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If I install a small air compressor/engine, generator, and tank in my garage, and I charge it up at night when electricity costs $\frac{5.4p}{kWh}$ and use it during the day to power my house when electricity costs $\frac{12.5p}{kWh}$ would this be able to save money on the electricity bill or not?

The tank, engine, and generator should be sized to charge up over 7 hours between 01:00 and 08:00 and release the energy during the other 17 hours of the day. I'm assuming that regardless of when during the day the energy is actually released it is either used by me or goes back into the grid and runs the meter backwards to offset my day-usage.

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    $\begingroup$ You can't beat the 2nd law of thermodynamics. Even if you store energy at hours of the day when power is cheaper, you always end up putting in more energy than you get out. Factoring in losses in energy along the way, i would be very surprised if you break even in cost, much less profit from it. $\endgroup$
    – Paul
    Jan 25 '15 at 7:07
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    $\begingroup$ @Paul of course you won't get back as much energy as you put in, but this question is about how to determine if those losses are economically viable, given the different prices at different times of day. $\endgroup$
    – jhabbott
    Jan 25 '15 at 18:43
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It isn't completely infeasible. Just to get a ROM (rough order of magnitude), let's assume that a typical household that isn't using electricity for heating uses about 1 kW on average, and that you'd like to be able to store a half day's energy, or 12 kWh, which is roughly 45 MJ.

Commercial air compressors can easily achieve 15 bar or so (over 200 PSI). The energy in a tank of compressed air is equal to the pressure times the volume, so to store 45 MJ at 15 bar would require

$$\frac{45\ \text{MJ}}{15\ \text{bar}} \cdot \frac{1\ \text{bar}}{10^5\ \text{Pa}} = 30\ \text{m}^3$$

... or about 8000 gallons. Can you get or build a tank that size that can hold the pressure?

The real key is what kind of thermodynamic efficiency you can achieve while making the conversion from electricity to pressure and back again. When you compress the air, it will get hot, and some of that heat will be lost to the environment. However, you can get some of that heat back if you run the expanding gas through a suitable heat exchanger (and get some "free" air conditioning in the process).

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  • $\begingroup$ If you were using an inert gas, you could probably achieve higher pressures which would allow you to reduce the size of the high pressure tank. Of course, you'd need an even bigger tank (although it could be cheaply constructed) to store all the gas when it's at atmospheric pressure. $\endgroup$
    – Ethan48
    Jan 24 '15 at 20:11
  • $\begingroup$ @Ethan48: A balloon, perhaps? But I kept the tank pressure at a level that's commonly used commercially in order to be able to use mainstream equipment. Going significantly higher would require much more speciallized (expensive) gear. $\endgroup$
    – Dave Tweed
    Jan 24 '15 at 20:33
  • $\begingroup$ Yeah, I was thinking along the lines of a hydraulic accumulator which (some types at least) compress inert gas to a very high pressure using a bladder. Certainly very high start-up cost, just might reduce space a bit. $\endgroup$
    – Ethan48
    Jan 24 '15 at 20:39
  • $\begingroup$ @Ethan48: Remember, we need to be able to do the compression and expansion at a rate corresponding to a kilowatt of electricity (a few hp) -- even more if we have to size it for peak loads. That's a fairly large multi-cylinder unit. $\endgroup$
    – Dave Tweed
    Jan 24 '15 at 20:57
  • $\begingroup$ As you pointed out, any solution to this problem will be fairly large. $\endgroup$
    – Ethan48
    Jan 24 '15 at 21:10
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I'm going to do some naïve math.

So while charging your setup at night, you take in $x$ kilowatt-hours per hour. Multiply this by 7 hours, and you've taken in $7x$ kilowatt-hours. At a cost of $\frac{5.4\text{p}}{\text{kWh}}$, you've paid $37.8x \text{ p}$.

Let's say that when the electricity is on, you use $y$ kilowatt-hours per hour. Multiply this by 17, and you've used $17y$ kilowatt-hours. At a cost of $\frac{12.5\text{p}}{\text{kWh}}$, you've paid $212.5y \text{ p}$ if you were to take in energy during the day.

For your setup to save money, $$37.8x<212.5y \to x<5.62y$$

At the same time, you have to take in as much energy during the night as you need during the day: $$7x \ge 17y \to x \ge 2.43y$$ so now we get our final equation (slightly simplified for convenience) of the ratio $\frac{x}{y}$: $$2.43 \le \frac{x}{y} < 5.62$$ And that's your naïve energy usage equation. You can't take in too little, or you won't have enough energy to run your home during the day. You can't take in too much or you'll pay too much (unless some goes backwards through your meter, in which case there's no upper bound). It also doesn't take into account the fact that some energy will be lost during the storage, in which case the lower bound may need to be higher.

You then have to figure out how much money you save: $$\text{Energy saved}=212.5y-37.8x$$ and how many cycles it will take to pay off the cost of the system: $$\text{Number of 24-hour cycles}=\frac{\text{Cost of the system}}{\text{Energy saved}}=\frac{\text{Cost of the system}}{212.5y-37.8x}$$ Again, this doesn't take energy loss into account, or running your meter backward.


That's the theoretical aspect. It's not incredibly helpful, because it doesn't take some factors into account, and it's general. The University of Dayton has a much, much more comprehensive analysis here. There are some minor problems with the analysis, namely that it doesn't cover the money saved in your scenario and that it doesn't cover specific, small-scale scenarios, as yours presumably is (it's also a bit boring unless you know exactly what you're looking for or you're a compressed air nut).

There's an interesting diagram on page 3 of the paper, though, discussing efficiency. A quick inspection finds that of all the energy storage methods discussed, compressed air storage was second-lowest in efficiency (beaten out only by fuels cells, at 59%). Compressed air technologies have an efficiency of 70% (ouch!), meaning that the lower bounds of the equation need to be raised. In terms of efficiency, it's not the best choice.

There are some points in its favor: low maintenance cost, environmentally friendly, and an extremely long lifespan (30 years!). So it's up there in the technologies to be considered, as it should. But in your scenario, it might not save you as much money as, say rechargeable batteries. You could choose to run it slightly longer during each cycle, or use slightly less electricity. But as it stands, you're only going to save a tiny amount. Although, let's face it: In an age when energy consumption is one of the biggest issues, and cheaper an environmentally-friendlier are better, everything counts. Most likely, the system won't hurt you.

See here for some interesting information on large-scale compressed air systems.

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  • $\begingroup$ Just to point out the obvious: "kilowatt-hours per hour" is simply kilowatts. :-) $\endgroup$
    – Dave Tweed
    Jan 24 '15 at 19:44
  • $\begingroup$ @DaveTweed I know, I just hate forgetting units later on. :-) $\endgroup$
    – HDE 226868
    Jan 24 '15 at 19:56
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The existing answers do a pretty good job of explaining the sizing and the economics, but surprisingly for an engineering site, skip over the equipment. And that's where this becomes totally infeasible.

LightSail is arguably the closest to making compressed air energy storage (CAES) economically feasible at any scale. According to LightSail's CEO, the problem is the efficiency.

Efficiency of compressors/expanders can be hard to pin down, so let's just look at the motor/generators first. The NEMA standards for motors are that large ones need to be mid-90's percent efficient. So let's assume Lightsail is using a 94% efficient motor/generator. If you are using the biggest compressor at the local home store, you're looking at at most 2 hp. NEMA suggests you'll be looking at 78% efficiency on that motor. So just running the motor to generate the compressed air and running it in reverse to get the electricity back out, you've already lost $1-.78^2=0.39$ of your energy.

Now, for the compressor/expander. These numbers are not regulated and are generally trade secrets (although sometimes you can back them out from datasheets). This website suggests though that a small low speed reciprocating compressor might also be 80% efficient (my experience is actually that that is much too high for a product like the one I linked above, but I can't find any sources to cite). Now let's also assume you can use that same device as an expander at the same efficiency (highly unlikely). That's another $1-0.8^2=0.34$ loss. So in total, we're looking at $.78^2-0.8^2=0.39$ efficiency of the process.

As for the economics, if electricity costs you 5.4 p/kWh and you can store it at 39% efficiency, your recovered price is $5.4/0.39=13.9$p/kWh. Bad news! That's more expensive than your daytime price, so no, you unfortunately can't do this cost effectively at home.

We can also look at the this heuristically. If Lightsail, and no one else, can do it economically at large scales with $37M research dollars, its almost impossible that you could do it at small scales with smaller off the shelf equipment.

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If you are looking for house size scale, some panels would help: PV for compression & or termal to boost heat exchange for decompression,you could make also a puffer (water tank)with 2 coils, 1 at the bottom & 1 at the top,throw the bottom one will pass & cool the compressed air and on reverse on the top coil so you could recuperate some of the heat energy. Depending on where you purchase the materials or where you gather (junk) plus your work you maybe come close to a sustenability .With all the Green advantages and long life span(20-30 years) i think that beat the batteries storage price at least(5-8 years)

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  • $\begingroup$ The original question is about the cost effectiveness of using electricity from the power grid when the usage rate is cheaper to store compressed air for energy use later. While you make good points about the usefulness of renewable energy sources, you haven't actually answered the question $\endgroup$ Mar 1 '17 at 14:15
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If you can get to like 3000 psi, you could store a lot more energy in a a smaller space. What if you had a several solar-powered, high pressure compressors and a fleet of high pressure tanks? If one were to get the numbers right, they could basically have an air-powered house, no?

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    $\begingroup$ This is more of a comment than an answer $\endgroup$
    – Fred
    Feb 25 '17 at 7:24
  • $\begingroup$ What benefit would you get from an air powered house? Any time you're converting energy from one form to another (like compressing the air, or getting useful work out of the compressed air) you have energy losses. Having a house like that would have a lot of transmission losses going from solar, to electricity (to run the compressor), to pressure, to whatever form you actually need the energy in. There's really no good reason to do that when most of the things you power run off of electricity. $\endgroup$
    – JMac
    Feb 25 '17 at 12:20

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