Modeling and Control for Pem Fuel Cell Stack System I

A nonlinear fuel cell system dynamic model tha t is suitable for control s tudy is presented. The t ransient phenomena captured in the model include the flow characterist ics and inertia dynamics of the compressor, the manifold filling dynamics, and consequently, the reactant part ial pressures. Character izat ion of the Fuel Cell polarization curves based on t ime varying current , part ial oxygen and hydrogen pressures, t empera tu re , membrane hydrat ion allows analysis and simulation of the t ransient fuel cell power generation. An observer based feedback and feedforward controller tha t manages the tradeoff between reduct ion of parasit ic losses and fast fuel cell net power response during rapid current (load) demands is designed. 1 I n t r o d u c t i o n Fuel cell stack systems are under intensive development by several manufacturers , with the P ro ton Exchange Membrane (PEM, also known as Polymer Electrolyte Membrane) Fuel Cells (FC) current ly considered by many to be in a relatively more developed stage for ground vehicle applications. There are three major control subsys tem loops in the fuel cell systern tha t regulate the air/fuel supply, the water management and the heat managemen t [1]. In this paper we concentra te on the air and direct hydrogen (/-/2) supply subsystems. In the air supply subsys tem we control the compressor motor power ( through voltage or current) in order to regulate (and replenish) the oxygen depleted from the FC cathode during power generation. This task needs to be achieved fast and efficiently to avoid degradat ion of the stack voltage and sluggish net power response [2]. Creat ing a control-oriented dynamic model of the overall sys tem is an essential first step, not only for the unders tand ing of the system behavior, but also for the development and design of model-based control methodologies. Fuel cell (propulsion) system models in the l i terature are most ly s teady-s ta te models which are typically used for component sizing [3, 4, 5], cumulat ive fuel consumption or bybridization studies [6], and forward-looking simulation models [7]. These models represent each component such as compressor, heat exchanger and fuel cell stack voltage as a static performance or efficiency map. The only dynamics considered is the vehicle inertia. The authors usually assume perfect conditions in the ca thode (stoichiometry, pressure, humidi ty and stack t empera tu re ) . Al though the dynamic FC behavior is not included, these studies established a good basis for unders tanding the fuel cell vehicle integration. Few papers address the effects of t ransient variations 1Support is provided by the U.S. Army Center of Excellence for Automotive Research, Contract DAAE07-98-3-0022 in the fuel cell sys tem performance. Excellent examples are the dominant but slow t e m p e r a t u r e effects on the stack efficiency [8, 9], and the effects of reformed hydrogen//2 feed rates in the stack response [10, 11]. Last but not least, the FC dynamic behavior due to changes in reactant flow is modeled in [12] and presented in [13]. The authors in [14] raise a lot of interest ing issues associated with the dynamic interactions of the flow, heat, and water subsystems but did not provide a comprehensive set of equat ions for their study. In this paper, the stack terminal voltage is modeled based on the FC load current and FC opera t ing conditions, including cell t empera tu re , air pressure, oxygen partial pressure and membrane humidity. The FC voltage is determined using a polarizat ion curve based on the reversible cell voltage, act ivat ion losses, ohmic losses and concentrat ion losses. Flow equations, mass and energy balance and electrochemical relations were used to create a lumped dynamic model of the FC cathode. Air pressure and humidi ty are calculated by balancing mass of air and water entering and leaving the FC stack, vapor carried by the air flow, oxygen consumed and water produced by chemical reaction. Thermodynamic principles are used to determine an average partial pressure of oxygen inside the ca thode channel. Water content, both vapor and liquid states, s tored inside fuel cell cathode are computed and used to represent the effect of membrane dehydra t ion and fuel cell water flooding. The physical parameters are cal ibrated based on da ta repor ted in l i terature and the sys tem is sized to represent the stack in the P2000 Ford exper imenta l vehicle [2]. The model is used to analyze and design an air flow controller for the FC stack supercharging device tha t allows fast and robust air flow supply to the cathode. The controller needs to avoid the compressor stall and surge regions during large current steps (up and down, respectively). Another control difficulty arises even during small current demands. Namely, the power utilized by the supercharger is a parasitic loss for the FC stack. We show tha t minimizing these parasit ic losses and providing fast air flow regulation are conflicting objectives. The conflict arises from the fact tha t the supercharger is using par t of the stack power to accelerate. One way to resolve this conflict is to augment the FC system with an auxiliary ba t t e ry or an ul tracapaci tor tha t can drive the auxiliary devices and can potential ly buffer the FC from transient current demands. These additional components, however, will introduce complexity and additional weight t ha t might not be necessary [15]. To judiciously decide about the system archi tecture and the component sizing we analyze the tradeoff between the two objectives using linear control theoret ic techniques. We finally provide a controller and a calibration methodology for exploring all