To grow one $rm m^2$ of crop plants, how many $rm m^2$ of solar panels do you need?

Question

In vertical farms you need to use LEDs to make plants grow, which in turn have to be powered e.g. by solar panels. If solar panels had the same efficiency as plants, then you would need the same amount of solar panels as you had plants before, if your LEDs had perfect efficiency. So the claim that vertical farms would use less surface area seems strange at first.
But it appears that solar panels are more efficient than plants. Although the accepted (at the time of writing) answer focused on creating electricity (burning biofuels), which is advantageous to solar panels as there are no further conversion steps.
So the question is, does it make sense to go the (Sunlight -> solarpanel -> electricity -> light -> plant) detour?
As you probably lose efficiency in every step this seems wrong intuitively, but reasons this might make sense are:

plants might be able to convert a smaller percentage of the light spectrum into energy, if solar panels can capture the entire spectrum and LEDs produce only that spectrum, you gain some efficiency
plants might only be able to use energy up to a certain point and "throw the rest away". If solar panels can capture all the energy you could split it up to multiple plants with dimmer lights

So the question is: To grow one square meter of crop plants, how many square meters of solar panels do you need?
(This might depend on the latitude)

CookieNinja · Accepted Answer

The most efficient solar panel boasts with an efficiency of 22.8%. While the best case for plants have 28.2% of sunlight absorbed by chlorophyll. Even if there are further energy losses in its path to become sugar the vertical farm doesn't circumvent those steps and is therefore irrelevant. So assuming the most generous case (100% electricity -> absorbed by chlorophyll) you would still end up using about $1/3$ more land area to provide for your vertical farm.
Traditional farming requires fertile soil, abundant water and sunlight. While the vertical farm setup only requires 1 of the 3. The solar panels could be located in a sunny location not suitable for crops while the vertical farm could be located next to the food processing plant. This way it doesn't compete with traditional farming for space and also reduce carbon emissions associated with transport. Farming in a closed environment reduces the need for pesticides to $0$ and also reduces water losses due to evaporation and drainage to effectively $0$.
So the answer to your question would be: It depends. If you have abundant fertile soils and water then the good old fashioned way is hard to beat. Scarce water, wasteland unsuitable for anything else? Then yea vertical farming could make perfect sense.
EDIT: There is also the alternative of using greenhouses on said wasteland. In that case I don't really see a case for using vertical farms powered by solar panels with technology available today.

To grow one $rm m^2$ of crop plants, how many $rm m^2$ of solar panels do you need?

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