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CN101915872B - Nonlinear-load electric energy measuring method - Google Patents

Nonlinear-load electric energy measuring method Download PDF

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CN101915872B
CN101915872B CN2010102732345A CN201010273234A CN101915872B CN 101915872 B CN101915872 B CN 101915872B CN 2010102732345 A CN2010102732345 A CN 2010102732345A CN 201010273234 A CN201010273234 A CN 201010273234A CN 101915872 B CN101915872 B CN 101915872B
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value
electric weight
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CN101915872A (en
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易龙强
宋慧娜
陈金玲
罗孝龙
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Wasion Group Co Ltd
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Abstract

The invention discloses a nonlinear-load measuring method having a high integral algebraic accuracy grade. Aiming at the traditional dot product measuring algorithm, the invention points out the algorithm accuracy deficiency under the condition of calculating nonlinear loads based on the analysis of algorithm characteristics, thereby providing a scheme to improve the accuracy and the adaptability of an electric energy meter on the modern nonlinear-load electric energy measurement by using a complex Newton-Cotes integral algorithm having a high-order measuring algebraic accuracy grade. Based on the theoretical analysis of the algorithm and the real-time operation characteristics of the current measuring system, the invention designs and provides a method for the real-time operation of the algorithm. Simulation and experiment results prove that the invention can effectively improve the accuracy of an electric meter in the electric energy measuring field, thereby improving the adaptability of the electric meter on wider nonlinear-load measurement.

Description

Nonlinear-load electric energy measuring method
Technical field
The invention belongs to electric system electric energy metrical field.
Background technology
Electric energy metrical is the basic basis that carries out economic balance between electricity power enterprise, power transmission and transformation enterprise and the electricity consumption client, and its accuracy directly influences three's interests.In the process of modern chemical industry industry develop rapidly, electric system has inserted a large amount of nonlinear-loads, and consequent a large amount of harmonic currents, harmonic voltage have not only had a strong impact on power transmission efficiency, and the accuracy of electric energy metrical produced seriously influences.
For effectively solving the influence of mains by harmonics to the electric energy metrical accuracy, each experts and scholars has launched the research to the nonlinear load electric energy metrical one after another.At present, industry generally solves the problems such as accuracy, rationality of nonlinear-load metering through research part throttle characteristics, electrical network modeling and based on the methods such as frequency analysis of FFT.
At present, industry generally adopts dot-product operation to calculate to be had, capacity of idle power, has, reactive power and parameters such as voltage, current effective value.Wherein concrete active energy computing formula is as follows:
Figure 759258DEST_PATH_IMAGE001
(1)
Figure 863350DEST_PATH_IMAGE002
is instantaneous power in the formula;
Figure 580770DEST_PATH_IMAGE003
is electric flux in the signal period;
Figure 162930DEST_PATH_IMAGE004
is maximum sub-range length; is the signal period, and
Figure 924398DEST_PATH_IMAGE006
is the signal sampling time interval.It is thus clear that dot-product operation directly prolongs the basic definition formula of having used integral operation.But in calculating process, how many formulas need count to participate in calculating could be satisfied the accuracy of calculating, and formula does not provide guidance.So, when being input as standard pure sinusoid signal, the accuracy of some integration method is different under the unlike signal sampling rate.
Be calculated as example with active energy; If input voltage, current signal are:
Figure 191432DEST_PATH_IMAGE007
,
Figure 328015DEST_PATH_IMAGE008
; In the formula
Figure 186774DEST_PATH_IMAGE009
;
Figure 117821DEST_PATH_IMAGE005
is input signal cycle, can get:
(2)
Substitution formula (1), then the electric energy theoretical value is in the signal period:
Figure 796113DEST_PATH_IMAGE011
(3)
With phase point sampling rate weekly signal is sampled; Then
Figure 873976DEST_PATH_IMAGE013
; ; can get:
(4)
Substitution formula (1) then with dot product mode signal calculated electric energy in the cycle, can get formula (5).
Figure 431679DEST_PATH_IMAGE017
(5)
Contrast formula (5) and Theoretical Calculation be formula (3) result of calculation as a result, can be as drawing a conclusion:
(1) for the pure sinusoid periodic signal, be parameters such as the electric weight of accurate signal calculated, power, effective value, the signals sampling rate must guarantee that weekly the phase samples more than 3 at least;
(2) signal of the highest for containing subharmonic; Want the parameters such as electric weight, power, effective value of accurate signal calculated, then the signals sampling rate must guarantee more than per primitive period signal sampling
Figure 429296DEST_PATH_IMAGE019
point;
Notice that conclusion (2) is the inference of conclusion (1), it is a non-adequate condition of necessity.For example, for a sine signal source that contains 21 subharmonic, if will accurately calculate their electric weight, then signal sampling rate must guarantee fundamental signal ripple sampling more than 63 weekly.
Above-mentionedly know that the basic definition formula of having used the definite integral computing is just directly prolonged in the dot product of industry-wide adoption and computing.When sampling number was confirmed, the class of accuracy of the right integrating meter formula was then confirmed thereupon.Numerical analysis in modern times theory is pointed out: if quadrature formula is accurately set up the polynomial expression quadrature of all number of times
Figure 864956DEST_PATH_IMAGE020
; But inaccurate for
Figure 823554DEST_PATH_IMAGE021
order polynomial, claim that then this integral algorithm has inferior algebraically accuracy.Obviously, the some integration method is a Riemann's ladder integral algorithm that has only 0 rank algebraically accuracy, and it is only accurately set up the integration of direct current measurement (0 order polynomial).Can know with reference to formula (4) and Fig. 1; Standard sine input signal instantaneous power is divided into constant component and positive string section; Because the odd symmetry property of sinusoidal signal; Make in the sinusoidal signal cycle more than 3 that evenly distribution each point sum is zero, the electric flux that therefore integral algorithm of 0 rank algebraically accuracy just can accurate Calculation two sinusoidal signals more than 3.But when input signal no longer be thereby that the standard sine signal is when having destroyed this symmetry; The error of calculation of algorithm will produce thereupon; This asymmetric non-standard sinusoidal input signal is very general in the nonlinear-load metering, causes existing ammeter error in dipping bigger.How could nonlinear-load accurately be measured, especially under asymmetric non-standard sinusoidal signal input condition, accurately to measure nonlinear-load, become present problem demanding prompt solution.
Summary of the invention
The object of the present invention is to provide and a kind ofly can improve the especially nonlinear-load electric energy measuring method of real time measure accuracy of the ammeter accuracy of measuring.
This nonlinear-load electric energy measuring method provided by the invention is at one-period
Figure 781332DEST_PATH_IMAGE005
sampling
Figure 133815DEST_PATH_IMAGE012
point; Gather current instantaneous voltage and momentary current; Calculate current instantaneous power [
Figure 14047DEST_PATH_IMAGE023
]; Based on the principle of high-order newton-Ke Tesi Numerical Integral Formulas current sampling instant electric weight is carried out real-time integration and obtain integral and calculating value (
Figure 638932DEST_PATH_IMAGE024
); And the real-time integration of electric weight is carried out the cycle accumulation obtain cycle electric weight accumulating value ( ); Multiply by a coefficient and multiply by the cycle electric flux (
Figure 469802DEST_PATH_IMAGE003
) that a factor obtains nonlinear-load with this accumulating value, the said factor is the ratio of periodic quantity
Figure 784850DEST_PATH_IMAGE005
and sampling number
Figure 647764DEST_PATH_IMAGE012
.
After obtaining above-mentioned electric weight accumulating value (
Figure 59023DEST_PATH_IMAGE025
); When definite current input signal zero passage; Calculate the electric weight (
Figure 120520DEST_PATH_IMAGE003
) of nonlinear-load, said integral and calculating value (
Figure 342554DEST_PATH_IMAGE024
) is fit to following two kinds of formula:
Formula one: Based on the second-order Simpson formula is
Figure 970030DEST_PATH_IMAGE026
Formula two:
Figure 89296DEST_PATH_IMAGE024
based on quadravalence Ke Tesi formula is:
Figure 465919DEST_PATH_IMAGE027
The electric weight of said nonlinear-load (
Figure 303425DEST_PATH_IMAGE003
) is fit to following two kinds of formula:
E
Figure 869536DEST_PATH_IMAGE028
corresponding to above-mentioned formula one
E
Figure 361085DEST_PATH_IMAGE029
corresponding to above-mentioned formula two
In the above-mentioned formula
Figure 659342DEST_PATH_IMAGE030
Following formula
Figure 233412DEST_PATH_IMAGE025
is crossed the electric weight accumulating value in null cycle for signal; Preserve in be with the instantaneous electric weight of current calculating gained and after electric weight accumulating value
Figure 431492DEST_PATH_IMAGE025
adds up before this, deposit back
Figure 415497DEST_PATH_IMAGE025
.
Figure 962016DEST_PATH_IMAGE024
carries out real-time integration to current sampling instant electric weight to obtain real-time integral and calculating value;
Figure 135509DEST_PATH_IMAGE031
is the instantaneous power value of current voltage, current sample;
Figure 333141DEST_PATH_IMAGE032
;
Figure 238780DEST_PATH_IMAGE033
: current voltage; The current sample instantaneous value;
Figure 524792DEST_PATH_IMAGE005
is periodic quantity;
Figure 236396DEST_PATH_IMAGE012
is sampling number,
Figure 39267DEST_PATH_IMAGE003
be the periodic signal electric energy value after the execution cycle computing.
The inventive method utilizes the Newton-Cotes integral algorithm to have the characteristics of high-order accuracy of measuring grade; Current sampling instant electric weight is carried out real-time integration; And the real-time integration of electric weight carried out the cycle accumulation; This method has the accuracy of high-order numerical integration algebraically; Therefore it has higher algorithm accuracy than industry conventional point integration method, can be adapted to nonlinear-load metering widely, has effectively improved electric energy meter to the accuracy of Modern Nonlinear load electric energy metering and the adaptability that all kinds of nonlinear-loads are measured.The inventor shows that through emulation and experiment show this method provided by the invention is highly effective to improving ammeter accuracy aspect.
Description of drawings
Fig. 1 is the synoptic diagram of prior art metering.
Fig. 2 is the process flow diagram of a kind of embodiment of the inventive method.
Fig. 3 is the process flow diagram of the another kind of embodiment of the inventive method.
The figure as a result that Fig. 4 experimentizes with the inventive method.
Embodiment
Embodiment one: this is an embodiment with 3 rank accuracy metering grades, referring to Fig. 2.
One-period ( ) some points of sampling (
Figure 886186DEST_PATH_IMAGE012
) at input signal; Signal time in cycle is divided into individual interval
Figure 245809DEST_PATH_IMAGE034
; According to current instantaneous voltage and momentary current; [
Figure 555568DEST_PATH_IMAGE035
] maybe can be abbreviated as
Figure 813243DEST_PATH_IMAGE036
to calculate current instantaneous power; Utilize the Simpson integral algorithm that the active power of by stages
Figure 804332DEST_PATH_IMAGE037
such as per 2 is carried out electric weight and calculate, be shown below:
Figure 833993DEST_PATH_IMAGE038
(1)
In the formula; Because the complexification integral formula is to adopt two adjacent sectors integrations and the single interval integral formula that substitutes the initial point integration method; For explaining conveniently, adopted the index different to represent that each computation interval originates in the even number index with former integral formula index .Simultaneously, please note the difference of following formula and hot just physiology opinion quadrature formula, because algorithm is the continuous integrated value of calculating two intervals, so aforementioned calculation formula coefficient is 2 times of the theoretical calculation formula coefficient.Then, following formula in the summation that adds up of the interval upper integral value of each equal portions, can be got:
(2)
Figure 220795DEST_PATH_IMAGE003
: current period electric energy metrical value
Figure 59307DEST_PATH_IMAGE042
is the instantaneous power value of current voltage
Figure 104623DEST_PATH_IMAGE043
electric current
Figure 437515DEST_PATH_IMAGE044
T: the signal period value
N: sampling number, i.e. signals sampling rate in the signal period
Above-mentioned formula (7) is a theoretical calculation formula, can not satisfy the real-time operation requirement of modern real-time digital signal processing system.In order in practical application, to utilize the Xin Fusheng algorithm to calculate in real time, need make suitable modification to following formula.Observe calculating formula (7), and launch and can get:
Figure 173259DEST_PATH_IMAGE045
(8)
Formula (8) is real-time computing formula, promptly in practical application, when whenever obtaining a sampled point, then according to the current sampling point index data is accumulated: when index is even number, data are directly accumulated; When index is odd number, then data are taken advantage of 2 accumulations.If
Figure 198984DEST_PATH_IMAGE046
is current sampling instant integral and calculating value; Above-mentioned formulate is become algorithm, and the formula of employing is:
Figure 466017DEST_PATH_IMAGE047
(9)
In the formula
Figure 843079DEST_PATH_IMAGE031
is the instantaneous power value of current voltage, current sample;
Figure 184062DEST_PATH_IMAGE032
;
Figure 629955DEST_PATH_IMAGE033
: current voltage; The current sample instantaneous value;
In the formula;
Figure 384285DEST_PATH_IMAGE048
is current sampling index or the address offset amount of data in internal memory;
Figure 58980DEST_PATH_IMAGE049
carries out mould 2 complementation computings to index
Figure 769316DEST_PATH_IMAGE048
, and symbol
Figure 136843DEST_PATH_IMAGE050
is the fixed-point data shift left operation.
Above-mentioned real-time integration type is carried out cycle accumulation
Figure 112889DEST_PATH_IMAGE030
; The electric weight that obtains at last is multiplied by coefficient more respectively and multiply by the factor
Figure 840543DEST_PATH_IMAGE051
; Run up to then in total electric weight, computing method are applicable to following formula:
Figure 421697DEST_PATH_IMAGE052
(10)
The cycle electric weight that
Figure 946744DEST_PATH_IMAGE030
obtains when being the input signal zero passage at last in the formula.
The electric weight that formula (5) is calculated is accumulated in total electric weight; Make ammeter accurately measure the electric weight that nonlinear load uses; And in this way; The signal of no matter importing is that the sinusoidal waveform or the asymmetrical waveform of symmetry can both accurately measure, and has effectively improved the accuracy of ammeter to the nonlinear-load metering.
Embodiment two: this is an embodiment with 5 rank accuracy metering grades, referring to Fig. 3.
The one-period of input signal (
Figure 613348DEST_PATH_IMAGE005
) some points of sampling ( ), signal time in the cycle is divided into Individual interval
Figure 820842DEST_PATH_IMAGE034
, according to current instantaneous voltage and momentary current, calculate current instantaneous power [
Figure 224010DEST_PATH_IMAGE035
], utilize quadravalence newton-Ke Tesi integral formula to whenever 4Deng the by stages
Figure 106515DEST_PATH_IMAGE053
Active power carry out electric weight and calculate, be shown below:
Figure 396682DEST_PATH_IMAGE054
(11)
In like manner; Note the relation between following formula index
Figure 526181DEST_PATH_IMAGE040
and the aforementioned index
Figure 901799DEST_PATH_IMAGE048
, and the formula coefficient is 4 times of these difference of theoretical calculation formula coefficient.Then, following formula in the summation that adds up of the interval upper integral value of each equal portions, can be got:
Figure 512296DEST_PATH_IMAGE055
(12)
: current period electric energy metrical value
Figure 770419DEST_PATH_IMAGE056
is the instantaneous power value of current voltage electric current
Figure 44592DEST_PATH_IMAGE044
Figure 371668DEST_PATH_IMAGE005
: signal period value
Figure 842970DEST_PATH_IMAGE012
: sampling number, i.e. signals sampling rate in the signal period
In like manner, above-mentioned formula (12) need suitably to be revised the aforementioned calculation formula and be convenient to the engineering real-time operation in order in practical application, to utilize.Observe calculating formula (12), expansion can get:
Figure 193179DEST_PATH_IMAGE057
(13)
Formula (13) is the real-time computing formula of 4 rank newton-Ke Tesi; Promptly in practical application; When whenever obtaining a sampled point; Then data are accumulated:, be added to the electric weight totalizer after current sampled data product enlarged 7 times when sampled voltage, when current data indicator memory mould 4 residual values are 0 according to the current sampling point index; When datarams desired value mould 4 residual values are 1, be added to the electric weight totalizer after then current sampled data product value being enlarged 16 times; When datarams desired value mould 4 residual values are 2, be added to the electric weight totalizer after then current sampled data product value being enlarged 6 times; When datarams desired value mould 4 residual values are 3, be added to the electric weight totalizer after then current sampled data product value being enlarged 16 times.So go round and begin again; Back and forth calculate; If
Figure 142550DEST_PATH_IMAGE024
is current sampling instant integral and calculating value; Above-mentioned formulate is become algorithm, and the formula of employing is:
Figure 324132DEST_PATH_IMAGE027
Figure 806771DEST_PATH_IMAGE030
calculates the signal period electric weight of gained in the formula when being the input signal zero passage.This embodiment can obtain 5 grades of integration algebraically class of accuracies, can measure more accurately nonlinear-load.
In order to confirm that the inventive method possesses the higher accuracy of measuring than prior art, the inventor has done following experiment:
If the input voltage and input current signal is respectively V;
Figure 346654DEST_PATH_IMAGE059
A; Here for realizing the asymmetry of input signal, current signal adopts nonsinusoidal signal.Make
Figure 159758DEST_PATH_IMAGE056
, its waveform can be referring to Fig. 4.Calculating should signal period electric flux theoretical value, can get:
Figure 484560DEST_PATH_IMAGE060
(14)
The trapezoidal quadrature of dot product, complexification and the above-mentioned two kinds of embodiments of the present invention of using prior art respectively carry out the cycle active energy to
Figure 775733DEST_PATH_IMAGE061
and calculate under the different mining sampling point.The error of calculation is listed in the table under each algorithm, and is as shown in table 1.
Table 1
Figure 869591DEST_PATH_IMAGE062
Can know in the table, when sampling number increases, the also corresponding increase of the accuracy in computation of each integral formula.But under identical sampling number, high-order Newton-Cotes integral algorithm exceeds 2 one magnitude than the dot product accuracy.It is thus clear that the inventive method can further improve the class of accuracy of integral and calculating for asymmetric load under identical sampling number situation.
Below be the inventive method to be applied to ammeter (the ammeter specifications and models are DTSD341-MA1,3 * 57.7V/100V, 3 * 1.5 (6) A; 20000imp/kWh, 50Hz, 0.1s level (the mark Q/OKRW 013-2010 of enterprise)); Enumerate the meritorious three-phase and four-line Measuring and testing accuracy data of forward, as shown in table 2.
Test result: uncertainty/accuracy is 0.01% (k=2).
Table 2
Figure 666645DEST_PATH_IMAGE064
Can find out from table 2, use ammeter down in the inventive method, its accuracy of measuring is lower than 20% of accuracy index that the highest domestic measurement standard GB/T17215.322-2008 stipulates, from minute having embodied the superiority of the inventive method.

Claims (1)

1. the electric energy gauging method of a nonlinear-load is characterized in that at one-period
Figure DEST_PATH_DEST_PATH_IMAGE002
Interior sampling
Figure DEST_PATH_DEST_PATH_IMAGE004
Individual, gather current instantaneous voltage and momentary current, calculate current instantaneous power P( k), based on the principle of high-order newton-Ke Tesi Numerical Integral Formulas current sampling instant electric weight is carried out real-time integration and obtain instantaneous integral and calculating value I k , and the real-time integration of electric weight is carried out the cycle accumulation obtain the electric weight accumulating value I, multiply by a coefficient and multiply by the cycle electric flux that a factor obtains nonlinear-load with this accumulating value E, the said factor is a periodic quantity TWith sampling number NRatio, obtain the electric weight accumulating value IAfter, when definite current input signal zero passage, calculate the electric weight of nonlinear-load E, said integral and calculating value I k Be fit to following two kinds of formula:
Formula one: based on second order Xin Fusheng formula I k For
Figure DEST_PATH_DEST_PATH_IMAGE006
Formula two: based on quadravalence Ke Tesi formula I k For:
Figure DEST_PATH_DEST_PATH_IMAGE008
The electric weight of said nonlinear-load EBe fit to following two kinds of formula:
Corresponding to above-mentioned formula one E
Figure DEST_PATH_DEST_PATH_IMAGE010
Corresponding to above-mentioned formula two E
Figure DEST_PATH_DEST_PATH_IMAGE012
In the above-mentioned formula
I=I+I k
Following formula
Figure DEST_PATH_DEST_PATH_IMAGE014
is crossed the electric weight accumulating value in null cycle for signal; Preserve in be with the instantaneous electric weight of current calculating gained
Figure DEST_PATH_DEST_PATH_IMAGE016
and after electric weight accumulating value
Figure DEST_PATH_176251DEST_PATH_IMAGE014
adds up before this, deposit back ;
In the formula;
Figure DEST_PATH_DEST_PATH_IMAGE018
is current sampling index or the address offset amount of data in internal memory;
Figure DEST_PATH_DEST_PATH_IMAGE020
carries out mould 2 complementation computings to index
Figure DEST_PATH_997762DEST_PATH_IMAGE018
, and symbol
Figure DEST_PATH_DEST_PATH_IMAGE022
is the fixed-point data shift left operation;
Figure DEST_PATH_16140DEST_PATH_IMAGE016
carries out real-time integration to current sampling instant electric weight to obtain real-time integral and calculating value;
Figure DEST_PATH_DEST_PATH_IMAGE024
is the instantaneous power value of current voltage, current sample;
Figure DEST_PATH_DEST_PATH_IMAGE026
; : current voltage; The current sample instantaneous value;
Figure DEST_PATH_955146DEST_PATH_IMAGE002
is periodic quantity;
Figure DEST_PATH_839926DEST_PATH_IMAGE004
is sampling number,
Figure DEST_PATH_DEST_PATH_IMAGE030
be the periodic signal electric energy value after the execution cycle computing.
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CN103344824B (en) * 2013-07-08 2016-05-04 国家电网公司 The electric flux integration method measuring based on markers
CN104316894B (en) * 2014-10-16 2017-10-17 国家电网公司 A kind of realistically displayed method of electric energy meter actual motion environment
CN106033098A (en) * 2015-03-19 2016-10-19 上海机电工程研究所 AC power measuring method and device based on data collection
CN104989381B (en) * 2015-06-15 2017-12-05 西安华瑞网电设备有限公司 A kind of flexible measurement method and device of beam pumping unit stroke cycle
CN110687348B (en) * 2019-10-29 2021-04-27 四川长虹电器股份有限公司 Electric energy metering device and electric energy metering method
CN113257638B (en) * 2021-06-23 2021-11-02 江苏能电科技有限公司 Universal type plastic shell circuit breaker

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