A Modelica Library for Simulation of Elecric Energy Storages...Keywords: Energy storages, library,...

A Modelica Library for Simulation of Elecric Energy Storages

M. Einhorn1 F. V. Conte1 C. Kral1 C. Niklas1 H. Popp1 J. Fleig2

1AIT Austrian Institute of TechnologyMobility Department, Electric Drive Technologies

Giefinggasse 2, 1210 Vienna, [email protected]

2Vienna University of TechnologyInstitute of Chemical Technologies and Analytics

Getreidemarkt 9/164ec 1060 Vienna, Austria

Abstract

This article gives an overview of the Electric EnergyStorage (EES) library, which is proposed for inclu-sion in the Modelica Standard Library. The librarycontains models with different complexity for simu-lating of electric energy storages like batteries (sin-gle cells as well as stacks) interacting with loads, bat-tery management systems and charging devices. It isshown how the models are defined and how they canbe parametrized. Finally, two example simulations arepresented.

Keywords: Energy storages, library, battery simula-tion

1 Introduction

Simulation is a commonly used technique to reducecosts during the design and development process. Theenergy storage system is a key issue, especially forelectric vehicles. Basic models of electric energy stor-ages (EES) are already included in the commercialSmartElectricDrives (SED) library [1]. TheEES library, presented in this article, provides basicas well as more complex models for battery cells andfor battery stacks. It includes models for battery mon-itoring and measurement, chargers, loads, sensors andbattery management. This library can be used to simu-late the behavior of electric energy storages in mobiledevices, stationary applications and in transportationsystems including hybrid as well as electric vehicles.The models of theEES library are designed as univer-sally as possible so that even very specific scenarioscan be simulated by varying the parametrization. Inthe future it is intended to include theEES library in

Figure 1: Electric Energy Stroage (EES) library struc-ture

theModelica Standard Library (MSL).This article shows how theEES library is structured,

how the fundamental models are defined and whichparameters are needed. Finally, two example simula-tions are presented. For implementing theEES library,Dymola 7.4 and Modelica 3.2 are used [2–4].

2 Library structure

The EES library is structured as shown in Fig. 1. Thefundamental packages and models are now explainedin more detail.

2.1 Batteries

TheBatteries package contains models for cells aswell as for stacks withns serially connected cells andnp cells in parallel. Its structure is shown in Fig. 2.

Proceedings 8th Modelica Conference, Dresden, Germany, March 20-22, 2011

436

mailto:[email protected]

Figure 2: Structure of theBatteries packageas apart of the EES library.

2.1.1 Cells

In the Cells package there are two different typesof cell models:Single andWithMeasurement.While theSingle cell models are models of the bat-tery cell only, theWithMeasurement cell mod-els extend theSingle cell models with basic mea-surement. Each of these models can either be asimple cell model with just an ohmic impedance(StaticResistance) or a more complex cellmodel considering basic self discharge, a variableohmic impedance and a variable number of variableRC elements (LinearDynamicImpedance).

SingleTheStaticResistance single cell model as wellas theLinearDynamicImpedance single modelare shown in Fig. 3 and combined in theSinglepackage.

Both single cell models have a positive (pin_p),a negative (pin_n) and an optional temperatureconnector (heatPort). If theheatPort is notused, it can be disabled and the model operatesat a fixed temperature (Toperational). The com-mon parameters of theStaticResistance andthe LinearDynamicImpedance cell models aregiven in Table 1. For theStaticResistance sin-gle cell model additionally to Table 1, the parame-ter given in Table 2 is necessary. Instead, for theLinearDynamicImpedance single cell model,additionally to Table 1 the parameters given in Table 3are necessary.

Table 1: Common input parametersof the StaticResistance and theLinearDynamicImpedance cell model.

name unit description

SOCini initial state of chargeOCV table V lookup table for the open circuit

voltageOCV vs. the state of chargeSOC

ttotal s total cell life timeQini C initial transferred chargeQtotal C total transferable chargeC0 C capacity atTref for Qabs = 0 and

t = 0

kC t C/s linear t dependency of the capacityC

kC QabsC/C linear Qabs dependency of the ca-

pacityCxC factor at which value of the capac-

ity C SOHC = 0

useHeatPort boolean variable for using the heatport

Toperational K operational temperature if the heatport is not used

Tref K reference temperaturealpℎaRs K

−1 linear temperature coefficient ofRs

alpℎaC K−1 linear temperature coefficient of the

capacityC

Table 2: Additional input parameter of theStaticResistance cell model.


Rsref Ω ohmic resistance at reference temperatureTref

The output variables both for theStaticResistance single cell model andthe LinearDynamicImpedance are given inTable 4 and the calculation of them are presented inthe following.

Starting fromSOCini the

SOC = SOCini −Q

C, (1)

with the removed charge

Q =

tstop∫

tstart

I(t)dt. (2)

The open circuit voltageOCV of a battery cellchanges withSOC and can be extracted from a lookuptableOCV table between the charging voltage limitCV L and the discharging voltage limitDV L. Thislinearly interpolated lookup table for a lithium ion (Li-ion) battery cell [5] is exemplarily shown in Fig. 4.


437

OC

V

+-

A

iCell

SOCOCVTable

Rs

iC

SOC

calculator

cycles

SOH

T

t

fixedTe

mpera

…

T=

TO

pe

rati…

clock

startTime=tstart

K

temp

pin_n

pin_p

heatPortintH…

(a) StaticResistance

OC

V

+-

A

iCell

iC

SOC

calculator

cycles

SOH

T

t

SOCOCVtable

selfDischarge

i

t

fixedTe

mpera

…

T=

TO

pe

rati…

num

SO

Ci

Rs

21

t

clock

startTime=tstart

K

temp

pin_n

pin_p

heatPortinter…

(b) LinearDynamicImpedance

Figure3: Single cell model with a static impedance (a) and with a variable number of variable RC elements, avariable ohmic impedance as well as with basic self discharge (b)

SOC

0 1

DVL

CVL

OCV

Figure 4: Linear interpolation of the measured opencircuit voltage (OCV) for different state of charge(SOC) of a Li-ion battery cell [5].

The total transferred charge betweentstart andtstop is

Qabs = Qini +

tstop∫

tstart

∣I(t)∣dt (3)

and the equivalent number of cycles

cycles = cyclesini +

tstop∫

tstart

∣I(t)∣

2 ⋅ Cdt, (4)

with

cyclesini =Qini

2 ⋅ C0+C(tstart,Qini,TℎeatPort)2

, (5)

relatesthe total transferred charge to the cell capacityC. Therefore, one cycle is equivalent to the chargetransfer (regardless in which direction) of one full dis-charge and one full charge of the current capacityC.

Both cell models consider basic aging, which can bedivided into calendaric aging and aging due to cycling.Calendaric aging of a cell is estimated from the timet and the absolute transferred chargeQabs defines theaging due to cycling. Aging of a battery mainly in-fluences the capacityC (decreasing) and the internalimpedance (increasing).

The cell capacity

C = (C0 + kC t ⋅ t+ kC Qabs⋅Qabs)

⋅ (1 + alpℎaC ⋅ (TℎeatPort − Tref )) (6)

is temperature dependent and decreases with increas-ing timet (calendaric aging) as well as with increasingtransferred chargeQabs (aging due to cycling).

The difference between theStaticResistanceand theLinearDynamicImpedance single cellmodel is the configuration of internal impedance onthe one hand and the self discharge on the other hand.

The StaticResistance single cell modelhas just a single, temperature dependent, ohmic


438

Table 3: Additional input parameters of theLinearDynamicImpedance cell model.


Isd0 A self discharge current atTref forQabs = 0 andt = 0

ksd t A/s linear t dependency of self dis-charge current

ksd QabsA/C linearQabs dependency of self dis-

charge currentalpℎasd K

−1 linear temperature coefficient ofself discharge currentIsd

Rs0 Ω series resistance atTref forQabs = 0 andt = 0

kRsSOC Ω linearSOC dependency ofRskRst Ω/C lineart dependency ofRskRsQabs

Ω/C linearQabs dependency ofRsnum number of series RC elements< Rd0 > Ω array of lengthnum of Rd atTref

for SOC = 0, Qabs = 0 andt = 0

< kRdSOC > Ω array of lengthnum of linearSOCdependency ofRd

< kRdt > Ω/s array of lengthnum of linear t de-pendency ofRd

< kRdQabs> Ω/C array of lengthnum of linearQabs

dependency ofRd< alpℎaRd > K

−1 array of lengthnum of linear tem-perature coefficient ofRd

< Cd0 > F array of lengthnum of Cd forSOC = 0, Qabs = 0 andt = 0

< kCdSOC > F array of lengthnum of linearSOCdependency ofCd

< kCdt > F/s array of lengthnum of linear t de-pendency ofCd

< kCdQabs> F/C array of lengthnum of linearQabs

dependency ofCdxZ factor at which value of the internal,

ohmic impedanceZ SOCZ = 0

impedance, modeled as

Rs =

Rsref ⋅ (1 + alpℎaRs ⋅ (TℎeatPort − Tref )). (7)

It does not consider impedance increase due to aging.

In contrast, theLinearDynamicImpedancesingle cell model has an ohmic impedance andnumserially connected RC elements for the transient be-havior of the electrodes of an electrochemical en-ergy storage as shown in Fig. 5 [6, 7]. All ohmicimpedances (Rs, Rd 1 . . . Rd num) are temperature de-pendent and have a linear dependency on state ofchargeSOC, on the timet (calendaric aging) as wellas on the transferred chargeQabs (aging due to cy-

Table 4: Calculated output variablesof the StaticResistance and theLinearDynamicImpedance cell model.


SOC stateof chargeOCV V open circuit voltageQabs C total transferred chargecycles number of equivalent cyclest s calendaric cell timeSOH state of healthSOS state of sicknessC C capacityV V cell voltage

cling). The serial resistorRs is modeledas

Rs =

(Rs0 + kRsSOC ⋅ SOC + kRst ⋅ t+ kRsQabs⋅Qabs)

⋅ (1 + alpℎaRs ⋅ (TℎeatPort − Tref )). (8)

Forn = 1 . . . num

Rd[n] = (Rd0[n]+

kRdSOC [n] ⋅ SOC + kRdt[n] ⋅ t+ kRdQabs⋅Qabs)

⋅ (1 + alpℎaRd[n] ⋅ (TℎeatPort − Tref )). (9)

and since there is no temperature dependency for ca-pacitances considered

Cd[n] = Cd0[n] + kCdSOC [n] ⋅ SOC

+ kCdt[n] ⋅ t+ kCdQabs[n] ⋅Qabs. (10)

Moreover, theLinearDynamicImpedance sin-gle cell model considers basic self discharge which islinear dependent on the temperature, the time (calen-daric aging) and the transferred charge (aging due tocycling).

While with theStaticResistance single cellmodel only the basic impedance behavior can be sim-ulated, theLinearDynamicImpedance can beused to simulate single cells very accurate if theparametrization work is well done.

The capacity as well as the internal impedance (onlywith the LinearDynamicImpedance single cellmodel) can change due to aging and the state of healthSOH (and accordingly the state of sicknessSOS)compares the current condition of a battery cell to itsideal (initial) condition. TheSOH is divided into theSOHC andSOHZ :

SOH = 1− SOS = SOHC ⋅ SOHZ , (11)


439

Rd1

Cd1

Rs

OCV Vcell

Rd2

Cd2

Rdnum

Cdnum

Icell

Figure 5: Battery model with one ohmic impedanceandnum serially connected RC elements.

as shown in Fig. 6.For a new cell,SOHC = 1 andSOHZ = 1 and

therefore alsoSOH = 1. When the capacityC de-creases (due to calendaric aging or aging due to cy-cling) to xC ⋅ C0 (e.g. withxC = 0.8), SOHC = 0.Hence,

SOHC =1

C0 ⋅ (1− xC)⋅ C −

xC1− xC

. (12)

Similarly, when the sum of all internal, ohmicimpedances

Z = Rs +Rd[1] +Rd[2] + . . .+Rd[num] (13)

increases (due to calendaric aging or aging due to cy-cling) toxZ ⋅ Z0 (e.g. withxZ = 2), where

Z0 = Rs0+Rd0[1]+Rd0[2]+ . . .+Rd0[num], (14)

SOHZ = 0. Therefore,

SOHZ =1

Z0 ⋅ (1− xZ)⋅ Z −

xZ1− xZ

. (15)

Fig.7 shows the dependency ofSOHC and SOHZ

from C andZ, respectively.

WithMeasurementIn the WithMeasurement packagethere are two cell models with measure-ment: The StaticResistance and theLinearDynamicImpedance. Both containbasic measurement and instances of the correspondingsingle cell model. Fig. 8 shows for example theLinearDynamicImpedance with measurement.The voltage, the current and the temperature of thesingle cell model are measured and provided with thesingleCellBus (cf. section 2.7). The cell modelswith measurement have the same connectors as thesingle cell models (pin_p,pin_n andheatPort)but have additionally thesingleCellBus. There-fore several instances of these can be connected

SOHZSOHC

SOH

00.2

0.40.6

0.81 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Figure 6: Dependancy of the state of healthSOHfrom SOHC andSOHZ .

0

C

1

0 C0xC ·C0

0.5

SOH

C

(a) SOHC

0

Z

SOH

Z

1

Z0 xZ ·Z0

0.5

C0

(b) SOHZ

Figure 7: Partial state of health with respect to thecapacityC and to the impedanceZ with paramters0 < xC < 1 andxZ > 1.

together (serially and in parallel) and the basicmeasurement of each cell is done.

The advantage of separating the cell models inSingle and WithMeasurement models showsup when it comes to stacks and the current ofeach cell should be measured. Fig. 9 shows theicons for theSingle andWithMeasurement forthe StaticResistance cell as well as for theLinearDynamicImpedance cell models with en-abledheatPort.

2.1.2 Stacks

Stacks arens serially connected cells andnp cells inparallel as shown in Fig. 10. TheStacks packageis structured in the same way as theCells package.There areSingle andWithMeasurement stackswhere each uses either theStaticResistance or


440

A

V T

i

T

v

+

--

fixedTe

mpera

…

T=

TO

pe

rati…

i

T

v

pin_p

pin_n

heatPort

sin

gle

CellB

us

inter…

Figure 8: Cell model with measurement. The mea-suredcurrent, temperature and voltage are provided tothe outside via thesingleCellBus

+

--

(a)

+

--

(b)

+

--

(c)

+

--

(d)

Figure 9: Icons for the StaticResistance(Single (a), WithMeasurement (b)) and forthe LiniearDynamicImpedance (Single (c),WithMeasurement (d)) cell model with enabledheat port.

theLinearDynamicImpedance cell models.TheStaticResistance single stack model is a

stack with all equal cells and therefore only one cellneeds to be calculated and parameterized. It is basi-cally aStaticResistance single cell model thatscales the parameters of the model components and be-haves likens ⋅ np equally parameterized instances ofStaticResistance single cell models. For exam-ple the value of the series resistance is thenRs0 ⋅ns/np

with the valueRs0 for a single cell. Hence, it is muchfaster than a model withns ⋅ np instances of equallyparametrized cell models.

The LinearDynamicImpedance sin-gle stack model hasns ⋅ np instances of theLinearDynamicImpedance single cell modeland the serial and parallel connections are textuallygenerated with loops:

equation//series connectionfor s in 1:ns-1 loopconnect(cell[s,1].pin_n,cell[s+1,1].pin_p);

end for;

1,1

2,1

3,1

ns,1

1,2 1,np

2,2

3,2

ns,2

2,np

3,np

ns,np

Figure 10: Battery stack withns seriallyandnp con-nected cells.

//parallel connectionfor p in 1:np-1 loopfor s in 1:ns loopconnect(cell[s,p].pin_p,cell[s,p+1].pin_p);connect(cell[s,p].pin_n,cell[s,p+1].pin_n);end for;

end for;//connector connectionfor s in 1:ns loopconnect(cell[s,1].pin_p,pin_pCell[s]);connect(cell[s,1].pin_n,pin_nCell[s]);

end for;//top connectionconnect(cell[1, 1].pin_p, pin_pPackage);//bottom connectionconnect(cell[ns, np].pin_n, pin_nPackage);//heatPort connectionconnect(cell[:,:].heatPort,heatPort[:,:]);

Each scalar parameter of theLinearDynamicImpedance single cell model isextended to an array of dimensionns×np and the arrayparameters of theLinearDynamicImpedancesingle cell model now have the dimensionns × np × num. Each cell in this stack can beparametrized individually and therefore also cellvariance in a stack can be simulated. All singlecell connectors and all temperature connector areconditionally available. Fig. 11 shows the iconsfor all different stack models. Therefore a separatethermal model can be considered. With the singlecell connectors and an additional model even cellbalancing can be simulated [8].

From each single stack model(StaticResistance andLinearDynamicImpedance) there is also aversion with measurement (StaticResistance


441

(a) (b)

ns

np

(c)

ns

np

(d)

Figure 11: Icons for the Single (a),WithMeasurement (b) StaticResistancestack models with enabled heat ports andthe Single (c), WithMeasurement (d)LinearDynamicImpedance stack modelswith enabled heat as well as single cell ports .

Table 5: Parameters of theVoltageCycling bat-tery management model.


ns numberof serially connected cellsnp number of parallel connected cellsIfinal A final charging switch off currentVmax V maximal cell voltageVmin V minimal cell voltagetc s delay time after chargingtd s delay time after dischargingini true for initial discharging

andLinearDynamicImpedance) in theStackspackage.

2.2 Battery Management

In the current version of the EES library there isa voltage cycling device (VoltageCycling) im-plemented. Fig. 12 gives an overview about theVoltageCycling model and its parameters aregiven in Table 5

It basically has two boolean outputs to operate withloads and charging devices (cf. section 2.3 and 2.4).ThecellBus can either be connected to a cell or astack. During charging ifVmax of any cell is reachedand the charging current of all parallel connected cellsis below Ifinal, the boolean outputdischarginggets true aftertc. WhenVmin of any cell is reachedduring discharging, the boolean outputcharginggets true aftertd. Therefore it is possible to cycle acell or a stack within its voltage limitsVmin andVmax

vMax

cycling

d…

vMin ch. f in.

ch.

yMax

yMin

u

vOut

i

vf inishediOut

sumsum

cellBus[:, 1]

cellBus[1, :]

discharging

charging

cellB

us

vMa

x

vMin

Figure 12: VoltageCycling model in theBatteryManagement package.

(in combination with a charging device and a load).

2.3 Chargers

In theChargers package there is a constant current,constant voltage (CCCV) charging device modeled. ACCCV charging device charges a battery with a con-stant current until itsCV L is reached (constant cur-rent phase). Then a constant voltage is applied and thecurrent decreases (constant voltage phase). The charg-ing device is switched off when the charging currentreaches the final charging switch off current (typically5% of the 1h discharging current).

When the boolean input of the modeled charg-ing device is true (e.g. the boolean charging outputcharging from theVoltageCycling model de-scribed in section 2.2), a current source provides a con-stant current. This current is controlled by a voltageinput (e.g. the maximal cell voltage in a battery stack),a reference voltage (parameterVmax) and limited bythe maximal charging current (parameterImax).

2.4 Loads

In theLoads package there are models to dischargea cell or a stack to cover typical lab situations (for ex-ample discharging a battery with a defined current orpower profile). In extension to the electrical currentsources (a current source parametrized with a negativecurrent can be used as a load) there are four differentloads considered:

∙ BooleanExternalControlledLoad

∙ BooleanConstantCurrent

∙ BooleanConstantPower


442

iOut

vOut

tempOut

vIn

iIn

tempIn

cellBus2

cellBus2

cellBus2cellBus1

cellBus1

cellBus1

cellB

us2

cellB

us1

(a) CellBus

sOCOut

sOHOut

cOut

cyclesOut

oCVOut

vOut

iOut

tOut

sOCIn

sOHIn

cIn

cyclesIn

oCVIn

vIn

iIn

tIn

controlBus2

controlBus2

controlBus2

controlBus2

controlBus2

controlBus2

controlBus2

controlBus2

controlBus1

controlBus1

controlBus1

controlBus1

controlBus1

controlBus1

controlBus1

controlBus1

contr

olB

us2

co

ntro

lBu

s1

(b) ControlBus

Figure 13: Structure of theCellBus (a) and theControlBus (b) with bus adaptors to all variables onthe bus (v, i, T for theCellBus andv, i, T , OCV ,SOC, SOH, cycles, C for theControlBus).

∙ SignalPower

All Boolean models have a boolean inputon whichfor example can be connected to the boolean outputdischarging of the VoltageCycling model(cf. section 2.2). Ifon is false the cell or the stackis not being discharged.

2.5 Sensors

The Sensors package provides models to esti-mate the energy, the charge and the absolute chargefrom/to a cell or a stack. The models providedin the Electrical.Analog.Sensors packagefrom theMSL are used and consequently extended.

2.6 Icons

In this package there are combined all icons used forthe packages.

Figure 14: Test cell at constant temperature in a cli-matechamber.

2.7 Interfaces

There are two buses available: TheCellBus and theControlBus. TheCellBus contains only measur-able variables such as the cell voltagev, the cell cur-renti and the cell temperatureT . It can be used whenlab situations are simulated and only measurable vari-ables are significant. It can also be used to test dif-ferent battery monitoring systems, based oni, v andT . TheControlBus contains the variables from theCellBus and additional the following:OCV , SOC,SOH, cycles andC. It could for example be the com-munication between the battery management systemand the control units in an electric vehicle simulation.

In the Interfaces package there are also busadapters to extract/inject all these variables (Realvalues) from/to theCellBus as well as from/to theControlBus. Figure 13 shows the structure of theCellBus and of theControlBus with the usage ofall bus adapters.

3 Examples

Two different examples are presented:First aLinearDynamicImpedance single cell

model with one (num= 1) RC element is param-eterized according to [9]. A realistic current profile,gained from the FTP72 cycle is continuously appliedto the parameterized model as well as to the real cell[10]. The FTP72 cycle is a standardized real life driv-ing cycle that simulates an urban route of12.07 km.


443

Vcell(V

)

measuredsimulated

t (min)

voltageerror(%

)

235 240 245 250 255 260

235 240 245 250 255 260

0

1

2

3.5

3.6

3.7

3.8

Figure 15: Comparison of the measured and simulatedcell voltage when applying the FTP72 current profileto the real cell and to parameterized model (top). Theerror refers to the measured voltage (bottom).

ns

np

stack

ground

p

switch

on

v

chargerload

on

cycling

dch.

ch.Vmin

Vmax

Figure 16: Simulation arrangement for cycling a bat-terystack.

This cycle is applied to a compact electric vehicle toextract the realistic current profile. The current profileis repeated starting from the full charged cell until itreaches discharging voltage limitDV L. This experi-ment is performed at constant temperature and Fig. 14shows the test cell in a climate chamber. Fig. 15 com-pares the simulated to the measured cell voltage. Theerror, related to the measured voltage, between thesimulated and the measured voltage stays below 2%at SOC ≈ 0.5 during one complete FTP72 cycle.Therefore the chosen model approach is appropriate.

For the second example, three serially connectedcells using theLinearDynamicImpedance stackmodel (without temperature and cell connectors) withdifferent capacities are simulated. The cell capacitiesareC1 = 35Ah, C2 = 40Ah, C3 = 45Ah and

Istack

(A)

t (h)Vcell

(V)

cell 1cell 2cell 3

0 1 2 3 4 5

0 1 2 3 4 5

3

4

5

-50

0

50

Figure17: Current profile and voltage response fromthe three cells from the example simulation.

parametrized using [5, 9]. The cells are cycled with a40A charging and a40A discharging current betweenCV L = 4.1V andDV L = 2.7V with a delayafter chargingingtc = 100 s and after dischargingtd = 50 s. Cycling means continuously chargingand discharging, which is a typical lab application forbatteries. Fig. 16 shows the simulation arrangementwith the charging device (charger), the battery man-agement (cycling), the battery stack (stack), thedischarger (load) and a switch (switch). Fig. 17shows the battery stack current and the voltage fromall three cells.

4 Conclusions

The Electric Energy Storage library, which is intendedto be included in the Modelica Standard Library, hasbeen described. The structure of the library and keyparameters as well as the equations of the models fordetermining the output variables have been presented.Two typical lab tests for batteries have been simulatedas an example to show the interaction of the modelsand to show the correctness of the model approach.

With the Electric Energy Storage library the user hasa powerful tool to cover various applications of energystorages with simulation. In combination with existinglibraries, (e.g. theSED) the behavior of electric energystorages and the interaction for example with the pow-


444

ertrain of an electric vehicle can be analyzed in detail.Futurework will focus on including of thermal mod-els of electirc energy storages and the coupling withthe electrical models.

References

[1] J. V. Gragger, H. Giuliani, C. Kral, T. Bäuml,H. Kapeller, and F. Pirker, “The smartelectric-drives library - powerful models for fast simula-tions of electric drives,”Proceedings of the 5thInternational Modelica Conference, vol. 2, pp.571–577, 2006.

[2] Modelica Association, “Modelica - a unifiedobject-oriented language for physical systemsmodeling, language specification version 3.2,”http://www.Modelica.org/, 2010.

[3] Dassault Systems, “Dymola 7.4,”http://www.3ds.com/, 2010.

[4] P. Fritzson,Principles of Object-Oriented Mod-eling and Simulation with Modelica 2.1. IEEEPress, Wiley-Interscience, 2004.

[5] EIG ePLB C020 lithium ion polymer celldatasheet, EIG, 2010.

[6] A. Jossen, “Fundamentals of battery dynamics,”Journal of Power Sources, vol. 154, pp. 530–538,2006.

[7] S. Buller, “Impedance-based simulation modelsfor energy storage devices in advanced auto-motive power systems,”Aachener Beitraege desISEA, vol. 31, 2002.

[8] M. Einhorn and J. Fleig, “Improving of ac-tive cell balancing by equalizing the cell en-ergy instead of the cell voltage,”Proceedings ofthe 25th International Battery, Hybrid and FuelCell Electric Vehicle Symposium and Exposition(EVS25), 2010.

[9] M. Einhorn, F. V. Conte, C. Kral, J. Fleig, andR. Permann, “Parametrization of an electricalbattery model for dynamic system simulation inelectric vehicles,”Proceedings of the IEEE Ve-hicle Power and Propulsion Conference (VPPC),September 2010.

[10] FTP72 Urban Dynamometer Driving Schedule(UDDS), U.S. Environmental Protection Agency.


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