Find suitable capacitor for wind energy device

[lilhoop]

Hello everyone,

currently I am kind of lost at my material science class homework because I basically have no real clue about electronics which is needed for this particular assignment.

For the down time of a wind energy device, a capacitor should be able to "keep" 150 kWh of energy while an electric field of min 350 MV/m is applied.

Basically I found a plastic-foil-capacitor suitable as it can handle electric fields of up to 500 MV/m.

But heres my problem:
Formula for the energy in a capacitor: E=0,5 C U²
and C = epsilonr*epsilon0*A/d

150kWh is equivalent about 520 MJ. If I choose a voltage of 220V as in most households in Europe, I get a capacity of about 20000 Farad which as I have seen on wikipedia is not do-able with normal capacitor. They tend to be around the mikrofarads or even smaller?
What I am doing wrong? Would be so great if someone could help me out. Thanks

 

[(*steve*)]

Don't worry about practicalities. Just do the calculations.

I would advise you to use the maximum possible voltage -- why?

 

[Laplace]

Since this is a materials science problem, should we assume that the task is to select the dielectric material and design the physical parameters of the capacitor? Is it sufficient that the capacitor just store 150kWh (540MJ) or do you also have to address the problem of getting the energy out of the capacitor and onto the grid? If the latter then power electronics enter into the design because it will be very difficult to extract the last joule stored in the capacitor, and that would complicate the problem well beyond the materials science. To store 540MJ in a capacitor you need to select the maximum operating voltage and from that the thickness of the dielectric material. Once you have the dielectric material and its thickness, calculate the capacitance per square meter assuming that the voltage across the capacitor will fall from its maximum to zero as the 150kWh of energy is extracted. Of course the practicalities are that there must be some power electronics that will take the maximum DC voltage on down through near zero DC voltage from the capacitor and convert it to a constant 220 VAC onto the grid. The best advice I've heard is, "Don't worry about practicalities. Just do the calculations."

 

[Merlin3189]

I'm surprised by your 500MV/m so, what plastic are you thinking of?
I'm no expert on this, but with air at 3MV/m (as a rule of thumb from TV days), I was sceptical and looked at Wikipaedia. The highest I could find was Mica 100MV/m or Teflon up to 200MV/m (which itself amazed me.)

What also really surprised me was the 150kWhr or 540MJ. It's not the sort of energy I'd expect to put in a capacitor (though, to be fair, not so many years ago I'd have been surprised if someone put even 10J in a capacitor.)
But following the advice of the others, I did some calculations.
I make that about 200 - 300 car batteries - say about 10cubic metres.
With the figures you give, but not knowing the dielectric constant of your plastic, I'm getting about 1000 cubic metres of polythene for your capacitor. Maybe not impossible, but not exactly handyl And so, I assumed the answer to your original problem was, "Don't be silly!"

What's interesting though, is that the volume of plastic needed seems to decrease with with the max field strength used (or allowed).
If C= K.A/d then C=K.Vol/d^2 or Vol=(C.d^2)/K implying that the volume needed is proportional to the thickness, for a given capacitance and thus, energy at a given Voltage.

So with your studying Materials Science, perhaps this is about materials with very high dielectric strength allowing, say 10x reduction in dielectric thickness and 100x reduction in volume to give capacitors the size of car batteries a similar energy storage (say half a kWhr ) at 10x less weight.

That also raises questions about whether one can extrapolate to very small thicknesses. At the 1um I assumed for this capacitor, we may be less than 1000 molecules thick. That still sounds enough for it to behave like the bulk material and even 100 molecules does, but if we go down to 10 molecules thick, might there not be significant holes? And if we go 10x thinner, we are into the realms of homeopathic capacitors!

It's all a bit more interesting than it sounded to start with.
And I wouldn't worry about the electronics. So far I've not even given that a thought. There's enough basic science of energy storage to think about. If we can actually store a GJ in a practical capacitor, then I'm sure the e&e.engineers will work out how to get at least 50% of that usefully out.