Your numbers don't seem to be set up for a solar calculation. The sun is only available for part of the day, while your power requirement appears to be for night as well. Since the solar panels do not supply power at night, unless through battery storage, the problem is ill-defined. Has the demand been 24-hr averaged, or is it the correct real-time demand? If the former, then the entire 24-hr demand has to be supplied by excess capacity from the daylight hours and stored somehow.
Additionally, there seems to be redundant mis-information. The 0.5 kWh/m^2/day appears to be a calculated/averaged output from a solar panel; I get about 1.048 kWh/m^2/day using MIL-HDBK-310's maximum solar day and your efficiency numbers, so for a place like England, 0.5 kWh/m^2/day might even be optimistic. The 240-W power rating is simply the best that the panel could every do, and should not be used for any normal calculations. 1120 W/m^2 * 15% * 75% = 201.6 W, which seems lower than the 240-W rating, but if you use the orbital solar constant of 1366W/m^2, you get 245.2 W, thus making the spec power value a bit meaningless and misleading.
So, the way I would approach it is to figure out the total W-hr demand required from the panels, and divide by the 0.5 Wh/m^2/day * 1.633m^2 to figure out how many panels you need. Note here, the problem gets progressively worse the more hours/day you need to supply the 136 MW. At 9 in the morning and 4 in the afternoon, the insolation is only about 65% that of solar maximum. That means that you are required to supply 136 MW at that time, you'll need 1.5x the number of panels you would have just calculated. Of course, the problem gets even worse than that, since the numbers I'm using apply to a summer solstice day, i.e., a winter solstice day would have dramatically lower insolation, even at noon
TTFN
faq731-376
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