How it works
The synchronous machine's rotor field (set by DC excitation current If) interacts with the stator rotating MMF to produce torque. The phasor diagram for a cylindrical rotor generator gives V = E − jIaXs − IaRa (Ra usually negligible). Active power P = (EV sinδ)/Xs per phase, where δ is the power angle between E and V; reactive power Q = (EV cosδ − V²)/Xs. If excitation is increased (over-excitation), Q becomes positive — machine supplies reactive power to the grid, acting like a capacitor bank. Under-excitation absorbs reactive power.
Key points to remember
Synchronising power is the restoring power when δ deviates from steady state: dP/dδ = (EV cosδ)/Xs, maximum at δ = 0° and zero at δ = 90°. Steady-state stability limit is P = EV/Xs at δ = 90°. Salient-pole machines have two reactances: Xd (direct axis, 0.8–1.2 pu) and Xq (quadrature axis, 0.5–0.8 pu), giving higher reluctance torque. V-curves show armature current Ia vs field current If at constant power: the minimum of each V-curve corresponds to unity power factor operation.
Exam tip
The examiner always asks you to draw the phasor diagram for a salient-pole synchronous generator at lagging power factor and identify the power angle δ — practice this diagram including both the Id and Iq components.