CN104076203B - A kind of intrasonic harmonic detection method considering that negative frequency affects - Google Patents

Abstract

It is an object of the invention to provide a kind of intrasonic harmonic detection method considering that negative frequency affects.It is different from traditional interpolation correction algorithm, this algorithm considers the negative frequency interference to intrasonic m-Acetyl chlorophosphonazo spectral line, become equation with three unknowns group to solve intrasonic m-Acetyl chlorophosphonazo frequency by three spectral line value simultaneous, and solve amplitude and the phase place of m-Acetyl chlorophosphonazo according to the spectrum value of maximum spectral line and conjugate thereof；Achieve the relevant feature parameters quickly and accurately extracting intrasonic m-Acetyl chlorophosphonazo in the short time, it is ensured that the real-time of algorithm and effectiveness requirement time actually detected.Derived when m-Acetyl chlorophosphonazo frequency is less than 1 frequency resolution simultaneouslyTime parameter correction formula, the actual m-Acetyl chlorophosphonazo frequency that can solve is as little asHereinafter, greatly breaching tradition and limited by frequency resolution based on DFT harmonic analysis, shorten the length analyzing signal, this is that other algorithm institute is irrealizable.And this algorithm is not affected by DC component and ensure that its accuracy and robustness to system noise is insensitive.

Description

A kind of intrasonic harmonic detection method considering that negative frequency affects

Technical field

The present invention relates to a kind of harmonic detecting method, a kind of intrasonic m-Acetyl chlorophosphonazo detection considering that negative frequency affects Method.

Background technology

For power system medium and low frequency m-Acetyl chlorophosphonazo (i.e. the subharmonic less than 50Hz) detection, the scheme that can realize at present has Window function and interpolation algorithm based on DFT (or FFT), IEC m-Acetyl chlorophosphonazo group and subgroup algorithm, based on Prony and expansion algorithm etc. thereof.And M-Acetyl chlorophosphonazo in power system has the feature such as undulatory property, randomness, simultaneously IEC61000-4-7 and GB GB/T 24337- 2009 consider for the stability detecting m-Acetyl chlorophosphonazo and real-time, it is stipulated that with entering based on adding rectangular window DFT frequency spectrum analysis method The measurement of harmonic wave in the ranks, and limit measurement time window as 10 fundamental frequency cycles (i.e. 200ms), the spectral line on frequency spectrum is spaced apart 5Hz.

Under IEC framework, for power system is likely to occur intrasonic m-Acetyl chlorophosphonazo (refer in particular to herein less than 10Hz time Harmonic wave), current detection algorithm based on DFT spectrum analysis lost efficacy substantially.Related algorithm based on DFT spectrum analysis is at IEC When detecting intrasonic m-Acetyl chlorophosphonazo under framework, i.e. the analysis frequency resolution of spectral line is 5Hz, and adjacent spectral line is by spectrum leakage and grid The impact of hurdle effect is serious, simultaneously because frequency is the lowest, is available for the spectral line number analyzed limited and can not ignore the impact of negative frequency, The existence of negative frequency has increased the weight of the interference to intrasonic m-Acetyl chlorophosphonazo further so that analyzes and lost efficacy.For obtaining abundant spectral line Information, tradition must increase sampling analysis based on DFT spectral analysis algorithm and count, but to too increase sample window long simultaneously, thus Have impact on the real-time of algorithm.

Prony and expansion algorithm (extension Prony method) thereof are based on the method in Modern spectral estimation, at detection low frequency with super Do not limited by frequency resolution during low frequency component, but large-scale matrix operations have to be carried out, in addition it is also necessary to be right Signal carries out determining rank accurately, and the signal for electrical network broadband multi-frequency cannot directly detect, and affects the real-time of algorithm and stablizes Property.Meanwhile, related algorithm based on Prony is very sensitive to system noise, and actually detected middle error is the biggest.

Can be seen that prior art there is also a lot of deficiency to the detection of intrasonic m-Acetyl chlorophosphonazo.And correlational study it is also shown that Intrasonic m-Acetyl chlorophosphonazo all it is likely to occur during generation low-frequency oscillation and in emerging electric power energy (such as wind energy, solar energy etc.) system, Therefore can accurately detect that intrasonic m-Acetyl chlorophosphonazo has actual meaning to researchs such as follow-up detection, improvement and system stability Justice.

Summary of the invention

It is an object of the invention to provide a kind of intrasonic harmonic detection method considering that negative frequency affects, its feature exists In, comprise the following steps:

Step one: under operation of power networks normal condition, sets up the unifrequency discrete signal model of power network signal:Wherein A_iFor the amplitude of power network signal, f_iFor power network signal frequency andFor power network signal Initial phase, n ∈ [0, N-1], N be intercept the total sampling number of discrete signal, f_sFor power network signal sample frequency；

Step 2: x (n) is added normalization discrete Fourier transform (DFT) (the Discrete Fourier of rectangular window Transform, DFT) obtainWherein k=0,1 ... N-1；

Step 3: set the frequency resolution of spectral line as Δ f, Δ f=f_s/ N, and will formula (1) substitution formula (2) obtain

If normalized frequency is f_i ¹, f_i ¹=f_i/ Δ f, is further simplified as formula (3): In formula

Step 3: take adjacent three spectral line k_m-1、k_mAnd k_mSpectrum X (the k of+1_m-1)、X(k_m) and X (k_m+ 1), k here_m≥ 2 for integer and meet the spectral line of its correspondence for maximum spectral line, obtain through calculating abbreviation

H[f_i ¹-(k_m+ 1)]=H [f_i ¹-(k_m-1)]=H (f_i ¹-k_m) (5)

NoteHave according to formula (4):

(f_i ¹-k_m-p)^-1H⁺+(f_i ¹+k_m+p)^-1H^--X(k_m+ p)=0 (6), wherein p=-1,0,1, three the unknowns in formula Number is H⁺、H^-And f_i ¹, when p=-1,0,1, a ternary linear function group can be become with simultaneous, therefrom can obtain f_i ¹、H⁺And H^-, Wherein solve frequency normalization f to be asked_i ¹Expression formula be

${f_i}^1=\sqrt{\left|\frac{{(k_m-1)}^{2}X(k_m-1)-2{\left(k_m\right)}^{2}X\left(k_m\right)+{(k_m+1)}^{2}X(k_m+1)}{X(k_m-1)-2X\left(k_m\right)+X(k_m+1)}\right|}---\left(7\right)$

Step 4: obtained the highest spectral line k by formula (4)_mEquation:

In formulaSinc (x)= Sin (π x)/(π x), takes formula (8) and is conjugated:Obtain f_iAfter, simultaneous formula (8) and Formula (9) composition equation group, only A inside equation group_iWithBeing unknown quantity, remaining is known quantity, therefore can solve:Step 5: formula (7) and formula (10) be consider negative frequency and interpolation ultralow between The frequency of harmonic wave, amplitude and phase estimation formula.

Detection in full frequency band time harmonic frequency comprises the following steps:

1) signal collected by electrical network, intercepts one section with rectangular window and makees FFT (DFT) spectrum analysis；

2) for the m-Acetyl chlorophosphonazo component of more than 50Hz, regulation m-Acetyl chlorophosphonazo detected according to IEC61000-4-7 standard, with M-Acetyl chlorophosphonazo group or the form of subgroup, measure between two harmonic waves and the m-Acetyl chlorophosphonazo parameter of frequency range between first-harmonic and second harmonic, and Using the meansigma methods of two harmonic wave sequence numbers as corresponding m-Acetyl chlorophosphonazo group or the frequency of subgroup；

3) m-Acetyl chlorophosphonazo for 0～50Hz frequency range must take into the impact of negative frequency；Between the intrasonic of 0～10Hz frequency range humorous Ripple calculates intrasonic m-Acetyl chlorophosphonazo parameter amplitude A according to intrasonic simple harmonic wave detection method_i, frequency f_iAnd phase placeAnd 10～50Hz The m-Acetyl chlorophosphonazo of frequency range calculates all spectral lines of residue except first-harmonic spectral line according to the method for IEC, removes the leakage of intrasonic intersegmental harmonic wave The root-mean-square value A of harmonic amplitude after impact_r；

4) step 3) inIt is the m-Acetyl chlorophosphonazo parameter of 0～50Hz subharmonic frequency range, according to IEC standard Regulation, be designated as 0.5 m-Acetyl chlorophosphonazo；

5) combining step 2) and step 4) obtain the m-Acetyl chlorophosphonazo parameter of full frequency band.

In an embodiment of the present invention, the k that intrasonic m-Acetyl chlorophosphonazo produces occurs_mIt is i.e. k on Δ f that spectral line falls just in frequency_m =1, (k_m-1) spectral line falls on direct current spectral line, carries out filtering DC component D every straight process before carrying out FFT spectrum analysis_c, Then X (k_m-1)=0 so that formula (6) can not be write as the form of ternary secondly equation group, now may select k_m-1 is-1, corresponding X (k_m-1)=X^*(k_m), " * " expression takes conjugation, and at this moment, the spectral line serial number (-1,1,2) of utilization, corresponding spectrum is (X^*(1)、 X (1), X (2)), formula f_i=f_i ¹Δ f can be reduced to:

The present invention is different from traditional interpolation correction algorithm, and this algorithm considers negative frequency to intrasonic m-Acetyl chlorophosphonazo spectral line Interference, becomes equation with three unknowns group to solve intrasonic m-Acetyl chlorophosphonazo frequency by three spectral line value simultaneous, and according to the frequency of maximum spectral line Spectrum and conjugate thereof solve amplitude and the phase place of m-Acetyl chlorophosphonazo；Intrasonic quickly and is accurately extracted in achieving the short time The relevant feature parameters of m-Acetyl chlorophosphonazo, it is ensured that the real-time of algorithm and effectiveness requirement time actually detected.The present invention derives simultaneously Parameter correction formula when m-Acetyl chlorophosphonazo frequency is less than 1 frequency resolution Δ f, the actual m-Acetyl chlorophosphonazo frequency that can solve is low To 0.3 below Δ f, greatly breach tradition and limited by frequency resolution based on DFT harmonic analysis, shorten analysis letter Number length, this is that other algorithm institute is irrealizable.And the algorithm of the present invention is not affected by DC component and to system noise Sound is insensitive ensure that its accuracy and robustness.

Accompanying drawing explanation

Fig. 1 negative frequency interference phenomenon to frequency spectrum.

Fig. 2 full frequency band based on IEC and intrasonic detection algorithm m-Acetyl chlorophosphonazo overhaul flow chart.

The amplitude error of Fig. 3 IEC61000-4-7 subharmonic m-Acetyl chlorophosphonazo group detection.

The amplitude detection result of 10 cycle code book motion algorithms of Fig. 4 IEC regulation.

The minimum m-Acetyl chlorophosphonazo frequency variation diagram that each algorithm of Fig. 5 ± 5% range of tolerable variance can detect.

Fig. 6 Prony algorithm (left) and herein algorithm (right) accuracy of detection changing trend diagram in a noisy environment.

Detailed description of the invention

Consider the voltage of electrical network in practical power systems and frequency always in change, and the detection of m-Acetyl chlorophosphonazo is always and electrical network Voltage closely related with frequency, according to voltage and the frequency transformation period speed of electrical network, signal model in actual electric network is entered Row classification: 1) long time stable state, the voltage magnitude of power network signal and frequency expected value long period constant stationary random signal；2) Stable in short-term, the voltage magnitude of power network signal and frequency expected value short period constant stationary random signal；3) astable shape State, during fault, voltage magnitude and the frequency of power network signal are the non-stationary signal of time-varying.And the foundation of the model of the present invention is pin For be analyzed under system normal operating condition, using the constant desired value of voltage magnitude in a period of time and frequency as reality E [A under voltage magnitude and frequency, i.e. a period of time steady statue in the electrical network of border_i(t)]=A_i, E [f_i(t)]=f_i；Consider simultaneously Noise signal in actual electric network is white Gaussian noise signal v (t) separate with each frequency component of electrical network.

The foundation power network signal mathematical model containing intrasonic m-Acetyl chlorophosphonazo:

A in formula_i、f_iWithFor the amplitude of each component, frequency and initial phase, D in power network signal_cFor actual electric network signal The middle direct-flow offset weight that may comprise, v (t) is the white Gaussian noise signal separate with each frequency component of electrical network, and M is The frequency component number comprised in power network signal；Time t ∈ [t₀,t₀+ T], T is the intercepting time period of signal analysis.

It is discrete series x in view of the signal collected in actual electric network^*N (), therefore by the mathematical model in formula (12) Change discrete form into:

F in formula_sFor the sample frequency of power network signal, n ∈ [0, N-1], N are the total sampling number of discrete signal intercepted.

It is pointed out that the when that the sampled signal to actual electric network carrying out spectrum analysis, typically can first carry out every directly Process and filter DC component D_c, it is therefore an objective to that improves computer integer FFT does spectrum precision, prevents windowing (except rectangular window) from producing Raw Frequency and interfering frequency.First ignore system noise part v (n) when carrying out the mathematical analysis of model, after analyze again Containing during system noise testing result being affected situation；It is also noted that the linear superposition that signal is each component in formula (12), Still this overlaying relation is met when it is carried out DFT (FFT) spectrum analysis.Therefore, for without loss of generality, analyze unifrequency from Scattered signal model:

From formula (14) it can be seen that the signal that reality gathers from electrical network is discrete real sequence x (n), n ∈ [0, N-1], Not single-frequency complex exponential signal sequence, adds the normalization discrete Fourier transform (DFT) (Discrete of rectangular window to it Fourier Transform, DFT)

$X\left(k\right)=\frac{1}{N}\underset{n=0}{\overset{N-1}{\Σ}}x\left(n\right)e^{-j\frac{2\mathrm{\π}}{N}nk}---\left(15\right)$

K=0 in formula, 1 ..., N-1.

If the frequency resolution of spectral line is Δ f, Δ f=f_s/ N, substitutes into formula (14) in formula (15):

In practical situation, General N value is bigger, therefore sin [π (f_i/Δf-k)/N]≈π(f_i/Δf-k)/N.If normalization Frequency is f_i ¹, f_i ¹=f_i/ Δ f, is further simplified as formula (15):

In formula

It can be seen that after actual electric network sampled signal carries out DFT spectrum analysis, frequency spectrum there will be two from formula (17) Frequency component f_iWith-f_i, wherein Section 2 is the negative frequency components composition of frequency spectrum.Tradition algorithm mould based on DFT spectrum analysis Have ignored the negative frequency impact on spectral line in type, directly take Section 1 in formula (17), do so has certain reason, reason Being that actual m-Acetyl chlorophosphonazo component works as distance 0 frequency spectrum enough far, negative frequency is micro-on the impact of actual m-Acetyl chlorophosphonazo component It is micro-, but for intrasonic m-Acetyl chlorophosphonazo, negative frequency is the biggest on its impact, and this is also that general algorithm is at pin The reason losing efficacy the detection of ultralow m-Acetyl chlorophosphonazo, reality have to consider negative frequency pair when detecting power network signal intrasonic m-Acetyl chlorophosphonazo Its impact.Negative frequency affects schematic diagram as shown in Figure 1 to frequency spectrum.

Consider the discrete spectrum of negative frequency impact, take adjacent three spectral line k_m-1、k_mAnd k_mSpectrum X (the k of+1_m-1)、X(k_m) With X (k_m+ 1), k here_m>=2 for integer and meet the spectral line of its correspondence for maximum spectral line.So

$\begin{array}{c}H\[{f_i}^1-(k_m-1)\]=\sin \[\mathrm{\π}({f_i}^1-k_m+1)\]e^{j\mathrm{\π}({f_i}^1-k_m+1)}\\ =\sin \[\mathrm{\π}({f_i}^1-k_m)+\mathrm{\π}\]e^{j\mathrm{\π}({f_i}^1-k_m)+j\mathrm{\π}}\\ =\sin \[\mathrm{\π}({f_i}^1-k_m)\]e^{j\mathrm{\π}({f_i}^1-k_m)}\\ =H({f_i}^1-k_m)\end{array}---\left(18\right)$

In like manner can verify

H[f_i ¹-(k_m+ 1)]=H [f_i ¹-(k_m-1)]=H (f_i ^1-k_m) (19)

Therefore, noteHave according to formula (15):

(f_i ¹-k_m-p)^-1H⁺+(f_i ¹+k_m+p)^-1H^--X(k_m+ p)=0 (20)

In formula, three unknown numbers are H⁺、H^-And f_i ¹, when p=-1,0,1, a ternary linear function group can be become with simultaneous, And equation existence and unique solution, therefrom can obtain f_i ¹、H⁺And H^-.For the convenience solved, formula (20) is considered as linear homogeneous Equation group, untrivialo solution vector is { H⁺, H^-,-1}^T, then its unique conditional existed is that the determinant of coefficient matrix C of equation group is Zero det (C)=0.

Coefficient matrix C is:

$C=\left[\begin{array}{ccc}{({f_i}^1-k_m+1)}^{-1}& {({f_i}^1+k_m-1)}^{-1}& X(k_m-1)\\ {({f_i}^1-k_m)}^{-1}& {({f_i}^1+k_m)}^{-1}& X\left(k_m\right)\\ {({f_i}^1-k_m-1)}^{-1}& {({f_i}^1+k_m+1)}^{-1}& X(k_m+1)\end{array}\right]---\left(21\right)$

Frequency normalization f to be asked can be solved by det (C)=0_i ¹Explicit Expression formula be

${f_i}^1=\sqrt{\left|\frac{{(k_m-1)}^{2}X(k_m-1)-2{\left(k_m\right)}^{2}X\left(k_m\right)+{(k_m+1)}^{2}X(k_m+1)}{X(k_m-1)-2X\left(k_m\right)+X(k_m+1)}\right|}---\left(22\right)$

In order to ensure the accuracy calculated, the k in formula (22) need to be ensured_mSpectral line is the highest spectral line, then k_m-1 and k_m+ 1 respectively For the most adjacent spectral line, then one of them must be second highest spectral line, then consider the intrasonic m-Acetyl chlorophosphonazo of negative frequency impact Frequency estimation is

f_i=f_i ¹·Δf (23)

In formula, Δ f is frequency resolution.

Consider the impact of system dc component: reality probably occurs the k that intrasonic m-Acetyl chlorophosphonazo produces_mSpectral line is lucky Falling in frequency is i.e. k on Δ f_m=1, so (k_m-1) spectral line falls on direct current spectral line.Owing to system may have direct current to divide originally The interference of amount, carried out filtering DC component D every straight process before carrying out FFT spectrum analysis_c, i.e. X (k_m-1)=0 so that formula (20) can not be write as the form of ternary secondly equation group, now be may select k_m-1 is-1, corresponding X (k_m-1)=X^*(k_m), " * " Represent and take conjugation.At this moment, the spectral line serial number (-1,1,2) of utilization, corresponding spectrum is (X^*(1), X (1), X (2)), formula (22) Can be with abbreviation:

$f_i=\mathrm{\Δ}f\·\sqrt{\left|\frac{X^{*}\left(1\right)-3X\left(1\right)+8X\left(2\right)}{X^{*}\left(1\right)-3X\left(1\right)+2X\left(2\right)}\right|}---\left(24\right)$

In order to ensure signal to noise ratio and the computational solution precision of actual signal spectral line, carry out intrasonic m-Acetyl chlorophosphonazo amplitude and phase place Estimate time similar with other interpolation algorithm, need selection locally the highest spectral line to calculate.By formula (17) the highest spectral line k_mEquation Formula:

In formula

Wherein sinc (x)=sin (π x)/(π x).

Formula (25) is taken and is conjugated:

F is obtained by formula (22)_iAfter, simultaneous formula (25) and formula (26) composition equation group, only A inside equation group_iWithIt is Unknown quantity, remaining is known quantity, therefore can solve:

Formula (22) and formula (27) are consideration negative frequency and the frequency of ultralow m-Acetyl chlorophosphonazo of interpolation, amplitude and phase estimation are public Formula.It should be noted that above-mentioned model is built upon what signal was intercepted by rectangular window (i.e. not windowing), this also meets The IEC61000-4-7 testing requirement to m-Acetyl chlorophosphonazo.

Have been detected as intrasonic m-Acetyl chlorophosphonazo for above-mentioned theory, and combine IEC61000-4-7 and GB GB/T The regulation that m-Acetyl chlorophosphonazo is detected by 24337-2009, can form a whole set of m-Acetyl chlorophosphonazo detection scheme being applicable to Whole frequency band, its stream Journey block diagram is as shown in Figure 2.Its detailed step is:

1) signal collected by electrical network, intercepts one section (such as 10 cycles of IEC regulation, 200ms, correspondence with rectangular window Frequency resolution is 5Hz) make FFT (DFT) spectrum analysis.

2) for the m-Acetyl chlorophosphonazo component of more than 50Hz, regulation m-Acetyl chlorophosphonazo detected according to IEC61000-4-7, humorous with Ripple group or the form of subgroup, measure between two harmonic waves and the m-Acetyl chlorophosphonazo parameter of frequency range between first-harmonic and second harmonic, and with two The meansigma methods of harmonic wave sequence number as corresponding m-Acetyl chlorophosphonazo group or subgroup frequency (as between 2 subharmonic and 3 subharmonic m-Acetyl chlorophosphonazo remember It is 2.5 m-Acetyl chlorophosphonazo group or subgroups).

3) m-Acetyl chlorophosphonazo (i.e. subharmonic) for 0～50Hz frequency range must take into the impact of negative frequency, the frequency of subharmonic The least, affected the most serious by negative frequency；M-Acetyl chlorophosphonazo quantity in view of same frequency range will not be too many, and electrical network exists frequency simultaneously Rate and the fluctuation of amplitude, as a example by the 5Hz frequency resolution that IEC specifies, the intrasonic m-Acetyl chlorophosphonazo of 0～10Hz frequency range is according to herein In the algorithm mentioned calculate intrasonic m-Acetyl chlorophosphonazo parameter (amplitude A_i, frequency f_iAnd phase place), and the m-Acetyl chlorophosphonazo of 10～50Hz frequency ranges Remain that all spectral lines (without first-harmonic spectral line) remove after intrasonic intersegmental harmonic wave leakage contribution mean square is calculated according to the method for IEC Root A_r。

4) the 3rd) in stepIt is the m-Acetyl chlorophosphonazo parameter of 0～50Hz subharmonic frequency range, marks according to IEC Accurate regulation, is designated as 0.5 m-Acetyl chlorophosphonazo.

5) combining step 2) and step 4) obtain the m-Acetyl chlorophosphonazo parameter of full frequency band.

The harmonic detection method proposed for the present invention carries out Digital Simulation, and simulated environment is Matlab 2012b, The 0.2s sampled signal length (synchronized sampling) specified with IEC61000-4-7 in emulation embodiment, corresponding 5Hz frequency resolution, If the frequency of intrasonic m-Acetyl chlorophosphonazo is 3.5Hz, it is 1% relative to the amplitude coefficient of fundamental frequency, the inspection of various algorithms under noise circumstance Survey result is as shown in table 1:

The accuracy of detection of each algorithm in table 1 noise circumstance

Note: when having noise, carries out 100 Monte Carlo simulation experiments and asks for the meansigma methods of result；" " represents correspondence Algorithm is without correct testing result.

As can be seen from Table 1, window function and interpolation algorithm based on DFT lost efficacy when detecting intrasonic m-Acetyl chlorophosphonazo, and reason is to be subject to Restriction to frequency resolution；Prony algorithm has high accuracy of detection when noiseless, but trickle noise can be made Become precision drastically drop to cannot detect, its robustness is bad；The method carried herein can have in bigger noise circumstance Higher accuracy of detection, it is ensured that algorithm real system detect in robustness and real-time.

The present invention and the comparison of other algorithms:

(1) algorithm and IEC standard method comparison herein

The m-Acetyl chlorophosphonazo group algorithm detection subharmonic that IEC61000-4-7 specifies, it is assumed that the relative magnitude of low-frequency inter-harmonic is A_i =0.1, frequency is f_i, phase place is 0.Sampling time is 0.2s, works as f_iWith the step-length of 0.05Hz from 0～40Hz change time, corresponding Testing result is as shown in Figure 3

As seen from Figure 3, IEC algorithm is 5Hz in frequency resolution, when range of allowable error is within ± 5%, it is possible to The minimum m-Acetyl chlorophosphonazo frequency of detection is about 7.5Hz, simultaneously takes account of the phase angle variations of intrasonic m-Acetyl chlorophosphonazo and stablizing of algorithm Property, the m-Acetyl chlorophosphonazo IEC algorithm of 0～10Hz frequency range cannot detect exactly.

And algorithm harmonic detecting intersegmental to intrasonic result such as Fig. 4 shows herein:

As seen from Figure 4, for the sampled signal of 0.2s length, doing frequency resolution corresponding to spectrum analysis is 5Hz, Algorithm herein can IEC standard regulation ± 5% range of error in detect that minimum m-Acetyl chlorophosphonazo frequency is that 1Hz is (the most right Answering m-Acetyl chlorophosphonazo phase place is 0), greatly shake off the restriction of frequency resolution, it is achieved that detect rapidly and accurately in the short period Excess of export low-frequency inter-harmonic.

Under noiseless disturbed condition, IEC regulation ± 5% range of tolerable variance in, the phase angle variations scope of m-Acetyl chlorophosphonazo is 0 ～2 π, obtain the minimum m-Acetyl chlorophosphonazo frequency that algorithm and IEC standard algorithm can detect when unlike signal length herein, enumerate Numerical value and changing trend diagram thereof are respectively as shown in table 2 and Fig. 5.

The minimum m-Acetyl chlorophosphonazo frequency that in table 2 range of tolerable variance, algorithm can identify

By table 2 and Fig. 5 it can be seen that herein algorithm can detect intrasonic m-Acetyl chlorophosphonazo in a short period of time, and nothing Need to increase signal length, thus quickly detect for the m-Acetyl chlorophosphonazo of ULF and provide new way.

(2) algorithm compares with Prony algorithm herein

As a example by 10 signal cycles of IEC standard regulation, m-Acetyl chlorophosphonazo frequency is in 0～10Hz change, its amplitude coefficient (phase For fundamental frequency) it is 1%, carry out 100 Monte Carlo simulation experiments under different noise circumstances and tie with Prony algorithm detection Fruit contrast is as shown in table 3:

Each algorithm accuracy of detection contrast situation during table 3 noise jamming

Note: " " represents the algorithm of correspondence cannot detect result.

In different noise circumstances, the accuracy of detection variation tendency of Prony algorithm and herein algorithm as indicated with 6:

By table 3 and Fig. 6 it can be seen that Prony algorithm is in noise-free environment, there is at a relatively high accuracy of detection (reach 10^-11The order of magnitude), and along with the increase (i.e. signal to noise ratio diminishes) of noise, its accuracy of detection drastically drops to detect (being approximately higher than the noise of 50dB intensity).And voltage and frequency due to electrical network is always being continually changing in practical power systems, with Time sampled signal inevitably introduce random noise, Prony algorithm is very sensitive to noise signal, is not suitable for power system The detection of intrasonic m-Acetyl chlorophosphonazo.Simultaneously it can also be seen that this paper algorithm noise immunity is preferable, when noise strengthens, testing result essence Degree change is little (stable 10^-4～10^-3The order of magnitude), it is possible to meet the demand that power system is actually detected.

In sum, the short time that can realize intrasonic m-Acetyl chlorophosphonazo of the present invention is quickly detected, and this algorithm is not simultaneously Affected by DC component and insensitive to system noise, it is ensured that this algorithm robustness in actually detected is with in real time Property.

The foregoing is only presently preferred embodiments of the present invention, all impartial changes done according to scope of the present invention patent with Modify, all should belong to the covering scope of the present invention.

Claims (3)

1. the intrasonic harmonic detection method considering that negative frequency affects, it is characterised in that comprise the following steps:

Step one: under operation of power networks normal condition, sets up the unifrequency discrete signal model of power network signal: Wherein A_iFor the amplitude of power network signal, f_iFor power network signal frequency andFor the initial phase of power network signal, n ∈ [0, N-1], N are The total sampling number of discrete signal intercepted, f_sFor power network signal sample frequency；

Step 2: x (n) is added normalization discrete Fourier transform (DFT) (the Discrete Fourier of rectangular window Transform, DFT) obtainWherein k=0,1 ... N-1；

Step 3: set the frequency resolution of spectral line as Δ f, Δ f=f_s/ N, and will formula (1) substitution formula (2) obtain

If normalized frequency is f_i ¹, f_i ¹=f_i/ Δ f, is further simplified as formula (3): In formula

Step 3: take adjacent three spectral line k_m-1、k_mAnd k_mSpectrum X (the k of+1_m-1)、X(k_m) and X (k_m+ 1), k here_m>=2 is whole Number and the spectral line meeting its correspondence are maximum spectral line, obtain through calculating abbreviation

H[f_i ¹-(k_m+ 1)]=H [f_i ¹-(k_m-1)]=H (f_i ¹-k_m) (5)

NoteHave according to formula (4):

(f_i ¹-k_m-p)^-1H⁺+(f_i ¹+k_m+p)^-1H^--X(k_m+ p)=0 (6), wherein p=-1,0,1, three unknown numbers in formula are H⁺、H^-And f_i ¹, when p=-1,0,1, a ternary linear function group can be become with simultaneous, therefrom can obtain f_i ¹、H⁺And H^-, wherein solve Go out frequency normalization f to be asked_i ¹Expression formula be

${f_i}^1=\sqrt{\left|\frac{{(k_m-1)}^{2}X(k_m-1)-2{\left(k_m\right)}^{2}X\left(k_m\right)+{(k_m+1)}^{2}X(k_m+1)}{X(k_m-1)-2X\left(k_m\right)+X(k_m+1)}\right|}---\left(7\right)$

Step 4: obtained the highest spectral line k by formula (4)_mEquation:

In formulaSinc (x)=sin (π X)/(π x), takes formula (8) and is conjugated:Obtain f_iAfter, simultaneous formula (8) and formula (9) Composition equation group, only A inside equation group_iWithBeing unknown quantity, remaining is known quantity, therefore can solve:

Step 5: formula (7) and formula (10) are consideration negative frequency and the frequency of ultralow m-Acetyl chlorophosphonazo, amplitude and the phase estimation of interpolation Formula.

The intrasonic harmonic detection method of consideration negative frequency the most according to claim 1 impact, it is characterised in that: entirely The detection of frequency range time harmonic frequency comprises the following steps:

1) signal collected by electrical network, intercepts one section with rectangular window and makees FFT or DFT spectrum analysis；

2) for the m-Acetyl chlorophosphonazo component of more than 50Hz, regulation m-Acetyl chlorophosphonazo detected according to IEC61000-4-7 standard, humorous with Ripple group or the form of subgroup, measure between two harmonic waves and the m-Acetyl chlorophosphonazo parameter of frequency range between first-harmonic and second harmonic, and with two The meansigma methods of harmonic wave sequence number is as corresponding m-Acetyl chlorophosphonazo group or the frequency of subgroup；

3) m-Acetyl chlorophosphonazo for 0～50Hz frequency range must take into the impact of negative frequency；The intrasonic m-Acetyl chlorophosphonazo of 0～10Hz frequency range is pressed Intrasonic m-Acetyl chlorophosphonazo parameter amplitude A is calculated according to intrasonic simple harmonic wave detection method_i, frequency f_iAnd phase placeAnd 10～50Hz frequency ranges M-Acetyl chlorophosphonazo calculate except all spectral lines of residue of first-harmonic spectral line according to the method for IEC, remove the leakage of intrasonic intersegmental harmonic amplitude Root-mean-square value A after impact_r；

4) step 3) inIt is the m-Acetyl chlorophosphonazo magnitude parameters of 0～50Hz subharmonic frequency range, according to IEC standard Regulation, be designated as 0.5 m-Acetyl chlorophosphonazo；

5) combining step 2) and step 4) obtain the m-Acetyl chlorophosphonazo parameter of full frequency band.

The intrasonic harmonic detection method of consideration negative frequency the most according to claim 1 impact, it is characterised in that: occur The k that intrasonic m-Acetyl chlorophosphonazo produces_mIt is i.e. k on Δ f that spectral line falls just in frequency_m=1, (k_m-1) spectral line falls on direct current spectral line, Carry out before carrying out FFT spectrum analysis filtering DC component D every straight process_c, then X (k_m-1)=0 so that formula (6) can not be write as three The form of unit's secondly equation group, now may select k_m-1 is-1, corresponding X (k_m-1)=X^*(k_m), " * " expression takes conjugation, this Time, the spectral line serial number (-1,1,2) of utilization, corresponding spectrum is (X^*(1), X (1), X (2)), formula f_i=f_i ¹Δ f can letter Turn to:

$f_i=\mathrm{\Δ}f\·\sqrt{\left|\frac{X^{*}\left(1\right)-3X\left(1\right)+8X\left(2\right)}{X^{*}\left(1\right)-3X\left(1\right)+2X\left(2\right)}\right|}---\left(11\right).$