Flywheels and energy storage.

[Massacure]

So I was bored and decided to do some back of the napkin calculations for how much energy could be stored with a flywheel. So I decided to calculate the energy of a steel cylinder that is 1 meter in radius and 10 meters in length.

To calculate the amount of energy it stores, we have the equation E = 1/2 * I * W^2. I = K * M * R^2. K is a constant of 2/5 because we are using a cylinder. The mass is equal to 7850 (The density of steel) times 1 * 1 * 3.14 * 10 or 31.4. R is 1. Therefor I = 98,956.

Now we take I and plug it into 1/2 * I * W^2 where W is how many radians the cylinder turns in a second. I was thinking of spinning it at 12000 rotations per minute, so that would be 24000 radians per minute or 400 radians per second. Hence we get a kinetic energy of 7,916,480,000 Joules of stored energy.

We need to convert to kilowatt hours. One watt is one Joule for one second, but we need Joules for an hour. So we divide 7,916,480,000 by 60 to get Joules for minute and by 60 again to get Joules for an hour. We could supply 2,199,000 joules per second (watts) for the period of an hour. We can divide by 1000 and this gives us 2,200 kW-hr of stored energy.

What do you people think? Does everything sound alright?

I was also thinking about trying to calculate frictional losses, but I don't know where to begin with that. We also need to account for efficiency in converting from kinetic to electrical energy, but I don't know how to calculate that either.

[Dead_Parrot]

1. Sounds about right...

I think friction can be almost ignored, since most "serious" flywheels these days are vacuum sealed with magnetic bearings: IIRC, the charge/discharge efficiency is around 90%.

[Massacure]

2. whether friction can be ignored depends on the timescale.

You may be able to ignore it on the timescale of an hour or so, but you cannot over a month, especially if there is no available trickle charge to overcome it.

[Dead_Parrot]

5. Ahem, you're right.

I was thinking in terms of the time taken to discharge at a kW or two, rather than as a "set and forget" solution. Once it's up to speed, you'd need to trickle a fistful of watts into it to keep it there. :)

[eallen]

3. Active Power, Inc. (ACPW)

[Old and In the Way]

4. It would take a lot of energy to get that sucker up to speed, no?

But once rotating, would the energy needed to maintain the rotation be be less than the energy it produces? If so, isn't this a perpetual motion machine?

[Dead_Parrot]

6. No...

The energy it produces (or more accuratley, releases) is always going to be less than the amount you've put it. In fact, over a long enough time period the beast would be a black hole for energy: Spin it up, keep it going for 20 years, then discharge it and you'll only get a tiny fraction of what you stuck into it.

It can release energy faster than you put energy in to maintain it - Is this what you're thinking of?

[Old and In the Way]

9. My best physics days are way behind me....

:-)

But you are obviously right. I am curious as to where this theoretical discussion is going, though...

[TreasonousBastard]

7. I'll take your word for the calculations, but...

what's this flywheel going to be used for? And what's the specific energy input?

Every car out there has a flywheel to smooth out engine rotation between power pules from the cylinders. Mercedes had a few hydrogen buses roaming around Frankfurt using huge flywheels to capture "regenerative" braking energy and then assist the buses in accelerating from a stop.

And then there's gyroscopes...

Anyway, my own small, and largely trivial, experiments with using flywheels to store energy led me to understand that they usually expend their energy much faster than they store it, so have some interesting uses, but seem to be limited as energy storage units. It's like a capacitor for storing electricity-- very useful, but not useful enough when a battery is needed.

[Massacure]

8. If you have a set of 100 you can expend them one at a time.

I was just thinking to myself of coupling wind turbines with flywheels rather than rewiring the grid to be capable of transferring massive quantities of power for hundreds of miles from windy regions to non-windy regions.

[TreasonousBastard]

10. I though of hooking up...

flywheel to a Savonius rotor on the deck in back, but started thinking that something more like a farmer's water tower would work better. Let the wind simply pump the water and work out proper head and flow to run a turbine generator. I know, the total energy to raise the water to the right head is probably close to the energy to overcome flywheel inertia, but you're only raising a little water at a time.

Maybe enough money could be spent on a major project to use flywheels that way, but I'm still thinking instinctively that flywheels are poor vehicles for that kind of storage.

[Massacure]

12. Where would you store all that water though?

You would need to flood large amounts of land, which would be ecologically destructive.

[TreasonousBastard]

13. Right now, I live on waterfront, but...

even if I didn't, the total volume isn't important, just the flow. The water would be recycled, whether it be in the creek or a pool.

So, if I have a 100 gallon tank up on the windmill, a 500 gallon goldfish pond at the base would be more than enough for filling and draining the tank. This isn't for drinking or irrigation, so I don't have to deal with another groundwater well or drainage.

BTW, I would not expect to be able to build a big enough structure to actually power the entire house with 110. This would be mainly to charge up a bunch of batteries to run the lights and other low-wattage stuff. I can use 12V lighting and some appliances, and either 12V or 120V DC can be easily converted to 120V AC for computers, TVs and such.

Truth is, the cost for all this wouldn't have much of a payback if I can't run the refrigerator, water pump, washing machinepower tools, and the other heavy stuff off of it.

So, the obvious question is why bother to pump the water when I could just hook the windmill up to a 12V generator?

If and when I do this project, I'll probably end up doing just that. The water tower is an old idea I've had for years and might do it if I ever have a chance, just to see if it works. In the long run, it's a much cheaper storage solution than batteries.

[Dead_Parrot]

14. Possible...

...but you'd need a bunch of them. I found a wind-less week at Cape Cod while looking at this earlier - so you'd need ~170 of the beasts in your OP (or over 13,000 of the Beacon Power 25k units) per turbine. Methinks cost could be an issue...

[jpak]

17. Windless at or near the boundary layer

but at 150 meters - that's a different issue.

Old story but...I worked a marine lab in Denmark a few years ago. There were 3 wind turbines there - I never observed them NOT spinning, even when there was no perceptible wind at ground level.

Also, I think that young Massacure's concept is a good one. You can use flywheels to buffer variation in local wind conditions (or solar conditions at PV farms), which would make grid management much easier.

The costs could be minimized by state PUC's, and state and federal tax codes. For example, mandate minimum standards for energy storage for new wind/PV farms (say 1 MWp per 10 MWp turbine capacity) and use rate structures and tax codes to make it profitable or minimize the costs to producers and consumers (i.e., provide tax credits to build the systems, set reasonable but lucrative rates for the electricity produced and tax the electricity - not the energy storage systems themselves)...

Biomass and (farm, landfill and sewage treatment) biogas power systems could be used to back up wind and PV as well - give them incentives to produce power when output from wind/PV systems declines or shuts down (at night and/or periods of low wind speeds).

[Dead_Parrot]

21. Possibly...

...although I'd be more impressed if I could see some data on it. If that is so, why is Denmark stuck on 15% and importing electricity? It just doesn't seem to fit the evidence.

Using flywheels for short-term balancing is a perfectly sane notion - as is using biogas as a back-up supply, although I think the quantities available might be a problem. After that we're back on NG, which I reserve the option to bitch about because of emissions. :)

[jpak]

29. Ugh

The effect of the surface boundary layer on wind velocity profiles is Met 101 stuff...

http://en.wikipedia.org/wiki/Wind_turbine#Tower_height

<snip>

The wind blows faster at higher altitudes because of the drag of the surface (sea or land) and the viscosity of the air. The variation in velocity with altitude, called wind shear is most dramatic near the surface. Typically, in daytime the variation follows the 1/7th power law, which predicts that wind speed rises proportionally to the seventh root of altitude. Doubling the altitude of a turbine, then, increases the expected wind speeds by 10% and the expected power by 34%. Doubling the tower height generally requires doubling the diameter as well, increasing the amount of material by a factor of eight.

In night time, or better: when the atmosphere becomes stable, wind speed close to the ground usually subsides whereas at turbine hub altitude it does not decrease that much or may even increase. As a result the wind speed is higher and a turbine will produce more power than expected from the 1/7th power law: doubling the altitude may increase wind speed by 20% to 60%. A stable atmosphere is caused by radiative cooling of the surface and is common in a temperate climate: it usually occurs when there is a (partly) clear sky at night. When the (high altitude) wind is strong (10 meter wind speed higher than approximately 6 to 7 m/s) the stable atmosphere is disrupted because of friction turbulence and the atmosphere will turn neutral. A daytime atmosphere is either neutral (no net radiation; usually with strong winds and/or heavy clouding) or unstable (rising air because of ground heating -by the sun). Here again the 1/7th power law applies or is at least a good approximation of the wind profile.

For HAWTs, tower heights approximately twice to triple the blade length have been found to balance material costs of the tower against better utilization of the more expensive active components.

<end snip>

Friction at the surface boundary layer can reduce wind velocities to near zero when wind velocities at turbine hub heights are still relatively strong.

This is why wind turbines and anemometers used to assess potential wind farm sites are deployed on "really tall towers".

:)

on edit: and Denmark isn't "stuck" a 15% - they're at 23% (current onshore) and climbing. New offshore turbines alone will produce ~40% of Denmark's electricity by 2030 (40+23 = 63% - that ain't stuck)

[Dead_Parrot]

30. So no data, then?

Glad to know I'm wrong about Denmark, though. :)

[amerikat]

11. Beacon Power works with flywheel energy.

I think it's a good storage medium.

http://www.beaconpower.com/products/EnergyStorageSystems/flywheels.htm

[skids]

15. And FTR they are now pushing 25KWh/unit...

Their existing units now in large scale test are 6Kwh and their lab protos are the newer 25KWh... both can be mass-arrayed.

They did the math a bit more rigorously :-)

[Massacure]

16. Doesn't the website say 8 can be connected?

That leaves 200 kW-hrs. Enough to run a house for about two weeks if it is energy efficient.

[skids]

19. Right now they are primarily targetting large arrays...

The smallest array they advertise is 10 of the 25Kwh. Their current target market is in the multi-MWh power regulation market for big power companies.

http://beaconpower.com/products/EnergyStorageSystems/SmartEnergyMatrix.htm

However, I'm optimistic that they might end up selling to homeowners -- they recently added a marketing/sales director from Evergreen, which is a company that is used to dealing with retailers.

[Dead_Parrot]

22. Any idea of cost?

It's the sort of thing that would be ideal for an off-grid house, but no amount of googling has dredged up a dollar value yet (real or predicted).

[skids]

28. I expect they are very expensive...

They aren't in mass production yet, and the company has a large amount of leeway with the power company market because the defrayed maintenance costs/improved round-trip efficiency offer a large cushion to absorb a price that is higher than an equivalent battery bank or alternative.

When they get into production, and the engineering costs are ammortized over a larger product volume who knows? from what I see they are basically a bunch of special polymer, steel, some copper, perhaps some rare earth magnets or perhaps not, and a gaggle of power electronics.

My best guess is these guys are playing purposefully in a market where their product can be viable despite a high pre-volume cost, and protecting the information about the cost of the units so as not to allow that pre-volume cost to have a negative PR impact -- they have to keep that stock price up.

[jpak]

18. Very cool - thanks!

:)

[phantom power]

20. Some flywheel fun facts

If you double the angular inertia, you double the stored energy. However, if you double the angular velocity you quadruple the stored energy. So a lot of hi-tech flywheel research these days focuses on things like high tensile strength, to allow for faster angular velocities.

If the lift-port carbon guys ever get a mass-produced CNT composite, I have a feeling that one early application may be for extremely high performance flywheels, since it ought to have a monster tensile strength. Already, some of the best flywheels are carbon fiber composites.

I've always wondered if you could attempt some kind of trick like embedding lead, or depleted uranium, in the composite. And if it would help or hurt? It might cause a tradeoff in reduced tensile strength, and end up being worse. CNT composites suggest some exotic tricks like nanotubes enclosing lead atoms. If you could ever manufacture them in bulk.

[Dead_Parrot]

23. DU is stronger than steel

- that's why the military use it for shells - so it would make a bitchin' flywheel, in theory. In practice, you really wouldn't want to be anywhere near one that went bang...

I like the idea of nanotubes filled with lead, though. :)

[phantom power]

24. Interesting, I thought they used it purely for it's density.

It's actually stronger than steel? As in hardness, or tensile strength?

[Dead_Parrot]

26. Ahh, hardness.

Sorry, I just checked. Tensile strength is comparable to steel, but there's more options for tempering steel: Wrought DU comes in at ~150 KSI - better than bog-standard 304 steel (73 KSI) but not as good as tempered 316 Steel (230 KSI).

:dunce:

[phantom power]

25. I was just thinking...

I also wouldn't want to be near any flywheel made of lead-filled CNTs, if it went bang. I imagine it would be like a trillion nano-paper-cuts from hell... Or something very bad, anyway.

[Ready4Change]

27. Already in some use, I've read.

Used for smoothing out power deliveries. Mostly for small scale smoothing, like matters of seconds or minutes, because of how quickly they can deliver all their energies. However, a lot of thought is being put into using them for larger purpose, like filling in for windless days, or over night for large PV solar arrays, rather than using battery banks.

I've also heard of them (as well as water tower-like and other systems) being used to store off peak power to use during peak hours. In most locales off peak power cna be bought at better rates than power during peak hours.

For all those things, that's about as technical as I can get. But I think it's all nifty.

[NNadir]

31. The conversion constant between rotations and radians is 2 pi.

When one rotates once, one has gone through 2 pi radians, not 2 radians.

The frictional force depends on the type of bearings, bearings being devices that are designed to minimize friction. There are magnetic bearings, but even those lose some energy owing to electromagnetic effects, small currents that dispense heat.

In normal bearings, the weight has bearing (pun intended) on the frictional force of course, those it could be an interesting exercise in combinatorial optimization to design your flywheel. On one hand the mass increases the amount of energy you can store, but it is offset by increasing the frictional force.

Also it matters a great deal if your flywheel is in a vaccum.

I thought the Wikipedia reference was most instructive:
http://en.wikipedia.org/wiki/Flywheel_energy_storage

[Massacure]

32. Which means that the end result must yet be multiplied by pi

So then the energy stored would be closer to 6,900 kW-hrs.

My primary question though: is it possible to spin a steel cylinder that fast without having the contraption shake itself apart and kill somebody. Would shielding it just in case that does happen significantly inhibit maintenance on it?

[Dead_Parrot]

33. Two options...

One is to make the wheel out of wire, rather than solid steel (think of a cotton reel). If the structure does go bang, the thing just unravels like a broken spring, rather than flinging great chucks of metal out.

The other method is bury the beast and leave it alone - I think the makes listed upthread are designed to be buried for ~20 years, without maintenance: If they go bang the surrounding ground will absorb the energy.