Model-based development of low-level control strategies for transient operation of solid oxide fuel cell systems

The exploitation of an SOFC-system model to define and test control and energy management strategies is presented. Such a work is motivated by the increasing interest paid to SOFC technology by industries and governments due to its highly appealing potentialities in terms of energy savings, fuel flexibility, cogeneration, low-pollution and low-noise operation.The core part of the model is the SOFC stack, surrounded by a number of auxiliary devices, i.e. air compressor, regulating pressure valves, heat exchangers, pre-reformer and post-burner. Due to the slow thermal dynamics of SOFCs, a set of three lumped-capacity models describes the dynamic response of fuel cell and heat exchangers to any operation change.The dynamic model was used to develop low-level control strategies aimed at guaranteeing targeted performance while keeping stack temperature derivative within safe limits to reduce stack degradation due to thermal stresses. Control strategies for both cold-start and warmed-up operations were implemented by combining feedforward and feedback approaches. Particularly, the main cold-start control action relies on the precise regulation of methane flow towards anode and post-burner via by-pass valves; this strategy is combined with a cathode air-flow adjustment to have a tight control of both stack temperature gradient and warm-up time. Results are presented to show the potentialities of the proposed model-based approach to: (i) serve as a support to control strategies development and (ii) solve the trade-off between fast SOFC cold-start and avoidance of thermal-stress caused damages.     

Computational model to predict thermal dynamics of planar solid oxide fuel cell stack during start-up process

Solid oxide fuel cell (SOFC) systems have been recognized as the most advanced power generation system with the highest thermal efficiency with a compatibility with wide variety of hydrocarbon fuels, synthetic gas from coal, hydrogen, etc. However, SOFC requires high temperature operation to achieve high ion conductivity of ceramic electrolyte, and thus SOFC should be heated up first before fuel is supplied into the stack. This paper presents computational model for thermal dynamics of planar SOFC stack during start-up process. SOFC stack should be heated up as quickly as possible from ambient temperature to above 700 °C, while minimizing net energy consumption and thermal gradient during the heat up process. Both cathode and anode channels divided by current-collecting ribs were modeled as one-dimensional flow channels with multiple control volumes and all the solid structures were discretized into finite volumes. Two methods for stack-heating were investigated; one is with hot air through cathode channels and the other with electric heating inside a furnace. For the simulation of stack-heating with hot air, transient continuity, flow momentum, and energy equation were applied for discretized control volumes along the flow channels, and energy equations were applied to all the solid structures with appropriate heat transfer model with surrounding solid structures and/or gas channels. All transient governing equations were solved using a time-marching technique to simulate temporal evolution of temperatures of membrane-electrode-assembly (MEA), ribs, interconnects, flow channels, and solid housing structure located inside the insulating chamber. For electrical heating, uniform heat flux was applied to the stack surface with appropriate numerical control algorithm to maintain the surface temperature to certain prescribed value. The developed computational model provides very effective simulation tool to optimize stack-heating process minimizing net heating energy and thermal gradient within the stack.     

Modelling of cells,stacks and systems based around metal-supported planar IT-SOFC cells with CGO electrolytes operating at 500–600 °C

Ceres Power Ltd. has developed a novel solid oxide fuel cell (SOFC) concept based upon depositing a thick film positive–electrolyte–negative (PEN) structure on a porous stainless steel substrate, and using gadolinia-doped ceria (CGO) as the electrolyte material. This approach allows the temperature of operation to be reduced to below 600 °C, well below the conventional SOFC operating temperature. Historically, the use of CGO as an electrolyte material has been viewed as impractical because of its poor stability in reducing atmospheres at elevated temperatures, leading to electronic conductivity, which effectively short-circuits the cell leading to a loss of efficiency. In this work, a model is developed which accurately simulates the polarisation behaviour of a Ceres cell including electronic leakage. The parameters of this model are set to give the best possible fit to experimental data. This cell model is then incorporated into a model of a 2.5 kW_e stack, and the stack model into a natural gas fuelled combined heat and power (CHP) system model. The system model demonstrates that high operating efficiencies are achievable for such a system based upon IT-SOFC cells with CGO electrolytes.     

Performance analysis and temperature gradient of solid oxide fuel cell stacks operated with bio-oil sorption-enhanced steam reforming

A high temperature gradient within a solid oxide fuel cell (SOFC) stack is considered a major challenge in SOFC operations. This study investigates the effects of the key parameters on SOFC system efficiency and temperature gradient within a SOFC stack. A 40-cell SOFC stack integrated with a bio-oil sorption-enhanced steam reformer is simulated using MATLAB and DETCHEM. When the air-to-fuel ratio and steam-to-fuel ratio increase, the stack average temperature and temperature gradient decrease. However, a decrease in the stack temperature steadily reduces the system efficiency owing to the tradeoff between the stack performance and thermal balance between heat recovered and consumed by the system. With an increase in the bio-oil flow rate, the system efficiency decreases because of the lower resident time for the electrochemical reaction. This is not, however, beneficial to the maximum temperature gradient. To minimize the temperature gradient of the SOFC stack, a decrease in the bio-oil flow rate is the most effective way. The maximum temperature gradient can be reduced to 14.6 K cm⁻¹ with the stack and system efficiency of 76.58 and 65.18%, respectively, when the SOFC system is operated at an air-to-fuel ratio of 8, steam-to-fuel ratio of 6, and bio-oil flow rate of 0.0041 mol s⁻¹.     

Three-dimensional computational analysis of gas and heat transport phenomena in ducts relevant for anode-supported solid oxide fuel cells

Various transport phenomena occurring in an anode duct of medium temperature solid oxide fuel cell (SOFC) have been simulated and analyzed by a fully three-dimensional calculation method. The considered composite duct consists of a thick porous layer, the gas flow duct and solid current interconnector. Unique fuel cell boundary and interfacial conditions, such as the combined thermal boundary conditions on solid walls, mass transfer associated with the electrochemical reaction and gas permeation across the interface, were applied in the analysis. Based on three characteristic ratios proposed in this study, gas flow and heat transfer were investigated and presented in terms of friction factors and Nusselt numbers. It was revealed that, among various parameters, the duct configuration and properties of the porous anode layer have significant effects on both gas flow and heat transfer of anode-supported SOFC ducts. The results from this study can be applied in fuel cell overall modeling methods, such as those considering unit/stack level modeling.     

Numerical evaluation of a parallel fuel feeding SOFC–PEFC system using seal-less planar SOFC stack

We propose a system that combines a seal-less planar solid oxide fuel cell (SOFC) stack and polymer electrolyte fuel cell (PEFC) stack. In the proposed system, fuel for the SOFC (SOFC fuel) and fuel for the PEFC (PEFC fuel) are fed to each stack in parallel. The steam reformer for the PEFC fuel surrounds the seal-less planar SOFC stack. Combustion exhaust heat from the SOFC stack is used for reforming the PEFC fuel. We show that the electrical efficiency in the SOFC–PEFC system is 5% higher than that in a simple SOFC system using only a seal-less planar SOFC stack when the SOFC operation temperature is higher than 973 K.     

Thermal start-up behaviour and thermal management of SOFC's

Solid oxide fuel cells (SOFCs) have many attractive features for widespread applications. The high operating temperature provides a valuable heat source and in contrast to low temperature fuel cells they not only tolerate substances such as CO but can even use them as fuel. Thus, reforming of hydrocarbon fuels for SOFCs can be done without additional gas purification. As both stack and hydrocarbon reformer unit have to be operated at high temperatures (700–1000 °C), thermal management plays an important role in the successful operation of SOFC systems. As the SOFC system contains ceramic components, both large thermal gradients in the system and thermal expansion coefficient (TEC) mismatch must be avoided.Matching TECs is done by selecting the suitable materials. Avoiding high temperature gradients is done by selecting the right system design and control strategies. In order to achieve both, we have built a finite element simulation for a complete SOFC systems which allows to study system parameters both during steady operation and during transients. Examples of the thermal start-up behaviour for several system configurations are given for selected components as well as internal temperatures of the SOFC-stack during start-up. The simulation model includes also the option to simulate the effects of internal methane reformation in the SOFC stack.As the minimum operation temperature is high, cooling down of the system has to be avoided if instant operation is desired. This can be achieved either passively by selecting suitable thermal insulation materials and/or actively by adopting a strategy for maintaining the temperature.     

Solid oxide fuel cell operating on liquid organic hydrogen carrier-based hydrogen – making full use of heat integration potentials

Our contribution demonstrates the technological potential of coupling Liquid Organic Hydrogen Carrier (LOHC)-based hydrogen storage and hydrogen-based Solid Oxide Fuel Cell (SOFC) operation. As SOFC operation creates waste heat at a temperature level of more than 600 °C, clever heat transfer from the SOFC operation to the LOHC dehydrogenation process is possible and results in an overall efficiency of 45% (electric output of SOFC vs. lower heating value of LOHC-bound hydrogen). Moreover, we demonstrate that LOHC vapour does not harm the operational stability of a typical 150 W SOFC short stack. By operating the stack with LOHC-saturated hydrogen, operation times of more than 10 years have been simulated without noticeable degradation of SOFC performance.     

3D multiphysics modeling aided APU development for vehicle applications: A thermo-structural investigation

Solid oxide fuel cells (SOFC) are suitable for on-board electricity generation as Auxiliary Power Unit (APU) to support the electric power supply in heavy-duty vehicles. In order to satisfy the requirements of a lightweight fuel cell stack for mobile applications, thin-walled components must be used for the stack structure. This necessity is associated with material, process and design difficulties that must be solved in order to achieve a successful utilization. In this work a novel lightweight SOFC stack design with metal-supported cell was studied both numerically and experimentally. The metallic components are made from the Intermediate Temperature Metal (ITM), a high performance, high chromium ferritic stainless steels alloy. The multiphysics modeling approach (fluid dynamics, heat transfer, structural mechanics) was utilized in this work to predict the temperature distribution and the thermo-structural behavior of the new developed design. Geometric details of the fuel cell stack components as well as appropriate nonlinear, temperature and time-dependent constitutive models were developed to describe the material behavior. Experimental data were used to determine the material model parameters and validated the simulation results. The three-dimensional stress and deformation distributions in the individual stack components were evaluated and their maximum values for elements at risk were identified. Thus, the developed model enables the investigation of sustainability and serviceability of the structural elements to ensure a reliable operation of the stack. The developed computational model can be used as a design tool for parametric studies and optimization analysis to investigate the effects of process boundary conditions, material properties as well as geometrical design parameters and their variation on the induced thermal stresses.     

Thermal stress analysis of a planar SOFC stack

The aim of this study is, by using finite element analysis (FEA), to characterize the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack during various stages. The temperature profiles generated by an integrated thermo-electrochemical model were applied to calculate the thermal stress distributions in a multiple-cell SOFC stack by using a three-dimensional (3D) FEA model. The constructed 3D FEA model consists of the complete components used in a practical SOFC stack, including positive electrode–electrolyte–negative electrode (PEN) assembly, interconnect, nickel mesh, and gas-tight glass-ceramic seals. Incorporation of the glass-ceramic sealant, which was never considered in previous studies, into the 3D FEA model would produce more realistic results in thermal stress analysis and enhance the reliability of predicting potential failure locations in an SOFC stack. The effects of stack support condition, viscous behavior of the glass-ceramic sealant, temperature gradient, and thermal expansion mismatch between components were characterized. Modeling results indicated that a change in the support condition at the bottom frame of the SOFC stack would not cause significant changes in thermal stress distribution. Thermal stress distribution did not differ significantly in each unit cell of the multiple-cell stack due to a comparable in-plane temperature profile. By considering the viscous characteristics of the glass-ceramic sealant at temperatures above the glass-transition temperature, relaxation of thermal stresses in the PEN was predicted. The thermal expansion behavior of the metallic interconnect/frame had a greater influence on the thermal stress distribution in the PEN than did that of the glass-ceramic sealant due to the domination of interconnect/frame in the volume of a planar SOFC assembly.     

An internal reformer for a pressurised SOFC system

A novel reformer design has been demonstrated that converts the methane required for a multi kilowatt SOFC stack. Results show the influence of temperature and the benefits of operating at elevated pressure on the reforming-catalyst fundamental reaction kinetics. Due to the high heat demand of the steam reforming reaction, efficient heat transfer between the SOFC stack and the reforming catalyst is essential. Parameters such as the volume/surface area ratio, choice of catalyst, and catalyst metal loading are key to the design, and these have been determined through a combination of computer modelling and experimental measurements. The thermal properties of the unit have been evaluated over a range of temperatures and fuel compositions that simulate system operating-conditions in the final product.     

Cold start dynamics and temperature sliding observer design of an automotive SOFC APU

This paper presents a dynamic model for studying the cold start dynamics and observer design of an auxiliary power unit (APU) for automotive applications. The APU is embedded with a solid oxide fuel cell (SOFC) stack which is a quiet and pollutant-free electric generator; however, it suffers from slow start problem from ambient conditions. The SOFC APU system equips with an after-burner to accelerate the start-up transient in this research. The combustion chamber burns the residual fuel (and air) left from the SOFC to raise the exhaust temperature to preheat the SOFC stack through an energy recovery unit. Since thermal effect is the dominant factor that influences the SOFC transient and steady performance, a nonlinear real-time sliding observer for stack temperature was implemented into the system dynamics to monitor the temperature variation for future controller design. The simulation results show that a 100 W APU system in this research takes about 2 min (in theory) for start-up without considering the thermal limitation of the cell fracture.     

System modeling of an air-independent solid oxide fuel cell system for unmanned undersea vehicles

To examine the feasibility of a solid oxide fuel cell (SOFC)-powered unmanned undersea vehicle (UUV), a system level analysis is presented that projects a possible integration of the SOFC stack, fuel steam reformer, fuel/oxidant storage and balance of plant components into a 21-in. diameter UUV platform. Heavy hydrocarbon fuel (dodecane) and liquid oxygen (LOX) are chosen as the preferred reactants. A maximum efficiency of 45% based on the lower heating value of dodecane was calculated for a system that provides 2.5 kW for 40 h. Heat sources and sinks have been coupled to show viable means of thermal management. The critical design issues involve proper recycling of exhaust steam from the fuel cell back into the reformer and effective use of the SOFC stack radiant heat for steam reformation of the hydrocarbon fuel.     

A computational fluid dynamics and finite element analysis design of a microtubular solid oxide fuel cell stack for fixed wing mini unmanned aerial vehicles

Computational fluid dynamics (CFD) and finite element analysis (FEA) are important modelling and simulation techniques to design and develop fuel cell stacks and their balance of plant (BoP) systems.The aim of this work is to design a microtubular solid oxide fuel cell (SOFC) stack by coupling CFD and FEA models to capture the multiphysics nature of the system. The focus is to study the distribution of fluids inside the fuel cell stack, the dissipation of heat from the fuel cell bundle, and any deformation of the fuel cells and the stack canister due to thermal stresses, which is important to address during the design process. The stack is part of an innovative all-in-one SOFC generator with an integrated BoP system to power a fixed wing mini unmanned aerial vehicle. Including the computational optimisation at an early stage of the development process is hence a prerequisite in developing a reliable and robust all-in-one SOFC generator system. The presented computational model considers the bundle of fuel cells as the heat source. This could be improved in the future by replacing the heat source with electrochemical reactions to accurately predict the influence of heat on the stack design.     

Simulation analysis of a system combining solid oxide and polymer electrolyte fuel cells

We evaluated the performance of system combining a solid oxide fuel cell (SOFC) stack and a polymer electrolyte fuel cell (PEFC) stack by a numerical simulation. We assume that tubular-type SOFCs are used in the SOFC stack. The electrical efficiency of the SOFC–PEFC system increases with increasing oxygen utilization rate in the SOFC stack. This is because the amount of exhaust heat of the SOFC stack used to raise the temperature of air supplied to it decreases as its oxygen utilization rate increases and because that used effectively as the reaction heat of the steam reforming reaction of methane in the stack reformer increases. The electrical efficiency of the SOFC–PEFC system at 190 kW ac is 59% (LHV), which is equal to that of the SOFC-gas turbine combined system at 1014 kW ac.     

SOFC stacks for mobile applications with excellent robustness towards thermal stresses

Solid oxide fuel cells (SOFC) are attractive power units for mobile applications, like auxiliary power units or range extenders, due to high electrical efficiencies, avoidance of noble metals, fuel flexibility ranging from hydrogen to hydrogen carriers such as ammonia, methanol or e-gas, and tolerance towards CO and other fuel impurities. Among challenges hindering more wide-spread use are the robustness under thermal cycling. The current study employs short stacks containing anode or metal supported SOFCs, which were subjected to thermal cycles in a furnace and under more realistic conditions without external furnace. Heating from 100 °C to operating temperature was accomplished by sending hot air through the cathode compartment and heating from bottom (and top) of the stack, reaching a fastest ramping time of ca. 1 h. The stacks remained intact under severe temperature gradients of at least 20 °C/cm for anode supported and 30 °C/cm for metal supported SOFCs.     

Two-dimensional temperature distribution estimation for a cross-flow planar solid oxide fuel cell stack

The uniform temperature distribution of a cross-flow planar solid oxide fuel cell (SOFC) stack plays an essential role in stack thermal safety and electrical property. However, because of the strict requirements in stack sealing struture, it is hard to acquire the temperature inside the stack using thermal detection devices within an acceptable cost. Therefore, accurately estimating the two-dimensional (2-D) temperature distribution of the cross-flow stack is crucial for its thermal management. In this paper, Firstly, a 2-D mechanism model of a cross-flow planar SOFC stack is established. The stack is divided into 5*5 nodes along the gas flow directions, which can reflect the stack states with moderate computational burden. Then, experimental test data is utilized to modify and validate the stack model, guaranteeing the model accuracy as well as the reliability of model-based state estimator design. Finally, easily-measured stack inputs and outputs are selected, and a temperature distribution estimator combined with unscented kalman filter (UFK) approach is developed to achieve accurate and fast temperature distribution estimation of a cross-flow SOFC stack. Simulation results demonstrate that the UKF-based temperature distribution estimator can precisely and quickly achieve the temperature distribution estimation of the cross-flow stack under both static state and dynamic state changes and is applicable to cross-flow stacks with different size or cell number as well, the maximum estimated absolute error is less than 0.15 K with an absolute error rate of 0.015%, which indicates the developed estimator has good estimation performances.     

Global failure criteria for positive/electrolyte/negative structure of planar solid oxide fuel cell

Due to mismatch of the coefficients of thermal expansion of various layers in the positive/electrolyte/negative (PEN) structures of solid oxide fuel cells (SOFC), thermal stresses and warpage on the PEN are unavoidable due to the temperature changes from the stress-free sintering temperature to room temperature during the PEN manufacturing process. In the meantime, additional mechanical stresses will also be created by mechanical flattening during the stack assembly process. In order to ensure the structural integrity of the cell and stack of SOFC, it is necessary to develop failure criteria for SOFC PEN structures based on the initial flaws occurred during cell sintering and stack assembly. In this paper, the global relationship between the critical energy release rate and critical curvature and maximum displacement of the warped cells caused by the temperature changes as well as mechanical flattening process is established so that possible failure of SOFC PEN structures may be predicted deterministically by the measurement of the curvature and displacement of the warped cells.     

Thermal management oriented steady state analysis and optimization of a kW scale solid oxide fuel cell stand-alone system for maximum system efficiency

This research attempts to ensure system safety while to maximize system efficiency by addressing steady state analysis and optimization for solid oxide fuel cell (SOFC) systems. Firstly, a thermal management oriented kW scale SOFC stand-alone system (primarily comprising a planar SOFC stack, a burner, and two heat exchangers) is developed, in which a special consideration for stack spatial temperature management is conducted by introducing an air bypass manifold around heat exchangers. The dynamic model of the system is performed using transient energy, species, and mass conservation equations. Secondly, based on the system model, the effects of operating parameters including fuel utilization (FU), air excess ratio (AE), bypass ratio (BR), and stack voltage (SV) on the system steady-state performances (e.g. system efficiency, stack inlet, stack outlet, and burner temperatures) are revealed. Particularly, an optimal relationship between the system efficiency and the operating parameters is proposed; the maximum system efficiency can certainly be obtained at the inlet outlet temperature critical point of the BR-AE or FU-AE planes for all SV operating points. Finally, according to the optimal relationship, a traverse optimization process is designed, and the maximum system efficiency and safe operating parameters at any efficient SV operating point are calculated. The results provide an optimal reference trajectory for control design, where the system is safe and efficiency optimization. Moreover, the results reveal two important system characteristics: (1) the burner operates within safe temperature zone as long as the temperature of the upstream stack is well controlled; (2) the control design for the system is a nonlinear optimal control with switching structure, which is a challenging control issue.     

A mathematical model of a tubular solid oxide fuel cell with specified combustion zone

A numerical model has been developed to simulate the effect of combustion zone geometry on the steady state and transient performance of a tubular solid oxide fuel cell (SOFC). The model consists of an electrochemical submodel and a thermal submodel. In the electrochemical model, a network circuit of a tubular SOFC was adopted to model the dynamics of Nernst potential, ohmic polarization, activation polarization, and concentration polarization. The thermal submodel simulated heat transfers by conduction, convention, and radiation between the cell and the air feed tube. The developed model was applied to simulate the performance of a tubular solid oxide fuel cell at various operating parameters, including distributions of circuits, temperature, and gas concentrations inside the fuel cell. The simulations predicted that increasing the length of the combustion zone would lead to an increase of the overall cell tube temperature and a shorter response time for transient performance. Enlarging the combustion zone, however, makes only a negligible contribution to electricity output properties, such as output voltage and power. These numerical results show that the developed model can reasonably simulate the performance properties of a tubular SOFC and is applicable to cell stack design.