Control Loop Design and Control Performance Study on Direct Internal Reforming Solid Oxide Fuel Cell

A solid oxide fuel cell (SOFC) stack is a complicated nonlinear power system. Its system model includes a set of partial differential equations that describe species, mass, momentum and energy conservation, as well as the electrochemical reaction models. The validation and verification of the control system by experiment is very expensive and difficult. Based on the distributed and lumped model of a one‐dimensional SOFC, the dynamic performance with different control loops for SOFC is investigated. The simulation result proves that the control system is appropriate and feasible, and can effectively satisfy the requirement of variable load power demand. This simulation model not only can prevent some latent dangers of the fuel cell system but also predict the distributed parameters' characteristics inside the SOFC system.     

平板式直接内重整固体氧化物燃料电池的一维动态建模与仿真

This article aims to investigate the transient behavior of a planar direct internal reforming solid oxide fuel cell (DIR-SOFC) comprehensively. A one-dimensional dynamic model of a planar DIR-SOFC is first developed based on mass and energy balances, and electrochemical principles. Further, a solution strategy is presented to solve the model, and the International Energy Agency (IEA) benchmark test is used to validate the model. Then, through model-based simulations, the steady-state performance of a co-flow planar DIR-SOFC under specified initial operating conditions and its dynamic response to introduced operating parameter disturbances are studied. The dynamic responses of important SOFC variables, such as cell temperature, current density, and cell voltage are all investigated when the SOFC is subjected to the step-changes in various operating parameters including both the load current and the inlet fuel and air flow rates. The results indicate that the rapid dynamics of the current density and the cell voltage are mainly influenced by the gas composition, particularly the H2 molar fraction in anode gas channels, while their slow dynamics are both dominated by the SOLID (including the PEN and interconnects) tem-perature. As the load current increases, the SOLID temperature and the maximum SOLID temperature gradient both increase, and thereby, the cell breakdown is apt to occur because of excessive thermal stresses. Changing the inlet fuel flow rate might lead to the change in the anode gas composition and the consequent change in the current den-sity distribution and cell voltage. The inlet air flow rate has a great impact on the cell temperature distribution along the cell, and thus, is a suitable manipulated variable to control the cell temperature.     

Dynamic modeling of a finite volume of solid oxide fuel cell: The effect of transport dynamics

A dynamic model for a finite volume of cell based on physical principles is built in the form of a nonlinear state-space model to investigate dynamic behaviors of tubular solid oxide fuel cell (SOFC) and develop a control relevant model for further control studies. Dynamic effects induced by diffusions, intrinsic impedance, fluid dynamics, heat exchange and direct internal reforming/shifting (DIR) reactions are all considered. Cell temperature, ingredient mole fractions, etc. are the state variables and their dynamics are investigated. Dynamic responses of each variable when the external load changes are simulated. Simulation results show that fuel flow, inlet pressure and temperature have significant effects on the dynamic performance of SOFC. Further it is shown that, compared to other inlet flow properties, cathode side air inlet temperature has the most significant effect on SOFC solid phase temperature and performance. Compared with inlet pressures and temperatures, the effect of flow velocity is not significant. Simulation also indicates that the transient response of SOFC is controlled mainly by the dynamics of cell temperature owing to its large heat capacity.     

The Performance of SOFC Model Under Different Three‐phase Load Conditions

In this paper, the dynamic performance of a modified thermal based dynamic model of a solid oxide fuel cell (SOFC) is presented under different three‐phase load conditions. The modified thermal based fuel cell model contains ohmic, activation and concentration voltage losses, thermal dynamics, methanol reformer and fuel utilization factor limiting stage. SOFC model and the power conditioning unit (PCU), which consists of a DC‐DC boost converter, a DC‐AC inverter, their controller, transformer and filter, are developed on Matlab/Simulink environment. The simulation results show that the real and reactive power management of the inverter is performed successfully in an AC power system with the proposed thermal based SOFC model under three‐phase load conditions such as ohmic loads, switched ohmic−inductive loads and a three‐phase induction motor. Finally, the three‐phase induction motor is performed both no load and load conditions. The simulation results show that the modified thermal based fuel cell model provides an accurate representation of the dynamic and steady state behavior of the fuel cell under different three‐phase load conditions.     

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.     

Direct Operation of IP‐Solid Oxide Fuel Cell with Hydrogen and Methane Fuel Mixtures under Current Load Cycle Operating Condition

The effects of methane concentration and current load cycle on the performance and durability of integrated planar solid oxide fuel cell (IP‐SOFC) obtained from Rolls Royce Fuel Cell Systems Ltd (RRFCS) has been investigated. The IP‐SOFC was operated with hydrogen–methane fuel mixture with up to 20% methane concentration at 900 °C for short term operation of the cells with high methane concentration increased the voltage of the IP‐SOFC due to increase in Gibbs free energy. However, it degraded the performance of the IP‐SOFC in long term operation due to carbon deposition on the anode surface. The current load cycle tests were carried out with 95% H₂–5% CH₄ and 80% H₂–20% CH₄ fuel mixtures at 900 °C with a constant current of 1 A. At low methane concentration, the decrease in the IP‐SOFC voltage was observed after operating nine current load cycles (384 h). At higher methane concentration, the voltage of IP‐SOFC decreased by almost 30% just after one current load cycle (48 h) due to faster carbon deposition. So future work is therefore required to identify viable alternative materials and optimum operating conditions.     

Emulator Rig for SOFC Hybrid Systems: Temperature and Power Control with a Real‐Time Software

This work is based on the hybrid system emulator plant developed by the Thermochemical Power Group (TPG) of the University of Genoa. This rig is composed of a 100 kW microturbine coupled with high temperature fuel cell emulation devices. A real‐time model is used for components not physically present in the laboratory (solid oxide fuel cell (SOFC), reformer, anodic circuit, off‐gas burner, cathode blower). It is necessary to evaluate thermodynamic and electrochemical performance related to SOFC systems. Using an User Datagram Protocol (UDP) based connection with the control/acquisition software, it generates a hardware‐in‐the‐loop (HIL) facility for hybrid system emulation. Temperature, pressure, and mass flow rate at the recuperator outlet and machine rotational speed are measured in the plant and used as inputs for the model. The turbine outlet temperature (TOT) calculated by the model is fed into the machine control system and the turbine electric load is changed to match the model TOT values (effective plant/model coupling to avoid modifications on microturbine controller). Different tests were carried out to analyze hybrid system technology through the interaction between an experimental plant and a real‐time model. Double step and double ramp tests of current and fuel provided the system dynamic response.     

A Control‐oriented Dynamic Model Adapted to Variant Steam‐to‐carbon Ratios for an SOFC with Exhaust Fuel Recirculation

The steam‐to‐carbon ratio (S/C) is a typical disturbance parameter in the operation of solid oxide fuel cell (SOFC) power generation system. A planar SOFC with a pre‐reformer and exhaust fuel recirculation system is investigated in this work. A lumped, nonlinear dynamic model is developed for the SOFC with consideration both of the spatial effect and the variant S/Cs. The dynamic model is deduced based on a fitting function so‐called Exponential Association Function, which is employed to describe the spatial distribution of state variables in SOFC. Three parameters of the fitting function are identified to integrate the spatial effect and S/C effect in the model. The parameters of Exponential Association Function are determined by function fitting on three‐dimensional numerical data at the sample operation points. Carbon formation activity is analysed using the simulation results and thermodynamic data. Dynamic simulation is implemented with the help of software MATLAB/SIMULINK. The results show that the developed model has good performance in predicting the responses of the state variables and catching the changes of S/C.     

负载动态变化时直接甲醇燃料电池的响应特性

直接甲醇燃料电池动态特性的研究对于实际应用来说非常重要.实验研究了直接甲醇单体燃料电池电流动态变化时电压的响应. 基于计算机控制的负载变化,得到了各种电流变化波形及不同的加载电流、放电/开路时间、加载斜率下的电池电压动态响应.结果表明电池电压对电流动态变换变化时的响应很迅速,动态运行时电池的开路电压要比稳态时的高,加载斜率对电池动态响应特性有重要影响. 电池内部电化学反应和传热传质瞬态变化的相互作用是电池动态响应的关键.     

Electrochemical impedance spectra of solid-oxide fuel cells and polymer membrane fuel cells

Electrochemical impedance spectroscopy (EIS) is a very useful method for the characterization of fuel cells. The anode and cathode transfer functions have been determined independently without a reference electrode using symmetric gas supply of hydrogen or oxygen on both electrodes of the fuel cell at open circuit potential (OCP). EIS are given for both polymer electrolyte fuel cells (PEFC) and solid oxide fuel cells (SOFC) at current densities up to 0.76 A cm⁻² (PEFC) and 0.22 A cm⁻² (SOFC). With increasing current density the PEFC-impedance decreases significantly in the low frequency range reaching a minimum at 0.4 A cm⁻². At even higher current densities an increasing contribution of water diffusion is observed: the cell impedance increases again. From EIS of SOFC a finite diffusion behavior is observed even at OCP, depending on water partial pressure of the anodic gas supply. This additional element reflects the influence of water partial pressure on the cell potential. The simulation of the measured EIS with an equivalent circuit enables the calculation of the individual voltage losses in the fuel cell.     

Comparison of two IT DIR-SOFC models: Impact of variable thermodynamic, physical, and flow properties. Steady-state and dynamic analysis

This paper compares two dynamic, one-dimensional models of a planar anode-supported intermediate temperature (IT) direct internal reforming (DIR) solid oxide fuel cell (SOFC): one where the flow properties (pressure, gas stream densities, heat capacities, thermal conductivities, and viscosity) and gas velocities are taken as constant throughout the system, based on inlet conditions, and one where this assumption is removed to focus on the effect of considering the variation of local flow properties on the prediction of the fuel cell performance. The refined model consists of mass, energy, and momentum balances, and of an electrochemical model that relates the fuel and air gas compositions and temperatures to voltage, current density, and other relevant fuel cell variables. Simulations for steady-state and dynamic conditions have been carried out and the results obtained from the two models compared. For a co-flow SOFC operating on a 10% pre-reformed methane fuel mixture, with 75% fuel utilisation, inlet fuel and air temperatures of 1023 K, average current density of , and an air ratio of 8.5, the results show that, although the error incurred in the prediction of the flow properties in the first model is significant, there is good agreement between both models in terms of the overall cell performance: the maximum difference in the local temperature values is about 7 K and the cell efficiency differs by less than 1%. However, the discrepancies between the two models increase, especially in the fuel channel, when higher current density values are assigned to the cell.     

平板状固体氧化物燃料电池电化学特性Simlink建模与仿真

在分析平板状固体氧化物燃料电池电化学特性的基础上,建立了Simlink仿真模型,探讨了工作温度和燃料中水蒸气含量对燃料电池理想电势和有效电势的影响。仿真结果表明,低电流密度下,温度的升高会导致有效电势的降低;高电流密度下,有效电势会随着温度升高而增加。水蒸气含量越低,燃料电池的理想电势和有效电势越高。     

Mathematical Modelling of Proton‐Conducting Solid Oxide Fuel Cells and Comparison with Oxygen‐Ion‐Conducting Counterpart

Proton‐conducting solid oxide fuel cells (H‐SOFC), using a proton‐conducting electrolyte, potentially have higher maximum energy efficiency than conventional oxygen‐ion‐conducting solid oxide fuel cells (O‐SOFC). It is important to theoretically study the current–voltage (J–V) characteristics in detail in order to facilitate advanced development of H‐SOFC. In this investigation, a parametric modelling analysis was conducted. An electrochemical H‐SOFC model was developed and it was validated as the simulation results agreed well with experimental data published in the literature. Subsequently, the analytical comparison between H‐SOFC and O‐SOFC was made to evaluate how the use of different electrolytes could affect the SOFC performance. In addition to different ohmic overpotentials at the electrolyte, the concentration overpotentials of an H‐SOFC were prominently different from those of an O‐SOFC. H‐SOFC had very low anode concentration overpotential but suffered seriously from high cathode concentration overpotential. The differences found indicated that H‐SOFC possessed fuel cell characteristics different from conventional O‐SOFC. Particular H‐SOFC electrochemical modelling and parametric microstructural analysis are essential for the enhancement of H‐SOFC performance. Further analysis of this investigation showed that the H‐SOFC performance could be enhanced by increasing the gas transport in the cathode with high porosity, large pore size and low tortuosity.     

A distributed dynamic model for chronoamperometry, chronopotentiometry and gas starvation studies in PEM fuel cell cathode

Electrochemical systems differ significantly from conventional chemical systems. The response of voltage to changes in current and that of current to changes in voltage is much faster compared to typical transients observed in transport variables. In this work, the transient characteristics of various transport and electrochemical phenomena are studied in the PEM fuel cell cathode using a dynamic model. Model-based chronoamperometry and chronopotentiometry studies are performed to investigate the interactions among the various phenomena and the limiting mechanisms under various operating modes. The dynamic response of current to changes in voltage under chronoamperometry and that of voltage to changes in current under chronopotentiometry are found to be significantly different. Moreover, it is also observed through simulations that the dynamics in the output variables are strongly influenced by the operating cell voltage. Results from chronoamperometry studies are used to highlight the problem of oxygen starvation, which is also reflected by the magnitude of oxygen excess ratio or stoichiometric ratio. Results from step tests in chronopotentiometry studies are used to study nonlinearities in the response of voltage to changes in inputs such as, current and air flow rate.     

Dynamic modelling and sensitivity analysis of a tubular SOFC fuelled with NH3 as a possible replacement for H2

A dynamic model of an ammonia fed-tubular solid oxide fuel cell (NH₃-SOFC) is developed and presented. The model accounts for diffusion, inherent impedance, transport (heat and mass transfer), electrochemical reactions, activation and concentration polarizations of electrodes and the ammonia decomposition reaction. Sensitivity analyses are conducted upon the effects of design parameters on the fuel cell performance. Dynamic output voltage, fuel-cell-tube temperature and efficiency responses to step changes in the inlet fuel flow pressure with different values of design parameters are discussed. It is found that among the studied parameters, the inner cell tube diameter has the strongest effect on fuel cell efficiency. On the other hand, the influence of cathodic porosity on fuel cell performance and transient response is higher than that of the anodic porosity. The transient response with different sizes of micro and macro-structures is studied and it is observed that changing the fuel cell length has the most effect. Also NH₃-SOFC is compared with H₂-SOFC and it is found that the performance of the former is close to that of the latter thus signifying that ammonia is a suitable fuel for substituting in place of hydrogen.     

Dynamic Modeling of Reversible Solid Oxide Cells

Reversible solid oxide cells (rSOCs) are highly efficient devices, which allow either the generation of electric power or the storage of energy via fuel production. In this paper, the characteristics of the mode switch are investigated by applying a dynamic 3D stack model. The responses of temperature, current density, and species mole fractions regarding a switch from storage (SOEC) to generation mode (SOFC) are examined in detail. Additionally, the impact of using excess air and continuous voltage variations to limit temperature gradients and fluctuations during the mode switch are analyzed.     

Dynamic modeling and validation studies of a tubular solid oxide fuel cell

Solid oxide fuel cell (SOFC) is a key component in the new vision of distributed power generation. However, for connecting SOFC reliably to a load-varying grid, its transient behavior needs to be studied in detail with a thoroughly validated dynamic model. Dynamic models are also important for synthesizing efficient controllers. In this paper, a detailed dynamic model of a tubular SOFC is validated using experimental data from an industrial cell operating over a broad operating range. Steps in voltages and flows are used to study the system response. In the process of validation, phenomena that affect the transient response of the cell significantly are identified. The effects of Knudsen diffusion along with that of the increased active area for the electrochemical reactions are considered in this model observing the deviations of the simulation results from the experimental data. A dynamic model that includes these effects provides a very good match with the experimental data. Characteristics of the transient responses and various nonlinearities in the fuel cell dynamics are also studied in detail.     

PEMFC电堆动态工况响应性能试验

质子交换膜燃料电池（PEMFC）电堆动态响应特性对PEMFC电堆的耐久性和可靠性具有很大影响。本文试验考察了PEMFC电堆在动态工况下的输出性能、单电池电压均衡性变化和动态响应特性。结果表明,在整个动态运行工况下,电堆运行良好,进出口冷却液温差小于5℃。电流阶跃变化时电堆电压均衡性出现突增变化,同时随着电流的增大,稳态时电堆均衡性变差。在超负荷（200A）运行工况下,电堆各单电池之间输出差异变大,均衡性持续变差,电堆中间和前端单电池电压明显降低。此外,在整个动态响应过程中电流阶跃上升时的电压最大下冲值比电流阶跃下降时的电压最大上调量大,但输出电压能在10s内达到相对稳定的状态（电压波动率＜0.02）。通过该研究,以期为实际车载电堆运行和控制优化提供参考。     

Modeling of Direct H2S Fueled Solid Oxide Fuel Cells with Reforming Chemical Kinetics

A direct H₂S fueled SOFC model is developed based on Ni‐YSZ/YSZ/YSZ‐LSM button cell test stand. The model considers the detailed reforming chemical processes of H₂S and multi‐physics transport processes in the fuel cell and fuel supply tubes. The model is validated using experimental data. Extensive simulations are performed to study the complicated interactions between multi‐physics transport processes and chemical/electrochemical reactions. The results elucidate the fundamental mechanisms of direct H₂S fueled SOFCs. It is found that suitably increasing the H₂O content in the supplied H₂S fuel can improve SOFC electrochemical performance; high operating temperature may facilitate the reforming of H₂S and improve the electrochemical performance. The sulfur poisoning effect may be mitigated by increasing the H₂O content in the fuel, increasing the operating temperature, decreasing the flow rate, and/or making the cell work at low voltage (or high current) conditions.     

Spatial Distribution of Electrochemical Performance in a Segmented SOFC: A Combined Modeling and Experimental Study

Spatially inhomogeneous distribution of current density and temperature in solid oxide fuel cells (SOFC) contributes to accelerated electrode degradation, thermomechanical stresses, and reduced efficiency. This paper presents a combined experimental and modeling study of the distributed electrochemical performance of a planar SOFC. Experimental data were obtained using a segmented cell setup that allows the measurement of local current‐voltage characteristics, gas composition and temperature in 4 × 4 segments. Simulations were performed using a two‐dimensional elementary kinetic model that represents the experimental setup in a detailed way. Excellent agreement between model and experiment was obtained for both global and local performance over all investigated operating conditions under varying H₂/H₂O/N₂ compositions at the anode, O₂/N₂ compositions at the cathode, temperature, and fuel utilization. A strong variation of the electrochemical performance along the flow path was observed when the cell was operated at high fuel utilization. The simulations predict a considerable gradient of gas‐phase concentrations along the fuel channel and through the thickness of the porous anode, while the gradients are lower at the cathode side. The anode dominates polarization losses. The cell may operate locally in critical operating conditions (low H₂/H₂O ratios, low local segment voltage) without notably affecting globally observed electrochemical behavior.