# Sizing supercapacitors



## jumpjack (Sep 9, 2012)

I have an e-bike with 60V/24Ah battery and a 1500W motor.
I'd like to add a supercapacitor in parallel to help the battery, just for a few seconds each time.

I found this interesting worksheet, but I don't understand how exactly it works:
http://www.cooperindustries.com/con...tor/BUS_Elx_App_Notes_Capacity_Calculator.xls

For example, how does it calculate maximum hold-up time?
And why *minimum *Energy needed during hold up is calculated as W = (Vw+Vmin)/2*I*t , i.e. using *average* voltage?!? 

I did some other calculations, for an 80V/12F/0.075 Ohm supercap: per this calculations, it holds 4500 Joules (= 1,25 Wh), and it lasts 8, 19 or 32 seconds depending on calculation.... 
Which should the total duration be according to *your* calculation, considering the motor running at full power? (1500W/25A)
The battery has 64V at full charge and 60V at full discharge.
I found a DC/DC converter capable of giving up to 80V getting 10-60 V as input, and I'd like to use it to be able to use a single 80V/12F supercap rather than 5 in series to reach 60V.

Does it exist an online tool to perform such calculations?


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## Elithion (Oct 6, 2009)

I hate to tell you, but it doesn't quite work as one might think initially.

To use all the energy in a capacitor, its voltage has to change from max to 0 V; yet, you can't do that if you place the capacitor across the battery, because they both have the same voltage.

The only way to do it is to have a bidirectional DC-DC converter between the capacitor and the DC bus (or, have a bidirectional motor driver between the capacitor and the motor). Are you prepared to do that? No? Nor are most companies, and that's why you don't see many instances of capacitors in vehicles.

Yes, you will get some advantage from connecting a capacitor directly across the battery, because the battery resistance is so much higher than the capacitor resistance, so the voltage can change a bit, allowing the capacitor to do part of its job. But you would get a higher increase in performance if you simply bought more cells for the same money spent on capacitors.

Capacitors do have their uses, but placing them in parallel with an EV battery is not one of them.


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## major (Apr 4, 2008)

jumpjack said:


> I have an e-bike with 60V/24Ah battery and a 1500W motor.
> I'd like to add a supercapacitor in parallel to help the battery, just for a few seconds each time.
> 
> I found this interesting worksheet, but I don't understand how exactly it works:
> ...


Hi jack,

Search this forum for ultracap or ultracapacitor and you'll find threads, some of which show calculations like this one.........http://www.diyelectriccar.com/forums/showthread.php?t=25994&highlight=ultracap 

One problem with the capacitor is that the terminal voltage must change to get energy in or out of it. Use E=½Cv²

also.... http://www.diyelectriccar.com/forums/showpost.php?p=50167&postcount=10

Regards,

major


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## Elithion (Oct 6, 2009)

jumpjack said:


> I found a DC/DC converter capable of giving up to 80V getting 10-60 V as input, and I'd like to use it to be able to use a single 80V/12F supercap rather than 5 in series to reach 60V.


A) Woefully inadequate power
B) Unidirectional

You would need a ~50 kW, bidirectional DC-DC converter.


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## jumpjack (Sep 9, 2012)

Elithion said:


> The only way to do it is to have a bidirectional DC-DC converter


Did you read my whole message ore just first line?


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## jumpjack (Sep 9, 2012)

major said:


> One problem with the capacitor is that the terminal voltage must change to get energy in or out of it.


Same comment of above applies.... 



Elithion said:


> A) Woefully inadequate power
> B) Unidirectional


I do not have regen on braking.



> You would need a ~50 kW, bidirectional DC-DC converter.


Yes, if I want to blow up my motor, I guess. 
12A would be enough to "help" my battery by decreasing by 50% the current it has to provide to the motor.

Guys, what's happening?
Can anybody please read my whole message and *then* reply?

Thanks in advance.


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## Elithion (Oct 6, 2009)

Sorry to see you "roll your eyes", but, yes, of course I did read your whole message, which talks about a tiny, one way DC-DC converter. I did say that that converter won't work, and said why. If you disagree with that assessment, please tell us, and explain why.



jumpjack said:


> Yes, if I want to blow up my motor, I guess.


You are correct. I apologize.


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## frodus (Apr 12, 2008)

Davide and Major know a hell of a lot more about batteries and supercaps than you do, so give some respect.

Caps only make power while discharging along their linear curve. Putting in parallel with batteries would help a tiny tiny amount, but not nearly as much as you want. If you want to put things in parallel with the pack, maybe try some high C rate batteries with low IR.

If you wanted to do what you suggest (use all of the 1.25Wh of energy in the capacitor), you'd need 2 separate power sources. One being the battery pack. The other being a Capacitor bank + bidirectional DC-DC converter. During discharge, you're going to need a converter that can operate across the entire (or most of) range of the capacitor, from VMax to 0V and still put out proper voltage to the controller. Good luck finding one that is cost effective.

Now, when the capacitor discharges, what do you do then? How do you recharge that capacitor? You need to charge it back up somehow, right? What if the pack is sitting at 60V, but the cap is at 30V.... you need to take power from the batteries and put the energy back into the capacitor bank..... hence the need for a Bidirectional DC-DC converter.

So before you start accusing people of not reading, Be sure you're right before you start with the attitude.



And if you still think we're not understanding you (or don't know what we're talking about), by all means, feel free to try it all out and let us know how things turn out.


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## jumpjack (Sep 9, 2012)

Elithion said:


> Sorry to see you "roll your eyes", but, yes, of course I did read your whole message, which talks about a tiny, one way DC-DC converter. I did say that that converter won't work, and said why. If you disagree with that assessment, please tell us, and explain why.


Well, I wrote "I found a DC/DC converter ", and you replied "The only way to do it is to have a bidirectional DC-DC converter"; so I thought you didn't even read that part of my message.
And as I read that buck and boost DC/DC is only needed if you have regenerative braking which recharges the SC, I don't understand why I need a buck and boost rather than just a boost DC/DC.
But if you say that, unlike batteries, capacitors need to change voltage to provide energy, that's quite different.

Anyway, I still need help in understanding how to properly use the above mentioned worksheet to determine how big my SC must be to have 3 or 4 seconds of high-power.


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## frodus (Apr 12, 2008)

Many people have tried SC's and had less-than-great results.... they almost always agree that putting high power batteries in parallel with each cell or buying a high discharge battery pack is a much better way of throwing money away.

You'd need an expensive bidirectional DC-DC, and a large bank of supercapacitors and a lot of room on the bike to get any measurable gain in performance.

So why not start with better batteries in the first place?


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## jumpjack (Sep 9, 2012)

frodus said:


> So before you start accusing people of not reading, Be sure you're right before you start with the attitude.


It would have been enough just to say "*that *DC/DC is not enough, you need a bi-directional one because..."

And suppoosing I'm an idiot ("Are you prepared to do that? No?") is not quite a good way to teach something to somebody asking for help, do you think?

But Elithion is quite used to useless replies, as far as I know, so I'll wait for other useful contributions just like yours.


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## Elithion (Oct 6, 2009)

jumpjack said:


> Elithion is quite used to useless replies


Again, my apologies. I regret burdening you, and I will not do so again. Sorry.

You may want to use the "scale" icon, above, to give me a negative "reputation".


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## frodus (Apr 12, 2008)

jumpjack said:


> It would have been enough just to say "*that *DC/DC is not enough, you need a bi-directional one because..."


He did:


Elithion said:


> The only way to do it is to have a bidirectional DC-DC converter between the capacitor and the DC bus


The reason why is just before that:


Elithion said:


> To use all the energy in a capacitor, its voltage has to change from max to 0 V





jumpjack said:


> And suppoosing I'm an idiot ("Are you prepared to do that? No?") is not quite a good way to teach something to somebody asking for help, do you think?


He didn't really suppose, It was a question.

--------------------------------


jumpjack said:


> But Elithion is quite used to useless replies, as far as I know, so I'll wait for other useful contributions just like yours.


Another great place to go for your type of vehicle is endless-sphere, they've got more people that are used to working with Bikes.


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## major (Apr 4, 2008)

jumpjack said:


> Did you read my whole message ore just first line?





jumpjack said:


> Same comment of above applies....


Yes, I read it, and read it again. It still does not make much sense. I tried to be nice in my initial reply and give you some reference.


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## Ziggythewiz (May 16, 2010)

jumpjack said:


> Anyway, I still need help in understanding how to properly use the above mentioned worksheet to determine how big my SC must be to have 3 or 4 seconds of high-power.


Plug the numbers in. 

Vw = 64
Vmin = 60
I = 25
t = 3
etc.

It says you need 24 of these: HV1840-2R7606-R


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## jumpjack (Sep 9, 2012)

I see there are several buck/boost converters around, some supporting high voltages, other not:
http://www.prodctodc.com/dc-nonisolated-converter-dc-boostbuck-converter-c-1_16

Can B&B DC be connected in series to reach desired voltage?

About the worksheet... once I'd get 24 supercaps 60F/2.7V, how long would the package last at 25A? How much voltage can I use, with and without B&B DC, considering that battery voltage can vary between 60 and 64V?
As I said, I got different numbers from those on the sheet, and I don't know if the calculations on the sheet are all right.


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## Ziggythewiz (May 16, 2010)

jumpjack said:


> About the worksheet... once I'd get 24 supercaps 60F/2.7V, how long would the package last at 25A?


3 seconds. For $1,000 more you could make it 10 seconds. That's from 64V to 60V, no DC-DC.

I don't know how accurate the sheet is, but it sounds reasonable.


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## frodus (Apr 12, 2008)

3s? hardly

~4V (64V down to 60V) drop works out to be 0.167V each Super-capacitor. Lets say he wants 12.5A (half of that 25A the controller supply).

The charge on a cap is a linear product of capacitance and voltage, Q=CV.

If you drop from 2.7V to 2.534V, the charge you remove is 0.167V*60F = 10.02 Coulombs. 

One Amp is one Coulomb per second, so 10.02C can provide 12.5A for 10.02C / (12.5 C/sec) or 0.8016 seconds.

0.8seconds of 12.5A discharge for $544.80.

That would be better spent on batteries.

As a comparison, 20 10Ah headway cells would cost you $380 and you could get 12.5A out of them continuously until they're dead.


That sheet agrees.
Capacitors in series are 1/ctot = 1/c1 + 1/c2 + 1/c3, so 24 in series is an eqivalent of 2.5F

24 caps in series would be:
Vw = *64*Volts
Vmin = *60*Volts
I = *12.5*Amps
t = *0.8*seconds
W = (Vw+Vmin)/2*I*t = 620.00Joules
C = 2 Vw*I*t / (Vw^2 - Vmin^2) = 2.5000Farads

A single cap would be:
Vw = *2.7*Volts
Vmin = *2.533*Volts
I = *12.5*Amps
t = *0.8*seconds
W = (Vw+Vmin)/2*I*t = 26.17Joules
C = 2 Vw*I*t / (Vw^2 - Vmin^2) = 59.8802Farads


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## jumpjack (Sep 9, 2012)

frodus said:


> 3s? hardly
> 
> ~4V (64V down to 60V) drop works out to be 0.167V each Super-capacitor.


I don't understand why you considered only 1 SC out of 24.


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## frodus (Apr 12, 2008)

Because each SC is in series with the next, and when you discharge 12.5A of current, it's all in series. Each cap sources 12.5A of current. You're looking for t=time, just like with a battery.

You need to consider each cap circuit. What is going out of each capacitor? 12.5A.

If you look above, I also did the calculation for the entire thing pack voltage. The equivalent F is 2.5F 60V cap, but you don't have that, you have 24 2.7V caps. If you put 24 60F caps in series, the equivalent series capacitance is 2.5F.

Either way you cut it, you ONLY get 0.8S of 12.5A out of 24 60F supercapacitors.


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## Ziggythewiz (May 16, 2010)

frodus said:


> 3s? hardly
> One Amp is one Coulomb per second, so 10.02C can provide 12.5A for 10.02C / (12.5 C/sec) or 0.8016 seconds.
> 
> 0.8seconds of 12.5A discharge for $544.80.
> ...


That's right. I didn't realize line 49 wasn't tied to the formulas, so line 50 has to be updated.

In summary, $3,000-$5,000 to make a noticeable difference..for a few seconds.

Or for ~$600 you can double the performance AND RANGE of your pack.. The ESR numbers listed don't even appear much if any better than LiFePO4.


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## jumpjack (Sep 9, 2012)

frodus said:


> If you look above, I also did the calculation for the entire thing pack voltage. The equivalent F is 2.5F 60V cap, but you don't have that, you have 24 2.7V caps. If you put 24 60F caps in series, the equivalent series capacitance is 2.5F.
> 
> Either way you cut it, you ONLY get 0.8S of 12.5A out of 24 60F supercapacitors.


What about this calculation (assuming full voltage usable)?

E = 1/2 * c* v^2 = 1/2 * 60 * (2,7)^2 = 1/2 * 60 * 7.29 =~ 219 Joule = 0.06 Wh
0.06 * 24 = 1.4 Wh

1500 W * 1/3600 h = 0.42 Wh used per second

Hence, 1.4/0.42 = 3,33 seconds


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## frodus (Apr 12, 2008)

You can't assume full useable voltage unless you have a Bidirectional DC-DC that can discharge AND charge the capacitors and convert that to a useable voltage for your controller. 

Lets assume you have that DC-DC:
If you drop from 2.7V to 0V, the charge you remove is 2.7V*60F = 162 Coulombs. You have to calculate for a single cell, because they're in series. If you want to calc using a pack, then it's 64.8V * 2.5F = 162Coulombs.... same thing as above. One Amp is one Coulomb per second, so 162Coulombs can provide 25A for 162C / (25 C/sec) or 6.48seconds. 

You still would need over $500 worth of supercapacitors and an expensive bidirectional DC-DC (if you can find one) that can handle 1500W. 

Why not just buy a battery pack that can supply that 25A to begin with? The supercapacitors + DC-DC converter. 1.4Wh of energy is next to nothing. Plus, your 24Ah pack of batteries would only be operating at a hair over 1C, which should be just fine for batteries.


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## jumpjack (Sep 9, 2012)

frodus said:


> Why not just buy a battery pack that can supply that 25A to begin with?


Why does anybody continue not reading my messages, suggesting alternatives, not answering my questions, not telling me if my calculations are correct but doing OTHER calculations, and telling me to buy batteries rather than SCs?

Can't I waste my money as I prefer? 
I already have batteries, I never had SCs, and I want to do some research.


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## njloof (Nov 21, 2011)

jumpjack said:


> Can't I waste my money as I prefer?


I've found it's much easier to waste money as I prefer if I don't post about it to DIYElectricCar first.


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## frodus (Apr 12, 2008)

jumpjack said:


> Why does anybody continue not reading my messages, suggesting alternatives, not answering my questions, not telling me if my calculations are correct but doing OTHER calculations, and telling me to buy batteries rather than SCs?


I did read everything. In response, I did calculations for you, I caught your mistake of not calculating series capacitance correctly and I also offered my opinion on the system you propose. There's nothing wrong with that. Feel free to leave this forum if you don't like the advice. You won't be missed.



jumpjack said:


> Can't I waste my money as I prefer?
> I already have batteries, I never had SCs, and I want to do some research.


Yes, you can waste it. I don't care. I said that it would be better to spend that same money on higher density power sources than Supercapacitors. That is my opinion of the matter and it offers a lower cost and higher yeild system. 

If you don't like my answers, don't listen to them. No one is keeping you from pouring money into this project or ignoring our advice. But you cannot stop me from offering opinion on your system design when you post on a public forum.... so deal with it, or cry to someone else..... because I could care less.


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## Siwastaja (Aug 1, 2012)

It's a pity that this forum is lacking the typical "ignore" function. It's pretty handy and makes life easier for everyone.


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## Siwastaja (Aug 1, 2012)

zsnemeth said:


> You can find it in the UserCP, but it's just for (or against) users, not for whole threads.


Oh, somehow I missed that but indeed it's there. Thanks!


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## Ziggythewiz (May 16, 2010)

jumpjack said:


> Why does anybody continue not reading my messages, suggesting alternatives, not answering my questions, not telling me if my calculations are correct but doing OTHER calculations, and telling me to buy batteries rather than SCs?
> 
> Can't I waste my money as I prefer?
> I already have batteries, I never had SCs, and I want to do some research.


If you don't want advice, just do the research and tell us how your purchase works out. Don't ask questions and then whine about getting answers.


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## andrew89 (Feb 27, 2013)

What is price difference between 25A battery pack and super capacitor?


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## frodus (Apr 12, 2008)

andrew89 said:


> What is price difference between 25A battery pack and super capacitor?


Read the entire thread.


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## Ziggythewiz (May 16, 2010)

25A doesn't mean anything. Do you mean w (A*V) or kWh (A*V*T)? A supercap is cheaper for w but orders of magnitude more expensive for kWh.


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## Siwastaja (Aug 1, 2012)

Start here:

http://www.diyelectriccar.com/forums/showthread.php?t=6535
http://www.diyelectriccar.com/forums/showthread.php?t=11708

And no, supercapacitors are still not viable in any practical sense. High-power lithium ion cells, on the other hand, are available. They will give you much more power than any practical DC/DC converter needed for supercaps can. If you think you'll be fine with a small, cheap DC/DC, you are more than fine with almost any li-ion cell directly.

Supercaps _*alone *_can be used in metro train like system for frequent regenerative stop&go that generates thousands of cycles quickly, *without* batteries, in a system where the DC/DC converter is (sort of) _*integrated*_ into the motor controller. This is, however, not viable even in a traditional hybrid car with very short electric range, because even they have longer range than one stop and one go.


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## Karter2 (Nov 17, 2011)

Siwastaja said:


> And no, supercapacitors are still not viable in any practical sense....
> ..., not viable even in a traditional hybrid car with very short electric range, because even they have longer range than one stop and one go.


 You are refering to use as a energy source for the traction drive i assume ?
But it is fair to say that supercaps are being used in cars for energy capture & storage from regen braking . 
http://www.sae.org/mags/aei/11845


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## Siwastaja (Aug 1, 2012)

Karter2 said:


> But it is fair to say that supercaps are being used in cars for energy capture & storage from regen braking .
> http://www.sae.org/mags/aei/11845


Yes they _can_ be used, if anyone wants to FURTHER decrease the electric range to just one start&stop in a hybrid. However, it is disputable if it's worth the extra weight and complexity of the hybrid drivetrain.

Generally, the direction hybrids are going to is to _increase_ the electric range as the battery tech has taken leaps forward (li-ion).

Supercaps can achieve around 99% round-trip efficiency, li-ion around 95% and NiMH around 70%. Despite this, NiMH was used in hybrids just until now.

The link you give, however, does not describe a HEV at all. It's just a kind of cheap and simple kludge that powers 12V systems such as headlights from regenerative energy. Actually, the same happens to some level in any gasoline car! I really dispute the claim of 10% anything. It's just marketing.

Ultracaps have a lot of uses. I'm naturally talking the scope of this forum; then, any ultracap currently available doesn't come even near to being useful in any EV or PHEV traction system.


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## Karter2 (Nov 17, 2011)

Siwastaja said:


> Ultracaps have a lot of uses......


 OK , but you may have confused some folk when you said..


Siwastaja said:


> And no, supercapacitors are still not viable in any practical sense....


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## Ai! (May 9, 2014)

http://www.ushybrid.com/documents/PDF/BDX4.pdf


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## major (Apr 4, 2008)

^^^^^ First post with only a link. I'm not clicking on it


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## jumpjack (Sep 9, 2012)

major said:


> ^^^^^ First post with only a link. I'm not clicking on it


I did.
It's an interesting PDF datasheet of high power bidirectional DC/DC converter for hybrid vehicles.
Where can I buy one rated 60V/1500W?


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## Ai! (May 9, 2014)

this converter is adjustable: 100-650V input and 150-750V output with 50-400A amperage and it is liquid cooled. I've found this product when ultracapacitors were in my mind... but now I see that the price to kwh ratio isn't going down fast enough, so I decided to go with li-xxx batteries.


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## jumpjack (Sep 9, 2012)

Which price?


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## Ai! (May 9, 2014)

jumpjack said:


> Which price?


Well this is a question... I didn't contacted them since I lost my faith in UC.


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## jk1981 (Nov 12, 2010)

http://web.mit.edu/first/kart/

This ^ site gives a good overview of how to integrate additional ultraCap energy storage.

FWIW as a general rule I think it's only worth doing for stop-start vehicles like buses or maybe a race vehicle. For anything else where regen charge rates are more moderate you're almost certainly better off in money, mass, volume and complexity terms to run a bigger pack and as much regen as the weakest link in the chain will tolerate.

jk


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