Section III:  Sequence Circuits for Synchronous Generator

The three-phase equivalent circuit of a synchronous generator is shown in Fig. 1.16. This is redrawn in Fig. 7.6 with the neutral point grounded through a reactor with impedance Z_n . The neutral current is then given by

Fig. 7.6 Equivalent circuit of a synchronous generator with grounded neutral.

The derivation of Section 1.3 assumes balanced operation which implies I_a + I_b + I_c = 0. As per (7.32) this assumption is not valid any more. Therefore with respect to this figure we can write for phase-a voltage as

Similar expressions can also be written for the other two phases. We therefore have

Pre-multiplying both sides of (7.34) by the transformation matrix C we get

Since the synchronous generator is operated to supply only balanced voltages we can assume that E_an0 = E_an2 = 0 and E_an1 = E_an . We can therefore modify (7.35) as

We can separate the terms of (7.36) as

	(7.37)
	(7.38)
	(7.39)

Furthermore we have seen for a Y-connected load that V_a1 = V _an1 , V_a2 = V_an2 since the neutral current does not affect these voltages. However V_a0 = V_an0 + V_n . Also we know that V_n = - 3Z_nI_a0 . We can therefore rewrite (7.37) as

The sequence diagrams for a synchronous generator are shown in Fig. 7.7.

Fig. 7.7 Sequence circuits of synchronous generator: (a) positive, (b) negative and (c) zero sequence.