Q5Power System - I

Negative-sequence network of a synchronous machine: since a synchronous generator's internal EMF is generated only at the fundamental positive-sequence frequency by the rotating field, there is no negative-sequence EMF source; the negative-sequence network is therefore represented simply as the negative-sequence reactance X2 connected between the reference bus (representing the machine neutral/ground reference) and the terminal, with no EMF source in the branch. Physically, negative-sequence currents produce an armature reaction MMF rotating at twice synchronous speed relative to the rotor, inducing eddy currents in the rotor/damper circuits, so X2 is approximately equal to the average of the direct-axis and quadrature-axis sub-transient reactances, X2 ≈ (Xd″+Xq″)/2, and is close in value to Xd″.

Zero-sequence network of a synchronous machine: the zero-sequence network is likewise EMF-free, represented as the zero-sequence reactance X0 between the neutral connection point and the reference bus, but critically, this network's connection to ground/reference also depends on the neutral grounding impedance Zn: since zero-sequence current in each phase is identical in magnitude and phase, the neutral must carry 3 times this current, so a grounding impedance Zn appears in the zero-sequence network as 3Zn in series with X0. If the neutral is solidly grounded, Zn = 0; if ungrounded, Zn = ∞, i.e., the zero-sequence network is open-circuited (no path for zero-sequence current at all). Typically X0 is smaller than X2 and much smaller than the direct-axis synchronous reactance Xd, since zero-sequence flux paths encounter higher magnetic reluctance (partly linking through slot-leakage and end-winding paths rather than the main air-gap flux path).

Zero-sequence network of a transformer: the zero-sequence equivalent circuit of a transformer depends strongly on the winding connections and grounding. For a star-star transformer with both neutrals solidly grounded, zero-sequence current can flow through the transformer from primary to secondary, represented by the leakage impedance connected between the two sides with both ends also connected to the reference bus through their respective (possibly zero) grounding impedances 3Zn; if either neutral is ungrounded, that side's zero-sequence path is open. For a star-delta transformer, zero-sequence current can circulate within the closed delta winding (since the delta provides a path for the sum of the three equal zero-sequence currents to circulate internally, acting like a short-circuited tertiary) but cannot flow out of the delta terminals into the external delta-side network, so the delta side is effectively shown as directly connected to the reference (grounded) on that side within the zero-sequence network, while the star side connects through its leakage impedance and any neutral grounding impedance to the reference bus. A delta-delta transformer has no path for zero-sequence current to flow from either external line at all (it is open on both sides in the zero-sequence network), since neither the star point (there is none) nor the delta winding provides a return path to an external neutral.