testing electrochemical capacitors

8/14/2019 Testing Electrochemical Capacitors

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Testing Electrochemical Capacitors: Part 1 Cyclic Voltammetry and Leakage CurrentIntroduction

Part 2 of this note discusses techniques that are also familiar to battery technologists. Part 3

describes theory and practice of EIS measurements on capacitors.

In contrast to batteries, ECs generally store energy by highly reversible separation of electricalcharge hile batteries use chemical reactions. ECs consist of to high!surface electrodes

immersed in a conductive liquid or polymer called the electrolyte. "he electrodes are separated

by an ionic!conducting separator that prevents shorts beteen the to electrodes.

Compared to a battery, an electrochemical capacitor has the folloing advantages#

1. Higher charge and discharge rates giving it a high power density2. Longer cyclelife (> 100,000 cycles)

3. Low toxicity aterials

!. "peration over a wide teperat#re range

$. Low cost per cycle

"hese are offset by some disadvantages#

1. Higher self%discharge rate

2. Lower energy density

3. Lower cell voltage

!. &oor voltage reg#lation

$. High initial cost

Some applications use electrochemical capacitors in parallel ith a battery. "his combination

provides better cycle life and higher poer than a battery alone.

State of the art applications for electrochemical capacitors include#

1. Hy'rid lectric ehicles (Hs)2. *iesel engine starting systes

3. +ordless power tools

!. ergency and safety systes

$or more information read %rian Conay&s boo' on electrochemical capacitor technology#
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Conay, %. E., Electrochemical Supercapacitors# Scientific $undamentals and "echnological

(pplications, )luer (cademic Press * Plenum Publishers, +e or', +, -.

Similar Technology Confusing Names

In technical papers and for commercial products a variety of terms is used to define types ofcapacitors. /nfortunately, arbitrariness leads to confusion and misleading designations.

"hese names are mostly product names and often used incorrectly. ( selection is listed belo#

1. #percapacitors2. -ltracapacitors

3. erogel capacitors

"his application note ill conform to terminology shon in $igure -.

Figure 10 Classification and designation of capacitors.

$igure - shos a schematic diagram of theification of capacitors divided into three ma1or groups#

Electrostatic capacitorsuse metal plates as electrodes that are separated by a dielectric ith loconductivity, e.g. ceramics, glass, or even air.

Electrolytic capacitorsuse a metal foil as anode, e.g. aluminum or tantalum. uring theanodiing process a metal o4ide is formed hich is used as dielectric. "he cathode also consists

of a metal foil.

Electrochemical capacitorsuse in contrast to electrostatic and electrolytic capacitors high!surface electrodes to increase capacitance. "hey can be divided in to subgroups depending on

the storage mechanism.

lectric do#'le layer capacitors (*L+s) #se electrostatic charge separationto store energy. s the nae says, a do#'le layer is '#ilt #p within theinterface 'etween electrolyte and electrode s#rface.

&se#docapacitors #se 'eside electrostatic charge separation also highlyreversi'le /aradaic s#rface reactions to store energy.


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"his application note uses only electrochemical capacitors for its measurements. 5ence

electrostatic and electrolytic capacitors ill not be discussed.

6enerally, E7Cs use activated carbon as electrode material. 8ith surface areas of -999 m2*gor more capacitances of 299 $*g can be reached. Pseudocapacitors use transition metal o4ides

:e.g. ;u


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Capacitor Nonideality

"he ideal capacitor does not e4ist. In reality, capacitors have alays limitations andimperfections. "he tests in this application note illustrate these limitations.

Voltage limitations

"he description of ideal capacitors did not mention voltage limitations. Capacitors can onlyoperate ithin a Dvoltage indo ith both an upper and loer voltage limit. Boltages outside

this indo can cause electrolyte decomposition damaging the device.

"he range of the voltage indo strongly depends on the electrolyte hich can be aqueous or

nonaqueous. 6enerally, aqueous electrolytes are safer and easier to use. 5oever, capacitorsith nonaqueous electrolytes can have a ider voltage indo.

Commercial single!cell ECs currently have an upper voltage limit belo 3.@ B. $or high!voltage

applications multiple cells in series are used.

(ll commercial ECs are specified to be unipolar 0 the voltage on the plus :F= terminal must bemore positive than the voltage on the minus :!= terminal. "he loer voltage limit is usually ero

volts.

ESR

;eal capacitors suffer from poer loss during charge and discharge. "his loss is caused by

resistances in electrical contacts, electrodes, and electrolyte. "he sum of these resistances is

called Equivalent Series ;esistance :ES;=. $or ideal capacitors ES; is ero. It is specified on

the data sheet for most commercial capacitors.

"he poer loss P7ossduring charge or discharge is given by Equation G#

:G=

"his poer is lost as heat 0 under e4treme conditions enough heat to damage the device.

"he ES; can be modeled as a resistor in series ith an ideal capacitor.

Leakage current

Ideal capacitors maintain constant voltage ithout current flo from an e4ternal circuit. ;ealcapacitors require a current, called lea'age current, Ilea'age, to maintain constant voltage.

7ea'age current ill sloly discharge a charged capacitor that has no e4ternal connections to its

terminals. "his process is called self discharge.


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Ilea'age can be calculated using Equation @, multiplying the capacitance by the rate of voltage

change#

:@=

7ea'age current can be modeled as resistor that is parallel ith a capacitor. "his model is a

simplification of the voltage and time dependence of lea'age current.

(s an e4ample, a lea'age current of - H( on a - $ capacitor held at 2.@ B implies a 2.@ Jlea'age resistance. "he time constant for the self!discharge process ould be 2.@4-9 Kseconds 0

nearly a month.

Time effects

"he time constant L for a charge or discharge process of an ideal capacitor in series ith an ES;can be calculated by Equation K#

:K=

"ypically, L is beteen 9.- and 29 seconds. ( voltage step into a capacitor ith ES; should

create a current that e4ponentially decays toards ero. In a device ith lea'age current, the

poststep current decay stops at the lea'age current.

"ime effects can be caused by slo $aradaic reactions occurring at imperfections on the surface

of the electrode material. Carbon surfaces used for most electrochemical capacitors have o4ygencontaining groups :hydro4yl, carbonylM= that are plausible reaction sites.

Commercial ECs do not sho this simple behavior. (s seen further belo, commercialcapacitors held at a constant potential ta'e days to reach their specified lea'age current. "he

time needed is much greater than predicted by L.

ielectric absorption is a phenomenon that can also occur on capacitors. It is a short!term time

effect and is caused by nonelectrostatic charge storage mechanisms ith very long timeconstants.

"ime effects also can be a side effect of porosity inherent in highcapacity electrodes. "he deepera pore, the higher the electrolyte resistance. 5ence different areas of the electrode surface see

different resistances.

(s discussed more precisely inpart 3 of this note, this complicates the simple capacitor modelinto a distributed element that is also called transmission line model.
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Cycle life

(n ideal capacitor can be charged and discharged for an infinite number of cycles. anycommercially available ECs approach this ideal 0 they are specified for -9@or even

-9Kcharge*discharge cycles. In contrast, secondary batteries& cyclelife specifications are

typically hundreds of cycles.

"he cycle life for all rechargeable devices depends on the e4act conditions under hich cyclingoccurs. (pplied current, voltage limits, device history, and temperature are all important. Part 2

ill go more into detail.

Cyclic Voltammetry

Cyclic Boltammetry :CB= is a idely used technique in electrochemistry. Early in a

development pro1ect, CB yields basic information about a capacitive electrochemical cell,

including#

oltage window +apacitance

+ycle life

( comprehensive description of CB is ell beyond the scope of this document. ost boo's

describing laboratory electrochemistry ill have at least one chapter discussing CB.

Description of CV

In a cyclic voltammogram the current, I, that flos through an electrochemical cell is plottedversus the voltage, /, that is sept over a given voltage range.

( linear voltage ramp is used in the seep. #

:>=

d/*dt is the scan rate of the linear voltage ramp. $or EC testing the rate is usually beteen

9.- mB*s and - B*s.

Scan rates at the loer end of this range allo slo processes to occur but ta'e a lot of testingtime. $ast scan rates often sho loer capacitances than sloer scan rates. "his effect ill be

discussed belo.
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+ote that fast scans on high capacitance ECs may require more current than the instrument can

output or measure. "he ma4imum alloed scan rate can be calculated by rearranging Equation >

and using the instrument&s ma4imum current.

$igure 2 shos a typical CB e4periment. "he capacitor voltage and current are plotted versus

time. "he dar'er colored, satoothed aveforms are the voltage applied to the cell, the lightercolored curves are the current. "hree and a half cycles are shon, each in a different color.

Figure )0 Boltage and current versus time are shon for three and a half cycles. $or details,see te4t.

$igure 3 shos 6amry&s P8;?99 setup for a CB test. $our voltage parameters define the seep

range. "he scan starts at Initial E, ramps to Scan 7imit -, reverses, and goes to Scan 7imit 2.

(dditional cycles start and end at Scan 7imit 2. "he scan ends at the $inal E.


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Figure *0 6amry&s P8;?99 setup for a CB e4periment.

CB e4periments can be run ith to electrode or three electrode cell connections.

"hree electrode configurations are common in fundamental research here it allos one

electrode to be studied in isolation, ithout complications from the electrochemistry of the otherelectrodes. "he three electrodes are#

oring lectrode the electrode 'eing tested. eference lectrode an electrode with a constant electrocheical potential.

+o#nter lectrode generally an inert electrode, present in the cell tocoplete the electric circ#it.

"esting of pac'aged capacitor requires to electrode connections. (ll potentiostats can operate

ith this cell configuration.

"he setup for a to electrode cell configuration ith a 6amry Instruments system is easy. %oth;eference :hite= and Counter electrode leads :red and orange= are connected to the minus :!=terminal of the capacitor. 8or'ing electrode :green= and 8or'ing sense :blue= leads are

connected to the plus :F= terminal.

Theoretical CV plot

$igure G shos a theoretical CB plot for a 3 $ E7C in series ith a @9 mJ ES;. "he scan rate

is -99 mB*s. "he scan limits ere#

4nitial 5 0.0 6 can Liit 15 72.! /inal 5 0.0 6 can Liit 25 %0.$

"he scan&s start is shon on the plot along ith arros shoing the direction of the scan. "he

second cycle is shon in red.


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Figure +0 "heoretical CB curve of a 3 $ E7C. Current versus voltage are shon for the firstto cycles. $or details, see te4t.

$or an ideal capacitor :ith no ES;= the shape of the CB diagram ould be a rectangle. "heheight for a charge and discharge step can be calculated using Equation >#

In reality, ES; causes slo rise in the current and rounds to corners of the rectangle at the

beginning of the charge and discharge process. "he time constant, L, affects the rounding of the

corners.

CV on a ! EDLC

$igure @ shos a cyclic voltammogram of a 3 $ E7C. "his e4periment illustrates ho CB

plots can be used to determine a capacitor&s voltage indo.

"he scan rate as -99 mB*s. "he voltage limits for the e4periment ere initially set to F@ Band 3 B hich is ell beyond the 2.> B specification of the E7C.

Figure ,0 CB curve of a 3 $ E7C. Current versus voltage are shon for the first cycle. $ordetails, see te4t.

+otice this plot&s differences in current behavior to the theoretical CB plot shon in $igure G.

"he CB curve does not loo' li'e a rectangle.

"he scan as manually reversed hen the current started to increase dramatically. Selecting $2!

S'ip in 6amry&s $rameor' reverses a seep.

"he first reversal occurred at F3.@ B. Increasing current indicated the beginning of electrolytedecomposition. (t the bac' scan current did start to increase belo 9 B. "he reverse seep as

manually reversed at !2.> B.


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%y integration of a segment of this curve the stored charge can be calculated. "he charge is

automatically calculated by the softare. "he integrated area is highlighted red in $igure @.

The integration range was selected using the Echem 'nalysts -elect "ange .sing/ey0oard %unction&

"he calculated charge beteen -.@ B and 2.@ B is 3.-@ C. /sing Equation -, the capacitance of

the device can be calculated#

"he calculated capacitance depends on the CB scan rate, the voltage region, and a variety of

other variables.

mportant 2ote: Capacitor nonideality precludes calculation o% a true capacitance (alue%or a real EC& Commercial ECs ha(e a speci%ied capacitance that is only (alid when aspeci%ic e3periment is used& 2ote4 techni5ues such as CV4 longterm potentiostatic andgal(anostatic tests4 and E- can gi(e (ery di%%erent capacitance (alues&

CV normali"ed #y scan rate

$igure K shos CB curves of a second 3 $ E7C used to e4plain the scan rate dependence on

CBs.

Scan rates of 3.-K, -9, 3-.K, -99, and 3-K mB*s ere used. "he capacitor as held at 9 B for

-9 minutes beteen the scans. "he scan limits ere set to 9 B and 2.> B.

Gamrys -e5uence !i6ard is a con(enient tool %or setting up comple3 e3periments like this&The $ V delay and the CV test were put inside a loop& The scan rate was multiplied 0y 71$a%ter each cycle&


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Figure 80 CB curves of a 3 $ E7C ith varying scan rates. :violet= 3-K mB*s,:blue= -99 mB*s, :green= 3-.K mB*s, :yello= -9 mB*s, :red= 3.-K mB*s. $or details, see te4t.

(ll CB curves sho the same shape. ES; leads to rounded corners in the CB curve.ifferences occur in the current that increases ith increasing scan rate.

$igure > shos the same CB curves normalied by dividing all currents by the scan rate.

(fter normaliation, the y!a4is unit is (s*B hich corresponds to capacitance in farads. "his

note ill call the y!a4is of a normalied CB plot apparent capacitance Capp.

.se in the Echem 'nalysts Common Tools menu the Linear Fit %unction to calculate theslope o% the cur(e&

$igure > 0 Scan rate normalied CB curves of a 3 $ E7C ith varying scan rates.

:violet= 3-K mB*s, :blue= -99 mB*s, :green= 3-.K mB*s, :yello= -9 mB*s, :red= 3.-K mB*s. $ordetails, see te4t.

$or ideal capacitors, scan rate normalied CB curves superimpose and capacitance does not

depend on the scan rate.

5oever, E7Cs are not ideal and scan rate normalied curves do not superimpose. In $igure >,Cappis around 2.@ $ on the curve ith the highest scan rate. "his curve resembles the CB curve

of an ideal capacitor plus ES;.

(s scan rate decreases, Capprises and shos stronger voltage dependence. "his phenomenon is

e4pected for voltage!driven chemical reactions.

"he increase in Cappby decreasing scan rate can be e4plained by 'inetically slo $aradaicreactions on the electrode surface and by transmission line behavior caused by electrode

porosity.


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In the case here slo surface reactions are present, fast scans are over before reactions occur 0

all current is due to capacitance. $aradaic current has time to flo hen scan rates are sloer,

increasing total current and Capp.

( distributed element model ill sho a similar scan rate behavior. (n electrode surface ith a

high electrolyte resistance ill not have time to respond to voltage changes during a fast scan. Ineffect, the fraction of electrode surface accessible to the electrolyte depends on the scan rate.

CV used to estimate cyclelife

Cyclic voltammetry can also differentiate beteen poor cyclelife and potentially useful cyclelife.

$igure ? shos the result of a CB e4periment ith a 3 $ E7C. @9 cycles beteen -.@ B and

2.> B ere recorded. "he -st, -9th, and @9th cycles are shon. "he scan rate for this test as-99 mB*s.

Figure #0 ifferent cycles of a CB test of a 3 $ E7C. :blue= -st cycle, :green= -9th cycle,:red= @9th cycle. $or details, see te4t.

"he first cycle e4hibits a quite bigger current compared to the others. Initial electrochemicalreactions that occur on the surface of the electrodes lead to higher currents. (fter a hile the EC

is in steadystate and differences in cyclic voltammograms are minor.

"here is very little change in the data beteen the -9th and the @9th cycle. 5ence this capacitor

could be orth of cyclelife testing using cyclic chargedischarge techniques, described inpart 2of this application note.

CV on a pseudocapacitor

CB measurements on pseudocapacitors differ from the results measured on an E7C.

$igure shos a CB test on a - $ P(S pseudocapacitor. Scan rate as set to 3.-K, -9, 3-.K,-99, and 3-K mB*s. "he scan range varied from 9 B to 2.G B. "he capacitor rested at 9 B for

-9 minutes beteen the scans. "he curves are normalied by scan rate.
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Figure 90 Scan rate normalied CB curves of a - $ P(S pseudocapacitor ith varying scanrates. :violet= 3-K mB*s, :blue= -99 mB*s, :green= 3-.K mB*s, :yello= -9 mB*s,

:red= 3.-K mB*s. $or details, see te4t.

"here is one ma1or difference compared to normalied CB plots of E7Cs :$igure >=. (t higherscan rates the CB plots do not superimpose. "he device&s Cappdepends on voltage at all scanrates. "his is e4pected, given the $aradaic nature of charge storage of pseudocapacitors.

Leakage Current $easurement

7ea'age current can be measured in at least to ays#

pply a *+ voltage to a capacitor and eas#re the c#rrent re8#ired toaintain that voltage.

+harge a capacitor to a fixed voltage. 9hen eas#re the change of the open

circ#it potential of the capacitor d#ring self discharge.

Conay&s boo' includes a chapter discussing lea'age current and self discharge of

electrochemical capacitors.

In an attempt to ma'e the specifications of an EC loo' good, some manufacturers specifylea'age current that is measured after >2 hours. /nder these conditions, lea'age current can be

as lo as - H(*$.

Direct leakage current measurement

irect potentiostatic measurement of lea'age current is quite challenging. ( C potential mustbe applied to the capacitor and very small currents must be measured.

"ypically, charging currents are in amps and lea'age currents are in microamps, a range of -9K.

+oise and*or drift in the C potential can create currents that are larger than the lea'age currentitself.


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$or e4ample, assume the 3 $ E7Cs used in this note have an ES; of -99 mJ. "o measure

lea'age currents of - H( on these capacitors current noise should be less than the - H( signal.

(t frequencies here ES; dominates the impedance, 9.- HB of noise in the applied voltage illcreate a noise in current of - H(. (t loer frequencies, here capacitance dominates the

impedance, a voltage drift of 9.3 HB*s creates a current of - H(.

$ast data acquisition, e4ternal noise sources, or lac' of a $araday cage can lead to large apparent

C currents or continual sitching beteen current ranges.

' special script has 0een de(eloped %or direct leakage current measurement using theP!"#$$ so%tware& This script was added to Gamrys Framework in "e(& ,&81 and isnamed:

P!" Leakage Current&e3p

The special script uses a user entered estimate %or E-" to a(oid E con(erter ranges where(oltage noise can o(erload the current measurement circuitry& ;o not use the potentiostatictest in Gamrys P!"#$$ so%tware to measure leakage currents&

$igure -9 shos a lea'age current measurement on a ne 3 $ E7C. Ilea'age is plotted

logarithmically versus time and as measured for five days. "he capacitor as charged to 2.@ Bpotentiostatically and held at this potential.

Figure 1$0 7ea'age current measurement on a 3 $ E7C over five days at 2.@ B. $or details,see te4t.

Ilea'age is still falling five days after applying the potential. (fter >2 hours the measured current

as about G.2 H(, after five days it reached 3.2 H(. "he manufacturer specifies lea'age currenton this capacitor at less than @ H( after >2 hours.

+ote the periodic noise signal at lo currents that is caused by daytime air conditioning. "he

data in this plot as smoothed using a Savit'y!6olay algorithm ith a K9 second indo.


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$easurement of self%discharge

Self discharge causes the open circuit voltage of a charged capacitor to decrease over time.7ea'age current discharges the capacitor during self discharge 0 even though there is no

e4ternal electrical current.

Conay&s boo' describes three different mechanisms for self discharge. "hey can be

distinguished by analying the shapes in voltage versus time curves recorded over long timeperiods. "his analysis as not done on the data presented here.

$igure -- shos the diagram of a self discharge measurement. ( 3 $ E7C as first charged to

2.@ B and the potential as held for -2 hours. "he open circuit voltage as measured and

recorded versus time.

The sel%discharge measurement was done with a special script& This script was added toGamrys Framework in "e(& ,&81 and is named:

P!" -el%;ischarge&e3p

.se in the Echem 'nalysts CV menu the 2ormali6e


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Conclusion

"his application note discussed theoretical and practical basics of electrochemical capacitors.

6amry&s P8;?99 cyclic voltammetry test setup as introduced. %ased on this, CB

measurements ere performed on E7Cs and pseudocapacitor to sho differences of theseenergy storage devices.

$urther on, to different methods ere shon to measure lea'age current. $or this, 6amryInstruments offers to special scripts.

esting Electrochemical Capacitors: Part ) =Cyclic Charge ;ischarge and -tacks

Purpose o% This 2ote"his application note is the second part of notes describing electrochemical techniques forenergy storage devices. It e4plains 6amryNs P8;?99 measurement softare and describes

techniques to investigate electrochemical capacitors. "his application note can also be e4tended

to battery testing.

Introduction

(n introduction to electrochemical capacitors can be found inpart -.It discusses techniques

familiar to chemists ho have or'ed outside of energy storage applications.Part 3 describestheory and practice of EIS measurements on capacitors.

E&perimental

"he data shon in this note ere recorded on a 6amry Instruments ;eference 3999 runningP8;?99 softare. "ests ere run ith commercial 3 farad :P*+ ES5S;!9993C9!992;>= and

@ farad :P*+ ES5S;!999@C9!992;>= electric double layer capacitors :E7Cs= from +esscap.

E7Cs e4hibit much loer charge and discharge times than batteries, reducing the time for

measurements dramatically.

'asics of Cyclic Charge Discharge

Cyclic Charge ischarge :CC= is the standard technique used to test the performance and

cycle life of E7Cs and batteries. ( repetitive loop of charging and discharging is called a cycle.

ost often, charge and discharge are conducted at constant current until a set voltage is reached.

"he charge :capacity= of each cycle is measured and the capacitance C, in farad :$=, is calculated
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:Equation -=. %oth are plotted as a function of cycle number. "his curve is called the capacity

curve.

In practice, charge is commonly called capacity. /sually, capacity has the unit of ampere!hour:(h= here - (h O 3K99 coulombs.

If capacity falls by a set value -9 or 29 are customary the actual number of cycles indicates

the cycle life of the capacitor. In general, commercial capacitors can be cycled for hundreds of

thousands of cycles.

$igure - shos CC data recorded on a ne 3 $ E7C. $ive cycles are shon ith current andvoltage plotted versus time ith each cycle in a different color.

"he lighter colored aveform is the current applied to the capacitor. "he dar'er colored

aveform shos the measured voltage. "he capacitor as cycled beteen 9 B and 2.> B ith a

current of 9.22@ (.

Figure 1&CC test on a ne 3 $ E7C. Boltage and current versus time are shon for fivecycles. $or details, see te4t.

"his ne E7C shos almost ideal behavior the slope of the curve :d/*dt= is constant and is

defined by Equation 2.

:-=

leads to

:2=

/ is the cell potential in volts :B=, I is the cell current in amperes :(=, and A is the charge in

coulombs :C= or ampere seconds :(s=.


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$igure 2 shos the same CC procedure but on a 3 $ capacitor damaged by e4cessive voltage.

"his capacitors behavior is obviously far from ideal.

Figure )&CC test on a damaged 3 $ E7C. Boltage and current versus time are shon for fivecycles. $or details, see te4t.

Increased self discharge causes an e4ponential shape of charge and discharge voltage versustime. ( higher equivalent series resistance :ES;= also leads to a large voltage drop :I; drop= at

each half cycle hich dramatically reduces poer and capacity. "he damage has greatly

decreased the efficiency of this E7C.

(amrys )*R+,, CCD

$igures - and 2 shoed individual charge and discharge curves. ore commonly, CC data are

plotted as a capacity curve capacity versus cycle number.

6amrys CC data file contains additional information used to plot capacity, energy, energyefficiency, Coulombic efficiency, and capacitance versus cycle number.

$igure 3 shos the typical setup screens for a P8;?99 CC e4periment, presented to the user in

three pages. ( simple CC test consists of a repetitive loop through several steps#

-. Constant current charge step2. Potentiostatic hold step :optional=

3. ;est at


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(fter finishing of cycling or reaching an end criterion the measurement is stopped. "he

e4periment can be cancelled at any time by pressing $- (bort.

Figure *&P8;?99 setup for a CC e4periment.

EIS measurements can be e4ecuted after each cycle or half cycle.

;eference 3999 users ith an (u4iliary Electrometer can measure the voltage of up to eight cellsin a serially connected stac'. Individual stop criteria can be set for each channel.


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Page 2 of the CC setup :$igure 3= specifies the parameters for each charge and discharge step.

"he user selects the currents, voltage limits, and ma4imum time.

"he discharge process can be done in three different modes Constant Current, ConstantPower, or Constant Load.

"he loop continues ith the ne4t step hen a charge or discharge step reaches a stop criterion.

If Voltage Finishis enabled, the charge step ill proceed to a potentiostatic step. "he Boltage$inish step ends after reaching a user specified time or hen the current falls belo a limiting

value.

"he cell is turned off during an optional "est Timeperiod. (fter this period the cell is turned onagain to proceed ith the ne4t step.

Page 3 of the CC setup in $igure 3 defines the save interval for the ra data :charge and

discharge curves=. "his page also sets up EIS parameters for optional EIS e4periments.

(fter each loop the parameters for the capacity curve are calculated. Balues are calculated forboth charge and discharge steps. "he cell is turned off hen the e4periment is finished.

CCD on Single ! EDLCs

Different -oltage limits

Cycle!life depends on a number of variables#

Liiting voltage +#rrent #sed for charge and discharge

9eperat#re

"o demonstrate the first point, four 3 $ E7Cs ere cycled to different voltage limits most of

them ell beyond the 2.> B ma4imum voltage specified for the E7C.

$igure G shos the corresponding curves ith the relative change of capacity for up to @9,999

:@9'= cycles.


21/28

Figure +&Percentage change of capacity of a 3 $ E7C during cycling to different voltagelimits. :blue= 2.> B, :green= 3.- B, :red= 3.@ B, :violet= G.9 B. $or details, see te4t.

"he capacitors ere charged and discharged ith a current of 2.2@ amps. "he loer voltage limit

as -.3@ B hich is the half rated voltage of the E7C. "he upper voltage limits ere set to

2.> B, 3.- B, 3.@ B, and G.9 B.

Capacity fade is more pronounced on the samples charged to higher voltage limits. "he capacity

is reduced by only -9 after @9' cycles at potentials belo 3.9 B. "he capacitor charged to

G.9 B lost 29 of its capacity after @99 cycles.

"he strong degradation of performance at higher potentials mainly occurs hen $aradaicelectrochemical reactions decompose the electrolyte. "his can inhibit the electrode surface, lead

to gas formation, damage the electrodes, and have other adverse effects.

Different charge and discharge currents

Cycle life also depends on the applied current. "o demonstrate the impact of higher currents on

CC e4periments, current values significantly beyond the specifications of the capacitor ere

chosen. "he 3 $ capacitors used in this application note are specified for currents of 3.3 (.

$or these e4periments currents larger than 3 ( ere needed. "hese currents require the use of a6amry Instruments ;eference 39' %ooster.

"hree capacity plots ith different charge and discharge currents are shon in $igure @. "he

E7Cs ere charged and discharged beteen -.3@ B and 3.@ B. "he applied current as set to2.2@ (, >.@ (, and -@ (.


22/28

Figure ,&Capacity curves of a 3 $ E7C during cycling ith different currents. :blue= 2.2@ (,:green= >.@ (, :red= -@ (. $or details, see te4t.

"he capacity curves at higher currents sho a steep capacity decline ith increasing cycle

number. "he to E7Cs that ere cycled ith >.@ ( and -@ ( failed before reaching G99 and

?99 cycles respectively.

Even on the first CC cycle, higher currents lead to reduced capacity. Boltage is lost due to

I; drop :/7oss= according to Equation 3#

:3=

"he I; drop voltage is not useful in charging and discharging the capacitor. %oth charge and

discharge have their effective voltage range /effreduced by tice the I; drop voltage.

(ssuming G9 m ES; for 3 $ capacitors, e ould e4pect these parameters for different currents#

Ta0le 1&Estimated I; drop voltage, effective voltage range, capacity, and poer loss for 3 $E7Cs ith G9 mES;. $or details, see te4t.

I

Q(R

/7ossQBR

/effQBR

A

Qm(hR

P7ossQ8R

2.2@ 9.9 -.> -.K 9.2

>.@ 9.3 -.@@ -.3 2.3

-@ 9.K 9.@ 9.? .9


23/28

"he I; drop reduces capacity by about - and @9 respectively. +ote the rough agreement

beteen the initial capacities of the measurements ith >.@ ( and -@ ( in $igure @ and "able -.

"he to capacitors cycled ith >.@ ( and -@ ( got quite hot before they failed.

"he heat generated by rapid cycling is also due to I; losses. (ssuming a constant ES;, the

poer loss P7ossin these devices can be estimated from Equation G#

:G=

"able - shos that poer loss is estimated to be greater than 2 atts, even at >.@ (. "he small

3 $ capacitors used for these tests cannot dissipate this much poer ithout getting very hot.

5eat can cause degradation of the electrolyte and dramatically reduce life time.

"he capacitor cycled at -@ ( as so badly sollen at the end of the test that it as surprising it

had not burst.

CCD on Stacks for .igher Voltages

'alanced stack

$or high poer applications several energy storage devices are often combined in serial and

parallel circuits. $or serially connected capacitors Equations @ and K apply#

:@=

:K=

"he total capacity for n identical capacitors is the nthfraction of the capacity of a single capacitor.

"he individual voltages of the capacitors are summed to give the total voltage of the stac'.

$igure K shos a schematic diagram for a serially connected stac' of capacitors.

Figure 8&iagram of serially connected capacitors ith (u4iliary Electrometer connections.


24/28

If all single cells in a stac' sho the same parameters the stac' is called balanced. "he stac' is

unbalanced if there are cells that differ in performance parameters li'e capacitance, ES;, or

lea'age resistance.

6amrys (u4iliary Electrometer enables detailed investigation of single cells in a stac'. Each

individual channel :(EC5 -, (EC5 2, (EC5 3, = measures the voltage across a cell.

Capacity curves cannot sho irregularities in stac's. (ll cells receive the same current so their

capacities are identical. In the folloing sections, tests ere done ith small stac's containing

three series connected E7Cs. "he stac's ere deliberately unbalanced to sho the impact of

to common irregularities. "o reveal these irregularities different plots ere used.

/n#alanced stack 0ith different capacitances

/sing capacitors ith different capacitances in a stac' leads to fluctuations in voltage defined by

Equation >.

:>=

(pplying a constant charge A on a stac' leads to a loer voltage /ifor single cells ith highercapacitance Ci.

( serial stac' made up of to 3 $ E7Cs :C-, C2= and one @ $ E7C :C3= :see also $igure K=

as used to test an unbalanced stac'. (ll three capacitors ere initially charged to -.3@ B beforebeing added to the stac', so the initial stac' voltage as close to G B.

"he stac' as cycled for @99 cycles ith a current of 9.22@ (. "he test started ith a charge

step. "he cycle limits ere set to G B and .@ B. Boltage of the single cells as measured ith

three (u4iliary Electrometer channels.

$igure > shos one presentation of the data from this test. "he limiting voltages of each channelfor the charge :dar'er colored= and discharge step :lighter colored= versus cycle number are

plotted.


25/28

Figure >&7imiting potentials for the charge :dar'er= and discharge process :lighter= of anunbalanced stac' ith to 3 $ E7Cs :blue C-, green C2= and one @ $ E7C :red C3=. $or

details, see te4t.

(s e4pected, the final discharge voltage for each cell :regardless of capacitance= is close to

-.3 B. "he small deviations from -.3 B are probably due to lea'age current imbalance, describedlater.

"he final charge voltage is more interesting. If e had a balanced stac', the fully charged stac'

voltage of .@ B ould be evenly divided among the cells so each cell ould charge to about3.-K B.

In the unbalanced stac' the 3 $ E7Cs :C-and C2= charge to around 3.3K B. "hey are each

overcharged by about 299 mB. "he @ $ capacitor :C3= is only charged to about 2.> B. It is

undercharged by G99 mB. +ote the voltage imbalance is independent of the cycle number.

In a capacitor stac' ith unbalanced capacitor values, the capacitors ith the highestcapacitances have a loer effective voltage range. "hese deviations in voltage also lead to

differences in energy.

$igure ? shos the calculated energy of the charge step versus cycle number for the same

measurement.


26/28

Figure #&Charge energy versus cycle number of single cells in an unbalanced stac' ith to 3 $E7Cs :blue C-, green C2= and one @ $ E7C :red C3=. $or details, see te4t.

"he energy of the @ $ E7C is reduced due to loer voltage limits. "he to 3 $ E7Cs try tobalance this voltage loss ith higher voltages. "heir energy content increased.

In e4treme cases, the voltage :and energy= increase can be large enough to damage the

capacitors.

/n#alanced stack 0ith different leakage resistances

7ea'age resistance affects both stac' performance and cycle life. It can change as a capacitor

ages. 7o lea'age resistances lead to higher lea'age currents hich discharge the cell ithout

e4ternal current applied.

7ea'age resistance can be modeled as a resistor parallel to a capacitor :see $igure =.

Figure 9. iagram of serially connected capacitors ith (u4iliary Electrometer connections.Parallel resistors ;-and ;2simulate different lea'age resistances.

$igure -9 shos the self discharge due to lea'age current. "o resistors :;-O -K.@ ',;2O -@G '= ere installed parallel to C-and C2. "he intrinsic lea'age resistance for C3is in the

range. (ll three capacitors had a nominal capacitance of 3 $.

"he stac' as charged to ?.- B using a charge current of 9.22@ (. (fter charging to ?.- B the

voltage as recorded in currentless state for K hours.


27/28

Figure 1$&Self discharge over K hours of an unbalanced stac' :violet= and its single cells :blueC-, green C2, red C3= ith different lea'age resistances. $or details, see te4t.

Internal lea'age current leads to a continuous voltage drift that discharges the cell. Capacitor C-ith the loest lea'age resistance has the highest lea'age current. It causes the highest loss in

voltage :about ?@9 mB=. In comparison, the total voltage loss of the stac' is about - B afterK hours.

"he calculated lea'age current for C-is G> ( hereas the other to capacitors e4hibit values ofonly > ( :C2= and 2 ( :C3=.

5igher lea'age currents also lead to increased loss in energy and poer. $igure -- shos thebehavior of energy during cycling.

"he prior stac' setup as cycled for @99 cycles beteen G B and ?.- B ith a current of9.22@ (.

Figure 11&Charge energy versus cycle number of single cells :blue C-, green C2, red C3= ithdifferent lea'age resistances in an unbalanced stac'. $or details, see te4t.

5igher lea'age currents cause continuous energy fade during cycling. "he energy of C-

decreases continuously due to higher self discharge. +ote this is in contrast to $igure > and

$igure ? here voltage and energy imbalances ere independent of the cycle number.

Capacitors C2and C3compensate for this loss and overcharge to higher voltages. Energyincreases but this may be at the cost of loer electrochemical stability and decreased cycle life.


28/28

Conclusion

"his application note described 6amrys P8;?99 CC softare by tests on single 3 $ E7Csand small stac's.

Impacts of different setup parameters on performance of E7Cs ere shon and the influenceof common irregularities in stac's as described.

"he combination of single cell investigation and recording of multiple parameters enablesaccurate evaluation of irregularities in stac's.

testing electrochemical capacitors

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