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of all components such as current transformers, 
circuit breakers, short bus runs, etc., should be considered. 
It should be remembered that the lower the voltage, the more effective 
Resistances are included for certain items. 
U s e R e a c t a n c e s of All S ign i f i can t Circuit Elements. 
SHORT-CIRCUIT-CURRENl CALCUUTING PROCEDURES 45 
a small impedance is in limiting the short-circuit-current magnitude. 
That is why extreme care should he used to include all circuit elements 
in the impedance diagram, particularly for large ZORY/lZO-volt or 
240-volt systems. If care is not used, the calculations will result in a 
value of current far higher than will actually be realized in practice. 
See the example outlined in Figs. 1.46 and 1.47. This often results in the 
adoption of low-voltage switchgear of higher interrupting rating and 
higher cost than are actually required. If care is used in including all 
reactances, the calculated reiults will be close to the short-circuit currents 
obtained in practice. Short-circuit calculations are of most value if 
they reflect accurate answers. 
The resistance of all generators, 
transformers, reactors, motors, and high-capacity buses (above about 
1000-amp rating) is so low, compared with their reactance, that their 
resistance is not considered, regardless of their voltage rating. The 
resistance of all other circuit elements of the high-voltage system (above 
600 volts) is usually neglected, because the resistance of these parts has 
no significant bearing on the total magnitude of short-circuit currents. 
In systems of 600 volts and less the error of omitting resistances of 
all parts of the circuit except cables and small ampere rating buses is 
usually less than 5 per cent. However, the resistance of cable circuits is 
often the predominant part of the total impedance of a cable. When 
appreciable lengths of cable are involved in the circuit through which 
short-circuit current flows in a system of GOO volts or less, the resistance 
as well as the reactance of the cable circuits should be included in the 
When Is Resistance Considered? 
GENERATOR 
_ _ _ -. . . -. 
1100 FT. 101 
AND RESISTANCE OF THESE 
IN GENERAL USF REACTANCE 
OF-THESE CIRCUIT ELEMENTS. 
SHORT CIRCUIT CURRENT CONSIDERING 
REACTANCE ONLY : 20800 AMPERES 
SHORT CIRCUIT CURRENT CONSIDERING 
REACTANCE OF ALL PARTS PLUS 
RESISTANCE OF COW VOLTAGE 
CABLE = 11500 4MPERES. 
---- 
(20 FT 
FIG. 1.31 One-line diagram showing effect of resistance in cable circuits. 
46 SHORT-CIRCUIT.CURRENT CALCULATING PROCEDURES 
impedance diagram. The example of Fig. 1.31 shows the error that 
might result in neglecting cable resistance. 
In secondary network systems of 600 volts and less, the resistance as 
well as the reactance of the tie-cable circuits between substation buses 
should be included in the impedance diagram. The example of Fig. 1.32 
shows the effect of cable resistance in reducing short-circuit current in a 
typical industrial network. 
n n 
SHORT CIRCUIT CURRENT USING 
REACTANCE ONLY = 51000 AMPERES, 
SHORT CIRCUIT CURRENT USING 
REACTANCE PLUS RESISTANCE OF 
T IE CIRCUIT= 41000 AMPERES. 
T I E CIRCUITS 
208 Y/ lZOVOLTS. 
200 FT 
2- 250 M,CM 
3 CONO. CABLES ~~~~~T 
I N PARALLEL 
200 F T 
FIG. 1.32 
resistance of cable tie circuits. 
One-line diogrtlm of low-voltage secondary network system showing effect of 
Where to Use Exact Multiplying Factors. In low-voltage systems 
having considerable lengths of cahle, the X / R ratio may be so low that 
the 1.25 multiplying factor would be considerably in error. Hence in 
these systems where resistance is considered, determine the correct 
X / R ratio and then use minimum multiplying factor. 
GUIDE FOR REPRESENTING THE REACTANCE O F A GROUP O F MOTORS 
A group of motors fed from one substation or from one generating 
station bus may range in rating from fractional to several thousand horse- 
power per motor. All motors that are running at the time a short circuit 
occurs in the power system contribute short-circuit current and therefore 
should be taken into consideration. 
In that portion of the power sys- 
tem operating at 600 volts or less, there are generally numerous small 
Motors Roted 600 Volts and Below. 
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES A? 
motors, i.e., under about 50 hp. I t becomes impractical to represent 
each small motor in the impedance diagram. These motors are con- 
stantly being turned off and on; so it is practically impossible to predict 
which ones will be on the line when a short circuit occurs. Furthermore, 
it would be impractical to obtain the characteristics of each small motor 
and to account for the effect of the impedance of their leads. 
Where more accurate data are not available, the following procedure 
may be used with satisfactory results for representing the combined 
reactance of a group of miscellaneous motors operating a t 600 volts or 
less. 
1. In systems rated 240, 480, or 600 volts a t each generator and/or 
transformer bus, assume that the maximum horsepower of motors 
runniug a t any one time is equal to the combined kva rating of the step- 
down transformer and/or generators supplying that one bus (see Figs. 
1.33 and 1.34). 
2. 10 systems rated 208Y/120 volts, a substantial portion of the load 
usually consists of lights and a lesser proportion of motor load than in 
240-, 480-, or 000-volt systems. Hence in 208Y/120-volt systems where 
more accurate data are not available, assume a t each generator and/or 
transformer bus that the maximum horsepower of motors running a t 
REbCTbNCE QOW, 
TO UTILITY SYSTEM OF UTILITY OR5.,s 0.25% OR 
25 % 
REbCTbNCE OF 
EQUIVALENT 
MOTOR 
SYSTEM 
REbCTbNCE 
OF 750 K V b 
TRbNSF. 5.5% 
IMPEObNCE OIbGRbM 
750 KVb BASE 
SHORT EQUIVALENT MOTOR 
CIRCUIT 7 5 0 K V b 
240, 480, 600 VOLT SYSTEMS 
TO UTILITY SYSTEM 
0.50% OR 
50 % 
REACTbNCE OF 
EQUIVALENT El MOTOR REbCTbNCE 
OF 750 KVb 
TRbNSF. 
REbCTbNCE 
OF UTILITY 
SYSTEM 
EQUIVILENT MOTOR SHORT CIRCUIT 
375 K V b IMPEObNCE OIbGRbM hKVA 750 KVb BASE 
208Y/120 VOLT SYSTEMS 
FIG. 1.33 Oiagromr illustrating how to include motors in low-voltage radial systems. 
40 SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 
any one time is equal t,o 50 per cent of the combined rating of all step- 
down trausformers and/or generators supplying power to that one bus, 
Fig. 1.33. For large commercial buildings the 50 per cent figure may 
be too low. Check carefully the mot,or load on all large 208Y/120-volt 
systems. 
In the generalized rases referred t o in paragraphs 1 and 2 , no specific 
ratio of induction to synchronous motors or no specific number of motors 
which prcduce unusually high short-circuit current,s has been set fort,h. 
T o account for these variables, an average motor reitctance ihcluding 
leads is assumed to be 25 per cent for the purpose of preparing application 
tables like Table 1.5 and in making short-circuit st,udies where no more 
accurat,e data are available. It will he noted that the average motor 
reactance of 25 per cent is based on the transformer or supply-generator 
kva rating. This figure is between the values of 28 per cent for induc- 
tion mot,ors and 21 per cent for synchronous motors given in Table 1.14. 
Where the division between synchronous and iuduction motors is known, 
then more accurate calculations can be made by using the assumed motor 
reactances of Table 1.14. The reactances given in Table 1.14 are based 
on motor kva ratings and not supply transformer or generator ratings. 
T 750 KVA 
A 500 KVA 750 KVA 
500 KVA 
v 
EQUIVALENT MOTORS WOULD BE 250 KVA AND 
FOR 280Y/120 VOLT SECONDARY SYSTEM 
375 K VA 
- 480 VOLTS 
FIG. 1.34 
rvrternr.