How much power do power stations in parallel supply?

Question

In modern power systems, the power is supplied by effectively connecting multiple generators in parallel. However, not all these generators are equal, some stations supply more power than others (I assume). What determines how much current is drawn from one generator or another? They all must be synchronized to the same voltage on each phase, and are all connected to the same load.

If I reduce this to a problem in circuit theory, and consider two ideal voltage sources and a load all in parallel, then the current drawn by each source is undefined unless I resort to symmetry arguments. My best guess is something to do with source impedance, since if you include these in series with the ideal voltage sources, then the current is no longer undefined.

Thought experiment: Say I got my home-brew alternator, running at a few dozen kV, and connected it to the power lines, what would happen? Would a massive over-current be drawn by the grid, or would the grid somehow "know" that my generator couldn't supply much and draw a lower current than if a full power station was connected?

How do power systems engineers predict and model this stuff? Is there some special terminology and links I could follow regarding this? Surely this is important, especially considering that these days we hear more and more about "giving back to the grid" via home generation of power.

Answer 1

It's quite simple. Each synchronous machine can act as generator or a motor. What makes the difference is the angle of rotor with respect to the rotating magnetic field. If the rotor has a leading angle, then it's a generator mode. If it's lagging then it's in motor mode.

The regulating loop just adds some negative torque to the generator, so it increases the generated power and keeps to the nominal output power/curent. For large distribution network this is also driven by a schedule, a predicted demand.

EDIT:

Before you connect the generator with the grid you have to sync it. The output has to have the same frequency, phase shift and amplitude. Then you do connect on mains. Now the generator will run at exact speed as mains frequency. If you lower the throttle the genset will become a motor until overloaded, if you apply throttle it will turn into a generator as long it is not overloaded.

Answer 2

In a large power system one large generator is dedicated as master and responsible for the frequency control and is governed(synchronised) to run at the system frequency.

Loads and generators are now added to the system. The load supplied by each generator is determined by the power source (steam turbine.) The whole systems runs at the same frequency.

If there are to much generation online, the system will start to speed up. The main generator's governor will back off and supply less steam. This will cause the whole system to slow down. If the load increases, the governor will see the slow-down, open more steam and speed up.

The system controllers will schedule generators to come online when they expect the load to increase and schedule generators to be taken offline if the load decreases.

This is a very basic explanation. In reality, both the active power (current) and the reactive power (voltage) needs to be balanced. The reactive power is controlled by automatic voltage regulators controlling the voltage of each generator.