Algorithm for Short Circuit Studies

Algorithm for Short Circuit Studies:

Algorithm for Short Circuit Studies – So far we have carried out short circuit calculations for simple systems whose passive networks can be easily reduced. In this section we extend our study to large systems. In order to apply the four steps of short circuit computation developed earlier to large systems, it is necessary to evolve a systematic general algorithm so that a digital computer can be used.

Algorithm for Short Circuit Studies

Consider an n-bus system shown schematically in Fig. 9.20 operating at steady load. The first step towards short circuit computation is to obtain prefault voltages at all buses and currents in all lines through a load flow study. Let us indicate the prefault bus voltage vector as

Algorithm for Short Circuit Studies

Let us assume that the rth bus is faulted through a fault impedance Zf. The postfault bus voltage vector will be given by

Algorithm for Short Circuit Studies

where ΔV is the vector of changes in bus voltages caused by the fault.

As step 2, we drawn the passive Thevenin network of the system with generators replaced by transient/subtransient reactances with their emfs shorted (Fig. 9.21).

Algorithm for Short Circuit Studies

As per step 3 we now excite the passive Thevenin network with -V°r in series with Zf as in Fig. 9.21. The vector ΔV comprises the bus voltages of this network.

Now

Algorithm for Short Circuit Studies

Where

Algorithm for Short Circuit Studies

Since the network is injected with current -If only at the rth bus, we have

Algorithm for Short Circuit Studies

Substituting Eq. (9.22) in Eq. (9.20), we have for the rth bus

Algorithm for Short Circuit Studies

By step 4, the voltage at the rth bus under fault is

Algorithm for Short Circuit Studies

However, this voltage must equal

Algorithm for Short Circuit Studies

We have from Eqs. (9.23) and (9.24)

Algorithm for Short Circuit Studies

At the ith bus (from Eqs (9.20) and (9.22))

Algorithm for Short Circuit Studies

substituting for If from Eq. (9.25), we have

Algorithm for Short Circuit Studies

For i = r in Eq. (9.27)

Algorithm for Short Circuit Studies

In the above relationship Vi0,s, the prefault bus voltages are assumed to be known from a load flow study. ZBUS matrix of the short-circuit study network of Fig. 9.21 can be obtained by the inversion of its YBUS matrix as in Example 9.6 or the ZBUS building algorithm presented in Section 9.7. It should be observed here that the SC study network of Fig. 9.21 is different from the corresponding load flow study network by the fact that the shunt branches corresponding to the generator reactances do not appear in the load flow study network. Further, in formulating the SC study network, the load impedances are ignored, these being very much larger than the impedances of lines and generators. Of course synchronous motors must be included in ZBUS formula­tion for the SC study.

Postfault currents in lines are given by

Algorithm for Short Circuit Studies

For calculation of postfault generator current, examine Figs. 9.22(a) and (b). From the load flow study (Fig. 9.22(a))

Prefault generator output = PGi+jQGi

Algorithm for Short Circuit Studies

Algorithm for Short Circuit Studies

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