Industrial Power Systems Handbook

987 Pages·1955·33.675 MB·English

by  Donald Beeman, Ed.

Industrial Power Systems
Handbook
DONALD BEEMAN, Editor
Manager, Industriaf Pwer Engineering
Industrial Engineering Seclwn
General Electric Company, Schenectady, New Yorlc
FIRST EDITION
McGRAW-HILL BOOK COMPANY, INC.
1955 New York Toronto London
Ch.UPh?r 1
by Donald Beeman, Alan Graeme Darling,
and R. H. Kaufmann
Short-circuit-current Calculating
Procedures
FUNDAMENTALS OF A-C SHORT-CIRCUIT CURRENTS
The determination of short-circuit currents in power distribution sys-
tems is just as basic and important as the determination of load currents
for the purpose of applying circuit breakers, fuses, and motor starters.
The magnitude of the shoncircuit current is often easier to determine
than the magnitude of the load current.
Calculating procedures have been so greatly simplified compared with
the very complicated procedures previously used that now only simple
arithmetic is required to determine the short-circuit currents in even the
most complicated power systems.
SHORT-CIRCUIT CURRENTS AND THEIR EFFECTS
If adequate protection is to he provided for a plant electric system, the
size of the electric power system must also be considered to determine
how much short-circuit current it will deliver. This is done so that cir-
cuit breakers or fuses may he selected with adequate interrupting capac-
ity (IC). This interrupting capacity should be high enough to open
safely the maximum short-circuit current which the power system can
cause to flow through a circuit breaker if a short circuit occurs in the
feeder or equipment which it protects.
The magnitude of the load current is determined by the amount Of
work that is being done and hears little relation to the size of the system
supplying the load. However, the magnitude of the short-circuit current
is somewhat independent of the load and is directly related to the size or
I
2 SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES
capacity of t,he power source. The larger the apparatus which supplies
electric power to the system, the greater the short-circuit current will be.
Take a simple case: A 440-volt three-phase lo-lip motor draws about
13 amp of current at full load and will draw only this amount whether
supplied by a 25-kva or a 2500-kva transformer bank. So, if only thc
load currcnts arc considered when selecting motor branch circuit break-
ers, a 15- or 20-amp circnit, breaker wnuld he specified. However, the
size of t,he power system back of the circuit breaker has a real bearing on
the amount of the short,-circuit, current. which can flow as a result of a
short circuit on the load side of the circuit breaker. Hence, a much
larger circuit breaker would be required to handle the short-circuit current
from a 2500-kva bank than from a 25-kva bank of transformers.
A simple mathematical example is shown in Fig. 1.1. These numbers
MUST BE CAPABLE OF INTERRUPTING 1000 AMPERES
El MOTOR LOAD
IOOV CURRENT
100 A 5 AMP
~ ~ 1 0O.HM1S
APPARENT
IMPEDANCE
20 OHMS
-
-E I00
SHORT CIRCUIT CURRENT = : = 1000- AMPERES
ZT 0.1
MUST BE CAPABLE OF INTERRUPTING 10,000 AMPERES
w
MOTOR LOAD
CURRENT
I000 A 5 AMP
2 1 = 0.01 OHMS
FIG. 1.1 Illustrotion showing that copocity of power source has more effect on rhort-
circuit-current magnitude than load.
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 3
have been chosen for easy calculation rather than a representation of
actual system conditions.
The impedance, limiting the flow of load current, consists mainly of
the 20 ohms apparent impedance of the motor. If a short circuit occurs
at F, the only impedance to limit the flow of short-circuit current is the
transformer impedance (0.1 ohm compared with 20 ohms for the motor);
therefore, the short-circuit current is 1000 amp, or 200 times as great as
the load current. Unless circuit breaker A can open 1000 amp, the
short-circuit current will continue to flow, doing great damage.
Suppose the plant grows and a larger transformer, one rated at 1000
amp, is substituted for the 100-amp unit. A short circuit at F, (bottom
in Fig. 1.1) will now be limited by only 0.01 ohm, the impedance of the
larger transformer. Although the load current is still 5 amp, the short-
circuit current will now he 10,000 amp, and circuit breaker A must be
able to open that amount. Consequently it is necessary to coiisider the
size of the system supplying the plant as well as the load current, to be
sure that circuit breakers or fuses are selected which have adequate
interrupting rating for stopping the flow of the short-circuit current.
Short-circuit and load currents are analogous to the flow of xvater in a
hydroelectric plant, shoivn in Fig. 1.2. The amount of water that flows
under normal conditions is determined by the load on the turbines.
Within limits, it makes little difference whether the reservoir behiiid the
dam is large or small. This flow of water is comparable to the flow of load
current in the distribution system in a factory.
On the other hand, if the dam breaks, the amount of water that will
flow will depend upon the capacity of the reservoir and will bear little
relation to the load on the turbines. Whether the reservoir is large or
small will make a great difference in this case. This flow of water is
comparable to the flow of current through a short circuit in the distribu-
tion system. The load currents do useful work, like the water that flows
down the penstock through the turbine water wheel. The short-circuit
currents produce unwanted effects, like the torrent that rushes madly
downstream when the dam breaks.
SOURCES OF SHORT-CIRCUIT CURRENTS
When determining the magnitude of short-circuit currents, it is
extremely important that all sources of short-circuit current he considered
and that the reactance characteristics of these sources be known.
There are three basic sources of short-circuit current:
1. Generators
2. Synchronous motors and synchronous condensers
3. Induction motors
4 SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES
All these can feed shorecircuit current into a short circuit (Fig. 1.3).
Generators are driven by turbines, diesel engines, water wheels, or
other types of prime movers. When a short circuit occurs on the circuit
fed by a generatar, the generator continues to produce voltage because the
field excitation is maintained and the prime mover drives the generator
at substantially normal speed. The generated voltage produces a short-
circuit current of a large magnitude which flows from the generator (or
generators) to the short circuit. This flow of short-circuit current is
limited only by the impedance of the generator and of the circuit between
the generator and the short circuit. For a short circuit at the terminals
of the generator, the current from the generator is limited only by its own
impedance.
FIG. 1.2 Normal load and short-circuit currents are analogous to the conditions shown in
the hydroelectric plant.
SHORT-CIRCUIT-CURRENT ULCULATlNG PROCEDURES 5
METAL CLAD SWITCHGEAR
SHORT CIRCUIT
CURRENT FROM
INDUCTION
MOTOR
FIG. 1.3 Generators, synchronous motors, and induction motors all produce short-circuit
current.
HOW SYNCHRONOUS MOTORS PRODUCE SHORT-CIRCUIT CURRENT
Synchronous motors are constructed substantially like generators; i.e.,
they have a field excited by direct current and a stator winding in which
alternating current flows. Normally, synchronous motors draw a-c
power from the line and convert electric energy to mechanical energy.
However, the design of a synchronous motor is so much like that of a
generator that electric energy can be produced just as in a generator, by
driving the synchronous motor 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 FIG. 1.4 Normally motors draw
load current from the source or
utility system but produce rhort-
UlILITY circuit current when a short cir-
SYSTEM
wit occurs in the dad.
SYNCHRONOUS
MOTOR -€t
,-
\
SHORT CIRCUIT
CURRENT FROM
MOTOR
. .- . . .
SYSTEM
-
SYNCMOYOUS '
Yoroll
F. .I-G . 1.. 5_ I,. Bm_l_o.w . ,l. l.r o.c.e. o.f. 0..s -
' . I
SHORT cillogrclm of short-circuit current
CIRCUIT produced by a synchronous
motor
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 at a point in
the circuit close to its input (stator) terminals at 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 at 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 at the time
of short circuit, cmesponds closely with the impedance at 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 in Fig. 1.7. The current starts
out at 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 Xi 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 Xd 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,
it has no value in short-circuit calculations for the application of circuit
breakers, fuses, and contactors but is useful for relay-setting studies.
Figure 1.8 shows the variation of current with time and associates the
various reactances mentioned above with the time and current scale.
Previous loading has an effect on the total magnitude of short-circuit
CURRENT DETERMINED
BY SYNCHRONOUS
OF TOTAL OSCILLOGRAM
OCCURS AT
ONLY TWO ENDS SHOWN
THIS TIME.
HERE. THIS REPRESENTS
THE BREAK BETWEEN
THE TWO PARTS.
FIG. 1.7 Trace of orcillograrn of hart-circuit current produced by a generator.