The reality is that coal plants are run at a capacity to match 'baseload,' meaning loads that go on for hours rather than minutes.
In the otherwise mostly insignificant country of Denmark, electricity production from wind-turbines in 2015 reached a coverage of 51%, which is a world record. (Because of import+export, the wind coverage on actual consumption was 42%, also a world record).
The (highly predictable) change in the remaining, non-wind-turbine power need is covered by interconnectors to neighbouring countries and with fossile fuel power plants. The necessary trade with electricity is handled in an open (public) and self-organizing way (i.e. using market forces), via the Nord Pool Spot electricity exchange.
While the power plant production is being reduced over the years and power plants are being closed down, the remaining power plants have found a new, useful role in the power grid.
Each interconnector is DC and use a converter station (with capacity of e.g. 1 GW). Like the wind-turbines and unlike the huge, spinning generators in the power plants, the converter stations do not have a stabilizing effect on the AC frequency of the power grid.
So to keep the power grid stable some of the power plants are kept running basically in idle (and thus consuming little fuel). The inertia of their large and heavy generators thus help to keep the AC frequency stable.
The fossile power plants most likely to remain active are CHP (Combined Heat and Power) plants, where the residual heat from the electricity production is being used for residential heating, thus increasing the overall efficiency.
The trade with electricity is helpful especially because the neighbouring countries Norway and Sweden have massive amounts of hydro-power, where the delivered power can be adjusted on a very small time scale:
The control room
The electricity production in Denmark can be followed in real time here (flash required):
Power right now
Maybe other countries could find some use for this approach as well.
