Synchronous generators: excitation, load angle and grid synchronization

How an alternator makes AC

A synchronous generator has a rotor carrying a DC field winding (supplied through slip rings in smaller machines) and a three-phase armature winding on the stator. A prime mover, such as a steam turbine, a hydro turbine or a diesel engine, spins the rotor. The rotating field cuts the stator conductors and induces three voltages 120° apart. The frequency is locked to the speed of the rotor:

f = p × n / 120

where p is the number of poles and n the speed in rpm.

• 4 poles at 1500 rpm: 50 Hz
• 4 poles at 1800 rpm: 60 Hz
• 2 poles at 3000 rpm: 50 Hz (typical steam turbine alternator)
• 24 poles at 250 rpm: 50 Hz (slow hydro alternator)

The machine is called synchronous because the rotor turns at exactly the speed of the rotating field set by the stator currents, with no slip, unlike an induction machine.

Excitation sets the voltage

The EMF induced in each phase, E_f, is proportional to the speed and to the field flux, which in turn depends on the field current. Increasing the excitation raises E_f. At no load the terminal voltage equals E_f, so the field current is the voltage control. The curve of E_f against field current is the open-circuit characteristic, and it bends over because the iron saturates.

Under load, the armature current flows through the synchronous reactance X_s of the machine, which represents the armature reaction and leakage together. One phase is described by

E_f = V + (R_a + jX_s) × I

Most of the drop is reactive, so the voltage depends strongly on the power factor of the load. A lagging (inductive) load demagnetises the field, so the voltage sags and the excitation must be raised. A leading (capacitive) load magnetises, and the voltage can rise above its no-load value. The automatic voltage regulator in a real plant adjusts the field current to keep the voltage steady.

The four conditions for synchronizing

Closing a breaker between an alternator and a live grid when they are not in step is like clutching two spinning shafts together: huge currents and torques flow. Before closing, four conditions must hold.

• Equal voltage: within a few per cent of the grid voltage.
• Equal frequency: almost the same, so that the phase difference changes only slowly.
• Equal phase angle: the generator voltage must pass through the same point of its cycle as the grid voltage at the moment of closing.
• Same phase sequence: A-B-C against A-B-C, not A-C-B. This is checked once at commissioning.

The operator brings the machine to speed, sets the field to match the voltage, and then trims the speed until the frequency is just slightly different from the grid. A synchroscope shows the phase difference as a pointer: if the generator is a little fast the pointer turns slowly one way, and a little slow the other way. The breaker is closed just before the pointer reaches the 12 o'clock position, where the phase angle is zero. Lamps and automatic synchronizers do the same job.

Closing off-angle makes a peak current limited only by the subtransient reactance of the machine, many times the rated current, and shocks the shaft.

Active power, reactive power and the load angle

Once the machine is paralleled with a large grid (an infinite bus), the grid fixes voltage and frequency, and the speed cannot change any more. The two controls then take distinct roles:

• The prime mover controls the active power. Opening the turbine valve pushes more shaft power into the rotor, and the rotor pole axis moves ahead of the stator field by a larger load angle δ. The power is

P = 3 × V × E_f × sin δ / X_s (neglecting resistance), per-phase quantities being used, and it is maximum at δ = 90°. Beyond that the machine cannot hold synchronism and slips a pole, a loss of stability.

• The field current controls the reactive power. An over-excited machine (E_f large) delivers reactive power to the grid, like a capacitor. An under-excited machine absorbs it. Changing the field changes the current and the power factor, but not the active power.

Plotting armature current against field current at constant power gives the V curve: the minimum is at unity power factor and the current rises on both sides, to the lagging side when over-excited and the leading side when under-excited.

A worked example

A 100 kVA, 400 V, 50 Hz, four-pole alternator has a synchronous reactance of 1.6 Ω per phase.

1. Speed: n = 120 × f / p = 120 × 50 / 4 = 1500 rpm. 2. Rated active power at a power factor of 0.8: 100 × 0.8 = 80 kW. The rated current is 100 000 / (√3 × 400) = 144 A. 3. Maximum power at δ = 90° with E_f equal to V (about 231 V per phase): P_max = 3 × 231 × 231 / 1.6 = 100 kW. With the field raised so E_f is 1.5 V, the maximum is 150 kW, so the field current is also a stability margin.

At 60% turbine power the generator delivers a bit under 48 kW to the grid. Increasing the field changes only the reactive power.

How the simulator models the synchronous generator

Curvo Studio's synchronous generator simulator uses a cylindrical-rotor per-phase model, E_f = V + (R_a + jX_s) × I, with X_s of 1 per unit derived from the rated point, R_a of 0.015 per unit and a saturating open-circuit curve. The prime mover is a hard drive: speed does not fall under load. There are two modes.

• Islanded: the alternator feeds its own constant-impedance load. The speed sets the frequency, the field current sets the voltage and the load decides the current and the voltage sag or rise.
• On the grid: an infinite bus fixes the voltage and frequency. The breaker can be closed only if the voltage (within ±5%), frequency (±0.2 Hz), phase angle (±10°) and phase sequence all agree. After closing, the turbine power sets the active power and the field current sets the reactive power. The load angle settles with a damped oscillation, and exceeding the stability limit shows loss of synchronism.

The synchroscope angle is a static slider, not a continuously rotating pointer; the pointer in the 3D scene turns only when the frequency difference is outside the limit. The model has no saliency, no governor droop and no automatic voltage regulator.

For the default 100 kVA, 400 V, 4-pole machine (synchronous reactance 1.6 Ω, rated field current 10 A), islanded at 1500 rpm with 60% load at 0.8 lagging and 8 A of field, the simulator gives 50 Hz, 403.7 V, 87.4 A and a load angle of 19.1°.

Try it in the synchronous generator simulator

Open the synchronous generator simulator and try the following.

• Islanded, lower the Field (excitation) current from 8 A to 6 A. The terminal voltage falls from about 404 V to about 308 V and an undervoltage warning appears. Set the Load to 0% with 8 A of field and the voltage rises to 584 V, because with no load the terminal voltage equals the excitation EMF.
• Change the Load type to Capacitive (leading) and see the voltage rise with load, while Inductive (lagging) makes it fall. (The Load power factor setting is separate.)
• Change the Prime-mover speed and watch the frequency, which follows f = p × n / 120.
• Switch the Operating mode to On the grid. Check the four conditions (Voltage, Frequency, Phase angle, Phase sequence) in the Synchronising panel: change the Synchroscope angle, the Grid frequency or Grid voltage until all four are met, and close the Circuit breaker only then. The Peak current if closed now readout shows why timing matters.
• With the breaker closed and the Turbine power at 60% (48 kW of shaft power), the machine delivers about 45.8 kW and, with 8 A of field, about 38 kvar. Raise the field to 12 A and the reactive power rises to about 105 kvar with the load angle falling to 11.6°, while the active power stays about the same. Lower the field to 5 A and the Reactive power readout becomes negative (absorbed), about −20 kvar, with the load angle rising to about 30°.
• Raise the Turbine power and watch the load angle δ and the Stability limit P_max. The Capability diagram (P–Q) shows the allowed region and the V curve chart shows the armature current against the field current.

Try it in the simulator