How it works
Any unbalanced three-phase phasor set can be decomposed into three balanced sets: positive sequence (Va1, aVa1, a²Va1 — same order as normal rotation), negative sequence (Va2, a²Va2, aVa2 — reverse rotation), and zero sequence (Va0, Va0, Va0 — all in phase). The operator a = 1∠120° = −0.5 + j0.866; a² = 1∠240°; 1 + a + a² = 0 always. The transformation matrix [A] relates phase quantities to sequence quantities: [Vabc] = [A][V012]. Sequence impedances Z1, Z2, Z0 are found from the positive, negative, and zero sequence networks — for a synchronous generator Z1 = Xd' (subtransient), Z2 ≈ 0.15–0.25 pu, Z0 ≈ 0.05–0.10 pu.
Key points to remember
Four fault types use sequence networks differently: three-phase fault uses only Z1; single line-to-ground (SLG) connects all three sequence networks in series; line-to-line fault connects Z1 and Z2 in series; double line-to-ground (DLG) connects Z1 with (Z2 ∥ Z0). For a SLG fault on phase A, Ia1 = Ia2 = Ia0 = Vf/(Z1 + Z2 + Z0). Zero-sequence current flows only if a grounding path exists — an ungrounded or delta winding blocks it. This is why transformer grounding configuration critically affects relay performance.
Exam tip
Every Anna University power systems fault analysis question involves SLG fault using symmetrical components — remember the boundary conditions Ib = Ic = 0, Va = 0, and connect all three sequence networks in series to find the fault current.