System Dynamics and Control

The National Fuel Cell Research Center (NFCRC) of the University of California, Irvine (UCI), has developed and applied a dynamic simulation and control system development approach for solid oxide fuel cell (SOFC) and solid oxide electrolysis cell (SOEC) systems for almost two decades. The approach is thoroughly vetted and peer-reviewed. Simplifications (for reasonable computational effort) are required to solve the dynamic conservation equations (mass, energy, momentum) for complete systems over time because transient responses range from milliseconds to hours and the systems are comprised of multiple highly coupled and integrated components with complex feedback and recirculation. Typical bulk model methodologies (e.g., representing each component as a single node with a single set of uniform conditions) avoid much of the computational rigor, but miss key system interactions and underlying SOFC and SOEC component constraints. Many bulk models attempt to address the non-uniform distribution of reactions, temperatures, and gas composition with linearization that approximates steady operation. These approximations, typically made at nominal operating conditions, are a poor proxy for the non-uniform distributions at part load and are particularly inadequate to represent the nonlinear transient responses that must be addressed with integrated control schemes. Since SOFC and SOEC performance is inherently spatially dependent, that is, the major performance characteristics (e.g., temperature and current density) cannot be well predicted without knowledge of the spatial variations in temperature, species concentrations, etc., some degree of spatial resolution is required. An approach is presented for determining the limited spatial resolution of the geometry in such a way as to capture only the directions in which major parameters that govern performance change significantly. When applicable, symmetry within the stack and within individual repeating units of the stack is used to reduce computational effort. Typically, the most significant spatial variations of the physics, chemistry, and electrochemistry governing performance are one-dimensional (1D), for example, representing a single gas flow channel or flow path. On the other hand, cross-flow or serpentine flow patterns, or significant heat loss near the cell edges necessitates a two-dimensional (2D) model. The key simplifications to geometric resolution and timescales that are recommended are presented in a detailed description of the dynamic modeling approach. Governing equations for the physics, chemistry, and electrochemistry for SOFC and SOEC systems are presented in a manner that allows ease of application in standard math toolboxes. A complete SOFC system model and modeling framework are presented, which includes a spatially resolved cell stack, spatially resolved variable flow direction heat exchangers, and spatially resolved reformer modules. When fuel and oxidant flow manifolds or significant heat losses effect the temperature distributions in the cell stacks, then an approach for accounting for the coupling of this physics with the cell performance is presented. Presentation of the dynamic SOFC/SOEC system modeling approach is followed by presentation of two examples of model verification by data–model comparisons. The model verification efforts include application to a stand-alone integrated fuel processing SOFC system and a hybrid solid oxide fuel cell–gas turbine (SOFC–GT) system. Control system development and evaluation using the dynamic system modeling approach are demonstrated by the application of the approach to stand-alone SOFC systems of various configurations and to an experimental SOFC–GT system. The transient response and control of these systems in response to fuel composition perturbations and load-following power demands are presented as examples that demonstrate the success of the control system development approach.