Double Line to Ground Fault (LLG):

Figure 11.9 shows a Double Line to Ground Fault at F in a power system. The fault may in general have an impedance Zf as shown.

Double Line to Ground Fault

The current and voltage (to ground) conditions at the fault are expressed as

Double Line to Ground Fault

The symmetrical components of voltages are given by

from which it follows that

Double Line to Ground Fault

From Eqs. (11.22a) and (11.22b)

or

Double Line to Ground Fault

From Eqs. (11.19), (11.22a) and (11.23), we can draw the connection of sequence networks as shown in Figs. 11.10 a and b. The reader may verify this by writing mesh and nodal equations for these figures.

Double Line to Ground Fault

In terms of the Thevenin equivalents, we can write from Fig. 11.10b

Double Line to Ground Fault

The above result can be obtained analytically as follows:

Substituting for Va1, Va2 and Va0 in terms of Ea in Eq. (11.1) and pre multiplying both sides by Z-1 (inverse of sequence impedance matrix), we get

Pre multiplying both sides by row matrix [1 1 1] and using Eqs. (11.19) and (11.20), we get

Double Line to Ground Fault

From Eq. (11.22a), we have

Substituting

or

Double Line to Ground Fault

Substituting this value of Ia0 in Eq. (11.26) and simplifying, we finally get

Double Line to Ground Fault

If the Double Line to Ground Fault takes place from loaded conditions, the positive sequence network will be modified.