# cost estimation for 2 grid energy storage systems

## CO2 mitigation costs

With modern gas turbines, burning natural gas makes perhaps 0.4 kg CO2 per kWh. I generally use $75/ton as a baseline target for CO2 mitigation costs; that's around what you see from various reasonable approaches like biomass conversion. $75/ton * 0.4 kg = $0.03/kWh. Maybe that seems cheap to those of you living in California, but it's a large fraction of the cost of generating electricity in the US. (People in California are now paying >$0.30/kWh, mostly because of corruption, and also lawsuits for fires from poor maintenance from corruption.)

So, $0.03/kWh is the target that should be met for the CO2 mitigation benefit of replacing natural gas with (energy storage systems + renewables). There can be other benefits that justify extra costs:
- If renewables are cheaper than eg natural gas, then that cost difference is compensation for storage costs. But of course, other power sources would probably still be needed for longer periods of low generation, and their cost per kWh probably increases when they're used less.
- Small systems that can store energy locally can provide backup power when electricity grids are down.
- Batteries can smooth out short-term power fluctuations.

But for the CO2 mitigation part, I think of ~$0.03 as being the target.

The grid energy storage systems I'm most optimistic about are (currently) water-compensated compressed air energy storage, and (for the future) chelate flow batteries. Below, I'll go through some of my cost estimation for those.


## Li-ion grid storage is expensive

A couple years ago Tesla was charging $265/kWh for just grid storage batteries, not including transformers, power lines, buildings, etc. (Yes, BloombergNEF costs were lower, those were biased by Chinese subsidies.) $265 / $0.03 is obviously at least 8833 cycles, and presumably more due to maintenance costs and interest rates.

Li-ion batteries do not last for 8833 cycles, especially if you charge and discharge them once a day. LiFePO4 battery lifetimes are generally overstated for grid storage applications, because a SEI layer forms over time from reaction with electrolyte, and charge cycles crack that, so there's an interaction between cycle life and calendar aging which makes battery life shorter than either individually. Some people were acting on the assumption that Li-ion battery prices would decline according to a linear regression to below $100/kWh, but over the last year they actually went up. (This isn't the main point of the post, just context, and I'm not going to argue about it again here.)

There are lots of other proposed systems: various hydrogen systems, Form Energy, vanadium flow batteries, zinc flow batteries, gravitational energy storage, etc. When I say I'm most-optimistic about some particular systems, I don't mean "these are the systems I've heard of that I like the best". What I mean is that I understand the entire conceptual space and every serious proposal, and those designs seem like the best ones that current human societies are able to develop. If that wasn't the case, I wouldn't be writing this post.


## compressed air

Gas turbines compress, heat, and expand air; you can store the compressed air for a while instead, but it gets hot from compression and storage wastes that heat. There are [existing CAES systems](https://en.wikipedia.org/wiki/Compressed-air_energy_storage#History) using that approach. Efficiency and cost-effectiveness have not been great, despite also using natural gas. It's possible to store the heat so it's not lost, but that's more expensive.

Compressed air can be stored cheaply in salt caverns made by solution mining, but the variable pressure is really bad for efficiency because it changes the turbine conditions and the pressure changes cause temperature changes. Also, this limits location options.

It's possible to get constant-pressure compressed air storage by filling the storage chamber with water. A simple way to do that is to have a water reservoir on the surface, and an underground chamber at a depth where water pressure matches air pressure. [Here's a video](https://www.youtube.com/watch?v=cOWjwwKSR78) from Hydrostor, a startup pursuing this approach. But this introduces new issues.

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If putting water in and out of a storage chamber, the chamber has to be waterproof, so it can't be made of salt. Mining hard rock underground in controlled shapes is expensive. For hard rock, mining costs are something like:

- solution mining in suitable salt caverns: ~$25/m^3
- surface pit: ~$30/m^3
- [block caving](https://www.youtube.com/watch?v=MWqMD85MVO4): ~$40/m^3
- stoping: ~$130/m^3

I'd say "stoping" is the mining type most similar in difficulty to making underground caverns for CAES.

Underground hard-rock mining generally uses drill-and-blast, but blasting is often banned under cities, which is a big part of why tunnel boring machines are used. If you want to build storage locations in cities, that's a problem. There are non-explosive approaches, such as [roadheaders](https://www.youtube.com/watch?v=g85K6SdD9aM), hydraulic breakers, and (disc cutter) tunnel-boring machines, but for hard rock, drill-and-blast is the cheapest, which is why mining uses it. Roadheader mining costs vary greatly with rock properties; for coal they're cheaper than blasting, but for very hard rock they're very expensive, because mining speed goes down and the carbide picks wear out faster.

For 70 bar pressure, you need 700m of water; this is a normal depth for underground mining, not a big problem, but small excavations at that depth are too expensive. Each CAES storage site would have to be large to keep costs down.

Another issue is that a little bit of high-pressure air can dissolve in water. If pressure drops cause water with dissolved gas to bubble, that decreases the hydrostatic pressure, and causes bubbling water to spout upwards - the "champagne effect". But this issue [seems solvable](https://www.osti.gov/biblio/6621019).

Some cost improvements do seem possible:
- Perhaps it's possible to use solution-mined salt caverns, by using a little extra effort to get them in the right shapes, then adding plastic or concrete linings.
- A guy I know has been working on non-explosive mining machine designs, and says systems he calls "Grond" and "Undine" could do non-explosive hard-rock mining for <$70/m^3. (Rock fracture dynamics are actually very complex and interesting, or at least so I'm told.) Per the names, they involve impact hammers and water. Those designs do seem like they could basically do what The Boring Company had hoped to but failed at, so let me know if somebody wants that.

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Energy in compressed gas is an integral of 1/x, so energy = volume * pressure * ln(pressure). At 70 bar, 1 m^3 is 8.26 kWh. Of course, that has to be adjusted by temperature when expanded and by turbine efficiency. For now, let's suppose you get 9 kWh. Assuming everything underground costs as much as stoping, you're up to $14.4/kWh capacity, and you need a reservoir on the surface too. Supposing reservoirs are cheap, we amortize costs over 10 years, and average 75% charge/discharge per day, that's ~$0.0055/kWh. Not bad.

Considering the cost of electricity from natural gas, and the fact that we don't need high-temperature turbine blades, we can suppose turbines only cost $0.005/kWh if run continuously. Supposing a 1/4 duty cycle, that's $0.02/kWh. Let's say the renewable power lost from inefficiency is worth $0.01/kWh output.

We also need heat exchangers, and those could be more expensive than the turbines. Supposing $2 per W/K and a 10° gradient, that's $200/kW, perhaps $34/kWh for 1-day storage. Let's say the heat exchangers add $0.01/kWh. Then you need something to store the heat, but water is cheap so let's just ignore that for now. Heat exchanger cost also depends greatly on manufacturing methods, temperature, and pressure; gasketed plate heat exchangers for warm water are cheaper than high-temperature shell-tube heat exchangers for gas turbines.

Instead of using heat exchangers and some fluid, another option is sending compressed air through beds of eg sand. Such "packed bed heat storage" might seem cheaper, but [this paper](https://www.sciencedirect.com/science/article/abs/pii/S1359431117375075) estimated ~$0.0685/kWh stored for packed bed heat storage - just for the tanks, rocks, and insulation. So, this approach is probably more expensive than using fluids but allows for higher temperatures.

We're now up to ~$0.0455/kWh incremental cost over generation. That's too high to be competitive for CO2 mitigation, and installations have to be large - but it's sort of competitive with nuclear power costs. I think better mining methods and various other improvements could plausibly bring that down to $0.04/kWh. There are lots of details to those potential improvements but that's good enough for this post.


## flow batteries

Let's estimate the cost of electrolyte for a chelated chromium-iron flow battery. [EDTA](https://en.wikipedia.org/wiki/Ethylenediaminetetraacetic_acid) is a common chelation agent; it doesn't actually work well for this, but it's a good enough approximation for production costs at large volumes.

- 1 mol of Cr is ~$0.50
- 1 mol of EDTA is ~$0.70
- at 2 volts, 1 mol of electrons is ~0.054 kWh

So, Cr and EDTA is only ~$22/kWh. The iron side would probably be cheaper, maybe half as much. So, electrolyte costs for flow batteries seem potentially very reasonable. The real problem is the cells that electrolyte would run through.

Batteries involve immobile materials with variable charge state, and mobile ions with constant charge. Normally, the variable charges are insoluble in a liquid, but flow batteries are defined by everything being soluble, which means ion-selective membranes are needed. Those membranes are obviously more expensive than liquid, and they make flow batteries more expensive than regular batteries per watt.

Nafion (or Aquivion) membranes are fluorinated and expensive. There are lots of papers on cheaper membranes with somewhat better conductivity, so why aren't they used? Those papers generally don't say, but it's because they're not durable enough. The membranes have a tendency to get oxidized or broken apart, which is (mostly) why the expensive fluorinated ones are used. But there is a new-ish type of membrane that I think is promising: [sulfonated phenylated polyphenylene](https://pubs.rsc.org/en/content/articlehtml/2021/ma/d1ma00511a). That seems suitable for hollow-fiber membranes.

With current membranes and current densities, and some rough estimation of other costs, and extrapolation from current systems like vanadium flow batteries, cells for chelated iron-chromium flow batteries seem ~$2000/kW for 90% efficiency, with large-scale production. That's too expensive. But with cheaper membranes and large-scale production, I think flow batteries could realistically be made for $300/kW, which might be $50/kWh for 1-day storage, not including the electrolyte. (Water desalination plants are much cheaper than that per membrane area, but also simpler. Still, they're useful as another reference point.)

That's a lower cost than CAES, but perhaps an even bigger advantage is that they can be smaller and placed more flexibly. Flow battery systems could provide local backup power, which obviously has some extra value. (Salty water isn't flammable, unlike Li-ion batteries, so there are fewer safety issues.) Placing storage where electricity is used would also reduce the number of power conversions. Even if homes have batteries, rooftop solar still doesn't make economic sense without subsidies, but solar panels over parking lots is only slightly more expensive than in open fields.


## seasonal storage

So far I've talked about 1-day storage, which helps with the sun not shining at night. It doesn't help with longer periods with little sunlight and wind, which can happen in the winter in Europe.

Storing compressed hydrogen or naturals gas in underground salt caverns has very cheap storage capacity, cheap enough for seasonal energy storage, but converting between electricity and hydrogen is much too expensive. Hydrogen fuel cells are expensive enough that burning it in gas turbines is better. I can't see this being economically practical, and I don't expect hydrogen from water electrolysis to be <$4/kg (before subsidies) anytime soon; see also [this post](https://www.bhauth.com/blog/chemistry/electricity%20to%20chemicals.html).

If you'd need more than 5 days of energy storage, and can't use natural gas or coal, and don't have enough land to get that energy from biomass, I don't see anything potentially competitive with nuclear power.