Stevenson J. Power system analysis

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396 CHAPTER 10 SYMMETRICAL FAULTS

marked x have the same potential, and so they can be joined together to yield

the equivalent circuit of Fig. 10.

(b) with a single voltage source Vr as shown. If

the switch S is open between bus

and the reference node, there is no short

circuit and no current ows in any branch of the network. When S is closed to

represen t the fault on bus ®, curren t ows in the circuit toward bus ®. This

current is



kk'

which agrees with Eq. C1 0.19), and it induces a voltage

drop (Zj

l Z

in the direclion ji'o/11 t he reference node toward bus . The

voltage from bus  to the reference changes therefore by the amount

-(Zj

so that the voltage at bus  during the fault is V

)



, which is consistent with Eq. (10.20).

Thus, by substituting appropriate numerical values for the impedances in

the simple equivalent circuit of Fig. 10.7(b), we can calculate the bus voltages of

the system before and after the fault occurs. With switch S open in the circuit,

the voltages at bus

and the representative bus  are equal to Vf. The same

uniform voltage prole occurs in Fig. 10.6 if there are no prefault currents so

that E� and E� equal Vf' If S is closed in Fig. 10.7(b), the circuit reects the

voltage of representative bus  with respect to reference while the faul t is on

bus ®. Therefore, if a three-phase short-circuit fault occurs at bus ® of a

large-scale network, we can calculate the current in the fault and the voltage at

any of the unfaulted buses simply by inserting the proper impedance values into

elementary circuits like those in Fig. 10.7. The following example illustrates the

procedure.

Example 10.4. A ve-bus network has generators at buses  and



rated 270

and 22

5 MVA, respectively. The generator subtransient reactances plus the

reactances of the transformers con necting them to the buses are each 0.30 per unit

on the generator rating as base. The turns ratios of the transformers are such that

the voltage base in each generator circuit is equal to the voltage rating of the

generator. Line impedances in per unit on a 100-MVA system base are shown in

Fig. 10.8. l resistances are neglected. Using the bus impedance matrix for the

network which includes the generalor and transformer react,

I1CCS, fi nd the

)0.126

1.0�

)0.168

jO.126

)0.210