Generators

Generators turn mechanical energy into electricity. Learn the alternator EMF equation, frequency–speed relationship, excitation and AVRs, governor droop and load sharing, and the conditions for synchronising to the grid.

Nearly all grid electricity comes from synchronous generators (alternators) spun by steam, gas, hydro or wind turbines. The rotor's magnetic field sweeps past the stator windings and induces a three-phase voltage whose frequency is locked to rotor speed.

Running a generator means controlling two things: voltage (by field excitation, through an automatic voltage regulator) and power/frequency (by the prime mover's throttle, through a governor).

An analogy

A generator on the grid is like one rower in a very long boat. Rowing harder doesn't make the boat go noticeably faster (frequency stays ~50 Hz); it just means you're carrying more of the load.

Speed sets frequency

f = PN/120: a 2-pole steam turbo-generator spins at 3000 rpm for 50 Hz, while a slow hydro generator with 40 poles turns at 150 rpm. Wind turbines use gearboxes or inverters because their rotor speed varies.

Excitation sets voltage

More field current → more flux → higher EMF. An automatic voltage regulator (AVR) adjusts excitation to hold terminal voltage as load changes. Small generators use brushless exciters or permanent-magnet pilot exciters.

Synchronising to the grid

Before closing the breaker, the incoming generator must match the grid in four ways, or a violent current and torque surge results.

• Voltage magnitude (within a few %).
• Frequency (slightly higher, to pick up load).
• Phase sequence (same rotation).
• Phase angle (close within ~10°) — checked by a synchroscope or auto-synchroniser.

Droop and load sharing

Governors are set with droop: frequency falls slightly as output rises (typically 4–5 % from no-load to full-load). When load increases, frequency dips and every generator raises output in proportion to its rating divided by its droop, so load is shared automatically without communication.

Capability curve and stability

A generator's P–Q capability is bounded by stator current (heating), field current (rotor heating, over-excited limit), turbine power and the stability limit when under-excited. Operators keep within this curve, and power system stabilisers damp electromechanical oscillations.

Inertia and the changing grid

Spinning generators store kinetic energy (H seconds of rated output) that resists frequency change instantly. Inverter-based solar and wind provide little natural inertia, so grids now procure 'synthetic inertia' and fast frequency response from batteries and grid-forming inverters.

Formulas

• Frequency: f = P · N / 120
• EMF equation: E = 4.44 · f · N_ph · φ · K_w
• Droop load change: ΔP / P_rated = (Δf / f_rated) / R
• Terminal voltage: V = E − I·(R_a + jX_s)

Worked example: Poles and speed for 50 Hz

Given: Hydro turbine speed = 150 rpm; f = 50 Hz

Find: Number of poles.

• P = 120 f / N
• = 120 × 50 / 150 = 40 poles

Answer: 40 poles

Worked example: Response to a frequency dip

Given: 100 MW unit, 5 % droop; Frequency falls 0.1 Hz on a 50 Hz grid

Find: Extra power the governor delivers.

• Δf/f = 0.1/50 = 0.002 = 0.2 %
• ΔP/P = 0.2 % / 5 % = 0.04
• ΔP = 0.04 × 100 = 4 MW

Answer: +4 MW

Common mistakes

• Wrong: Closing onto the grid 180° out of phase. — Right: Always synchronise voltage, frequency, sequence and phase angle; auto-synchronisers and sync-check relays enforce it.
• Wrong: Setting two paralleled gensets with zero droop (isochronous) and no load-sharing link. — Right: Use droop or a load-sharing controller, or the two governors fight each other.

Applications

• Standby diesel gensets: Hospitals and data centres start diesel generators within ~10 s of a mains failure; an ATS transfers the load.
• Power stations: Gigawatt turbo-generators with hydrogen or water cooling produce most of the world's electricity.
• Wind turbines: Doubly-fed induction generators and full-converter PMSGs decouple rotor speed from grid frequency to capture maximum wind energy.

Key takeaways

• f = PN/120; E = 4.44 f N φ K_w.
• AVR controls voltage; governor controls power and frequency.
• Synchronise voltage, frequency, sequence and phase before paralleling.
• Droop shares load changes in proportion to rating/droop.

Going further

• Automatic generation control: Secondary control (AGC) slowly adjusts generator setpoints to restore frequency and scheduled tie-line flows after droop has arrested the deviation, typically within minutes.
• Grid-forming inverters: New inverter controls emulate a synchronous generator's voltage source and droop behaviour, letting batteries and renewables stabilise a grid rather than merely follow it.
• Short-circuit behaviour: After a fault, generator current decays through subtransient (X″_d), transient (X′_d) and steady-state (X_d) reactances. Breakers and protection are sized from the subtransient current.