It's tempting to think of the grid as something grid operators control, feeding power from point A to point B, but the grid is actually largely uncontrolled - the power just flows wherever it wants to - and the only controls they have are turning on and off generators, adjusting their throttle, disconnecting loads (rolling blackouts) and sometimes opening circuit breakers (though this is not normally useful). They don't even have precise real-time monitoring of the whole grid - only specific measurements in specific locations, from which the rest is estimated using lots of maths (which is how you would design it too, if measurement devices cost $100,000 apiece). That's why it's not a trivial task to keep it working.

However, you're able to have your own, private miniature grid, on which you can power your own loads from your own generators. It's even possible to do this with solar inverters! You will need to specifically seek out this capability, and get extra hardware installed, which is probably why you don't have it. You need a "transfer switch" to definitively disconnect your private grid from the main grid when you're using your private grid capability - it's not allowed (and not safe, and will blow up your equipment anyway if you force it) to just feed power onto your local unpowered section of the grid.