Energy Systems Integration Using Reduced Order Methods

In integrating multi-component system models, such as polymer electrolyte fuel cells (PEFCs), situations often arise where information for one or more sub-components is not fully available; nor is direct integration among the disparate sub-components (especially in multi-scale systems) trivial. In these cases, one novel methodology for achieving system integration is to capture very complex sub-system information via simple parametric representations, yet keeping the essence of the physics. In this study, we explore whether such compact mathematical representations of the missing information exist.

We propose a generalized strategy for integration of two systems A & B, which can be represented via spatially distributed models, and for which direct model-integration is nontrivial. The essence of our methodology can be stated as the following:

Assuming a parametric representation of the adjoining boundary between systems A & B (which has to be determined), we repeatedly solve for system A only by spanning the entire parametric space, and generate snapshots for the output flux from system A towards system B. Through these snapshots, we construct a compact reduced order model (ROM) for the output flux. Finally, system B and the unknown boundary are determined using the above generated ROM for the flux as the input. Via this methodology we determine spatially distributed state information within systems A & B such that conditions of state and flux continuity at the adjoining boundary are satisfied.

For illustration, we present a benchmark case study for integration of catalyst layer (CL) – gas diffusion layer (GDL) sub-component models for our PEFC system [1]. Here, the GDL sub-component information is projected onto the adjoining boundary between GDL and CL, with manageable number of parameters and approximate integrated system solution is obtained. We obtained promising computational times & accuracy-levels for both simulation and optimization cases, when approximate solution is compared with previously obtained rigorous solution. The integration methodology described here can be applied to several unknown systems; using these ideas two different sub-systems can be easily linked with reduced number of parameters in conjunction with system optimization. Further, extension of integrating multi-scale systems will be given.

1. Jain P., Biegler L.T., and Jhon M.S., “Optimization of Polymer Electrolyte Fuel Cell Cathodes,”  Electrochem Solid-State Lett, 11 (10), B193 (2008).