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.