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Research Papers

# A Theoretical Solid Oxide Fuel Cell Model for System Controls and Stability Design

[+] Author and Article Information
George Kopasakis

National Aeronautics and Space Administration, Glenn Research Center, 21000 Brookpark Road, Cleveland, OH 44135

Thomas Brinson, Sydni Credle

Florida A&M University, Tallahassee, FL 32307

J. Fuel Cell Sci. Technol 5(4), 041007 (Sep 09, 2008) (8 pages) doi:10.1115/1.2971018 History: Received December 12, 2006; Revised July 13, 2007; Published September 09, 2008

## Abstract

As the aviation industry moves toward higher efficiency electrical power generation, all electric aircraft, or zero emissions and more quiet aircraft, fuel cells are sought as the technology that can deliver on these high expectations. The hybrid solid oxide fuel cell system combines the fuel cell with a microturbine to obtain up to 70% cycle efficiency, and then distributes the electrical power to the loads via a power distribution system. The challenge is to understand the dynamics of this complex multidiscipline system and the design distributed controls that take the system through its operating conditions in a stable and safe manner while maintaining the system performance. This particular system is a power generation and a distribution system, and the fuel cell and microturbine model fidelity should be compatible with the dynamics of the power distribution system in order to allow proper stability and distributed controls design. The novelty in this paper is that, first, the case is made why a high fidelity fuel cell model is needed for systems control and stability designs. Second, a novel modeling approach is proposed for the fuel cell that will allow the fuel cell and the power system to be integrated and designed for stability, distributed controls, and other interface specifications. This investigation shows that for the fuel cell, the voltage characteristic should be modeled, but in addition, conservation equation dynamics, ion diffusion, charge transfer kinetics, and the electron flow inherent impedance should also be included.

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## Figures

Figure 1

Hybrid SOFC power system structure

Figure 2

Gas turbine engine diagram

Figure 3

Fuel cell and power distribution equivalent interface network model

Figure 4

Nyquist stability of Zo(s)ZL(s) for absolute and conditional stability of ⩾60deg phase margin and ⩾6dB gain margin

Figure 5

Typical hybrid SOFC power system stability interfaces (Si)

Figure 6

Principle of the solid oxide fuel cell

Figure 7

Typical fuel cell I‐V characteristic

Figure 8

Fuel cell stack simulation for a step in load current (temp, voltage, and partial press)

Figure 9

Cell simulation of mass flow rate at the bulk channel and partial pressures at tpb due to a step in load current

Figure 10

Cell simulation of mass flow rate at the bulk channel and partial pressures at tpb due to a step in partial pressure at the bulk flow

Figure 11

Bode plot of the cathodic impedance

Figure 12

Equivalent fuel cell circuit

Figure 13

Circuit for computing output impedance

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