In Figure 7.14, E = e.m.f. per phase and the R phase is again taken as the reference phasor. In this case, IR = 0, Iy = —IB, and Vy = VB.
Figure 7.13 Interconnection of positive-, negative-, and zero-sequence networks for single-line-to-earth faults
Figure 7.14 Line-to-line fault on phases Y and B
From equation (7.4), and
As VY = VB (but not equal to zero) hence
This can be represented by the equivalent circuit in Figure 7.15, in which, of course, there is no zero-sequence network. If the connection between the two lines has an impedance Zf (the fault impedance), this is connected in series in the equivalent circuit.
Figure 7.15 Interconnection of sequence networks for a line-to-line fault (including fault impedance Zf, if present)
Line-To-Line-To-Earth Fault (Figure 7.16)
Figure 7.16 Line-to-line-to-earth fault
Figure 7.17 Interconnection of sequence networks-double line-to-earth fault
These can be represented by the equivalent circuit as shown in Figure 7.17.
The inclusion of impedances in the earth path, such as the star-point-to earth connection in a generator or transformer, modifies the sequence diagrams. For a line-to- earth fault an impedance Zg in the earth path is represented by an impedance of 3Zg in the zero-sequence network. Zg can include the impedance of the fault itself, usually the resistance of the arc. As Ij = I2 = I0 and 3Ij flows through Zg in the physical system, it is necessary to use 3Zg to obtain the required effect. Hence,
Again, for a double-line-to-earth fault an impedance 3Zg is connected as shown in Figure 7.18. Zg includes both machine neutral impedances and fault impedances.
The phase shift introduced by star-delta transformers has no effect on the magnitude of the fault currents, although it will affect the voltages at various points. If the positive-sequence voltages and currents are advanced by a certain angle then the negative-sequence quantities are retarded by the same angle for a given connection.
Figure 7.18 Modification of network in Figure 7.17 to account for neutral impedance Zg