The amount of power that a 10kW solar system produces in a day isn’t really a thing. A power measurement is instantaneous, and so the amount of power produced in a day isn’t really a thing.
Power is measured in watts (or kilowatts), so the power a 10kW solar photovoltaic (PV) system would be expected to produce is…10kW.
You could certainly ask what is the maximum power a nominal 10kW system might produce. In my own 10kW PV array, the recorded peak is 10,109 W. At night, I’ve seen the same set of solar panels produce tenths or even a few hundredths of a watt. I guess starlight and moonlight are enough to produce a measurable wattage. Today is cloudy and at the moment it’s producing about 320 Watts.
If you did mean energy instead of power…. My solar panels are in East Tennessee. It’s not the most ideal location for producing electricity from sunlight. We have no shortage of cloudy days and clouds certainly cut into the maximum wattage. Further, the noonday sun is pretty low in the sky from November through.