From Cells to Multi-Stack Modules: Model Validation and Simplification Approaches for Scaled-up Solid Oxide Cell Systems

Abstract

Solid Oxide Cells (SOCs) are highly efficient energy converters with significant potential for integrating renewable energy into strongly coupled energy systems. To enable their large-scale application, a thorough understanding of their capabilities and limitations at the system level is essential. One major research focus in the scientific community is to investigate and improve cell performance using single cell experiments in controlled laboratory furnaces, which do not represent the thermal boundary conditions of large-scale commercial systems. Conversely, model-based design of such systems typically employs lumped single cell or stack models. However, this extrapolation overlooks critical factors such as inhomogeneities, stack interactions and heat losses, typically leading to an overestimation of performance. To address this gap, the German Aerospace Center has developed the simulation framework TEMPEST [1,2,3] in Modelica/Dymola. This object-oriented platform integrates validated models spanning from cell to application scale multi-stack modules, enabling accurate representation of thermo-physical processes with adjustable complexity. For current research questions such as transient capabilities of SOC systems, spatially discretised models are required, as fully lumped models cannot adequately capture temperature and reaction rate inhomogeneities. Central challenges in this effort include developing performant and accurate simplification approaches and validating the resulting models with experimental data. This presentation will showcase the TEMPEST approach to overcome these challenges for stack and module modelling. Two test environments provide the experimental data for validation: a pressurised short-stack furnace test environment (HORST [4,5], -2 kW...0.5 kW in EC and FC mode), and an ambient pressure multi-stack module test environment (GALACTICA [6,7], -120 kW...40 kW in EC and FC mode). Exemplary fuel cell, steam- and co-electrolysis experimental data from HORST demonstrate the necessity of considering thermal interactions between the stack and its surrounding furnace to successfully validate a stack model. To avoid elaborate modelling of the surrounding, heat transfer parameters of a simplified test environment model are fitted, using a Python-based optimizer that iteratively adjusts the parameters and executes the model in Dymola to minimize errors in temperature profiles and cell voltages. Further, different simplification approaches are presented, including (i) reducing the number of ODEs at the cell level for different flow configurations and (ii) reducing the number of detailed cells within a stack for a multi-stack module model. The simplified module model is validated against experimental data from GALACTICA. In conclusion, the developed modelling and simplification approaches deliver reliable multi-stack module models that allow to investigate scale-up and the transient behaviour of thermally integrated SOC systems.

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