When making short-circuit calculations, the most accurate reactance data available should always be used. In particular, reactauce of specific generators, larger motors, and transformers should be obtained from the manufacturer.
Many short-circuit studies must he made without such specific data available, as for a proposed plant or in many older plants where the time and work required to obtain such data from the manufacturers make it impractical to do so. Since a great many short-circuit calculations fall in this category, it is desirable to use approximate reactance data. Such approximate data as are commonly used are given in Tables 1.11 to 1.31.
The most applicable reactances should be selected from these tables.
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 91
APPROXIMATE MACHINE CYCLES
Large Induction Motors. The approximate short-circuit reactance of an induction motor (or induction generator) in per cent on its own kva
times normal stalled rotor current*
Per cent =
TABLE 1.12 Approximate Reactances of 60-cycle Synchronous Machines Per Cent
Nearly all salient-pole generators built by General Electric Company 1935 have windings.
Add transformer reactance:
For compound-wound converters add 12 per cent.
For shunt-wound converters add 7 per cent.
These data are for estimating reactances individual large motors of several hundred or several horsepower.
* With rated voltage and frequency applied.
TABLE 1.13 Approximate Reactance of General Electric
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 93 1.13 Approximate Reactance of General Electric
Turhine Generators, 625 to 18,750 Kva. (Continued)
PROCEDURES
TABLE 1.13 Approximate Reactance of General Electric Company Turbine Generators. 625 to 18.750 (Continued)
0.8 power
0.5 hydrogen pressure.
TABLE 1.14 Reactances on Kvo of Connected Motors
Motors above 600 volt-induction Motors above 600
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 95
I n many short-circuit studies, the number and of motors, either induction or synchronous, are not known precisely. However, the short-circuit contri- bution from these motors must be estimated. I n such cases Table 1.14 is used to account for a large number of small induction and synchronous motors.
The proportions of synchronous and induction motors (at all voltages) should be known for short-circuit investigations. Some typical ratios of total plant motor load which are usable in preliminary work are given in Table 1.15.
The kva of the motors which are energized at one time varies also with the type of plant and should be investigated for the more complete studies. Approximate relations of energized to installed motors and of energized motors to source (transformer and/or generator) capacity are given in 1.16.
Assumed Motor Reactances- Group of Small Motors.
Cement
...
Machine
...
rolling mills..
...
Paper grinder
...
Commercial
...
TABLE 1.15 of Induction Synchronous Motors
40 60
TABLE 1.16 Rotio of Energized and Instolled Motors
Energized
APPROXIMATE IMPEDANCE O F TRANSFORMERS
The impedance of transformers ronsidered in a short-circuit study should be obtained from the name or the manufacturer. However, where such data cannot be obtained, the values given in Tables 1.17 to 1.19 may used in short-rircuit studies for estimating the short-circuit currents in the usual case.
I n the usual short-circuit study, the transformer reactance and imped- ance may assumed t o be the same without causing significant error for transformer banks above 300 kva. This assumption is useful because transformer name-plate data include impedance and not reactance.
Approximate Resistance, Reactance, and Impedance of TABLE 1.17
Single-phase Distribution Transformers
3
High voltage: volts
voltage; volts-
The reactance of a cable circuit is, generally speaking, a function of the spacing between conductor centers and the conductor diameter. Know- ing the conductor spacing and diameter, the reactance of three-conductor
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 97 Approximate Impedance of 60-cycle Power Transformers TABLE 1.18
Approximate Reactance o f Load-center-type
of insulation class.
This formula does not take into account any increase of reactance t o the spiraling of the strands. Such increase is usually negligible in three-conductor cables and in large single-conductor cables, but it may amount to to 2 per cent in small single-conductor cables.
The effect of irregular spacing of the and of magnetic binder causes an increase of reactance of single-conductor cables, com- pared with otherwise equivalent three-conductor cables. Cable insula- tion thickness varies with different types of insulation for a cable of a given voltage class. The approximate reactances of cables taking into account these variables are shown in Tables t o 1.22.
TABLE 1.20 Approximate Resistance, Reactance, and Impedance of Cables in Magnetic Ducts per 100 Ft
single-conductor per dud.
per 100
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 99
TABLE 1.22 Correction Factors for Nonmagnetic Ducts
Single-condudor
TABLE 1.22 Correction Factors for Nonmagnetic Ducts. (Continued)
Three-conductor Cables
Determine from corrected of X and R. N o required for interlocked
Three single-condudor in
iron conduit..
...
Three-conductor coble in iron con- duit or interlocked armored cable
...
Three-conductor cable in nonmag- netic duct..
...
armor.
Factor for correcting
o f
Factors for correcting resistances
1.075 TABLE 1.23 Per Cent Reactance of Typical Three-phase Cable Circuits
Per Cent Reactance o f 1000 Circuit Feet
Three single-conductor in
iron conduit.
...
Three-conductor cable in iron con- duit or interlocked armored cable.
...
Three-conductor cable in
duct..
...
Three ringlo-conductor in
...
Three-conductor iron con-
duit interlocked armored
...
CALCULATING PROCEDURES 101
APPROXIMATE REACTANCE OF BUS CYCLES
Unlike cable circuits the resistance of bus-bar circuits is so low com- pared with reactance t h a t the resistances of bus bars may he neglected in all a-c short-circuit calculations significant error. There been many papers written on the subject of bus-bar reactance calcula-
TABLE 1.24 Reactance Typical Three-phase Low-voltage Copper Busway Circuits
Although not used in short-circuit calculations the resistance of typical copper circuits is in Table 1.25.
TABLE 1.25 Resistance of Typical Copper Circuits Current Capacity Resistance.
of Amp Ohms 1000 Ft
FIG. 1.58 showing spacing of rectangular cycler).
FIG. 1.59 Chart showing reactance spacing of rectangular bur cycler).
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES
FIG. 1.60 Chart showing spacing of rectangular bus
FIG. 1.62 Chart showing spacing of channel cycler).
REACTANCE A N D RESISTANCE OF OVERHEAD LINES
To assist in obtaining the conductor spacings, typical
arrangements are shown in Fig. 1.63. The arrangements used in practice will vary from system t o system, b u t of space limitations only these two are
For ordinary single-phase circuits, the equivalent spacing is the dis- tance between For ordinary circuits, the equiva- lent spacing is by the formula where A , B , and
are the distances, center t o center, of the conductors follows:
T h e resistance of overhead lines may not always he neglected without significant error. In general, long runs of overhead lines (several miles) at 2.4 t o 13.8 k v with small conductors 250 MCM or less have significant resistance compared to reactance; therefore resistance should be con- sidered in short-circuit calculations for short circuits a t the ends of such long overhead lines. should he considered in low-voltage (600 volts or less) overhead lines.
Reactances and resistances may be taken from Table 1.26 for small
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 105
spacings (up t o 8 ft) and from Figs. 1.64 and 1.65 for spacings t o 20 ft.
Under usual application conditions, reactance varies over quite a narrow range. 1.27 includes the usual varia- tions as well as “average ohms per mile” which are normally satis- factory for quick estimating work. large conductors, used to carry unusually large amounts of power for short distances, have abnor- mally low reactance so that this is not applicable.
4 - P I N
A N D S P O O L - T Y P E SECONDARY RACK
6 - P I N
FIG, 1.63
or circuits.
of on four- six-pin for in calculating line
106
FIG. 1.64
hard-drown stranded copper cycle).
Chart of transmission lines using
SHORT-CIRCUIT-CURRENT 07
SEQUENCE 60 CYCLE
EQUIVALENTA SPACING OF IN FEET FIG. 1.65
ACSR conductors cycler).
Chart of liner
SHORT-CIRCUIT-CURRENT PROCEDURES I09 TABLE 1.27 Approximate Equivalent Delta Spacing Average
Reactance r M i l e of Three-phase 60-cycle Transmission Lines
Awg
155 i8520238.846.550.724.8 29.732.4 2.06 0.067 134 1631180 33.6 40.8 45.0 21.5 28.8 1.87 0.625 0.061
TABLE 1.28 Reactance of Typical Three-phase Medium- and Low-voltage Distribution Circuits*
,
. . .
, . 230 460 575Equivalent .
.
. . delta.
.. . .
spacing,. . .
42Volts Equivalent (line-to-lid in.
230 460
575 I8
2,300 30
4,160 30
6,900 36
13.800 42
48
33,000 54
SHORT-CIRCUIT-CURRENT PROCEDURES
line- delta
44 5.5
66 8.0
14.0 16.5 20.0
220 29.0
APPROXIMATE REACTANCE O F LOW- VOLTAGE BREAKERS A N D DISCONNECTING SWITCHES
I n some low-voltage circuit calculations, the reactance of switch- ing equipment may be significant. The reactance of circuit breakers varies greatly, depending upon the rating and design. For approxima- tion, however, the reactance in ohms of a circuit breaker may be taken as
0.2
continuous rating of circuit breaker in amperes The reactance of lever switches and disconnecting switches for
circuits (600 volts and below) is of the order of magnitude ranging
from 0.000050 t o per pole at from
4000 t o 400 amp, respectively, depending on the ampere rating, design, and phase spacing of the switches.
APPROXIMATE REACTANCE O F CURRENT TRANSFORMERS
These data are useful for calculation of short-circuit currents circuits 600 volts and below.
The reactance of current transformers depends their current rating and design arid varies over a wide range. Therefore, a value of reactance applicable to a variety of current transformers
given.
Current Transformers with Primary Circuits of t h e Wound Type.
Approximate data renctarice a t 60 cycles for current transformers of
SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES
type W, covering current ratings from 100 t o 800 amp based on tests at short-circuit currents, are given in Table 1.30. The values in Table
1.30 apply t o with a burden of I volt-amp less at 5 amp or a t For higher burdens, the
referred t o the primary side will somewhat increased, but the increase is far less than t h a t occurring a t normal currents, berause of the reduced mutual inductance between primary and secondary windings. The reactance values based on low burden are conservative fur calculations of maximum short-circuit current.
TABLE 1.30 Over-all Reactance of Type W Current Transformers, Referred to Primary Winding
Approximate at Short-circuit with D-C Component, Symmetrical from 15,000 55.000 Amp
Current of Reactance Primary Winding, 60 Cycles, reactance for current transformers of the following types, rated a t 5000
volts: and
Current Transformers Having a Bar-type Primary Conductor. For bar-type current transformers with from 1000 t o 4000
short circuits. Strictly speaking, the reactance the three phascs
he unequal i n a side-by-side assembly of current transformers, but for short-circuit-current calculations an average value can ordinarily be used without serious error.
T o say t h a t the reactance for bar-type transformers is equal t o the air reactance of the primary conductor, considering its length, size, and shape, and the spacing between phases, is a fair approximation.
No. of
..
2400..
4800 96
1 2400 lo 3 13,800
APPROXIMATE REACTANCE O F A - C REACTORS AND FEEDER REGULATORS
The reactance is proportional t o the rating.
voltage drop through the reactor at rated current and frequency divided hy the line-to-neutral voltage of the circuit gives the per-unit reactance on the current rating of the reactor. (This will also he the per-nnit reactance on the kva rating of the circuit if the rated reactor current is the same as the rated current of the circuit.)
The reactanre of a given step regulator is modified by the position of the tap changer and becomes a maximum a t maximum voltage It is minimum at neutral position, while at maximum the impedance is higher than at neutral.
TABLE 1.31 Short-circuit of Feeder of
Per cent of
Min
0 . 6 5
....
0.6....
0.70.15
....
No. of
Indue..
... !-
I or 3...
IStep
...
1Step.
...
3Step.
...
3SHORT-CIRCUIT-CURRENT CALCULATING PROCEDURES 113
REFERENCES
1. A I E C Committee Simplified Calculation of Fault Currents,
Committee Fault Trans.
G I . pp.
Revision to Report, Simplified Calculation of Fault Currents, February, p. 65.
A. Short for Systems,
GO, pp. 1121-1136.
5. 0. Drop and a t Short-circuit in
Circuits. Trans. A I E E , 1941, 60, pp.
Calculation of Fault Currents, Trans. A I E E ,
1948, 1433.