CN103941090A - Harmonic wave measurement method based on spectral energy interpolation - Google Patents

Abstract

The invention discloses a harmonic wave measurement method based on spectral energy interpolation. According to ten cyclic wave detection environments meeting the IEC standard, concrete parameters of a certain component are detected out accurately, and an IEC method only can roughly detect out the amplitude of signals within the certain frequency band; from the point of view of spectral energy in a signal frequency domain for the first time, transformation and interpolation of an energy spectrum are carried out by multiplying the frequency spectrum by a rotation phase factor, influence of overlaid leakage of sidelobes of the frequency spectrum is eliminated by mutual offset of energy of interference components, and the detection precision of the frequency, the amplitude and the phase position is improved; when the components in signals are likely submerged in noise signals, main signals are highlighted through transformation of the spectrum energy, and therefore usable signals are extracted from the noise signals effectively. The method is based on a DFT/FFT algorithm recommended by the IEC standard, the principle is simple, the effect and stability are good, and the method has certain engineering application value and good application prospects.

Description

Based on the harmonic measuring method of spectral line energy interpolation

Technical field

The present invention relates to a kind of harmonic measuring method based on spectral line energy interpolation, belong to power quality analysis technical field.

Background technology

The quality of the quality of power supply has vital impact to the firm operation of electrical network, and harmonic wave, a harmonic parameters index are important parameters weighing power supply quality, along with the access of the new forms of energy such as domestic flourish high ferro, electric automobile, wind-powered electricity generation and photovoltaic generation, can accurately detect harmonic wave, a harmonic parameters larger on its assessment impact.(the International Electrotechnical Commission of International Electrotechnical Commission, IEC) in the standard IEC 61000-4-7 putting into effect and IEC61000-4-30, regulation adopts DFT/FFT to carry out spectrum analysis, and specify that analysis window length is 10 cycles (50Hz systems), when having specified synchronized sampling, IEC standard carries out the frequency spectrum block detecting method of 10 cycle rectangular windows, advantage is to carry out rapidly harmonic wave, between harmonic content frequency-division section detect, shortcoming is to measure the design parameter of a certain frequency component, and in the time of non-synchronous sampling, there is larger measuring error.

For the defect in IEC standard, have at present and a lot of improve algorithm based on DFT/FFT, two conventional class algorithms are window function and interpolation algorithm and phase differential algorithm, window function and interpolation algorithm is generally to utilize the amplitude of near the maximum of component frequency and time large two spectral lines to carry out interpolation calculation, the type of its precision and institute's windowing has very large relation, better its accuracy of detection of Sidelobe Suppression performance of window function is higher, but main lobe width is larger simultaneously, in current method, adopt window function and interpolation algorithm can increase the length of data, make analysis window length reach tens cycles, can not meet the requirement of IEC standard, what phase differential algorithm adopted is based on two sections not data in the same time carry out spectrum analysis, ask for the parameter of component by the phase differential of corresponding spectral line, therefore sampling length is at least 20 cycles and could meets the 5Hz resolution standard of IEC standard, simultaneously, the secondary lobe that non-synchronous sampling brings leaks testing result impact larger, two kinds of above-mentioned algorithms calculate corresponding spectral line spectrum value time ignored other component secondary lobe leak disturb, be separated by near or leak when more serious when frequency component, can produce larger error.

Summary of the invention

The object of the invention is for the defect in IEC standard, two conventional class algorithms are deficiencies that window function and interpolation algorithm and phase differential algorithm exist.Harmonic measuring method based on spectral line energy interpolation of the present invention, can solve harmonic wave, the accurate test problems of a harmonic wave of lower 10 the cycle data lengths of IEC standard, the secondary lobe that can eliminate all the other components disturbs simultaneously, further to improve the detection degree of accuracy of harmonic wave between harmonic wave, come from the DFT/FFT algorithm of IEC standard recommendation, effect and stability are better, have certain engineering application and are worth and good application prospect.

To achieve the above object, the technical solution adopted in the present invention is:

Based on a harmonic measuring method for spectral line energy interpolation, it is characterized in that: comprise the following steps,

Step (1), for the discrete sampling of power network signal, (n Δ t) for sampled value g _nfor formula (1),

Wherein, Δ t is unit sampling interval, and M is sampled components number, f _i, A _i, for frequency, amplitude and the phase place of sampled components, n=0,1 ..., N-1, N is sample window length;

Step (2), (n Δ t) for the sampled value g to step (1) _naccording to 10 cycle windowings of IEC standard regulation, and spectrum analysis obtains frequency spectrum G (k) according to DFT/FFT,

Wherein, β _i=f _i/ Δ f is unit frequency values, and Δ f is that sample window is grown frequency resolution corresponding while being N, W (k-β _i) represent corresponding spectral line (k-β _i) the window spectrum value located, W (k+ β _i) represent corresponding spectral line (k+ β _i) the window spectrum value located, the spectrum value at the corresponding spectral line k of G (k) place;

Step (3), the frequency spectrum G (k) that step (2) is obtained takes advantage of rotatable phase factor treatment to obtain new frequency spectrum

Step (4), by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and asks for corresponding frequency offseting value obtain the frequency f of sampled components _i;

Step (5), according to new frequency spectrum do frequency spectrum square processing, be converted into the energy of spectral line, by the frequency f to sampled components _ieliminate secondary lobe stack power and disturb three spectral line energy phase Calais at place, and interpolation is tried to achieve the amplitude A of signal _iand phase value

The aforesaid harmonic measuring method based on spectral line energy interpolation, is characterized in that: (n Δ t) for the sampled value g of step (2) to step (1) _naccording to 10 cycle windowings of IEC standard regulation, in the time that fundamental frequency is synchronous, add the rectangular window of 10 cycles, when asynchronous, add the Hanning window of 10 cycles, in the time of sample window length N > > 1, the expression formula of corresponding window spectral function is as follows: rectangular window is

$W_R\left(\mathrm{\θ}\right)=e^{-j\frac{N-1}{N}\mathrm{\π\θ}}\frac{\sin \left(\mathrm{\π\θ}\right)}{\mathrm{\π\θ}}---\left(3\right)$

Hanning window is,

$W_H\left(\mathrm{\θ}\right)=e^{-j\frac{N-1}{N}\mathrm{\π\θ}}\frac{\sin \left(\mathrm{\π\θ}\right)}{2\mathrm{\π\θ}(1-{\mathrm{\θ}}^2)}---\left(4\right).$

The aforesaid harmonic measuring method based on spectral line energy interpolation, is characterized in that: step (3) takes advantage of rotatable phase factor treatment to obtain new frequency spectrum frequency spectrum G (k) method be,

(1) the frequency spectrum G (k) formula (2) being represented is converted to formula (5),

Wherein, in the phase factor of frequency spectrum G (k) component, contain two, it changes along with the difference of position of spectral line, when the increase impact of k value increases;

(2) be multiplied by the rotatable phase factor change with the variation of position of spectral line k with the phase value of offsetting in formula (5), take advantage of the rotatable phase factor to be substitution formula (5) obtains new frequency spectrum

(3) by the frequency values β of unit in formula (6) _iwrite as the form of formula (7),

${\mathrm{\β}}_i=k_i+{\∂}_i---\left(7\right)$

Wherein, k _i, for the frequency f of corresponding sampled components _imaximum spectral line sequence number and frequency offseting value, $-0.5<{\&PartialD;}_i\&le;0.5,$ New frequency spectrum be expressed as,

Be,

Wherein, for taking advantage of after the rotatable phase factor on frequency spectrum all the other components to sampled components frequency f _isecondary lobe disturb superposition value.

The aforesaid harmonic measuring method based on spectral line energy interpolation, is characterized in that: step (4), and by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and asks for corresponding frequency offseting value obtain the frequency f of sampled components _imethod be,

(1) according to formula (9), by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and makes Δ (k _i)+Δ (k _i+ 1) ≈ 0, defining ratio factor-alpha is formula (10),

$\mathrm{\&alpha;}=\frac{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i-1)|}{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}\&ap;\frac{\left|W(-{\&PartialD;}_i)\right|+\left|W(-1-{\&PartialD;}_i)\right|}{\left|W(-{\&PartialD;}_i)\right|+\left|W(1-{\&PartialD;}_i)\right|}---\left(10\right);$

(2), for rectangular window, have according to formula (3) formula (10) abbreviation is,

${\mathrm{\&alpha;}}_R\&ap;\frac{1-{\&PartialD;}_i}{1+{\&PartialD;}_i}---\left(11\right)$

Wherein, α _rfor ratio factor-alpha corresponding to rectangular window;

(3), for Hanning window, have according to formula (4) formula (10) abbreviation is,

${\mathrm{\&alpha;}}_H\&ap;\frac{2-{\&PartialD;}_i}{2+{\&PartialD;}_i}---\left(12\right)$

Wherein, α _hfor ratio factor-alpha corresponding to Hanning window;

(4) according to formula (13), the anti-frequency offseting value that solves

${\&PartialD;}_i=c_w\frac{\left|\stackrel{\&OverBar;}{G}(k_i+1)\right|-\left|\stackrel{\&OverBar;}{G}(k_i-1)\right|}{|\stackrel{\&OverBar;}{G}(k_i-1)+2\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}---\left(13\right)$

Wherein, c _wfor the amplitude coefficient of restitution of corresponding window function, c while adding rectangular window _w=1, c while adding Hanning window _w=2; for corresponding spectral line (k _i-1), k _i, (k _i+ 1) the new spectrum value of locating;

(5) according to formula (14), the frequency f of calculating sampling component _ifor,

$f_i=(k_i+{\&PartialD;}_i)\mathrm{\&Delta;f}={\mathrm{\&beta;}}_i\mathrm{\&Delta;f}---\left(14\right).$

The aforesaid harmonic measuring method based on spectral line energy interpolation, is characterized in that: step (5), interpolation is tried to achieve the amplitude A of signal _iand phase value method be,

(1) according to Parseval's theorem, utilize the spectrum value corresponding to three spectral lines at respective components ceiling capacity spectral line place to carry out a square processing and be converted into spectral line energy,

Wherein, in formula (15), (16), (17) for three spectrum values that spectral line is corresponding at respective components ceiling capacity spectral line place;

(2) in order to eliminate the interference of other component side-lobe energy, three spectral line energy of formula (15), (16), (17) are added up to,

(3) according to being multiplied by the sidelobe performance after phase rotation coefficient, do approximate processing, formula (18) abbreviation is,

(4) according to formula (19), obtain adding the amplitude of rectangular window or Hanning window, the expression formula of phase information,

For rectangular window be,

For Hanning window be,

Wherein, $K_e=\frac{4{(1-{\&PartialD;}_i^2)}^2}{(1+{3\&PartialD;}_i^4)\sin c^2\left({\&PartialD;}_i\right)},$ $K_H=\frac{16{(1-{\&PartialD;}_i^2)}^2{(4-{\&PartialD;}_i^2)}^2}{3(2+{\&PartialD;}_i^2)(4+{\&PartialD;}_i^2)\sin c^2\left({\&PartialD;}_i\right)},$ $\sin c\left({\&PartialD;}_i\right)=\sin \left(\mathrm{\&pi;}{\&PartialD;}_i\right)/\left(\mathrm{\&pi;}{\&PartialD;}_i\right);$

(5) according to formula (20) or (21), obtain amplitude A _iand phase value

The invention has the beneficial effects as follows: the harmonic measuring method based on spectral line energy interpolation of the present invention, compared with prior art, has the following advantages:

1) the present invention strictly meets 10 cycle testing environments of IEC standard regulation, can accurately detect the design parameter of certain component, and IEC method can only detect the amplitude in signal frequency range roughly;

2) the present invention is first from the angle of signal frequency domain spectral line energy, by being multiplied by the rotatable phase factor, carry out conversion and the interpolation of energy spectral line, on the impact of cancelling out each other to eliminate its secondary lobe stack leakage of interference components energy, improve the accuracy of detection of frequency, amplitude and phase place;

(3), when the component in signal may be submerged in noise signal, the present invention is outstanding by main signal by spectral line energy conversion, thereby effectively from noise signal, extracts useful signal;

(4) the present invention comes from the DFT/FFT algorithm of IEC standard recommendation, and principle is simple, and effect and stability are better, has certain engineering application and is worth and good application prospect.

Brief description of the drawings

Fig. 1 is the process flow diagram of the harmonic measuring method based on spectral line energy interpolation of the present invention.

Fig. 2 is the present invention's corresponding spectrogram add rectangular window under IEC standard time.

Fig. 3 is the present invention's corresponding spectrogram add Hanning window under IEC standard time.

Fig. 4 is frequency detecting Error Graph when different signal to noise ratio (S/N ratio) under IEC standard of the present invention.

Fig. 5 is amplitude detection Error Graph when different signal to noise ratio (S/N ratio) under IEC standard of the present invention.

Fig. 6 is phase-detection Error Graph when different signal to noise ratio (S/N ratio) under IEC standard of the present invention.

Embodiment

Below in conjunction with Figure of description, the invention will be further described.Following examples are only for technical scheme of the present invention is more clearly described, and can not limit the scope of the invention with this.

Harmonic measuring method based on spectral line energy interpolation of the present invention, can solve harmonic wave, the accurate test problems of a harmonic wave of lower 10 the cycle data lengths of IEC standard, the secondary lobe that can eliminate all the other components disturbs simultaneously, by spectral line energy conversion, main signal is outstanding, thereby effectively from noise signal, extract useful signal, further to improve the detection degree of accuracy of harmonic wave between harmonic wave, come from the DFT/FFT algorithm of IEC standard recommendation, effect and stability are better, as shown in Figure 1, comprise the following steps

Step (1), for the discrete sampling of power network signal, (n Δ t) for sampled value g _nfor formula (1),

Wherein, Δ t is unit sampling interval, and M is sampled components number, f _i, A _i, for frequency, amplitude and the phase place of sampled components, n=0,1 ..., N-1, N is sample window length;

Step (2), (n Δ t) for the sampled value g to step (1) _naccording to 10 cycle windowings of IEC standard regulation, and spectrum analysis obtains frequency spectrum G (k) according to DFT/FFT,

Wherein, β _i=f _i/ Δ f is unit frequency values, and Δ f is that sample window is grown frequency resolution corresponding while being N, W (k-β _i) represent corresponding spectral line (k-β _i) the window spectrum value located, W (k+ β _i) represent corresponding spectral line (k+ β _i) the window spectrum value located, the spectrum value at the corresponding spectral line k of G (k) place;

In the time that fundamental frequency is synchronous, add the rectangular window of 10 cycles, add the Hanning window of 10 cycles when asynchronous, in the time of sample window length N > > 1, the expression formula of corresponding window spectral function is as follows: rectangular window is,

$W_R\left(\mathrm{\&theta;}\right)=e^{-j\frac{N-1}{N}\mathrm{\&pi;\&theta;}}\frac{\sin \left(\mathrm{\&pi;\&theta;}\right)}{\mathrm{\&pi;\&theta;}}---\left(3\right)$

Hanning window is,

$W_H\left(\mathrm{\&theta;}\right)=e^{-j\frac{N-1}{N}\mathrm{\&pi;\&theta;}}\frac{\sin \left(\mathrm{\&pi;\&theta;}\right)}{2\mathrm{\&pi;\&theta;}(1-{\mathrm{\&theta;}}^2)}---\left(4\right);$

Step (3), the frequency spectrum G (k) that step (2) is obtained takes advantage of rotatable phase factor treatment to obtain new frequency spectrum make the phase place in each component main lobe strictly identical, phase place in secondary lobe strict contrary, amplitude is close, obtains new frequency spectrum method be,

(1) the frequency spectrum G (k) formula (2) being represented is converted to formula (5),

Wherein, in the phase factor of frequency spectrum G (k) component, contain two, it changes along with the difference of position of spectral line, when the increase impact of k value increases;

(2) be multiplied by the rotatable phase factor change with the variation of position of spectral line k with the phase value of offsetting in formula (5), take advantage of the rotatable phase factor to be substitution formula (5) obtains new frequency spectrum

(3) by the frequency values β of unit in formula (6) _iwrite as the form of formula (7),

${\mathrm{\&beta;}}_i=k_i+{\&PartialD;}_i---\left(7\right)$

Wherein, k _i, for the frequency f of corresponding sampled components _imaximum spectral line sequence number and frequency offseting value, $-0.5<{\&PartialD;}_i\&le;0.5,$ New frequency spectrum be expressed as,

Be,

Wherein, for taking advantage of after the rotatable phase factor on frequency spectrum all the other components to sampled components frequency f _isecondary lobe disturb superposition value, to single value Δ (k _m), its secondary lobe amplitude is close, phase directional is strictly contrary;

Step (4), by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and asks for corresponding frequency offseting value obtain the frequency f of sampled components _i, computation process is as follows,

(1) according to formula (9), by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and makes Δ (k _i)+Δ (k _i+ 1) ≈ 0, defining ratio factor-alpha is formula (10),

$\mathrm{\&alpha;}=\frac{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i-1)|}{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}\&ap;\frac{\left|W(-{\&PartialD;}_i)\right|+\left|W(-1-{\&PartialD;}_i)\right|}{\left|W(-{\&PartialD;}_i)\right|+\left|W(1-{\&PartialD;}_i)\right|}---\left(10\right);$

(2), for rectangular window, have according to formula (3) formula (10) abbreviation is,

${\mathrm{\&alpha;}}_R\&ap;\frac{1-{\&PartialD;}_i}{1+{\&PartialD;}_i}---\left(11\right)$

Wherein, α _rfor ratio factor-alpha corresponding to rectangular window;

(3), for Hanning window, have according to formula (4) formula (10) abbreviation is,

${\mathrm{\&alpha;}}_H\&ap;\frac{2-{\&PartialD;}_i}{2+{\&PartialD;}_i}---\left(12\right)$

Wherein, α _hfor ratio factor-alpha corresponding to Hanning window;

(4) according to formula (13), the anti-frequency offseting value that solves

${\&PartialD;}_i=c_w\frac{\left|\stackrel{\&OverBar;}{G}(k_i+1)\right|-\left|\stackrel{\&OverBar;}{G}(k_i-1)\right|}{|\stackrel{\&OverBar;}{G}(k_i-1)+2\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}---\left(13\right)$

Wherein, c _wfor the amplitude coefficient of restitution of corresponding window function, c while adding rectangular window _w=1, c while adding Hanning window _w=2; for corresponding spectral line (k _i-1), k _i, (k _i+ 1) the new spectrum value of locating;

(5) according to formula (14), the frequency f of calculating sampling component _ifor,

$f_i=(k_i+{\&PartialD;}_i)\mathrm{\&Delta;f}={\mathrm{\&beta;}}_i\mathrm{\&Delta;f}---\left(14\right);$

Step (5), according to new frequency spectrum do frequency spectrum square processing, be converted into the energy of spectral line, every spectral line on signal frequency domain contains energy information, considers every spectral line contained energy difference, by the frequency f to sampled components _ieliminate secondary lobe stack power and disturb three spectral line energy phase Calais at place, and interpolation is tried to achieve the amplitude A of signal _iand phase value computation process is as follows,

(1) according to Parseval's theorem, utilize the spectrum value corresponding to three spectral lines at respective components ceiling capacity spectral line place to carry out a square processing and be converted into spectral line energy,

Wherein, G (k in formula (15), (16), (17) _i-1), G (k _i), G (k _i+ 1) be three spectrum values that spectral line is corresponding at respective components ceiling capacity spectral line place;

(2) in order to eliminate the interference of other component side-lobe energy, three spectral line energy of formula (15), (16), (17) are added up to,

(3) according to being multiplied by the sidelobe performance after phase rotation coefficient, do approximate processing, formula (18) abbreviation is,

(4) according to formula (19), obtain adding the amplitude of rectangular window or Hanning window, the expression formula of phase information,

For rectangular window be,

For Hanning window be,

Wherein, $K_e=\frac{4{(1-{\&PartialD;}_i^2)}^2}{(1+{3\&PartialD;}_i^4)\sin c^2\left({\&PartialD;}_i\right)},$ $K_H=\frac{16{(1-{\&PartialD;}_i^2)}^2{(4-{\&PartialD;}_i^2)}^2}{3(2+{\&PartialD;}_i^2)(4+{\&PartialD;}_i^2)\sin c^2\left({\&PartialD;}_i\right)},$ $\sin c\left({\&PartialD;}_i\right)=\sin \left(\mathrm{\&pi;}{\&PartialD;}_i\right)/\left(\mathrm{\&pi;}{\&PartialD;}_i\right);$

(5) according to formula (20) or (21), obtain amplitude A _iand phase value

Above step (1)-step (5), has realized at IEC master gauge and having determined under testing requirement, and the angle from signal spectrum energy in 10 cycles is carried out harmonic parameters between harmonic wave and detected, below according to a specific embodiment, the present invention is carried out to algorithm simulating checking, specific as follows

Initiatively power distribution network carries out simulation analysis, and data length when IEC61000-4-7 standard specifies that between harmonic wave, harmonic wave detects is 10 cycles, and sampling DFT/FFT method is analyzed, and establishes the signal (table 1) that contains multiple frequency components, and sample frequency is f _s=10240Hz, the sampling period is 10 cycles, i.e. 2048 points, corresponding frequency resolution Δ f=5Hz,

The each component parameters theoretical value of table 1

Above-mentioned signal is carried out respectively to the present invention is aforesaid adds rectangular window and the analysis of Hanning window, and carry out spectral conversion, as shown in Figures 2 and 3, the result of using spectral line energy interpolation method to detect is as shown in table 2 for its spectral line profile,

The testing result of table 2 algorithm of the present invention

As can be seen from Table 2, the present invention all can fix and realize detecting comparatively accurately of harmonic wave, a harmonic parameters at IEC master gauge; In the time of fundamental frequency non-synchronous sampling, spectral line energy interpolation method (method 2) based on Hanning window has higher accuracy of detection than the spectral line energy interpolation method (method 1) based on rectangular window, and between harmonic wave when method 2 is more suitable for non-synchronous sampling, harmonic parameters is specifically measured.

Taking the signal that adds Hanning window as example, in order to verify the validity of institute of the present invention extracting method, to two kinds of main flow schemes in background technology: the testing result of the double spectral line interpolation method (method 3) based on Hanning window, the phase difference method (method 4) based on Hanning window contrasts, the sampled data length that simultaneously limits each method is 10 cycles, and the testing result of method 3 and method 4 is as shown in table 3.

The testing result of table 3 method 3 and method 4

For the noiseproof feature of checking the inventive method, contrast with the measuring error of method 3 and method 4 simultaneously, analogue noise environment is the white Gaussian noise signal of stack 10～100dB signal to noise ratio (snr), adopt respectively the testing result of above-mentioned 4 kinds of methods to contrast, obtain the detection error change situation (taking harmonic wave between 82Hz as example) of each algorithm under different noise intensities as Fig. 4, shown in Fig. 5 and Fig. 6, while all showing non-synchronous sampling, the measurement effect that employing adds Hanning window is better than and adds rectangular window, in the inventive method, add the spectral line energy interpolation method (method 2) of Hanning window than the double spectral line interpolation method (method 3) that adds Hanning window, add high 1～2 order of magnitude of phase differential method (method 4) measuring accuracy of Hanning window, verify thus in the present invention that institute's extracting method is in the substandard accuracy of IEC and validity, there is stronger interference free performance.

More than show and described ultimate principle of the present invention, principal character and advantage.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that in above-described embodiment and instructions, describes just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.The claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (5)

1. the harmonic measuring method based on spectral line energy interpolation, is characterized in that: comprises the following steps,

Step (1), for the discrete sampling of power network signal, (n Δ t) for sampled value g _nfor formula (1),

Wherein, Δ t is unit sampling interval, and M is sampled components number, f _i, A _i, for frequency, amplitude and the phase place of sampled components, n=0,1 ..., N-1, N is sample window length;

Step (2), (n Δ t) for the sampled value g to step (1) _naccording to 10 cycle windowings of IEC standard regulation, and spectrum analysis obtains frequency spectrum G (k) according to DFT/FFT,

Wherein, β _i=f _i/ Δ f is unit frequency values, and Δ f is that sample window is grown frequency resolution corresponding while being N, W (k-β _i) represent corresponding spectral line (k-β _i) the window spectrum value located, W (k+ β _i) represent corresponding spectral line (k+ β _i) the window spectrum value located, the spectrum value at the corresponding spectral line k of G (k) place;

Step (3), the frequency spectrum G (k) that step (2) is obtained takes advantage of rotatable phase factor treatment to obtain new frequency spectrum

Step (4), by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and asks for corresponding frequency offseting value obtain the frequency f of sampled components _i;

Step (5), according to new frequency spectrum do frequency spectrum square processing, be converted into the energy of spectral line, by the frequency f to sampled components _ieliminate secondary lobe stack power and disturb three spectral line energy phase Calais at place, and interpolation is tried to achieve the amplitude A of signal _iand phase value

2. the harmonic measuring method based on spectral line energy interpolation according to claim 1, is characterized in that: (n Δ t) for the sampled value g of step (2) to step (1) _naccording to 10 cycle windowings of IEC standard regulation, in the time that fundamental frequency is synchronous, add the rectangular window of 10 cycles, when asynchronous, add the Hanning window of 10 cycles, in the time of sample window length N > > 1, the expression formula of corresponding window spectral function is as follows:

Rectangular window is,

$W_R\left(\mathrm{\&theta;}\right)=e^{-j\frac{N-1}{N}\mathrm{\&pi;\&theta;}}\frac{\sin \left(\mathrm{\&pi;\&theta;}\right)}{\mathrm{\&pi;\&theta;}}---\left(3\right)$

Hanning window is,

$W_H\left(\mathrm{\&theta;}\right)=e^{-j\frac{N-1}{N}\mathrm{\&pi;\&theta;}}\frac{\sin \left(\mathrm{\&pi;\&theta;}\right)}{2\mathrm{\&pi;\&theta;}(1-{\mathrm{\&theta;}}^2)}---\left(4\right).$

3. the harmonic measuring method based on spectral line energy interpolation according to claim 1, is characterized in that: step (3) takes advantage of rotatable phase factor treatment to obtain new frequency spectrum frequency spectrum G (k) method be,

(1) the frequency spectrum G (k) formula (2) being represented is converted to formula (5),

Wherein, in the phase factor of frequency spectrum G (k) component, contain two, it changes along with the difference of position of spectral line, when the increase impact of k value increases;

(2) be multiplied by the rotatable phase factor change with the variation of position of spectral line k with the phase value of offsetting in formula (5), take advantage of the rotatable phase factor to be substitution formula (5) obtains new frequency spectrum

(3) by the frequency values β of unit in formula (6) _iwrite as the form of formula (7),

${\mathrm{\&beta;}}_i=k_i+{\&PartialD;}_i---\left(7\right)$

Wherein, k _i, for the frequency f of corresponding sampled components _imaximum spectral line sequence number and frequency offseting value, $-0.5<{\&PartialD;}_i\&le;0.5,$ New frequency spectrum be expressed as,

Be,

Wherein, for taking advantage of after the rotatable phase factor on frequency spectrum all the other components to sampled components frequency f _isecondary lobe disturb superposition value.

4. the harmonic measuring method based on spectral line energy interpolation according to claim 1, is characterized in that: step (4), and by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and asks for corresponding frequency offseting value obtain the frequency f of sampled components _imethod be,

(1) according to formula (9), by new frequency spectrum adjacent spectral line is added to eliminate the stack of part secondary lobe and leaks, and makes Δ (k _i)+Δ (k _i+ 1) ≈ 0, defining ratio factor-alpha is formula (10),

$\mathrm{\&alpha;}=\frac{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i-1)|}{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}\&ap;\frac{\left|W(-{\&PartialD;}_i)\right|+\left|W(-1-{\&PartialD;}_i)\right|}{\left|W(-{\&PartialD;}_i)\right|+\left|W(1-{\&PartialD;}_i)\right|}---\left(10\right);$

(2), for rectangular window, have according to formula (3) formula (10) abbreviation is,

${\mathrm{\&alpha;}}_R\&ap;\frac{1-{\&PartialD;}_i}{1+{\&PartialD;}_i}---\left(11\right)$

Wherein, α _rfor ratio factor-alpha corresponding to rectangular window;

(3), for Hanning window, have according to formula (4) formula (10) abbreviation is,

${\mathrm{\&alpha;}}_H\&ap;\frac{2-{\&PartialD;}_i}{2+{\&PartialD;}_i}---\left(12\right)$

Wherein, α _hfor ratio factor-alpha corresponding to Hanning window;

(4) according to formula (13), the anti-frequency offseting value that solves

${\&PartialD;}_i=c_w\frac{\left|\stackrel{\&OverBar;}{G}(k_i+1)\right|-\left|\stackrel{\&OverBar;}{G}(k_i-1)\right|}{|\stackrel{\&OverBar;}{G}(k_i-1)+2\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}---\left(13\right)$

Wherein, c _wfor the amplitude coefficient of restitution of corresponding window function, c while adding rectangular window _w=1, c while adding Hanning window _w=2; for corresponding spectral line (k _i-1), k _i, (k _i+ 1) the new spectrum value of locating;

(5) according to formula (14), the frequency f of calculating sampling component _ifor,

$f_i=(k_i+{\&PartialD;}_i)\mathrm{\&Delta;f}={\mathrm{\&beta;}}_i\mathrm{\&Delta;f}---\left(14\right).$

5. the harmonic measuring method based on spectral line energy interpolation according to claim 1, is characterized in that: step (5), interpolation is tried to achieve the amplitude A of signal _iand phase value method be,

(1) according to Parseval's theorem, utilize the spectrum value corresponding to three spectral lines at respective components ceiling capacity spectral line place to carry out a square processing and be converted into spectral line energy,

Wherein, in formula (15), (16), (17) for three spectrum values that spectral line is corresponding at respective components ceiling capacity spectral line place;

(2) in order to eliminate the interference of other component side-lobe energy, three spectral line energy of formula (15), (16), (17) are added up to,

(3) according to being multiplied by the sidelobe performance after phase rotation coefficient, do approximate processing, formula (18) abbreviation is,

(4) according to formula (19), obtain adding the amplitude of rectangular window or Hanning window, the expression formula of phase information,

For rectangular window be,

For Hanning window be,

Wherein, $K_e=\frac{4{(1-{\&PartialD;}_i^2)}^2}{(1+{3\&PartialD;}_i^4)\sin c^2\left({\&PartialD;}_i\right)},$ $K_H=\frac{16{(1-{\&PartialD;}_i^2)}^2{(4-{\&PartialD;}_i^2)}^2}{3(2+{\&PartialD;}_i^2)(4+{\&PartialD;}_i^2)\sin c^2\left({\&PartialD;}_i\right)},$ $\sin c\left({\&PartialD;}_i\right)=\sin \left(\mathrm{\&pi;}{\&PartialD;}_i\right)/\left(\mathrm{\&pi;}{\&PartialD;}_i\right);$

(5) according to formula (20) or (21), obtain amplitude A _iand phase value