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Optimal control of load changes for molten carbonate fuel cell systems: A challenge in PDE constrained optimization. (English) Zbl 1196.35218

The paper deals with the molten carbonate fuel cells that provide a promising technology for the operation of future stationary power plants. A family of hierarchically ordered mathematical models has been developed with the aim of simulating and optimizing the temporal and spatial dynamical behavior of the gas streams, chemical reactions, and potential fields within the fuel cells. Altogether, the most complicated system, which is investigated in the paper, results in a Pareto-optimal control problem with constraints in form of a huge system of 28 partial differential algebraic equations and ordinary integro-differential algebraic equations and boundary conditions which are themselves partly given by an ordinary differential algebraic system of dimension 9. The PDEs are of parabolic and hyperbolic type; some are degenerate. Moreover, the variables involved in the different submodels of this fully coupled multiphysical system live on considerably different time scales. Optimal control results are presented for a compromise between sufficiently fast load changes and sufficiently small temperature differences within the cell’s solid part by means of a specially tailored formulation of a chain of optimal control problems. This procedure benefits from the different time scales of the state variables and keeps the problem manageable and computable despite its tremendous complexity and scale, although standard numerical methods are employed.

MSC:

35Q93 PDEs in connection with control and optimization
35B25 Singular perturbations in context of PDEs

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