Synchronous Machines: Alternators and Synchronous Motors

A synchronous machine is an AC machine whose rotor spins exactly at the speed of the stator's rotating magnetic field — locked in step, with zero slip. As an alternator it generates the electricity for the entire power grid; as a motor it drives loads at perfectly constant speed.

Synchronous machines matter because every large power station — coal, hydro, nuclear — generates with a synchronous alternator, and grid frequency (50 Hz) is literally the speed of these machines. Synchronous motors also correct power factor, saving industries real money.

Key Concepts

• Synchronous speed: Ns = 120f/P rpm — the only steady-state speed possible.
• Alternator: generating mode — mechanical input spins a DC-excited rotor, inducing AC in the stator.
• Excitation: the rotor's DC field current; raising it raises the generated EMF and supplies reactive power.
• Synchronous reactance (Xs): the per-phase internal reactance in the equivalent circuit, in ohms.
• Load angle (δ): angle between rotor and stator fields; power grows with sin δ.
• Over/under-excitation: over-excited machines deliver reactive power; under-excited machines absorb it.
• Synchronous condenser: an unloaded over-excited motor run purely to supply reactive power for power-factor correction.
• Hunting: rotor oscillation after sudden load changes; damper windings suppress it.

Formulas

Generated EMF per phase: E = 4.44·f·Φ·T·Kw volts (f in Hz, Φ flux per pole in webers, T turns per phase, Kw winding factor). Per-phase equivalent: E = V + Ia·(Ra + jXs); Ra is usually negligible. Three-phase power: P = √3·VL·IL·cos φ watts, equivalently P = 3·V·E·sin δ/Xs with phase values. Pull-out power at δ = 90°: Pmax = 3·V·E/Xs; stable operation needs δ < 90°, or the machine slips a pole. Speed is fixed by the grid: a 4-pole machine on 50 Hz runs at exactly 1500 rpm. Assumes balanced sinusoidal operation and linear magnetics.

Worked Example

A 3-phase, 11 kV star alternator with Xs = 5 Ω/phase delivers 5 MVA at 0.8 pf lagging. Phase voltage V = 11000/√3 = 6351 V; IL = 5×10⁶/(√3 × 11000) = 262.4 A. With V as reference, Ia = 262.4∠−36.87° A. E = V + j·Xs·Ia = 6351 + j5 × 262.4∠−36.87° = 6351 + 1312∠53.13° = 6351 + (787 + j1049) = 7215∠8.36° V. Excitation must produce 7.215 kV per phase at load angle δ = 8.36°. Power check: P = 3 × 6351 × 7215 × sin(8.36°)/5 = 4.0 MW — matching 5 MVA × 0.8. Pushing δ past 90° would pull the machine out of step.

Common Misconceptions

• "A synchronous motor self-starts like an induction motor." It cannot — at standstill the 50 Hz field flips too fast to lock onto. It needs a VFD start, a pony motor, or damper windings for induction-style starting.
• "More excitation means more real power." No — watts come from the mechanical input (the turbine). Excitation controls reactive power and power factor.
• "Alternators produce DC." The stator output is AC; DC is only the small rotor excitation, fed via slip rings or a brushless exciter.

Real-World Applications

Hydro, thermal and nuclear stations generate with synchronous alternators up to 1000+ MVA. Synchronous motors drive constant-speed compressors, crushers and mills, and as synchronous condensers they correct power factor at substations. Grid operators rely on their inertia and excitation control to hold frequency and voltage stable.

Synchronous machines lock their rotors to the grid's rotating field — generating the world's electricity as alternators and holding perfect speed as motors.