Energy production of solar panels in space with received light If there were 47.1% efficient solar panels (the MJ concentrator cells created by the NREL) in space where there is no atmosphere, I want them to generate as much power as possible, so I would like to place them as close to the Sun as I can. The solar irradiance would increase as the distance to the Sun decreases, but they would get hotter and the efficiency of solar panels decrease as their temperature increases.
At what point (watts per square meter of sunlight) does the total energy produced max out?
(There is no active cooling system, but passive cooling is allowed.)
 A: The energy intensity of the sun in space can be found by considering the sun as a black body with a temperature of about 5800 K and considering the radius of the sun  $695 x 10^6 m$ the surface luminosity is about $H_sun$ = $64 x 10^6 W/m^2$. This lets use write an equation for the sun as a function of distance.
$H_o=\frac{R_{sun}^2}{D^2}H_{sun}$
At the earths orbit this works out to one solar sun or about 1366.1 $W/m^2$ if you assume the mean orbit of the earth around the sun, but since planets orbits are elliptical they will change some.
We can also use Stefan-Boltzmann law to find the equilibrium temperature of the satellite if we make some assumptions. Lets assume that we are in equilibrium which would mean the flux emitted back to the satellite is equal to the flux it is receiving. For this we need consider the emissivity $\epsilon$ and area $A$ of the satellite.
$A\epsilon\sigma$$T^4$=$\frac{R_{sun}^2}{D^2}H_{sun}$
The emissivity of solar cells is around 0.8 and the area A is one. So then the question becomes at what temperature T is your solar cell the most efficient. Most solar cells are measured at 25 C or 298.15 K, but if you cool them they will be a little more efficient. But can use the above equation for the temperature you decide is most efficient for your solar cell and solve for the orbit.
Some other things things to consider.
All the flux of the sun is being considered. If you put a reflecting    filter to reflect sunlight at wavelengths the solar cell is not         absorbing the effective flux from the sun would be reduced and the      temperature would be lower.
If you were in orbit around the earth you would need to consider the radiation of the earth heating the satellite. Satellites in LEO are measurably hotter than satellites in GEO orbits from the earth shine. You would also consider if you were in a sun synchronous orbit or going in an out of the earths shadow.
