dynamic modeling of a solid oxide fuel cell system in modelica · dynamic modeling of a solid oxide...

Dynamic modeling of a solid oxide fuel cell system in Modelica

Daniel Andersson Erik Åberg Jonas EbornModelon AB, Ideon Science Park, SE-223 70 Lund, Sweden

Jinliang Yuan Bengt SundénDepartment of Energy Science, Lund University, Box 118, SE-221 00

Abstract

In this study a dynamic model of a solid oxide fuelcell (SOFC) system has been developed. The work hasbeen conducted in a cooperation between the Depart-ment of Energy Sciences, Lund University, and Mod-elon AB using the Modelica language and the Dymolamodeling and simulation tool. The objective of thestudy is to investigate the suitability of the Modelicalanguage for dynamic fuel cell system modeling.Fuel cell system modeling requires a flexible modelingtool that can handle electronics, chemistry, thermody-namics and the interaction between these. The core ofthe fuel cell is the electrolyte and the electrodes. Thecell voltage generated depends on the fluid molar com-positions in the anode and cathode channels. The inter-nal resistance varies depending on several cell proper-ties. The electrical current through the cell varies overthe cell area and is coupled to the rate of the chemicalreactions taking place on the electrode surface. Otherparts of the system that is also included in the modelare pre-processing of the fuel, combustion of the fuelremaining after passing through the cell and heat re-covery from the exhaust gas.A cell electrolyte model including ohmic, activationand concentration irreversibilities is implemented andverified against simulations and experimental data pre-sented in the open literature. A 1D solid oxide fuel cellmodel is created by integrating the electrolyte modeland a 1D fuel flow model, which includes dynamic in-ternal steam reforming of methane and water-gas shiftreactions. Several cells are then placed with parallelflow paths and connected thermally and electricallyin series. By introducing a manifold pressure drop, astack model is created. This stack model is applied in acomplete fuel cell system model including an autother-mal reformer, a catalytic afterburner, a steam genera-tor and heat exchangers. Four reactions are modeled inthe autothermal reformer; two types of methane steam

reforming, the water-gas shift reaction and total com-bustion of methane. Several simulations of systemsand individual components have been performed, andwhen possible been compared with results in the liter-ature. It can be concluded that the models are accurateand that Dymola and Modelica are tools well suited forsimulations of the observed transient fuel cell systembehaviour.Keywords: SOFC; fuel cell; system model; dynamicreaction; reforming

Nomenclature

ASR Area specific resistanceC Cross-plane resistance areaD Diffusion coefficientE Ohmic symmetry factorF Faraday constantG Gibbs free energyH Specific Enthalpyi Current densityi0 Exchange current densityJ Non-dimensional strip widthL Characteristic lengthne Number of exchanged electronsp Partial pressureP PressureR Universal gas constantr Reaction ratet ThicknessT TemperatureV VoltageX Cell pitch lengthy Molar fraction

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

593

α Charge transfer coefficientβ Parameter in Eq. (10)γ Pre-exponential factorη Voltage lossν Effectiveness factorρ Resistivityσ ConductivityΩ Denominator in reaction kinetics

1 Introduction

A solid oxide fuel cell is an electrochemical device thatproduces energy by oxidizing fuel from a replenish-able source. A number of fuels are usable in SOFCs,thanks to internal reformation of the fuel. The overallreaction releasing energy is oxidation of hydrogen

2H2 +O2→ 2H2O (1)

and thus the only byproduct produced aside fromheat is water. The working principle is that oxygenis ionized at the cathode electrode by electrons froman external electrical circuit. The oxygen ions diffusethrough the electrolyte to the anode electrode wherethey react with hydrogen gas, forming steam.

The solid oxide fuel cell is a high temperature fuelcell, most oftenly operating at 750 - 800C. The hightemperature removes the need for expensive platinumcatalyst and allows gases such as natural gas to beused as fuel directly. SOFCs are suitable for manytypes of system configurations. These include allsizes of combined heat and power applications, wherea stationary fuel cell system is used to provide bothelectricity and heat to buildings, etc. The power gen-eration in such systems can range from 2 kilowatts toseveral megawatts. They can also be used as auxiliarypower units, or in hybrid systems where a fuel cell iscombined with a gas turbine [1, 2, 3]. For all typesof fuel cells it is important to keep track of the fuelcomposition going into the cell, as this affects theperformance of the cell and in some cases can damagethe cell. In this study a model of a SOFC systemfueled with natural gas has been developed usingModelica and Dymola. Hydrogen is obtained from thenatural gas via reformation. The fuel is reformed in anautothermal reformer prior to entering the cell, as wellas during the flow through the cell channel; a processknown as internal reforming. Heat is recovered fromthe exhaust gas and is used to generate steam fromliquid water, as well as pre-heating the natural gas andair supplies.

Figure 1: Geometry of the cell for calculation of theohmic resistance

2 Single cell model

The ideal open circuit cell voltage is given by theNernst equation [4]:

VNernst =−∆G2F− RT

2Fln

(pH2O p0.5

re f

pH2 p0.5O2

)(2)

where ∆G is Gibbs free energy from the reaction andpre f is the standard pressure 0.1 MPa. When a cur-rent is applied, the cell voltage drops due to ohmic,activation and concentration losses, and thus the totalvoltage over the cell can be expressed as

V =VNernst −ηOhmic−ηact −ηconc (3)

2.1 Ohmic loss model

The calculation of the ohmic loss is based on the for-mulas for ohmic resistance of a cell with diagonal ter-minals, which is based on the integrated planar cellgeometry as shown in Figure 1 [5]. For this geometrythe area specific resistance is given by

ASR =CJ[

coth(J)+B(

J− tanh(

12

J))]

(4)

where C is the cross-plane resistance area, given by:

C = ρctc +ρccctccc +ρeltel +ρata +ρccatcca (5)

B is given by

B =E

(1+E)2 (6)

E =

(tcca

ρcca+

taρa

)−1( tccc

ρccc+

tcρc

)(7)


594

where E is the ohmic symmetry parameter. J is givenby

J =XL

(8)

L =

√√√√ ρeltel(tccaρcca

+ taρa

)−1+(

tcccρccc

+ tcρc

)−1 (9)

where X is the cell pitch length as indicated in Figure1 and L is the characteristic length [5]. The ohmic con-ductivities of the cell materials are temperature depen-dent, and commonly (e.g. [5]) calculated according to:

σ = ρ−1 = β1 exp

(−β2

T

)(10)

The voltage drop is then calculated from the cellcurrent density and the area specific resistance accord-ing to:

ηOhmic = ASR · i (11)

2.2 Activation loss model

Activation losses occur at both the anode and cathodeand derives from the fact that the reacting species inchemical reactions must overcome an energy barrier,i.e. the activation energy of the reaction. The activa-tion loss shows a nonlinear current dependency relatedto a parameter known as the exchange current density,i0. For current densities i < i0 the activation loss islow, typically in the order of 0.01 V, and for currentdensities i > i0 the activation loss grows according tothe Tafel equation:

ηact =RT

2αFln(

ii0

)(12)

For current densities i < i0 the activation loss is as-sumed to be proportional to the logarithm of the cur-rent density on the form:

ηact = k · ln i (13)

Activation losses occur at both the anode and cathodesides which have different exchange current densities,denoted i0,a and i0,c respectively. These are calculatedfrom the Arrhenius law and the composition of the re-acting gases according to [5]:

i0,c = γc

(pO2

pre f

)0.25

exp(−Eact,c

RT

)(14)

i0,a = γa

(pH2

pre f

)(pH2O

pre f

)exp(−Eact,a

RT

)(15)

2.3 Concentration loss model

Concentration losses accounts for the fact that whenreactions occur, reactants and products must diffusefrom the bulk flow to the reaction sites (and viceversa), through the porous electrodes. Because of thisthe actual pressure of the reactants and products dif-fer from those in the bulk flow, and the voltage overthe cell decreases. Typically this voltage drop is verylow until the current density reaches a limiting cur-rent. Above this limit the concentration loss will havesevere impact on cell performance and life time. Thevoltage drop is expressed as a function of the molarfractions yi of the gases at the reaction sites as [5]:

ηconc =−RTneF

[ln

(y∗H2

yOH2O

yOH2

y∗H2O

)+

12

ln

(y∗O2

yOO2

)](16)

where y∗ indicate molar fraction at the reaction site,and yO indicate molar fraction in the bulk flow. Themolar fractions at the reaction sites are calculated fromthose in the bulk, the current density through the elec-trolyte, the thickness of the anode and cathode, thebulk pressure and the diffusion coefficients [5], ac-cording to:

y∗O2= 1+

(yO

O2−1)

exp(

iRTtc4neFDO2P

)(17)

y∗H2= yO

H2− iRTta

2neFDH2P(18)

y∗H2O = yOH2O +

iRTta2neFDH2OP

(19)

2.4 Simplified cell model

In addition to the complete polarization model, mod-elling the internal losses physically as describedabove, also a simplified cell model was developed. Inthis model the internal losses are approximated by thefollowing empirical correlation for area specific resis-tance [4]:

ASR(T ) = ASR0 exp(

Ea

R

(1T− 1

T0

))(20)

where the constant ASR0 is the area specific resistanceat temperature T0. This simple model is not as accurateas the complete model, but gives shorter simulationtimes.

2.5 Implementation

The cell models are based on a template model con-taining common parts in all cell models. This includes


595

connectors for mass flow, heat transfer and electricalcurrent. Also a temperature state is introduced and en-ergy balance is defined. The fuel and air compositionshave large variations along the flow path due to reac-tions. To take this into account the cell is discretizedin the fuel flow direction. The cell model is preparedfor this by vectorizing all connectors and states thatvary along the flow path. There is no heat transfer di-rectly between the temperature states, this is coveredby heat transfer to the surrounding wall and fluids,which also have heat transfer to the surrounding tem-perature states. The cell current is also discretized inthe same way. For each element the current is coupledto the mass flow rate, and thereby the reaction rate atthe electrodes, according to Faraday’s laws of electrol-ysis.

3 Substack model

The cell model is connected to flow channel modelsin what we call a substack model. The flow channelmodels are volume models, discretized in flow direc-tion. Every discrete element has a unique fluid com-position and energy content. The anode channel in-clude reactions for steam reforming of methane (21)and water-gas shift (22).

CH4 +H2O↔CO+3H2 (21)

CO+H2O↔ H2 +CO2 (22)

In the channel model these reactions are characterizedby a reaction object which contains the stoichiometrymatrix and calculates the equilibrium constants of thereactions. The equilibrium constant is calculated fromGibbs free energy of the reaction, which is evaluatedfrom the medium model, and the partial pressuresof the reactants. The actual reaction rate is thencalculated in the channel model from the deviation ofthe fluid composition from the calculated equilibrium.Medium properties are calculated by medium modelsfrom Modelon’s CombiPlant library which is a modellibrary for combined cycle power plant simulation.These medium models are compatible with the onesin the Modelica Standard Library, but also includesa model ReactionProperties which calculatesproperties related to reactions, such as Gibb’s freeenergy due to reaction and reaction constants.

The two channel models are connected to a cellmodel according to Figure 2. The number of discreteelements are equal in the channel models and the cell

Figure 2: Graphical layout of the substack model

Figure 3: Graphical layout of the stack model

model. Thus the connections for mass and heat trans-fer are done per element, and each element in the cellmodel has a unique fuel and air state to evaluate. Thesubstack models any number of cells by multiplyingthe affected quantities with the number of cells. Thepurpose of the substack model is to model a numberof cells in the stack which can be assumed to have thesame operating conditions.

4 Stack model

The complete stack is modeled by connecting severalsubstack models, electrically and thermally in series,as shown in Figure 3. This model consists of a vec-tor of substack models, inlet manifold volumes withpressure drop, and outlet manifold volumes. The firstand last substacks in the vector are also thermally con-nected to thermal masses, modeling the heat capac-ity of the metal casing. The pressure drops in the in-


596

Figure 4: Layout of the implemented fuel cell system

let manifold volumes generates a unique pressure ateach substack inlet, corresponding to a U-type man-ifold form. The stack model thereby has 3D effectsfrom the heat boundary conditions and flow distribu-tion.

5 System model

The system configuration is based on that presented in[6], with some modifications. The system layout, pre-sented in Figure 4, includes an autothermal reformer(ATR), a steam generator and a catalytic burner.The outlet gases from the stack are fed through heatexchangers in order to pre-heat air and is then fed toa catalytic burner. The hot burner exhaust gas is usedto vaporize liquid water to steam, which is needed forthe reforming reactions in the ATR and stack and topre-heat the natural gas from ambient temperature.

5.1 ATR unit

A large number of reactions can occur in an ATR unit,but in order to reduce the number of calculations onlythe most significant reactions are considered; steam re-forming (23), (24), the water-gas shift reaction (25)and total combustion of methane (26) [7]:

CH4 +H2O↔CO+3H2,

∆H = 206.2 kJ/mol (23)

CH4 +2H2O↔CO2 +4H2,

∆H = 164.9 kJ/mol (24)

CO+H2O↔CO2 +H2,

∆H =−41.1 kJ/mol (25)

CH4 +2O2↔CO2 +2H2O,

∆H =−802.7 kJ/mol (26)

The presented values for ∆H of the reactions are validat 298 K. These values are not used explicitly in themodel, but are presented to show the mix of endother-mic and exothermic reactions taking place in the ATRunit, allowing it to operate without any need for ex-ternal heating or cooling systems. In our model en-thalpies are evaluated from the medium model and de-pends on the thermodynamic state and composition ofthe gas in the ATR unit. The model is implemented asa volume model with dynamic reactions. The reactionrates are calculated as [7]:

R1 =k1

p2.5H2

(pCH4 pH2O−p3

H2pCO

KI)× 1

Ω2 (27)

R2 =k2

p3.5H2

(pCH4 p2H2O−

p4H2

pCO2

KII)× 1

Ω2 (28)

R3 =k3

pH2

(pCO pH2O−pH2 pCO2

KIII)× 1

Ω2 (29)

R4 =k4a pCH4 pO2

(1+KCCH4

pCH4 +KCO2

pO2)2+

k4b pCH4 pO2

1+KCCH4

pCH4 +KCO2

pO2

(30)

Ω = 1+KCO pCO +KH2 pH2+

KCH4 pCH4 +KH2OpH2O

PH2

(31)

Here R1, R2, R3 and R4 are the corresponding reac-tion rates to reactions (23), (24), (25) and (26), re-spectively. k j is the Arrhenius reaction constant forreactions j = 1, . . . ,4 and is calculated using parame-ters from literature [7]. K j is the equilibrium constantfor reaction j and is listed in Table 1. The Van’t Hoffspecies adsorption constants Ki and KC

i for species iare calculated in a similar way according to [7]:

Ki = Koi× exp(−4Hi

RT) (32)

KCi = KC

oi× exp(−4HC

iRT

) (33)

Reaction, j Equilibrium constant,K j

1 KI = exp(−26830

Ts+30.114)[bar2]

2 KII = KI ·KIII[bar2]

3 KIII = exp(4400

Ts−4.036)[bar2]

Table 1: Reaction equilibrium constants


597

The determined reaction rates are used for calculat-ing the rate of formation of each substance. This isdone according to [7]:

rCH4 =−ν1R1−ν2R2−ν4R4 (34)

rO2 =−2ν4R4 (35)

rCO2 = ν2R2 +ν3R3 +ν4R4 (36)

rH2O =−ν1R1−2ν2R2−ν3R3−2ν4R4 (37)

rH2 = 3ν1R1 +4ν2R2 +ν3R3 (38)

rCO = ν1R1−ν3R3 (39)

The ν factors are effectiveness factors used toaccount for the intraparticle transport limitation. Theirvalues are set to ν1 = 0.07, ν2 = 0.06, ν3 = 0.7and ν4 = 0.05, which are average values obtainedfrom simulations of the various species inside the Nicatalyst pellet [8]. The low values for all reactionsexcept the water gas shift reflect the severe limitationon the catalytic conversion of methane to synthesisgas due to intraparticle diffusion in the catalystpellets. Calculation of effectiveness factors usingvarious methods and a comparison of their effect onsimulation results is presented in [9].

5.2 Catalytic burner

The catalytic burner model includes reactions for oxi-dation of methane (40), carbon monoxide (41) and hy-drogen (42) [4]:

CH4 +2O2→CO2 +2H2O (40)

CO+12

O2→CO2 (41)

H2 +12

O2→ H2O (42)

The implementation of the burner is based on avolume model with air and fuel inlet ports and an airoutlet port. It also has a port for heat flow to the envi-ronment and a boolean input for ignition signals. Theburner operates in one of two states, either burningor mixing, where the difference is the stoichiometrymatrix defining how the fuel components is mixedinto the air flow. The burner can be ignited if theair/fuel ratio is low enough and the ignition signal istrue. The burner is set to mixing state if the air/fuelratio gets too high.When combustion occurs a combustion rate defined asthe fraction of fuel burned is calculated dynamically.

Figure 5: Graphical layout of the hotbox

Figure 6: Graphical layout of the system model

5.3 System implementation

The system model is implemented in Dymola. Fig-ure 5 shows a hotbox model, which includes the ATRunit, the steam generator, a mixing volume for natu-ral gas and steam, and two heat exchangers for heatrecirculation. In Figure 6 the complete system modelis shown. It includes the hotbox and stack models, aswell as the catalytic burner, a heat exchanger and flowsources of natural gas, water and air. Note that the im-plemented system uses co-flow of fuel and air in thestack, counter-flow can be obtained by reversing theair flow direction.


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Parameter ValueAnode thickness 1 mmCathode thickness 70 µmElectrolyte thickness 10 µmCell pitch length 5 mmActive cell area 361 cm2

Fuel molar fraction 26.3% H2, 17.1% CH4,2.9% CO, 4.4% CO2,

49.3% H2OAir oxygen fraction 23%

Table 2: Cell geometry and fuel composition used insimulation

6 Results

Several simulations of the complete system and indi-vidual components are carried out in order to showtheir behaviour. Three of them are presented here. Inall simulations the cells were discretized with four el-ements along the fuel flow direction. The effects ofvarying the number of elements has been investigatedand four elements were found to give a good compro-mise between accuracy and computation time. Whenchanging from 4 to 50 elements the resulting differ-ence in cell voltage was 1.4%, and the difference intotal heat production was 1.8%. If the purpose of thesimulation is to locate hotspots or other local phenom-ena in the cell, more elements should be used. Thecell geometry parameters and fuel composition usedduring the simulations are presented in Table 2. Thevalues correspond to a 5 kW SOFC stack manufac-tured by Forschungszentrum Jülich, Germany, whichis described in [2, 4].

6.1 Substack with simplified cell model

In this simulation the substack with the simplified cellmodel is simulated with a constant inlet flow rate offuel and air. During the simulation the external cur-rent is increased linearly from 1 to 150 A, which corre-sponds to a cell current density of 27.7 to 4155 A/m2.The resulting cell voltage and power generation isshown together with simulation results from [4] in Fig-ure 7. The reference model is a 0D SOFC model wherethe Nernst potential is evaluated using an average fuelcomposition between the stack inlet and outlet. Themarked upper and lower limits were obtained usingthe fuel composition at the stack inlet and outlet re-spectively. The difference between the results are notvery large, but except for the different modeling ap-proaches also different handling of heat contributes to

Figure 7: Simulation results for: (a) cell voltage, (b)cell power generation. Results from [4] is included forcomparison.

the deviation. In the reference model the temperaturewas kept constant at 760C, whereas in our model thestack was cooled only by heat transfer between thegases and the inner surfaces of the fuel and air chan-nels. This resulted in an increasing stack temperaturewith increased current, varying from 750C to 810C.

6.2 Substack with complete cell model

In this simulation the substack with the complete cellmodel is simulated with a constant inlet flow rateof fuel and air. During the simulation the externalcurrent is increased linearly from 10 to 520 A,which corresponds to a cell current density of 277 to14404 A/m2 and fuel utilization of 30% to 100% forthis specific cell.

In Figure 8(a) the cell voltage versus the cell currentdensity shows the expected characteristics with a fastvoltage drop for low current densities, a close to linearbehaviour for medium current densities and a fasterdrop at high current densities. In Figure 8(b) the cell


599

Figure 8: Simulation results for: (a) cell voltage, (b)cell power production and heat production in the fourdiscrete elements

shows maximum power production at 13000 A/m2.Also shown is the heat production in every discreteelement, numbered from inlet to outlet. The heat pro-duction grows with increased current density and isroughly the same in each discrete element, except forvery high currents when the heat production in the4th element decreases rapidly. Figures 9(a)-(d) showsthe fuel and air composition in every discrete element,numbered from inlet to outlet. The gradual consump-tion of hydrogen, methane and oxygen, and productionof steam, can be observed.

6.3 Complete system transient

The system in Figure 6 is simulated with a constantexternal current of 150 A, corresponding to a cellcurrent density of 4155 A/m2. Three substacks areincluded, the middle one modeling 30 cells, andthe top and bottom ones modeling 10 cells each.The inlet flow rates to the hotbox are chosen suchthat a steam carbon ratio of 1.2 and a oxygen gascarbon ratio of 0.2 is achieved in the autothermalreformer, and the stack temperature is initialized at800C. The simulation results for the system transientbehaviour are presented in Figures 10 - 14. Thesubstacks are numbered in the fuel flow direction ofthe manifold volume, i.e. substack 1 has the highestinlet pressure. In Figure 10 the middle substack

Figure 9: Simulation results for: (a) anode methanecontent, (b) anode hydrogen content, (c) anode steamcontent, (d) cathode oxygen content. Results shownfor each discrete element, numbered from inlet to out-let.

shows the highest voltage per cell, due to the highertemperature than in the other substacks, as shown inFigure 11(a). The voltage losses in the cell decreasewith increased temperature due to higher conductivityof the cell materials, and increased exchange currentdensity which gives lower activation losses. The fuelutilization, shown in Figure 11(b), is highest in thelowermost substack, due to the pressure drop in themanifold volumes, which gives lower mass flow ratesin the subsequent substacks. Presented in Figure 12are the power and heat generation of the stack.

The resulting temperature profiles for the ATR unitand the catalytic burner are presented in Figure 13, to-gether with the conversion ratios of methane and oxy-gen in the ATR. The oxygen conversion ratio is 1 ex-cept for the the first seconds after start up. This isdesirable, as oxygen in the stack inlet fuel flow de-creases the overall system efficiency and destroys thestack as the Ni catalyst is oxidized. The high tem-perature of the burner is required for steam generationand pre-heating in the hotbox. The conversion ratio ofmethane in the ATR gives the stack inlet fuel composi-tion presented in Figure 14. The composition reachesits steady-state value quickly, and then varies slightlywith temperature. This composition complies with theresults from similar simulations in [4].


600

Figure 10: Dynamic simulation results for the voltageof the stack and individual substacks

Figure 11: Dynamic simulation results for: (a) tem-peratures of the substacks, (b) hydrogen utilization ofeach substack

7 Conclusions

It is concluded that Dymola and Modelica are veryuseful tools for fuel cell system modeling. The posi-tive aspects are mainly the equation based language,the multi domain possibilities, and the flexibility of anobject oriented structure.

All developed components were simulated indi-vidually for verification. The comparison of thesubstack with the simplified cell model is presentedin this paper. For the complete system it has not beenpossible to make relevant comparisons of absolutevalues, as geometry parameters and correlations fordifferent components comes from different sources.The objective of this study was to assure that resultsobtained are phenomenologically sound. This wasverified by running several simulations of the devel-oped components under various boundary conditionsand studying the influence on the results. The resultsof these simulations are presented in the originalthesis [10].

Figure 12: Dynamic simulation results for: (a) powergeneration of stack and individual substacks, (b) heatproduction of the substacks

Figure 13: Dynamic simulation results for: (a) burnerand ATR unit temperature, (b) ATR conversion ratioof methane and oxygen

As discussed in the abstract and introduction,modeling all relevant physics in a fuel cell systemrequires a flexible tool capable of including severalphysical domains in the same model. The equationbased language and possibility for acausal modelsallows for physical models, which is very usefulif components are to be reused in multiple systemdesigns with different purposes. The system modeldeveloped in this study includes the electrochemistryof the cell, dynamic chemical reactions in the ATRunit as well as in the cell flow channel and the catalyticburner. It also includes heat exchanger models and asmall electrical system. The system could easily beexpanded to include a physical model of an electricload, or redesigned to another system configurationusing the same component models.

One negative aspect can be mentioned. There isno automatic way to perform discretization of partialdifferential equations in Dymola, as some other non-Modelica based tools provide. The discrete equationsmust be stated directly by the user which makes itharder and more time consuming than using tools de-


601

Figure 14: Dynamic simulation results for the ATRoutlet fuel composition

veloped for this purpose. On the other hand this ap-proach does not impose any limitations on how dis-cretizations can be made and is thereby useable formany different applications.

References

[1] J. Larminie and A. Dicks. Fuel Cell Systems Ex-plained, Second Edition. Wiley, 2003. ISBN 0-470-84857-X.

[2] M. Kemm. Dynamic Solid Oxide Fuel Cell Mod-elling for Non-steady State Simulation of SystemApplications. PhD thesis, Division of ThermalPower Engineering, Lund University, 2006.

[3] S.H. Chan, H.K. Ho, and Y. Tian. Modellingof simple hybrid solid oxide fuel cell and gasturbine power plant. Journal of Power Sources,109:111–120, 2002.

[4] J. Saarinen, M. Halinen, J. Ylijoki, M. Noponen,P. Simell, and J.Kiviaho. Dynamic model of 5kW SOFC CHP test station. Journal of Fuel CellScience and Technology, 4:397–405, 2007.

[5] P. Costamagna, A. Selimovic, M. Del Borghi,and G. Agnew. Electrochemical model ofthe integrated planar solid oxide fuel cell (IP-SOFC). Chemical Engineering Journal, 102:61–69, 2004.

[6] E. Fontell, T. Kivisaari, N. Christiansen, J.-B.Hansen, and J. Pålsson. Conceptual study ofa 250 kW planar SOFC system for CHP appli-cation. Journal of Power Sources, 131:49–56,2004.

[7] M.H. Halabi, M.H.J.M. de Croon, J. van derSchaaf, P.D. Cobden, and J.C. Schouten. Mod-eling and analysis of autothermal reforming ofmethane to hydrogen in a fixed bed reformer.Chemical Engineering Journal, 137:568–578,2008.

[8] Ann M. De Groote and Gilbert F. Froment.Simulation of the catalytic partial oxidation ofmethane to synthesis gas. Applied Catalysis A:General, 138:245–264, 1996.

[9] Krzysztof Gosiewski, Ulrich Bartmann, MarekMoszczynski, and Leslaw Mleczko. Effect of theintraparticle mass transport limitations on tem-perature profiles and catalytic performance of thereverse-flow reactor for the partial oxidation ofmethane to synthesis gas. Chemical EngineeringScience, 54:4589–4602, 1999.

[10] Daniel Andersson and Erik Åberg. Dynamicmodeling of a solid oxide fuel cell system inModelica. Master’s thesis, Department of EnergySciences, Lund University, 2010.


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