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-SHORT CIRCUIT CURRENT GOES THROUGH HERE 
41 
(1.20) 
Asymmetrical short-circuit current 
Asymmetrical short-circuit kva 
= (symmetrical current) (multiplying factor) 
= (symmetrical kva) (multiplying factor) 
DIAGRAMS 
One-line Diagram. The first step in making a short-circuit study is to 
prepare a one-line diagram showing all sources of short-circuit current, 
i.e., utility ties, generators, synchronous motors, induction motors, syn- 
chronous condensers, rotary converters, etc., and all significant circuit 
elements, such as transformers, cables, circuit breakers, etc. (Fig. 1.28). 
The second step is to 
make an impedance or reactance diagram showing all significant react- 
ances and resistances (Pig. 1.29). In the following pages this will be 
Make an Impedance or Reactance Diagram. 
C UTILITY SYSTEM I TRANS D GENERATOR GENERATOR 
CABLE E 
SHORT 
CIRCUIT 
LARGE CABLE J 
MOTOR 
FIG. 1.28 e diagram c 
480 VOLT 
MOTORS 
, typical large industrial power system. 
FIG. 1.29 Reactonce diagram of system shown in Fig. 1.28. 
42 SHORT-ClRCUIT.CURRENT CALCULAltNG PROCEDURES 
referred to as an impedance diagram, recognizing of course that only 
reactances will be used in many diagrams. The circuit element,s and 
machines considered in the impedance diagram depend upon many 
factors, i.e., circuit voltage, whether momentary or interrupting duty are 
to be checked, etc. 
The foregoing discussion and Table 1.2 explain when motors are to be 
considered and what motor reactances are to he used for checking 
the dut,y on a given circuit breaker or fuses of a given voltage class. 
There are other problems, i.e., (1) selecting the type and location of the 
short circuit in the system, (2) determining the specific reactance of a 
given circuit element or machine, and (3) deciding whether or not circuit 
resistance should be convidered. 
SELECTION OF TYPE AND LOCATION OF SHORT CIRCUIT 
Three-phase Short Circuits Generally Considered. I n most indus- 
trial systems, the maximum short-circuit current is obtained when a 
three-phase short circuit occurs. Short-rircuit-current magnitudes are 
generally less for line-to-neutral or line-to-line short circuits than for the 
three-phase short circuits. Thus, the simple three-phase short-circuit- 
current calculations will suffice for application of short-circuit protective 
devices in most industrial systems. 
In some very 
large systems where the high-voltage-system neutral is solidly grounded, 
maximum short-circuit current flows for a single phase-to-ground short 
rircuit. Such a system might be served from a large delta-Y trans- 
former bank or directly from the plant generators. 
Hence the only time that single-phase short-circuit-current calculations 
need be made is on large high-voltage systems (2400 volts and above) 
with solidly grounded generator neutrals or where main transformers 
that supply a plant from a utility are ronnected in delta on the high- 
voltage side (incoming line) and in Y with solidly grounded neutrals 
on the low-voltage (load) side. 
The calculations of unbalanced short-circuit currents in large power 
systems can best be done by symmetrical components, see Chap. 2. 
Normally, generator and large delta-Y transformer secondaries are 
grounded through a reactor or resistor to limit the short-circuit current 
for a single line-to-ground short circuit on the system to letis than the 
value of short-circuit current for a three-phase short circuit. 
Several tests have been 
made to evaluate the effect of arc drop at the point of short circuit in 
reducing the short-circuit-current magnitude. It was felt by some 
engineers that the current-limiting effect of the arc was pronounced. 
These tests showed, however, that for circuit voltages as low as 300 volts 
Unbalanced Short Circuits in Large Power Systems. 
Bolted Short Circuits Only Are Considered. 
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 43 
there may be no substantial difference in the current that flows for a 
bolted short circuit and when there is an arc of several inches of length. 
These test,s also confirmed modern calculating procedure as an accurate 
method of estimating the short-circuit-current magnitude in systems 
of 600 volts and less. 
.4rcs cannot be counted on to limit the flow of short-circuit currents 
even in louvoltage circuits; so short-circuit-current calculations for 
all circuit voltages are made on the basis of zero impedance at the point 
of short circuit, or, in other words, a bolted short circuit. This materially 
simplifies calculation because all other circuit impedances are linear in 
magnitude, whereas arcs have a nonlinear impedance characteristic. 
At What Point in the System Should the Short Circuit Be Considered 
to Occur? The maximum short-circuit current will flow through a cir- 
cuit breaker, fuse, or motor starter when the short circuit occurs at the 
4160V. 
I I I 
$? MAX.SHORT CIRCUIT DUTY ON $- $EW:RS FOR SHORT CIRCUIT BREAKERS ON THIS BUS 
1 
T 
?; 
A&?? 
Y T T - 3 
& + * + r y r-x 
MAX. DUTY FOR 
THESE BREAKERS 
OCCURS FOR 
SHORT CIRCUIT 
HERE 
FIG. 1.30 Location of faults for maximum Short-circuit duty on circuit breakers. 
44 SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 
terminals of the circuit breaker, etc. (Fig. 1.30). These devices, if 
properly applied, should be capable of opening the maximum short- 
circuit current that can flow through them. Therefore, only one short- 
circuit location (at the terminal of the device) need be considered for 
checking the duty on a given circuit breaker, fuse, or motor starter. 
DETERMINING REACTANCES AND RESISTANCES OF CIRCUITS AND MACHINES 
Typical reactances of circuit elements and machines are given at the 
end of this chapter. These 
tables may be used as a basis for assigning values to the various elements 
of the impedance diagram. The reactances and resistances are all line- 
to-neutral values for one phase of a three-phase circuit. Where the 
reactances of a specific motor, generator, or transformer are known, 
these values should he used in lieu of the typical reactances in this 
chapter. The following is a guide to general practice in selecting and 
representing reactances. 
Whether or not 
the reactance of a certain circuit element of a system is significant 
depends upon the voltage rating of the system where the short circuit 
occurs. In all cases, generator, motor, and transformer reactances 
are used. In systems rated above 600 volts, the reactances of short 
bus runs, current transformers, disconnecting switches, circuit breakers, 
and other circuit elements of only a few feet in length are so low that 
they may be neglected without significant error. 
In circuits rated 600 volts or less, the reactances of low-voltage current 
transformers, air circuit breakers, disconnecting switches, low-voltage bus 
runs, etc., may have a significant hearing on the magnitude of total short- 
circuit current. 
As a general guide, the reactance of the low-voltage secondary-switch- 
gear section in load-center unit substations with closely coupled trans- 
formers and secondary switchgear is not significant for all voltages of 
600 volts and below. However, where there are several transformers or 
generators paralleled on one bus, or connections several feet long between 
a single transformer and its switchgear, reactances of the bus connections 
will generally be significant and should be considered in short-circuit 
calculations. In systems of more than about 1000 kva on one bus a t 
208Y/120 or 240 volts, reactance of all circuit components such as short 
bus runs, current transformers, circuit breakers, etc., should be included 
in the short-circuit study. 
I n systems of more than about 3000 kva on one bus a t 480 volts or 
600 volts, reactances