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1. Koopman-Based Modeling of an Open Cathode Proton Exchange Membrane Fuel Cell Stack

   Huo, Da; Peng, Qian; Hall, Carrie (October 2023, Proceedings of the Modeling, Estimation, and Control Conference)

   open-cathode proton exchange membrane; data-driven modeling; Koopman operator; physics-based modeling; control-oriented modeling (Ed.)

   Accurate modeling is crucial for the effective design and control of fuel cell stacks. Although physics-based models are widely used, data-driven methods such as the Koopman operator have not been fully explored for fuel cell modeling. In this paper, a Koopman-based approach is utilized to model the thermal dynamics of a 5 kW open cathode proton exchange membrane fuel cell stack. A physics-based model is used as the baseline for comparison. By varying the cooling fan rotational speed, the dynamics of the fuel cell stack were measured from the low load of near 0 kW to about 5 kW. Compared to experimental results, the steady-state absolute errors of Koopman-based models are within 3%. Additionally, once given sufficient dimension, the development effort required for the Koopman-based model is relatively low compared to the traditional physics-based approach, while still achieving a high level of accuracy. These findings suggest the Koopman operator may be a suitable alternative approach for fuel cell stack modeling that enables the development of more accurate and efficient modeling methods for fuel cell systems and facilitates the implementation of the linear optimal algorithms. 

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2. Data-driven prediction of temperature variations in an open cathode proton exchange membrane fuel cell stack using Koopman operator

   https://doi.org/10.1016/j.egyai.2023.100289  

   Huo, Da; Hall, Carrie M. (October 2023, Energy and AI)

   In this study, a novel application of the Koopman operator for control-oriented modeling of proton exchange membrane fuel cell (PEMFC)stacks is proposed. The primary contributions of this paper are: (1) the design of Koopman-based models for a fuel cell stack, incorporating K-fold cross-validation, varying lifted dimensions, radial basis functions (RBFs), and prediction horizons; and (2) comparison of the performance of Koopman based approach with a more traditional physics-based model. The results demonstrate the high accuracy of the Koopman-based model in predicting fuel cell stack behavior, with an error of less than 3%. The proposed approach offers several advantages, including enhanced computational efficiency, reduced computational burden, and improved interpretability. This study demonstrates the suitability of the Koopman operator for the modeling and control of PEMFCs and provides valuable insights into a novel control-oriented modeling approach that enables accurate and efficient predictions for fuel cell stacks. 

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3. Effect of Membrane Properties on the Carbonation of Anion Exchange Membrane Fuel Cells

   https://doi.org/10.3390/membranes11020102  

   Zheng, Yiwei; Irizarry Colón, Lyzmarie Nicole; Ul Hassan, Noor; Williams, Eric R.; Stefik, Morgan; LaManna, Jacob M.; Hussey, Daniel S.; Mustain, William E. (February 2021, Membranes)

   null (Ed.)

   Anion exchange membrane fuel cells (AEMFC) are potentially very low-cost replacements for proton exchange membrane fuel cells. However, AEMFCs suffer from one very serious drawback: significant performance loss when CO2 is present in the reacting oxidant gas (e.g., air) due to carbonation. Although the chemical mechanisms for how carbonation leads to voltage loss in operating AEMFCs are known, the way those mechanisms are affected by the properties of the anion exchange membrane (AEM) has not been elucidated. Therefore, this work studies AEMFC carbonation using numerous high-functioning AEMs from the literature and it was found that the ionic conductivity of the AEM plays the most critical role in the CO2-related voltage loss from carbonation, with the degree of AEM crystallinity playing a minor role. In short, higher conductivity—resulting either from a reduction in the membrane thickness or a change in the polymer chemistry—results in faster CO2 migration and emission from the anode side. Although this does lead to a lower overall degree of carbonation in the polymer, it also increases CO2-related voltage loss. Additionally, an operando neutron imaging cell is used to show that as AEMFCs become increasingly carbonated their water content is reduced, which further drives down cell performance. 

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4. Optimal Control for Thermal Management of a Proton Exchange Membrane Fuel Cell Stack With Koopman-Based Modeling

   https://doi.org/10.1115/1.4066011  

   Huo, Da; Hall, Carrie M (March 2025, Journal of Dynamic Systems, Measurement, and Control)

   This study presents a novel approach to optimal control utilizing a Koopman operator integrated with a linear quadratic regulator (LQR) to enhance the thermal management and power output efficiency of an open-cathode proton exchange membrane fuel cell (PEMFC) stack. First, a linear time-invariant dynamic model was derived through Koopman operator to forecast the behavior of the PEMFC stack. Second, this Koopman-based model was directly integrated with LQR for optimizing temperature, temperature variations, and output power efficiency of the PEMFC stack by regulating fan speed, with a physics-based model serving as the plant model. Finally, the performance of the Koopman-based LQRs (KLQR) was compared to a baseline proportional-integral (PI) controller across various ambient temperatures and operating conditions, focusing on temperature, temperature variations, and net power output. The results demonstrate the proposed Koopman-based approach can be seamless integration with linear optimal control algorithms, effectively minimizing temperature, temperature variations across the PEMFC stack, and the net power outputs under different ambient temperature and operating conditions. 

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5. Solid‐State Alkaline Fuel Cell Performance of Pentablock Terpolymer with Methylpyrrolidinium Cations as Anion Exchange Membrane and Ionomer

   https://doi.org/10.1002/fuce.202000092  

   Hwang, M.; Sun, R.; Willis, C.; Elabd, Y. A. (October 2020, Fuel Cells)

   Abstract In this study, pentablock terpolymers with methylpyrrolidinium cations were characterized and investigated as anion exchange membranes and ionomers for solid‐state alkaline fuel cells. The pentablock terpolymer (with methylpyrrolidinium cations) membranes exhibited higher fuel cell power density and durability than commercial FuMA‐Tech (with quaternary ammonium cations) membranes at 30 °C, 100% relative humidity (RH). Optimization of the catalyst ink composition (i.e., solids and solvent ratio) and fuel cell performance of membrane electrode assemblies (MEAs) with pentablock terpolymers as both the membrane and ionomer were also investigated. Optimization of the fuel cell operating conditions corroborates with thein situelectrochemical impedance spectroscopy results. The pentablock terpolymer MEA exhibited a maximum power density of 83.3 mW cm⁻²and voltage decay rate of 0.7 mV h⁻¹after 100 h of operation under 40 °C, 100% RH. These results show promise for pentablock terptolymers with methylpyrrolidinium cations as a commercially attractive low‐cost alternative anion exchange membrane and ionomer for solid‐state alkaline fuel cells. 

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