Synchronous Machines Basics: Alternator EMF, Regulation and Sync Motors
Almost every unit of electricity in the Indian grid, whether from coal, gas, nuclear or hydro, comes from a synchronous generator, also called an alternator. The same machine can run as a synchronous motor, holding an exact speed regardless of load and offering adjustable power factor. Understanding synchronous machines explains how a power station controls voltage, why generators must be synchronised before connection, and how large industries improve power factor.
Construction and Synchronous Speed
The armature, carrying the three-phase winding, is on the stator. The field winding, carrying DC, is on the rotor and is supplied through slip rings or a brushless exciter. Keeping the high-voltage, high-current winding stationary avoids passing large currents through sliding contacts.
Ns = 120 f / P (rpm) f = 50 Hz: 2 poles -> 3000 rpm (steam and gas turbines) 4 poles -> 1500 rpm (some nuclear sets, diesel gensets) 24 poles -> 250 rpm (example hydro set)
| Rotor type | Shape | Speed | Typical prime mover |
|---|---|---|---|
| Cylindrical (non-salient) | Smooth long cylinder, small diameter | High, 1500 to 3000 rpm | Steam and gas turbines |
| Salient pole | Projecting poles, large diameter, short length | Low, below about 1000 rpm | Hydro turbines, diesel engines |
The machine is called synchronous because the rotor turns at exactly Ns. If a 2-pole turbo-generator runs at 3000 rpm, it produces exactly 50 Hz. Grid frequency is therefore a direct measure of the speed of every synchronous generator connected to it.
EMF Equation and Equivalent Circuit
Eph = 4.44 f Φ Tph Kp Kd (volts per phase) Tph = turns in series per phase Kp = pitch (coil span) factor, ≤ 1 Kd = distribution (breadth) factor, ≤ 1 Per-phase equivalent circuit (generator): E = V + I (Ra + j Xs) Xs = synchronous reactance (leakage + armature reaction)
The pitch and distribution factors account for coils that span slightly less than a full pole pitch and for coils spread over several slots. Both reduce the EMF slightly but greatly improve the waveform by suppressing harmonics. Synchronous reactance combines the leakage reactance with the effect of armature reaction, where the stator current's own field modifies the main field.
Worked Example: Excitation EMF and Regulation
A 3-phase, star-connected, 6.6 kV alternator delivers 100 A at 0.8 power factor lagging. Its synchronous reactance is 10 Ω per phase; armature resistance is negligible. Find the excitation EMF, load angle and voltage regulation.
- Phase voltage: V = 6600/√3 = 3810.5 V, taken as reference at 0°.
- Current phasor: I = 100 ∠ −36.87° = 80 − j60 A.
- Reactance drop: jXs I = j10 × (80 − j60) = 600 + j800 V.
- Excitation EMF: E = 3810.5 + 600 + j800 = 4410.5 + j800 V.
- Magnitude: |E| = √(4410.5² + 800²) = 4482.5 V per phase, or 7764 V line.
- Load angle: δ = tan⁻¹(800/4410.5) = 10.3°.
- Regulation = (4482.5 − 3810.5)/3810.5 × 100 = 17.6%.
Check with the power-angle equation (Ra neglected): P = 3 E V sin δ / Xs = 3 × 4482.5 × 3810.5 × sin 10.28° / 10 ≈ 915 kW Direct: P = 3 × 3810.5 × 100 × 0.8 = 914.5 kW ✓
Repeat the calculation at unity power factor and the EMF drops to about 3940 V, a regulation of only 3.4%. At a leading power factor the regulation can become negative, meaning the terminal voltage rises when load is applied. This is why an alternator supplying a long unloaded cable, which is capacitive, can show a voltage rise.
Connecting an Alternator to the Grid
An alternator can be paralleled with the grid or another running machine only when four conditions are met. Otherwise large circulating currents and mechanical shocks occur.
- Equal voltage magnitude, adjusted with field current.
- Equal frequency, adjusted with prime mover speed.
- Same phase sequence, checked once at commissioning.
- Phases in step at the moment of closing, checked with a synchroscope or lamp method.
After synchronising, increasing the steam or water input increases real power output and load angle; increasing field current increases the reactive power supplied. The grid fixes the frequency and voltage, so the generator can only change how much it shares.
Synchronous Motor and Synchronous Condenser
Supplied with three-phase AC on the stator and DC on the rotor, the machine runs as a motor locked to Ns. It is not self-starting, because the rotor cannot accelerate to synchronous speed within one half cycle; damper windings are used to start it as an induction motor, after which the DC field is switched on.
| Field excitation | Power factor | Behaviour |
|---|---|---|
| Under-excited | Lagging | Draws reactive power like an inductor |
| Normal | Unity | Minimum armature current for the load |
| Over-excited | Leading | Supplies reactive power like a capacitor |
Plotting armature current against field current at constant load gives the V-curves. An over-excited synchronous motor running with no mechanical load is called a synchronous condenser and is used to supply reactive power and support voltage.
Summary
A synchronous machine runs at exactly 120f/P. As a generator, E = V + jXsI per phase, and the angle δ between E and V governs real power transfer. Regulation is high at lagging power factor and can be negative at leading power factor. As a motor, field current sets the power factor, making it a useful source of reactive power.