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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.

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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.

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  • \$\begingroup\$ If you know, I'd be curious to know how this extends to other types of generation, like solar panels? \$\endgroup\$ – hddh Nov 14 '18 at 11:25
  • \$\begingroup\$ This answer also doesn't seem to explain much about how to determine how much power is supplied by a generator in parallel with others. What determines the magnitude of power supplied by each generator? Could you try to explain this? The statement of motor vs. generator operation didn't really explain much. Thanks. \$\endgroup\$ – hddh Nov 14 '18 at 11:30
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    \$\begingroup\$ Normally your inverter would synchronize with your incoming AC. If it's backfeeding the distribution network to sell power, it also adjusts your voltage (up to some maximum amount) so that the current flow is reversed. Note that if your local line loses (main generator plant) power the backfeed system must disconnect from the network (by detecting the overcurrent condition) as it has lost line synchronization, and also presents a hazard to any utility workers. \$\endgroup\$ – isdi Nov 14 '18 at 14:27
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    \$\begingroup\$ Regarding the parallel power question, it again is done by adjusting the output voltage of the generating station. Since electricity is considered a commodity it can be bought and sold on an as-needed basis, so if nobody wants your plants' output you reduce your output voltage so that your net current output from the plant is zero. This keeps you in-phase with the grid, ready to sell your power relatively quickly (base load vs peak load plant design is another topic). You can shut the plant off to save fuel/operating costs, but it takes much longer to restart if it's a base load plant. \$\endgroup\$ – isdi Nov 14 '18 at 14:37

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