(497b) Optimizing Model Complexity for System Level Models of Fuel Cell Power Systems

Chemical process industries and power plants manage some of the most sophisticated and expensive engineered systems in the world, spending large amounts of money in plant design, operation, and maintenance. To achieve performance targets and at the same time reduce the number of costly pilot-scale and demonstration facilities, the designers of these plants increasingly rely on high-fidelity computer process simulations to design and evaluate virtual plants. Existing commercial simulation software products employ two main levels of model abstraction: 1) models of the overall process (a forest-level description) and 2) more detailed models of individual equipment items in the process (a tree-level description) [1] The system level models used in the forest-level description of a chemical process tend to use simpler and reduced order models for various reasons including: 1) speedup of computation 2) more emphasis on the overall flowsheet output rather than detailed output of individual modules. This is a trade-off between the degree of accuracy achieved, and the speed and complexity of computation which leads to uncertainties in the design. Fuel cell power systems are no exception.

Recently, we characterized the uncertainties in system level models of a Solid Oxide Fuel Cell (SOFC))-Proton Exchange Membrane (PEM) fuel cell hybrid power plant conceptual design [2]. Optimizing this conceptual design involved consideration of a number of objectives which resulted in a multi-objective optimization problem [3] where the following goals are simultaneously achieved:

? Minimize capital cost ? Minimize cost of electricity ? Minimize CO2 emissions ? Maximize SOFC current density ? Maximize PEM current density ? Maximize overall efficiency ? Maximize power rating

The fact that these multiple objectives are often conflicting in nature and can have completely different trends with respect to multiple process variables and parameters, make the representation and analysis of the trade-off between these objectives very important. The plant was designed using simplified models for both the fuel cell systems and moreover the hybrid fuel cell technologies are new and futuristic. Hence the system level models used for the SOFC's and PEM's performance have significant uncertainties in them. These individual models were found to deviate from experimental results for as much as 30% and hence it was important to study the effect of uncertainties on the optimal result of the objectives. Substantiating this fact, it was found that there was a considerable difference between the deterministic and the stochastic trade-off surfaces. The focus of this paper is an extension of that work, where we are reducing the uncertainties introduced by the simpler fuel cell models, by using higher level models for the PEM and SOFC [4,5]. These models are obviously not free from errors too but it introduces a significant improvement over the previous ones. We then perform deterministic and stochastic multi-objective optimization with the new models and compare the Pareto surfaces [3] (trade-off surfaces) to the stochastic Pareto surface computed with the old models. Through this exercise, we identify the degree of model complexity required, in order to provide the decision maker with a proper trade-off surface that has no or low impact of modeling uncertainties. The study tries to answer the most important questions concerning uncertainty: to what extent imperfect information is acceptable.

Keywords: system level model, trade-off surface, uncertainty reduction, reduced order models, model complexity

References:

1. National Energy Technology Laboratory (NETL), ?Aspen Plus ? Fluent Integration toolkit document', 2004 2. Subramanyan, K., Diwekar U. and Goyal A.; ?Multi-objective optimization of hybrid fuel cell power system under uncertainty', Journal of Power Sources, 132(1-2), 99-112, 2004 3. Diwekar, U. M.; ?Introduction to Applied Optimization', Kluwer Academic Publishers, Dordrecht, 2003. 4. Chan, S. H., K. A Khor, and Z. T. Xia; 'A complete polarization model of a solid oxide fuel cell and its sensitivity to the change of cell component thickness', Journal of Power Sources, 93(1-2), 130-140, 2001. 5. Maggio G., V. Recupero, and L. Pino: Modeling polymer electrolyte fuel cell: an innovative approach, Journal of Power Sources 101:275-286 2001.