# 2

Imagine a world that is fuelled exclusively by solar energy that comes from space. This would happen by having many solar panels in orbit, beaming down energy through microwave transmission.

I am trying to understand how a firm or government might price this sort of energy to consumers based on its costs. Suppose that a large energy company pays a company like spaceX to put solar satellites in orbit - how would the price of energy vary as a function of the cost of putting satellites into orbit? I am not formally trained in economics, and I was looking for a way to start framing this problem properly.

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Caridorc Tergilti

### May 14, 2022

10

SpaceX's Falcon 9 now advertises a cost of \$62 million to launch 22,800 kg to LEO, \$2,720/kg. https://ttu-ir.tdl.org/bitstream/handle/2346/74082/ICES_2018_81.pdf

Given an average solar silicon price of around \$9 US per kilogram in 2020 https://www.solarquotes.com.au/blog/solar-silicon-price-hike/#:~:text=Compared%20to%20the%20average%20solar,%2434%20Australian%20dollars%20per%20panel.

This would increase costs 2720 / 9 = 302 times.

The cost of a solar electric system is measured in dollars per watt. The average cost for a residential system is currently \$3-5 per watt. That means the average 5-kW residential system will cost \$15,000-\$25,000, prior to tax credits or incentives. https://sites.energycenter.org/solar/homeowners/cost#:~:text=The%20cost%20of%20a%20solar,to%20tax%20credits%20or%20incentives.

So this system would cost about 4*302 = 1208\$ per watt.

This calculation is extremely approximate, but no, it will never work, even if the cost of sending a kg to orbit plummets.

This is probably the worst-case comparison for space solar, since it assumes you're just going to pack a bunch of terrestrial systems onto a rocket and shoot them into space, where they will (just like terrestrial systems) only work at a fraction of capacity due to clouds, bad sun angles, getting dirty, and night-time.

In practice they would provide a lot more power per unit mass by at least one order of magnitude and possibly two. Mirrors in space can be relatively flimsy thin things and still work since they don't need to withstand winds and other loads, ...

1mikbp
Can you elaborate more on that? It was clear to me that in space PV in space can give much more energy/mass than in Earth, but close to 2 orders of magnitudes is huge! Is this "only" due to temperatures losses + constantly running at full capacity + concentration?
1JBlack
Almost all of the mass of solar panels on Earth is structural strength to deal with various types of weather (mostly wind). That alone would increase power per unit mass by a factor of 5-10, though some of that would be eaten by beamed power equipment that isn't necessary on Earth. Permanent cloudless daylight with the light coming from an essentially fixed direction increases average power by a factor of about 4-6, while not affecting mass. Using thin-film mirrors for concentration could enable even more power for given mass.
1mikbp
Ahhh! What I was missing is the structure part. I was thinking in E/surface not on E/mass. Thanks.
1Caridorc Tergilti
I am not really sure about that. There is not only a huge money cost but also a huge energy cost when sending something into orbit, would the panels even make back the fuel spent to send them? Even if the rocket hardware is reused 100% with no serious maintenance costs (reusing costs more fuel) would the panel even make back that fuel energy alone? I did not do the math but maybe not even that. If we could put them in orbit with a space elevator almost for free the tune would be way different though.
2JBlack
Oh yes, there is no question at all that they would make back the fuel energy cost. In money terms the fuel is a tiny fraction of launch costs (less than 1%). In fuel energy terms it costs about 400 MJ/kg to get payload into orbit via Falcon-9. With fairly standard terrestrial designs you can get about 5 W/kg rated power (mass including support electronics), which in space would be available nearly continuously. That gives a energy payback time of about 2.5 years. With solar power designs more suited to space use, I would be very surprised if that couldn't be reduced to weeks.

Sorry, I might be missing something here but

• Isn't price of energy typically measured in kW hours. Energy = Power x Time.
• If a space solar system can output more energy since it stays on for longer, wouldn't this mean that the cost per watt hour would naturally decrease? This would be because the price of a watt hour I imagine would be Energy / price. So, if our launch cost is a fixed cost, then we would find that E / price decreases.
1Caridorc Tergilti
* Very good point: I think the website I linked to refers to peak power, so the Kilowatthours would be lower. (not sure on this, sorry) * If the panels on orbit last double the time and produce double the energy that is only a factor of 4, while the system is about 300 times more expensive. (but again you have transmission losses that I did not consider)

[-][anonymous]10

no, it will never work, even if the cost of sending a kg to orbit plummets.

A solar electric system on earth doesn't make 1 watt all the time.  Obviously there is night, and there is geographic differences.

A quick and dirty approximation is here: https://unboundsolar.com/solar-information/sun-hours-us-map .  The idea of "sun hours".  Let's take the median "sun hours" of 4.

this means just 1/6 of the time do you get a rated solar panel's full output.

Negating the microwave transmission system's cost and other costs, if the cost of sending a kg t...

1Caridorc Tergilti
Yes, I meant plummeting "within reason" (like x10) not plummeting to extremely low values that, as you correctly said, are not possible given the energy cost.
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An interesting question to be sure, and an inspiring vision for the future. However, I think at this is too wide of a question to generate a sufficient answer and a better start would be to read more in general about energy markets (pricing, how utilities decide pricing and assess expansion projects) and the general engineering concepts behind space solar power (SSP).

Some thoughts to generate conversation:

What is the design of the power satellite system? ie are there swarms of small ones or a few large ones

What is the power beaming design? You mention microwaves however I am under the impression that the best choice wavelengths for microwave beaming are very low density- this would massively change the ground system infrastructure design and thus impact cost.

I do not work with the grid so please take the following with a healthy dose of 'I should probably at least google this...':

Pricing varies between consumers, large scale customers (heavy industry, factories, etc) may be cheaper or actually more expensive depending on load usage than households.

Transmission costs would either be negligible or hugely impactful based on the ground system infrastructure (power beamed directly to user or one large plant)

Your description mentions "a world that is fuelled exclusively", this is very unlikely in almost any scenario unless the world is radically different than the world of today and more likely SSP would play a role in modifying current electrical generation.

At some point I'd imagine it all comes down to a massive estimates spread sheet where if the cost of total construction normalized over expected lifetime + cost of estimated maintenance < price per kwh in current grid market then BUILD. Some other factors play a role as in 'has this been done before?' and 'what do we estimate demand will be in the future?' but is mostly is down to cost (this mythical cost accounting spreadsheet has been corroborated by some discussions online I've had).