CN101950012A - Field tester for alternating current (AC) energy meter - Google Patents

Abstract

The invention provides a field tester for an alternating current (AC) energy meter, which comprises an input unit, an analog-digital conversion unit, a windowing treatment unit, an amplitude calculation unit, a phase computation unit and an output unit, wherein the input unit is used for obtaining an analog grid signal of alternating current (AC); the analog-digital conversion unit is connected to the input unit, and used for sampling the analog grid signal of the alternating current (AC) and conversing the analog grid signal into a digital grid signal; the windowing treatment unit is connected to the analog-digital conversion unit, and used for carrying out haiming windowing fast Fourier transform (FFT) on the digital grid signal so as to obtain a sampling sequence; the amplitude calculation unit is connected to the windowing treatment unit, and used for calculating the amplitude of the alternating current (AC) according to the sampling sequence and a first preset algorithm; the phase computation unit is connected to the windowing treatment unit, and used for calculating the phase of the alternating current (AC) according to the sampling sequence and a second preset algorithm; and the output unit is connected to the amplitude calculation unit and the phase computation unit, and used for outputting the calculated amplitude and phase. The amplitude and the phase of the alternating current (AC) can be calculated more accurately by using the field tester for the alternating current (AC) energy meter of the invention.

Description

The AC energy meter on-spot tester

Technical field

The present invention relates to a kind of AC energy meter on-spot tester.

Background technology

At present, in correlation technique, use AC energy meter on-spot tester (hereinafter to be referred as on-spot tester) when alternating current is measured, usually adopt harmonic analysis method that power factor of electric network is measured in real time, comprise and adopt discrete Fourier transform (DFT) (Discrete FourierTransform, abbreviate DFT as) or fast fourier transform (Fast Fourier Transform abbreviates FFT as) algorithm measurement and calculate the amplitude and the phase place of power network signal.

But, the frequency of electric system is not constant all the time, but near specified power frequency, fluctuate, can't guarantee that sample frequency is the integral multiple of actual operating frequency, be difficult to realize electric power signal being carried out complete synchronized sampling, in the actual samples process with on-spot tester, normally non-synchronous sampling or accurate synchronized sampling, thereby having fence effect and spectrum leakage phenomenon, frequency, amplitude and phase place that the on-spot tester meter is calculated are inaccurate, can not satisfy the actual measurement accuracy requirement.

As seen, in correlation technique, exist when using on-spot tester that ac signal is carried out the non-synchronous sampling measurement, can't calculate the amplitude of alternating current and the problem of phase place comparatively exactly.

Summary of the invention

In view of this, the present invention proposes a kind of AC energy meter on-spot tester, in order to solve the problems referred to above that exist in the correlation technique.

According to an aspect of the present invention, provide a kind of AC energy meter on-spot tester.

AC energy meter on-spot tester according to the present invention comprises:

Input block is used to obtain the simulation power network signal of alternating current;

AD conversion unit is connected to input block, is used for the simulation power network signal of alternating current is sampled, and will simulate the electrical network conversion of signals and become digital power network signal;

The windowing process unit is connected to AD conversion unit, is used for digital power network signal is added hamming window fast fourier transform, obtains sample sequence;

The amplitude computing unit is connected to the windowing process unit, is used for according to the amplitude of sample sequence with the first algorithm computation alternating current of presetting;

Phase calculation unit is connected to the windowing process unit, is used for according to the phase place of sample sequence with the second algorithm computation alternating current of presetting;

Output unit is connected to amplitude computing unit and phase calculation unit, is used to export the amplitude and the phase place that calculate.

Preferably, above-mentioned simulation electrical network signal sampling to alternating current comprises: with sample frequency f _sSimulation power network signal x (t) to single-frequency samples, the digital power network signal x (n) that obtains dispersing, and wherein, the frequency of x (t) is f ₀, amplitude is A, initial phase is θ,

N is a natural number.

Preferably, above-mentionedly digital power network signal is added hamming window fast fourier transform handle and to comprise: according to algorithm X (f) x (n) is added hamming window fast fourier transform, obtain the X as a result (f) after the conversion, wherein,

W (n) is the hamming window function, and W (n)=0.54-0.46cos (2 π n/N), the continuous frequency spectrum of W (n) are W (2 π f), n=0, and 1.。。，N-1)；

Ignore negative frequency-f ₀Place's summit secondary lobe influence frequently is at positive frequency f ₀Near continuous frequency spectrum function can be expressed as

This formula is carried out discrete sampling, can obtain the expression formula of discrete Fourier transform (DFT):

Wherein, discrete frequency is spaced apart Δ f=fs/N, and N is a data truncation length.

Preferably, above-mentioned first algorithm comprises:

f ₀=k ₀Δ f, k ₁, k ₂Be k ₀About spectral line, A ₁, A ₂It is the amplitude of left and right sides spectral line.

Preferably, above-mentioned second algorithm comprises:

$\mathrm{\&theta;}=\arg \left[X({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HSA00000042022800012.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;\mathrm{\&Delta;f})\right]+\frac{\mathrm{\&pi;}}{2}-\arg \left[W(2\mathrm{\&pi;}(1-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HSA00000042022800012.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+k_1)/N)\right].$

By means of technical scheme provided by the invention, can calculate the amplitude and the phase place of alternating current more exactly.

Other features and advantages of the present invention will be set forth in the following description, and, partly from instructions, become apparent, perhaps understand by implementing the present invention.Purpose of the present invention and other advantages can realize and obtain by specifically noted structure in the instructions of being write, claims and accompanying drawing.

Description of drawings

Accompanying drawing is used to provide further understanding of the present invention, and constitutes the part of instructions, is used from explanation the present invention with embodiments of the invention one, is not construed as limiting the invention.In the accompanying drawings:

Fig. 1 is the structured flowchart according to the AC energy meter on-spot tester of the embodiment of the invention;

Fig. 2 is the simulate signal illustraton of model of the embodiment of the invention.

Embodiment

Below in conjunction with accompanying drawing embodiments of the invention are described, should be appreciated that embodiment described herein only is used for description and interpretation the present invention, and be not used in qualification the present invention.

AC energy meter on-spot tester provided by the invention comprises: input block 1 is used to obtain the simulation power network signal of alternating current; AD conversion unit 2 is connected to input block 1, is used for the simulation power network signal of alternating current is sampled, and will simulate the electrical network conversion of signals and become digital power network signal; Windowing process unit 3 is connected to AD conversion unit 2, is used for digital power network signal is added hamming window fast fourier transform, obtains sample sequence; Amplitude computing unit 4 is connected to windowing process unit 3, is used for according to the amplitude of sample sequence with the first algorithm computation alternating current of presetting; Phase calculation unit 5 is connected to windowing process unit 3, is used for according to the phase place of sample sequence with the second algorithm computation alternating current of presetting; Output unit 6 is connected to amplitude computing unit 4 and phase calculation unit 5, is used to export the amplitude and the phase place that calculate.Below the present invention is described in detail.

In correlation technique, when power factor of electric network being measured in real time, adopt DFT or fft algorithm usually with harmonic analysis method.Yet the frequency of electric system is not constant all the time, but near specified power frequency, fluctuate, can't guarantee that sample frequency is the integral multiple of actual operating frequency, complete synchronized sampling to electric power signal is difficult to realize, the actual samples process is non-synchronous sampling or accurate synchronized sampling normally, thereby have fence effect and spectrum leakage phenomenon, and make the frequency, amplitude and the phase place that calculate inaccurate, can not satisfy the accuracy requirement in the actual measurement.

Adopt the way of windowed interpolation to revise fft algorithm, can effectively suppress the error that causes by non-synchronous sampling.In the process of specific implementation, can adopt dsp chip to realize windowing process unit 3, amplitude computing unit 4, phase calculation unit 5.

1, FFT harmonic analysis method

If power network signal is a periodic signal, be expressed as follows formula

F wherein _i, A _i, Be respectively frequency, the amplitude of i subharmonic, phase place; M is higher harmonics number of times.

With sample frequency fs with formula (1) discretize calling sequence x (n)

Wherein Ts is 1/f _sBe the sampling period.

Formula according to the DFT conversion

$X\left(k\right)=\mathrm{DFT}\left[x\left(n\right)\right]=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left(n\right)W_N^{\mathrm{<figure-callout\; id="0"\; label="nk"\; filenames="HSA00000042022800012.png"\; state="\{\{state\}\}">nk</figure-callout>}}$ 0≤n≤N-1 signal fundamental voltage amplitude:

$X_k=\frac{2\left|X\left(k\right)\right|}{N}$ (k＝1)

2, windowed interpolation fft analysis method

(1) selection of window function

Because the existence of truncation effect, the phenomenon of spectral leakage become inevitable, yet use suitable window function can effectively suppress this phenomenon.Window function commonly used has Cosine Window, triangular window, peaceful (Hanning) window of the Chinese, hamming (Hamming) window, Blackman window, Gaussian window etc.The Fourier transform of weighting windows function can reduce the secondary lobe influence of signal spectrum greatly, blanketing frequency is leaked well, but the windowing Fourier transform is when suppressing the secondary lobe of signal spectrum, the amplitude of main lobe is descended, particularly main lobe width increases, cause spectral resolution to descend, this is the shortcoming that the windowing Fourier transform can't overcome.Selecting the principle of window function is that its main lobe of requirement is narrow, secondary lobe is little, and the two is taken into account.Up to the present in the window function that is proposed, rectangular window has the narrowest main lobe width, but has maximum side lobe peak, and the hamming window has less secondary lobe and the relative moderate main lobe of size.Consider each window function performance, because the hamming window can be with 99.963% concentration of energy in main lobe, main lobe is wide to be 8 π/N, and the secondary lobe amplitude is less, and side lobe peak is less than 1% of the main lobe peak value.So the hamming window is the selection preferably of electrical network analysis.

On time domain, add the hamming window and in fact be exactly that to make the starting point of periodic signal and the phase place of terminating point be 0, overcome the sampled signal phase place that causes owing to frequency jitter in top and the discontinuous situation of terminal.

It is noted that during windowed function after the sequence windowing that when carrying out FFT, deviation will appear in the amplitude of each harmonic, this mainly be because windowing be to signal does not wait weighting, cause the analysis result variation.Table 1 has been listed corresponding different amplitude correction factor 1/ α of different window functions.

Table 1

Window function	Expression formula	Correction factor	1/ α
				Hanning window	W(n)＝0.5-0.5cos(2 πn/N)	2
The hamming window	W(n)＝0.54-0.46cos(2 πn/N)	1.852
			Blacknam	W(n)＝0.42-0.5cos(2 πn/N)+	2.381
	0.08cos(4 πn/N)

Be doing after the FFT conversion after the windowing, the signal amplitude formula is calculated as

$X_k=\frac{2\left|X\left(k\right)\right|}{N}\&CenterDot;\frac{1}{\mathrm{\&alpha;}}---\left(3\right)$

Add different window functions and different requirements is also arranged adding choosing of window width.Do not produce than mistake for the main lobe that makes two adjacent harmonic components is not superimposed, then need frequency interval between these two harmonic components greater than this two and half main lobe widths sum, promptly greater than the window main lobe width.I.e. 2 π f ₀T _s＞Q2 π/N

F in the formula ₀Side frequency poor equals fundamental frequency on the numerical value; Q is a main lobe and the ratio of secondary lobe amplitude.Be not difficult to release: adding window width is sampling period l＞Q.

The Q value of hamming window is 4, and according to the Nyquist law, one-period sampling number＞2f (f ≈ 50Hz), FFT requirement sampling number are 2 power, so one-period is sampled as minimum 128 points.For improving frequency resolution, take all factors into consideration the sampling of this problem 4 cycles, totally 512 point data.

(2) value is inserted computing

When sample frequency is not the integral multiple (being that signal is non-integer-period sampled) of actual operating frequency, even if signal only contains single-frequency, DFT can not obtain the accurate parameter of signal, and this phenomenon is called fence effect usually, and interpolation algorithm can be eliminated the error that fence effect causes.

We establish a frequency is f ₀, amplitude is A, and initial phase is the simple signal x (t) of θ, and having passed through sample frequency is f _sDiscrete signal after the discretize is:

x(n)＝Asin(2πf ₀n/f _s+θ) (4)

The time domain form of hamming window is:

$w\left(n\right)=0.54-0.46\cos \left(\frac{2\mathrm{\&pi;n}}{N}\right)---\left(5\right)$

0≤n in the formula＜N-1;

Its continuous frequency spectrum is:

$W\left(2\mathrm{\&pi;f}\right)=0.54W_R\left(2\mathrm{\&pi;f}\right)$

$+0.23[W_R(2\mathrm{\&pi;f}-\frac{2\mathrm{\&pi;}}{N})+W_R(2\mathrm{\&pi;f}+\frac{2\mathrm{\&pi;}}{N})]---\left(6\right)$

W wherein _R(2 π f) is the continuous frequency spectrum of rectangular window.

The continuous Fourier transform of this signal is after the windowing:

$X\left(f\right)=\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}x\left(n\right)\&CenterDot;w\left(n\right)\&CenterDot;e^{-j2\mathrm{\&pi;fn}}=$

$\frac{A}{2j}[e^{\mathrm{j\&theta;}}W\left(\frac{2\mathrm{\&pi;}(f-f_0)}{f_s}\right)-e^{-\mathrm{j\&theta;}}W\left(\frac{2\mathrm{\&pi;}(f+f_0)}{f_s}\right)]---\left(7\right)$

If ignore the secondary lobe influence at peak frequently of negative frequency place, then the Fourier transform expression formula is:

$X\left(f\right)=\frac{A}{2j}{e}^{\mathrm{j\&theta;}}W\left(\frac{2\mathrm{\&pi;}(f-f_0)}{f_s}\right)---\left(8\right)$

This formula is carried out discretize, is signal and adds hamming window Fourier transform expression formula afterwards:

$X(k\&CenterDot;\mathrm{\&Delta;f})=\frac{A}{2j}{e}^{\mathrm{j\&theta;}}W\left(\frac{2\mathrm{\&pi;}(k\&CenterDot;\mathrm{\&Delta;f}-f_0)}{f_s}\right)---\left(9\right)$

Formula medium frequency variable f discrete frequency interval delta f=f _s/ N normalization, N is a data truncation length.

In frequency f ₀=k ₀Δ f is a peak value, but owing to be difficult to reach sample-synchronous, generally is not integer.Be located at k ₀About spectral line be respectively k ₁And k ₂The bar spectral line, they are near maximum and inferior maximum spectral lines of the amplitude peak point.Obvious k ₁≤ k ₀≤ k ₂=k ₁+ 1, the amplitude of establishing these two spectral line correspondences is respectively Y ₁=| X (k ₁Δ f) | with Y ₂=| X (k ₂Δ f) |, introduce parameter δ=k ₀-k ₁

The numerical range of δ is in [0,1].Introduce parameter γ:

$\mathrm{\&gamma;}=\frac{Y_1}{Y_2}=\frac{\left|W\right[2\mathrm{\&pi;}(-\mathrm{\&delta;})/N\left]\right|}{\left|W\right[2\mathrm{\&pi;}(1-\mathrm{\&delta;})/N\left]\right|}---\left(10\right)$

Y ₁With Y ₂Value can obtain by fft algorithm, amplitude just can determine that than γ key point is to obtain δ.And δ is exactly the function of γ, and for given window function, formula (10) can become by abbreviation

γ＝f(δ)

Its inverse function is

δ＝f ^-1(γ)

Calculate δ=f ^-1(γ) method that adopts polynomial expression to approach.Since when window function w (n) is real coefficient, its frequency response | W (2 π f) | be even symmetry.So function f (δ) and inverse function f thereof ^-1(γ) all be odd function.Approach odd function f when adopting Chebyshev polynomials ^-1In the time of (γ), it is 0 that institute asks polynomial expression even item coefficient, and its polynomial expression approaches available following formula and expresses:

δ＝a ₁γ+a ₃γ ³+...+a _2m+1γ ^2m+1

(6) formula substitution (10) formula can be solved:

δ＝1.21874943?γ+0.13349531?γ ³

+0.05301420?γ ⁵+0.03656014?γ ⁷ (11)

When revising amplitude, in order to overcome the shortcoming that unimodal spectral line correction algorithm is vulnerable to spectral leakage and noise, the information of inferior intense line also can be used to revise amplitude, promptly adopts the weighted mean of two spectral lines to revise amplitude

$A=\frac{A_1\left|W\right[2\mathrm{\&pi;}(-\mathrm{\&delta;})/N\left]\right|+A_2\left|W\right[2\mathrm{\&pi;}(1-\mathrm{\&delta;})/N\left]\right|}{\left|W\right[2\mathrm{\&pi;}(-\mathrm{\&delta;})/N\left]\right|+\left|W\right[2\mathrm{\&pi;}(1-\mathrm{\&delta;})/N\left]\right|}$

$=\frac{2({\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000042022800012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1+Y_2)}{\left|W\right[2\mathrm{\&pi;}(-\mathrm{\&delta;})/N\left]\right|+\left|W\right[2\mathrm{\&pi;}(1-\mathrm{\&delta;})/N\left]\right|}---\left(12\right)$

The weight that two spectral lines are adopted is directly proportional with their amplitudes separately.The correction formula of phase angle and frequency is:

$\mathrm{\&theta;}=\arg \left[X({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HSA00000042022800012.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;\mathrm{\&Delta;f})\right]+\frac{\mathrm{\&pi;}}{2}-\arg [W(2\mathrm{\&pi;}(1-\mathrm{\&delta;})/N]---\left(13\right)$

f ₀＝(k ₁+δ)·Δf (14)

This algorithm is known as bimodal spectral line interpolation algorithm.

3, simulation result

For feasibility and the validity of verifying window function and interpolation algorithm, and the correctness of optimized Algorithm, we have set up signal model as shown in Figure 2, verify respectively.

The expression formula of signal is as follows:

$x\left(n\right)=1.0\cos \left(2\mathrm{\&pi;}\frac{f_1}{f_s}n\right)+0.01\cos (2\mathrm{\&pi;}\frac{2f_1}{f_s}n+10)+0.3$

$\cos (2\mathrm{\&pi;}\frac{3f_1}{f_s}n+20)+0.01\cos (2\mathrm{\&pi;}\frac{4f_1}{f_s}n+30)+0.2$

$\cos (2\mathrm{\&pi;}\frac{5f_1}{f_s}n+40)+0.15\cos (2\mathrm{\&pi;}\frac{7f_1}{f_s}n+60)+0.1$

$\cos (2\mathrm{\&pi;}\frac{9f_1}{f_s}n+80)---\left(20\right)$

F in the formula ₁Be 50.1Hz, sample frequency 6400Hz, the data length N of truncated signal are 512 points.Emulation respectively to not windowing, add the comparison of revising amplitude and phase place after hamming window, the windowing, and provided the algorithm degree of accuracy relatively.See Table 3, table 4, table 3 is not windowing, add frequency of amendment and amplitude after hamming window, the windowing relatively reach the error comparison sheet, table 4 is revised phase place and error comparison sheet for not windowing, after adding hamming window, windowing.

Table 3

Compare item	FFT	Windowing FFT	Interpolation FFT
				f	48.7047	50.1200	50.0100
A1	0.9821	0.9981	1.0010
				A2	0.0084	0.0109	0.0104
A3	0.2844	0.2979	0.3003
				A4	0.0067	0.0098	0.0101
A5	0.1875	0.1998	0.2002
				A7	0.1292	0.1512	0.1504
A9	0.0894	0.1031	0.1001
				Error ratio is item	FFT	Windowing FFT	Interpolation FFT

f	1.68％	0.04％	0.02％
				A1	1.79％	0.19％	0.10％
A2	16.2％	0.90％	0.40％
				A3	5.21％	0.71％	0.01％
A4	33.2％	0.20％	0.10％
				A5	6.25％	0.02％	0.02％
A7	13.8％	0.80％	0.27％
				A9	10.6％	0.31％	0.01％

Table 4

Compare item	FFT	Windowing FFT	Interpolation FFT
				φ 1＝0	11.012	8.34	0.00004
φ 2＝10	73.520	19.450	10.717
				φ 3＝20	-48.811	27.343	20.030
φ 4＝30	99.951	43.126	30.042
				φ 5＝40	120.762	21.009	40.024
φ 7＝60	153.421	65.480	60.002
				φ 9＝80	209.725	104.451	80.009
Error ratio is item	FFT	Windowing FFT	Interpolation FFT
				φ 1＝0	11.0％	8.344％	0.0004％
φ 2＝10	635％	9.45％	0.71％

φ 3＝20	144％	3.61％	0.15％
				φ 4＝30	133％	43.3％	0.13％
φ
	5＝40	200％	47.5％	0.06％
φ 7＝60					155％	8.3％	0.002％
	φ 9＝80	161％	30.1％	0.01％

The present invention can adopt following steps to realize when specific implementation.

Step 1: by high-precision high-speed AD signal is gathered among the DSP in real time, be kept at designated memory space among the DSP with the form of array;

Step 2: bring this array into hamming window formula, carry out the FFT conversion;

Step 3: from FFT result of calculation, draw respectively suc as formula (10) Y ₁With Y ₂Value (spectral line amplitude);

Step 4: adopt polynomial approximation method, calculate correction factor, and to amplitude, phase place and frequency are revised respectively.

The above is the preferred embodiments of the present invention only, is not limited to the present invention, and for a person skilled in the art, the present invention can have various changes and variation.Within the spirit and principles in the present invention all, any modification of being done, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (5)

1. an AC energy meter on-spot tester is characterized in that, comprising:

Input block is used to obtain the simulation power network signal of alternating current;

AD conversion unit is connected to described input block, is used for the described simulation power network signal of described alternating current is sampled, and described simulation electrical network conversion of signals is become digital power network signal;

The windowing process unit is connected to described AD conversion unit, is used for described digital power network signal is added hamming window fast fourier transform, obtains sample sequence;

The amplitude computing unit is connected to described several windowing processes unit, is used for according to the amplitude of described sample sequence with the described alternating current of presetting of first algorithm computation;

Phase calculation unit is connected to described windowing process unit, is used for according to the phase place of described sample sequence with the described alternating current of presetting of second algorithm computation;

Output unit is connected to described amplitude computing unit and described phase calculation unit, is used to export the described amplitude and the described phase place that calculate.

2. AC energy meter on-spot tester according to claim 1 is characterized in that,

Described simulation electrical network signal sampling to described alternating current comprises:

With sample frequency f _sDescribed simulation power network signal x (t) to single-frequency samples, the described digital power network signal x (n) that obtains dispersing, and wherein, the frequency of described x (t) is f ₀, amplitude is A, initial phase is θ,

N is a natural number.

3. AC energy meter on-spot tester according to claim 2 is characterized in that,

Describedly digital power network signal is added hamming window fast fourier transform handle and to comprise: according to algorithm X (f) x (n) is added hamming window fast fourier transform, obtain the X as a result (f) after the described conversion, wherein,

W (n) is the hamming window function, and W (n)=0.54-0.46cos (2 π n/N), the continuous frequency spectrum of W (n) are W (2 π f), n=0, and 1.。。，N-1)；

Ignore negative frequency-f ₀Place's summit secondary lobe influence frequently is at positive frequency f ₀Near continuous frequency spectrum function can be expressed as This formula is carried out discrete sampling, can obtain the expression formula of discrete Fourier transform (DFT): Wherein, discrete frequency is spaced apart Δ f=f _s/ N, N are data truncation length.

4. AC energy meter on-spot tester according to claim 3 is characterized in that,

Described first algorithm computation comprises:

$A=\frac{A_1\left|W\right[2\mathrm{\&pi;}(k_1-k_0)/N\left]\right|+A_2\left|W\right[2\mathrm{\&pi;}(1-k_0+k_1)/N\left]\right|}{\left|W\right[2\mathrm{\&pi;}(k_1-k_0)/N]|+\left|W\right[2\mathrm{\&pi;}(1-k_0+k_1)/N\left]\right|},$ f ₀=k ₀Δ f, k ₁, k ₂Be k ₀About spectral line, A ₁, A ₂It is respectively the amplitude of described left and right sides spectral line.

5. AC energy meter on-spot tester according to claim 4 is characterized in that,

Described second algorithm computation comprises:

$\mathrm{\&theta;}=\arg \left[X(k_1\&CenterDot;\mathrm{\&Delta;f})\right]+\frac{\mathrm{\&pi;}}{2}-\arg \left[W(2\mathrm{\&pi;}(1-k_0+k_1)/N)\right].$

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