1、 NEMA C12.24 TR-2011 Definitions for Calculations of VA, VAh, VAR, and VARh for Poly-Phase Electricity Meters NEMA C12.24 TR-2011 NEMA C12.24TR-2011 iii NEMA C12.24 TR-2011 Definitions for Calculations of VA, VAh, VAR, and VARh for Poly-Phase Electricity Meters A Technical Report prepared by NEMA an
2、d registered with ANSI Secretariat: National Electrical Manufacturers Association Registered May 29, 2011 American National Standards Institute, Inc. NEMA C12.24 TR-2011 NOTICE AND DISCLAIMER The information in this publication was considered technically sound by the consensus of persons engaged in
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17、ation 1300 North 17th Street, Rosslyn, VA 22209 Copyright 2011 by National Electrical Manufacturers Association All rights reserved including translation into other languages, reserved under the Universal Copyright Convention, the Berne Convention for the Protection of Literary and Artistic Works, a
18、nd the International and Pan American Copyright Conventions. No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. Printed in the United States of America NEMA C12.24 TR-2011 ii This page inte
19、ntionally left blank.NEMA C12.24TR-2011 iii Contents Page 1 Scope 1 2 Abbreviations and Letter Symbols 1 2.1 Abbreviations 1 2.2 Letter Symbols 1 3 Definitions for Single-Element VAR 2 3.1 Fundamental Waveform Method 2 3.2 Integral Phase-Shift Methods . 3 3.2.1 Integral Phase-Shift: Exact Frequency
20、Method . 3 3.2.2 Integral Phase-Shift: 50 Hz Fixed Method . 3 3.2.3 Integral Phase-Shift: 60 Hz Fixed Method . 4 3.3 Differential Phase-Shift Method 4 3.4 Quarter-Cycle Delay Method 5 3.5 Vector Methods . 5 3.5.1 Vector Method Using VA RMS 5 3.5.2 Vector Method Using VA Average Responding 6 3.5.3 Si
21、gned Vector Method Using VA RMS and Fundamental Waveforms . 7 3.5.4 Signed Vector Method Using VA RMS and Manufacturer-Specified Sign Assignment Technique 7 3.6 Cross-Connected Phase-Shift Method . 8 3.7 Individual Harmonic Method . 9 4 Definitions for netVAR (Total Meter VAR) 10 4.1 Sum of Element
22、Methods . 10 4.1.1 Sum of Three Elements Method 10 4.1.2 Sum of Two Elements Method 10 4.1.3 Sum of Two Elements Cross-Connected Method . 11 4.2 Vector Method 12 5 Definition for Single-Element VARh 12 6 Definitions for NetVARh (Total Meter VARh) . 13 6.1 Sum of Single-Element VARhs Method . 13 6.2
23、NetVAR Method 13 7 Definitions for Single-Element VA 13 7.1 Vector Method 13 7.2 RMS Method . 14 7.3 Average Responding Method . 14 7.4 Individual Harmonic Method . 15 8 Definitions for netVA (Total Meter VA) . 16 8.1 Sum of Element Methods . 16 8.1.1 Sum of Three Elements Method 16 8.1.2 Sum of Two
24、 Elements Method 16 8.2 Vector Method 17 9 Definition for Single-Element VAh 17 10 Definitions for netVAh (Total Meter Vah) 17 10.1 Sum of Single-Element VAh Method 17 10.2 netVA Method . 18 NEMA C12.24 TR-2011 iv Foreword (This Foreword is not part of Technical Report C12.24TR-2011.) Publication of
25、 this Technical Report that has been registered with ANSI has been approved by the Accredited Standards Developer (NEMA, 1300 North 17th Street, Suite 1752, Rosslyn, VA 22209). This document is registered as a Technical Report according to the Procedures for the Registration of Technical Reports wit
26、h ANSI. This document is not an American National Standard and the material contained herein is not normative in nature. Comments on the content of this document should be sent to: National Electrical Manufacturers Association Vice President, Technical Services 1300 North 17th Street, Suite 1752 Ros
27、slyn, VA 22209 This Technical Report establishes definitions for calculations of VA, VAh, VAR, and VARh for poly-phase electricity meters. It is intended to ease identification of algorithms used in electricity meters and to facilitate accurate testing. This technical report was processed and approv
28、ed for submittal to ANSI by Accredited Standards Committee for Electricity Metering, C12. At the time the committee approved this technical report, the C12 Committee had the following members: Tim Everidge, Chairperson ANS C12/SC24 Tom Nelson, Chairperson ANS C12 Paul Orr, Secretary ANS C12 Main Com
29、mittee Organization Represented: Name of Representative: Organization Represented: Name of Representative: General Interest Austin Energy H. Millican MET Laboratories, Inc. R. Subramaniam Center for Neighborhood Technology L. Kotewa NIST T. Nelson EnerNex Corporation A. Snyder Plexus Research D. Sco
30、tt Future DOS R see Equation (1). 22)s in ( )s in ( iiiii W A T TVAVAR (9) where i =phase angle between the fundamental potential and current, (1)i minus (1)i (h)i =phase angle of the potential for harmonic order (h) of phase i (h)i =phase angle of the current for harmonic order (h) of phase i | iii
31、 IVVA dtIVkTW A T T ikTii 1 and where the RMS voltage and RMS current are dtVkTV kT ii 21| dtIkTI kT ii 21|and k =number of fundamental periods T =fundamental period =start time of integration iI =generalized current waveform of phase i (fundamental and all harmonics) iV =generalized potential wavef
32、orm of phase i (fundamental and all harmonics) i =phase number in the poly-phase network NOTEThe notation | | generally represents the norm of the wave function: 1-norm (average) or 2-norm RMS. 3.5.4 Signed Vector Method Using VA RMS and Manufacturer-Specified Sign Assignment Technique NEMA C12.24TR
33、-2011 8 The definition for VAR using the VA RMS and manufacturer-specified sign-assignment technique is based on VA RMS and power. The VA is calculated by multiplying the RMS voltage times RMS current. The fundamental and all harmonics are included in the calculation. The VAR for each element (VARi)
34、 is calculated from the power triangle by taking the square root of the quantity VA squared minus power (WATT) squared. The method of determining the polarity of the sign of VARi is specified by the manufacturer. 22 iii W A T TVAVAR (10) where | iii IVVA dtIVkTW A T T ikTii 1 and dtVkTV kT ii 21| dt
35、IkTI kT ii 21|and k =number of fundamental periods T =fundamental period =start time of integration iI =generalized current waveform of phase i (fundamental and all harmonics) iV =generalized potential waveform of phase i (fundamental and all harmonics) i =phase number in the poly-phase network NOTE
36、The notation | | generally represents the norm of the wave function: 1-norm (average) or 2-norm RMS. 3.6 Cross-Connected Phase-Shift Method The definition for VAR using the cross-connected phase-shift method is based on creating a voltage that is 90 delayed from the voltage axis and adjusting the am
37、plitude to match the amplitude of the voltage axis input. The 90 delay is created by subtracting the voltage phase that is 240 behind from the voltage phase that is 120 behind. The amplitude is then adjusted by dividing it by the 3. This phase shift and amplitude adjustment assumes that the voltages
38、 are balanced and spaced 120 apart. The VAR for each element (VARi) is calculated by multiplying the 90 delayed, amplitude-adjusted voltage times the current and integrating over the fundamental period: NEMA C12.24TR-2011 9 dtxVIkTVAR ikTii (11) where 321 33 VVxV 132 33 VVxV 213 33 VVxV and =fundame
39、ntal angular frequency 2f0, where f0 is the fundamental frequency k =number of fundamental periods T =fundamental period =start time of integration iI =generalized current waveform of phase i (fundamental and all harmonics iV =generalized potential waveform of phase i (fundamental and all harmonics)
40、 i =phase number in the poly-phase network 3.7 Individual Harmonic Method The definition for VAR using the individual harmonic method is based on measuring only a specific harmonic of the voltage and current signals and does not include any other harmonics, including the fundamental that may be pres
41、ent in the voltage or current signals. The VAR for each element (VAR(h)i) is calculated by multiplying the specific harmonic of the voltage times the specific harmonic of the current times the sine of the phase angle between them. )s i n (| )()()()()( ihihihihih IVVAR (12) where (h)i = phase angle o
42、f the potential for harmonic order (h) of phase i (h)i = phase angle of the current for harmonic order (h) of phase i and dtVkTV kT ihih 2)()( 1| dtIkTI kT ihih 2)()( 1|and NEMA C12.24TR-2011 10 k =number of fundamental periods T =fundamental period =start time of integration ihV)( =potential compon
43、ent for harmonic order of phase i (h) ihI)( =current component for harmonic order of phase i (h) i =phase number in the poly-phase network NOTEThe notation | | generally represents the norm of the wave function: 1-norm (average) or 2-norm RMS. 4 Definitions for netVAR (Total Meter VAR) 4.1 Sum of El
44、ement Methods 4.1.1 Sum of Three Elements Method The definition for total meter VAR (netVAR) using the sum of three elements method is based on summing the VARs of the individual elements (VARi) of a three-element meter. If the VAR definition for the meter specified by the manufacturer allows both p
45、ositive and negative VAR readings, the sum of the VARs may be smaller than the individual VARs. NetVAR is calculated using the formula 31net i iVARVAR 4.1.2 Sum of Two Elements Method The definition for netVAR using the sum of two elements method is based on summing the VARs of the individual elemen
46、ts (VARi) of a two-element meter. The input voltages to the individual elements are transformed by Blondels theorem to allow a two-element meter to measure a three-phase system. If the VAR definition for the meter specified by the manufacturer allows for both positive and negative VAR readings, the
47、sum of the VARs may be smaller than the individual VARs. NetVAR is calculated using the formula 31net i iVARVAR where the transformed voltages for the input to the single elements from Blondels theorem are 211 VVbV 02bV 233 VVbV and (13) (14) NEMA C12.24TR-2011 11 VAR2 =0 4.1.3 Sum of Two Elements C
48、ross-Connected Method The definition for netVAR using the sum of two elements cross-connected method is the specific application of Equation (14) to a cross-connected two-element meter. The definition is based on summing the VARs of the individual elements (VARi), and the input voltages to the indiv
49、idual elements are transformed by Blondels theorem to allow a two-element meter to measure a three-phase system. If the VAR definition for the meter specified by the manufacturer allows for both positive and negative VAR readings, the sum of the VARs may be smaller than the individual VARs. NetVAR is calc
