Line to Line Fault

Line to Line Fault (LL):

Figure 11.7 shows a Line to Line Fault at F in a power system on phases b and c through a fault impedance Zf. The phases can always be relabelled, such that the fault is on phases b and c.

Line to Line Fault

The currents and voltages at the fault can be expressed as

Line to Line Fault

The symmetrical components of the fault currents are

Line to Line Fault

from which we get

Line to Line Fault

The symmetrical components of voltages at F under fault are

Line to Line Fault

Writing the first two equations, we have

Line to Line Fault

From which we get

Line to Line Fault

Now

Line to Line Fault

Substituting Ib from Eq. (11.15) in Eq. (11.14), we get

Line to Line Fault

Equations (11.11) and (11.16) suggest parallel connection of positive and negative sequence networks through a series impedance Zf as shown in Figs. 11.8a and b. Since Ia0 = 0 as per Eq. (11.12), the zero sequence network is unconnected.

Line to Line Fault

In terms of the Thvenin equivalents, we get from Fig. 11.8b

Line to Line Fault

From Eq. (11.15), we get

Line to Line Fault

Knowing Ia1,we can calculate Va1 and Va2 from which voltages at the fault can be found.

If the fault occurs from loaded conditions, the positive sequence network can be modified

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