Synchronous machines
Constant-speed AC machines — alternators and synchronous motors built around the rotating field.
Lessons
The rotating magnetic field
Three pulsating MMFs 120° apart in space and time add up to one constant-magnitude rotating wave.
Alternator armature reaction
How the load's power factor sets the angle between F_a and F_f — magnetising, demagnetising, or cross-magnetising.
Synchronous equivalent circuit
E_f = V_t + I_a(R_a + jX_s) — one source, one resistance, one reactance, and the phasor diagram that tells you everything.
Power-angle equation and stability
P = (E_f·V_t / X_s)·sin δ — the heartbeat of synchronous-machine analysis, with pull-out at δ = 90°.
Synchronous motor V-curves
I_a vs I_f at constant load — the operator's chart for choosing field current and power factor at any operating point.
Generator capability curve (P-Q chart)
Five constraints — armature, field, prime-mover, stability, under-excitation — bounding the safe operating envelope.
Synchronising onto a grid
Four matching conditions, three-dark-lamp method, two-bright-one-dark, synchroscope, and modern auto-synchroniser.
Salient-pole two-reaction theory
Blondel's d/q decomposition + reluctance-power term explains hydro alternators and the reluctance motor.
Methods to determine synchronous reactance — OCC, SCC, ZPF, slip test
EMF method (air-gap line ÷ SCC), Potier construction for X_L vs X_ar, and the slip test for X_d / X_q in salient-pole machines. Saturated vs unsaturated Z_s.
Hunting & damper (amortisseur) windings
Synchronous-machine swing equation J·δ̈ + D·δ̇ + K_s·δ = 0. Damper bars in pole faces suppress hunting via induction-motor action. Other roles: line-starting synchronous motors, NSC absorption.
Synchronous-machine excitation systems
DC exciter (legacy), brushless AC (rotating diodes), static thyristor (<100 ms, 3-4× ceiling). AVR closed-loop with OEL/UEL/V-Hz limiters. PSS for rotor-swing damping. IEEE 421.5 standardized models.
Synchronous condenser
Synchronous machine with no shaft load, smooth variable Q via field control. Provides INERTIA + FAULT MVA that capacitors / SVC / STATCOM cannot. Modern comeback for low-inertia high-renewable grids and HVDC support.