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Fuel Cells are electrochemical devices that convert the chemical energy of a gaseous fuel directly into electricity. They are widely regarded as a potential future stationary and mobile power source. The response of a fuel cell system depends on the air and hydrogen feed, flow and pressure regulation, and heat and water management. In this paper, we develop a dynamic model suitable for the control study of fuel cell systems. The transient phenomena captured in the model include the flow and inertia dynamics of the compressor, the manifold filling dynamics (both anode and cathode), reactant partial pressures, and membrane humidity. It is important to note, however, that the fuel cell stack temperature is treated as a parameter rather than a state variable of this model because of its long time constant. Limitations and several possible applications of this model are presented.

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This paper presents a numerical calculation of the evolution of the spatially resolved solid concentration in the two electrodes of a lithium-ion cell. The microscopic solid concentration is driven by the macroscopic Butler–Volmer current density distribution, which is consequently driven by the applied current through the boundary conditions. The resulting, mostly causal, implementation of the algebraic differential equations that describe the battery electrochemical principles, even after assuming fixed electrolyte concentration, is of high order and complexity and is denoted as the full order model. The full order model is compared with the results in the works of Smith and Wang (2006, “Solid-State Diffusion Limitations on Pulse Operation of a Lithium-Ion Cell for Hybrid Electric Vehicles,” J. Power Sources, 161, pp. 628–639) and Wang et al. (2007 “Control oriented 1D Electrochemical Model of Lithium Ion Battery,” Energy Convers. Manage., 48, pp. 2565–2578) and creates our baseline model, which will be further simplified for charge estimation. We then propose a low order extended Kalman filter for the estimation of the average-electrode charge similarly to the single-particle charge estimation in the work of White and Santhanagopalan (2006, “Online Estimation of the State of Charge of a Lithium Ion Cell,” J. Power Sources, 161, pp. 1346–1355) with the following two substantial enhancements. First, we estimate the average-electrode, or single-particle, solid-electrolyte surface concentration, called critical surface charge in addition to the more traditional bulk concentration called state of charge. Moreover, we avoid the weakly observable conditions associated with estimating both electrode concentrations by recognizing that the measured cell voltage depends on the difference, and not the absolute value, of the two electrode open circuit voltages. The estimation results of the reduced, single, averaged electrode model are compared with the full order model simulation.

A nonlinear fuel cell system dynamic model that is suitable for control study is presented. The transient phenomena captured in the model include the flow characteristics and inertia dynamics of the compressor, the manifold filling dynamics, and consequently, the reactant partial pressures. Characterization of the Fuel Cell polarization curves based on time varying current, partial oxygen and hydrogen pressures, temperature, membrane hydration allows analysis and simulation of the transient fuel cell power generation. An observer based feedback and feedforward controller that manages the tradeoff between reduction of parasitic losses and fast fuel cell net power response during rapid current (load) demands is designed.