# Inductor energy storage - can it compete with capacitor?

#### RogueRose

Joined Oct 10, 2014
375
I remember reading that inductors can be used to store electric charge similar to a capacitor but I'm curious as to how these can compare to a cap in total energy stored, speed of release and size. Wiki wasn't too helpful in determining the aplicability of coils/inductors. Could they be used to generate high energy pulses?

#### Aleph(0)

Joined Mar 14, 2015
597
Inductor energy storage - can it compete with capacitor?
Plz try to understand about electrical reactors! Energy is stored in electrostatic field for cap and magnetic field for inductor so XC is to change in voltage and XL is to change in current! So their reactions are mathematical additive inverse to each other! So answer to your question is yes but practical problems decide which is best for given use!

I remember reading that inductors can be used to store electric charge
Sry no not charge! Electric energy yes! But in magnetic field!
speed of release and size.
That's more tricky with inductor cuz it's fabricated from a conductor which is always lossy at standard temps and even if cryocooled magnetic lines of force in wound configuration would interfere with SC properties unless very well thought out!
No new news there!

#### crutschow

Joined Mar 14, 2008
25,675
A large superconducting inductor can store more energy, I believe, than any practical capacitor of similar size.

#### BR-549

Joined Sep 22, 2013
4,938
RogueRose, the question should be can a cap compare to a coil?

The answer is no. Forget about power storage and size. We can build caps and coils to store the same amount of energy. And ignore size for the time being.

The main difference is the discharge time. To discharge a cap, we need current flow, which takes time.

This is because the change in an electric field needs to transfer charge. An electric field can not be cut.

But a magnetic field is a different animal. Magnetic fields can be cut. No charge has to move when the field is cut for the field to fall. I should say that if we prevent charge from flowing, the magnetic field will still fall.

A magnetic field can collapse much quicker than an electric field. The electric field of a coil can collapse quicker than a cap electric field also. The electric field of a coil, is not the same kind of electric field caused by charge separation. It's a secondary or second order electric field.

This is a good question. I'm quite sure you will get some more responses.

#### wayneh

Joined Sep 9, 2010
16,401
My gut tells me that an electrolytic capacitor has a higher power density - joules per cm^3 - than an inductor, and also a higher J/$density. Caps are inferior to batteries on these measures, but a copper coil is "big" and expensive. One part of my thinking is that the power stored in a coil depends on the current passing through it. You need a lot of turns of fat (low resistance) wire to get a powerful field, and that all adds weight, volume and cost. I'm too lazy to make the calculations but I'd be curious to see them. #### GopherT Joined Nov 23, 2012 8,012 A large superconducting inductor can store more energy, I believe, than any practical capacitor of similar size. @RogueRose It depends on your definition of "store" - do you include the cost/inconvenience of maintain the cryogenic conditions? What are the expectations of "stored energy for a capacitor? #### WBahn Joined Mar 31, 2012 26,305 From an energy storage perspective, you are comparing 1/2 CV² to 1/2 LI². Capacitors significantly larger that 1 F are pretty uncommon and most of those have pretty low voltage ratings. Though, of course, that's changing. I don't know what the state of the art is, but I just did a quick Google search and see a 63 F capacitor with a 125 V rating (for over$5000). Getting large inductances is not too difficult. More than a quarter century ago I was working with 100+ H magnets that had about 200 A of current -- and those were intended as magnets, not energy storage devices.

As for rate of discharge, both can be designed to provide rapid discharge, but discharging a capacitor fast requires very high currents, while discharging an inductor fast requires very high voltages. There are lots of practical considerations that limit the maximum current that a capacitor can produce, but very few things that limit the maximum voltage that an inductor can produce, so you can generally get much higher and shorter pulses from an inductor. Whether you can do it without destroying something is a separate issue.

#### GopherT

Joined Nov 23, 2012
8,012
From an energy storage perspective, you are comparing 1/2 CV² to 1/2 LI². Capacitors significantly larger that 1 F are pretty uncommon and most of those have pretty low voltage ratings. Though, of course, that's changing. I don't know what the state of the art is, but I just did a quick Google search and see a 63 F capacitor with a 125 V rating (for over $5000). Getting large inductances is not too difficult. More than a quarter century ago I was working with 100+ H magnets that had about 200 A of current -- and those were intended as magnets, not energy storage devices. As for rate of discharge, both can be designed to provide rapid discharge, but discharging a capacitor fast requires very high currents, while discharging an inductor fast requires very high voltages. There are lots of practical considerations that limit the maximum current that a capacitor can produce, but very few things that limit the maximum voltage that an inductor can produce, so you can generally get much higher and shorter pulses from an inductor. Whether you can do it without destroying something is a separate issue. Just for reference, how much did the inductor weigh? How much did it cost? #### WBahn Joined Mar 31, 2012 26,305 Just for reference, how much did the inductor weigh? How much did it cost? That particular one I was talking about was a superconducting magnet (and remember that it was NOT intended for energy storage). The magnet itself was (going from memory here) about 8" tall and perhaps a foot in diameter (the dimensions were dictated largely by the 5" bore and field homogeneity specifications). I don't know how much it weighed because I never had the opportunity to work with it separate from its support structure. But another magnet (10 T radial-access) was a bit larger physically and I'm going to guess it (just the magnet) weighed about fifteen pounds, perhaps somewhat more. The cost was enormous and not useful for comparison purposes -- as a research magnet it was very cutting edge at the time and was pushing the limits of the technology (30 years ago). I think it cost about$200,000 and was several years late in delivery.

I haven't been able to quickly find any examples of inductors intended for energy storage. Places like Digikey aren't good sources because they don't have these kinds of inductors. Their selection goes from high inductance (150 H) but low current to high current (200 A) but low inductance. Energy storage inductors are going to be physically large (in diameter at least) in order to get lots of area for the flux. They also have the problem that, unlike a capacitor's leakage issue which is quit manageable, you have to keep the current flowing in them. Not a problem with a superconducting system, but then you have the cryoplant overhead.

Some numbers for SMES units (superconducting magnetic energy storage) show energy storage densities of upward of 40 kJ/l but the really impressive number is the specific power (which gets at what the TS is asking) which can get up into the 100 MW/kg range. I ran across a reference to a small SMES unit (from 2008 time frame) that is about two feet tall and two feet in diameter. It has an inductance of 2 H but a rated current of over 2600 A. It stores 7.3 MJ and can deliver 5 MW of power. It's used for voltage dips in power systems.

In either case (capacitor or inductor), a huge determining factor is the requirements of the specific application. In some instances there will be a clear winner and in others it will need to be based on an analysis of what factors are more important than others.

#### BR-549

Joined Sep 22, 2013
4,938
It's just a simple fact that you can converge the magnetic.

This is why the magnetic holds an atom together, not the electric.

The electric can only attract. (weak) It takes the magnetic to bond. (strong)

When one completely converges the magnetic........you get real power.

This is hard for some to realize because of the slow charge velocities that we use. Our electric current physical movement is too slow to see it. When current flows, we get a completely converged magnetic field. But it's weak, because of velocity. But that's where the power is. This is why circuits work.

If our current velocities were near c, you would have no problem seeing the power in the magnetic. The Amount of charge separation controls the electric............BUT, it's the Speed of charge makes the magnetic.

On particle scales, the charge particle moves much closer to c. The magnetic interaction between particles is much stronger.

#### MrAl

Joined Jun 17, 2014
7,849
I remember reading that inductors can be used to store electric charge similar to a capacitor but I'm curious as to how these can compare to a cap in total energy stored, speed of release and size. Wiki wasn't too helpful in determining the aplicability of coils/inductors. Could they be used to generate high energy pulses?
Hi,

You can probably see by now from the other posts that you probably have to set some constraint on what it is you want to compare about the two. For example, energy to weight ratio, energy to volume ratio. Inductance goes up with wire length and inverse coil separation distance, capacitance goes up with plate area and the inverse plate separation distance. There are other considerations too though, such as core permeability and dielectric permittivity, but then we get into the question of what is the state of the art and that limits us to understanding only what is available today.

#### wayneh

Joined Sep 9, 2010
16,401
This discussion is useless, IMHO, without numbers. Here's a flag planted for the capacitor, in this case a somewhat randomly chosen electrolytic.
1000µF
500V
50x80 DxL in mm = 0.157 cm^3
~$20 (for 100 or more)​ Energy stored = 1/2•C•V^2 = 1/2•(1x10^-3)•250,000 = 125 FV^2 = 125 Joules since a farad is a Joule/V^2 That's 6.25 J/$ and 796 J/cm^3. I don't have the weight.

Show us what a coil can do.

#### Cubrilo

Joined Oct 17, 2010
2
I find this thread very interesting since the question had been bothering me ever since my student days, so I'll dare to answer.
wayneh, you made an error in calculus, it is actually 0.157 dm^3 so the energy density amounts to 0.796 J/cm^3, which is pretty much standard value for electrolytic capacitors.
Now about the magnetic energy density: in theory iron can produce maximum magnetic field of 2 T, so the energy in air gap will be:
(1/2)B^2/u = (1/2)2^2/(4πx10-7) = 1.6 J/cm^3
Consequently, in theory, magnetic energy density is higher, or at least not lower than electrostatic.
Obviously in practice the gap has to be small, or enormous currents are required (with air core instead of iron), so coils are far worse energy stores than capacitors in J/kg and J/$terms. #### wayneh Joined Sep 9, 2010 16,401 wayneh, you made an error in calculus... Agreed, and obvious by inspection if I'd taken a second to think about it. ...so coils are far worse energy stores than capacitors in J/kg and J/$ terms.
You confirmed my suspicion, sort of. I think the question was about the energy stored in the entire inductor, not the energy density possible in any air gap.

My intuition remains that inductors are relatively costly and big as energy storage goes. They are excellent for what they do, but "long" term energy storage is not their thing.

#### Cubrilo

Joined Oct 17, 2010
2
Inductor energy storage cannot compete capacitor in principle (if you think of it) due to its "dynamic nature" - it needs current to run so electrons are colliding all the time producing losses in the conductor, whereas capacitor needs just a tiny leakage current to stay charged. Indeed only superconducting inductor can compete (as participants already stated) - but it's very expensive.

#### neonstrobe

Joined May 15, 2009
83
Inductor energy storage cannot compete capacitor in principle (if you think of it) due to its "dynamic nature" - it needs current to run so electrons are colliding all the time producing losses in the conductor, whereas capacitor needs just a tiny leakage current to stay charged. Indeed only superconducting inductor can compete (as participants already stated) - but it's very expensive.
Sorry, a capacitor wants NO leakage current to stay charged. Dynamic RAMs are essentially capacitor stores but the tiny transistor leakage currents means they lose charge - and need replenishing every so often to preserve memory.

#### wayneh

Joined Sep 9, 2010
16,401
Sorry, a capacitor wants NO leakage current to stay charged.
I think you're both arguing the same point, that real capacitors leak a small amount of current that must be made up if the capacitor is to remain fully charged. An inductor requires a constant current and therefore suffers ohmic losses.

But consider an optimized resonant pair, an inductor and a capacitor, designed to send the largest energy back and forth. Energy is lost on each cycle, by each device, but the pair might ring for dozens of cycles. I believe the capacitor will be cheaper member of the pair.

#### GopherT

Joined Nov 23, 2012
8,012
I think you're both arguing the same point, that real capacitors leak a small amount of current that must be made up if the capacitor is to remain fully charged. An inductor requires a constant current and therefore suffers ohmic losses.

But consider an optimized resonant pair, an inductor and a capacitor, designed to send the largest energy back and forth. Energy is lost on each cycle, by each device, but the pair might ring for dozens of cycles. I believe the capacitor will be cheaper member of the pair.
Superconducting magnets like used in every NMR or MRI is essentially an energy storage ring of constant current. Taking the magnet down for service can be a big deal. Maybe @bertus can advise - I think he may have some experience in this area.

#### RichardO

Joined May 4, 2013
2,271
Capacitors have another advantage over inductors. Caps are made with light, thin aluminum whereas coils use heavy copper and iron.