Thread by @JHildenMinton

1/ Here is a simple model for understanding how power price volatility impacts LCOE and value of electrolyzers.

LCOE = P.mean + (C.fix - P.std f(z))/F(z)

2/ P is price of power MWh, assumed normal.
C.fix is fixed costs MW capacity allocated per hour.
F and f are the standard normal cdf and pdf.
Z = (P - P.mean)/P.std
F(z) is also the capacity factor operating whenever X <= x.

3/ LCOE is minimized when
C.fix / P.std = z F(z) + f(z)

When cost to volatility is 1, LCOE is minimized at 81.6% CF, z = 0.90.
At a ratio of 0.5, 57.5% CF, z = 0.19.
At a ratio of 0.25, 36.7% CF, z = -0.34

4/ So as volatility P.std increases, the minimum LCOE is obtained at lower CF.
Decreasing capex also leads to obtaining minimal LCOE at lower CF.

5/ But minimizing LCOE is not how one optimizes the value of an electrolyzer per MW per hour.

NV = (V.h - LCOE) F(z)
= (V.hy - P.mean) F(z) + P.std f(z) - C.fix

6/ Net value of an electrolyzer, NV is optimized by operating when P = P.mean + z P.std < V.hy the value of hydrogen per MWh used.

The option theoretic value of an electrolyzer is obtained by maximizing NV.

7/ Let's put some numbers to this to see the implications.
V.hy = $40/MWh = $2.00/kg
C.fix = $10/MWh ~ $876/kW capex
P.mean = $30/MWh

At 100% CF this is breakeven, NV = $0/MWh. We can do better.

8/ At P.std = $10/MWh,
MaxNV = $0.83/MWh at CF 84%
MinLCOE = $38.99/MWh at CF 82%
Electrolyzer NPV = $73/kW

9/ At P.std = $20/MWh,
MaxNV = $3.96/MWh at CF 69%
MinLCOE = $33.76/MWh at CF 57%
Electrolyzer NPV = $347/kW

10/ At P.std = $30/MWh,
MaxNV = $7.63/MWh at CF 59%
MinLCOE = $25.83/MWh at CF 33%
Electrolyzer NPV = $668/kW

11/ In conclusion, the volatility of power prices is a key driver of the option theoretic value of electrolyzer. It is not necessary to break even at 100%. Volatility makes operating at lower CF more valuable.

12/ Adding more VRE to grid can increase volatility while decreasing mean power prices. So an electrolyzer operator will want to invest in VREs, perhaps buying PPAs and selling pricey power back to the grid.

Correction here V.hy=$40/MWh ~ $1.78/kg. But this of course depends on efficiency, 75% here.

If you are scratching your head, wondering how to derive this, it is an application of the truncated normal distribution plus a reallocation of C.fix from CF=1 to CF=F(z).
en.m.wikipedia.org/wiki/Truncated…

Nuclear power plants can become unprofitable as avg power prices decline. How might we avoid value erosion by operating a fleet of electrolyze? My simple model above provides insights.

14/ The red line is that value of power if simply sold on market without hedge. Blue line shows how electrolyzer gains value as avp power price declines. Yellow indicates optimal CF of electrolyzer. Gray is the combined value of nuclear hedged with electrolyzer.

15/ The gray line is shifted up with a decrease in electrolyzer capex. If you could lease for half the price, $5/MWh, that would lift the hedged value of nuclear by as much. This impacts the price threshold where hedging becomes more attractive than nuclear alone.

16/ The capacity factor of the electrolyzer is interesting. The complement, 1-CF, is amount of power sent to the grid. Rather than shutting down a marginally unprofitable plant, some fraction of it can be diverted to the electrolyzer when prices are low.

17/ The value of the electrolyzer depends on volatility (P.std). This application shows how volatility has real value and can preserve the value of nuclear even as long term VREs drive avg power prices below what is profitable for nuclear.

18/ Ok, let's add one more application. The value of a gas generator is mathematically the complement of the value of an electrolyzer. (Happy to spell out the formula if asked.)

19/ So what happens when we mash up an electrolyzer and a CC gas generator? There may be some engineering gains sharing an interconnection, water supply, and heat recovery. But my interest is more financial.

Firstly, let's assume that the value of generating hydrogen from a MWh of power is equal marginal cost of generating power from our gas generator. This chart shows how the value and CFs of this system varies with seasonal average prices.

21/ The solid green line show that the combined value is convex with a minimum net value of $4/MWh when the seasonal average is $40 that rises to $15/MWh net at extreme prices of $10 and $70. Thus, seasonal variation, even y/y changes will tend to boost the value of this system.

22/ This sort of net value convexity on seasonal prices is precisely what is needed to do seasonal balancing.
Note also that combined CF is 100%, indication that the electrolyzer kicks in when generation becomes marginally unprofitable and vice versa.

23/ But suppose that the value of electrolysis is at a $10/MWh spread above marginal cost for generation. Combined value is still convex but shifted up an extra $6/MWh, a minimum net value of $10/MWh.

24/ Notice also that combined CF reaches 113%. This means that 13% of the time this system is simultaneously generating power and hydrogen, with zero net power to the grid. Essentially high demand in the hydrogen market is rewarding the system for a net increase of H2 supply.

This is obviously not the most efficient way to produce hydrogen from natural gas (~33% efficient), but it does enable the system to pay for capex. So this is capital efficient, and will attract more electrolyzers to the market.

So what happens when the hydrogen spread is negative, which would be the case if the hydrogen market were to be oversupplied or natural gas undersupplied? Net value of system drops as does combined CF.

27/ So in this negative hydrogen case, the gas markets are pushing this system to consume less natural gas and produce less hydrogen. I do not expect this to be a frequent case as markets decarbonize. Rather the opposite, positive spread, should dominate.

28/ The upshot here is that the combination of gas plants and electrolyzers can prove a capital efficient way both to do seasonal balancing while advancing hydrogen markets and a growing fleet of electrolyzers. This is part of an economical path to deep decarbonization.

I've tried to keep the math details brief here, but am happy to answer questions. My hope is that curious people will try out these simple models in excel spreadsheets. I find that's the best way to get an intuitive feel for matter.

29/ We need to ask if this gas-electrolyzer system is compatible with deep decarbonization and how does it transition. While the annual avg price remains near $40, the value of hydrogen, it is a net zero producer of power, and consumes 3 btu of gas for every 1 btu of hydrogen.

30/ But what is obtained is the ability to do seasonal balancing. The system becomes carbon neutral when the gas consumed is carbon neutral. There are two basic ways to get there with electrolyzers.

31/ First, the annual avg price of power can fall to $20/MWh where electrolyzer CF is 3X the gas generator CF.
Second, build our 3MW electrolyzer for 1 MW gas.
The first substantially boosts the ROi of electrolyzers which would induce more investment in more capacity.

32/ So between these two extremes of avg power price falling from $40 to $20 and electrolyzers tripling, we'd arrive at an equilibrium that enables this system to be a net producer of gas. And getting beyond that threshold is essential for decarbonizing beyond the grid.

33/ The question that owners of gas and nuclear plants should be asking is whether investing in electrolyzers can defend the value of their thermal assets. Insufficient investment will delay decarbonization while burgeoning wind and solar erodes the value of thermal generators.

34/ Even a small decline in annual avg prices can make efficient CC generators unprofitable, while portfolio value can be preserved by the inclusion of electrolyzer.
Next, I will argue that battery storage will be of little help to stop value erosion of thermal fleets.

***negative hydrogen to gas spread case