Modeling and Simulation of a Modern Pem Fuel Cell System

Recent trends and advances in hydrogen/air Proton Exchange Membrane Fuel Cells (PEMFC) are incorporated into a dynamic control oriented model. This type of model is important for development of control systems for PEMFC powered transportation where unpredictable and widely varying changes in power demand can be expected. Self humidification and low pressure operation are the two major changes to past systems. As a result, a high pressure air compressor, air cooler, and inlet gas humidifiers are no longer required. Also, the likelihood of cathode flooding is reduced. The overall fuel cell model consists of four basic sub-models: anode, cathode, fuel cell body, and cooling. Additionally, the oxidant supply blower, cooling pump, and cooling fan are explicitly incorporated. Mass and energy conservation are applied to each using a lumped parameter control volume approach. Empirical modeling is minimized as much as possible, however it is necessary for model manageability in a control context. Interactions between each subsystem and balance of plant components are clearly defined. The overall model is capable of capturing the transient behavior of the flows, pressures, and temperatures as well as net output power. The influence of the charge double layer effect on transient performance is also explored. Numerical simulations of the system are presented which illustrate the usefulness of the model. Finally, future control work is described. ∗Address all correspondence to this author. NOMENCLATURE A Area (cm2, m2) cn Fuel cell voltage equation constant cp Average specific heat at constant pressure (J/kg K) cv Average specific heat at constant volume (J/kg K) C Equivalent capacitance of fuel cell body (F) CS Control surface CV Control volume E Open circuit voltage (V) Eth Thermal neutral reversible voltage (V) fn Pressure rise equation constant h Specific enthalpy (J/kg) hc Convective heat transfer coefficient (W/m2K) i Current density (A/cm2) J Rotational inertia (kg m2) k Ratio of specific heats, cp/cv KF Nozzle flow efficiency coefficient m Mass (kg) M Molar mass (kg/gmol) n Unit vector normal and away from control volume surface N Number of p Pressure (Pa) Q Energy or heat produced (J) R Resistance (Ohm) T Temperature (K) u Specific internal energy (J/kg K) V Single fuel cell voltage (V) V Velocity (m/s) V0 Activation polarization empirical constant 1 Copyright c © 2006 by ASME Va Activation polarization empirical constant Vi Voltage (V) Vi Volume (m3) W Work (J) ∆ Difference η Efficiency λ Air stoichiometry ratio ρ Material density (kg/m3) φ Relative humidity Φ Flux Linkage (Vs/rad) ω Angular velocity (rad/s) Subscripts act Activation air Dry air amb Ambient conditions an Anode ca Cathode clt Coolant co Crossover dyn Dynamic f Liquid fluid f an Cooling fan f c Fuel cell f s Fuel supply ha Humidified air hex Heat exchanger H2 Hydrogen H2O Water m Motor mbr Membrane N2 Nitrogen ohmic Resistance os Oxidant supply out Control volume outlet O2 Oxygen pl Poles pmp Pump reg Regulator rqs Rotor reference frame, stator q-axis rx Reaction s Stator v Vapor → To INTRODUCTION The PEMFC is a device that is able to produce electrical power via oxidation and reduction half reactions that are separated in space. Oxidation occurs at the anode, reduction at the cathode. In this case, the fuel and oxidant are hydrogen gas and air, respectively. There is no requirement that either the air or hydrogen be dry. The chemical reactions that occur: Oxidation : H2 → 2H+ +2e− (1) Reduction : 1 2 O2 +2e−+2H+ → H2O (2) Overall : H2 + 1 2 O2 → H2O (3) The overall fuel cell reaction is also known as the Faradic reaction. A cross section of a typical fuel cell is shown in Fig. 1. Individual cells are joined in series into stacks, anode to cathode bipolar plate, to increase the voltage output. Hydrogen enters the anode channels, permeates the gas diffusion layer and undergoes oxidation with the help of a catalyst that traditionally includes platinum. Electrons are then free for work while the hydrogen ions or protons travel through the proton exchange membrane. At the cathode, hydrogen ions, electrons, and oxygen from the air are combined by reduction into water, again with the help of a catalyst that typically contains platinum. The Faradic reaction product water and the remnants of the air are exhausted via the cathode channels. A charge can build up at the interfaces between the anode/membrane and cathode/membrane that behaves much like an electrical capacitor. This is known as the charge double layer. Performance of the fuel cell depends on many factors including the partial pressures of hydrogen and oxygen, temperature, and membrane humidity or water content. The complete PEMFC system has not only a fuel cell stack, but also fuel and oxidant supply devices, valves, and cooling components. PEMFC systems have emerged as a possible replacement for internal combustion engines due to their efficiency, zero emission potential, and use of renewable fuels. Those used in transportation applications will experience unpredictable and widely varying power demand changes just like internal combustion engines in the majority of present vehicles. To satisfy the needs of dynamic performance, the PEMFC system will have to have a suitable control system able to manage its operation. However, before the design of any good control system there must also be a good control model to work from. Models for control development attempt to capture the essence of the system dynamics in the simplest possible manner. Mechanistic models have been proposed that describe the fuel cell operation [1, 2] in great detail; however, often the equations can only be solved through numerical iteration and some 2 Copyright c © 2006 by ASME Fuel Flow Gas Diffusion Layer Gas Diffusion Layer Membrane Conductive Bipolar Plate