How does the grid handle small deviations of power consumption when most of load is regulated?
Where will excess power go?

The excess power goes to speed up all the generators connectors to the same synchronised grid. That's a lot of spinning inertia, the speed up will be quite slow. Control equipment spots the speed-up, and reduces the power input into the turbines driving the generators. That control action will be sufficient for small excesses of power.
Sometimes, a generator will have to deal with very large excesses of power. Consider a power station tied to the grid by a large feeder, which fails. The power station has now lost 100% of its load, and the speed up on the turbines will be very quick indeed, too fast to be controlled by closing steam valves. To maintain safety, these power stations are equipped with load dump resistors. Think of something the size of a football field, arrayed with a few 100s of MW of electric heaters. They would get switched on line for a few 10s of seconds to load the generators for the time that it took to reduce the steam input.
At least that's the way it used to work when the grid was 100% spinning iron. With the increased penetration of solar, wind and battery storage all driving very quickly responding inverters, some of the power can be turned off very quickly.