Can I get a rough estimate of the power (in watts) needed to produce light to grow enough food for one person, using vertical farming of the kind proposed for space habitats?
Any reasonable outpost/colony concept that grows most of its food and does not use direct light, but has information on the base's energy source (kWe of a nuclear reactor, area of photovoltaic arrays) would be useful for finding conservative estimates.
The 3 kW/person figure in the original report may just be for general life support - it's caveated as "in the habitat" and the report goes on to explicitly say that the manufacturing unit will have extra power. The farm is shown as a third module.
The South Pole greenhouse (entirely indoors) is estimated to run at an efficiency of "...assuming that fuel costs about \$4.50 per litre, greens cost about \$50 per pound". A litre of diesel seems to produce approximately 10kwh of power, so you're looking at 100 kWh to produce a pound of vegetables. That could be anything from 100 calories (spinach) upwards; rice and wheat have much higher energy densities (500-1500 cal/lb) but they also have a lot of additional inedible weight, eg in the stalk. Let's say you can get 500 cal/lb with really intensive farming approaches and clever reuse of heat, probably a generous estimate.
This means you need enough energy input for about four and a bit pounds of growth per person per day, or 450 kWh. Assuming 24-hour farming, you're then looking at ~20 kW of solar power on a continual basis.
This seems challenging. The whole ISS (assuming the arrays work about 50% of the time) would produce just enough power to feed a three-person crew with nothing left over for life support...
Looking around for data on indoor agriculture, the most relevant stuff I could find was for marijuana growing in High Times magazine. It appears to be fantastically energy-intensive, possibly using up as much as 1% of the US's electrical energy output. Growing a kilogram of marijuana seems to require about $E=2\times10^{10}$ J of energy. Let's assume we can grow a kilogram of wheat with the same energy input. Wheat has an energy density of about $d=3400$ kcal/kg. A human needs about $c=0.02$ kcal/s of food.
The result is $cE/d\sim100$ kW of electrical power to support one human being with indoor farming. Given all the very rough order-of-magnitude assumptions involved, this seems to be roughly in line with Anthony X's estimate in a comment of 500 kW. No matter what, this is a fantastic amount of energy, dwarfing the approximately 2 kW per person used at Antarctic bases, which ship in their food.
It seems that a self-supporting space colony would do well to use sunlight, not electrical lighting, for their agriculture.
For comparison with $E\sim10^{10}$ J to grow a kg of wheat indoors, it only costs something like $5\times10^8$ J to accelerate a kg to the same velocity as the earth's orbital velocity around the sun. This suggests that if you're somewhere that doesn't have enough sunlight (surface of Titan?), you might be smart simply to import your food.
If you accept the numbers at http://www.theoildrum.com/node/6252 (which are sourced, but that doesn't make them necessarily accurate), it takes 0.430 kWh of energy to produce 390 food calories (390 kcal) worth of corn, for an efficiency rating of 102%.
I thought this was impossible at first, since it would seemingly violate the Second Law of Thermodynamics, but the calculation only includes the light energy required: the additional caloric energy comes from the physical matter that makes up corn, primarily carbon, hydrogen, and oxygen. In other words, creating corn requires both energy and raw materials, and the raw materials themselves contain stored energy.
Assuming you could live primarily (though not entirely) on corn, this number is close enough to 100% that we can assume roughly 1-to-1 transfer of light energy to caloric energy.
The average healthy person burns at least 2000 calories a day (right around 100 watts), though this assumes very little activity. With a reasonable amount of activity, this is closer to 3000 calories (about 150 watts).
So, somewhat uninterestingly, the amount of energy you need is, assuming you have sufficient raw materials, is pretty much the amount of energy an average person burns.
