CN101915872A - Nonlinear-load electric energy measuring method - Google Patents

Nonlinear-load electric energy measuring method Download PDF

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CN101915872A
CN101915872A CN 201010273234 CN201010273234A CN101915872A CN 101915872 A CN101915872 A CN 101915872A CN 201010273234 CN201010273234 CN 201010273234 CN 201010273234 A CN201010273234 A CN 201010273234A CN 101915872 A CN101915872 A CN 101915872A
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formula
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nonlinear
value
electric weight
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CN101915872B (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 the industrial develop rapidly of modernization, 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 is generally by research part throttle characteristics, electrical network modeling and the problems such as accuracy, rationality that solve the nonlinear-load metering 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)
In the formula
Figure 863350DEST_PATH_IMAGE002
Be instantaneous power, Be electric flux in the signal period,
Figure 162930DEST_PATH_IMAGE004
Be maximum sub-range length,
Figure 914985DEST_PATH_IMAGE005
Be the signal period,
Figure 924398DEST_PATH_IMAGE006
Be the signal sampling time interval.As seen, 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, some integration method accuracy difference under the unlike signal sampling rate.
Be calculated as example with active energy, establish input voltage, current signal is: ,
Figure 328015DEST_PATH_IMAGE008
, in the formula
Figure 186774DEST_PATH_IMAGE009
,
Figure 117821DEST_PATH_IMAGE005
Be 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 weekly
Figure 257181DEST_PATH_IMAGE012
The point sampling rate is sampled to signal, then , ,
Figure 328408DEST_PATH_IMAGE015
, can get:
Figure 158830DEST_PATH_IMAGE016
(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) the highest for containing
Figure 160601DEST_PATH_IMAGE018
The signal of subharmonic is wanted the parameters such as electric weight, power, effective value of accurate signal calculated, and then the signals sampling rate must guarantee per primitive period signal sampling
Figure 429296DEST_PATH_IMAGE019
More than the 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.
As can be known above-mentioned, 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 determined, the class of accuracy of the right integrating meter formula was then determined thereupon.Numerical analysis in modern times theory is pointed out: if quadrature formula is to all number of times The polynomial expression quadrature accurately set up, but for
Figure 823554DEST_PATH_IMAGE021
Order polynomial is inaccurate, then claims this integral algorithm to have 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).With reference to formula (4) and Fig. 1 as can be known, standard sine input signal instantaneous power is divided into constant component and positive string section, because the odd symmetry of sinusoidal signal, make in the sinusoidal signal cycle more than 3 that evenly distribution each point sum is zero, therefore the electric flux that the 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 is gathered current instantaneous voltage and momentary current, calculate current instantaneous power [ ], based on the principle of high-order newton-Ke Tesi Numerical Integral Formulas to current sampling instant electric weight carry out real-time integration obtain the integral and calculating value (
Figure 638932DEST_PATH_IMAGE024
), and to the real-time integration of electric weight carry out the cycle accumulation obtain cycle electric weight accumulating value (
Figure 997232DEST_PATH_IMAGE025
), with this accumulating value multiply by a coefficient and multiply by the cycle electric flux that a factor obtains nonlinear-load (
Figure 469802DEST_PATH_IMAGE003
), the described factor is a periodic quantity
Figure 784850DEST_PATH_IMAGE005
With sampling number Ratio.
Obtain above-mentioned electric weight accumulating value (
Figure 59023DEST_PATH_IMAGE025
) after, when definite current input signal zero passage, calculate nonlinear-load electric weight ( ), described integral and calculating value (
Figure 342554DEST_PATH_IMAGE024
) suitable following two kinds of formula:
Formula one: based on second order Xin Fusheng formula
Figure 942031DEST_PATH_IMAGE024
For
Figure 970030DEST_PATH_IMAGE026
Formula two: based on quadravalence Ke Tesi formula
Figure 89296DEST_PATH_IMAGE024
For:
Figure 465919DEST_PATH_IMAGE027
The electric weight of described nonlinear-load (
Figure 303425DEST_PATH_IMAGE003
) suitable following two kinds of formula:
E corresponding to above-mentioned formula one
Figure 869536DEST_PATH_IMAGE028
E corresponding to above-mentioned formula two
Figure 361085DEST_PATH_IMAGE029
In the above-mentioned formula
Figure 659342DEST_PATH_IMAGE030
Following formula
Figure 233412DEST_PATH_IMAGE025
Crossing electric weight accumulating value in null cycle for signal, is with the instantaneous electric weight of current calculating gained
Figure 603213DEST_PATH_IMAGE024
With electric weight accumulating value before this
Figure 431492DEST_PATH_IMAGE025
After adding up, deposit back The middle preservation.
Figure 962016DEST_PATH_IMAGE024
Be current sampling instant electric weight to be carried out real-time integration obtain real-time integral and calculating value;
Figure 135509DEST_PATH_IMAGE031
, be the instantaneous power value of current voltage, current sample;
Figure 333141DEST_PATH_IMAGE032
, : current voltage, current sample instantaneous value;
Figure 524792DEST_PATH_IMAGE005
Be periodic quantity, Be sampling number, 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, effectively improve electric energy meter the accuracy of Modern Nonlinear load electric energy metering and the adaptability that all kinds of nonlinear-loads are measured.The inventor shows that by 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.
The one-period of input signal (
Figure 365075DEST_PATH_IMAGE005
) some points of sampling (
Figure 886186DEST_PATH_IMAGE012
), signal time in the cycle is divided into
Figure 322853DEST_PATH_IMAGE012
Individual interval
Figure 245809DEST_PATH_IMAGE034
, according to current instantaneous voltage and momentary current, calculate current instantaneous power [
Figure 555568DEST_PATH_IMAGE035
] maybe can be abbreviated as
Figure 813243DEST_PATH_IMAGE036
, utilize the Simpson integral algorithm to by stages such as per 2
Figure 804332DEST_PATH_IMAGE037
Active power carry out electric weight and calculate, be shown below:
Figure 833993DEST_PATH_IMAGE038
(1)
In the formula,,, adopted and former integral formula index for explaining conveniently because the complexification integral formula is the single interval integral formula that adopts two adjacent sectors integrations and substitute the initial point integration method
Figure 314653DEST_PATH_IMAGE039
Different indexs
Figure 544777DEST_PATH_IMAGE040
Represent that each computation interval originates in the even number index.Simultaneously, please note the difference of following formula and hot Pu's 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
, be current voltage
Figure 104623DEST_PATH_IMAGE043
Electric current
Figure 437515DEST_PATH_IMAGE044
The instantaneous power value
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 to utilize the Xin Fusheng algorithm to calculate in real time in actual applications, 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 actual applications, 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
For current sampling instant integral and calculating value, above-mentioned formulate is become algorithm, the formula of employing is:
Figure 466017DEST_PATH_IMAGE047
(9)
In the formula
, be the instantaneous power value of current voltage, current sample;
Figure 184062DEST_PATH_IMAGE032
,
Figure 629955DEST_PATH_IMAGE033
: current voltage, current sample instantaneous value;
In the formula,
Figure 384285DEST_PATH_IMAGE048
The address offset amount in internal memory for current sampling index or data,
Figure 58980DEST_PATH_IMAGE049
Be to index Carry out mould 2 complementation computings, symbol
Figure 136843DEST_PATH_IMAGE050
Be the fixed-point data shift left operation.
Above-mentioned real-time integration type is carried out the cycle accumulation
Figure 112889DEST_PATH_IMAGE030
, the electric weight that obtains at last is multiplied by coefficient more respectively and multiply by the factor , running up to then in total electric weight, computing method are applicable to following formula:
Figure 421697DEST_PATH_IMAGE052
(10)
In the formula
Figure 946744DEST_PATH_IMAGE030
The cycle electric weight that obtains at last when being the input signal zero passage.
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 (
Figure 692163DEST_PATH_IMAGE012
), 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 following formula index
Figure 526181DEST_PATH_IMAGE040
With aforementioned index
Figure 901799DEST_PATH_IMAGE048
Between relation, 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
, be current voltage
Figure 882601DEST_PATH_IMAGE043
Electric current The instantaneous power value
Figure 371668DEST_PATH_IMAGE005
: the 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 to utilize in actual applications.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 actual applications, 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, establish For current sampling instant integral and calculating value, above-mentioned formulate is become algorithm, the formula of employing is:
Figure 717068DEST_PATH_IMAGE029
In the formula
Figure 806771DEST_PATH_IMAGE030
Calculate the signal period electric weight of gained when being the input signal zero passage.Present embodiment can obtain 5 grades of integration algebraically class of accuracies, can carry out more accurate metering to 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
Figure 310565DEST_PATH_IMAGE058
V,
Figure 346654DEST_PATH_IMAGE059
A, for realizing the asymmetry of input signal, current signal adopts nonsinusoidal signal here.Order
Figure 159758DEST_PATH_IMAGE056
, its waveform can be referring to Fig. 4.Calculate this signal period electric flux theoretical value, can get:
Figure 484560DEST_PATH_IMAGE060
(14)
Use the trapezoidal quadrature of dot product, complexification of prior art and the above-mentioned two kinds of embodiments of the present invention respectively under the different mining sampling point, right
Figure 775733DEST_PATH_IMAGE061
The cycle of carrying out active energy calculates.The error of calculation is listed in the table under each algorithm, and is as shown in table 1.
Table 1
In the table as can be known, 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 orders of magnitude than the dot product accuracy.As seen, 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
As can be seen from Table 2, the ammeter under the inventive method is used, its accuracy of measuring be lower than the highest domestic measurement standard GB/T17215.322-2008 regulation the accuracy index 20%, from minute having embodied the superiority of the inventive method.

Claims (2)

1. the electric energy gauging method of a nonlinear-load, its feature is being at one-period
Figure 2010102732345100001DEST_PATH_IMAGE001
Sampling
Figure 588049DEST_PATH_IMAGE002
Point is gathered 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 to current sampling instant electric weight carry out real-time integration obtain instantaneous integral and calculating value ( I k ), and to the real-time integration of electric weight carry out the cycle accumulation obtain the electric weight accumulating value ( I), with this accumulating value multiply by a coefficient and multiply by the cycle electric flux that a factor obtains nonlinear-load ( E), the described factor is a periodic quantity TWith sampling number NRatio.
2. nonlinear-load electric energy measuring method according to claim 1, it is characterized in that obtaining the electric weight accumulating value ( I) after, when definite current input signal zero passage, calculate nonlinear-load electric weight ( E), described integral and calculating value ( I k ) suitable following two kinds of formula:
Formula one: based on second order Xin Fusheng formula I k For
Figure 2010102732345100001DEST_PATH_IMAGE003
Formula two: based on quadravalence Ke Tesi formula I k For:
Figure 811089DEST_PATH_IMAGE004
The electric weight of described nonlinear-load ( E) suitable following two kinds of formula:
Corresponding to above-mentioned formula one E
Figure 2010102732345100001DEST_PATH_IMAGE005
Corresponding to above-mentioned formula two E
Figure 374926DEST_PATH_IMAGE006
In the above-mentioned formula
I=I+I k
Following formula
Figure 2010102732345100001DEST_PATH_IMAGE007
Crossing electric weight accumulating value in null cycle for signal, is with the instantaneous electric weight of current calculating gained
Figure 184881DEST_PATH_IMAGE008
With electric weight accumulating value before this
Figure 492366DEST_PATH_IMAGE007
After adding up, deposit back
Figure 648540DEST_PATH_IMAGE007
The middle preservation.
Figure 632546DEST_PATH_IMAGE008
Be current sampling instant electric weight to be carried out real-time integration obtain real-time integral and calculating value;
Figure 2010102732345100001DEST_PATH_IMAGE009
, be the instantaneous power value of current voltage, current sample;
Figure 179065DEST_PATH_IMAGE010
,
Figure 2010102732345100001DEST_PATH_IMAGE011
: current voltage, current sample instantaneous value;
Figure 772464DEST_PATH_IMAGE001
Be periodic quantity,
Figure 783145DEST_PATH_IMAGE002
Be sampling number,
Figure 751101DEST_PATH_IMAGE012
Be the periodic signal electric energy value after the execution cycle computing.
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CN103344824A (en) * 2013-07-08 2013-10-09 国家电网公司 Electric energy integration method based on time mark measurement
CN104316894A (en) * 2014-10-16 2015-01-28 国家电网公司 Simulation and calibration method for practical running environment of electric energy meter
CN104989381A (en) * 2015-06-15 2015-10-21 西安华瑞网电设备有限公司 Soft measuring method and device for stroke period of beam-pumping unit
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
CN110687348A (en) * 2019-10-29 2020-01-14 四川长虹电器股份有限公司 Electric energy metering device and electric energy metering method
CN113257638A (en) * 2021-06-23 2021-08-13 江苏能电科技有限公司 Universal type plastic shell circuit breaker

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CN103344824A (en) * 2013-07-08 2013-10-09 国家电网公司 Electric energy integration method based on time mark measurement
CN103344824B (en) * 2013-07-08 2016-05-04 国家电网公司 The electric flux integration method measuring based on markers
CN104316894A (en) * 2014-10-16 2015-01-28 国家电网公司 Simulation and calibration method for practical running environment of electric energy meter
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
CN104989381A (en) * 2015-06-15 2015-10-21 西安华瑞网电设备有限公司 Soft measuring method and device for stroke period of beam-pumping unit
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
CN110687348A (en) * 2019-10-29 2020-01-14 四川长虹电器股份有限公司 Electric energy metering device and electric energy metering method
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
CN113257638A (en) * 2021-06-23 2021-08-13 江苏能电科技有限公司 Universal type plastic shell circuit breaker

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Application publication date: 20101215

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Denomination of invention: Nonlinear-load electric energy measuring method

Granted publication date: 20120829

License type: Exclusive License

Record date: 20131112

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