(Adapted from Wikipedia): The Sun as seen from Earth has an apparent diameter of about 0.5°, so it covers a solid angle of about 0.20 deg² or square degrees, thus it covers a fractional area of approximately 0.0047% of the total celestial sphere which is about 6×10⁻⁵ steradian.

So if the clouds scatter the sunlight over your local hemispherical sky, that means that the equivalent area in the sky equal to the sun's area would only have about 0.0094%, or call it 0.01%, of the sun's unobstructed energy. And that's assuming all of the sun's light came through the clouds (instead of some being reflected back into space).

So at most a parabolic collector would produce about 0.01% (0.0001) of the energy on a cloudy day as it does on a sunny day. A flat solar cell array might be a better choice.

Your calculation seems very different from real life experience: cloud covered sun does not feel like it is 0.01 % of direct sun.

The figure given is probably not far off. If you wish to perform your own experiment, try using a magnifying glass to focus light on a cloudy day. You'll find what you get is *far* less concentration of light at the focal point than on a sunny (cloudless) day. Since concentrating solar collectors only transfer heat at the focal point, such a collector would fail to pick up the vast majority of solar flux from an obscured (cloudy) sky.

Your body is (probably) not parabolic, so you are experiencing the scattered energy from the sun coming from all angles over the two pi steradian hemisphere of the sky.

My solar panels will run as little as 1% or as much as 10% of their sunny day production on a cloudy day; depends how cloudy. I don't know of any way to efficiently collect sunlight on a cloudy day. Try searching insolation.

As others have posted, concetrating collectors are not effective for diffuse light sources.

If your looking to capture solar heat for water heating, you might want to research evacuated tube technologies and coatings for the cloudy conditions you describe. Flat plate collecters may also be a preferred option to a parabolic type collecter in you particular climate.

This is the extreme case where the reflector is perfect and focuses just the disk of the sun on the entire solar cell. I would think that in reality, the concentrator might focus on a larger piece of sky.

If it's usually cloudy, I believe you are better off to forego focusing optics in order to capture all the light that you can.

This is a piece of useful real life data, thx !! It confirm what I read .

I was considering for steam electricity generation

For solar steam generation, use the assumption when the sun is not directly shining on the collector system the steam generation will stop.