Solid Oxide Fuel Cell Model Research Articles

Parameter Identification of Solid Oxide Fuel Cell Using Elman Neural Network and Dynamic Fitness Distance Balance-Manta Ray Foraging Optimization Algorithm

An accurate solid oxide fuel cell model is a prerequisite for optimizing the operation and state estimation of subsequent cell systems. Hence, this work aimed to utilize a vigoroso algorithmic tool, i.e., Elman neural network, for data prediction to enrich cell measurement data and employ the trained network model for noise reduction of voltage–current data. Furthermore, to obtain reliable cell parameters, a novel parameter identification model based on the dynamic fitness distance balance-manta ray foraging optimization (dFDB-MRFO) algorithm is proposed. Two datasets were applied to extract the electrochemical model and simple electrochemical model parameters of the solid oxide fuel cell model. To verify adequately the superiority of this method, which is compared with another seven conventional heuristic algorithms, four performance indicators were selected as evaluation criteria. Comprehensive case studies demonstrated that through data processing, the precision and robustness of identification could be effectively heightened. In general, the model fitting data obtained via parameter identification using dFDB-MRFO have excellent fitting precision contrast with the measured voltage–current data. Notably, the fitting degree obtained by dFDB-MRFO in the simple electrochemical model reached 99.95% and 99.91% under the two datasets, respectively.

10-Cell Direct Ammonia Solid Oxide Fuel Cell Stack Design Development with Improved Efficiency and Resilience to Thermal Shock

Hydrogen's potential as a green fuel faces a storage challenge, which has prompted recent studies to explore methods to advance solid and liquid storage, with a particular focus on utilizing ammonia. Employing hydrogen in the form of ammonia has shown considerable promise as it capitalizes on well-established and mature technologies. Nevertheless, establishing effective and resilient direct ammonia Solid Oxide Fuel Cell (SOFC) stacks demands a high degree of congruence with stack design, uniform species distribution, and temperature regulation. This research compared the conventional simple cross flow configuration with a novel approach involving two alternating fuel and air flow configurations within a 10-cell direct ammonia SOFC stack. An experimentally validated model of the direct ammonia SOFC was utilized for multi-physics modeling. The results revealed that the alternating fuel and air stacking method creates a superior ammonia decomposition profile compared to simple cross flow stacking. Moreover, the results demonstrate a lower temperature difference of 55 K within the stack. The implementation of the alternating fuel flow and air flow method enhanced the stack's efficiency by 0.74%, primarily due to its improved thermal management capabilities within the stack. This study achieved its goal of optimizing a 10-cell direct ammonia SOFC stack by refining the design while maximizing performance and durability.

The Impact of Flow-Thermal Characteristics in Ship-Board Solid Oxide Fuel Cells

Hydrogen is increasingly recognized as a clean and reliable energy vector for decarbonization in the future. In the marine sector, marine solid oxide fuel cells (SOFCs) that employ hydrogen as an energy source have already been developed. In this study, a multi-channel plate-anode-loaded SOFC was taken as the research object. A three-dimensional steady-state computational fluid dynamics (CFD) model for anode-supported SOFC was established, which is based on the mass conservation, energy conservation, momentum conservation, electrochemical reactions, and charge transport equations, including detailed geometric shapes, model boundary condition settings, and the numerical methods employed. The polarization curves calculated from the numerical simulation were compared with experimental results from the literature to verify the model’s accuracy. The curved model was applied by enlarging the flow channels or adding blocks. Numerical calculations were employed to obtain the current density, temperature distribution, and component concentration distribution under the operating conditions of the SOFC. Subsequently, the distribution patterns of various physical parameters during the SOFC operation were analyzed. Compared to the classical model, the temperature of the curved model was reduced by 1.3%, and the velocities of the cathode and anode were increased by 4.9% and 5.0%, respectively, with a 2.42% enhancement in performance. The findings of this study provide robust support for research into and the application of marine SOFCs, and offer they insights into how we may achieving “dual carbon” goals.

Optimal parameter identification of solid oxide fuel cell using modified fire Hawk algorithm

An accurate and efficient approach is required to identify the unknown parameters of solid oxide fuel cell (SOFC) mathematical model for a robust design of any energy system considering SOFC. This research study proposes a modified fire hawk algorithm (MFHA) to determine the values of SOFC model parameters. The performance evaluation of MFHA is tested on two case studies. Firstly, the performance of MFHA is tested on commercially available cylindrical cell developed by Siemens at four temperatures. Results reveal that the least value of sum of squared error (SSE) is 1.04E−05, 2.30E−05, 1.03E−05, and 1.60E−05 at 1073 K, 1173 K, 1213 K, and 1273 K respectively. Results obtained using MFHA have been compared with original fire hawk algorithm (FHA) and other well established and recent algorithms. Secondly, MFHA is implemented for estimating unknown parameters of a 5 kW dynamic tabular stack of 96 cells at various pressures and temperatures. The obtained value of SSE at different temperatures of 873 K, 923 K, 973 K, 1023 K and 1073 K is 1.18E−03, 6.12E−03, 2.21E−02, 5.18E−02, and 6.00E−02, respectively whereas, SSE at different pressures of 1 atm, 2 atm, 3 atm, 4 atm, and 5 atm is 6.05E−02, 6.11E−02, 5.53E−02, 5.11E−02, and 6.64E−02 respectively.

Thermodynamic and electrochemical performance coupling analysis of single ammonia-fueled tubular solid oxide fuel cell toward low operating temperatures

The primary development strategy for ammonia-fueled solid oxide fuel cell (SOFC) focuses on enhancing the cell lifetime by reducing the operating temperature, albeit inevitably affecting the cell output performance. This study has established a multi-physics model of the single ammonia-fueled tubular SOFC and conducted a thorough analysis and weighing of the improvements in cell stress and the losses in output performance at low temperature operating conditions. As the operating temperature is reduced from 800 °C to 700 °C, the inhomogeneity in its internal temperature distribution and stress distribution is significantly reduced, albeit with a concomitant increase in ohmic impedance by 1.75 Ω cm2 and a reduction in maximum power density by 42.16 %. The study employs the reduction of electrolyte thickness to compensate for the ohmic losses incurred by low temperature, while simultaneously incorporating a material thermal deformation constraint mechanism. As the electrolyte thickness is reduced from 200 μm to 20 μm, the overall thermal deformation variance ranges from 0.0977 to 0.1214. When the electrolyte thickness falls below 80 μm, there is a significant increase in thermal deformation variance. However, adjusting the electrolyte thickness within the range of 80–200 μm results in a relatively small change in overall thermal deformation variance, while also achieving a power density improvement of 0–30.57 %.

Combining physical modeling and machine learning for micro-scale modeling of a fuel cell electrode

Abstract Microscale modeling plays a critical role in fuel cell development, offering deep insights into the microscale transport phenomena and electrochemical reactions. This level of detail is essential for optimizing the performance of a single fuel cell, enabling the precise design and improvement of materials and structures at the microscale and consequently enhancing the overall efficiency of a stack. Here, we show a comprehensive transition from white-box models, characterized by their reliance on physical laws, to black-box models exemplified by neural networks, which excel in pattern recognition from provided data without necessitating a clear understanding of the underlying processes. This spectrum encompasses the inherent challenges and merits of both methodologies. While white-box models are recognized for their reliability due to their foundation in mathematical equations that describe physical phenomena, they often require the integration of empirical parameters and are susceptible to experimental errors, much like their black-box counterparts. The core novelty in this study lies in the synergistic integration of these two paradigms, specifically tailored for enhancing the predictive accuracy in solid oxide fuel cell modeling. In this approach, the neural network is employed to replace different parts of the mathematical model, from refining empirical parameters in the electrochemical model to replacing the entire electrochemical model. The adjustment of parameters is conducted by an evolutionary strategy based on the outputs of the mathematical model. The results underscore the superiority of the gray box in achieving higher prediction accuracy and in minimizing the requisite data volume for network training. This presented approach not only bridges the gap between the deterministic clarity of white-box models and the data-driven insights of black-box models but also strategically distributes the computational load between them, thereby offering a promising solution to the prevalent challenges in solid oxide fuel cell modeling.

Optimized design of planar solid oxide fuel cell interconnectors.

Solid oxide fuel cells (SOFCs) are vital for alternative energy, powering motors effi-ciently. They offer fuel versatility and waste heat recovery, making them ideal for various applications. Optimizing interconnector structures is crucial for SOFC advancement. This paper introduces a novel 2D simulation model for interconnector SOFCs, aiming to enhance their performance. We initially construct a single half-cell model for a conventional interconnector SOFC, ensuring model accuracy. Subsequently, we propose an innovative interconnector SOFC model, which outperforms the conventional counterpart in various aspects.

Overall scheme design of a closed solid oxide fuel cell hybrid engine for ships

A scheme of compact closed solid oxide fuel cell hybrid engines for ship power and propulsion on ships is proposed. A zero-emission closed engine at the effective equivalence ratio of 1 is achieved by recirculating water and fuelling by liquid hydrocarbon fuel and oxygen. The adiabatic pure oxygen reforming temperature of the reformer is higher than the specified anode inlet temperature. A turbine is placed in front of the solid oxide fuel cell anode. Detailed potential distributions are considered using a two-dimensional solid oxide fuel cell model, and thermodynamic models of the hybrid engine are built. The performance of the reformer is more sensitive to the oxygen-carbon ratio rather than the steam-carbon ratio, which leads to a huge change of the pressure ratio of the turbine. Therefore, the power ratios of turbines and SOFC are also affected by the oxygen and steam carbon ratio and excess oxygen coefficient. The optimized power ratio is 1.02–1.13, which results in a significant change in the efficiency of the engine. Under the specified operating conditions, the engine can achieve a high efficiency of 67 %. Under the off-design conditions, with the increase of the mass flow of fuel or the current density, the power of the engine can be changed from 20 % to 160 % of the designed power.

On the validation and applicability of multiphysics models for hydrogen SOFC

Solid oxide fuel cells (SOFC) are a viable alternative for environmentally-friendly conversion of hydrogen into energy and multiphysics simulation can be used to diminish the experimental effort to improve their efficiency. However, an appropriate model of the involved processes and their parameters must be chosen. This paper studies the effects of choice between Maxwell–Stefan and Fick’s law models, and uncertainty of electrode ionic conductivity σion and anodic reference exchange current density i0,ref,f, on cell performance as implemented in the COMSOL Multiphysics® software. In the case of Maxwell–Stefan, peak average power output increased by 21.9% as σion varies from 10−3 to 10−1 S/cm, while the model based on Fick’s law shows an increase of 55.2%. The Maxwell–Stefan model exhibits an increase in peak power of 6% as i0,ref,f ranges from 0.4 to 0.8 A/cm2, and the Fick’s law model an increase of 8.2%. The dependence of the Maxwell–Stefan model on σion is characterized as logarithmic in the studied range. The Maxwell–Stefan model is deemed preferable because its lower sensitivity to the studied parameters helps mitigate uncertainty. It is concluded that despite its limitations, multiphysics modeling is a useful tool for directing research on SOFC materials owing to its descriptive potential.

Transient modeling of a solid oxide fuel cell using an efficient deep learning HY-CNN-NARX paradigm

Control and monitoring systems are crucial for ensuring optimal performance, efficiency, and longevity of Solid Oxide Fuel Cells (SOFC). Developing a model to accurately capture the transient behavior of the SOFC under dynamic operation is essential for these applications. As electrochemical, mass-transfer, and thermal equations are involved in SOFCs’ dynamic, physics-based approaches to capture all the complexity of SOFC systems are often too computationally expensive for real-time implementation. In this paper, an innovative multi-input neural network is developed to build an accurate model of SOFC that is computationally efficient. The proposed algorithm uses experimental data and is a modified nonlinear autoregressive exogenous (NARX) network. An optimal sequence of the most recent observations (output voltages) that characterize the SOFC dynamics is passed through stacked 1D convolutional layers (CNN) to extract latent spatial/temporal information. Then the output is concatenated with current and past exogenous inputs. The fusion of learned features, representing the internal dynamics and the effect of exogenous inputs, is then fed to a fully connected network for one-step ahead performance prediction. This hybrid structure, called HY-CNN-NARX, is capable of identifying the transient dynamics of the SOFCs by unrolling information from historical outputs and inputs within a feedforward framework. To evaluate the model performance, lab-scale tubular SOFCs are experimentally tested at 650–750 °C under various dynamic operations and initial conditions, and the transient and steady-state responses of the SOFC are collected. Once the model is validated using a wide operating range of data, the generalization and prediction performance of the proposed network is compared with a conventional NARX and a recurrent stacked Long short-term memory (LSTM) model. The comparative results demonstrate that the proposed HY-CNN-NARX model outperforms the NARX model on unseen data with an accuracy improvement of 59.2% for root mean square error and 53.7% for mean absolute percentage error. In addition, the prediction performance of the HY-CNN-NARX is comparable to its recurrent counterpart, the LSTM model, but with a 39.3% faster execution time.

Numerical Study on Effects of Flow Channel Length on Solid Oxide Fuel Cell-Integrated System Performances

The structural dimensions of the SOFC have an important influence on the solid oxide fuel cell (SOFC)-integrated system performance. The paper focuses on analyzing the effect of the flow channel length on the integrated system. The system model includes a 3-D SOFC model, established using COMSOL 6.1, and a 1-D model of the SOFC-integrated system established, using Aspen Plus V11. This analysis was conducted within an operating voltage range from 0.4 V to 0.9 V and flow channel length range from 6 cm to 18 cm for the SOFC-integrated system model. Performance evaluation indicators for integrated systems are conducted, focusing on three aspects: net electrical power, net electrical efficiency, and thermoelectric efficiency. The purpose of the paper is to explore the optimal flow channel length of SOFC in the integrated system. The results indicate that there is inevitably an optimal length in the integrated system at which both the net electrical power and net electrical efficiency reach their maximum values. When considering the heat recycling in the system, the integrated system with a flow channel length of 16 cm achieves the highest thermoelectric efficiency of 65.68% at 0.7 V. Therefore, there is a flow channel length that allows the system to achieve the highest thermoelectric efficiency. This study provides optimization ideas for the production and manufacturing of SOFCs from the perspective of practical engineering applications.

Neural network-based modeling of solid oxide fuel cells for marine applications

As the solid oxide fuel cell (SOFC) experimental test is still quite cost-effective and time-consuming, there is a growing need for developing effective simulation tools to reduce the time and cost of the marine SOFC performance test and optimization. The present paper is aimed to study the modeling and simulation of marine solid oxide fuel cells by artificial intelligence method. A neural network based on a particle swarm optimization algorithm is used to establish a marine solid oxide fuel cell model for voltage/current characteristic analysis. The model is also compared with BP neural network and Hopfield neural network methods. The simulation results compared with experimental data show that the effectivity of the particle swarm optimization neural network algorithm is best, which can accurately predict the voltage/current characteristic curves of a SOFC under different fuel flow-air volume ratios. The model study can provide support for SOFC performance characteristics analyses and has significant potential in SOFC optimization applications.

Design and Optimization of an Integrated Power System of Solid Oxide Fuel Cell and Marine Low-Speed Dual-Fuel Engine

A combined system including a solid oxide fuel cell (SOFC) and an internal combustion engine (ICE) is proposed in this paper. First, a 0-D model of SOFC and a 1-D model of ICE are built as agent models. Second, parameter analysis of the system is conducted based on SOFC and ICE models. Results show that the number of cells, current density, and fuel utilization can influence SOFC and ICE. Moreover, a deep neural network is applied as a data-driven model to conduct optimized calculations efficiently, as achieved by the particle swarm optimization algorithm in this paper. The results demonstrate that the optimal system efficiency of 51.8% can be achieved from a 22.4%/77.6% SOFC-ICE power split at 6 000 kW power output. Furthermore, promising improvements in efficiency of 5.1% are achieved compared to the original engine. Finally, a simple economic analysis model, which shows that the payback period of the optimal system is 8.41 years, is proposed in this paper.

Crossflow flat solid oxide fuel cell (SOFC) semi-empirical modeling and the multi-fuel property based on a commercial 700 W stack

Solid Oxide Fuel Cell (SOFC) technology has attracted vast attention for combined heat and power (CHP) application on low or zero carbon emissions because of its high efficiency and multi-fuel selectivity. Due to the high operation temperature, a commercial SOFC system requires a complex system thermal balance and stack self-heating ability which are dramatically influenced by the inlet temperature, reaction heat and thermal radiation of the stack. Multi-fuel selectivity is a further distinct advantage when considering the future variety of renewable fuel sources, such as ammonia (from animal farming), bio-methane (from agriculture), and the other hydrocarbons using carbon capture as an effective H2 carrier. However, the alternating between different fuel types may result in reduced power and the internal heat balance to change, which may further lead to the stack cooling down or over heated. An appropriate model with fast calculation processing capability is necessary to assess the internal changes before switching the fuel source and to inform further decision making to enable the control system to adapt to the change. In this paper, a cross-channel, flat SOFC semi-empirical model is proposed and validated by a commercial 700 W stack using real testing data to assess the accuracy of the simulation results. The SOFC model has multi-fuel ability which presents different properties and internal understanding for H2, NH3, and reformed CH4 through relevant charts (for feed, velocity, temperature, reaction rate, current, power, heat, efficiency). The power outputs for the different fuel sources, H2, NH3, and reformed CH4, are 721.0 W, 628.9 W and 679.7 W respectively when calculated at an air inlet temperature of 893 K. The modeling work was completed using Aspen Plus for SOFC system thermal balance simulations which determined the power output property for 813.3 W (H2), 744.5 W (direct NH3) and 740.7 W (reformed CH4) at the 2.0 times stoichiometric ratio of air feed, and CHP rate of 0.903 (H2), 0.787 (direct NH3) and 0.311 (reformed CH4). This work has the potential to contribute to the United Nation Sustainable Development Goal for Affordable and Clean Energy, Goal 7.

Influence of Interface Morphology on the Thermal Stress Distribution of SOFC under Inhomogeneous Temperature Field

Excessive thermal stress can cause the failure of a solid oxide fuel cell (SOFC), and an inhomogeneous temperature field is one of the reasons for thermal stress in the cell. In the present work, the bi-dimensional thermo-mechanical coupling models of SOFCs with different interface morphologies including planar and corrugated cells are proposed. The temperature distribution of two types of cells under the action of heat conduction is analyzed. Further, the inhomogeneous temperature field caused by gas flow is used as the thermal load to compare the thermal stress distribution of planar and corrugated cells. The influence of interface morphology on the temperature distribution, stress distribution and the contribution of the temperature gradient to stress distribution are investigated. This research provides a reference for reducing thermal stress and improving the stability of SOFC.

Physics-Based Model to Represent Membrane-Electrode Assemblies of Solid-Oxide Fuel Cells Based on Gadolinium-Doped Ceria

This paper reports a physics-based model that predicts membrane-electrode assembly (MEA) performance of solid-oxide fuel cells (SOFCs) with Ce0.9Gd0.1O2−δ (GDC10) electrolyte membranes. The paper derives self-consistent thermodynamic and transport properties for GDC1o mobile charged defects (oxide vacancies and reduced-ceria small polarons) by fitting published measurements of oxygen non-stoichiometry and conductivity over ranges of temperature and O2 partial pressures. The button-cell model is applied to evaluate how mixed ionic-electronic conductivity influences the performance of an SOFC MEA with a GDC10 electrolyte sandwiched between a porous, composite Ni-GDC10 anode and a porous, composite cathode of Sm0.5Sr0.5CoO3−δ (i.e., SSC) and GDC10. SSC properties are also derived by fitting published conductivity and oxygen non-stoichiometry measurements. Mixed conductivity of GDC10 and competing charge transfer reactions at both electrodes reduce open circuit voltages due to leakage current and buildup of defect concentrations at electrode-electrolyte interfaces. To fit polarization data, the button-cell model includes heterogeneous reaction rates for defect incorporation on the GDC10 surface along with Butler–Volmer expressions derived for competing charge transfer reaction rates from rigorous analyses assuming rate-limiting, elementary charge transfer reactions for each electrode. The calibrated MEA model can support rigorous SOFC modeling with GDC10 electrolytes over the range of conditions within a fully operating cell.

Thermodynamics and electrochemical performance of co- and counter-flow planar solid oxide fuel cells under an adiabatic operation environment

Solid oxide fuel cell (SOFC) is a promising energy conversion technology for accelerating the process of carbon neutrality. This paper develops and validates a 1D mathematical model for a planar SOFC (10 cm × 10 cm) along the fluid flow direction with a less than 0.2% deviation. When the SOFC operates in an adiabatic environment with different inlet gas temperatures (Tin) and current density (Iavg), the distributions of its key parameters are calculated and analyzed. The results show that the optimal inlet gas temperature for the SOFC working in an adiabatic environment is between 873 K and 973 K when Iavg varies from 0.05 A cm−2 to 0.25 A cm−2. The maximum temperature appears at the outlet position and between the outlet and the center point along the flue flow for the co-flow and counter-flow SOFC. Compared with the co-flow pattern, the counter-flow design can benefit the fuel cell power output when Tin and Iavg are identical, especially with lower Tin and higher Iavg. The output power of counter-flow SOFC is larger 11.3% than that of the co-flow one at most with the research range in this work.

Numerical Modeling of a Pressurized Solid Oxide Fuel Cell for Electric Aircraft

Electric aircraft have attracted attention to reducing carbon dioxide emissions and fuel consumption. Compared with conventional aircraft, distributed propulsion with electric motors is expected to increase the efficiency of the propulsion systems for the above purpose. Furthermore, the application of solid oxide fuel cell (SOFC) – gas turbine (GT) hybrid systems to their electric power sources is promising for higher efficiency. We have thus developed a three-dimensional numerical model of a planar SOFC pressurized for the combination with a GT for the optimal design and operation of practical cells. A software package with the finite element method (COMSOL Multiphysics 5.4) is employed to analyze the current and temperature distributions in a cell. Exchange current densities under pressurized conditions are experimentally evaluated using a symmetric test cell for the electrochemical kinetics in the model.

Performance Prediction of Solid Oxide Fuel Cells Based on a Neutral Network Model

Predicting various parameters in a fast and accurate way plays an important role for the development of high-temperature sealed reactors such as the solid oxide fuel cells (SOFCs). However, the analysis of SOFC performance parameters mainly focuses on the development of multiphysics models, which is complicated and slow, causing inefficiency in the prediction of key parameters. In our study, a neural network prediction model of SOFCs was developed in combination with the deep learning method. The neural network model was trained by using the results from a multiphysics model validated by experiments. The trained SOFC neural network model was found to have good consistency with the simulation results of multiphysics model. The neural network model was further utilized in a system-level model to provide fast and accurate prediction of the system performance.Keywords: SOFC, Multiphysics model, Neural network model, System simulation

A Policy optimization-based Deep Reinforcement Learning method for data-driven output voltage control of grid connected solid oxide fuel cell considering operation constraints

Solid oxide fuel cells (SOFCs) have many applications in microgrids, but they often face the challenge of maintaining the fuel utilization within a safe range, which affects their lifespan. To address this issue, we propose a Data-driven Output voltage control (DDD-OVC) approach that treats the SOFC output voltage controller as an intelligent agent. The agent can design a reward function that incorporates the fuel utilization constraint and learn the optimal control policy through offline training. The objective is to optimize both the SOFC output voltage control performance and lifetime. Furthermore, we develop a policy optimization-based Deep Reinforcement Learning (PO-DRL) algorithm that adopts the idea of proximal policy optimization to enhance the learning speed and convergence of the agent, as well as the policy stability and quality of DDD-OVC. We validate the effectiveness of our method on a 5kW SOFC model.