The Solomon Islands pay almost $1/kWh for electricity. You could provide beamed solar power to them on a demonstration basis for a fraction of that price.
Unfortunately, being in the ocean is one of the worst places for beamed power, since you have lots of clouds and moisture and also saltwater which likes to corrode things. Even so, you could probably demonstrate space-based solar power to them on a scale that would be relevant but without costing too much. It’d be competitive with their $1/kWh pricing, once you set it up.
The military is tolerant of high energy prices, too. If you could setup a transportable, lightweight 200m diameter receiver that could power a whole military base day and night, you’d have a lot of interest, even if it cost $5-10/kWh. Those prices make beamed propulsion start to look viable, even if you end up throwing away 90% of your energy due to losses and an undersized receiver.
So how would we design such a system? Well, if we’re using microwaves (in order to reduce rainfade to only occur in the worst conditions, like heavy rain) at 10GHz and 3cm, then we’re limited to still needing very large antenna if at GSO. The antenna do not scale down well at all, so we can try getting closer to the Earth. That means we need multiple satellites (though we can start with just a single demo satellite). Equatorial orbiting or close to it is necessary to keep the size of the constellation small, but this also means we must keep the altitude fairly high or we lose coverage over most of the planet. A compromise is about 1 Earth radius, 6400km in altitude. The biggest antenna you can probably fit in a (modified, most likely) Falcon Heavy fairing while having room for the rest of a satellite is probably 300m, and you have a 8000km distance to your receiver (due to being at an angle), so your receiver would need to be:
6400km/(300m/(3cm)) = 800m in diameter to get the vast majority of the beam.
But… It turns out that the majority of the energy in the beam is in the center, so if you reduce the size of the receiver, you don’t lose power in proportion to area.
Let’s say you had a 250m diameter effective receiver size (probably needs to be about 300m due to being flat on the Earth and not tracking the satellite). Turns out the power inside a circle that’s 1/3.2 times as big as the 800m one is about 21% of the beam’s power (as opposed to 83% for 800m). I will dig into this later, but rough figures for now. You throw away another half the power due to conversion losses, so let’s say you only get 10% of the solar array’s generated power.
Let’s say you start with 20MW array (1kW/kg, weighing 20 tons), 15 ton thermal management system, 5 ton antenna with stearing system, 5 ton transmitters (it might make sense to electronically steer the antenna… but this is tough with a short wavelength and such a huge, lightweight aperture), 5 ton structure and reaction control for a total of 50 tons. ~$100m is the going price for a Falcon Heavy launch, and even with scrimping and saving, you probably pay at least that much for the satellite, not counting your extensive development costs. $200 million for the satellite and launch, maybe $50 million for your 300m receiver and associated electronics. But you’ll need like 10 of these satellites, with on average about 2 transmitting power to your receiver at any one time (4 Megawatts). About $2 billion for 4 Megawatts of power, $500/Watt. But operating for 15 years, that’s about $4/kWh, which is something the military would tolerate. If you had like 4 receivers spaced evenly around the world, you’d be more efficient, so about $1.25/kWh. (You would get about 20-30 minutes of shadow at most, but 25 minutes of battery power is cheap and lightweight, easily a rounding error in the above $50 million for the receiver.)
…however, I don’t think the slew rates required for that size of antenna are realistic. Also, I’m pretty sure solar plus storage can beat the crap out of that cost of electricity (as does nuclear, if you can find a small and portable reactor and can tolerate having one), and I will show that later on.
But this is a pretty modest constellation with very large assumed inefficiencies. If you were able to capture 55% of the power, with evenly spread out stations, with lowered launch costs due to reusability (also, I just assumed you’d get SEP tug from LEO to 6400km for free), you could start competing with electricity prices in Europe, parts of South America, etc.
…but again, you have the slew rate problem. If you solve in-space modular assembly of a large GSO satellite and set aside a large receiver in a desert somewhere (on the order of a 500MW solar farm footprint), you actually have much better chance of competing in the much larger $0.20/kWh market, especially considering you’ll be providing nighttime power. I tend to think the future lies in multiple-kilometer-wide space antenna, though, since the advantage over ground-based solar power is you’re offloading the large area requirements to orbit (and you need a small beam footprint). This would allow area-constrained places like Singapore or Luxembourg to get a lot of energy without requiring a lot of space.
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