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with a prime mover. Actually, during a 
system short circuit the synchronous motor acts like a generator and 
delivers shortcircuit current to the system instead of drawing load cur- 
rent from it (Fig. 1.4). 
As soon as a short circuit is established, the voltage on the system is 
reduced to a very low value. Consequently, the motor stops delivering 
energy to the mechanical load and starts slowing down. However, the 
inertia of the load and motor rotor tends to prevent the motor from slow- 
ing down. In other words, the rotating energy of the load and rotor 
drives the synchronous motor just as the prime mover drives a generator. 
6 SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 
The synchronous motor then becomes a generator and delivers short- 
circuit current for many cycles after the short circuit occurs on the system. 
Figure 1.5 shows an oscillogram of the current delivered by a synchronous 
motor during a system short circuit. The amount of current depends 
upon the horsepower, voltage rating, and reactance of the synchronous 
motor and the reactance of the system to the point of short circuit. 
LOAD CURRENT 
SYNCHRONOUS 
MOTOR 
-€t 
FIG. 1.4 Normally motors draw 
load current from the source or 
utility system but produce rhort- 
circuit current when a short cir- 
wit occurs in the d a d . 
U l I L I T Y 
SYSTEM 
,- \ 
SHORT CIRCUIT 
CURRENT FROM 
MOTOR 
. . -. . . 
SYSTEM 
SYNCMOYOUS ' 
FIG 1 5 IBmlowl l roce of 0s- 
Yoroll 
. . - . . ._ ,. _ _ .. ,. . . .. . . .. 
cillogrclm of short-circuit current 
produced by a synchronous 
motor 
SHORT ' . - I 
CIRCUIT 
SHORT CIRCUIT CURRENT DELIVERED BY 
A SYNCHRONOUS MOTOR. 
SHORT.CIRCUIT-CURRENT CALCULATING PROCEDURES 7 
HOW INDUCTION MOTORS PRODUCE SHORT-CIRCUIT CURRENT 
The inertia of the load and rotor of an induction motor has exactly the 
same effect on an induction motor as on a synchronous motor; i.e., it 
drives the motor after the system short circuit occurs. There is one 
major difference. The induction motor has no d-c field winding, but 
there is a flux in the induction motor during normal operation. This flux 
acts like flux produced by the d-c field winding in the synchronous motor. 
The field of the induction motor is produced by induction from the 
stator rather than from the d-c winding. The rotor flux remains normal 
as long as voltage is applied to the stator from an external source. How- 
ever, if the external source of voltage is removed suddenly, as it is when a 
short circuit occurs on the system, the flux in the rotor cannot change 
instantly. Since the rotor flux cannot decay instantly and the inertia 
drives the induction motor, a voltage is generated in the stator winding 
causing a short-circuit current to flow to the short circuit until the rotor 
flux decays to zero. To illustrate the short-circuit current from an 
induction motor in a practical case, oscillograms were taken on a wound- 
rotor induction motor rated 150 hp, 440 volts, 60 cycles, three phase, ten 
poles, 720 rpm. The external rotor resistance was short-circuited in each 
case, in order that the effect might he similar to that which would he 
obtained with a low-resistance squirrel-cage induction motor. 
Figure 1.6 shows the primary current when the machine is initially 
running light and a solid three-phase short circuit is applied a t a point in 
the circuit close to its input (stator) terminals a t time TI. The current 
shown is measured on the motor side of the short circuit; so the short- 
circuit current contribution from the source of power does not appear, but 
only that contributed by the motor. Similar tests made with the machine 
initially running a t full load show that the short-circuit current produced 
T. 
FIG. 1.6 , Tracer of oxillograms of short-circuit currents produced by an induction motor 
running at light load. 
8 SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 
by the motor when short-circuited is substantially the same, regardless of 
initial loading on the motor. Note that the maximum current occurs in 
the lowest trace on the oscillogram and is about ten times rated full-load 
current. The current vanishes almost completely in four cycles, since 
there is no sustained field current in the rotor to provide flux, as in the 
case of a synchronous machine. 
The flux does last long enough to prodnce enough short-circuit current 
to affect the momentary duty on circuit breakers and the interrupting 
duty on devices which open within one or two cycles after a short circuit. 
Hence, the short-circuit current produced by induction motors must he 
considered in certain calculations. The magnitude of short-circuit cur- 
rent produced by the induction motor depends upon the horsepower, 
voltage rating, reactance of the motor, and the reactance of the system to 
the point of short c. "cuit. The machine impedance, effective a t the time 
of short circuit, cmesponds closely with the impedance a t standstill. 
Consequently, the i iitial symmetrical value of Short-circuit current is 
approximately equnl to the full-voltage starting current of the motor. 
TRANSFORMERS 
Transformers are often spoken of as a source of short-circuit current. 
Strictly speaking, this is not correct, for the transformer merely delivers 
the short-circuit current generated by generators or motors ahead of the 
transformer. Transformers merely change the system voltage and mag; 
nitude of current but generate neither. The short-circuit current deliv- 
ered by a transformer is determined by its secondary voltage rating and 
reactance, the reactance of the generators and system to the terminals of 
the transformer, and the reactance of the circuit from the transformer to 
the short circuit. 
ROTATING-MACHINE REACTANCE 
The reactance of a rotating machine is not one simple value as it is for a 
transformer or a piece of cable, but is complex and variable with time. 
For example, if a short circuit is applied to the terminals of a generator, 
the short-circuit current behaves as shown i n Fig. 1.7. The current starts 
out a t a high value and decays to a steady state after some time has 
elapsed from the inception of the short cirroit. Since the field excitation 
voltage and speed have remained snbstantially constant within the short 
interval of time considered, a change of apparent react,ance of the machine 
may he assumed, to explain the change in the magnitude of short-circuit 
current with time. 
The expression of such variable reactance at any instant after the 
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 9 
occurrence of any short circuit requires a complicated formula involving 
time as one of the variables. For the sake of simplification in short-cir- 
cuit calculating procedures for circuit-breaker and relay applications, 
three values of reactance are assigned to generators and motors, viz., 
subtransient reactance, transient reactance, and synrhronous reactance. 
The three reactances can be briefly described as follows: 
1. Subtransient reactance X y is the apparent reactance of the stator 
winding at the instant short circuit occurs, and it determines the current 
Row during the first few cycles of a short circuit. 
2. Transient reactance X i is the apparent initial reactance of the 
stator winding, if the effect of all amortisseur windings is ignored and 
only the field winding considered. This reactance determines the cur- 
rent following the period when subtransient reactance is the controlling 
value. Transient reactance is effective up to 45 see or longer, depending 
upon the design of the machine. 
3. Synchronous reactance X d is the apparent reactance that deter- 
mines the current flow when a steady-state condition is reached. It is not 
effective until several seconds after the short circuit occurs; consequently,