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Optimal start-up of microfabricated power generation processes employing fuel cells. (English) Zbl 1202.49005

Summary: Microfabricated fuel cell systems have the potential to outperform batteries for man-portable power generation. Because many electronic devices operate at various loads, with frequent start-ups and shut-downs, transient aspects are highly important and must be considered thoroughly. In this paper, the focus is on the optimal start-up of microfabricated fuel cell systems using numerical open-loop optimal control. For start-up purposes, a small rechargeable battery is used to provide the energy needed to heat up the fuel cell stack and meet the power demand when the fuel cell is unavailable or can only satisfy part of the demand. The objective of the start-up problem is to bring the system to a desired operating point with a minimal total mass of the system (battery and fuels), while meeting the nominal power demand at any time and satisfying the operational restrictions. The model for the fuel cell stack consists of partial differential-algebraic equations with multiple time scales and numerical techniques that exploit a separation of these time scales are used for efficient and reliable integration of the state and sensitivity equations. A case study of a microfabricated power generation system employing a high-temperature solid-oxide fuel cell and using ammonia and butane as fuels is presented.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
49N90 Applications of optimal control and differential games
93A30 Mathematical modelling of systems (MSC2010)

Software:

SNOPT; DASPK 3.0; DAEPACK
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Full Text: DOI

References:

[1] Linden, Handbook of Batteries (2001)
[2] Microfabricated Power Generation Devices: Design and Technology (2009)
[3] Mitsos, Methodology for the design of man-portable power generation devices, Industrial and Engineering Chemistry Research 46 (22) pp 7164– (2007)
[4] Mitsos, Alternatives for micropower generation processes, Industrial and Engineering Chemistry Research 43 (1) pp 74– (2004)
[5] Mitsos, Product engineering for man-portable power generation based on fuel cells, AIChE Journal 51 (8) pp 2199– (2005)
[6] Chachuat, Optimal design and steady-state operation of micro power generation employing fuel cells, Chemical Engineering Science 60 (16) pp 4535– (2005)
[7] Yunt, Designing man-portable power generation systems for varying power demand, AIChE Journal 54 (5) pp 1254– (2008)
[8] Mitsos A Man-portable power generation devices: product design and supporting algorithms 2006
[9] Barton, Computer Aided Chemical Engineering 20B pp 1093– (2005)
[10] Larminie, Fuel Cell Systems Explained (2003) · doi:10.1002/9781118878330
[11] Hotz, Syngas production from butane using a flame-made Rh/Ce0.5Zr0.5O2 catalyst, Applied Catalysis B 73 (3/4) pp 336– (2007)
[12] Arana, A microfabricated suspended-tube chemical reactor for thermally efficient fuel processing, IEEE Journal MEMS 12 (5) pp 600– (2003) · doi:10.1109/JMEMS.2003.817897
[13] Ganley, Porous anodic alumina microreactors for production of hydrogen from ammonia, AIChE Journal 50 (4) pp 829– (2004)
[14] Deshmukh, Microreactor modeling for hydrogen production from ammonia decomposition on ruthenium, Industrial and Engineering Chemistry Research 43 (12) pp 2986– (2004)
[15] Mitsos A Chachuat B Barton PI Justification of the modeling assumptions in the intermediate fidelity models for portable power generation 2005 Internal Report Massachusetts Institute of Technology Cambridge, MA http://yoric.mit.edu/reports.html
[16] Martinson, A differentiation index for partial differential-algebraic equations, SIAM Journal on Scientific Computing 21 (6) pp 2295– (2000) · Zbl 0956.35026
[17] Martinson, Index and characteristic analysis of linear PDAE systems, SIAM Journal on Scientific Computing 24 (3) pp 905– (2002) · Zbl 1036.65081
[18] Bessette, A mathematical model of a solid oxide fuel cell, Journal of The Electrochemical Society 142 (11) pp 3792– (1995)
[19] Achenbach, Three-dimensional and time-dependent simulation of a planar solid oxide fuel cell, Journal of Power Sources 49 (1/3) pp 333– (1994)
[20] Schefer, Catalyzed combustion of H2/air mixtures in a flat plate boundary layer: II. Numerical model, Combustion and Flame 45 pp 171– (1982)
[21] Westbrook, Chemical kinetic modeling of hydrocarbon combustion, Progress in Energy and Combustion Science 10 (1) pp 1– (1984)
[22] Gao, Dynamic lithium-ion battery model for system simulation, IEEE T Components Packaging Technology 25 (3) pp 495– (2002)
[23] Stamps, Analysis of capacity fade of a lithium ion battery, Journal of Power Sources 150 pp 229– (2005)
[24] Barton, Modeling, simulation, sensitivity analysis and optimization of hybrid systems, ACM Transactions on Modeling and Computer Simulation 12 (4) pp 256– (2002) · Zbl 1390.93118
[25] Vande Wouwer, Adaptive Method of Lines (2001)
[26] Feehery, Efficient sensitivity analysis of large-scale differential-algebraic systems, Applied Numerical Mathematics 25 (1) pp 41– (1997) · Zbl 0884.65086
[27] Li, Software and algorithms for sensitivity analysis of large-scale differential algebraic systems, Journal of Computational and Applied Mathematics 125 (1-2) pp 131– (2000) · Zbl 0971.65074
[28] Chachuat, Progress in Industrial Mathematics at ECMI 2006, Mathematics in Industry pp 512– (2007)
[29] Khalil, Nonlinear Systems (2002)
[30] Asher, Computer Methods for Ordinary Differential Equations and Differential-algebraic Equations (1998) · doi:10.1137/1.9781611971392
[31] Tolsma JE Block solver manual (version 1.0) 2000
[32] Tolsma, DAEPACK: an open modeling environment for legacy models, Industrial and Engineering Chemistry Research 39 (6) pp 1826– (2000)
[33] Srikar, Structural design considerations for micromachined solid-oxide fuel cells, Journal of Power Sources 125 (1) pp 62– (2004)
[34] Brusch, Solution of highly constrained optimal control problems using nonlinear programming, AIAA Journal 11 (2) pp 135– (1973)
[35] Teo, Pitman Monographs and Surveys in Pure and Applied Mathematics (1991)
[36] Neuman, A suboptimal control algorithm for constrained problems using cubic splines, Automatica 9 (5) pp 601– (1973) · Zbl 0276.49026
[37] Tsang, Optimal control via collocation and nonlinear programming, International Journal of Control 21 (5) pp 763– (1975) · Zbl 0318.49028
[38] Vassiliadis, Solution of a class of multistage dynamic optimization problems. 2. Problems with path constraints, Industrial and Engineering Chemistry Research 33 (9) pp 2123– (1994)
[39] Gill, SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM Review 47 (1) pp 99– (2005) · Zbl 1210.90176
[40] Schlegel, Dynamic optimization using adaptive control vector parameterization, Computers and Chemical Engineering 29 (8) pp 1731– (2005)
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