System Dynamics and Control

Chapter
Part of the Green Energy and Technology book series (GREEN)

Abstract

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.

Keywords

Dynamic model SOFC system model Control system SOFC dynamics System transients 

References

  1. 1.
    Brouwer JF, Leal EM, Orr T (2006) Analysis of a molten carbonate fuel cell: numerical modeling and experimental validation. J Power Sources 158(1):213–224CrossRefGoogle Scholar
  2. 2.
    Roberts RA, Brouwer J (2006) Dynamic simulation of a 220 kW solid oxide fuel cell gas turbine hybrid system with comparison to data. ASME J Fuel Cell Sci Technol 3(1):18–25CrossRefGoogle Scholar
  3. 3.
    Mueller F, Brouwer J, Jabbari F et al (2006) Dynamic simulation of an integrated solid oxide fuel cell system including current-based fuel flow control. ASME J Fuel Cell Sci Technol 3(2):144–154CrossRefGoogle Scholar
  4. 4.
    Kaneko T, Brouwer J, Samuelsen GS (2006) Power and temperature control of fluctuating biomass gas fueled solid oxide fuel cell and micro gas turbine hybrid system. J Power Sources 160(1):316–325CrossRefGoogle Scholar
  5. 5.
    Roberts RA, Brouwer J, Jabbari F et al (2006) Control design of an atmospheric solid oxide fuel cell/gas turbine hybrid system: variable versus fixed speed gas turbine operation. J Power Sources 161:484–491CrossRefGoogle Scholar
  6. 6.
    Mueller F, Brouwer J, Kang SG et al (2007) Quasi-three dimensional dynamic model of a proton exchange membrane fuel cell for system and controls development. J Power Sources 163(2):814–829CrossRefGoogle Scholar
  7. 7.
    Traverso A, Massardo A, Roberts RA et al (2007) Gas turbine assessment for air management of pressurized SOFC/GT hybrid systems. ASME J Fuel Cell Sci Technol 4:373–383CrossRefGoogle Scholar
  8. 8.
    Mueller F, Gaynor RM, Auld AE et al (2008) Synergistic integration of a gas turbine and solid oxide fuel cell for improved transient capability. J Power Sources 176(1):229–239CrossRefGoogle Scholar
  9. 9.
    Gaynor R, Mueller F, Jabbari F et al (2008) On control concepts to prevent fuel starvation in solid oxide fuel cells. J Power Sources 180(1):330–342CrossRefGoogle Scholar
  10. 10.
    Mueller F, Jabbari F, Brouwer J et al (2009) On the intrinsic transient capability and limitations of solid oxide fuel cell systems. J Power Sources 187(2):452–460CrossRefGoogle Scholar
  11. 11.
    Roberts RA, Brouwer J, Samuelsen GS (2010) Fuel cell/gas turbine hybrid system control for daily load profile and ambient condition variation. ASME J Eng Gas Turbines Power 132:1–7CrossRefGoogle Scholar
  12. 12.
    McLarty D, Kuniba Y, Brouwer J (2012) Experimental and theoretical evidence for control requirements in solid oxide fuel cell gas turbine hybrid systems. J Power Sources 209:195–203CrossRefGoogle Scholar
  13. 13.
    Brendan S, Brouwer J (2012) Dynamic model for understanding spatial temperature and species distributions in internal-reforming solid oxide fuel cells. J Fuel Cell Sci Technol 9:9Google Scholar
  14. 14.
    McLarty D, Brouwer J, Samuelsen S (2013) A spatially resolved physical model for transient system analysis of high temperature fuel cells. Int J Hydrogen Energ 38:7935–7946CrossRefGoogle Scholar
  15. 15.
    McLarty D, Brouwer J, Samuelsen S (2014) Fuel cell–gas turbine hybrid system design part II: dynamics and control. J Power Sources 254:126–136CrossRefGoogle Scholar
  16. 16.
    Fardadi M, McLarty D, Brouwer J et al (2014) Enhanced performance of counter flow SOFC with partial internal reformation. Int J Hydrogen Energ 39:19753–19766CrossRefGoogle Scholar
  17. 17.
    McLarty D, Brouwer J (2014) A poly-generating closed cathode fuel cell with carbon capture. Appl Energ 131:108–113CrossRefGoogle Scholar
  18. 18.
    McLarty D, Brouwer J (2015) Micro-grid energy dispatch optimization and predictive control algorithms; A UC Irvine case study. Int J Electrical Power Energ Sys 65:179–190CrossRefGoogle Scholar
  19. 19.
    Mueller F, Jabbari F, Brouwer J et al (2007) Control design for a bottoming solid oxide fuel cell gas turbine hybrid system. ASME J Fuel Cell Sci Technol 4:221–230CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Fuel Cell Research Center, University of CaliforniaIrvineUSA
  2. 2.Clean Energy Systems Integration LabWashington State UniversityPullmanUSA
  3. 3.Wright State UniversityDaytonUSA

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