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Publication# Approaches on the Thermal Management and Parameter Estimation of Solid Oxide Fuel Cells and their Systems

Résumé

Solid Oxide Fuel Cells (SOFCs) are electrochemical devices that convert chemical energy from fuel directly into electrical and thermal energy. They present high electrical efficiency and because of this feature they are considered to be an important power source alternative. However, due to their high temperature of operation, SOFCs are subject to degradation, that is, their ability to produce electricity deteriorates in time. The reasons and the conditions that contribute to degradation are multiple. Among the studied factors, operating temperature is an important one. It has been found that a stable and controllable thermal environment can mitigate this undesirable phenomenon. Therefore, the pursuit of appropriate thermal conditions during their operation is of paramount importance for their lifetime and consequently for their commercialisation. Studying and obtaining such conditions is also known as thermal management. Another important point regarding the study of SOFCs is the development and use of adequate mathematical models that the engineer and generally the researcher will use as tools to analyse their behaviour and will determine conditions for safe and efficient operation. For practical applications, these models must be validated against experimental data. The result of such validation is the determination, or calibration, of the model parameters so that the output of the model fits measurements taken in the laboratory to the best possible extent. This process is called parameter estimation or system identification. This thesis tackles both aspects. In its first part it works on the thermal management of a specific product, an SOFC autonomous unit fed with methane, producing electrical power and liberating hot off-gases that can be used as a source of thermal power. A dynamic model of the physical system is developed and validated against experimental data. During this process, it was found that measurement of gas temperatures using thermocouples may be severely biased due to radiation effects of surrounding solids to the thermocouples. In order to overcome this hurdle, the phenomena that take place around the thermocouple were incorporated into the system's mathematical model. Such a systematic error may have important consequences on the thermal management and generally on the control of the SOFC system. Indeed, an investigation effectuated in this thesis revealed how incorrect gas temperature measurements affect the system's control to such an extent that, depending on the conditions, may lead to system failure. The validation of the system model proved to be particularly challenging. This fact incited the author to investigate the factors that contribute to reliable parameter estimations. This is the subject of the second part of this thesis. A first study was performed on model-based Design of Experiments (DoE) for SOFC button cells, i.e. on how measurements on small cells may be optimised. To our knowledge the study treats for the first time the issue of repetitive measurements and their impact on the quality of parameter estimation systematically. It distinguishes the notion of measurements, which can be repetitive, from that of measurement points (or design points), which are defined once for an experiment. Introducing a new type of graph that provide information on quality criteria as functions of the number of measurement points for constant number of measurements, it stresses the importance of repetitions of measurements during experiments, which up to now has been neglected. A mathematical formula is also given that helps the experimenter define the necessary number of repetitions for a specific degree of precision of the information matrix. The theoretical findings on Design of Experiments are validated experimentally with measurements on button cells. The thesis introduces a novel method with which repetitive parameter estimations are obtained using data from polarisation curves. This method allows the calculation of histograms for the model parameters approximating this way their stochastic behaviour. Standard deviations, covariance and correlation matrices are calculated directly from the available data, avoiding the approximate calculation based on sensitivity (Jacobian) matrices. The experimental results showed again the importance of repetitions on the quality of parameter estimation. A rule-of-thumb is introduced suggesting that the number of repetitions of measurements needs to be at least equal to the number of calculated parameters plus three in order to avoid high correlations. However, repetitions do not influence the values of parameters or the fit to the experimental data, but their precision. These values are influenced by the number of measurement points. Another point of importance shown in this thesis is that there is a counterbalance between the parameters' variances and covariances and their correlations, that is, if the one improves, the other deteriorates. This is demonstrated to be in accordance with the Cramèr-Rao theorem in statistics. A consequence of this is the conclusion that parameter estimation cannot be obtained to an arbitrarily high precision. Another consequence is that assessment of system identification based on only one of the widely known criteria may not be adequate, a result that concurs with the findings of other authors in the field of DoE. Finally the available results from the afore-mentioned method revealed a potential relation between correlations of parameters and the non-uniformity of their histograms. Among the investigated examples, a case of fast degradation exhibits how the introduced parameter estimation method may be used as a diagnostics tool. However such a use requires the employment of models that describe the phenomena adequately, especially after degradation. The thesis ends with the calculation of the histograms of the parameters of the SOFC unit's heat exchanger providing a stochastic perspective of parameter estimation at an SOFC system level.

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Joel Albrektsson, Daniel Favrat, Leonidas Tsikonis, Jan Van Herle

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2011The increasing cost of carbon based fuels pushes the electricity generation market towards more efficient electricity generation technologies. In this context, fuel cells offer the opportunity to increase efficiency and lower CO2 and NOx emissions, in particular with co-generation units. The complexity, as well as the number and different combinations of components involved with a SOFC stack make their analysis impossible without dedicated tools. The simultaneous consideration of economic and thermodynamic considerations is a key challenge for engineers and decision makers. The present work contributes to the development of design tools for fuel cells and energy systems. A detailed model of fuel cell stack and a model of a complete system were developed. Based on a commercial CFD code, additional routines were implemented to model the electro-chemical behavior of a fuel cell as well as the reforming reaction schemes. The model is able to predict cell behavior under various fuel feeds. The detailed 3-D model of stack repeat unit allowed to identify weaknesses of a first stack geometry. With the combination of experimental observations and modeling activities, specific problems of the existing concept were identified and a new geometry designed, together with the corresponding stack concept. A new stack design is presented with successful experiments up to 1 kWe. Besides the stack, a co-generation fuel cell system is composed of multiple components such as heat exchangers, reformer, recycle loops... The number, the type and size of those components influence the system costs but also its efficiencies (thermal and electrical). A multi-objective thermo-economic optimization methodology was defined, allowing to optimize at the same time the configuration and operating parameters of a system. This method was applied to two sizes of co-generators : a 1 kW unit and a 30 kW unit. HTceramix SA (Yverdon, Switzerland) is developing part of a co-generation unit. The work indicates the potential improvement of their prototype. The 1 kW unit was optimized in a first phase on thermal and electrical efficiencies, and in a second phase on electrical efficiency and installed costs. Those two results indicate the influence of the objective function selection on the results. The high operating temperature of Solid Oxide Fuel Cells (SOFC) offers good opportunity for coupling with a gas turbine. A simple concept of pressurized SOFC-µGT was studied and optimized, for an net electrical output of 30 kW. The simple layout described in this work allows present technical feasibility of the concept. Moreover, the costs of electricity, lower than 0.20$/kWh, makes it economically viable solutions. The methodology and the tools developed allow the engineer to explore the solution space through optimal configurations, in order to select those fitting with its priorities and technical constraints.

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