1、AlEENo. 66July 1957Proposed GuideforDETERMINATION OFSHORT-CIRCUIT CHARACTERISTICSOF DIRECT-CURRENT MACHINERY(Published for trial use)Published byAMERICAN INSTITUTE OF ELECTRICAL ENGINEERS33 West Thirty-ninth Street, New York 18, N. Y.ACKNOWLEDGEMENT The Institute wishes to acknowledge its indebtedne
2、ss to those who have so freely given of their time and knowledge, and have conducted experimental work on which many of the AIEE Guides are based. The work of preparing this Guide was carried out by a Working Group of the Direct-Current Machinery Subcommittee of the AIEE Rotating Machinery Committee
3、. The personnel of this Working Group was: A. T. McClinton, Chairman O. C. Coho R. Lamborn W. R. Crites J. P. OConnor J. S. Ewing D. S. Pearson L. Greer . H. Schneider C. B. Hathaway C. Weilbaecher L. H. Hirsch CONTENTS Purpose 3 1.0 Scope2.0 Calculations From Design Parameters 3 2.1 Equations for T
4、ransient Armature Current2.2 Equations for Transient Field Current 3 3.0 Calculations from Nameplate Data3.1 Effective Armature-Circuit Resistance 3 3.2 Initial Rate, of Rise of Armature Current 4 4.0 Effect of Flashover _ 5 5.0 Nomenclature 8 6.0 Bibliography2 Proposed Guide For Determination of Sh
5、ort-Circuit Characteristics of Direct-Current Machinery Purpose The purpose of this Guide is to: (a) Review the factors that affect the short-circuit characteristics of direct-current ma chinery. (b) Recommend equations for calculating the transient armature and field current from design parameters.
6、 (c) Recommend methods for approximating the rate of rise and peak value of armature cur rent from nameplate data. (d) Discuss the causes of flashover and its effect on short-circuit current and effective armature-circuit resistance. 1.0 Scope, 1.0.1 This Guide presents general recommendations for d
7、etermining, by approximate methods from name-plate data and by more exact methods from design data, the short-circuit characteristics of direct-current motors and generators. Both methods are applicable to General Purpose, General Industrial Mill Motors, and Special Purpose direct-current machines.
8、This includes constant-speed and adjustable-speed motors and machines with and without compound windings, and with and without compensating windings. 1.0.2 This Guide is intended to help those con cerned with the transient characteristics of direct-current machines and direct-current systems and the
9、 effects of these transients on their operation. The cal culated values of rate of rise and peak armature cur rent will facilitate the proper selection of system com ponents which will safely withstand the mechanical and thermal stresses during fault. When only name-plate data is available, the appr
10、oximate methods pre sented will yield results sufficiently accurate for estimates. Values computed by this method will be high, in general, thus on the safe side. Additional data from machine design sheets, or tests, will permit use of the more exact methods of computation with the view of minimizin
11、g the size of components and circuit protective equipment. 1.0.3 For an exact and rigorous analysis it should be emphasized that the variability and non-linearity of the parameters involved in short-circuit calculations present a difficult, if not insuperable task. For these reasons, the equations r
12、ecommended for the more exact method involve simplifying assumptions and errors within the limits of approximately 5 to +10 percent in peak armature current. The approximate method utilizing only nameplate data will have a range of accuracy from 20 to +30 percent. These accuracies refer to condition
13、s where no flashover exists. 2.0 Calculations from Design Parameters 2.1 Equations for Transient Armature Current It is recommended that the methods of computa tion presented in references 6, 9, 20 and 21 be used to determine the peak and transient value of armature current from design data. 2.2 Equ
14、ations for Transient Field Current It is recommended that the method of computation presented in references 6, 9, 20 and 21 be used to determine the peak and transient value of field cur rent from design data. 3.0 Calculations from Nameplate Data 3.0.1 In the preliminary design of direct-current pow
15、er systems, generally only the voltage and power rating of the machines are known. Even with this minimum data some knowledge of system design re quirements may be provided by an estimate of peak armature current and peak fault current under assumed conditions. The approach is as follows: A simple s
16、chematic representation consisting of a voltage source and a resistance can be made for each direct-current machine. The voltage source represents the generated voltage of the machine at the initial speed, which is assumed constant up to the time of peak short-circuit current. The resistance is an e
17、ffec tive internal resistance which represents all factors tending to limit the flow of current from the genera tor, or motor, which operates as a generator under fault condition. These factors are: armature circuit ohmic resistance, brush contact drop, reactance volt age, and flux reduction and dis
18、tortion. 3.0.2 A similar simple schematic representation can also be employed to obtain an approximation of the initial rate of rise of armature current. The circuit consists of a voltage source, and an inductance where the voltage is the generated voltage prior to short circuit and the inductance i
19、s an equivalent armature circuit inductance for the machine. 3.0.3 These two equivalent circuits, which will be discussed more fully in the sections to follow, cannot be combined in an attempt to obtain the overall trans-sient response to short circuit. Each is applicable only for its specific purpo
20、se. When more than one machine is connected to a system reasonable accuracy can be expected on system calculations for total fault cur rent if the time to reach peak current is essentially equal for all machines on the system. 3.1 Effective Armature Circuit Resistance 3.1.1 The transient armature cu
21、rrent of a direct-current machine on short circuit rises rapidly to a peak value and then decays slowly to a sustained value (zero magnitude if the machine is self-excited). The decay to the sustained value is dependent on the 3 time constant of the exciting windings which is of the order of 0.1 to
22、1.0 second. The peak value of armature current, which is reached prior to this time, will cause flashover in large machines if the current is not interrupted quickly. Therefore, it is apparent that the peak armature current is the most important quantity. Since the effective armature circuit resista
23、nce varies considerably throughout the transient the value cor responding to peak armature current is presented. This resistance will be referred to as rd in the per unit system. “ i l MM i I I | HI i I I III I I 111 i i I I III i i i l II HP i RPM i 10“ Fig. 1Per Unit Equivalent Armature Circuit Re
24、sistance Generalized Curve for Motors and Generators, Initial Condition No Load 3.1.2 The per unit effective internal armature cir cuit resistance, r of the direct-current machine has been generalized from available data on a wide range of direct-current machines, and shown as a function of the prod
25、uct of horsepower and speed in Figure 1. Data for plotting this curve have been obtained for calculations on these machines as presented in refer ence 10. However, in some cases where test data were available it was used in preference to calculated results. It is recognized that the type of field wi
26、nd ings, pole-face windings, rated voltage, temperature rise, type of machine (i.e., NEMA General Purpose or Mill), and the design of the machine all have some influence on the value of rd. Figure 1 is suitable for the general purpose machines, shunt or compound wound, constant or adjustable speed,
27、with or without pole-face windings, continuous duty and having a voltage rating in the range from 115 volts to 750 volts. The value of rfd for the low-voltage machine usually will be nearer the top curve and for the high-voltage machine will be near the lower curve on Figure 1. All values of r/d are
28、 for base speed and voltage, zero external resistance and no initial load. The initial load current affects the magnitude short-circuit cur rent. This can be introduced as a correction to the per unit short-circuit current calculated from rd ob tained from Figure 1. The correction is added for machi
29、nes operating as generator prior to short circuit and subtracted for motor action. The magnitude of this correction is the initial load current expressed in per unit. 3.1.3 Experience has shown that the effective armature-circuit resistance of a direct-current machine can be expressed as a function
30、of rating-speed prod ucts provided the same basis for rating is used for all motors and generators. Thus, all units (motors or generators) should be rated either in terms of horse power or kilowatts in any system study. Figure 1 has been plotted on the basis that the rating of all machines will be e
31、xpressed in horsepower for the purpose of obtaining the effective armature-circuit resistance. Thus the equivalent horsepower-rpm prod uct for a generator will be: hp X rpm X 10“5 = 1.34 kw X rpm X 105 (1) 3.1.4 The value of effective resistance obtained from Figure 1 along with a voltage source equ
32、al to the generated voltage in per unit can be utilized to represent the equivalent circuit of each direct-current machine on a system for fault-current calculations. Resistance external to the machines also must be in cluded in this equivalent circuit. However, the external resistance reflected int
33、o each machine cannot exceed approximately twice the value of rfd obtained from Figure 1. When this condition is obtained, the ma chine is not considered to be short-circuited and therefore must be treated as if it were overloaded. It should be emphasized that the resulting circuit representation is
34、 for peak magnitudes of short-circuit current. If the short-circuit current contribution of all machines in a system reach peak at nearly the same time, the overall system accuracy should be com mensurate with the accuracy of rd values. If there are large variations in the time to peak current, accu
35、racy can be improved only by using the more exact method of computation found in Section 2. 3.2 Initial Rate of Rise of Armature Current 3.2.1 When a step voltage, E is placed across a circuit consisting of a resistance and inductance, L, in series the initial and maximum rate of rise of cur rent is
36、 given by the equation (S)-= E/L amperes/sec. (2) where E is in volts and L is in henrys. 3.2.2 Usually the rate of rise of armature current of greatest interest occurs when a machine is short-circuited while operating at or near its rated voltage and speed. It is shown in the literature6 that the q
37、uantity, L p called “unit inductance“ and defined as T 2X60 27TPN, (3) is proportional to the unsaturated armature circuit in ductance for machines that fall in the same class. Et is the base voltage, Ial is base armature current, P is the number of poles, and Nx is base speed. Hence, for machines i
38、n the same class, the initial armature circuit inductance is L0=CXL0I (4) where Cx is a characteristic constant for a particular class of machines. From equations (2, 3, 4) the initial 4 rate of rise of armature current of a direct-current machine under short circuit, may be expressed as /d - Eo - 2
39、,rPNi EQli (5) dt ; CxLai 2X60CX * E, Replacing the constant numerical ratio - by its equivalent value 1/19.1, and the ratio E0/El by e0, gives where average values of Cx for four broad classifications of direct-current machines are given in Table I, and e0 is the per unit armature voltage before sh
40、ort circuit. When the current is expressed in per unit, equation (6) becomes (dF)=l93tperumt/sec- (7) Values of Cx are given in Table I for the classifications into which all direct-current machines have been grouped for the purpose of approximate rate of rise calculations. These values of Cx are av
41、erage values which have been obtained from calculations18 of unsaturated machine in ductance for a large number of machines.15 For detailed information on the variation of Cx from the average values given in the table below the referenced paper15 should be consulted. Values of the factor 1/19.1 Cx c
42、or responding to the listed values of Cx are also given in Table I for convenience in computation of rate of rise in equations (6) or (7). Table I. Per Unit Inductance Approximate 1 Values of Cx 19.1 Cx Motors: Without pole-face windings 0.4 0.13 With pole-face windings 0.1 0.52 Generators: Without
43、pole-face windings 0.6 0.09 With pole-face windings 0.2 0.26 Equation (7) is plotted in Figure 2 for the several values of Cx shown in Table I. 1000 MOO 3000 4000 9000 O0O 7000 No Of POLES RPM (PN,) Fig. 2Curves Showing Initial Rate of Rise of Short-Circuit Current 3.2.3 If a direct-current machine,
44、 when short-circuited, behaved as a resistance-inductance circuit hav ing constant parameters there would be little difficulty in describing the complete transient. However, the unsat urated inductance of the armature circuit, L (which is a maximum at no load), and rd change due to saturation and ed
45、dy currents so that they cannot be considered constant. Although these parameters do not remain con stant during the transient, the oscillographs of actual tests show that the current will rise at a nearly constant rate, as determined by equation (7), until the current reaches approximately two-thir
46、ds its maximum value. Hence, from the behavior of observed transients on direct-current machines it may be concluded that the initial voltage of a machine, E0, before short circuit, and its unsaturated inductance, L provide the essential data for representing a very important part of the transient.
47、4.0 Effect of Flashover 4.1 Definition of a Flashover 4.1.1 A suddenly appearing arc, flashing over the commutator surface and accompanied by an explosive noise, is simple but positive evidence of the occurrence of a flashover. Very often, the ensuing damage to com mutator, brush holders, and brushe
48、s is additional com plementary evidence. Flashovers are characterized by extremely long extensions of the commutation arc at the trailing edge of the brushes, or by complete arcs from brushholder to brushholder, either across the commutator surface, or from brushholder to mechanical structure then t
49、o the brushholder of opposite polarity from another point in the mechanical structure. 4.1.2 The resulting damage from flashovers vary greatly depending upon the severity. In some instances, the damage is minor, and the machine may continue in operation without maintenance attention, provided the cause is external to the machine itself. From a damage standpoint, minor flashovers of this nature often manifest themselves by burned spots on the edges of the brushes, elimination of polish of the commutator film, and arcing pits on the commutator bars,
