Nope. The infinite bus is a reasonably useful high level approximation during reasonably steady conditions but does not actually exist.
Again, it all goes back to how "frequency" is defined, there are many possibilities, from instantaneous angular velocity of the generator shafts to averaging a multitude on positive zero crossings. The tighter the measurement, the greater the variation across a large interconnection and the more different "frequencies" within that interconnection. Within a stable system there are limits to how much variation there can be and how the df/dt at various locations must relate to each other. But there are variations. Small, sure (no, not 59Hz in a 60Hz world, there in lies madness), but real none the less.
When Palo Verdi trips the Arizona area slows down more and faster than the Pacific North West. No place is still at 60Hz, or what ever the pre-event frequency was determined to be, but there are a range of frequencies across the interconnection. The South West and the North West probably start oscillating against each other for a while. Each slower and then faster than the other as things come into tighter and tighter stability. As long as none of those frequency changes are enough to push anything out of stability all is good. The ending frequency isn't the starting frequency. It can take seconds or minutes to come to a new equilibrium.
Don't confuse stable with quasi-stable. In a "stable" system, defined as one in which the machines don't lose synch, the system frequency isn't actually stable; it moves all the time and different parts move differently. The system frequency is quasi-stable, it keeps tending back to the mean and doing so with sufficient strength that everything holds together. Lots of calculations can safely ignore the actual frequency and instead assume a fixed system frequency and a variable rotor angle. An extremely useful fiction, makes lots of simulations solvable. But just because it's useful, just because it makes the calcs much easier, doesn't mean it's true. Close enough for all purposes if the system hangs together and if the system falls apart it doesn't matter.
Define frequency as the average number of positive zero crossings per second measured over the past hour on a sliding window, and sure the whole system has the same frequency everywhere to a phenomenal degree of accuracy. Define frequency based on instantaneous angular velocity of the shaft over the past 4 milliseconds and with enough resolution you'll find that every machine on the system has a different frequency, including units sharing the same GSU.
Nobody's been willing to define what frequency is. Is it like the definition of pornography from one former supreme court justice "I know it when I see it" and nobody can actually define it? Or are we willing to arrive at a consensus definition, including measurement techniques and time resolutions?
Much of the back and forth here to fore in this thread could be reduced if we could place one statement in one measurement bin and a different statement in a different measurement bin. We argue like we know what the other posters are talking about, but maybe we don't. Maybe the "there's only one frequency" crowd is is total agreement with the "there's lots of frequencies" crowd because they're talking two different thing. "Well if that's what you mean by frequency, well, then perhaps you have a point...".
We may still be the blind men arguing about how an elephant is to be perceived. It all depends. Well, for whether or not there's one precise frequency or a bunch of different frequencies that all smudge around a common value it just depends. It's both, or it's neither. Or, it's somewhere in between, it just depends.
