；And produce step signal accordingly, nonsinusoidal wave and step signal are done difference sampling at equal intervals, draws difference value；The magnitude of voltage of difference value with staircase waveform step is added, in kth subharmonic, carry out discrete Fourier transform (DFT) calculating on each staircase waveform step from the sampled point of s to t, then the result that all discrete Fourier transform (DFT) calculate is averaged is calculated corresponding pseudo-sinusoidal coefficients a'_kWith pseudo-cosine coefficient b'_k, wherein s, t meet condition t s+1=m/2, and t+s=m；The true sinusoidal coefficients a in kth subharmonic is calculated according to equation group (1) (2)_kWith true cosine coefficient b_k.The invention provides a series of measurement non-sinusoidal voltage signal theory and technology, there is higher accuracy of measurement.

Description

A kind of method of accurate measurement non-sinusoidal voltage signal and system thereof

Technical field

The present invention relates to the measurement of non-sinusoidal voltage signal, particularly relate to the side of a kind of accurate measurement non-sinusoidal voltage signal Method and system thereof.

Background technology

Due to the development of power industry, the supervision to the harmonic wave on electrical network is paid attention to widely with control, and then to electricity The electricity consumption product such as machine, household electrical appliance proposes prescription, does not produce the harmonic component beyond power frequency to pollute electrical network.Thus anon-normal The measurement of string ripple is by more and more developing application.The level that this field is best at present is 3 × 10^-5Left and right, typically 1 × 10^-3Level.

Due to the appearance of josephson voltage standard able to programme, alternating voltage its trend traced to the source oriented.American National meter Amount institute NIST proposes and achieves tracing to the source of sinusoidal wave direction josephson voltage standard able to programme.Specifically use difference sampling skill Art, measures sine wave to be measured and the difference of a staircase waveform being made up of josephson voltage standard able to programme.Due to able to programme Josephson voltage standard has up to 10^-10The accuracy of level, and the difference of two signals can control at a less model (such as 10 in enclosing^-3To 10^-2), thus the requirement of sampled measurements is if having (10^-5To 10^-6) level, entirety is i.e. up to 10^-8Level. The method that NIST proposes, one of them important thought be be positioned at sampled data at transient process abandon need not, and being positioned at Smooth step up-sampling data retain, and are used for being calculated measurement result, thus reach in the range of (60-400) Hz (10^-8～10^-7) level.

But above-mentioned technology is typically only applicable to sine wave, there is shortcoming for non-sinusoidal waveform.This is because sinusoidal wave with In the difference of staircase waveform, due to the existence of ladder start-up portion transient process, making measurement produce bigger error, for this, they will The sampling being positioned at transient process abandons, and the sampling of flat is stayed, and i.e. loses half, stays half.If staircase waveform has n If step, then leave n sampling.According to sampling thheorem, can analyze to n/2 subharmonic, non-sinusoidal waveform measurement is by this Inadequate.

Summary of the invention

The features and advantages of the present invention are partly stated, or can from this description it is clear that or Person can learn by putting into practice the present invention.

For overcoming problem of the prior art, the present invention provides a kind of method of accurate measurement non-sinusoidal voltage signal and is System, is calculated corresponding pseudo-sinusoidal coefficients a' based on multiple spot discrete Fourier transform_kWith pseudo-cosine coefficient b'_k, and to this Result is corrected for matrix relationship formula, calculates the true sinusoidal coefficients a in k subharmonic_kWith true cosine coefficient b_k, finally give each The amplitude of subharmonic and phase angle.

It is as follows that the present invention solves the technical scheme that above-mentioned technical problem used:

According to an aspect of the present invention, it is provided that a kind of method of accurate measurement non-sinusoidal voltage signal, it is characterised in that Including step:

S1, sampled value according to nonsinusoidal wave to be measured, determine the magnitude of voltage of n staircase waveform step；

S2, magnitude of voltage according to n this staircase waveform step produce step signal, by this nonsinusoidal wave and this ladder Ripple signal does difference sampling at equal intervals, draws difference value, this staircase waveform step the most each has m sampled point；

S3, the magnitude of voltage of this difference value with this staircase waveform step is added, in kth subharmonic, to this staircase waveform each On step, the sampled point from s to t carries out discrete Fourier transform (DFT) calculating, then these discrete Fourier transform (DFT) all is calculated Result be averaged and be calculated corresponding pseudo-sinusoidal coefficients a'_kWith pseudo-cosine coefficient b'_k, wherein s, t meet condition t-s+1 =m/2, and t+s=m；

S4, the true sinusoidal coefficients a calculated in kth subharmonic_kWith true cosine coefficient b_k；Wherein this true sinusoidal coefficients a_kWith puppet Sinusoidal coefficients a'_kMeet equation group (1), this true cosine coefficient b_kWith pseudo-cosine coefficient b'_kMeet equation group (2), solve the two side Journey group, can obtain this true sinusoidal coefficients a_kWith true cosine coefficient b_k；

In equation group (1), when k < during n/2,Work as k=n/2 Time,

In equation group (2), when k < during n/2,Work as k=n/ When 2,

Note: in the expression formula of above-mentioned matrix, only occur in that parameter m, illustrate that matrix is only determined by m, the above-mentioned square provided Battle array expression formula, can be used in different n (the step number of staircase waveform).

Preferably, in order to determine the magnitude of voltage of n this staircase waveform step more accurately, this step S1 specifically includes step:

D1, measuring the sampled data of this nonsinusoidal wave according to predetermined parameter n, m, every m sampled data is divided into one Group, altogether n group, preliminary as a staircase waveform step of the sampled data often group being positioned on the point in the middle of predetermined parameter s, t Magnitude of voltage, draws the preliminary magnitude of voltage of n staircase waveform step respectively；

D2, preliminary magnitude of voltage according to n this staircase waveform step produce corresponding preliminary step signal, measure this anon-normal String ripple signal and the difference value of this preliminary step signal；

D3, the difference value observed in this step D2, and judge the difference value that often group is positioned on the point in the middle of predefined parameter s, t Whether meet smaller requirement, if undesirable, then the difference value in this step D2 is compensated as corrected value Again as the preliminary magnitude of voltage of staircase waveform step in the preliminary magnitude of voltage of n the staircase waveform step drawn；

D4, repetition step D2, D3, until meeting this step D3 requirement, determine the preliminary magnitude of voltage of this staircase waveform step Magnitude of voltage for this staircase waveform step.

Preferably, in this step S3, corresponding average computation and Fourier transform computing formula thereof be:

${a^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{a^{\&prime;}}_k\left(j\right),{a^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\sin k(i,j)$

${b^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{b^{\&prime;}}_k\left(j\right),{b^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\cos k(i,j)$

Wherein (i j) represents k rank sine basic function, the jth sampled point being positioned on i-th step to sink.

Preferably, in this step S2 or S3, the sampled point on this staircase waveform step each is represented sequentially as 0, and 1,2 ..., M-1, wherein m is the integer more than 4 less than 100.

Preferably, described in this step S3, the magnitude of voltage of staircase waveform step is to be measured described rank one by one by digital voltmeter The magnitude of voltage of each staircase waveform step of ladder ripple signal obtains, for being added with this difference value in this step S2.

According to a further aspect in the invention, also providing for the system of a kind of accurate measurement non-sinusoidal voltage signal, its feature exists In, including:

Signal source, for producing nonsinusoidal wave to be measured；

Second analog-digital converter, for carrying out sampled measurements to this nonsinusoidal wave；

Para-position module, is connected with this second analog-digital converter, for determining n ladder according to nonsinusoidal wave sampled value The magnitude of voltage of ripple step；

Digital to analog converter, is connected with this para-position module, for producing rank according to the n determined this staircase waveform plateau voltage value Ladder ripple signal；

First analog-digital converter, is connected with digital-to-analogue converter with this signal source, for by this nonsinusoidal wave and ladder Ripple signal does difference sampling at equal intervals, obtains difference value；

Summation module, is connected with this first analog-digital converter and para-position module, for this difference value is individual with the n determined This staircase waveform plateau voltage value is added；

Pseudo-coefficients calculation block, in kth subharmonic, on this staircase waveform step each from the sampled point of s to t Carry out discrete Fourier transform (DFT) calculating, then the result that these discrete Fourier transform (DFT) all calculate is averaged be calculated corresponding Pseudo-sinusoidal coefficients a'_kWith pseudo-cosine coefficient b'_k, wherein s, t meet condition t-s+1=m/2, and t+s=m；

True coefficient computing module, calculates the true sinusoidal coefficients a in kth subharmonic_kWith true cosine coefficient b_k；Wherein this is real String coefficient a_kWith pseudo-sinusoidal coefficients a'_kMeet equation group (1), this true cosine coefficient b_kWith pseudo-cosine coefficient b'_kMeet equation group (2)；Solve the two equation group, true sinusoidal coefficients a can be obtained_kWith true cosine coefficient b_k；

In equation group (1), when k < during n/2,Work as k=n/2 Time,

In equation group (2), when k < during n/2,Work as k=n/ When 2,

Preferably, in this puppet coefficients calculation block, corresponding average computation and Fourier transform computing formula thereof are:

${a^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{a^{\&prime;}}_k\left(j\right),{a^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\sin k(i,j)$

${b^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{b^{\&prime;}}_k\left(j\right),{b^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\cos k(i,j).$

Preferably, this second analog-digital converter is for measuring, according to predetermined parameter n, m, the non-sine that this signal source produces The sampled data of ripple signal, every m sampled data is divided into one group, altogether n group；This para-position module, for being positioned at often group in parameter s, t The middle sampled data on point, as the magnitude of voltage of a staircase waveform step, determines the magnitude of voltage of n staircase waveform step respectively.

Preferably, also include digital voltmeter, be connected with this digital to analog converter and summation module, for measure one by one by Each staircase waveform plateau voltage value of the step signal that this digital to analog converter produces under DC mode, and staircase waveform will be obtained Plateau voltage accurate measurements is transported to summation module.

Preferably, this first analog-digital converter and this second analog-digital converter are same analog-digital converter.

The invention provides a kind of method measuring non-sinusoidal voltage signal and system thereof, first will be produced by signal source Non-sinusoidal waveform to be measured, together with the staircase waveform produced by digital to analog converter, is that a Sampling device (analog-digital converter) institute difference is surveyed Amount, then the data of difference measurement are added with accurately being measured the stepped-up voltage numerical value obtained by digital voltmeter, then oppose On this staircase waveform step each, the sampled point from s to t carries out discrete Fourier transform (DFT) calculating, then by these discrete Fu all The result that vertical leaf transformation calculates is averaged and is calculated corresponding pseudo-sinusoidal coefficients a'_kWith pseudo-cosine coefficient b'_k, overcome transition The impact of process, then by the matrix solution equation group provided, obtains amplitude and the phase angle of each harmonic.

The present invention, by special alignment method, significantly improves the level of Synchronization Control, reduces it to final result Impact.

By reading description, those of ordinary skill in the art will be best understood the feature of these technical schemes and interior Hold.

Accompanying drawing explanation

Below with reference to accompanying drawing and combine example be specifically described the present invention, advantages of the present invention and implementation will Becoming apparent from, wherein content shown in accompanying drawing is only used for explanation of the present invention, and does not constitute to the present invention in all senses On restriction, in the accompanying drawings:

Fig. 1 is the schematic flow sheet of the method measuring non-sinusoidal voltage signal of the embodiment of the present invention.

Fig. 2 is the schematic diagram of the sampling aliasing effect of the embodiment of the present invention.

Fig. 3 is the structural representation of the system measuring non-sinusoidal voltage signal of the embodiment of the present invention.

Fig. 4 is the para-position effect that nonsinusoidal wave reaches with differential signal.

Detailed description of the invention

As it is shown in figure 1, a kind of method that the present invention provides accurate measurement non-sinusoidal voltage signal, it is characterised in that include Step:

S1, sampled value according to nonsinusoidal wave to be measured, determine the magnitude of voltage of n staircase waveform step；

S2, produce step signal according to the magnitude of voltage of n staircase waveform step, by nonsinusoidal wave and step signal Do difference sampling at equal intervals, draw difference value, the most each staircase waveform step has m sampled point；

S3, the magnitude of voltage of difference value with staircase waveform step is added, in kth subharmonic, on each staircase waveform step Carry out discrete Fourier transform (DFT) calculating from the sampled point of s to t, then the result that all discrete Fourier transform (DFT) calculate is entered Row average computation obtains corresponding pseudo-sinusoidal coefficients a'_kWith pseudo-cosine coefficient b'_k, wherein s, t meet condition t-s+1=m/2, and t + s=m；

S4, the true sinusoidal coefficients a calculated in kth subharmonic_kWith true cosine coefficient b_k；The trueest sinusoidal coefficients a_kWith puppet just String coefficient a'_kMeet equation group (1), true cosine coefficient b_kWith pseudo-cosine coefficient b'_kMeet equation group (2), solve the two equation Group, can obtain true sinusoidal coefficients a_kWith true cosine coefficient b_k；

In equation group (1), when k < during n/2,Work as k=n/2 Time,

In equation group (2), when k < during n/2,Work as k=n/ When 2,

In the expression formula of above-mentioned matrix, only occur in that parameter m, illustrate that matrix is only determined by m, the above-mentioned matrix table provided Reaching formula, can be used in different n, parameter n represents the step number of staircase waveform.

In step S1, the present invention proposes the para-position side being determined required step signal by nonsinusoidal wave sampled value Method, it is the highest that the para-position of these two signals requires, and in the case of non-sine exports, it is also highly difficult for will controlling its phase angle , but this is the key point of difference sampled measurements.In order to determine the magnitude of voltage of n this staircase waveform step more accurately, should Step S1 specifically includes step:

D1, measuring the sampled data of this nonsinusoidal wave according to predetermined parameter n, m, every m sampled data is divided into one Group, altogether n group, preliminary as a staircase waveform step of the sampled data often group being positioned on the point in the middle of predetermined parameter s, t Magnitude of voltage, draws the preliminary magnitude of voltage of n staircase waveform step respectively；Such as, as n=10, m=6, it is numbered j=0, and 1, 2,3,4,5, s, t of now meeting step S2 conditional are respectively 2,4, and the point in the middle of parameter s, t is j=3.

D2, preliminary magnitude of voltage according to n this staircase waveform step produce corresponding preliminary step signal, measure this anon-normal String ripple signal and the difference value of this preliminary step signal；

D3, the difference value observed in this step D2, and judge that every group is positioned at the difference of predefined parameter s, t intermediate point (j=3) Whether value meets smaller requirement, if undesirable, is then compensated as corrected value by the difference value in this step D2 Again as the preliminary magnitude of voltage of staircase waveform step in the preliminary magnitude of voltage of n the staircase waveform step drawn；

D4, repetition step D2, D3, until meeting this step D3 requirement, determine the preliminary magnitude of voltage of this staircase waveform step Magnitude of voltage for this staircase waveform step.

Above-mentioned steps D1 to D4 is that the present invention proposes that one more convenient and technique of counterpoint that accuracy is higher, but the present invention Be not limited thereto, only need to as described in step S1 sampled value according to nonsinusoidal wave to be measured, after carrying out para-position process, really Determine the magnitude of voltage of n staircase waveform step, and ensure that the retention point meeting condition has less difference value,.

In step s3, s, t need to meet condition t-s+1=m/2, and t+s=m.Table 1 below lists and meets above-mentioned bar The value of m, s, t of part, certainly, the present invention is not limited thereto.

m	s	t	t-s+1
				6	2	4	3
10	3	7	5
				14	4	10	7

The eligible m of table 1, the combination of t, s

As a example by m=6, now 6 points of each staircase waveform step up-sampling in step signal, need each staircase waveform Carry out discrete Fourier transform calculating from the 2nd to the 4th sampled point on step, so, be no longer at equal intervals between sampled point The relation of sampling, it is assumed that be spaced apart 1 from the 2nd to the 4th sampled point, then three on adjacent 2 staircase waveform steps Interval between sampled point is then 4.How such sampling relation, carry out the discrete Fourier transform (DFT) of higher order frequencies component (DFT) it is a problem, needs to solve theoretically.The present invention proposes the concept of rule unequal interval sampling (RUEIS)；Its In, described unequal interval sample, on the basis of equal interval sampling regular abandon some sampled datas formed, therefore It is well-regulated, is referred to as rule unequal interval sampling.The Fourier transform that this present invention proposes this concept of adaptation is newly managed Opinion and new method, specifically, be to carry out discrete Fourier on each described staircase waveform step from the sampled point that s to t is individual Leaf transformation calculates, then the result that all described discrete Fourier transform (DFT) calculate is averaged and is calculated corresponding pseudo-sinusoidal system Number a'_kWith pseudo-cosine coefficient b'_k, this average computation and Fourier transform computing formula thereof are as follows:

${a^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{a^{\&prime;}}_k\left(j\right),{a^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\sin k(i,j)$

${b^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{b^{\&prime;}}_k\left(j\right),{b^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\cos k(i,j)$

Wherein, k represents which staircase waveform step harmonic order, label i represent, j represents on each staircase waveform step Which sampled point；And the sampling on a step is represented sequentially as 0,1,2 ..., m-1；And sink (i, j) then represent k rank just String basic function, the jth sampled point being positioned on i-th step.

Refer to the schematic diagram that Fig. 2, Fig. 2 are sampling aliasing effects, it is seen that in the example of n=10, m=6, when to be measured When nonsinusoidal wave exists more than 5 subharmonic, the pseudo-sinusoidal coefficients a' obtained in step S2_kWith pseudo-cosine coefficient b'_kTo deposit In aliasing effect, the harmonic order that generally, there are aliasing effect is that { k, n-k, n+k} exist aliasing effect to group as n=10 The harmonic order answered includes group: { 1,9,11}, { 2,8,12}, { 3,7,13}, { 4,6,14}, { 5,15}.It is known that in group be Exist in aliasing effect, but the most do not exist in aliasing effect between group.

As a example by first group 1,9,11}, if the pseudo-sinusoidal coefficients calculated in step S2 and pseudo-cosine coefficient are designated as C'₁=(a'₁,a'₉,a'₁₁,b'₁,b'₉,b'₁₁), they are inaccurate, and original coefficient accurately is designated as C₁=(a₁,a₉, a₁₁,b₁,b₉,b₁₁), but these coefficients we have no knowledge about.

Relation between them can be written as:

${\mathrm{CC}}_1^T=C_1^{\&prime;T}$

Wherein C is the matrix of 6 × 6.If its inverse matrix exists, required solution can be derived as

$C_1^T=C^{-1}{C}_1^{\&prime;T}$

Research shows, in some conditions, Matrix C has a succinct form:

$C=\left(\begin{array}{cc}A& D\\ E& B\end{array}\right)=\left(\begin{array}{cc}A& 0\\ 0& B\end{array}\right)$

Wherein A and B is the matrix of 3 × 3, and the present invention has also derived matrix A, and the General Analytical form of B, for third-order matrix Form, it is that s, t need to meet condition t-s+1=m/2, and t+s=m that Matrix C has the condition of reduced form.At this point it is possible to Draw in step S3 as k < A during n/2_k、B_kExpression formula and as k=n/2 A_k、B_kExpression formula.

So, the real string system in k subharmonic can be drawn further according to the equation group (1) in step S3 and equation group (2) Number a_kWith true cosine coefficient b_k。

Above-mentioned group 1,9,11}, and 2,8,12}, 3,7,13}, in 4,6,14}, for k=1,2,3,4, can first basis Matrix A_k、B_kSolve corresponding inverse matrixAnd can from which further follow that with equation group (2) according to equation group (1):

$\left(\begin{array}{c}{a}_k\\ a_{10-k}\\ a_{10+k}\end{array}\right)=A_k^{-1}\left(\begin{array}{c}{a^{\&prime;}}_k\\ {a^{\&prime;}}_{10-k}\\ {a^{\&prime;}}_{10+k}\end{array}\right)$

$\left(\begin{array}{c}{b}_k\\ b_{10-k}\\ b_{10+k}\end{array}\right)=B_k^{-1}\left(\begin{array}{c}{b^{\&prime;}}_k\\ {b^{\&prime;}}_{10-k}\\ {b^{\&prime;}}_{10+k}\end{array}\right)$

And for group, { situation of 5,15} is that institute is different, i.e. k=5, n=10, now pseudo-cosine coefficient b'₁₅With b'₅Between There is proportionate relationship, so b'₁₅It is not put into consideration, it may be assumed that

$\left(\begin{array}{c}{a}_5\\ a_{10}\\ a_{15}\end{array}\right)=A_5^{-1}\left(\begin{array}{c}{a^{\&prime;}}_5\\ {a^{\&prime;}}_{10}\\ {a^{\&prime;}}_{15}\end{array}\right)$

$\left(\begin{array}{c}{b}_5\\ b_{10}\end{array}\right)=B_5^{-1}\left(\begin{array}{c}{b^{\&prime;}}_5\\ {b^{\&prime;}}_{10}\end{array}\right)$

Wherein a₁₀With a₅,a₁₅Put together and be only used to convenient reason, a₁₀It is independent, there is not direct current Under premise, b₁₀Equally.

At n=10, m=6, three data of reservation are j=2, in the case of 3,4, matrix A_k、B_kAnd their inverse matrix Form is as follows: (wherein k=1,2,3,4)

$A_k=\left(\begin{array}{ccc}1& 2/3& -2/3\\ 2/3& 1& 0\\ -2/3& 0& 1\end{array}\right),A_k^{-1}=\left(\begin{array}{ccc}9& -6& 6\\ -6& 5& -4\\ 6& -4& 5\end{array}\right)$

$B_k=\left(\begin{array}{ccc}1& -2/3& -2/3\\ -2/3& 1& 0\\ -2/3& 0& 1\end{array}\right),B_k^{-1}=\left(\begin{array}{ccc}9& 6& 6\\ 6& 5& 4\\ 6& 4& 5\end{array}\right)$

$A_5=\left(\begin{array}{ccc}5/3& 0& -2/3\\ 0& 1& 0\\ -2/3& 0& 2/3\end{array}\right),A_5^{-1}\left(\begin{array}{ccc}1& 0& 1\\ 0& 1& 0\\ 1& 0& 5/2\end{array}\right)$

$B_5=\left(\begin{array}{cc}1/3& 0\\ 0& 1\end{array}\right),B_5^{-1}=\left(\begin{array}{cc}3& 0\\ 0& 1\end{array}\right)$

These matrixes have actually used value.The feelings that all sampled points on one staircase waveform step are all utilized Condition, now Matrix C becomes a unit matrix, it is not necessary to inverse matrix solves.Visible in step s3, it is proposed that pass through dematrix Equation group overcomes aliasing effect, the method obtaining corresponding true sinusoidal coefficients and true cosine coefficient；And give the concrete of matrix Structure and rule thereof.

It should be noted that in step s3, need first to solve matrix A_k、B_kInverse matrix, to this end, applicant also confirms that The existence of matrix inversion matrix.When m is the integer being less than 100 more than 4, matrix A_k、B_kDeterminant be not zero.Thus demonstrate,prove Aliasing effect in real regular unequal interval sampling (RUEIS) can solve；Sampling thheorem can also be used to estimation and can analyze Highest frequency component.Third-order matrix by analyze highest frequency component from 0.5nf₀Extend 3 times, to 1.5nf0.

In step s3, also include utilizing the true sinusoidal coefficients a calculated_kWith true cosine coefficient b_kObtain non-sinusoidal waveform The amplitude of k subharmonic and phase angle in signal, wherein amplitude isPhase angle is arctan (a_k/b_k)。

In the present embodiment, in order to promote the accuracy of measurement further, the electricity of this staircase waveform step in this step S3 Pressure value is that the magnitude of voltage of each staircase waveform step being measured described step signal by digital voltmeter one by one obtains, for Difference value in step S2 is added.Specifically, step signal is produced by digital to analog converter, and rank in step s3 The magnitude of voltage of ladder ripple step is then to be measured, by digital voltmeter, the ladder produced under DC mode by this digital to analog converter one by one Obtained by each staircase waveform plateau voltage value of ripple signal, it is the voltage of the step of staircase waveform the most accurately of actual measurement Value.The present invention uses the DC voltage (staircase waveform) that current accuracy of measurement is higher to approach nonsinusoidal signal, both difference controls System, in less scope, although this is measured exchange, but can significantly lower requirement, thus obtain on the whole relatively High accuracy of measurement.

Refer to Fig. 3, the present invention also provides for a kind of system measuring non-sinusoidal voltage signal, it is characterised in that including: letter Number source 1, for producing nonsinusoidal wave to be measured；Second analog-digital converter 7, for sampling to this nonsinusoidal wave Measure；Para-position module 8, is connected with this second analog-digital converter 7, for determining n ladder according to nonsinusoidal wave sampled value The magnitude of voltage of ripple step；Digital to analog converter 2, is connected with this para-position module 8, for according to the n determined this staircase waveform step electricity Pressure value produces step signal；First analog-digital converter 3, is connected with digital-to-analogue converter 2 with this signal source 1, for this is to be measured Nonsinusoidal wave and step signal do difference sampling at equal intervals, obtain difference value；Summation module 4, with this first modulus Transducer and para-position module 8 are connected, for being added with this staircase waveform plateau voltage value by this difference value；Pseudo-coefficients calculation block 5, in kth subharmonic, carry out discrete Fourier transform (DFT) meter on this staircase waveform step each from the sampled point that s to t is individual Calculate, then the result that these discrete Fourier transform (DFT) all calculate is averaged is calculated corresponding pseudo-sinusoidal coefficients a'_kAnd puppet Cosine coefficient b'_k, wherein s, t meet condition t-s+1=m/2, and t+s=m；True coefficient computing module 6, calculates kth subharmonic In true sinusoidal coefficients a_kWith true cosine coefficient b_k；Wherein this true sinusoidal coefficients a_kWith pseudo-sinusoidal coefficients a'_kMeet equation group (1), This true cosine coefficient b_kWith pseudo-cosine coefficient b'_kMeet equation group (2)；

In equation group (1), when k < during n/2,Work as k=n/2 Time,

In equation group (2), when k < during n/2,Work as k=n/ When 2,

Note: in the expression formula of above-mentioned matrix, only occur in that parameter m, illustrate that matrix is only determined by m, the above-mentioned square provided Battle array expression formula, can be used in different n (the step number of staircase waveform).

This true coefficient computing module 6 is additionally operable to utilize the true sinusoidal coefficients a calculated_kWith true cosine coefficient b_kObtain non- The amplitude of k subharmonic and phase angle in sine wave signal, wherein amplitude isPhase angle is arctan (a_k/b_k)。

In pseudo-coefficients calculation block 5, corresponding average computation and Fourier transform thereof in this puppet coefficients calculation block Computing formula is:

${a^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{a^{\&prime;}}_k\left(j\right),{a^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\sin k(i,j)$

${b^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{b^{\&prime;}}_k\left(j\right),{b^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\cos k(i,j).$

In the present embodiment, this second analog-digital converter 7 is non-for produce this signal source according to predetermined parameter n, m Sine wave signal does sampled measurements, and every m sampled data is divided into one group, altogether n group；This para-position module 8, for being positioned at often group in ginseng The sampled data on point in the middle of number s, t, as the magnitude of voltage of a staircase waveform step, determines the electricity of n staircase waveform step respectively Pressure value.It should be noted that the first analog-digital converter 3 and the second analog-digital converter 7 divide, in reality to describe convenient During the operation of border, both can be same analog-digital converter, completes to work accordingly at different time.

Utilize how analog-digital converter realizes step signal and nonsinusoidal wave below in conjunction with concrete example explanation Para-position, to determine the magnitude of voltage of n staircase waveform step more accurately.In this example, each staircase waveform step there are six During sampled data, they be labeled as j=0,1,2,3,4,5, condition t-s+1=m/2 met according to s, t, and t+s=m can Should be as j=2,3,4 with three data drawing reservation.Wherein when j=3, it is necessary to allow two signals overlap, getting over of coincidence Good, differential voltage i.e. difference value is the least.

Comprising the concrete steps that now: first by analog-digital converter (the e.g. second analog-digital converter 7) sampled measurements non-sine Signal, corresponding predetermined n and m=6.In the sampled data in a cycle, every six data are divided into one group.Those data Transmission is to para-position module 8, and para-position module 8 selects the non-sinusoidal waveform sampled value ladder electricity as this step of j=3 in each group Pressure value, after each step determines, forms the preliminary magnitude of voltage of n staircase waveform step.

The preliminary magnitude of voltage of this n staircase waveform step is input in digital to analog converter 2 by then para-position module 8 again, produces Corresponding preliminary step signal.Then this nonsinusoidal wave is measured by analog-digital converter (the such as first analog-digital converter 3) With the difference value of this preliminary step signal, observe those difference values, and judge whether to meet on j=3 position smaller Requirement；Because now the differential voltage on j=3 position should be the least, will without little i.e. not meeting to desired degree Ask, the difference value now measured can be compensated as corrected value in the preliminary magnitude of voltage of n the staircase waveform step drawn, Again as the preliminary magnitude of voltage of staircase waveform step, then para-position module 8 is again by defeated for the preliminary magnitude of voltage of this n staircase waveform step Enter in digital to analog converter 2, produce corresponding preliminary step signal, and measure this nonsinusoidal wave and this preliminary staircase waveform The difference value of signal, it is judged that whether meet smaller requirement on j=3 position, so repeat, until meeting the requirements. The magnitude of voltage of these satisfactory n staircase waveform steps determined also needs to be transported to summation module for follow-up calculating.

In order to obtain the magnitude of voltage of n staircase waveform step of reality more accurately, also include that digital voltmeter (does not shows in figure Show), it is connected with this digital to analog converter 2 and summation module 4, for measuring by this digital to analog converter 2 under DC mode one by one Each staircase waveform plateau voltage value of the step signal produced, and the staircase waveform step the most accurately of actual measurement will be obtained Magnitude of voltage is transported to summation module 4.

Actual measure during, in order to ensure the accurate of difference measurement, in addition it is also necessary in signal source 1, digital-to-analog converter 2, the Between one A-D converter 3, Synchronization Control link is set.In the present embodiment, signal source synchronizing signal is provided.

The present invention is also by the method for experimental verification above-mentioned measurement non-sinusoidal voltage signal and system thereof, in an experiment, non- Sinusoidal signal is provided with first-harmonic, 3 times, 5 times and 11 order harmonic components.Use above-mentioned measurement non-sinusoidal voltage signal method or System, and parameter n=10 is set, m=6, carry out the measurement in 50 cycles, from first-harmonic to the measurement result of 15 subharmonic such as figure Shown in 4, compared with original value arranged, find that error, less than signal source degree of stability level, connects in nonsinusoidal wave amplitude In the case of nearly 1V, the differential voltage major part at j=3 is less than 0.001V, and minority is less than 0.01V, and this is current instrument and equipment Under the conditions of preferable result.

The present invention provides method and the system thereof of a kind of accurate measurement non-sinusoidal voltage signal, uses current accuracy of measurement Higher DC voltage (staircase waveform) approaches nonsinusoidal signal, and both differences are controlled the measurement in less scope, to this Although or exchange, but can significantly lower requirement, thus obtain higher accuracy of measurement on the whole.The present invention proposes Series of theories and technology, the problem produced during solving to realize above-mentioned imagination.Mainly include proposing adaptation rule non-etc. The Fourier transform new theory for higher order frequencies component of interval sampling (RUEIS) concept and new method；Propose by anon-normal String ripple signal sampling value determines the alignment method of required step signal；Have employed the DFT method of middle retention point；Propose logical Cross dematrix equation group and overcome aliasing effect, the method obtaining corresponding true sinusoidal coefficients and true cosine coefficient；And give square The concrete structure of battle array and rule thereof；Propose concrete measurement system structure.

The present invention can be used for the foundation of high-caliber harmonic standard, and (staircase waveform is produced by josephson voltage standard able to programme Raw) it can also be used to the exploitation of widely used high-grade non-sinusoidal waveform measuring instrument (staircase waveform is by high-quality electronics DAC Produce).

Illustrating the preferred embodiments of the present invention above by reference to accompanying drawing, those skilled in the art are without departing from the scope of the present invention And essence, multiple flexible program can be had to realize the present invention.For example, as the shown partially of an embodiment or describe Feature can be used for another embodiment to obtain another embodiment.These are only the embodiment that the present invention is the most feasible, not Therefore the interest field of the present invention is limited to, the equivalence change that all utilization description of the invention and accompanying drawing content are made, it is both contained in Within the interest field of the present invention.

Claims (10)

1. the method for an accurate measurement non-sinusoidal voltage signal, it is characterised in that include step:

S1, sampled value according to nonsinusoidal wave to be measured, determine the magnitude of voltage of n staircase waveform step；

S2, magnitude of voltage according to n described staircase waveform step produce step signal, by described nonsinusoidal wave and described rank Ladder ripple signal does difference sampling at equal intervals, draws difference value, the most each described staircase waveform step has m sampled point；

S3, the magnitude of voltage of described difference value with described staircase waveform step is added, in kth subharmonic, to each described ladder On ripple step, the sampled point from s to t carries out discrete Fourier transform (DFT) calculating, then by all described discrete Fourier transform (DFT) The result calculated is averaged and is calculated corresponding pseudo-sinusoidal coefficients a'_kWith pseudo-cosine coefficient b'_k, wherein s, t meet condition t- S+1=m/2, and t+s=m；

S4, the true sinusoidal coefficients a calculated in kth subharmonic_kWith true cosine coefficient b_k；Wherein said true sinusoidal coefficients a_kWith puppet just String coefficient a'_kMeet equation group (1), described true cosine coefficient b_kWith pseudo-cosine coefficient b'_kMeet equation group (2), solve the two side Journey group, can obtain described true sinusoidal coefficients a_kWith true cosine coefficient b_k；

In described equation group (1), when k < during n/2,Work as k=n/2 Time,

In described equation group (2), when k < during n/2,Work as k=n/2 Time,

The method the most accurately measuring non-sinusoidal voltage signal, it is characterised in that in order to the most true Determining the magnitude of voltage of n described staircase waveform step, described step S1 specifically includes step:

D1, according to predetermined parameter n, m measure described nonsinusoidal wave sampled data, every m sampled data is divided into one group, N group altogether, is positioned at using often group in the preliminary voltage as a staircase waveform step of the sampled data on predetermined parameter s, point middle for t Value, draws the preliminary magnitude of voltage of n staircase waveform step respectively；

D2, preliminary magnitude of voltage according to n described staircase waveform step produce corresponding preliminary step signal, measure described anon-normal String ripple signal and the difference value of described preliminary step signal；

D3, the difference value observed in described step D2, and judge that the difference value that often group is positioned on the point in the middle of predefined parameter s, t is No meet smaller requirement, if undesirable, then the difference value in described step D2 is compensated as corrected value Again as the preliminary magnitude of voltage of staircase waveform step in the preliminary magnitude of voltage of n the staircase waveform step drawn；

D4, repetition step D2, D3, until meeting described step D3 requirement, determine the preliminary magnitude of voltage of described staircase waveform step Magnitude of voltage for described staircase waveform step.

The method the most accurately measuring non-sinusoidal voltage signal, it is characterised in that in described step S3 In, corresponding average computation and Fourier transform computing formula thereof are

${a^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{a^{\&prime;}}_k\left(j\right),{a^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\sin k(i,j)$

${b^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{b^{\&prime;}}_k\left(j\right),{b^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\cos k(i,j)$

Wherein (i j) represents k rank sine basic function, the jth sampled point being positioned on i-th step to sink.

The method the most accurately measuring non-sinusoidal voltage signal, it is characterised in that in described step S2 or In S3, the sampled point on each described staircase waveform step is represented sequentially as 0, and 1,2 ..., m-1；Wherein m is less than 100 more than 4 Integer.

The method the most accurately measuring non-sinusoidal voltage signal, it is characterised in that in described step S3 The magnitude of voltage of described staircase waveform step is each staircase waveform step being measured described step signal by digital voltmeter one by one Magnitude of voltage obtains, for being added with the described difference value in described step S2.

6. the system of an accurate measurement non-sinusoidal voltage signal, it is characterised in that including:

Signal source, for producing nonsinusoidal wave to be measured；

Second analog-digital converter, for carrying out sampled measurements to described nonsinusoidal wave；

Para-position module, is connected with described second analog-digital converter, for determining n staircase waveform according to nonsinusoidal wave sampled value The magnitude of voltage of step；

Digital to analog converter, is connected with described para-position module, for producing rank according to the n determined a described staircase waveform plateau voltage value Ladder ripple signal；

First analog-digital converter, is connected with digital-to-analogue converter with described signal source, for by described nonsinusoidal wave and ladder Ripple signal does difference sampling at equal intervals, obtains difference value；

Summation module, is connected with described first analog-digital converter and para-position module, for described difference value is individual with the n determined Described staircase waveform plateau voltage value is added；

Pseudo-coefficients calculation block, in kth subharmonic, clicks on from the sampling that s to t is individual on each described staircase waveform step Row discrete Fourier transform (DFT) calculates, then the result that all described discrete Fourier transform (DFT) calculate is averaged be calculated corresponding Pseudo-sinusoidal coefficients a'_kWith pseudo-cosine coefficient b'_k, wherein s, t meet condition t-s+1=m/2, and t+s=m；

True coefficient computing module, calculates the true sinusoidal coefficients a in kth subharmonic_kWith true cosine coefficient b_k；Wherein said real string Coefficient a_kWith pseudo-sinusoidal coefficients a'_kMeet equation group (1), described true cosine coefficient b_kWith pseudo-cosine coefficient b'_kMeet equation group (2)；Solve the two equation group, true sinusoidal coefficients a can be obtained_kWith true cosine coefficient b_k；

In described equation group (1), when k < during n/2,Work as k=n/2 Time,

In described equation group (2), when k < during n/2,Work as k=n/2 Time,

The system of accurate measurement non-sinusoidal voltage signal the most according to claim 6, it is characterised in that at described pseudo-coefficient In computing module, corresponding average computation and Fourier transform computing formula thereof are:

${a^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{a^{\&prime;}}_k\left(j\right),{a^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\sin k(i,j)$

${b^{\&prime;}}_k=\frac{1}{t-s+1}\underset{j=s}{\overset{t}{\&Sigma;}}{b^{\&prime;}}_k\left(j\right),{b^{\&prime;}}_k\left(j\right)=\frac{2}{n}\underset{i=0}{\overset{n-1}{\&Sigma;}}{y}_{i,j}\cos k(i,j)$

Wherein which staircase waveform step i represents, j represents which sampled point on each staircase waveform step.

The system of accurate measurement non-sinusoidal voltage signal the most according to claim 6, it is characterised in that described second modulus Transducer, for measuring the sampled data of the nonsinusoidal wave that described signal source produces according to predetermined parameter n, m, is adopted for every m Sample data are divided into one group, altogether n group；Described para-position module, for being positioned at by often group in the described sampled data conduct in the middle of parameter s, t The magnitude of voltage of one staircase waveform step, determines the magnitude of voltage of n staircase waveform step respectively.

The system of accurate measurement non-sinusoidal voltage signal the most according to claim 6, it is characterised in that also include numeral electricity Pressure table, is connected with described digital to analog converter and summation module, for measuring by described digital to analog converter at DC mode one by one Each staircase waveform plateau voltage value of the step signal of lower generation, and the conveying of staircase waveform plateau voltage accurate measurements will be obtained To summation module.

The system of accurate measurement non-sinusoidal voltage signal the most according to claim 6, it is characterised in that described first mould Number converter and described second analog-digital converter are same analog-digital converter.