( t) Fuel Cell Stack System. Fuel Cells. Reactant Flow Subsystem. Fuel Cell Characteristics: Polarization

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1 Stack Syem ater, electril energy and heat arise through the controlled coination of hydrogen and oxygen. s Polarization Cure V cell Anna Stefanopoulou Control Laboratory Uniersity of Michigan i H + H O + heat ork funded by US Army National Science Foundation United Technologies Co Ford Motor Company Toyota Uniersity of Michigan annaef@umich.edu 1 I I ia ack cell cell Vack n Vcell Pack n Vcell i Acell 1cell0.6x /cm 1cell (300cm 0.15 k (~7 cells per k Uniersity of Michigan Characteriics: Polarization Reactant Flow Subsyem Current drawn from the traction motor and auxiliaries V V Oxygen Hydrogen Pressure Temperature Humidity ( i( t, p( t, T ( t, ( t λ H O Outline: 1. Air Flow Control Modeling Limitations Control. Power Management 3. ater Dynamics Modeling Model Order Reduction Hardware Vales Blower Compressor Pump Ejector Flow meters Transducers Issues Merane Parasitic power Flooding Goal: Proide rapidly sufficient reactant flow slightly higher pressure than Cathode High thode pressure high FC power but high parasitic loss Excess Ratio Supply/Use.0 for Oxygen 1. for Hydrogen (purging necessary I Uniersity of Michigan 3 Uniersity of Michigan 4

2 Air Flow Control Syem Dynamics e consider a compressor drien 75k proton exchange merane fuel cell. The fuel cell ack and reactant flow models are based on electrochemiry, mass balances for lumped olumes in the ack and peripheral olumes, and rotational dynamics of compressor and motor. The OXYGEN EXCESS RATIO (OER λ O, in, rct is a conenient lumped ariable, which if regulated to a desired alue ensures adequate supply of oxygen in the fuel cell ack. patm Air Flow Control cm Air Hydrogen Pressure Control Hydrogen Tank Compressor Motor M Electrochemiry ni O M, rct O 4F Manifold filling dp sm R Tsm ( M V cp, in Supply Manifold k Air psm a, atm sm, in ( p Humidifier and Temperatire Controller in sm cp p I Stack p, in Hydrogen Air & ater out Mass balances dpo RT ( M V patm dp out Compressor motor dωcp J cp τ cm τ cp kt τ ( cm ηcm cm kωcp Rcm Stack oltage V n RT M V CD A RT T (, in f ( p, in, p atm, out, out ( E act ohm conc, rct Uniersity of Michigan Pukrushpan et al, ACC001, CSM004 5 Uniersity of Michigan Pukrushpan et al, ASME JDSMC004 6 Electril and Flow Subsyem Interactions The Control Problem FC air supply controller adjus the air flow through a compressor motor command to minimize oxygen aration periods. General control configuration Linear transfer functions The olume of supply manifold including humidifier and heat exchanger uses signifint lag or delay in regulating oxygen excess ratio inside the ack (Motozono et al. 003, Rodatz et al. 003, Pukrushpan et al. 004 High compressor control efforts n use inabilities due to the directly-coupled compressor power loss (Mufford and Strasky, 1999 Uniersity of Michigan K. Suh et al, IJRE Uniersity of Michigan 8

3 Intrinsic Limitations Exact feedforward ncellation is not possible Exact feedback ncellation is not possible Tradeoff between initial excursion and recoery time in Experimental Confirmation Nexa FC ack syem 1k, air cooled, low pressure Net current input Static feedforward with filter 0.4 sec in simulation 10 1 Diurbance response ratio R zw I net 0A ep Magnitude atic K uw τ f ilter 0.01 τ f ilter 0.1 τ f ilter 0.4 open-loop Frequency (rad/sec δ λ atic K uw τ filter 0.01 τ filter τ 0.4 filter open-loop Time (sec Uniersity of Michigan K. Suh et al, ea14 (10.50am ACC Uniersity of Michigan 10 Experimental Confirmation (cont. Load Goernor Stack oltage input A load goernor n be used if an auxiliary power source is aailable Slow down the FC load to meet conraints I net (k+1i net (k+β(i dem (k-i net (k, β [0,1] β 1: I net (k+1i dem (k β0: I net (k+1 I net (k Load Goernor Same air dynamics and control in FC syem Maximize β, at each ep, subject to the conraints: Surge Choke Oxygen Staration G net Uniersity of Michigan 11 Uniersity of Michigan Sun and Kolmanosky, ACC004 1

4 Time Response after Conraint Enforcement Compressor Conraints (Animation Operational conraints are enforced by slowing down the power response Actie Conraint Uniersity of Michigan Vahidi et al, ACC Uniersity of Michigan Vahidi et al, ACC Hybrid Electric Architecture Hybridization is essential for autonomy in artup and fa power response. The electric (oltage and current architectures of the hybrid PEMFC ehicle affect the hybridization leel and require different models and control tuning! High Voltage Battery Low Voltage Battery Hybridization: High Voltage Battery (series hybrid? The DC/DC conerter controller defines loadfollowing to load-leeling rategies. Minimizing battery power with load following libration is followed by large deiation in oxygen excess ratio Ford, US Patent 004/ A1. Ishikawa et al., IFAC MECHA04, A1 Uniersity of Michigan Rajashekara, SAE Uniersity of Michigan K. Suh et al, SAE

5 FC Usage - US06 Highway Control libration does NOT affect FUEL ECONOMY, but determine the HYBRIDIZATION LEVEL (FC/battery usage. Hybridization: Low Voltage Battery Aoiding the DC/DC conerter for the majority of power transfers Load following is a natural rategy for this configuration Small battery Uniersity of Michigan 17 Uniersity of Michigan 18 Heat & Temperature Subsyem Goal: Fa warm-up, no temperature oershoot ater Management Subsyem Goal: Maintaining merane hydrated, aoiding flooding, balancing water Hardware Pump Fan Heat Exchangers Flow meters Thermocouples I Hardware Vales Pumps Bubbler Hot plate Injection Chiller I Similar to ICE cooling? ICE Mechanil energy: 33% Energy in exh. gas: 33% Energy in cooling: 33% Temp difference:(10-30 o C 90 o C FCS 40% 10% 50% (80-30 o C 50 o C Sensitiity In a small ack 1 degree temperature error corresponds to 10.7% error in power (64/600 Muller and Stefanopoulou, ASME Science, May 005 Requirements High coolant flow or radiator area Fronk et al., SAE Uniersity of Michigan 19 RH meters Flow meters Transducers Interactions Air flow Hydration/Dryness Hydrogen purge Flooding Temperature Humidity Implitions Humidifition components 0% olume and weight of FCS Improper humidifition 0-40% FCS performance Uniersity of Michigan Buchi and Sriniasan (1997, J. Electrochem Soc. 144(8 0

6 Syem Model N w, Cathode Mass Balance, in, in in, out, out out, react + gen Anode Mass Balance w, an, in, out, react an, in an, out + mer mer M M ni M F Uniersity of Michigan 1 ni 4F Electrochemil Relationships ni F, react, react gen Merane apor mass transport i an, M Ancells nd Dw F t mer ( c c Modeling the Gas Diffusion Layer Effectie Diffusiity D i Di fi ( ε ( 1 s,s Vl / V p Effectie diffusiity is function of porosity, and saturation leel of liquid water in the GDL As liquid water accumulates, pores become partially blocked, and diffusion path for hydrogen/oxygen increases in tortuosity Nam and Kaiany, Int J Heat & Mass Transfer (46, 003 c j Concentration ( n j DjAfc y c j t c j D j s r y ( y + y Gas flow Capillary Flow of ater Caused by pillary pressure gradient As saturation of liquid increases, more paths for liquid flow are aailable, and flow increases A film of liquid is generated in the channels, reducing cell actie area Liquid olume Vl Vl g NL ( Vl t y r V M sat Uniersity of Michigan p ρ Reaction (in our se eaporation r γ ( p, /( RT c l Gas Diffusion Layer Model Summary Gas Diffusion Layer Model Summary Discretize GDL GDL Model Description Tunable Parameters Discretize each GDL into 3 layers Calculate concentrations and molar flows Keep track of olume of water in each layer Eimate cell oltage Uniersity of Michigan 3 c j Cell Voltage Time-arying Channel Boundary Conditions c j y Merane ater Transport dc j dp c Time-arying Boundary Merane/Cataly Reactions r V l s l n j y p c y p c n j Merane apor mass transport mer M An n Thickness of water layer 1 ml, an(3 Aapp Afc n ρ t A cells l wl I i app A V f ( ph,,,,, an, p, λm T iapp Uniersity of Michigan 4 D j d i F fc D w ( c c t an, Thickness of water layer between channel and GDL, rericts apparent actie area texp J app Lack practil means of directly measuring two phase flow in large ack, therefore use cell oltage to tune parameters by minimizing: T ( V ( τ Vˆ ( τ ( V ( τ Vˆ ( τ dτ

7 Experimental Hardware and Parameter ID Model Validation Model Inrumented Stack Experimental Set-Up 4-cell ack PEMFC (A fc 300cm.4 k max power 1. k continuous power at 0.6A/cm Real-Time DSpace and LabView data acquisition & control integration The model predicts the species concentrations across the gas diffusion layers, the apor transport across the merane, the degree of flooding in the electrodes, and eimates the resulting dey in cell oltage oer time. The model has two tunable parameters identified using the oerall ack oltage characteriics. Inputs to the model Anode Purges Thermoatic Temp Control Uniersity of Michigan 5 Uniersity of Michigan McKay et al, ASME IMECE Model Validation ~ Electrode Not Flooding Model Inputs Anode Purges Thermoatic Temp Control Model Model Outputs Uniersity of Michigan 7 Model Order Reduction Physics-based models proide accurate representation. They are important for the underanding of the fuel cell behaior Parameter diributed diffusion-reaction coupled with time arying boundary The complexity of model increases Parameter identifition (sensitiity, interconnection Control design (tuning, ructure Methodologies: Model order deduction (right nuer of discretization ilson and Stein 1995 (proper models Lou et al 1997, 1998 (actiity Model order reduction (reduce nuer of ates Kokotoic et al (singular perturbations Balas et al 1988 (residual mode filters Scherpen 1993 (balancing for nonlinear syems Lou et al 1998 (actiity Daoutidis, Chriofides, Armaou (inertial manifolds, Kerekidis 000 (order reduction of diributed reacting sys Hahn and Edgar 00 (minimal realization to able nonlinear plants Marsden et al 00 (subspace balanced truntion Uniersity of Michigan 8

8 Actiity Approach Use Actiity as an energybased measure of element importance: For a gien input and syem parameters, lculate for each element: Power ---> Actiity Index Sort the Actiity Indices in descending order. Keep the elements that account for a gien actiity leel, e.g., set threshold to 99%. Lou et al, ICBGM 1997 From 4 to 14 ates Oxygen and hydrogen concentration and liquid olume ates are lumped in one GDL olume! McCain, ASME FC 006 Uniersity of Michigan 9 Actiity Analysis Results for the 3-Section Discretization (75 90A ep, T 1000 sec Element Diffusion Sec1 Diffusion Sec Diffusion Sec3 Conc Channel Conc Sec1 Conc Sec Conc Sec3 Diffusion Sec1 Diffusion Sec Diffusion Sec3 Conc Channel Conc Sec1 Conc Sec Conc Sec3 Actiity E E E E % of Total Cathode Actiity 1.9J 0.410% 0.409% 0.406% 0.004% 0.001% 0.000% 0.000% 0.011% 0.506% 7.076% 0.031% 0.003% 0.003% 0.003% * Element Diffusion Sec1 Diffusion Sec Diffusion Sec3 Conc Channel Conc Sec1 Conc Sec Conc Sec3 Diffusion Sec1 Diffusion Sec Diffusion Sec3 Conc Channel Conc Sec1 Conc Sec Conc Sec3 Actiity Anode Actiity 1.J % of Total 0.434% 0.433% 0.434% 0.545% 0.06% 0.06% 0.06% 0.011% 0.011% 0.110% 0.033% 0.00% 0.00% 0.003% Some key elements hae negligible actiity! Uniersity of Michigan 30 * Control of Power Syems Our ability to optimize and control the reactant flow and pressure, ack temperature, and merane humidity is critil for the iability, efficiency, and robuness of the fuel cell ack syem in real world applitions Uniersity of Michigan 31 References 1. "Control of Power Syems: Principles, Modeling, Analysis, and Feedback Design," by Jay T. Pukrushpan, Anna G. Stefanopoulou, and Huei Peng, Springer Verlag, London, UK, ISBN , Sept 004. Control and Coordination of Air Compressor and Voltage Conerter in Load-Following s, K.-. Suh, A. G. Stefanopoulou, International Journal of Energy Research, in print. 3. Coordination of Conerter and Controllers, Kyung-on Suh and Anna G. Stefanopoulou, in Proceedings of 13th Mediterranean Conference on Control and Automation (MED'05, June Conraint Management in s: A Fa Reference Goernor Approach, A. Vahidi, I. V. Kolmanosky, A. G. Stefanopoulou, in Proceedings Amerin Control Conference, June Control-Oriented Modeling and Analysis for Automotie Syem, Jay T. Pukrushpan, Huei Peng, and Anna G. Stefanopoulou, Journal of Dynamic Syems, Measurement, and Control, 16 (1, pp. 14-5, March 004 and in Proceedings IMECE conference, IMECE00-DSC Control of Breathing, J.T. Pukrushpan, A.G. Stefanopoulou, H. Peng, IEEE Control Syems Magazine, 4( pp30-46, April, Analysis, Modeling, and Validation for the Thermal Dynamics of a Polymer Electrolyte Merane Sytems, E. A. Muller, A. G. Stefanopoulou, the ASME 3rd International Conference on Science, Engineering and Technology, May Mechatronics in Syems, A. G. Stefanopoulou, in Proceedings of International Federation of Automatic Control, 3rd Symposium on Mechatronic Syems, pp , 004 and to appear in IFAC Control Engineering Practice 9. Parameterization and Validation of a Lumped Parameter Diffusion Model for Stack Merane Humidity Eimation, D. A. McKay, A. G. Stefanopoulou, in IEEE Proceedings of 004 Amerin Control Conference, Model Predictie Control for Staration Preention in a Hybrid Syem, A. Vahidi, A.G. Stefanopoulou, and H. Peng, in IEEE Proceedings of 004 Amerin Control Conference, Dynamics of Low-Pressure and High-Pressure Air Supply Syems, S. Gelfi, A.G. Stefanopoulou, J.T. Pukrushpan, H. Peng, 003 IEEE Proceedings of the Amerin Control Conference, pp , Modeling and Control of PEM Stack Syems, Jay Pukrushpan, Anna Stefanopoulou, Huei Peng, in Proceedings of 00 Amerin Control Conference, pp , Anchorage, AK. Uniersity of Michigan 3