tisdag 12 juli 2022
fredag 17 september 2021
The first privately funded Fusion Plant
Suppose you are a future entrepreneur in the emerging fusion market. In this scenario, the technology risk is substantially lower (i.e. we know fusion works), but there is still the matter of bringing fusion to mass use. Hopefully as quickly as possible, since 1) Early actors can make a lot of money, and 2) Also we are in a hurry to save the Earth. Your job is to convince investors that they will get a better return on investment than from other entrepreneurs. Your job is also to convince government bureaucrats that they should let you build your plant.
Where to put the first plant? It depends on which of these factors dominates.
1. Fusion experts are hard to come by
Everyone who has worked with fusion until now are concentrated in a few clusters around major projects. Only a few of them will be willing to uproot for your cause, and only for a hefty pay raise/equity. If this makes your option much less likely to succeed than the government projects, then you will have to put the first plant near Boston or Oxford. Unfortunately, this can reduce the comparative advantage of a private option. The comparative advantage of a private option is that it often accepts higher risks, and is therefore able to iterate faster. Fusion researchers presumably want to advance fusion technology as fast as possible. Maybe the key challenge will be to attract some of the most respectable fusion researchers, and if some of those are on board then getting others to move will be mostly a matter of making it convenient.
2. Governments are reluctant to let private enterprises build fusion plants
This could be due to safety concerns or wanting to retain control for national energy security purposes. It could also be a matter of just demanding a high tax, or requiring a list of security measures that is essentially a security theater, in order to avoid blame for potential accidents. Luckily, unless all of the US federal government, the UK, and the EU (and also all other locations where experts live/could be convinced to move) put in place a moratorium on private fusion, then there is a way to make it economically viable. That is to say, you only have to find one defector. Not being dependent on a particular location is also good for negotiation.
The problem is: if you put down a fusion plant next to no particular location (i.e. where the best tax deal is), then chances are there will not be a demand for an extra 500 MW of utility power nearby [1]. So the local price will go down. However, you can just mine bitcoin with the surplus power. The fact that bitcoin mining is possible makes fulfilling the following wish list more promising:
- A bit away from a population center, for safety.
- Permissive regulations for industrial development.
- Low tax.
- Cooling available.
- Large capacity for power transmission.
What will be the business model?
- Announce the building of plant in a location that fulfills above.
- When it seems likely that the plant will actually be operational soon, bitcoin miners will start to move in close to the location.
- From day one, the plant has a guaranteed selling price for its electricity that is limited by the price of energy in other bitcoin mining locales.
- The miners make a neat profit, but since their market has low barriers to entry, the plant owners get most of the surplus.
- From the perspective of the nearby population center, the plant acts as a reservoir of energy: it means that their local energy price will not be significantly higher than the energy price in other bitcoin mining locales. This is less of a social benefit than having electricity that is basically free, but it is still a significant social benefit, especially if the current power sources are unreliable or relatively expensive (such as in Germany).
- Over time, industries that produce more value per unit of energy than bitcoin mining may establish near the site.
- When the above steps have been carried out, there will be an established trust in the economic viability of fusion plants, and the energy revolution will be a matter of fact. Your company has hopefully already attracted more capital and started building next generation sites, attracting more actors to the market, which indirectly increases the viability of new industries that can leverage cheap electricity, further increasing demand for fusion power, and so on.
Is there gold at the end of the rainbow?
What will the energy market be like when fusion is mature? Will the original fusion companies enjoy defensible oligopoly profits for a long time?
Maybe the energy market will be like the air travel market. On the lowest level (furthest away from the end user) are the airplane manufacturers. Airplane manufacturing is a global oligopoly of Boeing, Airbus, and a bunch of military companies. Boeing and Airbus are pretty valuable, a combined value of a bit over $300 billion. This just so happens to be approximately equal to the value of all airlines combined [2]. In a similar scenario for fusion power, there would be two or three global manufacturers of standard models of reactors. These would be operated by more local or regional energy companies. They would split the profits roughly equally, however spread out over much fewer manufacturers. How big is the energy market compared to the airline market? According to Wikipedia, about 3 times larger [3]. Most of those are oil companies, however, so that value can only be realized with grid energy in a world with only electric cars, for instance. On the other hand, making energy much cheaper will increase the size of the market. In any case, if we believe that this is what the energy market with fusion looks like, then a fusion startup definitely has potential "Google-scale" value.
Maybe the energy market will be like the digital technology market. On the lowest level there are hardware companies such as Intel, AMD, and Nvidia (super expensive to build chip fab, big companies, good profits). Second level are machine manufacturers such as Samsung, Sony, Asus, Lenovo (rather low barriers to entry). Third level are ISPs (they don't make any money - unless they're crooked!). Top level are software companies and web service companies, which are pretty interchangeable nowadays. This is where the big profits are made, I don't even need to mention the names of these companies. But anyway, we only care about the lowest level here. The dominating factor in the profits of the lowest level companies seems to be the massive cost of building a state-of-the-art chip fab (factory). Is it likely that production of new fusion plants will be similarly expensive? Depends on which technology wins out in the end. If it requires new superconductors whose manufacturing depends on super clean environments, then yes. If it can be make with relatively bulk materials, then perhaps not so much. (Westinghouse, the French one, which else?).
Wait, is the bitcoin mining actually more profitable than just selling as a utility?
Probably several times over. In Sweden, a country which in 2011 had plentiful electricity from sources with low operational cost (hydro and fission), the profit from selling electricity was about $50/MWh [4]. This means a profit of $200M per year for a 500 MW plant. Bitcoin miners make about $50M per day [5], using 80TWh annually [6]. The revenue from a 500 MW plant would therefore be about $1B per year. The unknown here is the operational cost of a fusion plant. This should be low, since most of fission power operational cost seems to be fuel acquisition and safety systems, both of which should be considerably less for fusion plants.
References
[1] Omega Tau episode 304, "Past, Present, and Future of Fusion", archive. Around the 1:50 mark, they discuss how fusion would integrate with the energy economy.
fredag 10 september 2021
The value of more options
I took a course on Statistical Modeling of Extreme Values in university. The following results may have been covered elsewhere, but it was missing from the course I took. I think that's a shame because they lend themselves more easily to quick estimations than the GEV. When valuating insurance it may of course be important to use the formal tools, but for most cases in extreme value analysis we just want to know whether something has the chance to be Really Bad.
Suppose we pick N samples from a stochastic variable X that are independent and identically distributed. What is the expected value of the Max of these samples? In particular, how does it grow with respect to N?
1. X ~ U(0, 1)
Another way to see this is that the expected value of 1 - Max(X) shrinks with the speed of O(1/N). So with N=10, the max will be about 0.9, with N=100, the max will be about 0.99, and so on...
2. X ~ Exp(1)
At this point, I had to take help from Wolfram Alpha [1]. The expression evaluates to the Digamma function of N, plus a constant [2]. The constant is about 0.58. The Digamma function grows as ln(N) - 1/(2N). Calculating some values:
| N | E(Max({X})) |
|---|---|
| 10 | 2.8 |
| 100 | 5.2 |
| 1000 | 7.5 |
| 1,000,000 | 14.4 |
Basically, the expected max grows logarithmically. Every extra order of magnitude adds about 2.3 (ln(10)) to the expected max value.
3. X ~ Pow(a), a > 1
Once again, the waters were too deep for me here, so I had to take help of Wolfram Alpha [3][4]. The answer for the whole expression comes out to:
The value of (-1/a)! can be calculated with a gamma function calculator. For a=2, it comes out to about 1.77. Note that the input to the gamma function should be (1-1/a). For the remainder of the expression, we can use the Stirling approximation, which says that:
Also assuming that N is fairly large, so we replace N-1 with N. Now we have:
The first term goes to 1/e as N becomes large. The second term is approximately N^(1/a). The approximation E(Max({X})) = N^(1/a) is used in the table below.
| N | E(Max({X})), a=2 | E(Max({X})), a=3 |
|---|---|---|
| 10 | 3.16 | 2.15 |
| 100 | 10 | 4.64 |
| 1000 | 31.6 | 10 |
| 1,000,000 | 1000 | 100 |
References
[1] Wolfram Alpha input
[2] Digamma function (wikipedia)
[3] Wolfram Alpha input
[4] Why, do you ask, did I not just use WA on the original expression? Actually, computation time in the free version times out then.
lördag 4 september 2021
Back of the Envelope: Carbon Capture
How difficult will carbon capture be? The principle is that a fan blows air through some process that captures the CO2 out of it. I am assuming some things:
- The fan operates 24/7
- The wind speed through the fan is constant at 5 m/s
- The process captures 100% of the CO2
This gives me the result that each m^2 of fan surface captures 92 kg of CO2 per year, and therefore about 110 m^2 is needed per person.
fredag 14 maj 2021
söndag 9 maj 2021
torsdag 6 maj 2021
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