IEEE 58-1978 - IEEE Standard Induction Motor Letter Symbols.pdf

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1、IEEE Std 58-1978 (Revision of IEEE Std 58-1956) IEEE Standard Induction Motor Letter Symbols Sponsor Rotating Machinery Committee of the IEEE Power Engineering Society 0 Copyright 1978 by The Institute of Electrical and Electronics Engineers, Inc. No part of this publication may be reproduced in any

2、 form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. Approved March 11,1976 IEEE Standards Board William R. Kruesi, Chairman Irvin N. Howell, Jr., Vice Chairman Ivan G. Easton, Secretary William E. Andrus Irving Kolodny William J. Neiswender J

3、ean Jacques Archambault Benjamin J. Leon Gustave Shapiro Dale R. Cochran John P. Markey Ralph M. Showers Warren H. Cook Thomas J. Martin Robert A. Soderman Louis Costrell Donald T. Michael Leonard W. Thomas, Sr. Jay Forster Voss A. Moore Charles L. Wagner Joseph L. Koepfinger William S. Morgan Willi

4、am T. Wintringhamt ?Deceased Foreword (This Foreword is not a part of IEEE Std 58-1978, Standard Induction Motor Letter Symbols.) Originally issued as a trial-use standard in 1956, IEEE Standard Induction Motor Letter Symbols has been enlarged to reflect those additional symbols required by the stat

5、e of the art, and it has been approved and published as a full-status IEEE Standard. It is expected that experience with the present document may generate interest in further additions or other modifications. Suggestions for changes should be forwarded to: Secretary IEEE Standards Board 345 East 47t

6、h Street New York, NY 10017 At the time it approved this standard, the Working Group on Induction Motor Letter Symbols of the Induction Machinery Subcommittee of the Rotating Machinery Committee had the following members: E. J. Michaels, Chairman J. J. Brockman J. W. Gahan P. C. Krause C. E. Linkous

7、 Contents SECTION PAGE 1 . Introduction . 5 2 . Scope . 5 4 . PolyphaseMotors . 7 3 . Guiding Principles . 5 5 . Single-phase Motors-Revolving-Field Theory . 8 6 . Single-phase Motors-Cross-Field Theory . 10 7 . Single-phase Motors-Symmetrical Components Theory . 10 8 . Letter Symbols for Equivalent

8、 Circuit . 12 8.1 Additional Subscripts . 18 9 . Letter Symbols for Dimensional Values . 18 FIGURES Fig 1 Fig 2 Fig 3 Equivalent Circuit of a Polyphase Induction Motor. with Alternate Iron Loss Circuits (a) Basic Circuit (b) Alternate Methods of Showing . . Equivalent Circuits for Multiple-Cage Poly

9、phase Induction Motors (a) Double-Cage Motor (b) Triple-Cage Motor . Equivalent Circuit of a Single-phase Induction Motor Running on Main Winding Only-Revolving-Field Theory (a) Detailed Circuit (b) Simplified Circuit (c) Simple Circuit Alternate Iron Loss Circuit . 8 Equivalent Circuit of a Capacit

10、or Motor Running with Both Windings Energized-Revolving-Field Theory (a) Main Winding (b) Auxiliary Winding 8 Equivalent Circuits of a Capacitor Motor Under Locked-Rotor Conditions 9 Schematic Representation of a Single-phase Motor-Cross-Field Theory . 9 Fluxes in a Single-phase Motor-Cross-Field Th

11、eory . 10 One Form of the Equivalent Cireuit. Based on the Cross-Field Theory . 10 Another Form of Equivalent Circuit for the Single-phase Motor. Based on the Cross-Field Theory . 10 Schematic Representation of a Capacitor Motor Running with Both Windings Energized-Cross-Field Theory . 10 An Equival

12、ent Circuit (Network Form) for the Capacitor Motor Running with Both Windings Energized-Cross-Field Theory . 11 Equivalent Circuits for Polyphase Motors with Unbalanced Voltages- Symmetrical Component Theory (a) Detailed Circuits (b) Simplified Circuits . 11 Equivalent Circuit of a Capacitor Motor R

13、unning with Both Windings Energized-Symmetrical Component Theory (a) Detailed Circuit (b) Simplified Circuit (These Circuits Simulate One-Half the Total Power of 7 7 Fig 4 Fig 5 Fig 6 Fig 7 Fig 8 Fig 9 Fig 10 Fig 11 Fig 12 . (a) Main Winding (b) Auxiliary Winding (c) Simplified Circuit . Fig 13 theM

14、Otor) . 12 Fig 14 Stator and Rotor Slot Dimensions . 19 Fig 15 End Winding Dimensions. Rotor Bar Shapes and Skew Angle . 20 IEEE Standard Induction Motor Letter Symbols 1. Introduction 3.1 All secondary quantities (such as imped- ances, currents, etc) are understood to be in primary winding terms, u

15、nless otherwise speci- fied. In the case of single-phase motors primary winding terms mean the main winding terms unless otherwise indicated. induction lected by their too much time becoming familiar with the symbols used by each author. It has long been by many in 3.2 Impedances of a single winding

16、 onlysuch this field that a fair exchange of ideas on induc- tion machinery would be promoted if all writ- ers used the same letter symbols for the same as a primary or written in lower quantities. A Working Group was set up by the Rotating Machinery Committee to unified system of letter symbols tha

17、 3.3 Impedances of a combination of primary and secondary winding (all secondary windings if there are more than one) are written in upper used for “this purpose. This standard is the out- come of a trial period of several years as a pro- posed standard. The standard usually appliesLn1 state or quas

18、i-steady-state condition 3 2. Scope Section 8 gives the letter symbols for those quantities needed to define an induction motor in terms of a recognized equivalent cir- cuit, with lumped constants or parameters. Sec- tion 9 gyes the letter symbols for dimensional case letters. (Partial exception: Zf

19、 and Zi-do not include primary leakage impedance.) 3.4 Impedances of external auxiliary devices, such as capacitors, for example, are written in upper case letters. 3.5 The sum of two or more like impedances, both of which are written in upper case letters, is usually indicated by use of the single

20、upper case letter with the two or more applicable subscripts. (Example: R, + Rc = Rat.) This rule does not apply to lower case symbols. 3.6 All impedances for three-phase motors re- fer to line-to-neutral quantities or equivalents, values. he “3” is used for the cage nearest the air gap, “4” for the

21、 next. That is, the cages are numbered consecutively starting at the air gap and working away from it. Mutual impedances between cages are denoted by use of multidigit (for example, two-digit) subscripts to indicate the cages concerned. 3.9 For single-phase motors, primary inped- ances of the main w

22、inding are denoted by the subscript “1”; those of the auxiliary winding by “la.” Secondary impedances, referred to the main winding, are denoted the same as for polyphase motors. If secondary impedances are referred to the auxiliary winding, “a” is added to the subscript. 3.10 Magnetizing reactance

23、is denoted by the symbol xM which, in this report, means the ap- parent magnetizing reactance due to the space fundamental component of the mutual air-gap flux. For polyphase motors, this refers to the reactance voltage developed in each phase by the mutual air-gap flux set up by all the phases. 3.1

24、1 Total impedance, at any slip, is denoted by a single upper case letter with subscripts as follows : Polyphase motors, line-to-neutral-no subscript. Single-phase motors, main winding only -no subscript, or T. (When motor is run- ning on main winding only, this is simply the ratio of impressed volta

25、ge divided by the current drawn; when both windings are energized, this is not true because of voltages induced from the other wind- ing.) Single-phase motors, auxiliary phase im- pedance-Ta. 3.12 Impressed voltages are denoted by an up- per case V,2 with suitable subscripts as needed. Generally spe

26、aking, these are the same as for a ANSI Y10.5-1968 recommends designating the symmetrical components of the currents and potential differences in unbalanced polyphase systems by adding double subscripts to the symbols, The first subscript designates phase and the second designates the se- quence; 1

27、for positive, 2 for negative, and 0 for zero sequence. Subscripts 1 and 2 have been so firmly estab- lished in the literature of induction-motor theory as identification of primary and secondary quantities that the above shown usage of p, n, and z are herein recom- mended. impedances, so far as prac

28、ticable. The positive direction of the voltage should be indicated. 3.13 Impedance drop and induced voltages are denoted by an upper case E, with suitable sub- scripts, generally paralleling the subscripts used for impedance quantities. 3.14 Root-mean-square currents are indicated by an upper case I

29、 with suitable subscripts, gen- erally the same as the impedance through which the current flows. 3.15 Efforts have been made to keep to a mini- mum the number of subscripts. However, it is recognized that there are not enough single subscripts. Consequently, double subscripts are frequently used, a

30、nd occasionally triple sub- scripts, particularly when the logic of the situa- tion makes the double or triple subscript easier to learn. 3.16 Additional subscript letters can usually be avoided by use of explanatory notes. However, if necessary, they may be added to indicate quantities at specific

31、slips as follows: (a) “L” for locked-rotor quantities, (b) “0” for no-load quantities, (c) “fl” for full-load quantities. 3.17 For certain other areas, some of which are covered explicitly in this standard, the follow- ing subscripts are recommended. (a) for shading-coil quantities in shaded-pole mo

32、tors: s; (b) for positive-sequence quantities: p; (c) for negative-sequence quantities; n; (d) for zero-sequence quantities: z; (e) for direct-axis quantities (two-reaction (f) for quadrature-axis quantities (two-reac- theory): d; tion theory): q. The circuits employed to illustrate the letter symbo

33、ls are not to be interpreted as official or necessarily recommended. They are merely typical and serve to illustrate the usage of the symbols. It is hoped that authors using other circuits will follow the guiding principles as far as possible. When other circuits are developed, using quantities not

34、covered by the guiding principles of this standard, it is recommended that the author of the paper show the cor- relation between the new quantities he is establishing in terms of the quantities given in MOTOR LETTER SYMBOLS IEEE Std 58-1978 Fig 1 Equivalent Circuit of a Polyphase Induction Motor, w

35、ith Alternate Iron Loss Circuits (a) Basic Circuit (b) Alternate Methods of Showing 2, this standard, so far as possible. (For an example of this practice, see Figs 8 and 9.) 4. Polyphase Motors For a single-cage or wound rotor motor, a com- monly used equivalent circuit is shown in Fig 1. The lette

36、r symbols recommended are shown. At no-load, the line current I becomes I,. For load conditions, the symbols would be as shown. For locked-rotor conditions the sub- script L can be used (example I, and rZL) if it is not convenient to indicate otherwise, that is, by note or prefatory phrase, that the

37、se are values with rotor locked. For double- and triple-cage rotors, equivalent circuits with letter symbols are given in Fig 2. The cages are numbered consecutively away from the air gap, starting with “3.” If the cages have independent end rings, all individual im- pedance quantities, r3, r, r5, x

38、3, x4, and x, in- clude resistances and the leakage reactances of the end rings. If the rotor has common end rings, these quantities refer to the resistances and leakage reactances of the bars of cages, 3, 4, and 5, respectively; and in this case, the re- sistance and leakage reactance values of the

39、 end rings are re and xe.This numbering system can be extended to any number of cages and any other combinations. 1 _ I I I .x34 I I I I I I I I I I (b) Fig 2 Equivalent Circuits for Multiple-Cage Polyphase Induction Motors (a) Double-Cage Motor (b) Triple-Cage Motor Wound-rotor motors involve actua

40、l quantities referred to the secondary as well as some re- ferred to the primary. Recommended addition- al symbols for line-to-neutral quantities are : Leakage impedance of rotor winding referred to itself = Z, = r, + jx, . Impedance of external secondary controller, actual = Z, - r2, + jx,. Impedan

41、ce of external secondary controller, referred to the stator = Zx = rx + jx,. Actual current in slip ring = I, . Actual secondary voltage, line-to-neutral =E_. - Actual secondary voltage, ring-to-ring = dFE,. 7 r IEEE Std 58-1978 IEEE STANDARD INDUCTION =f =b I R Z X (a) Fig 3 Equivalent Circuit of a

42、 Single-phase Induction Motor Running on Main Winding Only - Revolving-Field Theory (a) Detailed Circuit (b) Simplified Circuit (c) Simple Circuit (d) Alternate Iron Loss Circuit (a) (b) Fig 4 Equivalent Circuit of a Capacitor Motor Running with Both Windings Energized - Revolving-Field Theory (a) M

43、ain Winding (b) Auxiliary Winding A guide for nomenclature of polyphase mo- is used as the reference phase. Positive se- tors under unbalanced conditions is shown by the equivalent circuits of Fig 12. The case of unbalanced voltages is shown, which may serve as a guide for extension to the cases of

44、specific unbalanced windings. quence is in the order from phase A to B. 5. Single-phase Motors-Revolving-Field Theory Circuits and applicable letter symbols are il- Phase voltages and currents are used. Phase A lustrated in Figs 3, 4, and 5. 8 MOTOR LETTER SYMBOLS IEEE Std 58-1978 ! a2xMua2r2 Fig 5

45、Equivalent Circuits of a Capacitor Motor Under Locked-Rotor Conditions (a) Main Winding (b) Auxiliary Winding (c) Simplified Circuit TRANSFORMER VOLTAGES : IN CROSS-FIELD AXIS ETm IN MAIN AXIS SPEED VOLTAGES GENERATED : E5m BY MAIN-AXIS FLUX Esc BY CROSS-AXIS FLUX Fig 6 Schematic Representation of a

46、 Single-phase Motor - Cross-Field Theory 9 IEEE Std 58-1978 IEEE STANDARD INDUCTION 6. Single-phase Motordross-Field Theory Quantities needed to define a single-phase in- duction motor in terms of the classical cross- field theory are given in Fig 6, wherein the three circuits are represented. Fig 7 shows the fluxes according to this theory. Fig 6 repre- sents the motor in terms of three coupled cir- cuits. By suitable transformations of the equa- tions of these basic circuits, numerous net- work-type circuits have been developed. Fig 8 shows a network-type cir