What I found out is that the BH1750 has a conversion to W/m2: lux * 0.0078. And sunshine is calculated from 120 W/m2
What do you think about it?
I have found a range of lux -> W/m
2 conversion factors for silicon devices. I can't see a conversion factor listed in the datasheet, so 0.0078 seems a reasonable place to start experimenting.
From the datasheet, the directional characteristics of the BH1750 may cause a mount orientation issue. By 45 degrees away from perpendicular to the sensor face, response has dropped to between 50% to 60% of the maximum response, depending on the orientation of the sensor face. By 60 degrees, its down to 30% to 40%, depending on orientation.
Bear in mind that you are measuring whole of sky radiation, not just direct radiation. Unless you are trying for a scientific paper, this is not a fatal flaw for experimentation. What this will mean is that you will have an error band around your readings due to the presence or absence of clouds. That is, the reading with direct sunlight surrounded by dark clouds will be lower than what you will get with a clear sky, but it will be higher if there are reflective clouds (like Cumulus) around as more radiation will be reflected to the sensor.
If you are just looking to detect bright sunlight, you need to see what readings you can expect under a variety of cloud conditions. In my location, I haven't seen any conditions (away from sunrise/sunset) where the cloud in the area reduces the reading so much that direct sun on the sensor can't be detected as sunlight, or increases it so much that I confuse reflected sunlight with direct sunlight.
If you want a calibrated power reading of direct sunlight, you have the wrong setup. If you are happy to experiment, you can get a good idea of when there is direct sunshine on the sensor. As far as using multiplication or division goes, I think that the other uncertainties will swamp any variations between using multiplication or division.