Minimum viable microwave-based space-based solar power system

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.

The Airy Disk diffraction pattern from a circular aperture

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.

spacebasedsolarpowerinitialconstellation

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.

The following two tabs change content below.

Chris Stelter

Latest posts by Chris Stelter (see all)

This entry was posted in Uncategorized. Bookmark the permalink.

9 Responses to Minimum viable microwave-based space-based solar power system

  1. Hop David says:

    Okay, 10 sats and 4 receiving stations I get 2.2 billion dollars. Each station is 4 megawatts so a total of 16 megawatts or 16,000 kilowatts. 15 years is 15*365*24 hours or 131400 hours. 131400*16000 is 210.24 billion kilowatt hours. So I’m getting about a buck per kilowatt hour. Maybe I’m making an arithmetic error that is stubbornly evading my notice.

    A kg per kilowatt is a very optimistic alpha in my opinion. Roll Out and Passively Deployed Array (RAPDAR) might deliver 250 watts/kg. I understand this has about the thickness of the milk jug plastic. But would about structure? And gimbals to keep the array pointed at the sun. If you have a kilowatt per kilogram you get what I call Acres of Seran Wrap.

    If memory serves, orbiting at 6378 km altitude would put the solar arrays in the thick of the Van Allen belts. Are the sats you imagine rad hard?

    There is also overhead for the sats as well as ground stations, I don’t see those included in the calculations.

    Over all it seems like you’re making some optimistic assumptions. But it looks like you’re heading for a thumbs down for this scheme regardless. So I think we’re on the same page.

    I believe space solar power will be viable. But providing power consumption near the arrays, not beaming to earth’s surface.

  2. Chris Stelter says:

    Yes, orbiting Saran Wrap. But it is doable. ROSA arrays are supposed to do 500W/kg, but we need to think differently anyway. Thin film solar cells are incredibly lightweight. With the right substrate, you could make them 10,000-20,000W/kg (at the cell level)… Especially considering the efficiency gains that have been made in the last decade. More realistic is 1,000W/kg, or roughly twice as good as ROSA arrays and 4 times as good as MegaFlex. But those arrays are much stiffer than our arrays would need to be.

    Structures for spacecraft are passively stable, and are made to have a high fundamental frequency or operate while deployed and under non-negligible acceleration (during thrusting). We’ll have to relax those constraints a bit, operate at a lower fundamental frequency and perhaps use some active damping and compensating electronically for the antenna. And by being in GSO, the antenna will not have to move, only the arrays, and even there they’ll only have to rotate in one axis once per day.

    As a side note, the spin-stabilized IKAROS, the Japanese solar sail, also contained embedded thin film solar cells that demonstrate the equivalent of 1000W/kg specific power, if they covered the whole sail (and these are fairly low efficiency devices… we can make ones twice as efficient today). I don’t think 1000W/kg is in the least unrealistic, especially at GSO. In fact, we probably can manage to do at least double that with some further thinning of the substrate, operating at higher voltage, using lithium-based conductors (or at least aluminum-based conductors), clever structural schemes, etc.

    To get extremely high specific power, we could also spin the solar array and have it be essentially an entirely tensile-dominated structure. It would point at the sun at all times, with the antenna being the part that gimbals.

    To achieve extremely good specific power for the solar array, stop thinking about how you’d make improvements on existing array concepts, and start thinking about how you build a solar sail. A square sail is probably the easiest solar sail concept to use for extremely high specific power arrays, but a heliogyro or spinning disk could also be used.

  3. For a proof of concept. What can be done in the 10kW – 100kW range in the next 4-5 years?

  4. Hop David says:

    When did a 6400 km orbit morph to GSO? That would mean an approximately six fold increase in the diameter of the receiving station.

    Acres of Seran Wrap spin stabilized? Yeah it might be possible to keep the arrays spread and pointed toward the sun.

    But then the 300 meter antenna would pass through the spinning fan blades twice each orbit. If the orbit altitude’s 6400 km, the large antenna will pass through the array’s plane each 2 hours. If the orbit’s GSO, it will pass through the array’s plane each 12 hours.

  5. Robert Clark says:

    It’s that 10% transmitted that’s the problem. You might as well cover the receiver area with solar concentrators and use batteries for night time.
    Good point about concentrators for reducing weight. This can at least solve the launch weight and cost problem. Mystified why this isn’t worked on more for space as it is for ground based. For ground based, it’s done for cost since mirrors are cheaper than solar cells. In space the cost of the cells is a small part of the satellite and launch cost. But in space mass IS cost, so it should be just as important to use solar concentrators in space as well. Note it’s important for large satellites to provide power and also for recent uses of electric propulsion to reach GEO.

    Some research on solar concentrators:

    The Solar Sunflower: Harnessing the power of 5,000 suns
    The Sunflower has a massive total efficiency of around 80%, thanks to very clever tech.
    by Sebastian Anthony (UK) – Aug 30, 2015 8:10am EDT
    http://arstechnica.com/science/2015/08/the-solar-sunflower-harnessing-the-power-of-5000-suns/

    Solar power when it’s raining: NRL builds space satellite module to try.
    http://www.nrl.navy.mil/media/news-releases/2014/solar-power-when-its-raining-nrl-builds-space-satellite-module-to-try

    Bob Clark

  6. Paul451 says:

    I think the problem with solar concentrators is that you either end up pushing the solar arrays outside of their most efficient operating temperature range, or you need radiators to keep them cool. That eliminates the current advantage of most arrays to use the simple passive cooling that comes from their sheer panel area. And radiators can be stupidly heavy. Your mass gains from using thin film concentrators is eaten by the mass of the radiators.

  7. svjak says:

    Considering the massive reduction in terrestrial solar (now below $1.00/watt w.o. balance of system costs) and projected to fall anohter 40% before 2020, it might make more sense to launch a mirror and use it to direct sunlight 24/7 at a solar array on the ground than to launch a huge microwave transmitter. A mirror is a lot simpler and could be made much lighter. In geosynchronous orbit there should be sunlight 24/7 except for a few times a year.

  8. Andrew_W says:

    svjak, the problem with that idea is the angular size of the sun. Even with an ideal parabolic reflector the diameter of the area illuminated on the Earth will be about 1% of the distance between the reflector and the Earth – as the diameter of the Sun is about 1% of the distance to the Sun.

  9. Sunny Marueli says:

    Where do the weight numbers come from?
    For the 300m antenna, the area of the transmitter is 70,000 m^2 – or 0.07kg/m^2.
    This seems very optimistic. What is the antenna made of?

Leave a Reply

Your email address will not be published. Required fields are marked *