There is a physical reason for that - all the generators connected to the grid, including massive nuclear/coal-steam-turbine powered ones, literally slow down d

There is a physical reason for that - all the generators connected to the grid, including massive nuclear/coal-steam-turbine powered ones, literally slow down due to increased load. Thats why in AC grid actually the frequency decreases and not the voltage (though voltage may drop also because of higher currents in wires). I'm generally curious how battery-backed sources or solar plants respond to that, since their output frequency is artificial due to DC-AC inverters being used. Do they adapt to the grid frequency following some kind of control mechanism, or do they literally experience higher load when out of sync?