High-fidelity dynamic models of solid oxide fuel cells (SOFCs) capture the spatial distribution of key performance variables by considering the cells as distributed parameter systems. As such, they are often complex and require extensive computational resources. In this paper, driven by the need to support the control strategy development and system optimization, we develop a low-order SOFC model by approximating the mass and energy balance dynamics in the fuel and air bulk flows using quasi-static relations. However, due to the coupling between the quasi-static mass balance and current distribution, this approximation leads to a large set of coupled nonlinear algebraic equations that have to be solved online using iterative computation. In order to mitigate the computational cost involved, an efficient iterative algorithm is proposed to solve these equations. The new algorithm requires to iterate on only one variable—the cell voltage—to determine the current and flow compositions and their distributions. The low-order model with 16 states is compared to the baseline model, which has 160 states that incorporates fully the mass and energy balance dynamics. Simulations are performed to evaluate the model performance for both steady-state and transient operations, and to assess the computational cost associated with the low-order and full order models. It is shown that the low-order model closely matches the original baseline model, while the computation time is reduced by more than 50% compared to the baseline model.

1.
Singhal
,
S.
, and
Kendall
,
K.
, eds., 2004,
High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications
,
Elsevier Science
,
New York
.
2.
Achenbach
,
E.
, 1994, “
Three-Dimensional and Time-Dependent Simulation of a Planar Solid Fuel Cell Stack
,”
J. Power Sources
0378-7753,
49
, pp.
333
348
.
3.
Haynes
,
C.
, 1999, “
Simulation of Tubular Solid Oxide Fuel Cell Behavior for Integration Into Gas Turbine Cycles
,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
4.
Ota
,
T.
,
Koyama
,
M.
,
Wen
,
C.
,
Yamada
,
K.
, and
Takahashi
,
H.
, 2003, “
Object-Based Modeling of SOFC System: Dynamic Behavior of Micro-Tube SOFC
,”
J. Power Sources
0378-7753,
118
, pp.
430
439
.
5.
Petruzzi
,
L.
,
Cocchi
,
S.
, and
Fineschi
,
F.
, 2003, “
A Global Thermo-Electrochemical Model for SOFC Systems Design and Engineering
,”
J. Power Sources
0378-7753,
118
, pp.
96
107
.
6.
Aguiar
,
P.
,
Adjiman
,
C.
, and
Brandon
,
N.
, 2004, “
Anode-Supported Intermediate Temperature Direct Internal Reforming Solid Oxide Fuel Cell. I: Model-Based Steady-State Performance
,”
J. Power Sources
0378-7753,
138
, pp.
120
136
.
7.
Mueller
,
F.
,
Brouwer
,
J.
,
Jabbari
,
F.
, and
Samuelsen
,
S.
, 2005, “
Dynamic Simulation of an Integrated Solid Oxide Fuel Cell System Including Current-Based Fuel Flow Control
,”
Proceedings of Third International Conference on Fuel Cell Science, Engineering and Technology
.
8.
Xi
,
H.
, and
Sun
,
J.
, 2005, “
Dynamic Model of Planar Solid Oxide Fuel Cells for Steady State and Transient Performance Analysis
,”
Proceedings of ASME International Mechanical Engineering Congress and Exposition
.
9.
Achenbach
,
E.
, 1995, “
Response of a Solid Oxide Fuel Cell to Load Change
,”
J. Power Sources
0378-7753,
57
, pp.
105
109
.
10.
Aguiar
,
P.
,
Adjiman
,
C.
, and
Brandon
,
N.
, 2005, “
Anode-Supported Intermediate Temperature Direct Internal Reforming Solid Oxide Fuel Cell. II: Model-Based Dynamic Performance and Control
,”
J. Power Sources
0378-7753,
147
, pp.
136
147
.
11.
Xi
,
H.
, and
Sun
,
J.
, 2006, “
Analysis and Feedback Control of Planar SOFC Systems for Fast Load Following in APU Applications
,”
Proceedings of ASME International Mechanical Engineering Congress and Exposition
.
12.
Braun
,
R.
, 2002, “
Optimal Design and Operation of Solid Oxide Fuel Cell Systems for Small-Scale Stationary Applications
,” Ph.D. thesis, University of Wisconsin-Madison, Madison, WI.
13.
Gemmen
,
R.
, and
Johnson
,
C.
, 2005, “
Effect of Load Transients on SOFC Operation-Current Reversal on Loss of Load
,”
J. Power Sources
0378-7753,
144
, pp.
152
164
.
14.
Larminie
,
J.
, and
Dicks
,
A.
, 2003,
Fuel Cell Systems Explained
, 2nd ed.,
Wiley
,
New York
.
15.
Campanari
,
S.
, and
Iora
,
P.
, 2005, “
Comparison of Finite Volume SOFC Models for the Simulation of a Planar Cell Geometry
,”
Fuel Cells
1615-6846,
5
(
1
), pp.
34
51
.
16.
Selimovic
,
A.
, 2002, “
Modeling of Solid Oxide Fuel Cells Applied to the Analysis of Integrated Systems With Gas Turbines
,” Ph.D. thesis, Lund University, Sweden.
17.
Campanari
,
S.
, and
Iora
,
P.
, 2004, “
Definition and Sensitivity Analysis of a Finite Volume SOFC Model for a Tubular Cell Geometry
,”
J. Power Sources
0378-7753,
132
, pp.
113
126
.
18.
Xi
,
H.
, and
Sun
,
J.
, 2006, “
Comparison of Dynamic Planar SOFC Models With Different Assumptions of Temperature Layers in Energy Balance
,”
Proceedings of ASME International Mechanical Engineering Congress and Exposition
.
19.
Bradie
,
B.
, 2006,
A Friendly Introduction to Numerical Analysis
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
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