Index analysis and numerical solution of a large scale nonlinear PDAE system describing the dynamical behaviour of Molten Carbonate Fuel Cells

Abstract

This paper deals with the efficient simulation of the dynamical behaviour of Molten Carbonate Fuel Cells (MCFCs). MCFCs allow an efficient and environmentally friendly energy production via electrochemical reactions. Their dynamics can be described by large scale systems of up to currently 22 nonlinear partial differential algebraic equations (PDAE). The paper also serves as a basis for later parameter identification and optimal control purposes. Therefore, the numerical simulations are particularly based on hierarchically embedded systems of PDAE, first of all in one space dimension. The PDAE are of mixed parabolic-hyperbolic type and are completed by nonlinear initial and boundary conditions of mixed type. For a series of embedded models in one space dimension, the vertical method of lines (MOL) is used throughout this paper. For the semi-discretization in space appropriate difference schemes are applied depending on the type of equations. The resulting system of ordinary differential algebraic equations (DAE) in time is then solved by a standard RADAU5 method. In order to justify the numerical procedure, a detailed index analysis of the PDAE systems with respect to time index, spatial index and MOL index is carried through. Because of the nonlinearity of the PDAE system, the existing theory has to be generalized. Moreover, MOL is especially suited for near optimal real time control on the basis of a sensitivity analysis of the semi-discretized DAE system, since a theoretically safeguarded sensitivity analysis does not exist so far for PDAE constrained optimal control problems of the above type. Numerical results complete the paper and show their correspondence with the expected dynamical behaviour of MCFCs.