Imagine you've got two cables coming into your factory. One is 500 meters longer than the other. That would mean that the sine waves are 0.01% out of sync.

I'm pretty sure for home electronics the phase difference doesn't even matter that much. Everything sensitive seems to be converted to DC anyway.

Maybe it matters in large industrial applications, I have no idea. But I also imagine in their situation it's probably pretty straightforward to clean up the power supply.

I wonder if the solution is similar to routing traces on PCBs where there's high-frequency stuff going on - you add and subtract length from the line pairs until the phases match up. Sometimes the dumb solutions are the best ones?

Weird how all the replies so far misunderstood your question.

In reality, the phase difference is always small, and it ends up not mattering.

But... If you had a worldwide electricity grid running at 60Hz, it would start to matter, and you would make sure to use local capacitors/inductors to make phase shifts to make sure that you didn't have big circulating currents in loops (they just are wasting energy)

The sum of two sine waves of differing phase is a sine wave with some phase between the two.

An airport or hospital might be fed from two different nearby substations. The substations are probably fed from the same transmission lines with parallel circuits. The substations will have transformers with the same winding configuration for a consistent phase shift from transmission to distribution level voltages.

The airport or hospital will procure transformers that have the same winding configuration and impedance so the phase shift and voltage drop across them will also be the same. The low voltage windings of the transformers at the hospital can be paralleled so they both feed the load. Reverse power protection would be implemented so the hospital can’t back feed the distribution line.

What phase difference do you expect in this case? What effect would it have?

In most cases where you do have more than one source (say datacenter for redundancy) you don't just tie them together directly, in simplest config you'd just switchovered from one to another if one failed.

you would have to be in a location to straddle synchronous grid. There may be some places that allow that. Otherwise, the two sources are already in approximately in phase anyways. To put it simply though, you put some devices on one feed and some devices on another feed. So it is a non-issue.

If you have local generation you want to combine with grid power you usually just sync your local generation to the grid. If you don't want to do that you can just use a DC intertie that is local. Basically you'd have two AC -> DC converters and a single DC -> AC converter.