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SIITME2009 - 15th International Symposium for Design and Technology of Electronics Packages

Power Converters Study Regarding the ESR of a SUPERCAPACITOR

Adrian Taut, Alin Grama, Ovidiu Pop, Serban Lungu

26/28 G. Baritiu StreetApplied electronics department, Technical University ofCluj-Napoca, Cluj-Napoca, Romania

Adrian. Taut@ael. utcluj .ro

Abstract: This paper proposes a switching power converter that allows determining the ESR valuefor a supercapacitor. The model proposed intends to be one ofthe future methods for charging ofthesupercapacitor tacking into account the necessary charging conditions, constant current andmaximum voltage across the capacitor. Also this model of converter propose by us can be used forother types ofsupercapacitors with different limiting values and parameters such as time ofchargingand maximum voltage across the capacitor.

1. INTRODUCTION

Electrical energy storage is required in manyapplications: telecommunication devices, such as cellphones and PDA's, stand-by power system andelectric/hybrid vehicles. The specifications for thevarious energy storage devices are given in terms ofenergy stored and maximum power as well as size andweight, initial cost and life. As power requirementsfor many applications become more demanding, it isoften reasonable to consider separating the energy andpower requirements by providing for the peak power apulse power device (capacitor) that is chargedperiodically from a primary energy storage unit(battery). The traditional capacitors cannot storeenough energy in volume and weight available, forapplications where significant energy is needed inpulse form. For these applications, the developmentof high energy density capacitors (supercapacitor) hasbeen undertaken by various groups around the world.

Charging of supercapacitors is simple while at thesame time may present some unique challenges.Unlike batteries, supercapacitors may be charged anddischarged at similar rates. This is very useful inenergy recovery systems such as dynamic braking oftransport systems.

In this paper we present some characteristics ofsupercapacitors and a method of charging it.

The paper is organized as follows: we first presentthe supercapacitor and the energy stored in this(Section II), power converter which was implementedfor the supercapacitor (Section III), measurements andresults (Section IV) and finally conclusion (SectionV).

2. SUPERCAPACITORS

Supercapacitors are components for energystorage, dedicated for applications where both energyand power density are needed. Even if their energydensity is ten times lower than the energy density ofbatteries, supercapacitors offer new alternatives forapplications where energy storage is needed.

Supercapacitors are based on a Carbon NanoTube(CTN) technology; this technology used creates avery large surface area with an extremely smallseparation distance. Capacitors consist of two metalelectrodes separated by a dielectric material. Thedielectric not only separates the electrodes but alsohas electrical properties that affect the performance ofcapacitors. Supercapacitors do not have a traditionaldielectric material like ceramic, polymer films oraluminum oxide to separate the electrodes. Insteadthey have a physical barrier made from activatedcarbon that when an electrical charge is applied to thematerial a double electric field is generated whichacts like a dielectric. The charging/discharging occurs

978-1-4244-50330309/$26.00 ©2009 IEEE 277 17-20 Sep 2009, Gyula, Hungary

SIITME2009 - 15th International Symposiumfor Design and Technology of Electronics Packages

where C is its capacitance (Farads) and U is thevoltage between the terminal plates. The capacitanceof the dielectric capacitor depends on the dielectricconstant (K) and the thickness (th) of the dielectricmaterial and its geometric area (A) .

in an ion absorption layer formed on the electrodes ofactivated carbon.

The simplest capacitors store energy by chargeseparation. The simplest capacitors store the energy ina thin layer of dielectric material that is supported bymetal plates that act as the terminals for the device.The energy stored in capacitor is given by:

Potous. high surtKe~iJ p¥licles.or tners 0000-2000 m2fgrnl

Separalor(ionie eondltCtor}

Electrolyte between partic !es or fi bers

I..I

Fig. 1. Schematic of a double layer supercapacitor

The model of supercapacitor we used in this paperis characterized by capacitance about 350F and anominal voltage of 14V.

(1)cu:

W=2

KAc=th

(2)3. POWER CONVERTER

Energy in electric field, stored in a supercapacitoris given by following equation:

and the needed capacitance of supercapacitor is givenby:

where C represents the capacitance and U is thevoltage across the capacitor. This equation representsthe total energy accumulated in a capacitor. Forpractical application it is acceptable discharging on50% voltage drop from its nominal value. Thereforefor capacitor with nominal voltage U a decrease onU/2 level is acceptable. Therefore supercapacitorenergy W, which is under these conditions todisposal, it will be:

cirW=

2

w=~[U2 -(~)}~CU2

(3)

(4)

The most reliable method of chargingsupercapacitor is to charge at constant current orconstant power.

A de-to-de constant current regulator is the simpleform of active charging. Either a buck or boostregulator may be used depending on the application .The buck regulator is the preferred topology due tothe continuous output charge current. The powerlosses or supercapacitor heating is proportional tocurrent squared times the duty cycle.

For the proposed project we have created a buckconverter with current and voltage limitation. Bucktopology is simple and consists of two unidirectionalswitches. One can be controlled transistor and anotherone can not be controlled diode. The current limit wasset to the lOA charge current and the voltage limitwas set to the maximum required voltage atsupercapacitor 14V. The schematic of the powerconverter can be seeing in figure 2. This topology isone of methods propose by us for charging thesupercapacitor.

(5)



~ p:~:: ;;~: .~'~, .. ~o L.,-"' ......"'

, r~, '

' 0

rrtr' "~.., ': : ~ " r :,' l'

~,

~' 0

period or frequency, /),.Vo represent the ripple ofoutput voltage.

Vo ' ~ - is the output and input voltage of

converter.

1L - is the curent across inductance.

10 - is the output current.

Other calculations were made have on the stabilityand efficiency of the converter in this situation.

4. MEASUREMENTS AND RESULTS

Fig. 2. Schematic of powerconverter lOA and 14V

This converter presents two loop adjustment whensupercapacitor is conected to output its. First loop, thecurrent loop, works when supercapacitor is charging.After the maximum voltage at the terminal ofsupercapacitor is achieved, the second loop is "on"and the first loop is desactivated. This loop is forvoltage limitation and requires the maximum voltage.

To achive the requirements imposed bysupercapacitor and the buck topology a series ofcalculations were made:

c- (~-~)~- 8~!'J.~f2L

L= (~-~)~~O.31of

!'J.V =LM~o Ci'.o

(6)

(7)

(8)

(9)

(10)

The experimental bench consists in a powerconverters implemented by us and presented insection III (lOA and l4V), a 3S0F supercapacitor, anelectronic load that can be set to sink SA constantcurrent or pulsed constant current, and a dataloger tomonitor the voltage across the supercapacitor. Thedataloger saves across the supercapacitor at everysecond; its internal impedance it about 1GO.

Fig. 3. Experimental benchdiagram

The first step is to charge the supercapacitor withthe constant current 6A. The voltage across thesupercapacitor is measured at every second and it ismemorized in the dataloger. The curve of voltageversus time at constant current charge is representedin figure 4.

The measurements were done more than once, tohave a rigorously results.

To determine the value of equivalent seriesresistance (ESR) were used two methods ofcalculation. Graphs and tables taken from thedataloger can be viewed in next figures.

Where C is the output capcacitor of buckconverter, L is inductance of buck converters in

978-1-4244-50330309/$26.00 ©2009 IEEE 279 17-20Sep 2009, Gyula, Hungary


(11 )ESR= I1UI Disch

Or

\\ .............. ~~

V ........... ,.

Vmax V*max llVI Disc

ESR

13,637 13,154 0,483 2 0,241

13,208 12,826 0,382 2 0,182

13,282 12,881 0,401 2 0,202

13,233 12,82 0,413 2 0,208

13,254 12,84 0,414 2 0,207

13,221 12,818 0,403 2 0,201

13,355 12,97 0,285 2 0,143

13,302 12,898 0,404 2 0,202

13,278 12,871 0,407 2 0,203

13,289 12,882 0,407 2 0,203

13,256 12,801 0,455 2 0,227

13,398 12,978 0,42 2 0,21

13,475 13,065 0,41 2 0,205

13,327 12,912 0,415 2 0,207

13,342 12,953 0,289 2 0,144

o

0.05

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

nr masuratoare

Fig. 7. Graphs for ESR

ESR -=2,509 mO

ESR- descarcare la curent constant

Tab. 1. ESR value for discharging constant current

0.3

0.25

E 0.2J:'£' 0.150::

:3 0.1

ESR = Vmax- V;axI Disch

ESR calculation is done using the equation:

Where Al.l is the exponential discharge of

supercapacitor and I Disch is discharge current.

,

, .......-1

, ././

././

/.....

1000.oe~•t ....M

......l ' 1 ' ll m ~ rn m~ m m ", n, m m m ~ ~ 'W lm ~,u" m~ 1~"'~- ,.

------------r--- l-I

: VdI,

, : ~+--VfVmin ~----------- _~ .Vr

,I,

Fig. 4. The constant current charge curve at 6A

The first method to determinate the ESR value isto implemented an experimental stall where theultracapcacitor is discarged at a constant current in adinamic maner.

Fig. 5. Theoretical waveform for constant currentdischarged.

The measured waveforms for the voltage acrossthe supercapacitor at constant current charge,respectively for constant current discharge arepresented and are used to determinate the ESR valueof the supercapacitor.

For the experimental stall we use a supercapacitorwith a capacitance of 350F, 14V nominal voltage,2200 mm high, 2700mm length, and weight 24 kg.

Fig. 6. Supercapcacitor

978-1-4244-50330309/$26.00 ©2009 IEEE 280 17-20 Sep 2009, Gyu1a, Hungary

SIITM E2009 - 15th International Symposium for Design and Technology of Electronics Packages

Figure 8 represents the waveforms captured withthe oscilloscope. In the bottom side of the picture youcan see the discharge current (we used a currenttransducer), and in upper side of the picture you cansee the voltage across the supercapacitor. The scale inchanel one is 50mY/div, and for chanel two is200mv/div . The voltage variation is appreciativety40mY. This mean, at a discharge current at about15A, the value of ESR is :

Measurem e I:!.V [V] I Disc [A]ESR [mO.]

nts

1 0,047 24 1.958

2 0,028 19 1.474

3 0,041 20 2.050

4 0,04 20 2.000

5 0,041 40 1.025

6 0,039 17 2.294

7 0,042 19 2.211

8 0,041 22 1.864

9 0,044 22 2.000

10 0,039 23 1.696

ESR= /1U = 41.6mV =2.77mQi -: 15A

(12)

Tab. 2. ESR value for different discharging constant current

2.500

2.000 r:-:~/ \ / '0-

~::; 1500

V ....."0E 1000

0 500

00001 2 3 4 5 6 7 8 9 10 11

Fig. 8. Graphs for ESR

The second method represents the discharge of thesupercapacitor in a dynamic cycle.

After we charge the supercapacitor, he will bedischarged by the specifications below:

High level current: 15 A, Low level current: 0 A,Period : 200ms, Duty Factor: 50%, Slew-Rate: 1600rnA.

-a;, . , !oJlI ~'Il ! 1 !l 1l ~ Ji. JUj,i~~ .!iEl 1i- om. ~,. h . Clll'KdcJ , 3.098HIF!~~= !i H;: lim I Vacdc

n IVl.....no. 10 ) 127 Ult t26 11'1.....noe11)12. n ln;~ W1~~~~! ~~ l:~ 1! !!!

1;H;i~liOi:; j: II III• •UIJ7

'D 111J... lllOt II II 36 1111 1n U....t-'1... 1OII)S II I n

~~ U:1r;: ::~ : ~~ nlU... _-----"._-- -_.

,,~ I".". I".". I".I

". '--------". -". -- -')'11... +"."....

._,..J...',b'

'--_"'1'"to__ ...... 1.·_.. ...It-·....

Fig. 10. Value of ESR determinated by dataloger

As you can see the values obtain with these twomethods are aproximately equal. However, we cansay the value of ESR is around 2mQ.

Regarding power supply with current limited forthis application we made a lots of mesurements.

'\\\l

\\

Input voltage/Output voltage (1=1 A)

11.8911.8811.8811.87

> 11.8711.8611.8611.8511.85

o 10 20

v30 40 50

Fig. 9. Dynamic discharge of supercapacitor

978-1-4244-50330309/$26.00 ©2009 IEEE 281

Fig. 11. Output voltage/Input voltage for I=IA

17-20 Sep 2009 , Gyula, Hungary


Output voltage/Input voltage (3A) REFERENCES

\-,

<,

--- -......---- ----.... ----.

r "\j \.

"\\..

\\.

Fig. 12. Output voltage/Input voltage for I=3A

Output voltage/Load current (Input voltage 30V)

[6] R.W.Erickson, D.Maksimovic "Fundamental of PowerElectronics SE", Kluwer Academic Publisher, ISBN 07923-7270-0.

[1] J. M. Miller, D. Nebrigic , M. Ererett, "Ultracapacitordistributed model equivalent circuit for powerelectronic circuit simulation", Ansoft Leading InsightsWorkshop, Los Angeles, USA, October 19,2006.

[2] 1.R.MilIer, "Batery-capacitor power sourcefordigitalcommunication aplications: simulations usingadvanced electrochemical capacitors",Electrochem.Soc. Proc., vol. 29-95.pp.246- 254, 1995

[3] A. F. Burke, J. R. Miller, "Test procedures for highenergy density electrochemical capacitors ,"Electrochem. Soc. Proc., vol. 29-95, pp. 280-297,1995.

[4] P. Barrade, A. Rufer, "Current capability and powerdensity of supercapacitors: considerations on energyefficiency", EPE 2003, European Conference onPower Electronics and Applications, 2-4 September,Toulouse , France, ISBN 90-75815-07-7.

[5] J. H. Chen, W. Z. Li, Z. P. Huang, D. Z. Wang, S. X.Yang, 1. G. Wen, Z. F. Ren, "Electrochemistry ofCarbon Nanotubes and their potential application insupercapacitors", Proceedings of the 197th Meeting ofElectrochemical Society, Toronto, Canada, May 14-18,2000.

6

50

5

40

4

30

v

3

20

2

10

12.05

1211.95

11.9

11.85

11.811.75

11.7

11.65

11.6

o

11.76511.76

11.75511.75

> 11.74511.74

11.73511.73

11.725

o

Fig. 13. Output voltage/Load current for input voltage 30Y[7] S.Lungu, D.Petreus "Surse in comutatie", MediaMira,

Cluj-Napoca 1999, ISBN 973-9358-32-2

5. CONCLUSION

Capacitors are devices capable of higher chargestorage several hundred times more than conventionalcapacitors. They are different from batteries and forcertain types of application have several advantages.The state-of-charge is a simple function of voltageand this coupled with high power density and goodcycle-life enable them to be useful in applicationsranging from light-weight electronic fuses, memoryback-up power sources, and surge protection devicesto pulse power sources for smart weapons. Suchdevices are also likely to help the global transition tomore energy-efficient technologies.

In this paper an overview of a supercapacitor waspresented. We presented the way of functioning of asupercapacitor, and the methods of fabrication. Wepresented a model of charging for this supercapacitor.Two methods for calculated the ESR value ispresented.


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