Models for Solid Oxide Fuel Cell Systems

This chapter provides an introduction to the problem of solid oxide fuel cells modeling. A brief review of the industrial context with emphasis on the role of model-based approaches in supporting the development of systems for large-scale diffusion is given. Also the benefits of integrating different methodologies through the merging of models, experiments, and applied mathematics are briefly reported. Thus a conceptual framework for scientists, engineers, and practitioners primarily engaged in the design of both control and diagnostic algorithms is sketched. Moreover, such a framework is also a reference for all modelers whose work entails an accurate balance between accuracy and computational speed. Therefore, all engineering activities involving system design, component sizing as well as prognostic algorithms for lifetime prediction may also benefit from the modeling approaches outlined. A literature survey is reported at the end of the chapter; that section is thought to acknowledge the most relevant works whose topics fall within the boundaries of model-based applications, which inspired this book.

This chapter presents a hierarchical approach to model SOFC behavior during both steady and transient conditions. The recourse to such an approach is motivated by the high computational intensity characterizing optimization algorithms, especially those aiming at large-scale design and definition of on-field applicable control and diagnosis strategies for SOFC-based systems, either destined to stationary generation or transport applications (Rizzoni et al. in Modeling, simulation, and concept design for hybrid-electric medium-size military trucks, pp. 1–12, 2005). In principle, this issue may be satisfactorily addressed by exclusively using black-box/lumped models of the system under development. Nevertheless, against such choice are major drawbacks, such as the much extended data sets required for identification and validation of black-box models, together with the need of running new experiments whenever system specifications change. It was demonstrated, with regard to internal combustion engine modeling (Arsie et al. in A hierarchical system of models for the optimal design of control strategies in spark ignition automotive engines, pp. 473–488, 1999), that the best compromise between accuracy, experimental costs, computational time, and flexibility is achieved by using a mixed modeling approach, with white, gray- and black-box models integrated within a hierarchical structure. This approach can be usefully extended to flexible SOFC systems, especially because of the high costs to be faced to run transient experiments and the high variety of fuel cell designs, which are under current investigation.

Real-world deployment of SOFC systems entails developing suitable control strategies, which particularly have to guarantee meeting electrical load demand, while limiting as much as possible thermal stresses for ceramic components. In this way, undesirable excessive degradation can be prevented and, in turn, longer lifetime can be achieved. Therefore, the main targets are to control the operating load and manage air and fuel inlet flows so as not to induce severe thermal gradients across fuel cell length, as well as to reduce temperature derivative during both cold-start and shutdown phases. Of course, such control goals are to be pursued taking into account the final application of the SOFC system, depending on which load demand fluctuations considerably vary (e.g., compared to stationary generation, transportation applications exhibit more fluctuating load demand). Therefore, depending on how much articulated is the designed SOFC system, which can particularly include hybridizing components (e.g., batteries and fly wheels) to enable limited power rate operation of the SOFC stack, different control levels must be developed to ensure desired control targets be appropriately met. The current chapter initially focuses on the analysis of the physical relationship between main control and controlled variables, depending on which the multilevel control structure can be appropriately defined. Then, specific analyses are presented and discussed to demonstrate the great potential offered by the model-based approach, to ensure appropriate control strategies be developed for on-field energy-efficient and safe operation of SOFC systems.

The correct operation of an SOFC system is ensured by combining optimal design and effective control and diagnostic strategies, to guarantee system efficiency and prevent excessive degradation or undesired faulty states. In this way, system lifetime can increase and market requirements be fulfilled, with a consequent growth in SOFC systems production and market deployment. The aim of a diagnostic algorithm is to detect and isolate undesired events (i.e., faulty states) within the entire system (i.e., stack and ancillaries). During faulty operation, the inference on the system state can feed suitable control strategies in order to drive the system toward a safer operating condition, ensuring in such a way a continuous operation to the final user. The current chapter gives an overview on the development of a suitable diagnostic algorithm, based on a model-based approach. The main features are illustrated and discussed, with focus on the dominant issues to be addressed for their optimal design. The background on model-based diagnosis is summarized along with the basic concepts of diagnostics. Details on the theory behind are available in the main references reported throughout the chapter. Several applications dedicated to an SOFC system are presented to exhibit the diagnostic algorithm capability of suitably detecting and isolating different kinds of faults.