How a Synchronous Generator Works, and How It Stays in Step

In this guide we follow one spinning rotor from the turbine to the grid, with animated diagrams, and see how a generator keeps in step with hundreds of others.

The problem: one rhythm for the whole grid

The grid has one heartbeat. In most countries it beats 50 times every second. We write this as 50 hertz, or 50 Hz. In North America it is 60 Hz. Every generator on the grid must beat at the same rate, at the same moment.

A big grid has hundreds of generators, hundreds of kilometres apart. So how do they all turn at exactly the same speed? And how does each one turn the push of steam or water into electricity at all?

One machine answers both questions. It is the synchronous generator. Steam, gas, nuclear and hydro plants all use it. It is still the main source of electricity on the grid today.

What is inside a synchronous generator

The machine has two main parts. The first is the rotor. This is the part that spins. It carries a coil called the field winding. We feed this coil with DC current, called the excitation. The DC current turns the rotor into an electromagnet with a north pole and a south pole.

The second part is the stator. This is the fixed outer frame. It holds three sets of coils, called the three-phase windings. They sit 120 degrees apart around the frame. The thin gap between rotor and stator is the air gap. The magnetic field crosses it.

A third part sits outside. It is the prime mover, the turbine or engine that spins the rotor through a shaft.

The core idea: a spinning magnet makes AC

The physics is simple. A moving magnet near a coil makes a voltage in it. This is electromagnetic induction. A changing magnetic field pushes the electrons in the wire.

In the generator, the north pole sweeps past a coil. The voltage in the coil rises one way. Then the south pole sweeps past. The voltage rises the other way. So the voltage goes up and down in a smooth wave. That wave is AC.

Three coils, spaced 120 degrees apart, give three waves. Each peaks one third of a turn after the one before. This is why the output is called three-phase.

Now the key rule. The AC frequency depends on two things: the number of poles on the rotor, and its speed. The formula is: frequency = poles × speed (rpm) ÷ 120. A 2-pole machine must turn at 3000 rpm to make 50 Hz. It must turn at 3600 rpm to make 60 Hz. Speed and frequency are locked together. That is the meaning of synchronous.

Step by step: joining the grid

A generator cannot just be switched onto the grid. It must first get in step. Here are the four moments.

What if we skip the matching? Then the breaker closes while the two sides are far apart. A big current surge and a heavy mechanical shock follow. So the check is done carefully, often by an automatic synchronizer.

The load angle: why it stays in step

Once connected, the generator must stay in step. Why does the rotor not drift away? Think of two magnets. One is the rotor field. The other is the field that the grid sets up in the stator. The two fields lock together and turn as a pair.

But they do not sit exactly on top of each other. The rotor field is a little ahead of the grid field. The angle between them is the load angle, written δ (the Greek letter delta). In the diagram, E is the voltage made by the rotor field and V is the grid voltage.

This is the heart of staying in step. When we push harder with the prime mover, the rotor moves a little further ahead. The angle δ grows. A bigger angle means more power goes into the grid. If the load drops, the angle shrinks back. The restoring pull is called the synchronizing torque.

The pull-out limit, with a worked example

How much power does the angle deliver? The formula is: P = (E × V ÷ X) × sin δ. Here X is the machine’s internal opposition to current, called the synchronous reactance. The sine shape means the power is largest at 90 degrees. This is the pull-out limit.

Below 90 degrees, the machine is stable. A small push ahead gives more power, and the machine is pulled back. Past 90 degrees, more angle gives less power. The pull disappears and the rotor breaks away. This is called losing synchronism, or pole slipping. Protection then trips the machine off the grid.

The rotor also carries short bars called the damper winding. When the rotor swings, the bars cut the field and make a braking force. It calms the swing the way a shock absorber calms a bounce.

Worked example. Use per-unit values, where 1.0 means the rated value. Let V = 1.0, X = 1.2, and let the generator deliver 0.85, which is rated power at a 0.85 power factor. With normal excitation, E = 1.6. The limit is P max = 1.6 × 1.0 ÷ 1.2 = 1.33. The load angle is arcsin(0.85 ÷ 1.33) = about 40°. That is comfortable.

Now weaken the excitation to E = 1.2. P max falls to 1.00, and the angle rises to about 58°. Weaken it to E = 1.0, and P max is 0.83. That is below the 0.85 load. There is no stable angle left, so the machine slips out of step. This is why operators keep a minimum excitation.

Now feel the same effect yourself. Move the slider and watch the angle. It climbs slowly at first, then jumps near the limit.

This is a simplified model. Real machines also have saliency and fast transient effects. But the lesson holds: keep the angle well below 90 degrees.

Where synchronous generators are used

Almost all bulk power comes from synchronous generators. They sit in coal, gas and nuclear plants, driven by steam or gas turbines. They sit in hydro plants, driven by water turbines. They sit in diesel and gas-engine sets for backup power and small grids. Large units reach hundreds of megavolt-amperes.

They give the grid two more gifts. First, the DC excitation lets them control voltage and reactive power. Second, their heavy spinning rotors store energy. This slows any sudden frequency change, which gives the grid time to react.

Key takeaways

• A synchronous generator is a spinning DC-fed magnet (rotor) inside three-phase coils (stator). The moving field induces AC.
• Frequency = poles × rpm ÷ 120. A 2-pole machine turns at 3000 rpm for 50 Hz and 3600 rpm for 60 Hz.
• Before connecting, match voltage, frequency and phase with the grid. Then close the breaker.
• The load angle δ is the lead of the rotor field over the grid field. It acts like a spring.
• More load changes δ, not the speed. Power follows P = (E × V ÷ X) × sin δ.
• The pull-out limit is δ = 90°. Weak excitation lowers the limit, so keep excitation up and the angle well below 90°.