This seemed very much to me, so I immediately jumped to the conclusion that you might have mistaken kW and kWh, and were talking about energy for a whole day... but no, you're right. A quick google search gives 50 W/m^2 even for a rainy day, 150 W/m^2 for heavily clouded. So 1-2 kW might be a bit high, but not off by an order of magnitude. (Confirmed by looking up multiple sources to make sure they didn't confuse kW and kWh)