But if you have a grid with a large number of nodes, how do you impose which node is running at the correct (reference) frequency and phase? Do the edges of the grid impose a master-slave relationship?
I'm trivialising the problem, but whichever station energises the grid first becomes the reference. An operating grid has what may as well be infinite inertia (it isn't infinite of course), so new stations coming online must match it (or try and change the phase of the grid to match theirs). I visited a power station in Melbourne many years ago, and they have the shattered remains of a turbine and generator that was connected with a phase mismatch.
In the event that there's a phase mismatch, I assume that gets physically transmitted back to the generating device? (Mode subject to type of device) Or am I over-trivializing it?
E.g., will an out of phase turbine have a physical resistance against it, as a consequence of the rest of the grid?
Of a sort. If it's a phase mismatch of a few degrees, the generator may attempt to physically rotate to match the phase.
This kills the generator. Also, less amusingly, anyone nearby at the time.
If it's a larger mismatch, then that's more likely to fry the wiring before too much other damage happens. On rare occasions generators get connected while they are (exactly) 180 degrees out of phase; this is a dead short, and its internals will instantly vaporize. The vaporized copper may then proceed to explore the outer limits of the generator's physical integrity.
(Disclaimer, etc: I've only worked with DC generation, AC would be somewhat different especially if it's three-phase.)
I've synced 10 mw 900 rpm hydro units as much as 7 degrees out of phase. There is a bit more of a thunk as the unit snaps in to sync but it's not the end of the world.
Diesel units in hospitals will sync to each other as much as 30 degrees out of sync because just get thing online because it the load is critical.
I've also been told two second hand reports of the breaker closing drastically out of sync. One was a person closing the breaker manually when the unit was stopped. It essentially just puts a fault on the machine and it trips right away. Another case the close circuit was poorly designed and has only one relay, whose contacts eventually failed but happened to fail welded closed, and in conjunction with a poorly maintained breaker that developed a variable delay between the close coil being energized and actually closing. It made a big boom like faults do but the unit synced after the relay was replaced and breaker maintained and is fine.
Maybe medium and larger units with more inertia have tighter tolerances. Over certainly heard of broken shafts and generators being ejected through concrete walls.
A nice party trick is to do phase matching instead of syncing with slip so I can keep the unit exactly in phase with the grid as long as the grid doesn't wobble too much. This keeps the sync scope needle exactly at 12 o clock so you can close the breaker to put the unit online at will. Unfortunately i don't often get the budget for The additional inputs to get the nice phase difference signal so I can't perform my trick.
Ok but imagine a circular grid of N nodes. Following the circle, the stations are connected to the grid. Of course there is a small, inevitable mismatch at every connection. Then, when connecting the last node, you might get a problem which can only be solved by adjusting the settings at the other nodes.
Generally systems try to avoid too much loop power in the first place for this reason, setting up a directed but acyclic graph with some redundancy links carrying zero or near-zero power as standby.
The grid doesn't really pass through each of the points though so you don't really get the frequency mismatch between one side of a node on the grid and another. Instead of a ring of nodes it's closer to a ring with nodes hanging off of it so you never really get two frequencies observed at one power station because it's only connected to the rest of the grid at a single point.
The reference frequency is interconnection wide. To bring a three phase ac generator online the terminal voltage, phase rotation, frequency, and phase angle must be within some tolerance.
[1] Synchronizing AC generators -- Part 1 (introduction and sync lamps)
[2] Synchronizing AC generators -- Part 2 (strobe light view)
[3] Synchronizing AC generators -- Part 3 (sync and unsync)
[4] Synchronizing AC generators -- Part 4 (phase deviation)
The first video explains all the concepts and shows a sync, but the later videos bring additional conditions and detail.
[1] https://www.youtube.com/watch?v=RGPCIypib5Q [2] https://www.youtube.com/watch?v=sFohkp2aaU4 [3] https://www.youtube.com/watch?v=GRk_qJxaxh8 [4] https://www.youtube.com/watch?v=RT1ySBc-Bls