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 Z^f. The phases can always be relabelled, such that the fault is on phases b and c.

The currents and voltages at the fault can be expressed as

The symmetrical components of the fault currents are

from which we get

The symmetrical components of voltages at F under fault are

Writing the first two equations, we have

From which we get

Now

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

Equations (11.11) and (11.16) suggest parallel connection of positive and negative sequence networks through a series impedance Z^f as shown in Figs. 11.8a and b. Since I_a0 = 0 as per Eq. (11.12), the zero sequence network is unconnected.

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

From Eq. (11.15), we get

Knowing I_a1,we can calculate V_a1 and V_a2 from which voltages at the fault can be found.

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