Kati Sternberg

Optimal Control of Load Changes for Molten Carbonate Fuel Cell Systems: a Challenge in PDE Constrained Optimization

Molten carbonate fuel cells provide a promising technology for the operation of future stationary power plants. In order to enhance service life, a detailed understanding of the dynamical behavior of such fuel cell systems is necessary. In particular, fast load changes shall be simulated, (resp., optimized) without risking material stress due to the extreme temperature differences usually accompanying fast load changes. Fast load changes are important for daily operations in order to react on varying demands. Material stress may lead to irreparable damage of the fuel cell stack. For these contradicting goals, 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 present paper, results in a Pareto-optimal control problem with constraints in form of a ...

Parametric Sensitivity Analysis of Fast Load Changes of a Dynamic MCFC Model

Molten carbonate fuel cells are well suited for stationary power production and heat supply. In order to enhance service lifetime, hot spots, respectively, high temperature gradients inside the fuel cell have to be avoided. In conflict with that, there is the desire to achieve faster load changes while temperature gradients stay small. For the first time, optimal fast load changes have been computed numerically, including a parametric sensitivity analysis, based on a mathematical model of Heidebrecht. The mathematical model allows for the calculation of the dynamical behavior of molar fractions, molar flow densities, temperatures in gas phases, temperature in solid phase, cell voltage, and current density distribution. The dimensionless model is based on the description of physical phenomena. The numerical procedure is based on a method of line approach via spatial discretization and the solution of the resulting very large scale optimal control problem by a nonlinear programming approach.

Suboptimal control of a 2D molten carbonate fuel cell PDAE model

Numerical results for suboptimal boundary control of an integro partial differential algebraic equation system of dimension 28 are presented. The application is a molten carbonate fuel cell power plant. The technically and economically important fast tracking of the new stationary cell voltage during a load change is optimized. The nonstandard optimal control problem s.t. degenerated PDE is discretized by the method of lines yielding a very large DAE constrained standard optimal control problem. An index analysis is performed to identify consistent initial conditions.

Optimale Steuerung eines dynamischen Schmelzcarbonat-Brennstoffzellen-Modells (Optimal Control of a Molten Carbonate Fuel Cell Model).

Zusammenfassung In diesem Artikel werden Ergebnisse der optimalen Steuerung eines Schmelzcarbonat- Brennstoffzellensystems unter Lastwechseln präsentiert. Den umfangreichen Berechnungen liegt ein detailliertes, validiertes mathematisches Modell zugrunde, das die zeitliche und örtliche Dynamik der Gasströme, deren elektro-chemische Reaktionen und die in der Zelle herrschenden Temperaturen und elektrischen Spannungen beschreibt. Das mathematische Modell besteht aus einem hochdimensionalen, nichtlinearen partiell differential-algebraischen Gleichungssystem mit einer parabolischen Gleichung für die Wärmeleitung im Elektrolyten der Zelle sowie hyperbolischen Transportgleichungen für den reaktiven Gastransport. Die Potentialfelder werden in jedem Ortspunkt durch ein differential-algebraisches Gleichungssystem beschrieben. Darüber hinaus gehen in die rechten Seiten der Differentialgleichungen Integralterme ein. Der Gasstrom zwischen Anode und Kathode wird über einen katalytischen Nachbrenner und eine Mischkammer geführt, sodass die Verknüpfung von Anode zu Kathode durch ein differential- algebraisches Gleichungssystem beschrieben wird. Die Einlassbedingungen am Anodeneingang und am Lufteinlass bieten die Möglichkeit der Steuerung der Brennstoffzelle. Damit sind numerische Simulationen und extrem zeitaufwändige optimale Steuerungen, z. B. eines Lastwechsels möglich, die den Brennstoffzellenstapel optimal von einem stationären Zustand in einen anderen überführen. Die numerischen Resultate belegen die Leistungsfähigkeit moderner Methoden der Optimalen Steuerung. Hier kommt eine Methode zum Tragen, bei der alle Gleichungen erst diskretisiert, dann optimiert werden.

Towards the Numerical Solution of a Large Scale PDAE Constrained Optimization Problem Arising in Molten Carbonate Fuel Cell Modeling

Molten carbonate fuel cells (MCFCs) allow an efficient and environmentally friendly energy production by converting the chemical energy contained in the fuel gas in virtue of electro-chemical reactions. Their dynamical behavior can be described by large scale embedded systems of 1D or 2D nonlinear partial differential algebraic equations (PDAEs) up to dimension 28. They are of mixed parabolic-hyperbolic type with integral terms in the right hand side and initial and nonlinear boundary conditions, the latter governed by a system of ordinary differential equations.

Optimal Load Changes for a Molten Carbonate Fuel Cell Model

Molten carbonate fuel cells are a promising technology for future stationary power plants. In order to enhance service life a more detailed understanding of the dynamical behavior is needed. This is enabled by a hierarchy of mathematical models based on chemical and physical laws. These mathematical models allow numerical simulation and optimal control of load changes. Mathematically speaking, we solve an optimal control problem subject to a degenerated partial differential equation system coupled with an integro differential-algebraic equation system. New numerical results are presented.