CN102539892A - Method for obtaining true effective values of AC (alternating current) signals - Google Patents

Method for obtaining true effective values of AC (alternating current) signals Download PDF

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CN102539892A
CN102539892A CN2012100117321A CN201210011732A CN102539892A CN 102539892 A CN102539892 A CN 102539892A CN 2012100117321 A CN2012100117321 A CN 2012100117321A CN 201210011732 A CN201210011732 A CN 201210011732A CN 102539892 A CN102539892 A CN 102539892A
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CN102539892B (en
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庞吉耀
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NANJING PANENG ELECTRIC POWER TECHNOLOGY CO LTD
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Abstract

The invention discloses a method for obtaining true effective values of AC (alternating current) signals, and the method comprises the following steps: (1) carrying out equal interval sampling on signals x(t) at a certain interval of T5 so as to obtain a signal sequence {x(n)}; (2) carrying out squaring on the signal sequence so as to obtain a new sequence {x(n)<2>}; (3) according to the lowest frequency in the signals x(t) and the accuracy requirements on results, determining the stopband cut-off frequency omega5 of a filter and the unit sampling response length N and stopband attenuation alpha5 of the filter according to the following principles: omega5 is less than omega1, omega5 is the stopband cut-off frequency, omega1 is the fundamental frequency of signals, N is greater than T1/T5, T1 is the fundamental period of signals, T5 is the sampling interval, alpha5 is greater than 201g(delta/10), and delta is the relative error of a result value corresponding to a full scale; (4) carrying out filtering on the {x(n)<2>} by using a low-pass filter; and (5) taking the square root of the result obtained in the step (4) so as to obtain the true effective values of the signals. According to the method, after low-pass filtering is carried out on the square sequence {x(n)<2>} of the signals, evolution is carried out on the obtained result so as to obtain the true effective values of the signals.

Description

A kind of acquisition AC signal real effective method
One, technical field
The invention belongs to electric measurement, digital signal processing and power automation field, be used for calculating the real effective of the periodic signal of random waveform.The present invention is applicable to need be to the occasion that harmonic alternating current signal real effective is accurately measured that contains of digital sampling.
Two, background technology
RMS (real effective) is to the measuring basically of AC signal amplitude, can reflect that electric current flows through the thermal effect that conductor produces, and has actual using value.In fact with being defined as: the real effective of AC signal equals in same load, to produce the required DC quantity of equal heat; And mathematical definition is:
Figure 2012100117321100002DEST_PATH_IMAGE004
; And necessary long enough of the time of averaging is so that be operated in required low-limit frequency.In scientific experiment and production reality; Can run into a large amount of non-sinusoidal waves, and the traditional measurement instrument is assumed to the sine wave of standard with measured signal, employing be that the mean value transformation approach comes it is measured; Multiply by correction factor then, it is bigger that this will cause nonsinusoidal signal to measure time error.
The AC signal effective value both measure can by specialized hardware with also can be through the Digital Measuring Technique realization, as long as and Digital Measuring Technique satisfies the Nyquist sampling frequency condition and just can record real effective.Use measuring method mainly to comprise following several types at present:
1. use real effective RMS/DC conversion hardware
Use custom-designed real effective RMS/DC converter to be used as the front end change-over circuit of instrument [1] [2] [3] [4] [5], like the MAX536A of MAXIM company, the AD637 of ADI company etc., through these chips are changed into the effective value that numerical value can obtain signal through ADC.
2. thermocouple mensuration
The principle of work of this mensuration is that the output potential of thermopair becomes quadratic relationship with the electric current that flows through heater strip, obtains current effective value indirectly through the output potential of measuring thermopair.
3. digital sample computing method
The digital sample method is divided into simple numerical integration algorithm [10] [11], quasi-synchronous algorithm [9]And interpolation algorithm [6] [7]These algorithms all are based on the definition of signal real effective; Earlier through adopting synchronously or methods such as synchronously accurate and interpolation reduce signals sampling and leak, confirm signal period by negative to positive rising edge according to two of signals again, pass through the effective value of root mean square method signal calculated at last.
Above-mentioned first method and second method all convert AC value into direct current by special hardware, convert digital signal to through ADC again.Though accuracy is high, bandwidth, complex structure, system cost is high, and the measuring error of the non-linear introducing of switching device will sharply increase along with the reduction of measured signal frequency.The third method utilizes numerical integral method to realize that effective value calculates based on the definition of signal real effective; Through adopt synchronously, method such as synchronously accurate or interpolation reduces sampled leakage; Calculation of complex not only; And complicated at waveform, one-period exists can cause calculating under the situation of a plurality of zero crossings makes mistakes.
To the problems referred to above, the present invention proposes a kind of real effective computing method based on LPF, and is fast simple, and computational accuracy is high.
List of references
Big Zhu of Chen Ren Yue Xi young tiger green for a long time pin-point accuracy effective value design of switching circuit with realize electronic measurement technique in June, 2010
2. Charles Kitchin、Lew CountsRMS-to-DC Application Guide Second Edition 1986 Analog Devices, Inc
3. the prosperous real effective digital watch of Peng Guang and use Yunnan power technology in June, 2009
4. the just big king of Wu builds realization relay Dec calendar year 2001 that subtle discipline is prolonged ultra arbitrary signal waveform real effective detection
5. Gao Rui is based on real effective frequency compensation algorithm and the improved measuring system machinery and electronics 2010 (5) of RMS/DC transformation approach
6. Xu Ken AC signal real effective digital measuring method Central China University of Science and Technology journal in February, 2006
7. Ceng Zehao is surplus has spirit to be permitted spectrum leakage analysis and the analogue system emulation technology 2005.10 of dimension victory based on the interpolation synchronized algorithm
8. Li Yi takes advantage of the sampling computing method to measure alternating voltage effective value error analysis electronic surveying and instrument journal supplementary issue in 2008
9. Wang Shi's note is taken charge of tin just accurate synchronized sampling and the science and technology of the applications in digital measurement of common electronical parameter 2003.11 thereof
10. the expensive sampling method measurement of the big refined Tan Wei Cheng Rong of Lee a kind of of effective value improves one's methods 2006 the 2nd phases of modern electronic technology
11. 1994 the 5th phases of digitized measurement algorithm instrumental technique of Chen Long road low-frequency voltage real effective
Three, summary of the invention
The objective of the invention is; A kind of acquisition AC signal real effective methods and applications are proposed; Be used for calculating the real effective of the periodic signal of random waveform, being specially adapted to need be to the occasion that harmonic alternating current signal real effective accurately calculates that contains of digital sampling.The method that real effective of the present invention obtains contains to digital sampling that harmonic alternating current signal real effective is accurately measured or the application of measurement mechanism in electric system.
Technical scheme of the present invention is: a kind of acquisition AC signal real effective method, realize through following step:
(1). at first through the AC signal that contains harmonic wave is carried out equal interval sampling, picked up signal sequence {
Figure 2012100117321100002DEST_PATH_IMAGE008
} with interval
Figure 2012100117321100002DEST_PATH_IMAGE006
;
(2). burst is carried out square new sequence {
Figure 2012100117321100002DEST_PATH_IMAGE010
} of acquisition;
(3). according to lowest frequency frequency in the signal
Figure DEST_PATH_IMAGE002AA
and accuracy requirement as a result, confirm stopband cutoff frequency
Figure 2012100117321100002DEST_PATH_IMAGE012
, wave filter unit-sample response length
Figure 2012100117321100002DEST_PATH_IMAGE014
and the stopband attenuation of wave filter by following principle:
Figure 2012100117321100002DEST_PATH_IMAGE018
Figure DEST_PATH_IMAGE012A
--stopband cutoff frequency,
Figure 2012100117321100002DEST_PATH_IMAGE020
--signal fundamental frequency
Figure 2012100117321100002DEST_PATH_IMAGE022
Figure 2012100117321100002DEST_PATH_IMAGE024
- Signal fundamental cycle
Figure DEST_PATH_IMAGE006A
--- sampling interval
Figure 2012100117321100002DEST_PATH_IMAGE026
Figure 2012100117321100002DEST_PATH_IMAGE028
- the results of full-scale value corresponding to the relative error
(4). require to make up low-pass filter according to step (3) {
Figure DEST_PATH_IMAGE010A
} carried out filtering;
(5). the result of step (4) root of making even is promptly obtained containing the real effective of the AC signal of harmonic wave.Especially through behind the LPF to the square sequence {
Figure DEST_PATH_IMAGE010AA
} of signal, again to the real effective of evolution picked up signal as a result.
The method that real effective of the present invention obtains contains to digital sampling that harmonic alternating current signal real effective is accurately measured or the application of measurement mechanism in electric system.
The invention has the beneficial effects as follows:
1. digital calculating need not the conversion hardware of special RMS/DC;
2. the error that does not have algorithm in the past to cause because of sampled leakage;
3. do not receive the signal waveform influence, need not detection signal computation period at zero point;
4. the introducing of low-pass filter can reduce the influence of high frequency noise;
5. the bandwidth through the choose reasonable low-pass filter can satisfy the low frequency signal true rms measurement;
6. wave digital lowpass filter has mature theory and tool support, and design and realization are simple;
7. algorithm structure is simple, is fit to the DSP/FPGA accelerating algorithm.
Four, description of drawings
Fig. 1 is a discrete spectrum AC signal synoptic diagram.
Fig. 2 is a discrete spectrum AC signal instantaneous energy synoptic diagram.
Five, concrete implementation
1. the principle of algorithm
According to nyquist sampling theorem; Need the bandwidth of digitized simulating signal must be limited in below half of SF
Figure 2012100117321100002DEST_PATH_IMAGE030
; If measured signal has discrete spectrum (like accompanying drawing 1); Obtain
Figure DEST_PATH_IMAGE002AAA
through behind the preposition simulation low-pass filter; Its highest frequency is
Figure 2012100117321100002DEST_PATH_IMAGE032
, and then following formula is set up
Figure 2012100117321100002DEST_PATH_IMAGE034
(
Figure 2012100117321100002DEST_PATH_IMAGE036
) - sampling interval (1)
Figure 2012100117321100002DEST_PATH_IMAGE040
- signal fundamental frequency (2)
The high reps of
Figure 2012100117321100002DEST_PATH_IMAGE042
expression harmonic wave in the following formula; Function expression rounds downwards, and the fourier expansion that can get
Figure DEST_PATH_IMAGE002AAAA
does
Figure 2012100117321100002DEST_PATH_IMAGE046
（3）
In the following formula;
Figure DEST_PATH_IMAGE020A
is signal first-harmonic angular frequency;
Figure 2012100117321100002DEST_PATH_IMAGE048
is respectively the maximal value of DC component and each harmonic component, and is the initial phase angle of each harmonic component.Squared to formula 3 both sides, have
Figure 2012100117321100002DEST_PATH_IMAGE052
Figure DEST_PATH_IMAGE054
（4）
Make
Figure DEST_PATH_IMAGE058
(5)
Figure DEST_PATH_IMAGE060
Figure DEST_PATH_IMAGE056A
（6）
Then have
Figure DEST_PATH_IMAGE062
（7）
Claiming
Figure DEST_PATH_IMAGE064
is the instantaneous energy of signal
Figure DEST_PATH_IMAGE002AAAAA
; It forms (like accompanying drawing 2) by two parts; Wherein
Figure DEST_PATH_IMAGE066
is the DC component in the signal transient energy, AC portion in the signal transient energy then represented.
According to the definition of signal real effective, the effective value
Figure DEST_PATH_IMAGE070
of signal
Figure DEST_PATH_IMAGE002AAAAAA
is represented as follows:
（8）
And have according to formula 7 and formula 8:
Figure DEST_PATH_IMAGE074
（9）
Guaranteeing that
Figure DEST_PATH_IMAGE068A
cycle numerical integration is 0 in the formula 9 under the synchronized sampling condition.And according to formula 6; Low-limit frequency is the fundamental frequency of signal
Figure DEST_PATH_IMAGE002AAAAAAA
for
Figure DEST_PATH_IMAGE020AA
in ; If utilize the ideal low-pass filter of a stopband cutoff frequency that formula 7 is carried out filtering for
Figure DEST_PATH_IMAGE020AAA
; To obtain the result same behind filtering
Figure DEST_PATH_IMAGE068AAA
component, again the result of the wave filter root of making even promptly got the real effective of signal with formula 9.
This shows, adopt low pass filtering method more superior, need not the condition of synchronized sampling, as long as wave filter is selected the suitable satisfied result that just can obtain than integral method
2. concrete implementation
Can realize acquisition AC signal real effective method of the present invention through following step:
(1). with interval signal
Figure DEST_PATH_IMAGE002AAAAAAAA
is carried out uniformly-spaced continuous sampling, obtain discrete series {
Figure DEST_PATH_IMAGE076
} (hereinafter to be referred as {
Figure DEST_PATH_IMAGE078
});
(2). sequence {
Figure DEST_PATH_IMAGE078A
} is carried out point-to-point multiply each other and obtain sequence { }, and guarantee
Figure DEST_PATH_IMAGE082
;
(3). confirm the stopband cut off band width of low-pass filter according to sampling rate (
Figure DEST_PATH_IMAGE084
) and the minimum frequency component of signal
Figure DEST_PATH_IMAGE002AAAAAAAAA
; Confirm the stopband attenuation of low-pass filter according to signal maximum amplitude and computational accuracy; And designing filter in view of the above, obtain unit-sample response
Figure DEST_PATH_IMAGE086
;
(4). { } carries out digital filtering to sequence
Figure DEST_PATH_IMAGE088
（11）
(5) for the formula 11 that was the result of prescribing signal
Figure DEST_PATH_IMAGE002AAAAAAAAAA
In
Figure DEST_PATH_IMAGE090
RMS moment
3. the low-pass filter parameter is selected
Based on algorithm of the present invention, low-pass filter influences calculated amount and computational accuracy, below some factor must consider:
(1). low-pass filter can adopt
Figure DEST_PATH_IMAGE092
also can adopt
Figure DEST_PATH_IMAGE094
; But
Figure DEST_PATH_IMAGE094A
wave filter has cumulative errors; So must be when using
Figure DEST_PATH_IMAGE094AA
by enough word lengths; And
Figure DEST_PATH_IMAGE092A
do not have cumulative errors, if use fixed-point processor should use
Figure DEST_PATH_IMAGE092AA
as far as possible;
(2). according to formula 9; The sequence of participating in integral mean is at least the one-period of signal; And the middle lowest frequency components of signal
Figure DEST_PATH_IMAGE002AAAAAAAAAAA
is
Figure DEST_PATH_IMAGE020AAAA
in the formula 6; It is corresponding that the cycle is
Figure DEST_PATH_IMAGE024A
(
Figure DEST_PATH_IMAGE096
), so the length
Figure DEST_PATH_IMAGE014A
of the unit-sample response of wave filter
Figure DEST_PATH_IMAGE086A
should satisfy following formula:
Figure DEST_PATH_IMAGE022A
--- sampling interval (12)
Promptly
Figure DEST_PATH_IMAGE014AA
depends on the cycle of lowest frequency components in the signal; And be to guarantee filter effect, the shock response length of filtering generally will be got more than 4 times of signal period.According to formula 6; Lowest frequency components is
Figure DEST_PATH_IMAGE020AAAAA
in
Figure DEST_PATH_IMAGE068AAAA
; Think and guarantee that wave filter has enough decay to
Figure DEST_PATH_IMAGE068AAAAA
, should guarantee the stopband cutoff frequency
Figure DEST_PATH_IMAGE018A
of wave filter;
(3). if establish , have according to formula 7
Figure DEST_PATH_IMAGE100
（13）
Press handle type 7 is rewritten as follows:
Figure DEST_PATH_IMAGE102
（14）
By formula 5, formula 13 and formula 14, definition error remainder is:
Figure DEST_PATH_IMAGE104
（15）
Visible by formula 15; The molecule of error term and denominator are at the same order of magnitude; If will control the full scale error of effective value; Need enough decay be arranged to the error remainder, can be calculated as follows stopband attenuation.
（16）
When satisfying following formula, just resultant error can be controlled, certain surplus should be remained with during actual the realization.According to following formula,, just must the stopband attenuation of low-pass filter be improved an one magnitude if need to improve an one magnitude to computational accuracy.

Claims (5)

1. method that obtains the AC signal real effective is characterized in that step is following:
(1). at first through signal
Figure 400251DEST_PATH_IMAGE001
is carried out equal interval sampling, picked up signal sequence { } with interval
Figure 2012100117321100001DEST_PATH_IMAGE002
;
(2). to the burst square new sequence {
Figure 2012100117321100001DEST_PATH_IMAGE004
} of acquisition;
(3). according to lowest frequency frequency in the signal
Figure 102070DEST_PATH_IMAGE001
and accuracy requirement as a result, confirm stopband cutoff frequency
Figure 646315DEST_PATH_IMAGE005
, wave filter unit-sample response length
Figure 2012100117321100001DEST_PATH_IMAGE006
and the stopband attenuation
Figure 154526DEST_PATH_IMAGE007
of wave filter by following principle:
Figure 2012100117321100001DEST_PATH_IMAGE008
Figure 913051DEST_PATH_IMAGE005
--stopband cutoff frequency, --signal fundamental frequency
Figure 2012100117321100001DEST_PATH_IMAGE010
Figure 2809DEST_PATH_IMAGE011
- Signal fundamental cycle
Figure 2012100117321100001DEST_PATH_IMAGE012
--- sampling interval
Figure 416342DEST_PATH_IMAGE013
Figure 2012100117321100001DEST_PATH_IMAGE014
- The results of full-scale value corresponds to the relative error
(4). require to make up low-pass filter according to step 3 {
Figure 904306DEST_PATH_IMAGE004
} carried out filtering;
(5). the result of step 4 root of making even is promptly obtained the real effective of signal.
2. AC signal real effective computing method according to claim 1; It is characterized in that: behind LPF, again to the real effective of evolution picked up signal as a result to the square sequence { } of signal.
3. AC signal real effective computing method according to claim 1; It is characterized in that:, confirm stopband cutoff frequency
Figure 49744DEST_PATH_IMAGE005
, wave filter unit-sample response length
Figure 2012100117321100001DEST_PATH_IMAGE016
and the stopband attenuation
Figure 762354DEST_PATH_IMAGE017
of wave filter by following principle according to lowest frequency frequency in the signal and accuracy requirement as a result:
Figure 919797DEST_PATH_IMAGE008
--stopband cutoff frequency,
Figure 606398DEST_PATH_IMAGE009
--signal fundamental frequency
Figure 635665DEST_PATH_IMAGE010
Figure 895002DEST_PATH_IMAGE011
- Signal fundamental cycle
Figure 559070DEST_PATH_IMAGE012
--- sampling interval
Figure 111405DEST_PATH_IMAGE013
Figure 920312DEST_PATH_IMAGE014
- The results of full-scale value corresponds to the relative error.
4. AC signal real effective computing method according to claim 1; It is characterized in that: confirm filter stop band cutoff frequency and impulse response length by low-limit frequency in the signal
Figure 481874DEST_PATH_IMAGE015
when low-pass filter makes up, confirm the stopband attenuation of wave filter according to accuracy requirement as a result;
1) fourier expansion of
Figure 62766DEST_PATH_IMAGE015
does
（3）
In the following formula;
Figure 428413DEST_PATH_IMAGE019
is signal first-harmonic angular frequency;
Figure 2012100117321100001DEST_PATH_IMAGE020
is respectively the maximal value of DC component and each harmonic component, and
Figure 602911DEST_PATH_IMAGE021
is the initial phase angle of each harmonic component; Squared to formula (3) both sides, have
（4）
Make
Figure DEST_PATH_IMAGE025
(5)
Figure DEST_PATH_IMAGE027
（6）
Then have
Figure 2012100117321100001DEST_PATH_IMAGE028
（7）
Claiming
Figure 2012100117321100001DEST_PATH_IMAGE029
is the instantaneous energy of signal
Figure 535593DEST_PATH_IMAGE015
; It is made up of two parts; Wherein
Figure 2012100117321100001DEST_PATH_IMAGE030
is the DC component in the signal transient energy,
Figure 109007DEST_PATH_IMAGE031
AC portion in the signal transient energy then represented;
According to the definition of signal real effective, the effective value of signal is represented as follows:
Figure DEST_PATH_IMAGE033
（8）
And have according to formula 7 and formula 8:
Figure 2012100117321100001DEST_PATH_IMAGE034
（9）
Guaranteeing that cycle numerical integration does in the formula 9 under the synchronized sampling condition; Low-limit frequency is the fundamental frequency of signal
Figure 139892DEST_PATH_IMAGE015
for
Figure 809274DEST_PATH_IMAGE009
in
Figure 256720DEST_PATH_IMAGE031
; If utilize the ideal low-pass filter of a stopband cutoff frequency that formula 7 is carried out filtering for
Figure 413617DEST_PATH_IMAGE019
; To obtain equifinality behind filtering
Figure 855093DEST_PATH_IMAGE031
component, again the result of the wave filter root of making even promptly got the real effective of signal;
2) sequence {
Figure DEST_PATH_IMAGE035
} is carried out point-to-point and multiply each other and obtain sequence {
Figure 2012100117321100001DEST_PATH_IMAGE036
}, and guarantee
Figure DEST_PATH_IMAGE037
;
3) confirm the stopband cut off band width of low-pass filter according to sampling rate (
Figure DEST_PATH_IMAGE039
) and the minimum frequency component of signal ; Confirm the stopband attenuation of low-pass filter according to signal maximum amplitude and computational accuracy; And designing filter in view of the above, obtain unit-sample response
Figure 2012100117321100001DEST_PATH_IMAGE040
;
4) sequence {
Figure 514406DEST_PATH_IMAGE036
} is carried out digital filtering
Figure DEST_PATH_IMAGE041
（11）
5) of the formula (11) taking the square root of the result of that get the signal
Figure 324362DEST_PATH_IMAGE015
In RMS moment
The unit sample response of the filter
Figure DEST_PATH_IMAGE043
length
Figure 2012100117321100001DEST_PATH_IMAGE044
should satisfy the following formula:
Figure 213206DEST_PATH_IMAGE010
--- sampling interval (12)
Promptly
Figure 621578DEST_PATH_IMAGE006
depends on the cycle of lowest frequency components in the signal; And be to guarantee filter effect, the shock response length of filtering generally will be got more than 4 times of signal period; For lowest frequency components in the filtered signal
Figure 293999DEST_PATH_IMAGE015
, should guarantee the stopband cutoff frequency
Figure 2012100117321100001DEST_PATH_IMAGE046
of wave filter;
By formula (7); If wave filter is to obtaining signal
Figure 2012100117321100001DEST_PATH_IMAGE048
after the decay that AC compounent produces
Figure DEST_PATH_IMAGE047
, instantaneous energy is expressed as:
Figure 617938DEST_PATH_IMAGE049
（13）
Corresponding with it real effective is expressed as:
Figure 2012100117321100001DEST_PATH_IMAGE050
（14）
Error when employing
Figure 880817DEST_PATH_IMAGE051
substitutes
Figure 2012100117321100001DEST_PATH_IMAGE052
depends primarily on
Figure 98040DEST_PATH_IMAGE053
; And
Figure 69538DEST_PATH_IMAGE031
is identical with the order of ; If will improve an one magnitude to computational accuracy, the stopband attenuation of low-pass filter is improved an one magnitude.
5. the method that obtains of the described real effective of claim 1-4 contains to digital sampling that harmonic alternating current signal real effective is accurately measured or the application of measurement mechanism in electric system.
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CN105548667A (en) * 2016-03-07 2016-05-04 温州大学 Alternating current signal effective value measuring device
CN105954569A (en) * 2016-06-07 2016-09-21 浙江腾腾电气有限公司 Voltage effectiveness value sampling method applied to alternating-current voltage-stabilizing power supply
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CN108508255A (en) * 2017-12-25 2018-09-07 南京丰道电力科技有限公司 Industrial frequency AC signal measurement method based on fixed sample rate
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CN117147945A (en) * 2023-07-20 2023-12-01 威胜能源技术股份有限公司 Estimation method for effective value of embedded acquisition alternating current signal

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CN114047702A (en) * 2021-11-24 2022-02-15 中国核动力研究设计院 Self-adaptive extraction method and system for effective value of rotating current of control rod drive wire
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