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10th International Symposium „Topical Problems in the Field of Electrical and Power Engineering“ Pärnu, Estonia, January 10-15, 2011
Capacitance balancing for supercapacitive energy storage system
Ugis Sirmelis, Linards Grigans Riga Technical University; Institute of Physical Energetics usirmelis@inbox.lv, linardsgrigans@gmail.com
Abstract
In this paper capacitance balancing is proposed as an efficient method to decrease cell voltage disbalance and increase effective energy capacity of superca

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38
10
th
International Symposium„Topical Problems in the Field of Electrical and Power Engineering“Pärnu, Estonia, January 10-15, 2011
Capacitance balancing for supercapacitive energy storage system
Ugis Sirmelis, Linards GrigansRiga Technical University; Institute of Physical Energeticsusirmelis@inbox.lv,linardsgrigans@gmail.com
Abstract
In this paper capacitance balancing is proposed as an efficient method to decrease cell voltage disbalance and increase effective energy capacity of supercapacitor bank. Efficiency of the method is demonstrated theoretically and verified experimentally using 8 supercapacitor cells.
Keywords
Energy storage, supercapacitor, voltage balancing,capacitance measurement
Introduction
Application of supercapacitors (SC) in recent yearshas become widespread. Due to excellent powercapability and extremely high cycle life SCs areused in variety of industries, e.g., in consumerelectronics, in uninterruptible power supply devices,in electric transport to store braking energy andbattery assist, in solar and wind stations as energystorage component etc. [1].SCs are low voltage devices with the typicalmaximum voltage 2.7 V. Therefore, to meet therequirements of higher voltage applications, SCsmust be connected in series. For example, anonboard energy storage system (ESS) in tram T3Amay contain a supercapacitor bank of two parallelbranches, each consisting of 180 series connectedSCs [2]. However, charging and discharging SCsconnected in series leads to unequal voltages acrossindividual cells due to different SCs capacitancevalues. According to manufacturer product datasheetSC charge until 2.5 V ensures prolonged lifetime incomparison to 2.7 V. Charging SC seriesconnection, the smallest capacitor will reach first the2.5 V threshold. If then charging is terminated, theenergy capacity of other cells is not effectivelyutilized [1, 3].For entire utilization of ESS energy capacity it isnecessary to eliminate voltage disbalance byapplying measures, which allow all SCs to becharged to 2.5 V. In literature and in practice thisproblem is solved using passive or active voltagebalancing methods, however, the main disadvantageof these methods are cost and additional energylosses [4].In this work it is proposed to eliminate voltagedifference by capacitance balancing. By measuringSCs capacitances, modules of two capacitorsconnected in parallel are matched in a way tominimize capacitance dispersion of these modules.Connection of these modules in series reducesvoltage disbalance significantly.The capacitance balancing method is theoreticallyanalyzed for onboard ESS application example. Alsoefficiency of the method is verified experimentallyusing 8 SC cells.
1 Theoretical analysis
To study voltage disbalance an example for tramonboard ESS with 2x180 3000 F SCs proposed in[2] is chosen. For theoretical analysis it is necessaryto know SCs capacitance distribution. Maxwell fortheir BCAP3000 capacitors gives only capacitancetolerance -0%/+20%, however, distribution functionis not provided. According to manufacturer research[5], SC capacitances for BCAP0008 (1800 F, ±20%)are normally distributed with standard deviation
σ
=1% of mean (
µ
= 1920 F) value. Therefore, weassume that capacitances of BCAP3000 are alsonormally distributed (
σ
= 2%,
µ
= 3300 F).For analysis of voltage disbalance effect on ESSenergy capacity, 360 capacitance values shown inFig. 1 are generated using Matlab randn function.The actual distribution mean value
µ
= 3304 F andstandard deviation
σ
= 2.05 % is obtained.
300031003200330034003500360001234567Capacitance, F
N u m b e r o f s u p e r c a p a c i t o r s
AB
Fig. 1. A – theoretical capacitance dispersion curve, B – randomly generated 360 capacitance values
39Theoretical energy capacity of all these SCs can becalculated using Eq. (1) and is 1.03 kWh.
2360max1
2
n ESSn
CV W
=
⋅=∑
, (1)where
n
C
– capacitance value of n-th SC;
max
V
– maximum SC voltage (2.5 V).To match application power and energyrequirements, SC bank can be arranged either inseries/parallel (Fig. 2, a) or parallel/series (Fig. 2, b).
Fig. 2. Supercapacitor bank arrangement inseries/parallel (a), parallel/series (b)
1.1 Series/parallel supercapacitor arrangement
Previously generated 360 capacitances are randomlyarranged into two parallel strings of 180 SCs in eachas in Fig. 2, a. Resulting capacitances of thesecapacitor strings are 18.346 F and 18.348 F, whichmeans that currents in both strings will be practicallyequal. Thus, effective energy capacity of SC bank can be calculated as:
2360minmaxmin1
2
ESSnn
CV C W C
=
=∑
, (2)where
min
C
– smallest capacitance connected inseries.In this case the energy capacity is 0.92 kWh, whichis 89% of theoretical maximum.If capacitances of both branches are not equal, thenwe have to calculate energy capacity of each branch,to obtain total effective energy capacity of SC bank.That in which branch smallest capacitance will firstreach 2.5 V results from:
min21max1max2min12
CC VV CC
ΣΣ
=
, (3)where,
min1
C
,
min2
C
– smallest capacitances of each branch;
1
C
Σ
,
2
C
Σ
– total capacitances of each branch.If
min21min12
1
CC CC
ΣΣ
>
, effective energy capacity of 1
st
and2
nd
branch is calculated as:
2180min1maxmin111
2
nn
CV C W C
=
=∑
, (4)
1221
WC W C
ΣΣ
=
. (5)If
min21min12
1
CC CC
ΣΣ
<
, effective energy capacity of 1
st
and2
nd
branch is calculated as:
2180min2maxmin221
2
nn
CV C W C
=
=∑
, (6)
2211
WC W C
ΣΣ
=
. (7)To evaluate SCs arrangement influence on effectiveenergy capacity of SC bank, 360 SCs of Fig. 1 wererandomly arranged in two branches 100,000 times.Results show that energy capacity varies from0.905 kWh to 0.925 kWh.
0.88 0.9 0.92 0.94 0.96 0.9800.511.522.5x 10
4
Energy capacity, kWh
N u m b e r o f o c c u r e n c e s
Fig. 3. SCs arrangement influence on effectiveenergy capacity of SC bank in series/parallelconnection
1.2 Parallel/series supercapacitor arrangement
Arranging SCs in parallel/series connection asshown in Fig. 2, b, reduces series connectedcapacitance dispersion [3]. Theoretically standarddeviation of these capacitances in comparison tostandard deviation of individual cell capacitances isreduced by2. Randomly pairing individual SCcapacitances, we obtained capacitance values asshown in Fig. 4.
6000 6200 6400 6600 6800 7000 7200-0.500.511.522.533.544.5Capacitance, F
N u m b e r o f s u p e r c a p a c i t o r s
AB
Fig. 4. A – theoretical capacitance dispersion, B – random realization of capacitance pairing
The actual
µ
= 6608 F and
σ
= 1.5% is obtained.Energy capacity for such capacitance distribution is0.94 kWh.
40For 100,000 random parallel/series arrangementseffective energy capacity of SC bank is as shown inFig. 5. The energy capacity varies from 0.915 kWhto 0.985 kWh.
0.9 0.92 0.94 0.96 0.98 10100020003000400050006000Energy capacity, kWh
N u m b e r o f o c c u r e n c e s
Fig. 5. SCs arrangement influence on energycapacity of SC bank in parallel/seriesl connection
1.3 Capacitance balancing
Parallel/series connection on average gives largereffective energy capacity if compared toseries/parallel connection. However, lower energycapacity may also occur. Therefore, to maximizeeffective energy capacity it is necessary to findoptimal combination of SCs arrangement. Accordingto Eq. (2), larger energy capacity is obtained if seriesconnected capacitances are equal.Simple way to achieve best arrangement in mostcases is by pairing largest SC with smallest, secondlargest with second smallest and so on. If SCscapacitances in SC bank were symmetricallydistributed, then it would be possible to pair SCs in away that series connected modules capacitanceswere equal and the total effective energy capacitywould be 100%.In Fig. 6 series/parallel, parallel/series andcapacitance balancing method is compared. It isobvious that capacitance balancing method givessignificantly better results. If series/parallel averageeffective energy capacity is 89% and 92% forparallel/series connection then capacitance balancingmethod gives 99%.
0.9 0.92 0.94 0.96 0.98 1 1.02 1.0400.511.522.5x 10
4
Energy capacity, kWh
N u m b e r o f o c c u r e n c e s
series/parallelparallel/seriesbalanced capacitancestheoretical maximum
Fig. 6. Comparison of series/parallel, parallel/seriesand capacitance balancing method
2 Experimental results
For practical application of capacitance balancingmethod it is important to know capacitance of eachSC. Therefore, capacitance measurement of 8 SCs isperformed and obtained results are used forcapacitance balancing demonstration.
2.1 Capacitance measurement
Capacitance measurement was performed usingconstant current 100 A charge-discharge test bench(Fig. 7).
Fig. 7. 100A constant current SC charge/dischargetest bench (1. 100A current source;2. SCs; 3. SC voltage indicator; 4. current indicator;5. constant current discharger power circuit and controller;6. load resistor; 7. USB-4716 16-bit ADC; 8. laptopwith WaveScan 2.0 data logging software).
We charged SCs from approx. 1.25 V to 2.5 V with100 A 4 times (Fig. 8).
0 100 200 300 400 500 60011.21.41.61.822.22.42.62.8Time, s
V o l t a g e , V
Fig. 8. SC cycling with 100 A
As we can see voltage is not rising linearly, whichshows that SC capacitance is voltage dependent.Using Eq. (9), SC dynamic capacitance can becalculated at different voltages.
It C V
∆=∆
(9)In Fig. 9 changes in dynamic capacitance of one SCduring four charge/discharge cycles are shown. Wecan see that dynamic capacitance curves forcharging and discharging are not the same. Thesecurves cross at about 2.1 V. Capacitance at thisvoltage is chosen for capacitance balancing, becauseat this point charging and discharging dynamiccapacitance values are equal.
41
1.4 1.6 1.8 2 2.2 2.4260027002800290030003100320033003400Voltage, V
C a p a c i t a n c e , F
Fig. 9. Dynamic capacitance of one SC cell
The measured capacitances at 2.1 V are summarizedin Table 1. We can see that maximum capacitancedifference is 210 F.
Table 1
. SCs capacitance measured at 2.1 VSC number Capacitance (F)1. 30752. 30003. 30004. 29905. 32006. 31507. 31808. 3075
2.2 Capacitance pairing
Eight SCs can be arranged into 4 pairs according toEq. (10) in 105 different ways.
2
!!22
n
n N n
= ⋅
, (10)where n – number of SCs (n=8).Calculation results of energy capacity of all 105arrangements are shown in Fig. 10.
0 20 40 60 80 100949596979899100Combination number
E n e r g y c a p a c i t y o f t o t a l S C c a p a c i t y , %
Fig. 10. Eight SCs effective energy capacity indifferent parallel/series arrangements
The arrangements that give the best effective energycapacity are shown in Table 2.
Table 1
. Balanced capacitancesArrangement Capacitance (F)1.+8. 1.+8. 61502.+5. 2.+6. 62003.+6. 3.+5. 61504.+7. 4.+7. 6170After pairing, the maximum capacitance differenceis reduced to 50 F.
Conclusions
Theoretical and experimental results show thatcapacitance balancing in parallel/series connectionsignificantly improves effective energy capacity of SC bank.Capacitance balancing method requires capacitancemeasurement. As SC capacitance depends onvarious factors, measurement must be performed atidentical conditions.Due to the degradation of SCs capacitance inoperation life, to evaluate the efficiency of thecapacitance balancing method, long-term experiencewith large number of SCs is needed.
Acknowledgement
The paper is supported by the European Social FundProject “Scientific Group Supporting LatvianActivities of the European Strategic EnergyTechnology Plan”No. 1DP/1.1.1.2.0/09/APIA/VIAA/027
References
1. Product Guide –BOOSTCAP Ultracapacitors –Doc. No. 1014627.1, Maxwell Technologies, Inc.,2009, pp. 54.2. L. Latkovskis and V. Bražis, “Simulation of theregenerative energy storage with supercapacitorsin tatra T3A type trams,” Computer Modeling andSimulation, UKSIM 2008, pp. 398–403.3. P. Barrade, “Series Connection of Supercapacitors: Comparative Study of Solutionsfor the Active equalization of the Voltages,”Electrimacs 2002, 7
th
International Conference onModeling and Simulation of Electric Machines,Converters and Systems, vol. 2, Aug. 2002, p. 4.4. D. Linzen, S. Buller, E. Karden, andR.W. De Doncker, “Analysis and evaluation of charge-balancing circuits on performance,reliability, and lifetime of supercapacitorsystems,” Industry Applications, IEEETransactions on, vol. 41, 2005, pp. 1135–1141.5. A. Schneuwly et. al. “Boostcap Double-LayerCapacitors for Peak Power AutomotiveApplications,” Procedings of the 2
nd
AABCConference, Las Vegas (USA), 2002.

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