Interval Methods for Control-Oriented Modeling of the Thermal Behavior of High-Temperature Fuel Cell Stacks

Solid oxide fuel cells (SOFCs) can be used as decentralized energy supply devices for providing electricity and heat directly by converting chemical energy. In such applications of SOFCs, the electric power demand is commonly varying over time. Therefore, all processes in fuel cell systems are typically instationary. For example, the heating and cooling phases for starting up and shutting down the fuel cell system as well as the response to varying electrical load demands characterize the instationarity of the operating conditions for the thermal subprocess. In contrast to most existing control approaches, which only cover stationary operating strategies, our work aims at controlling SOFC systems in instationary operating regions. This means that a mathematical system model for these regions is necessary. Such control-oriented models for the temperature distribution in a fuel cell stack module can be obtained by the method of finite volume discretization. On the basis of the first law of thermodynamics, local energy balances are derived for each volume element, which leads to a system of coupled nonlinear ordinary differential equations. In this paper, parameter identification routines are compared which are based both on classical floating point techniques and on verified interval arithmetic approaches. In particular, interval techniques are employed to deal with imperfect system knowledge expressed by bounded parameter uncertainties and to search for globally instead of locally optimal system parameterizations.