Synchronisation is purely local. They are, from the point of view of a sky observer, out of phase by the amount you say, but that doesn't matter. Each generator need only sync up at the time of connection.
Imagine you are on half a tandem bicycle. You are in a room with the chain of the tandem vanishing beyond the wall. You can't see, but clearly someone else is pedalling the thing as the pedals are rotating. Getting on it is tricky, as you have to rotate your feet at the right speed, but once you're on you can sit there and let it carry them round - or you can start applying pressure through your feet to do work and accelerate the chain system.
At this point you discover the thing on the other end of the chain is not a person but a 60Hz synchronous motor-generator. Congratulations, you are in sync with the grid and (when pushing on the pedals) contributing power.
(A corollary of this is that if your grid connection is down or the grid is split into two pieces, you can't start up again until you get a grid input to know you're in phase. See "black start" for details on this.)
Okay, but what if you are at point A, and connected to points B and C, which are 1000 km away from you and also 1000 km away from each other, and connected to each other. Now if you would synchronize with B and C, then seen from the sky B and C would be in sync with each other because they're at the same distance from you. But how would B and C then transfer power over the 1000 km link between each other without phase problems?
It's like a very long pipe with standing water in it. AC power is like attaching a pump column at one point and adding/removing pressure at just that point. This creates a /wave/ of energy that propagates, but the actual water (electrons) do not. It's more accurate to say they vibrate.
Continuing the metaphor, power plants increase the amplitude of this sloshing wave, and must be synchronized to the phase of the wave /where they connect/ (in order to be additive instead of subtractive). Consumers of the power are always subtractive, '(active/passive) power factor correction' in switching power supplies is about attempting to keep the consumption timed for efficiency. AC Motors are continuous users and mostly just draw all the time.
Remember that power stations do not generate the same single phase signal that you tap into in your house. They generate three phase AC current. They also don't link up directly: there are transmission substations in between.
This is what I wondered, is network topology carefully arranged to avoid triangular connections, or 'loops' where a generator could interfere (indirectly) with itself?
Today the physical topology is usually somewhat random mesh, but not all interconnection lines are active at the same time.
In early days of electrification the physical topology usually was spanning tree and in fact this was the motivation for research into minimal spanning tree algorithms at the time.
Nope! They're connected in triangles all the time. I was stuck on this phase synchronization for a while, but really it's just the local phase lead or lag that is required.
Think of the phase as a distributed signal that indicates the current state of the local system taking into account all connected generators. It's weird but true!
This makes it sound more complex than what I learned when I last tried to figure it out =)
They seem to be describing that where two grids meet they go through a synchronizer that disconnects one or the other if they aren't in sync, so implies manually disconnections throughout the network as needed locally.
This explanation is necessarily wrong. There exist multiple paths of different phase lengths between two nodes (eg in a triangle configuration), unlike your bicycle example. In particular, the L1 and L2 distance metrics are equivalent on a line but not on a 2D plane or sphere.
My confusion always comes when I try to think of it as a propagating wave.
If instead of a tandem bicycle, it is a very long rope that someone is moving up and down, then when I try to join some distance away there will seem to be a wave passing me. Even if I join in at the correct phase, I will also be generating a wave traveling back to the first 'generator' and interfering with the existing wave along the way. With the right distance and relative strength then we will produce a standing wave between us. Is there an apparent 'direction' to the wave of electric potential in a large grid?
Then there is the issue of triangular arrangements the sibling comment raised, when the radial distances and relative phases don't align.
Maybe my issue is always trying to think through physical analogues I can 'see'.
Your issue is seeing 2d (perpendicular) waves where there are actually 1d (parallel) waves. Also, you're not really creating a new wave, you're just giving a "push" to the existing one.
Imagine you are on half a tandem bicycle. You are in a room with the chain of the tandem vanishing beyond the wall. You can't see, but clearly someone else is pedalling the thing as the pedals are rotating. Getting on it is tricky, as you have to rotate your feet at the right speed, but once you're on you can sit there and let it carry them round - or you can start applying pressure through your feet to do work and accelerate the chain system.
At this point you discover the thing on the other end of the chain is not a person but a 60Hz synchronous motor-generator. Congratulations, you are in sync with the grid and (when pushing on the pedals) contributing power.
(A corollary of this is that if your grid connection is down or the grid is split into two pieces, you can't start up again until you get a grid input to know you're in phase. See "black start" for details on this.)