Double Line to Ground Fault

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

Double Line to Ground Fault

from which it follows that

Double Line to Ground Fault

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

Double Line to Ground Fault

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. 11.10a and b. The reader may verify this by writing mesh and nodal equations for these figures.

Double Line to Ground Fault

Double Line to Ground Fault

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

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 premultiplying both sides by Z-1 (inverse of sequence impedance matrix), we get

Double Line to Ground Fault

Premultiplying 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

Double Line to Ground Fault

Substituting

Double Line to Ground Fault

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 fault takes place from loaded conditions, the positive sequence network will be modified as discussed in Sec. 11.3.

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