Stevenson J. Power system analysis

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406 AER 10 SYMMETRICAL FAULTS

prefault current. Subtransient reactance is used for generators in the E j X

method, and fo r synchronous motors the recommended reactance is the X� of

the motor times 1.5, which is the approximate value of the transient reactance

Xd of the motor. Induction motors below 50 hp are neglected, and various

multiplying factors are applied to the X� of larger induction motors depending

on their size. If no motors are present, symmetrical short-circuit current equals

subtransient current.

The impedance by which the voltage

f at the fault is divided to nd

short-circuit current must be examined when the E j X method is used. In

speciing a breaker for bus

, this impedance is Zkk of the bus impedance

matrix with the proper machine reactances since the short-circuit current is

eressed by Eq. (10.19). If the radio of XjR of this impedance is 15 or less, a

breaker of the correct voltage and kilovoltamperes may be used if its interrupt

ing current rating is equal to or exceeds the calculated current. If the X j R ra

is unknown, the calculated curren t should be no more than 80 of the allowed

value for the breaker at the existing bus voltage. The SI application guide

species 'a corrected method to account for ac and dc time constants for the

cay of the current amplitude if the XjR ratio exceeds 15. The corrected

method also considers breaker speed.

Example 10.7. A 25,000-kVA 13

8-kV generator with X = 15% is connected

through a transformer to a bus which supplies four identical motors, as shown in

Fig. 10.13. The subtransient reactance X; of each motor is 20% on a base of 5000

kVA, 6.9 kV. The three-phase rating of the transformer is 2

,000 kYA, 13.8/6.9

kV, with a leakage reactance of 10%. The bus voltage at the motors is 6.9 kV when

a three-phase fault occurs at point P. For the fault specied, determine (a) the

subtransient current in the fault, (b) the subtransicnt current in breaker A,

and CC)

the symmetrical short-circuit interrupting current (as defined fo r circuit-breaker

applications) in the fault and in breaker A.

Solution. (a) For a base of 25,000 kV A, 13.8 kV in the generator circuit the base

for the motors is 25,000 kVA, 6.9 kV. The subtransicnt reactance of each motor is

25,000

0.20

1.0 per unit

5000

Figure 10.14 is the diagram with sub transient values of reactance marked. For a

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