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> What is wrong with present methodologies of energy storage? For example using surplus power to pump water up hill, to later recuperate during peak hours?

Say you want to store 1 kilowatt-hour of electricity (most places in the United States, about $0.12 worth). That's 3.6 million joules of energy. The potential energy gained by moving an object away from the Earth is approximately m * g * h, were m is mass, g gravity, and h height. g is approximately 10, and in a home system let's say h is also approximately 10. Probably less. Then the amount of water you need to move is approximately 36,000 kilograms. At 1 kilogram per liter, that's 36,000 liters or approximately 9,000 gallons. For comparison, that's roughly the size of a moderate swimming pool.

And of course, there are many other problems: converting electricity to pump action to water movement to potential energy back to electricity is not 100% efficient. That much water is extremely heavy; there's a reason swimming pools are often built in the ground. Etc. And all that for just 1 kilowatt hour!

My urban apartment uses O(10) kilowatt hours per day, so even if only a small fraction of that must be stored, my roommate and I would require a swimming pool or three. Hard to find space in a city...this could all be done remotely, but then transmission loss cuts the efficiency further.

Not really relevant to the discussion, but O(10) doesn't mean "approximately 10".

O(f(x)) denotes a function that is bounded by a constant multiple of f(x), and really only makes sense in the context of a dependent variable x. (e.g. O(2^x) denotes an exponential-bounded relationship with x).

So O(10) in the above context effectively means your apartment uses some unknown number of kWh.

To expand on this: O(10) is the same as O(9) or O(1) and O(k). (k is a constant)

Key to understanding this: Note that if you graphed out all the above as functions, they would all be horizontal lines.

O is about the kind of function something is, specifically relating to how fast it expands.

When dealing with numbers, the notation means "order of magnitude," which is the nearest power of 10. Strictly, this places is between 5 and 50 (4 rounds down to 1, 51 rounds up to 100).

Most people use it a little more loosely in conversation. More than 1, not 100, etc.

While I've occasionally seen O(...) used to mean "approximate upper bound" or even "approximate bound" in a more general way than the math for Big-O notation would permit, I've assumed it was either error or analogy, not a specific other function. Can you give a citation for this being an established usage?

(Note that I'm certainly familiar with orders of magnitude, just not this notation for them.)

It may be informal. I seem to recall people also using ~ for this, as in

"The detector is measuring eV, but this effect is ~ meV |O(meV) so we won't see it."

I didn't know this. I'm used to just talking about "order of magnitude."

You are completely correct, of course. At best it's an abuse of notation and perhaps an abuse of idea. But hopefully a fairly readable abuse!

I don't know a better shorthand for "of approximately the same order of magnitude." There's ~, but it also has its problems...if I say "I am ~175cm tall," I am not allowing for the possibility that I am 100cm tall or 500cm tall.

Is there an established convention?

I don't know of an established convention. I've heard people just say "within an order of magnitude." This may be a readable abuse to some, but not all; when I saw O(10) I just saw a horizontal line graph in my head and thought "huh?"

And now I know :) Thanks for taking the time to make this detailed & informative reply!

So basically the point is that Vanadium presents the most efficient method of power storage we know of to date?

I don't think so. In energy storage, pumped-storage hydroelectricity(PSH) is still the undisputed king. It currently represents >99% of installed capacity, and has a quite good efficiency. As I understand, Vanadium redox battery is not more efficient than PSH. And no energy storage system is proven to scale to PSH scale.

About the only problem with PSH is need for a reservoir and hence site selection. In Europe, it is said that Norway, which has lots of good sites for PSH, alone, can support entire energy storage demand of Europe. As I understand it is more problematic in US.

To what extent could you pressurize the water to restrict the volume? I can imagine an egg timer style device with heavy pressurised immiscible liquids and some turbine in the middle that you turn over physically instead of pumping.

someone has already had the idea:

http://www.myfreeinventions.com/electricity-generation/porta...

oh here's another one - might be interesting to strap two of these together:

http://fivegallonideas.com/hydroelectric-generator/

Well, air compresses better. People are trying to store energy in compressed air. I found LightSail Energy to be interesting.

http://www.lightsail.com/

From http://en.wikipedia.org/wiki/Properties_of_water#Compressibi...

> The low compressibility of water means that even in the deep oceans at 4 km depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume.

With some simplifications, the stored energy is approximately P*deltaV/2 (when P>>1atm), where P is the pressure and deltaV is the volume change. So in 1 litter (1/4 galon) at -4Km, the energy is only 400J (.1Wh), and you need submarine grade technology to store it.

The potential energy of 1 litter (1/4 galon) of water at 40m (130 ft, a 15 story building) is also 400J (.1Wh) and is much easier to build.

the volume of a liquid hardly changes under pressure.

The biggest site in the UK (built in the 70s for the same problem from nuclear power) was built into an abandoned quarry, surely there must be plenty of those around?

http://en.wikipedia.org/wiki/Dinorwig_Power_Station

Yes, but probably not ones on the top of a mountain.

We have a 1728MW pumped storage facility here in Wales.

http://en.wikipedia.org/wiki/Dinorwig_Power_Station

http://www.electricmountain.co.uk/

"Metallic vanadium is not found in nature, but vanadium compounds occur naturally in about 65 different minerals. Economically significant examples include patronite (VS4),[26] vanadinite (Pb5(VO4)3Cl), and carnotite (K2(UO2)2(VO4)2·3H2O). Much of the world's vanadium production is sourced from vanadium-bearing magnetite found in ultramafic gabbro bodies. Vanadium is mined mostly in South Africa, north-western China, and eastern Russia. In 2010 these three countries mined more than 98% of the 56,000 tonnes of produced vanadium.[27]

Vanadium is also present in bauxite and in fossil fuel deposits such as crude oil, coal, oil shale and tar sands. In crude oil, concentrations up to 1200 ppm have been reported. When such oil products are burned, the traces of vanadium may initiate corrosion in motors and boilers.[28] An estimated 110,000 tonnes of vanadium per year are released into the atmosphere by burning fossil fuels.[29] Vanadium has also been detected spectroscopically in light from the Sun and some other stars.[30]"

"Vanadium metal is obtained via a multistep process that begins with the roasting of crushed ore with NaCl or Na2CO3 at about 850 °C to give sodium metavanadate (NaVO3). An aqueous extract of this solid is acidified to give "red cake", a polyvanadate salt, which is reduced with calcium metal. As an alternative for small-scale production, vanadium pentoxide is reduced with hydrogen or magnesium. Many other methods are also in use, in all of which vanadium is produced as a byproduct of other processes.[31] Purification of vanadium is possible by the crystal bar process developed by Anton Eduard van Arkel and Jan Hendrik de Boer in 1925. It involves the formation of the metal iodide, in this example vanadium(III) iodide, and the subsequent decomposition to yield pure metal.[32]"

Source: https://en.wikipedia.org/wiki/Vanadium#Occurrence

So not only is extracting this stuff going to involve mining, the process of extraction itself relies on extremely toxic substances, and the most economic areas to mine it are places it's less than prudent to rely upon economically (China, Russia, South Africa)

Neither salt nor sodium carbonate is particularly toxic. The sodium carbonate is pretty reactive, as are hydrogen, magnesium and calcium. The various stages of vanadium compounds are likely a bigger concern than the various reaction agents.

The big reason pumped storage isn't more prevalent is that it isn't all that trivial to make it economical (you need a big reservoir to have much capacity). You also end up needing a lot of concrete, which also comes from mines (and requires a bunch of energy to produce).

The better tradeoff is probably to examine and carefully control mining practices (as opposed to sort of endorsing the status quo material consumption).

The problem with mining is rock rarely contains only one metal. The ore is crushed, the desired metal is extracted, and slag filled with heavy metal is deposited on the ground, where rain leaches poisonous metals into the water supply.

Not so much "commoditised" in the economic sense, but "can be deployed widely".

Inefficient storage is pointless. If it ends up being cheaper to throw the surplus away and then later run a fossil fuel generator, people will do that.

Time-shifted heating has long been a thing in the UK; "Economy 7" electricity is cheaper at night, used in conjunction with oil-filled storage heaters.

"Pump water up hill" requires a suitable hill. There are not nearly as many of these as you think, and flooding them is environmental damage of its own.

There's also a difference between using a substance re-usably for energy storage, versus extracting a non-renewable resource and burning it.

Grid-scale batteries are key to getting to a situation where most energy is renewable. The other tech that might work here is the molten salt battery, but that's harder to handle and doesn't scale down well.

It seems to me that the molten salts make the most sense and seems to be the farthest along:

https://www.solar-reserve.com

The case for small scale electric storage seems less obvious to me https://en.wikipedia.org/wiki/Molten_salt_battery#Vehicles but lithium ion seems to be working for now.

Because no thermodynamic cycle is 100% efficient.

>using surplus power to pump water up hill, to later recuperate during peak hours

Consider e.g.

http://www.forum-netzintegration.de/uploads/media/DUH_Sintef...

>Or heating water?

This is thermodynamically ridiculous. There's huge energy losses involved, cf Carnot efficiency of such a system.

>From reading further, and to answer my own question, the problem is that all research in this field is geared towards the identification of materials or energy sources that can be commoditized.

Oh please. It's a difficult problem. If there was an easy way to solve it cheaply without consequences it would have been done already. There are problems with dams and hot water and "layman" solutions like those. There are also problems with compressed air, batteries, and molten salts, not to mention loopy stuff like superconductors and nanosprings.