Modeling and Control of a Proton Exchange Membrane Fuel Cell

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Ind. Eng. Chem. Res. 2009, 48, 8999–9005

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Modeling and Control of a Proton Exchange Membrane Fuel Cell System with Alternative Fuel Sources Wei Wu* and Che-Chuan Pai Department of Chemical and Materials Engineering, National Yunlin UniVersity of Science and Technology, Douliou, Yunlin 64002, Taiwan, R.O.C.

The aim of this work is to study the control of the proton exchange membrane (PEM) fuel cell stack system with alternative methanol fuel. An external circulating water flow design not only plays the role of heat exchanger, but also it is the one of reactants of the methanol reforming system. The open-loop tests show that the variation of water flow causes unsteady hydrogen production at the exit of fuel processing units (FPUs) to seriously affect the stack temperature and reduce the performance of the power system. Since the reforming-integrated fuel cell system has strongly nonlinear behavior, the model-free fuzzy control technique is used to ensure the stable output regulation. On the basis of the proportional-integral-derivative (PID) configuration with one tuning parameter, the closed-loop simulation shows that the controller reliability is satisfactory when unknown inlet perturbations and loads appear. 1. Introduction Fuel cells are widely recognized as one of the most promising technologies to become the powerful renewable energy in the future. The proton exchange membrane (PEM) fuel cells (FCs) are very suitable for residential or automotive applications.1 The reasons for this include the following: (i) they can operate at relatively low temperature; (ii) they have relatively high power density; (iii) their maintenance is simple. However, the performance of the PEMFC may be strictly affected by the unsteady hydrogen feed flow, operating temperature, and membrane humidity during high current/power demand and fast load changes. In addition, the source of pure hydrogen and the storage method may challenge commercial developments. Recently, liquid hydrocarbons such as methanol, ethanol, and gasoline are usually treated as alternative fuel streams,2 and control methodologies have been incorporated to improve fuel utilization and enhance power efficiency.3 Regarding the fuel-reforming system, the major concerns include the pursuit of hydrogen enrichment, adequate operating temperature, and heat energy optimization. Choi and Stenger4 provided some simulations of the integrated system with respect to effects of the reformer volume, temperature, and water addition. Wang and Wang5 used thermodynamic and exergetic analysis to optimize a methanol autothermal generating hydrogen system. Xu et al.6 provided a case study to observe the heat integration of the fuel cell power generation system. Notably, the heat exchanger network structures provided guidance through the optimization algorithm subject to constraints of the system. Regarding many facets of the fuel cell control problem, Woo and Benziger7 showed that proportional-integral-derivative (PID) feedback control of the reactant feeds could be incorporated to speed up the PEMFC system response to changes in load. Lauzze and Chmielewski8 provided a set of feedback structures for the power/temperature/relative humidity/oxygen controller. They indicated that the nonlinear and highly coupled nature of the PEMFC should increase the additional degrees of freedom to improve the control performance. Recently, specific model-based predictive control schemes have been adopted to show the control performance by using the fuzzy Hammerstein * To whom correspondence should be addressed. Phone: 886-55342601. Fax: 886-5-5312071. E-mail address: [email protected].

model9 or neural network techniques.10 For the control relevant modeling of the H2 fuel cell systems, it is usually considered to be a low-order and simplistic model.11 In this article, the fuel processing units (FPUs) mainly consist of a methanol reformer (MR), water gas shift (WGS) reactor, preferential oxidation (PROX) reactor, and water cooling systems. The chemical kinetics and the whole thermal effect are realized in the Matlab/Simulink environment which can predict the hydrogen amount and the temperature of the FPUs. Wu and Pai12 shows that the external circulating water flow from the stack to the reforming system is used to enhance the heat integration. However, the time-varying hydrogen production rate as well as strictly nonlinear dynamics usually degrades the performance of the reforming-integrated fuel cell system. Within the single-input single-output (SISO) feedback control framework, model-free fuzzy control is verified as a feasible control implementation. 2. PEM Fuel Cell System Considering an individual PEMFC stack system which consists of 35 cells in series shown in Figure 1A, the pure hydrogen is fed to the anode, its excess gas can be recirculated, and the system is internally humidified by a circulating water system. If all gases are ideal and the stack system is adiabatic, then the differential equations of the stack system according to the principles of mole conservation and energy balance are written by Va dPH2 RT dt Vc dPO2 RT dt dT ) Ct dt

nI 2F nI - Pamb) 4F

) n˙HFC2,in - ka(PH2 - Pamb) ) n˙OFC2,in - kc(PO2

nI ∆H - 35VfcI - Ct(T - Tamb)/ 2F (T - Tc,in) - (T - Tc,out) τ - (hcond + hconvI) ln((T - Tc,in)/(T - Tc,out)) dTc,out FwVwCpw )m ˙ cwCpw(Tc,in - Tc,out) + dt Tc,in + Tc,out UA T 2

(

10.1021/ie801460t CCC: $40.75  2009 American Chemical Society Published on Web 08/25/2009

)

(1)

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Ind. Eng. Chem. Res., Vol. 48, No. 19, 2009

( 498T )) +

(

Eact ) β1 + β2T + β3T ln 1.97 × 10-7PO2 exp

β4T ln(I)

(5)

where the parametric coefficients β1 ) -0.948 β2 ) 0.00286 + 0.0002 ln(Afc) +

(

( -77 T ))

4.3 × 10-5 ln 9.174 × 10-7PH2 exp

β3 ) 7.6 × 10-5

(6)

β4 ) -1.93 × 10-4

and the ohmic overvoltage is given by

[ [

Vohm )

Figure 1. (A) Diagram of the individual PEMFC stack system with external cooling device. (B) Diagram of the reforming-integrated power generation system.

According to above system formulations, the current density, cell temperature, hydrogen, and oxygen partial pressure directly influence the stack system.

The methanol is treated as a hydrogen-rich fuel stream of the FPUs in which the configuration is associated with the increase of H2 production and the reduction of CO emission. Under conditions of ideal gas and single phase,7 the components of the FPUs are formulated as follows: 3.1. Methanol Reformer (MR). The MR reactor would dominate the hydrogen production. The catalysts Cu/ZnO catalyze the steam reformation of methanol to produce H2 and CO2 well. The reaction networks and kinetics are given as follows: (i) steam reforming

Tamb ) 25 °C Tc,in ) 25 °C UA1 ) 241 W K-1 UA2 ) 856 W K-1 Cpw ) 4.184 kJ kg-1 K-1 Cpm ) 41.84 kJ kg-1 K-1 Fw ) 1000 kg m-3 Fm ) 1000 kg m-3 τ ) 2.06 Afc ) 232 cm2 lm ) 178 × 10-4 cm R ) 8.314 J mol-1 K-1 Cdl ) 0.035 × 232 F kc ) 0.065 mol s-1 atm-1

cat

where the state variables include the hydrogen pressure PH2, the oxygen pressure PO2, the stack temperature T, and the outlet water temperature Tc,out. The description of other symbols are given in the Notation section. Parameter values are also given in Table 1. Moreover, the cell voltage Vfc is given by the following equation: Vfc ) E - Vact - Vohm

(7)

3. Fuel Processing Units

Table 1. Parameter Values for the Reforming-Integrated Power System Va ) 0.005 m3 ka ) 0.065 mol s-1 atm-1 n˙HFC2,in ) 1.33 × 10-5 m3 s-1 Pamb ) 1 atm Vc ) 0.01 m3 Vm ) 0.01 m3 Vw ) 2.5 × 10-3 m3 n˙OFC2,in ) 2 × 10-3 m3 s-1 F ) 96485 ∆H ) 285.5 kJ mol-1 Ct ) 17.9 kJ °C-1 hcond ) 35.55 W °C-1 hconv ) 0.025 W °C-1 A-1 λ ) 12.5

( ) ( )( ) ] ( )] [ ( )]

I T 2 I 2.5 + 0.062 Ilm Afc 303 Afc I T - 303 Afc 11.866 - 3 exp 4.18 Afc T

181.6 1 + 0.03

(2)

where the open circuit cell potential E via the Nernst equation is described by

MeOH + H2O {\} CO2 + 3H2, ∆H1 ) 49.5 kJ/mol the reaction rate r1 (mol gcat-1 s-1) is shown by

(

Keq,R ) 1.849 × 1010 exp -

56087 RT

)

PCO2PH23

EqR ) 1 -

Keq,RPMeOHPH2O 81000 r1 ) 6.75 exp PMeOHEqR RT1

(

(8)

)

(ii) partial oxidation of methanol RT E ) 1.229 - 8.5 × 10-4(T - 298.15) + ln[PH2(PO2)0.5] 2F (3) the activation overvoltage Vact is described by a first-order dynamic dVact EactI I ) + dt Cdl VactCdl Notably, the activation drop Eact is defined by

cat 1 MeOH + O2 98 CO2 + 2H2, ∆H2 ) -192kJ/mol 2

the reaction rate is r2 (mol gcat-1 s-1) is shown by

(

kOX,M ) 0.466 exp (4)

r2 ) kOX,MPMeOHPO2 (iii) methanol decomposition

65000 RT2

0.5

)

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Ind. Eng. Chem. Res., Vol. 48, No. 19, 2009

(

cat

r6 ) -2.053 × 102 exp

MeOH {\} CO + 2H2, ∆H3 ) 90.6 kJ/mol the reaction rate is r3 (mol gcat-1 s-1) is shown by

(

Keq,D ) 1.718 × 1014 exp EqD ) 1 -

95418 RT

)

PCOPH22

(10)

Keq,DPMeOH 76000 r3 ) 1.12 exp PMeOHEqD RT3

(

)

cat

CO + H2O {\} CO2 + 2H2, ∆H4 ) -41.15 kJ/mol

(14)

Remark 1. Since all reactions in FPUs are temperaturedependent, the operating temperature dominates the H2 production rate and the efficiency of FPUs. In our approach, every reactor temperature is assumed as the same as the temperature of FPUs (Tm), i.e., Tm ) T1 ) T2 ) ... ) T6. The energy balance of PFUs, assuming constant volume (Vm), heat capacity (Cpm), and density (Fm), is described by FmCpmVm

By each of the reactions above, the equilibrium constants are temperature-dependent and experimentally determined.2 Notably, MeOH, H2O, and O2 are treated as the feeds of MR. 3.2. Water-Gas Shift (WGS) Reactor. Since the undesired CO and desired H2 are produced in the MR reactor simultaneously, a WGS reactor in which the mixture of CO and H2 takes part in the reversible exothermic shift reaction to carry out the CO reduction and produce more hydrogen. The WGS reaction is given by

)

-18742 PO20.5 RT6

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dTm ) FfFmCpm(Tf - Tm) + dt

(∑ ) 6

∆Hiri Vm -

i)1

UA2(Tm - Tc,out)

(15)

Notably, the thermal model cannot describe the temperature variation of and individual unit in the FPUs. The FPUs is simplified to a reactor system, so the heat transfer connections of every unit as well as the operating condition for every unit are all neglected. Moreover, the inlet concentration is composed of 1 mol CH3OH with 1.2 mol O2. The feed temperature Tf ) 27 °C and the feed flow Ff ) 0.5 m3/s. In general, the reforming system was precisely described with distributed models.2,14 In our approach, the FPUs are integrated as a simple hydrogenproduced apparatus.

Referring the issue in the work of Murshed et al.,13 the equilibrium constant Kwgs is expressed as a function of temperature Kwgs ) exp

(

5693.5 + 1.077 ln(T4) + 5.44 × 10-4T4 T4 49170 1.125 × 10-7T42 - 13.148 (11) T42

)

and the WGS reaction rate r4 (mol gcat-1 s-1) is found by the following equation MR MR MR (Kwgs - 1)r42 - (n˙HMR + n˙CO + n˙HMR )r + n˙CO n˙H2O ) 0 2 2O 4 (12) -1 -1 -1 ˙ MR ˙ MR where n˙MR H2 (mol s ), n CO (mol s ), and n H2O (mol s ) represent the molar flow rates of H2, CO, and H2O in the MR reactor, respectively. 3.3. Preferential Oxidation (PROX) Reactor. Choi and Stenger4 showed that a PROX reactor is used to reduce the CO amount at the exit of WGS reactor and burn a few H2 to supply the heat of reaction in FPUs. (i) CO oxidation

cat 1 CO + O2 98 CO2, ∆H5 ) -282.99kJ/mol 2

and the corresponding reaction rate is r5 (mol gcat-1 s-1) shown by

(

r5 ) -3.528 × 102 exp

)

-33092 PO20.5PCO-0.1 RT5

(13)

(ii) H2 oxidation cat 1 H2 + O2 98 H2O, ∆H6 ) -285.84kJ/mol 2

and the corresponding reaction rate is r6 (mol gcat-1 s-1) shown by

Figure 2. Open-loop responses of the reforming-integrated power generation system in regard to step changes of water flow and methanol feed.

Furthermore, the open-loop test for above reformingintegrated fuel cell system is demonstrated. The water or steam is not only treated as reactants of MR and WGS units, but also its heat duty may affect the temperature of FPUs as well as the hydrogen production, i.e., hydrogen pressure at the anode. Figure 2A shows that step changes of the water flow obviously stimulate the stack temperature. Figure 2B depicts that step changes of methanol flow strongly changing the hydrogen pressure. Besides, both figures imply that the system has strongly

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Figure 3. Simulink blocks for the fuzzy PID controller.

nonlinear behaviors, and the changeable water flow could obviously affect the stack temperature as well as the hydrogen production. 4. Fuzzy PID Control According to the open-loop test in Figure 2, the water flow is appropriately treated as a manipulated variable. The nonlinear dynamic behavior and unsteady hydrogen production rate may obviously affect the performance of power generation system. In our approach, the stack temperature is considered as a controlled variable and a fuzzy PID controller15 is used to cope with the temperature regulation problem. The presented control scheme is realized in the Matlab/Simulink depicted in Figure 3 in which the fuzzy logic control block consists of a specified fuzzy rule and a Λ-type membership function fΛ, i.e. a triangular fuzzy variable, is described by

{

xbµ(x) ) x b0,

a , ifa e x e b a c , ifb e x e c c otherwise

(16)

where x represents the input. In Figure 4A, two inputs and one output membership were scaled between the [-1, +1] interval. Moreover, the input-output mapping as fuzzy inference system is depicted in Figure 4B according to the if-then relationship between the membership functions vs both inputs Ei and CEi. In Table 2, the fuzzy set of linguistic variables is defined as follows: NB (negative big), NM (negative medium), NS (negative small), ZE (zero error), PS (positive small), PM (positive medium), and PB (positive big). On the basis of the present fuzzy PID control structure, the controller output is expressed by n

Un ) K

∑f

Λ(KpEi, KdCEi)

× Ts

(17)

i)1

where Kp and Kd are tuning parameters, the error Ei and change in error CEi represent the inputs of the fuzzy logic controller, and Ts is the sampling period. Moreover, the fuzzy controller is based on intuition and experience instead of a system model, the rule base (Table 2) and the shape of the membership functions are refined through simulation and testing. 4.1. Control of a Fuel Cell System. For an individual PEMFC system, the stack temperature is affected by manipulating water flow. On the basis of the fuzzy PID control scheme, Figure 5 shows that the output tracking response can be achieved at the desired operating temperature of the stack system by tuning a parameter K, and other tuning parameters Kp ) 0.1 and Kd ) 30. Notably, the larger value of proportional gain K cannot effectively improve the output tracking performance, and it may cause the large oscillation on the manipulation of water flow rate. When the current

Figure 4. (A) Membership function in regard to fuzzy inference system (FIS) variables. (B) Input-output mapping for fuzzy logic controller in regard to the number of fuzzy set 3 × 3.

Ind. Eng. Chem. Res., Vol. 48, No. 19, 2009

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Table 2. Symmetric Arrangements of Fuzzy Rule Base Using 3 × 3 Linguistic Variables Ei

CEi

NS ZE PS

NS

ZE

PS

PM PS ZE

PS ZE NS

ZE NS NM

load is step changed from 40 to 50 A at the operating temperature 75 °C, Figure 6 shows that the stable temperature regulation can be achieved by tuning the same values of parameter K. The large value of proportional gain can improve the performance of temperature regulation. If a large load change from 40 to 60 A is demanded, then Figure 7 depicts that the stable temperature regulation can be achieved using another small value of K. Regarding both figures, Figures 6 and 7, the fuzzy control scheme not only ensures no offset tracking of the system in the face of step changes of current load, but also it verifies the controller reliability in regard to disturbance attenuation. 4.2. Control of a Reforming-Integrated Fuel Cell System. For a reforming-integrated fuel cell system, Figure 2 has indicated that the stack temperature as well as hydrogen pressure at the anode are simultaneously affected by manipulating the water flow. Using the fuzzy PID control with the same tuning parameters, Figure 8 shows that the set point tracking and the temperature regulation of the power system in the face of a time-variant hydrogen pressure can be successively achieved. Moreover, Figure 9 shows that the stable temperature regulation can be achieved while a timevarying hydrogen pressure suddenly increases. Notably, the larger K of fuzzy control can improve the output regulation performance regardless of a sudden increase or decrease in hydrogen pressure.

Figure 6. Fuzzy PID control of the individual stack system in the face of a 10 A increase of current demand: (A) stack temperature regulation; (B) corresponding water flow rate.

Figure 7. Fuzzy PID control of the individual stack system in the face of a 20 A increase of current demand: (A) stack temperature regulation; (B) corresponding water flow rate. Figure 5. Fuzzy PID control of the individual stack system in the face of set point change: (A) responses of the stack temperature; (B) corresponding water flow rate.

By the above closed-loop simulations, the tuning procedure of the fuzzy controller is quite simple, and it can effectively reduce the temperature variation of a reforming-integrated fuel

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hydrogen production. This kind of a time-varying perturbation of hydrogen pressure easily reduces the effectiveness of the fuel cell system. 5. Conclusions In this paper, the fuzzy PID control framework is successfully implemented to the reforming-integrated fuel cell system. The dynamic modeling of FPUs including heat exchange connections is not only reduced but the preheater and postcombustion as heat sources of FPUs at the start moment are also neglected. Under the new energy and material balances for the reforming system, its modeling can predict the operation of the stack system in the face of current load and unsteady hydrogen flow. The closed-loop simulation indicates that the unsteady and fluctuant hydrogen flow can obviously change the stack temperature, and the single-loop fuzzy logic control implemented can ensure satisfactory control performance and robustness. Acknowledgment The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC 97-2221-E-224-018. Notation Figure 8. Fuzzy PID control of the reforming-integrated power system in the face of a set point change and low hydrogen pressure: (A) responses of the stack temperature; (B) corresponding hydrogen pressure at the anode; (C) corresponding water flow rate.

Afc ) effective cell area [cm2] Cpw ) heat capacity of water [kJ kg-1 K-1] Cpm ) heat capacity of FPUs [kJ kg-1 K-1] Cdl ) double layer capacitance [F] Ct ) thermal capacitance [kJ °C-1] F ) Faraday constant [C mol-1] hcond ) parameter for conduction property of heat exchanger [W °C-1] hconv ) parameter for convection property of heat exchanger [W °C-1 A-1] ka ) anode flow constant [mol s-1 atm-1] kc ) cathode flow constant [mol s-1 atm-1] lm ) membrane thickness [cm] n˙HFC2,in ) hydrogen inlet flow rate n˙OFC2,in ) oxygen inlet flow rate [mol s-1] Pamb ) ambient pressure [atm] R ) universal gas constant [J mol-1 K-1] Tamb ) ambient temperature [°C] Tc,in ) inlet water temperature [°C] UA1 ) stack heat transfer coefficient [W K-1] UA2 ) heat transfer coefficient of heat exchanger [W K-1] Va ) anode volume [m3] Vc ) cathode volume [m3] Vm ) volume of FPUs [m3] Greek Letters λ ) membrane resistivity parameter Fw ) water density [kg m-3] Fm ) the mean density of FPUs [kg m-3] ∆H ) hydrogen enthalpy of combustion [kJ mol-1] τ ) time constant

Figure 9. Fuzzy PID control of the reforming-integrated power system in the face of increasing hydrogen pressure: (A) responses of the stack temperature; (B) corresponding hydrogen pressure at the anode; (C) corresponding water flow rate.

cell system by tuning one parameter. In addition, the developed FPUs with an external circulating water flow will cause unsteady

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(11) Wu, W.; Xu, J. P.; Hwang, J. J. Multi-loop nonlinear predictive control scheme for a simplistic hybrid energy system. Int. J. Hydrogen Energy 2009, 34, 3953. (12) Wu, W.; Pai C. C. Control of a heat-integrated proton exchange membrane fuel cell system with methanol reforming. J. Power Sources 2009, 194, 920. (13) Murshed, AKM M.; Huang, B.; Nandakumar, K. Control relevant modeling of planer solid oxide fuel cell system. J. Power Sources 2007, 163, 830. (14) Sommer, M.; Lamm, A.; Docter, A.; Agar, D. Modelling and dynamic simulation of a fuel cell system with an autothermal gasoline reformer. J. Power Sources 2004, 127, 313. (15) Jantzen, J. Tuning of Fuzzy PID Controllers; Technical University of Denmark, Department of Automation, Lecture notes, 1998.

ReceiVed for reView September 29, 2008 ReVised manuscript receiVed August 10, 2009 Accepted August 11, 2009 IE801460T