CN101852826B - Harmonic analysis method for power system and device thereof - Google Patents

Abstract

The invention provides a harmonic analysis method for a power system. The method comprises the following steps: calculating fundamental frequency of the power system and windowing and performing Fourier transform on a sampled signal sequence of the power system; taking the calculated fundamental frequency of the power system as an actual frequency of the power system so as to obtain an approximate formula for windowed Fourier transform spectrum; calculating the frequency of the harmonic wave of the power system according to the calculated fundamental frequency of the power system and calculating the amplitudes of the fundamental frequency and the harmonic wave of the power system according to the approximate formula; and calculating the phases of the fundamental frequency and the harmonic wave of the power system according to the frequency difference between the frequency of the sampled signal of the power system and the frequency of the power system. The method can calculate the harmonic wave of the power system with an extremely high accuracy; and meanwhile, the method has simple calculation and meets the requirements for real-time detection of the power system.

Description

A kind of harmonic analysis method of electric system and device thereof

Technical field

The present invention relates to harmonic analysis method and device thereof, relate in particular to a kind of device that in electric system, carries out harmonic analytic method and this method of realization.

Background technology

For the real-time electric power monitoring equipment, need to adopt high precision, the simple electric harmonic analytical approach of calculating that the signal of electric system is carried out real-time analysis, so that the monitoring of equipment and adjustment.Harmonic frequency, amplitude and the phasing degree of extensively adopting quick Fu Li leaf transformation (FFT, Fast Fourier Transform) to calculate measuring-signal in the electric system at present.Be difficult to realize the synchronized sampling of signal but a shortcoming that adopts this method is, thereby cause spectral leakage, cause the inaccurate of computational data.

Usually adopt two kinds of methods to reduce the influence that spectral leakage is brought in the prior art.A kind of method is that measuring-signal is carried out synchronized sampling, therefore can carry out the Fu Li leaf transformation to the sampled signal of an integral multiple signal period, avoids spectral leakage.But,, almost be difficult to measuring-signal is carried out synchronized sampling because the frequency of electric system is a real-time change.No matter be that the phaselocked loop (PLL, Phase Lock Loop) or the software of microcomputer (MCU, Micro Computer Unit) control are sampled, all be difficult to realize fully synchronized sampling.

A kind of in addition method is to use windowing-interpolation Fu Li leaf transformation to reduce the influence that spectral leakage is brought.Fig. 1 is typical windowing-interpolation Fu Li leaf transformation process flow diagram.The steps include: at first, the sampled signal sequence of electric system is carried out windowing, and carry out quick Fu Li leaf transformation.Secondly, the result according to quick Fu Li leaf transformation uses interpolation to come the reference frequency of calculating sampling signal and the value of delta between the power system frequency.Once more, the result according to quick Fu Li leaf transformation calculates the harmonious wave frequency of electric system fundamental frequency, amplitude and phase place.At last, proofread and correct the harmonious wave frequency of electric system fundamental frequency, amplitude and phase place according to the reference frequency and the value of delta between the power system frequency of sampled signal.

Though above-mentioned windowing-interpolation Fu Li leaf transformation can be handled the spectral leakage problem preferably, in use has following problem.The first, the precision of this method is relevant with employed windowed function, usually the above windowed function in preferred 4 rank or 4 rank.But the exponent number of windowed function is high more, and the computation complexity of this method is big more, and this is for totally unfavorable as far as the exigent electric system pick-up unit of real-time.The second, use the frequency of the resulting electric system of this method to compare with actual frequency, certain error is still arranged, that is to say that the computational accuracy of this method is not high enough.

Summary of the invention

Fundamental purpose of the present invention is to provide a kind of device that in electric system, carries out harmonic analytic method and this method of realization; Can calculate the harmonious wave frequency of the fundamental frequency of electric system, amplitude, phase place more exactly through this method, and this method is simple relatively, computation complexity is low.

For realizing above-mentioned purpose, the invention provides a kind of harmonic analysis method of electric system, the method includes the steps of:

(1) calculates the frequency of electric system first-harmonic, and the sampled signal sequence of electric system is carried out windowing process and carried out the Fu Li leaf transformation, try to achieve the amplitude of first-harmonic and the amplitude and the initial phase of initial phase and each harmonic;

(2), thereby obtain the approximate analysis formula of the Fu Li leaf transformation frequency spectrum after the windowing with the frequency of the electric system first-harmonic that calculates actual frequency as electric system;

(3) calculate the correction factor of first-harmonic and each harmonic amplitude according to said approximate analysis formula, and the amplitude of above-mentioned first-harmonic of trying to achieve and harmonic wave is proofreaied and correct;

(4) utilize the phase-frequency characteristic of said window function to revise the initial phase of first-harmonic and each harmonic.

Wherein, the frequency of calculating electric system first-harmonic may further comprise the steps in the said step (1):

(11) obtain the power system signal of more than one signal sampling period;

(12) frequency of said electric system first-harmonic is calculated for the first time;

(13), the actual frequency of said electric system first-harmonic is carried out secondary approach according to Fu Li leaf transformation complex coefficient, fundamental frequency and the SF of the said sampled signal first-harmonic that calculates for the first time;

(14) approach the fundamental frequency that obtains according to said secondary signal sampling series is adjusted, the actual frequency of said electric system first-harmonic is carried out three times approach.

Wherein, in the said step (12) frequency of electric system first-harmonic calculated for the first time and may further comprise the steps:

(121) sampled signal in each signal sampling period is carried out the Fu Li leaf transformation, thereby calculate the Fu Li leaf transformation complex coefficient of said sampled signal first-harmonic;

(122) calculate the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

(123) difference of the starting phase angle between two adjacent signal sampling period of calculating;

(124) mean value of the difference of the said starting phase angle of calculating;

(125) according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Wherein, in the said step (13) actual frequency of said electric system first-harmonic being carried out secondary approaches and may further comprise the steps:

(131) adjust said Fu Li leaf transformation complex coefficient according to the frequency of the said first-harmonic that calculates for the first time;

(132) calculate the starting phase angle of each signal period;

(133) difference of the starting phase angle between two adjacent signal sampling period of calculating;

(134) mean value of the difference of the said starting phase angle of calculating;

(135) according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Wherein, in the said step (14) actual frequency of said electric system first-harmonic carried out approaching for three times and may further comprise the steps:

(141) approach the hits of each signal sampling period in the frequency adjustment sampling series of resulting electric system first-harmonic according to said secondary;

(142) sampled signal in adjusted each signal sampling period is carried out the Fu Li leaf transformation, thereby calculate the Fu Li leaf transformation complex coefficient of said sampled signal first-harmonic;

(143) calculate the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

(144) difference of the starting phase angle between two adjacent signal sampling period of calculating;

(145) mean value of the difference of the said starting phase angle of calculating;

(146) according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

According to a preferred version of the present invention, in said step (11), said power system signal is a voltage signal.

According to a preferred version of the present invention, when calculating the frequency of electric system first-harmonic, said Fu Li leaf transformation is discrete Fu Li leaf transformation.

Correspondingly, the present invention proposes a kind of frequency analysis device of electric system, is used for the harmonic wave of electric system is analyzed, and said device comprises:

Electric system fundamental frequency computing module is used to calculate the frequency of electric system first-harmonic;

Windowing and Fu Li leaf transformation frequency spectrum computing module are used for the sampled signal sequence of electric system is carried out windowing process and carried out the Fu Li leaf transformation, try to achieve the amplitude of first-harmonic and the amplitude and the initial phase of initial phase and each harmonic;

Correction module; Calculate the correction factor of first-harmonic and each harmonic amplitude according to the approximate analysis formula of the Fu Li leaf transformation frequency spectrum after the windowing; And the amplitude of above-mentioned first-harmonic of trying to achieve and harmonic wave proofreaied and correct, and utilize the phase-frequency characteristic of windowed function to revise the initial phase of first-harmonic and each harmonic.

Wherein, said electric system fundamental frequency computing module comprises:

Acquisition module is used to obtain the power system signal of more than one signal sampling period;

First computing module is used for the frequency of said electric system first-harmonic is calculated for the first time;

Secondary approaches module, according to Fu Li leaf transformation complex coefficient, fundamental frequency and the SF of the said sampled signal first-harmonic that calculates for the first time, the actual frequency of said electric system first-harmonic is carried out secondary approach;

Approach module three times, approach the fundamental frequency that obtains according to said secondary signal sampling series is adjusted, the actual frequency of said electric system first-harmonic is carried out three times approach.

Wherein, said first computing module comprises:

Fu Li leaf transformation complex coefficient calculating sub module is used for the sampled signal in each signal sampling period is carried out the Fu Li leaf transformation, thereby calculates the Fu Li leaf transformation complex coefficient of said sampled signal fundamental frequency;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Wherein, said secondary approaches module and comprises:

Fu Li leaf transformation complex coefficient adjustment submodule is adjusted said Fu Li leaf transformation complex coefficient according to the frequency of the said first-harmonic that calculates for the first time;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Wherein, saidly approach module three times and comprise:

Hits is adjusted submodule, is used for approaching according to said secondary the hits of each signal sampling period of frequency adjustment sampling series of resulting electric system first-harmonic;

Fu Li leaf transformation complex coefficient calculating sub module is used for the sampled signal in adjusted each signal sampling period is carried out the Fu Li leaf transformation, thereby calculates the Fu Li leaf transformation complex coefficient of said sampled signal fundamental frequency;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Adopt the inventive method and device thereof, make and can carry out the high calculating of precision to Harmonious Waves in Power Systems, the calculating of this method simultaneously is simple, has satisfied the needs for the electric system of real-time detection.

Description of drawings

Be described in further detail below in conjunction with the accompanying drawing specific embodiments of the invention, wherein:

Fig. 1 shows windowed interpolation Fu Li leaf method flow diagram of the prior art;

Fig. 2 shows the method flow diagram that the harmonic wave of electric system is analyzed of the present invention;

Fig. 3 has provided in the method that the harmonic wave of electric system is analyzed of the present invention, and the frequency of electric system first-harmonic is carried out the Calculation Method process flow diagram.

Fig. 4 has provided the spectrum diagram of 4 Blackman-Harris window functions.

Embodiment

Fig. 2 shows the method flow diagram that the harmonic wave of electric system is analyzed of the present invention.Serve as that row specify this method with 6 signal sampling period below.

Step 1: calculate the frequency of electric system first-harmonic, and the sampled signal sequence of electric system is carried out windowing process and carried out the Fu Li leaf transformation, try to achieve the amplitude of first-harmonic and the amplitude and the initial phase of initial phase and each harmonic.Fig. 3 has provided in the method that the harmonic wave of electric system is analyzed of the present invention, and the frequency of electric system first-harmonic is carried out the Calculation Method process flow diagram.In this step, comprise following steps:

The first, obtain 6 voltage signals in the signal sampling period.

The second, the frequency of electric system first-harmonic is calculated for the first time, this is first to calculate and realizes on the calculating basis that is based on the phase differential of voltage signal.Specifically carry out following steps:

At first, to the sampled signal in each signal sampling period, the Fu Li leaf transformation that all disperses earlier, thus calculate the Fu Li leaf transformation complex coefficient of sampled signal first-harmonic;

Secondly, calculate the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Once more, calculate the difference of the starting phase angle between per two adjacent signal sampling period in 6 periodic voltage signals;

Then, calculate the mean value of the difference of said starting phase angle;

At last, according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

The 3rd, according to Fu Li leaf transformation complex coefficient, fundamental frequency and the SF of the said sampled signal first-harmonic that calculates for the first time, the actual frequency of said electric system first-harmonic is carried out secondary approach.In this step, comprise following steps again:

At first, adjust said Fu Li leaf transformation complex coefficient according to the frequency of the said first-harmonic that calculates for the first time;

Secondly, calculate the starting phase angle of each signal period;

Once more, calculate the difference of the starting phase angle between two adjacent signal sampling period;

Then, calculate the mean value of the difference of said starting phase angle;

At last, according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

The 4th, approach the fundamental frequency that obtains according to said secondary signal sampling series is adjusted, the actual frequency of said electric system first-harmonic is carried out three times approach.In this step, specifically comprise:

At first, approach the hits of each signal sampling period in the frequency adjustment sampling series of resulting electric system first-harmonic according to said secondary;

Secondly, the sampled signal in adjusted each signal sampling period is carried out the Fu Li leaf transformation, thereby calculate the Fu Li leaf transformation complex coefficient of said sampled signal first-harmonic;

Once more, calculate the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Then, calculate the difference of the starting phase angle between two adjacent signal sampling period;

Then, calculate the mean value of the difference of said starting phase angle;

At last, according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Adopt formula that the above-mentioned result of approaching is analyzed below:

The frequency of electric system can be represented as follows:

Wherein, f _SysBe the actual frequency of electric system,

f _sBe the reference frequency (f of electric system _sThe sampling number in=SF/each sampling period),

is the mean value of the difference of the starting phase angle that calculates.

In addition, the first-harmonic of sampled voltage signal can be represented as follows:

f ₁(t)＝C ₁sin((w+Δw)t+φ)＝C ₁[cosφ·sin((w+Δw)t)+sinφ·cos((w+Δw)t)] (2)

Wherein, w is reference angle frequency (w=2 π f _s), Δ w is angular frequency poor of reference angle frequency w and electric system.Suppose A here ₁=C ₁Sin φ, B ₁=C ₁Cos φ.Can obtain discrete Fu Li leaf transformation first-harmonic complex coefficient by following two formulas:

$A_1^{*}=\frac{{2C}_1}{T}{\∫}_0^T[\cos \left(\mathrm{wt}\right)\×\sin ((w+\mathrm{\Δw})t+\mathrm{\φ})]\mathrm{dt}---\left(3\right)$

${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^{*}=\frac{{2C}_1}{T}{\&Integral;}_0^T[\sin \left(\mathrm{wt}\right)\&times;\sin ((w+\mathrm{\&Delta;w})t+\mathrm{\&phi;})]\mathrm{dt}---\left(4\right)$

Wherein $T=\frac{2\mathrm{\&pi;}}{w}.$

Obviously, when Δ w=0, when promptly reference frequency is identical with power system frequency, $A_1^{*}=A_1,$ ${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^{*}={\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">B</figure-callout>}}_1,$ Amplitude $C_{}^{}$ ${}_1^{*}=\sqrt{A_1^{*2}+{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^{*2}}={\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">C</figure-callout>}}_1,$ There is not the error of calculation this moment.

If Δ w ≠ 0 can obtain:

${\&Integral;}_0^T\cos \mathrm{wt}\&CenterDot;\sin ((w+\mathrm{\&Delta;w})t+\mathrm{\&phi;})\mathrm{dt}=\frac{w+\mathrm{\&Delta;w}}{\mathrm{\&Delta;w}(2w+\mathrm{\&Delta;w})}[\cos \mathrm{\&phi;}-\cos (\mathrm{\&phi;}+\frac{2\mathrm{\&pi;}\&times;\mathrm{\&Delta;w}}{w})]---\left(5\right)$

If it is very little (after first calculating power system frequency that Δ w compares with w; Δ w is usually less than one of percentage of w), the first order Taylor of

is:

$\cos (\mathrm{\&phi;}+\frac{2\mathrm{\&pi;\&Delta;w}}{w})=\cos \mathrm{\&phi;}-\frac{2\mathrm{\&pi;}}{w}\sin (\mathrm{\&phi;}+\frac{2\mathrm{\&pi;\&Delta;w}}{w}){|}_{\mathrm{\&Delta;w}\&ap;0}\&CenterDot;\mathrm{\&Delta;w}---\left(6\right)$

with in formula (6) replacement formula (5) can obtain following formula:

$A_1^{*}=\frac{\mathrm{<figure-callout\; id="1"\; label="w\; C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">w</figure-callout>}{C}_{}{}_1}{\mathrm{\&pi;}}\&CenterDot;\frac{w+\mathrm{\&Delta;w}}{\mathrm{\&Delta;w}(2w+\mathrm{\&Delta;w})}\&CenterDot;(\cos \mathrm{\&phi;}-\cos \mathrm{\&phi;}+\frac{2\mathrm{\&pi;}}{w}\sin \mathrm{\&phi;}\&CenterDot;\mathrm{\&Delta;w})=\frac{2(w+\mathrm{\&Delta;w})}{2w+\mathrm{\&Delta;<figure-callout\; id="1"\; label="w\; C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">w</figure-callout>}}{C}_{}{}_1\sin \mathrm{\&phi;}=\frac{2(w+\mathrm{\&Delta;w})}{2w+\mathrm{\&Delta;w}}{A}_1---\left(7\right)$

Similarly, can obtain:

${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^{*}=\frac{\mathrm{<figure-callout\; id="1"\; label="w\; C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">w</figure-callout>}{C}_{}{}_1}{\mathrm{\&pi;}}\&CenterDot;\frac{w}{\mathrm{\&Delta;w}(2w+\mathrm{\&Delta;w})}\&CenterDot;(\sin \mathrm{\&phi;}+\cos \mathrm{\&phi;}\&CenterDot;\frac{2\mathrm{\&pi;}}{w}-\sin \mathrm{\&phi;})=\frac{2w}{2w+\mathrm{\&Delta;<figure-callout\; id="1"\; label="w\; C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">w</figure-callout>}}{C}_{}{}_1\cos \mathrm{\&phi;}=\frac{2w}{2w+\mathrm{\&Delta;w}}{B}_1---\left(8\right)$

From formula (7) and formula (8), can obtain following formula:

$\tan {{\mathrm{\&phi;}}_1}^{*}=\frac{A_1^{*}}{{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">B</figure-callout>}}_1^{*}}=\frac{2(w+\mathrm{\&Delta;w})A_1}{{2\mathrm{<figure-callout\; id="1"\; label="wB"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">wB</figure-callout>}}_1}=\frac{w+\mathrm{\&Delta;w}}{w}\tan \mathrm{\&phi;}---\left(9\right)$

Suppose correction factor

$\mathrm{\&delta;}=\frac{w}{w+\mathrm{\&Delta;w}}---\left(10\right)$

φ wherein ₁It is the real starting phase angle of electric system.

Can find out that from formula (9) the deviation delta w of angular frequency can cause the calculation deviation of starting phase angle, through with coefficient δ to Fu Li leaf transformation first-harmonic complex coefficient A ₁ ^*Or B ₁ ^*Revise calculation deviation that can the correction signal initial phase.

Owing in second step, the frequency of electric system first-harmonic is calculated for the first time, is made w _{S_cal}Represent this frequency and replace the w+ Δ w in the formula (10), obtain correction factor thus with it

$\mathrm{\&delta;}=\frac{w}{w_{s\_\mathrm{cal}}}---\left(11\right)$

So far, the first calculating of electric system fundamental frequency (frequency of first-harmonic) is accomplished.The secondary that carries out the electric system fundamental frequency subsequently approaches, and at first uses the first-harmonic (A of the electric system that calculates for the first time according to the method described above ₁ ^*Or B ₁ ^*) frequency proofread and correct Fu Li leaf transformation complex coefficient, carry out the first calculation process of similar electric system fundamental frequency then and (promptly calculate the starting phase angle of each signal period according to Fu Li leaf transformation complex coefficient; Calculate the difference of the starting phase angle between two adjacent signal sampling period; Calculate the mean value of the difference of starting phase angle; Frequency according to the mean value calculation electric system first-harmonic of the difference of starting phase angle).So far, the secondary of accomplishing the electric system fundamental frequency approaches.

When the actual frequency to the electric system first-harmonic subsequently approaches for the third time, need to adjust earlier the sampling number in each sampling period in the sampled signal sequence.This adjustment based on

$n=\frac{f_s}{f_{\mathrm{sys}}}N---\left(12\right)$

Wherein, f _sAnd f _SysBe respectively the reference frequency of electric system and the actual frequency of electric system, N is the sampling number in each sampling period, the sampling number in adjusted each sampling period of n.

Subsequently, employed step on the basis of the sampling number n in adjusted each sampling period, repeating the frequency of electric system first-harmonic calculated is for the first time accomplished approaching for the third time the actual frequency of electric system first-harmonic.

So far, accomplished calculating to the electric system fundamental frequency.

Step 2 with the frequency of the electric system first-harmonic that the calculates actual frequency as electric system, thereby obtains the approximate analysis formula of the Fu Li leaf transformation frequency spectrum after the windowing;

Step 3 is calculated the correction factor of first-harmonic and each harmonic amplitude according to said approximate analysis formula, and the amplitude of above-mentioned first-harmonic of trying to achieve and harmonic wave is proofreaied and correct;

Step 4 utilizes the phase-frequency characteristic of said window function to revise the initial phase of first-harmonic and each harmonic.

Still adopt formula that above-mentioned steps is analyzed below:

The discrete series representation of supposing measuring-signal x (t) is { x (n) }.For reduce based in the method for quick Fu Li leaf transformation because spectral leakage problem that non-synchronous sampling brought before carrying out quick Fu Li leaf transformation, needs to use window sequences { w (n) } carry out weighting (being windowing) to discrete series { x (n) }.After the windowing, can obtain the discrete series of a new measuring-signal:

x _w(n)＝x(n)w(n)，n＝0～N-1 (13)

Wherein, N is the number of discrete series.

The frequency spectrum that this discrete series is corresponding is:

$x_w\left(f\right)={\&Integral;}_{-\&infin;}^{+\&infin;}X\left(y\right)W(f-y)\mathrm{dy}---\left(14\right)$

In formula (14),

$X\left(f\right)={\&Integral;}_{-\&infin;}^{+\&infin;}x\left(t\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{dt}$ (15)

$W\left(f\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}w\left(n\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;fn}{T}_s}$

In order to simplify the theoretical analysis process of this algorithm, at first only consider the first-harmonic part in the measuring-signal, that is:

x(t)＝C ₀sin(2πf ₀t+φ ₀) (16)

With x (t) the substitution formula (15) in (16), can obtain:

$X\left(f\right)=\frac{{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">C</figure-callout>}}_0}{2j}[e^{j{\mathrm{\&phi;}}_0}.\mathrm{\&delta;}(f-f_0)-e^{-j{\mathrm{\&phi;}}_0}.\mathrm{\&delta;}(f+f_0)]---\left(17\right)$

Can obtain x thus _w(f) as follows:

$X_w\left(\mathrm{\&lambda;}\right)=\frac{{\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">C</figure-callout>}}_0}{2j}[e^{j{\mathrm{\&phi;}}_0}.W(\mathrm{\&lambda;}-{\mathrm{\&lambda;}}_0)-e^{-j{\mathrm{\&phi;}}_0}.W(\mathrm{\&lambda;}+{\mathrm{\&lambda;}}_0)]---\left(18\right)$

Wherein, F=1/NT _s, λ=f/F, λ ₀=f ₀/ F, T _sBe the SI.

In order to make measurement have higher precision, select 4 Blackman-Harris window functions here to electric harmonic.This window function is:

$w\left(n\right)=0.3635819-0.4891775\&CenterDot;\cos \left(\frac{2\mathrm{\&pi;n}}{N-1}\right)+0.1365995\&CenterDot;\cos \left(\frac{4\mathrm{\&pi;n}}{N-1}\right)-0.01168\&CenterDot;\cos \left(\frac{6\mathrm{\&pi;n}}{N-1}\right)---\left(19\right)$

The quick Fu Li leaf transformation of this window function is:

$W\left(\mathrm{\&lambda;}\right)\&ap;\sin \mathrm{\&pi;\&lambda;}\&CenterDot;e^{-\mathrm{j\&pi;\&lambda;}}\&CenterDot;\underset{h=0}{\overset{3}{\mathrm{\&Sigma;}}}{a}_h\frac{\mathrm{\&lambda;}}{\mathrm{\&pi;}({\mathrm{\&lambda;}}^2-h^2)}---\left(20\right)$

Fig. 4 has provided the spectrum diagram of 4 Blackman-Harris window functions.

Consider the symmetry of frequency spectrum, with the W (λ-λ in the formula (18) ₀) replace with formula (20), the fundamental voltage amplitude that can obtain actual signal is:

${\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="H2009101303195E00041.png"\; state="\{\{state\}\}">C</figure-callout>}}_0=\frac{2X_w\left({\mathrm{\&lambda;}}_s\right)}{W({\mathrm{\&lambda;}}_s-{\mathrm{\&lambda;}}_0)}---\left(21\right)$

X wherein _w(λ _s) be after adding the quick Fu Li leaf transformation of window signal, the peak value that in its frequency spectrum, searches (being fundamental voltage amplitude), λ _sBe normalized frequency corresponding to this peak value,

Can be counted as amplitude correction factor, be used for the caused error of non-synchronous sampling is proofreaied and correct.

Because real normalized signal frequency lambda in the formula (18) ₀The unknown, C ₀Can not directly calculate from formula (18).Traditional calculating C ₀Method be based on interpolation, but interpolation can cause the calculating out of true to power system frequency.And in the present invention,, can think that the frequency of the electric system that calculates is exactly the actual frequency of this system, so the deviation λ in the formula (18) because power system frequency accurately calculated _s-λ ₀Can be by λ _s-λ _{0_cal}The approximate replacement.Wherein, λ _{0_cal}It is the normalized system frequency that calculates.Like this, can from formula (20), directly calculate correction factor at an easy rate

According to formula (17) and (18), can directly calculate amplitude C ₀Because λ ₀Computational accuracy very high, so amplitude C ₀Precision equally very high.

At last, the phasing degree can be calculated and proofread and correct through following formula:

${\mathrm{\&phi;}}_0=\arg \left(X_w\left({\mathrm{\&lambda;}}_s\right)\right)-\arg \left(W({\mathrm{\&lambda;}}_0-{\mathrm{\&lambda;}}_s)\right)+\frac{\mathrm{\&pi;}}{2}---\left(22\right)$

Wherein, first starting phase angle for signal after the windowing, second is the starting phase angle of window function.

Similar with the computing method of above-mentioned first-harmonic, can draw the amplitude and the phase place of each harmonic wave of electric system equally, repeat no more here.

The frequency analysis device of a kind of electric system of the present invention is to be used for the harmonic wave of electric system is analyzed, and this device comprises:

Electric system fundamental frequency computing module is used to calculate the frequency of electric system first-harmonic;

Windowing and Fu Li leaf transformation frequency spectrum computing module are used for the sampled signal sequence of electric system is carried out windowing process and carried out the Fu Li leaf transformation, try to achieve the amplitude of first-harmonic and the amplitude and the initial phase of initial phase and each harmonic;

Correction module; Calculate the correction factor of first-harmonic and each harmonic amplitude according to the approximate analysis formula of the Fu Li leaf transformation frequency spectrum after the windowing; And the amplitude of above-mentioned first-harmonic of trying to achieve and harmonic wave proofreaied and correct, and utilize the phase-frequency characteristic of windowed function to revise the initial phase of first-harmonic and each harmonic.

Said electric system fundamental frequency computing module comprises like lower module:

Acquisition module is used to obtain the power system signal of more than one signal sampling period;

First computing module is used for the frequency of said electric system first-harmonic is calculated for the first time;

Secondary approaches module, according to Fu Li leaf transformation complex coefficient, fundamental frequency and the SF of the said sampled signal first-harmonic that calculates for the first time, the actual frequency of said electric system first-harmonic is carried out secondary approach;

Approach module three times, approach the fundamental frequency that obtains according to said secondary signal sampling series is adjusted, the actual frequency of said electric system first-harmonic is carried out three times approach.

Said first computing module comprises:

Fu Li leaf transformation complex coefficient calculating sub module is used for the sampled signal in each signal sampling period is carried out the Fu Li leaf transformation, thereby calculates the Fu Li leaf transformation complex coefficient of said sampled signal fundamental frequency;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Said secondary approaches module and comprises:

Fu Li leaf transformation complex coefficient adjustment submodule is adjusted said Fu Li leaf transformation complex coefficient according to the frequency of the said first-harmonic that calculates for the first time;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

Saidly approach module three times and comprise:

Hits is adjusted submodule, is used for approaching according to said secondary the hits of each signal sampling period of frequency adjustment sampling series of resulting electric system first-harmonic;

Fu Li leaf transformation complex coefficient calculating sub module is used for the sampled signal in adjusted each signal sampling period is carried out the Fu Li leaf transformation, thereby calculates the Fu Li leaf transformation complex coefficient of said sampled signal fundamental frequency;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

In said device of the present invention, first computing module, secondary approach module, approach module common in the module for three times can be set to one.For example be set to the mean value calculation submodule of a starting phase angle calculating sub module, a starting phase angle difference calculating sub module, a starting phase angle difference, an electric system fundamental frequency calculating sub module.Realize the required device of the inventive method thereby simplify.

The above only is a preferred implementation of the present invention; Should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the principle of the invention; Can also make some improvement and retouching, these improvement and retouching also should be regarded as protection scope of the present invention.

Claims (10)

1. the harmonic analysis method of an electric system is characterized in that, the method includes the steps of:

(1) calculates the frequency of electric system first-harmonic, and the sampled signal sequence of electric system is carried out windowing process and carried out the Fu Li leaf transformation, try to achieve the amplitude of first-harmonic and the amplitude and the initial phase of initial phase and each harmonic;

(2), thereby obtain the approximate analysis formula of the Fu Li leaf transformation frequency spectrum after the windowing with the frequency of the electric system first-harmonic that calculates actual frequency as electric system;

(3) calculate the correction factor of first-harmonic and each harmonic amplitude according to said approximate analysis formula, and the amplitude of above-mentioned first-harmonic of trying to achieve and harmonic wave is proofreaied and correct;

(4) utilize the phase-frequency characteristic of the window function that uses in the said windowing process to revise the initial phase of first-harmonic and each harmonic;

Wherein, the frequency of calculating electric system first-harmonic may further comprise the steps in the said step (1):

(11) obtain the power system signal of more than one signal sampling period;

(12) frequency of said electric system first-harmonic is calculated for the first time;

(13), the actual frequency of said electric system first-harmonic is carried out secondary approach according to Fu Li leaf transformation complex coefficient, fundamental frequency and the SF of the said sampled signal first-harmonic that calculates for the first time;

(14) approach the fundamental frequency that obtains according to said secondary signal sampling series is adjusted, the actual frequency of said electric system first-harmonic is carried out three times approach.

2. the harmonic analysis method of a kind of electric system according to claim 1 is characterized in that, in the said step (12) frequency of electric system first-harmonic is calculated for the first time may further comprise the steps:

(121) sampled signal in each signal sampling period is carried out the Fu Li leaf transformation, thereby calculate the Fu Li leaf transformation complex coefficient of said sampled signal first-harmonic;

(122) calculate the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

(123) difference of the starting phase angle between two adjacent signal sampling period of calculating;

(124) mean value of the difference of the said starting phase angle of calculating;

(125) according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

3. the harmonic analysis method of a kind of electric system according to claim 2 is characterized in that, in the said step (13) actual frequency of said electric system first-harmonic is carried out secondary and approaches and may further comprise the steps:

(131) adjust said Fu Li leaf transformation complex coefficient according to the frequency of the said first-harmonic that calculates for the first time;

(132) calculate the starting phase angle of each signal period;

(133) difference of the starting phase angle between two adjacent signal sampling period of calculating;

(134) mean value of the difference of the said starting phase angle of calculating;

(135) according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

4. the harmonic analysis method of a kind of electric system according to claim 3 is characterized in that, in the said step (14) actual frequency of said electric system first-harmonic is carried out approaching for three times may further comprise the steps:

(141) approach the hits of each signal sampling period in the frequency adjustment sampling series of resulting electric system first-harmonic according to said secondary;

(142) sampled signal in adjusted each signal sampling period is carried out the Fu Li leaf transformation, thereby calculate the Fu Li leaf transformation complex coefficient of said sampled signal first-harmonic;

(143) calculate the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

(144) difference of the starting phase angle between two adjacent signal sampling period of calculating;

(145) mean value of the difference of the said starting phase angle of calculating;

(146) according to the frequency of the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

5. the harmonic analysis method of a kind of electric system according to claim 2 is characterized in that, in the said step (11), said power system signal is a voltage signal.

6. according to the harmonic analysis method of the described a kind of electric system of arbitrary claim in the claim 2 to 5, it is characterized in that said Fu Li leaf transformation is discrete Fu Li leaf transformation.

7. the frequency analysis device of an electric system is used for the harmonic wave of electric system is analyzed, and it is characterized in that said device comprises:

Electric system fundamental frequency computing module is used to calculate the frequency of electric system first-harmonic;

Windowing and Fu Li leaf transformation frequency spectrum computing module are used for the sampled signal sequence of electric system is carried out windowing process and carried out the Fu Li leaf transformation, try to achieve the amplitude of first-harmonic and the amplitude and the initial phase of initial phase and each harmonic;

Correction module; Calculate the correction factor of first-harmonic and each harmonic amplitude according to the approximate analysis formula of the Fu Li leaf transformation frequency spectrum after the windowing; And the amplitude of above-mentioned first-harmonic of trying to achieve and harmonic wave proofreaied and correct, and utilize the phase-frequency characteristic of windowed function to revise the initial phase of first-harmonic and each harmonic;

Wherein, said electric system fundamental frequency computing module comprises:

Acquisition module is used to obtain the power system signal of more than one signal sampling period;

First computing module is used for the frequency of said electric system first-harmonic is calculated for the first time;

Secondary approaches module, according to Fu Li leaf transformation complex coefficient, fundamental frequency and the SF of the said sampled signal first-harmonic that calculates for the first time, the actual frequency of said electric system first-harmonic is carried out secondary approach;

Approach module three times, approach the fundamental frequency that obtains according to said secondary signal sampling series is adjusted, the actual frequency of said electric system first-harmonic is carried out three times approach.

8. the frequency analysis device of a kind of electric system according to claim 7 is characterized in that, said first computing module comprises:

Fu Li leaf transformation complex coefficient calculating sub module is used for the sampled signal in each signal sampling period is carried out the Fu Li leaf transformation, thereby calculates the Fu Li leaf transformation complex coefficient of said sampled signal fundamental frequency;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

9. the frequency analysis device of a kind of electric system according to claim 7 is characterized in that, said secondary approaches module and comprises:

Fu Li leaf transformation complex coefficient adjustment submodule is adjusted said Fu Li leaf transformation complex coefficient according to the frequency of the said first-harmonic that calculates for the first time;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

10. the frequency analysis device of a kind of electric system according to claim 7 is characterized in that, saidly approaches module three times and comprises:

Hits is adjusted submodule, is used for approaching according to said secondary the hits of each signal sampling period of frequency adjustment sampling series of resulting electric system first-harmonic;

Fu Li leaf transformation complex coefficient calculating sub module is used for the sampled signal in adjusted each signal sampling period is carried out the Fu Li leaf transformation, thereby calculates the Fu Li leaf transformation complex coefficient of said sampled signal fundamental frequency;

The starting phase angle calculating sub module is calculated the starting phase angle of each signal period according to said Fu Li leaf transformation complex coefficient;

Starting phase angle difference calculating sub module is calculated the difference of the starting phase angle between two adjacent signal sampling period;

The mean value calculation submodule of starting phase angle difference is used to calculate the mean value of the difference of said starting phase angle;

Electric system fundamental frequency calculating sub module is used for the frequency according to the mean value calculation electric system first-harmonic of the difference of said starting phase angle.

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