IEEE-86-1987.pdf

IEEE Std 86-1987 (Revision of ANSIAEEE Std 86-1975) IEEE Recommended Practice: Definitions of Basic Per-Unit Quantities for AC Rotating Machines Published by The Institute of Electrical and Electronics Engineers, Inc 345 East 47th Street, New York, NY 10017, USA SHI 0900 February IS, 1987 IEEE S t d 86-1987 (Revision of ANSI/IEEE SM 861975) IEEE Recommended Practice: Definitions of Basic Per-Unit Quantities for AC Rotating Machines Sponsor Rotating Machinery Committee of the IEEE Power Engineering Society Copyright 1987 by The Institute of Electrical and Electronics Engineers, Inc 345 East 47th Street, New York, NY 10017, USA 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. IEEE Standards documents are developed within the Technical Com- mittees of the IEEE Societies and the Standards Coordinating Committees of the IEEE Standards Board. 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Since IEEE Standards represent a consensus of all concerned interests, it is important to ensure that any interpretation has also received the concurrence of a balance of interests. For this reason IEEE and the members of its technical committees are not able to provide an instant response to interpretation requests except in those cases where the matter has previously received formal consideration. Comments on standards and requests for interpretations should be ad- dressed to: Secretary, IEEE Standards Board 345 East 47th Street New York, NY 10017 USA Foreword (This Foreword is not a part of IEEE SM 86-1987, IEEE Recommended Practice: Definitions of Basic Per-Unit Quantities When machine parameters are expressed in a properly selected per-unit system, the parameters of a wide range of machine sizes fall into relatively narrow ranges even though the actual values of these same parameters may vary over extremely wide ranges. The per-unit system thereby makes possible an easy comparison between different machines, essentially independent of size, without the use of conversion factors, and facilitates the identification of gross calculation errors. The proper selection of base values is fundamental to the usefulness of a per-unit system. Although per-unit quantities have been used for many years by designers of rotating machinery, the base quantities were not standardized, and it was necessary to define them in each publication. A working group of the Rotating Machinery Committee was created to propose a set of standard definitions. In 1961, a proposed standard (AIEE No. 86) was published for trial use. A critical review of that proposed standard resulted in ANSI/IEEE Std 86-1975. Recently, systems analysts and some designers of rotating electrical machinery have found it useful to have a single generic model for all types of machines. Therefore, alternate per-unit definitions, using input voltamperes as base power for in- duction motors, have been included in this new revision, as well as an example of an induction generator. for AC Rotating Machines.) The members of the working group responsible for this revision were as follows: Edward J. Michaels, Chairman P. G. Cummings H. Majmudar M. H. Heme J. W. York J. C. White The following persons were on the balloting committee that approved this document for submission to the IEEE Standards Board: P. D. Adarwal J. C. Andreas R. H. Auerbach R. G. Bartheld T. H. Barton J. M. Brown L. W. Buchanan G. W. Buckley A. W. W. Cameron M. V. K. Chari J. L. Cohon J. L. Craggs P. G. Cummings N. A. Demerdash W. C. Dumper J. S. Edmonds J. S. Ewing C. V. Fields C. E. Flick N. K. Ghai G. L. Godwin D. R. Green F. H. Grooms H. B. Hamilton G. E. Herzog G. W. Herzog M. H. Hesse T. J. Higgins V. B. Honsinger R. F. Horrell N. H. Jones H. E. Jordan W. Kerber E. I. King W. H. Koch P. R. H. Landrieu I. M. Levy T. A. Lip0 T. J. Lorenz H. Majmudar W. J. Martiny C. H. Merrifield E. J. Michaels R. C. Moore E. H. Myers N. E. Nilason P. I. Nippes D. W. Novotny J. L. Oldenkamp J. A. Oliver W. B. Penn M. Poloujadoff J. V. Pospisil E. P. Priebe G. M. Rosenberry C. M. Rowe M. S. Sarma P. W. Sauer R. M. Saunders P. T. Schuerman D. K. Sharma M. W. Sheets W. J. Sheets E. P. Smith J. F. Szablya R. A. Tome P. H. Trickey P. J. Tsivitse J. P. Vogelwede P. Walker T. C. Wang R. F. Weddleton J. C. White E. C. Whitney J. J. Wilkes R. L. Winchester E. J. Woods When the IEEE Standards Board approved this standard on June 19, 1986, it had the following membership: John E . May, Chairman Irving Kolodny, Vice Chairman Sava I. Sherr, Secretary James H. Beall Fletcher J. Buckley Paul G. Cummings Donald C. Fleckenstein Jay Forster Daniel L. Goldberg Kenneth D. Hendrix Irvin N. Howell *Member emeritus Jack Kinn Joseph L. Koepfinger' Edward Lohse Lawrence V. McCall Donald T. Michael' Marco W. Migliaro Stanley Owens John P. Riganati Frank L. Rose Robert E. Rountree Martha Sloan Oley Wanaselja J. Richard Weger William B. Wilkens Helen M. Wood Charles J. Wylie Donald W. Z i p Contents SECTION PAGE 1 . Scope and Introduction 2 . Definitions 3 . Conversions . APPENDIXES Appendix A Application Examples Appendix B Examples of Machine Constants Appendix C Calculations of Per-Unit Values . APPENDIX TABLES Table A1 Examples of Base Values Table B1 Examples of Machine Parameters . Table C1 Calculations of Per-Unit Values 7 7 8 9 10 11 9 10 11 IEEE Recommended Practice: Definitions of Basic Per-Unit Quantities for AC Rotating Machines 1. Scope and Introduction Since rotating electrical machines convert me- chanical energy to electrical energy, or electrical energy to mechanical energy, base values for each kind of energy appear desirable in for- mulating a per-unit system. However, the rela- tionship between these energies involves power factor and efficiency, which are not fundamental quantities and which vary considerably between different designs. Traditionally, designers of generators consid- ered rated apparent output power as base power, and designers of synchronous motors considered rated apparent input power as base power. De- signers of synchronous motors used rated ap parent input power as the base even though it was necessary to estimate efficiency. This per- mitted the use of the same design equations for both synchronous generators and synchronous motors. Designers of induction motors generally have used rated output power as base apparent power, eliminating assumptions of power factor and ef- ficiency. This was particularly desirable when working with small machines or machines with many poles, where accurate estimates of power factor and efficiency were difficult to make. However, some induction machines are used as induction generators, so that the definitions of input power and output power depend on the mode of operation. Systems analysts, and some authors and ma- chine designers, prefer the use of a single base system for all types of machines in order to sim- plify analysis, particularly when incorporating different machine types in a given study. Machine equivalent circuit calculations of mo- tors made with rated output power as a base give per-unit torque values in relatively “con- ventional numbers,” that is, close to unity for rated load. However, values of per-unit current are “unconventional”-rated current is not unity. When rated apparent input power is used as a base, values of per-unit current are “con- ventional,” but torque values become “uncon- ventional.” Both systems have been in use for a long time, with proponents of each system con- vinced that their system best serves their pur- poses. Hence this recommended practice considers both bases in formulating acceptable definitions. Since there are two systems in general use, it is important that in the transmittal of machine data, or in technical papers, the base be iden- tified. 2. Definitions base apparent power (alternating-current ac rotating machinery). A reference value expressing an electrical power rating of the ma- chine. Note: Base apparent power may be either input or output power, and the numerical value may be either real power (watts wl) or total apparent electrical power (voltamperes VA), depending upon machine type. Base apparent power is usually expressed in voltamperes, but any consistent set of units may be used. For synchronous generators, induction gen- erators, and synchronous motors, base apparent power is the total apparent electrical power at rated voltage and rated current. In induction motors (preferred method), base apparent power is numerically equal to the rated power output. For induction motors (alternate method), base apparent power is the total apparent electrical power at rated voltage and rated current. Note: When the alternate method is used it shou!d be identified as “input voltampere base.” 7 IEEE Std 86-1987 IEEE RECOMMENDED PRACTICE: DEFINITIONS OF base voltage (ac rotating machinery). The rated phase voltage. Note: The value of the base voltage is the value of the rated line voltage for a deltaconnected machine, and is the value of the rated line voltage divided by 8 for a wye- connected machine. Base voltage is usually ex- pressed in volts (V), but any consistent set of units may be used. base current (ac rotating machinery). The value of phase current corresponding to the value of base apparent power, base voltage, and the number of phases. Note: Base current is usu- ally expressed in amperes (A), but any consistent set of units may be used. Base current equals the base apparent power divided by the product of base voltage and the number of phases. base impedance (ac rotating machinery). The value of impedance corresponding to the value of the base voltage divided by the value of the base current. Note: Base impedance is usually expressed in ohms (CL), but any consistent set of units may be used. base speed (ac rotating machinery). The rated synchronous speed. Note: Synchronous speed equals 120 times the value of line fre- quency, divided by the number of poles. Base speed is usually expressed in revolutions per minute (r/min), but any consistent set of units may be used. base torque (ac rotating machinery). The value of torque corresponding to the value of base apparent power and base synchronous speed. The value of base torque in pound-force feet (lbf-ft) is 7.043 times the value of the base apparent power (in voltamperes PA), divided by the value of base speed in revolutions per minute (r/min). The value of base torque in new- ton meters per radian (N.m/rad) is 9.549 times the value of the base apparent power (in voltam- peres), divided by the value of the base speed in revolutions per minute. Note: Base torque has conventionally been expressed in pound-force feet or in newton meters (N-m). To avoid con- fusion with the unit of energy, which is also the newton meter, the designation newton meter per radian is recommended. per-unit value (ac rotating machinery). The actual value divided by the value of the base quantity when both actual and base values are expressed in the same units. 3. Conversions Per-unit values in reference to a given base can be converted to per-unit values in reference to a new base by a two-step process. First, con- vert the per-unit value to an actual value by multiplying by the old base value and by any conversion factor necessary to make the units consistent with the new base. Second, divide this actual value by the new base value. 8 IEEE Std 86-1987 BASIC PER-UNIT QUANTITIES FOR AC ROTATING MACHINES 2 .d 3 8 0 L 9 IEEE Std 86-1987 IEEE RECOMMENDED PRACTICE DEFINITIONS OF 1 10 IEEE S t d 86-1987 BASIC PER-UNIT QUANTITIES FOR AC ROTATING MACHINES C 11