Solid Oxide Fuel Cell Model Research Articles

Nonlinear multivariable modeling of solid oxide fuel cells using core vector regression

This paper presents new steady-state and dynamic models for solid oxide fuel cells (SOFCs) using core vector regression (CVR). So far, most of conventional SOFC models have been presented based on conversion laws. Due to complex mathematical equations used in these models, they are time-consuming and need large amount of memory to be applied for controller design, especially power electronic interface controller design, generation and load predictions, optimization and other studies. To overcome these problems, some black-box models, such as support vector machine (SVM) and artificial neural network (ANN)-based models have been also proposed for SOFC. In this paper, in order to model nonlinear multivariable behavior of SOFC two CVR-based black-box models are proposed for each operation mode, one for steady-state and the other one for dynamic modeling. The proposed models are trained in a very little time and need small amount of memory in comparison with existing black-box models. This is due to usage of fewer number of support vectors (SVs). In order to demonstrate the efficacy of the proposed models, they are applied to a 5-kW SOFC stack. Simulation results illustrate the effectiveness of the proposed models for both steady-state and dynamic studies.

Steady-state multiplicity in a solid oxide fuel cell: Practical considerations

Steady-state multiplicity in a solid oxide fuel cell (SOFC) in three modes of operation, constant ohmic external load, potentiostatic and galvanostatic, is studied using a detailed first-principles lumped model. The SOFC model is derived by accounting for heat and mass transfer as well as electrochemical processes taking place inside the fuel cell. Conditions under which the fuel cell exhibits steady state multiplicity are determined. The effects of operating conditions such as convection heat transfer coefficient and inlet fuel and air temperatures and velocities on the steady state multiplicity regions are studied. Depending on the operating conditions, the cell exhibits one or three steady states. For example, it has three steady states: (a) at low external load resistance values in constant ohmic external load operation and (b) at low cell voltage in potentiostatic operation.

Robust Real-Time Optimization of a Solid Oxide Fuel Cell Stack

On-line control and optimization can improve the efficiency of fuel cell systems, whilst simultaneously ensuring that the operation remains within a safe region. Also, fuel cells are subject to frequent variations in their power demand. This paper investigates the real-time optimization (RTO) of a solid oxide fuel cell (SOFC) stack. An optimization problem maximizing the efficiency subject to operating constraints is defined. Due to inevitable model inaccuracies, the open-loop implementation of optimal inputs evaluated off-line may be suboptimal, or worse, infeasible. Infeasibility can be avoided by controlling the constrained quantities. However, the constraints that determine optimal operation might switch with varying power demand, thus requiring a change in the regulator structure. In this paper, a control strategy that can handle plant-model mismatch and changing constraints in the face of varying power demand is presented and illustrated. The strategy consists in the integration of RTO and model predictive control (MPC). A lumped model of the SOFC is utilized at the RTO level. The measurements are not used to re-estimate the parameters of the SOFC model at different operating points, but to simply adapt the constraints in the optimization problem. The optimal solution generated by RTO is implemented using MPC that uses a step-response model in this case. Simulation results show that near-optimality can be obtained, and constraints are respected despite model inaccuracies and large variations in the power demand.

Simulation of alternative fuels for potential utilization in solid oxide fuel cells

Fuel cells are promising with advantages of higher energy conversion efficiency and lower emissions of SOX, NOX, and CO2 than conventional power systems. Solid oxide fuel cell (SOFC) is a high temperature fuel cell, which operates at 873–1273 K. This allows SOFCs to operate with different types of fuels from both fossil and renewable sources because of their general higher tolerance to contaminants than other fuel cells. It opens up for an easier transition from conventional power generation of hydrocarbon-based fuels to hydrogen energy by fuel cells. With increased interest in the use of renewable fuels, fuel cells have the potential to play a significant role in a sustainable solution. Attractive fuels, which are reviewed here and analyzed through thermodynamic calculations in this study, are methanol, ethanol, di-methyl-ether, and biogas. It is concluded that it is feasible for SOFCs to handle all the studied fuels. Further, a CFD model of an anode-supported SOFC is simulated with biogas as fuel. An analysis of the fuels is conducted at 1000 K, in terms of the heat required for each mole H2 converted. It shows that methane uses twice as much heat as methanol and di-methyl-ether do, and if efficiently distributed where needed, it can work as a possible performance enhancement. A composed table of comparable studies in the literature of different alternative fuels is provided. The case study of an anode-supported SOFC fueled with biogas of varying amount of methane and steam-to-fuel ratio revealed that biogas needs a high inlet temperature to enable the reforming and keep a constant current density distribution. Copyright © 2011 John Wiley & Sons, Ltd.

Effects of operating and design parameters on the performance of a solid oxide fuel cell-gas turbine system

We present a steady-state thermodynamic model of a hybrid solid oxide fuel cell (SOFC)–gas turbine (GT) cycle developed using a commercial process simulation software, AspenPlus™. The hybrid cycle model incorporates a zero-dimensional macro-level SOFC model. A parametric study was carried out using the developed model to study the effects of system pressure, SOFC operating temperature, turbine inlet temperature, steam-to-carbon ratio, SOFC fuel utilization factor, and GT isentropic efficiency on the specific work output and efficiency of a generic hybrid cycle with and without anode recirculation. The results show that system pressure and SOFC operating temperature increase the cycle efficiency regardless of the presence of anode recirculation. On the other hand, the specific work decreases with operating temperature. Overall, the model can successfully capture the complex performance trends observed in hybrid cycles. Copyright © 2010 John Wiley & Sons, Ltd.

A planar anode-supported Solid Oxide Fuel Cell model with internal reforming of natural gas

Solid Oxide Fuel Cells (SOFCs) are of great interest due to their high energy efficiency, low emission level, and multiple fuel utilization. SOFC can operate with various kinds of fuels such as natural gas, carbon monoxide, methanol, ethanol, and hydrocarbon compounds, and they are becoming one of the main competitors among environmentally friendly energy sources for the future. In this study, a mathematical model of a co-flow planar anode-supported solid oxide fuel cell with internal reforming of natural gas has been developed. The model simultaneously solves mass, energy transport equations, and chemical as well as electrochemical reactions. The model can effectively predict the compound species distributions as well as the cell performance under specific operating conditions. The main result is a rather small temperature gradient obtained at 800 °C with S/C = 1 in classical operating conditions. The cell performance is reported for several operating temperatures and pressures. The cell performance is specified in terms of cell voltage and power density at any specific current density. The influence of electrode microstructure on cell performance was investigated. The simulation results show that the steady state performance is almost insensitive to microstructure of cells such as porosity and tortuosity unlike the operating pressure and temperature. However, for SOFC power output enhancement, the power output could be maximized by adjusting the pore size to an optimal value, similarly to porosity and tortuosity. At standard operating pressure (1 atm) and 800 °C with 48% fuel utilization, when an output cell voltage was 0.73 V, a current density of 0.38 A cm-2 with a power density of 0.28 W cm-2 was predicted. The accuracy of the model was validated by comparing with existing experimental results from the available literature.

Decentralized Control of Solid Oxide Fuel Cells

Environmental concerns and limited availability of natural resources have made solid oxide fuel cells (SOFC) a promising alternative for large-scale electricity production. A control system is needed for SOFCs to meet operational objectives and ensure safe operation. Previous studies showed that the control of SOFC is challenging due to its slow response time, tight operating constraints and unavailability of some key measurements. In this work, simple yet reliable decentralized proportional-integral-derivative (PID) controllers are systematically designed based on a benchmark nonlinear dynamic model of SOFC . The design procedure involves selection of controlled variables (CVs), input-output pairing selection, and PID controller tuning. For CV selection, a novel method is proposed such that maintaining the CVs at constant setpoints facilitates constraint satisfaction for all key variables. Closed-loop simulations demonstrate that the proposed decentralized PI controllers are able to closely meet the control objectives of SOFC even in the presence of changing operating conditions.

Fabrication of Cathode-supported Tubular Solid Oxide Electrolysis Cell for High Temperature Steam Electrolysis

The cathode-supported tubular solid oxide electrolysis cell (SOEC) fabricated by dip-coating and co-sintering techniques have been studied for high temperature steam electrolysis application. The microstructure and electrochemical performeances were investigated in both SOEC and solid oxide fuel cell (SOFC) modes. In SOFC model, the maximum power densitity reached 390.7, 311.0 and 248.3 mW cm-2 at 850, 800, and 700 °C, respectively, running with H2 (105 mL min-1) and O2 (70 mL min-1) as working gases. In SOEC mode, the results indicated that the steam ratio had a strong impact on the performance of the tubular SOEC, and it’s better to operate the tubular SOEC in high steam ratio. I-V curves and EIS results suggested that the microstructure of the tubular SOEC needs to be optimized for mass transportation.

Film percolation for composite electrodes of solid oxide fuel cells

A film percolation model is proposed for composite electrodes of solid oxide fuel cells (SOFCs). The model is developed to predict the percolation properties of 2D-infinite structures which represent the structural characteristics of composite electrodes of electrochemical devices such as SOFCs. The model can be used to estimate electrode properties, such as percolation probability, active three-phase boundary length and interfacial polarization resistance. Compared with the classic percolation theory, which is particularly applicable to 3D-infinite bulks, the model can explicitly capture the effects of thinly layered nature of composite electrodes, and describes a cross-over between 2D-infinite films and 3D-infinite bulks. It also permits the prediction within whole electrode composition range, and can be easily applied in SOFC modeling.

Parameter optimization for tubular solid oxide fuel cell stack based on the dynamic model and an improved genetic algorithm

The tubular solid oxide fuel cell (SOFC) stack has important parameters that need to be identified and optimized for the control of high performance. In this paper, a simple SOFC electrochemical model which its parameters need to be optimized is introduced to implement stack control for high output power. A dynamic SOFC model is built based on three sub-models to provide a large numbers simulated data and different condition for optimization. Unlike the traditional parameter optimization method--simple genetic algorithm (SGA), an improved genetic algorithm (IGA) is introduced. The proposed method shows more accuracy and validity by comparing the different results using SGA and IGA methods, the simulated data, and experimental data. The models and IGA method are adapted to control processes.

Application of a detailed dimensional solid oxide fuel cell model in integrated gasification fuel cell system design and analysis

Integrated gasification fuel cell (IGFC) systems that combine coal gasification and solid oxide fuel cells (SOFC) are promising for highly efficient and environmentally sensitive utilization of coal for power production. Most IGFC system analysis efforts performed to-date have employed non-dimensional SOFC models, which predict SOFC performance based upon global mass and energy balances that do not resolve important intrinsic constraints of SOFC operation, such as the limits of internal temperatures and species concentrations. In this work, a detailed dimensional planar SOFC model is applied in IGFC system analysis to investigate these constraints and their implications and effects on the system performance. The analysis results further confirm the need for employing a dimensional SOFC model in IGFC system design. To maintain the SOFC internal temperature within a safe operating range, the required cooling air flow rate is much larger than that predicted by the non-dimensional SOFC model, which results in a larger air compressor design and operating power that significantly reduces the system efficiency. Options to mitigate the challenges introduced by considering the intrinsic constraints of SOFC operation in the analyses and improve IGFC design and operation have also been investigated. Novel design concepts that include staged SOFC stacks and cascading air flow can achieve a system efficiency that is close to that of the baseline analyses, which did not consider the intrinsic SOFC limitations.

Single solid oxide fuel cell modeling and optimization

In this paper a dynamic model of a single solid oxide fuel cell (SOFC) is developed using a volume element methodology. It consists of a set of algebraic and ordinary differential equations derived from physical laws (e.g., the first law of thermodynamics, Fick's law, and Fourier's law), which allow for the prediction of the temperature and pressure spatial distribution inside the single SOFC, as functions of geometric and operating parameters. The thermodynamic model is coupled with an electrochemical model that is capable of determining the voltage, current, and power output. Based on the simulation results, the internal configuration (structure of the positive electrode–electrolyte–negative electrode assembly) and the operating conditions (air stoichiometric ratio and fuel utilization factor), as well as their impact on the performance of the single SOFC are discussed. Optimal geometric and operating parameters are obtained so that electrical power of the single SOFC at the nominal operating point is maximized. The method used is general and the fundamental optimization results are sharp, showing up to a 357% single SOFC performance variation within the studied parameters’ range, therefore these findings show the potential to use the model as a tool for future SOFC design, simulation and optimization.

Three-dimensional computational fluid dynamics modeling of anode-supported planar SOFC

Modeling plays a very important role in the development of fuel cells and fuel cell systems. The aim of this work is to investigate the electrochemical processes of a Solid Oxide Fuel Cell (SOFC) and to evaluate the performance of the proposed SOFC design. For this aim a three-dimensional Computational Fluid Dynamics (CFD) model has been developed for an anode-supported planar SOFC with corrugated bipolar plates serving as gas channels and current collector. The conservation of mass, momentum, energy and species is solved by using the commercial CFD code FLUENT in the developed model. The add-on FLUENT SOFC module is implemented for modeling the electrochemical reactions, loss mechanisms and related electric parameters throughout the cell. The distributions of temperature, flow velocity, pressure and gaseous (fuel and air) concentrations through the cell structure and gas channels is investigated. The relevant fuel cell variables such as the potential and current distribution over the cell and fuel utilization are calculated and studied. The modeling results indicate that, for the proposed SOFC design, reasonably uniform distributions of current density over the active cell area can be achieved. The geometry of the cathode gas channel has a substantial effect on the oxygen distribution and thus the overall cell performance. Methods for arriving at improved cell designs are discussed.

Optimization of a Single-Cell Solid-Oxide Fuel Cell Using Computational Fluid Dynamics

To determine the effects of various parameters on the performance of a solid-oxide fuel cell (SOFC), a series of simulations was performed using computational fluid dynamics (CFD). The first step in this process was to create a three-dimensional CFD model of a specific single-cell SOFC for which experimental performance data had been published. The CFD simulation results developed using this baseline model were validated by comparing them to the experimental data. Numerous CFD simulations were then performed with various thermal conditions at the cell’s boundaries and with different fuel and air inlet temperatures. Simulations were also conducted with fuel utilization factors from 30% to 90% and air ratios from 2 to 6. As predicted by theory, conditions that resulted in higher cell temperatures or in lower air and fuel concentrations resulted in lower thermodynamically reversible voltages. However, the higher temperatures also reduced Ohmic losses and, when operating with low to moderate current densities, activation losses, which often caused the voltages actually being produced by the cell to increase. Additional simulations were performed during which air and fuel supply pressures were varied from 1 atm to 15 atm. Although the increased pressure resulted in higher cell voltages, this benefit was significantly reduced or eliminated when air- and fuel-compressor electrical loads were included. CFD simulations were also performed with counterflow, crossflow, and parallel-flow fuel-channel to air-channel configurations and with various flow-channel dimensions. The counterflow arrangement produced cell voltages that were equal to or slightly higher than the other configurations, and it resulted in a differential temperature across the electrolyte that was significantly less than that of the parallel-flow cell and was close to the maximum value in the crossflow cell, which limits stress caused by uneven thermal expansion. The use of wider ribs separating adjacent flow channels reduced the resistance to the electrical current conducted through the ribs. However, it also reduced the area over which incoming fuel and oxygen were in contact with the electrode surfaces and, consequently, impeded diffusion through the electrodes. Reducing flow-channel height reduced electrical resistance but increased the pressure drop within the channels. Plots of voltage versus current density, together with temperature and species distributions, were developed for the various simulations. Using these data, the effect of each change was determined and an optimum cell configuration was established. This process could be used by fuel cell designers to better predict the effect of various changes on fuel cell performance, thereby facilitating the design of more efficient cells.

An analytical model of view factors for radiation heat transfer in planar and tubular solid oxide fuel cells

Radiant heat transfer plays an important role in the distribution of cell temperature and current density in solid oxide fuel cells (SOFC). The objective of this paper is to introduce a mathematical model of view factors for radiation heat exchange in an in-house longitudinally distributed SOFC model. A differential view factor model is first developed for planar and tubular SOFC configurations, but is found invalid when the infinitesimal element size is comparable to the characteristic size. Then, a finite-difference view factor model is developed to solve the problem of discontinuities in the differential view factor model. Starting from a classical problem of convective and radiant heat transfer for a transparent gas flow in a gray-wall tube, a fast and accurate computation is available for the finite-difference view factor model without extra mathematical derivations of the governing equations. Compared to the simple modeling which only takes into account the surface-to-surface radiation exchange between two directly opposed elements, the detailed radiation model based on analytical view factors predicts more uniform distribution of cell temperature and current density in the overall SOFC modeling.

Bifunctionally Graded Electrode Supported SOFC Modeling and Computational Thermal Fluid Analysis for Experimental Design

A comprehensive 3D computational fluid dynamics (CFD) model is developed for a bi-electrode supported cell (BSC) solid oxide fuel cell (SOFC). The model includes complicated transport phenomena of mass/heat transfer, charge (electron and ion) migration, and electrochemical reactions. The uniqueness of the modeling study is that functionally graded porous electrode property is taken into account, including not only linear but also nonlinear porosity distributions. The model is validated using experimental data from open literature. Numerical results indicate that BSC performance is strongly dependent on both operating conditions and porous microstructure distributions of electrodes. Using the proposed fuel/gas feeding design, the uniform hydrogen distribution within the porous anode is achieved; the oxygen distribution within the cathode is dependent on porous microstructure distributions as well as pressure loss conditions. Simulation results also show that fairly uniform temperature distribution can be obtained with the proposed fuel/gas feeding design. This modeling work can provide a pre-experimental analysis and guide experimental designs for BSC test.

Study of species, temperature distributions and the solid oxide fuel cells performance in a 2-D model

A two-dimensional mathematical model for a planar SOFC (solid oxide fuel cell) is constructed. The distribution of the chemical species, the temperature and the performance (power) and the current density were calculated using a single-unit model with double channels of co-flow pattern. The finite volume method was employed for the calculation. The method was based on the fundamental conservation laws of continuity, momentum, energy and mass. The equations are implemented in FORTRAN language. The effects of several heat sources and flow rates on the calculated results were also investigated. The reference SOFC polarization curve has been calculated by imposing a uniform temperature of 800 K, a pressure equal to 1 atm; H2 and O2 molar fractions equal to 0.97 and 0.21 respectively. Results of temperature, chemical species distributions, performance and efficiency under several heat sources are shown and discussed. At a current density of about 23500 A/m2, the power densities under all sources and chemical sources reached their maximums of 12965 W/m2 and 16209 W/m2 (i.e. 25% lower) respectively. However the temperature increment in the anode is analyzed toward all sources and chemical reaction. The temperature maximum values for each heat source type reached 1005.81 K and 984.69 K respectively.

Numerical Investigation of a Delta High Power Density Cell and Comparison With a Flattened Tubular High Power Density Cell

The thermal, electrical, and fluid flow fields associated with a Siemens Power Generation Inc., Stationary Fuel Cells, flattened tubular high power density (HPD) solid oxide fuel cell (SOFC) were investigated comprehensively in a previous study. The present computational investigation is the subsequent part of an ongoing numerical pursuit at Siemens of an optimized cell geometry, commercialization of SOFC technology being the ultimate objective. A Delta type HPD cell featuring eight air channels was investigated and compared with a flattened tubular HPD cell. The computational models were developed using the commercial computational fluid dynamics software FLUENT 6.2 along with its SOFC user defined routine to model the electrochemical effects. The SOFC model parameters were derived from experimental data. The cathode, the anode, and the interconnection layers of the cell were resolved in the model and all modes of heat transfer, conduction, convection, and radiation were included. The resulting electrical performance and the thermal hydraulic characteristics of the cells for fully reformed natural gas fuel flow (reformed external to the cell) are presented and discussed. It was clear from these studies that the Delta HPD cell has distinct advantages over the flattened HPD cell in terms of system electrical performance as well as power density.

Dynamic modeling of tubular SOFC for marine power system

Solid oxide fuel cell (SOFC) has been identified as an effective and clean alternative choice for marine power system. This paper emphasizes on the dynamic modeling of SOFC power system and its performance based upon marine operating circumstance. A SOFC power system model has been provided considering thermodynamic and electrochemical reaction mechanism. Subcomponents of lithium ion battery, power conditioning unit, stack structure and controller are integrated in the model. The dynamic response of the system is identified according to the inertia of its subcomponent and controller. Validation of the whole system simulation at steady state and transit period are presented, concerning the effects of thermo inertia, control strategy and seagoing environment. The simulation results show reasonable accuracy compare with lab test. The models can be used to predict performance of a SOFC power system and identify the system response when part of the component parameter is adjusted.

Effects of Electrode Microstructure on Intermediate Temperature Solid Oxide Fuel Cell Performance

Abstract In this study, the effects of electrode microstructure and electrolyte parameters on intermediate temperature solid oxide fuel cell (ITSOFC) performance were investigated using a one-dimensional solid oxide fuel cell model from the Pacific Northwest National Laboratory (PNNL). The activation overpotential was investigated through the exchange current density term, which is dependent on the cathode activation energy, the cathode porosity, and the pore size and grain size at the cathode triple phase boundary. The cathode pore size, grain size, and porosity were not integrated in the PNNL model, therefore, an analytical solution for exchange current density from Deng and Petric (2005, “Geometric Modeling of the Triple-Phase Boundary in Solid Oxide Fuel Cells,” J. Power Sources, 140, pp. 297–303) was utilized to optimize their effects on performance. Through parametric evaluation and optimization of the electrode microstructure parameters, the activation overpotential was decreased by 29% and the overall ITSOFC maximum power density was increased by almost 400% from the benchmark PNNL case. The effects and importance of electrode microstructure parameters on ITSOFC performance were defined. Optimization of such parameters will be the key in creating viable ITSOFC systems. Although this was deemed successful for this project, future research should be focused on numerically quantifying and modeling the electrode microstructure in two- and three-dimensions for more accurate results, as the electrode microstructure may be highly multidimensional in nature.