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Dynamics and Control of a Tubular Solid-Oxide Fuel Cell S. Ahmad Hajimolana Department of Chemical Engineering, Azad UniVersity of Shahrud, Shahrud, Iran
Masoud Soroush* Department of Chemical and Biological Engineering, Drexel UniVersity, Philadelphia, PennsylVania 19104
This paper presents a study of the dynamic behavior and control of a tubular solid oxide fuel cell system. A dynamic compartmental model that is based on first principles is developed. The model accounts for diffusion processes, inherent impedance, transport (heat and mass transfer) processes, electrochemical processes, anode and cathode activation polarizations, and internal reforming/shifting reactions, among others. Dynamic outlet voltage, current, and fuel-cell-tube temperature responses of the cell to step changes in external load resistance and conditions of the feed streams are presented. Simulation results show that the fuel cell is a multitimescale system; some of the cell output responses exhibit consecutive apparent dominant time constants, ranging from ∼0.2 ms to ∼40 s. They also reveal that the temperature and pressure of the inlet air stream and the temperature of the inlet fuel stream strongly affect the dynamics of the fuel cell system. The temperature of the inlet air stream has the strongest effect on the cell performance, and the effects of the inlet air and fuel velocities on the cell response are weaker than those of inlet feed pressures and temperatures. A simple control system is then implemented to control the fuel-cell outlet voltage and cell-tube temperature through manipulation of the pressure and temperature of the inlet air stream, respectively. The results show that the control system can successfully reject unmeasured step changes (disturbances) in the load resistance, the velocity of the inlet air stream, and the pressure, temperature, and velocity of the inlet fuel stream. 1. Introduction Solid oxide fuel cells (SOFCs) are considered to be one of the most advanced designs for mid- to large-scale applications (up to 2 MW).1 They are among the most promising types of fuel cells currently being considered as a power source for automobiles and stationary power plants.2,3 Because the electrolyte is a layer of ceramic material with high-temperature endurable porous-media electrodes, SOFCs can generally operate in a high-temperature range (800-1000 °C). High operating temperature has some advantages, such as high energy conversion efficiency, flexibility of usable fuel type, and hightemperature exhaust gas. Disadvantages include potential thermal fatigue failure of the cell material and sealing under the high temperature, as well as the fact that cell temperature fluctuations induce thermal stress in the cell ceramics. Thus, it is important to operate SOFCs in such a way that the stack temperature remains within a tight design range. The history of solid oxide technology extends as far back as the late 1930s, when Swiss scientist Emil Bauer and his colleague H. Preis experimentally studied zirconium, yttrium, cerium, lanthanum, and tungsten as electrolytes. In the late 1950s, Westinghouse began experimenting with zirconium compounds, and researchers in The Netherlands, the Consolidation Coal Company in Pennsylvania, and General Electric in New York conducted small-scale research on SOFCs. However, the research progress was not significant, because melting, shortcircuiting, and high electrical resistance inside the cell materials created many technical difficulties. Various SOFC models have been investigated and developed since the early 1990s. The models have been used to study the complicated interactions between the various phenomena occurring inside the cell and to optimize the system performance. * To whom correspondence should be addressed. Tel.: +1-215-9851710. Fax: +1-215-895-5837. E-mail address:
[email protected].
Dynamic models are especially beneficial for testing control strategies in the development stage of SOFCs. Dynamic modeling of SOFC can be traced back to Achenbach’s work,4,5 in which the transient cell voltage response to changes in temperature and current density was investigated. Padulle´s et al.6 proposed a model based on species dynamics. Zhu and Tomsovic7 performed load-following analysis that was based on Padulle´s’ model. Transport phenomena plays an important role in the SOFC performance. However, it is not yet clear which of the phenomena are significant in a particular design and a given operating region. After a modeling approach was selected, significant simplifications are typically made to solve the model equations. The impact of these simplifications on the predictive capability of the model is usually not clearly understood. It is quite possible that the accuracy that is expected from a detailed model is greatly reduced because of a simplification. Bhattacharyya et al.8 have discussed the importance of modeling various phenomena and the region of operation in which the phenomena are significant. They developed models with and without the momentum conservation equations. They also observed that a change in velocity, especially inside the cathode gas flow channel, can have a significant effect on the cell performance, depending on the percentage conversion of oxygen. They also stated the necessity of incorporating momentum balance in higher-power ranges. Mass transfer by diffusion of species through porous electrodes have been considered in many studies. The diffusion through the porous media is either modeled by writing detailed mass-transfer equations9-11 or by considering concentration polarization expressed in terms of a limiting current.12 Xue et al.13 considered the anode-electrolyte-cathode assembly as a single solid body. The diffusivity coefficient of gases diffusing through the electrodes have been considered to be constant9,14 or temperature-dependent.10,11,15
10.1021/ie801555d CCC: $40.75 2009 American Chemical Society Published on Web 04/28/2009
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The voltage loss due to activation polarization at the anode and cathode is normally addressed using Butler-Volmer kinetics. Exchange current densities in the equation for activation polarization have been considered constant in many studies.11,12 Several investigators have accounted for the exchange current density dependence on temperature, activation energy, and partial pressure of reactants and products.10,15 The lack of activation polarization at the anode and cathode has been assumed in many studies.14,16 Al-Qattan et al.17 neglected activation polarization, assuming rapid chemical kinetics in the SOFC electrodes. Ohmic resistance has been considered constant in many studies.9,11-14,16 Costamagna and Honegger15 assumed that the electrical resistance for electrolytes was dependent on temperature, and the anode and cathode electrical resistivities were constant. They compared their model predictions with experimental data. Al-Qattan et al.17 considered the dependence of resistivities of electrodes, electrolytes, and interconnects on temperature. Recently, the mathematical modeling of tubular SOFCs has been studied extensively. Nagata et al.9 developed a onedimensional (1D) steady-state tubular SOFC model that accounted for electrochemical and internal reforming reactions. They divided the fuel cell into several control volumes that behave as continuous stirred tank reactors (CSTRs). Campanari18 developed a tubular SOFC that took the effects of thermodynamic nonidealities on cell performance, in terms of parameters correlations, into consideration. Aguiar et al.19,20 developed models for direct and indirect internal reforming of CH4. They showed that mass and heat flux and cell resistance are specific to particular operating conditions. Sedghisigarchi and Feliachi21 considered the heat transfer and species dynamics in their model. More-detailed models for a tubular SOFC were presented by Li and Chyu.,22,23 whose models accounted for mass transfer, heat transfer, momentum, and electrochemical and chemical reactions. However, in these models, the oxygen diffusion through the porous cathode and heat transfer via radiation were neglected. Chan et al.24 developed a model in which the rates of the electrochemical reactions were expressed entirely in terms of exchange current densities and were assumed to remain constant along the cell length. This assumption can cause errors in the determination of the current density profile along the cell length, because the kinetics of electrochemical reactions are strongly dependent on temperature and local species concentrations.9,15,25 Campanari and Iora26 presented a tubular SOFC model that was supplied by methane-reformed gases. In their model, the momentum transport phenomena were not taken into account, and their calculation of the heat-transfer coefficients was based on a constant Nusselt number (Nu) for both the air and fuel sides, which is valid only when a constant heat flux is transferred to the fluid flow. Heat generation within a SOFC is dependent on the rate of electrochemical reaction, which is not uniform. Haynes16 proposed a dynamic model that took heattransfer effects into account. In this model, the concentration polarization was neglected. Ota et al.27 presented the dynamic behavior of a microtube SOFC with the assumption that the gases are incompressible and also the heat conduction between the defined slices and the effect of viscosity can be neglected. Cooper et al.14 explored a steady-state tubular SOFC model, including the reaction and species transport process. Heat transfer was not included in the model. Many have incorporated the mass/species conservation, momentum conservation, and energy conservation in the anode and cathode gas flow channels. Qi et al.10,28 developed a detailed dynamic first-principles model for a tubular SOFC system and studied the dynamic behavior
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of the cell system extensively. They neglected spatial variation of the bulk concentration in the gas flow channel. Al-Qattan et al.17 did not consider oxygen species conservation in the cathode flow channels, with the assumption that air is always provided in excess quantities. Despite the importance of velocity variation inside the flow channels under certain operating conditions, momentum conservation was not incorporated in several studies.9,11,15-17,19 Many SOFC models have been developed that are based on energy conservation in the flow channels.9,12,13,15,17,19 Control of SOFCs has also received attention recently. Kandepu et al.29 showed that the power generated and the cell temperature in a SOFC system can be controlled by manipulating the fuel and air feed flow rates, using proportional-integralderivative (PID) control. Aguiar et al.30 studied temperature control of a stack-level SOFC using numerical simulations. Their control strategy had two main loops. One loop had a master controller that set fuel and air feed flow rates proportional to the current, while keeping the fuel utilization and air ratio constant. The other loop had a PID temperature controller that, at a given outlet fuel temperature, responds by changing the air flow (air ratio) around the default value set by the master controller. This study further confirmed the need for process control to enhance the reliability and minimize the degradation of a SOFC.30 A power controller was designed and implemented on a SOFC model by Kaneko et al.;31 a standard PID control strategy was used to manipulate fuel feed flow rate, to control the power output of the system. Chaisantikulwat et al.32 developed a dynamic model of a SOFC and implemented PI controllers. The control objective was to maintain a constant voltage in the presence of load changes by manipulating the hydrogen concentration in the fuel. The load current was considered to be a disturbance to the SOFC system. Sedghisigarchi and Feliachi21 proposed two completely decentralized proportional-integral (PI) controllers to control SOFC power and voltage by adjusting the firing angle and modulation index of the converter according to the power and voltage deviations, respectively. The fuel cell inverter has the capability to adjust its firing angle quickly, so that the inverter maintains constant a power output under fast transient disturbances. With a controloriented simulator, Sorrentino et al.33 used a PI controller to maintain the SOFC temperature variation under a safety threshold by adjusting the excess air flow rate. Auld et al.34 used a PID controller to regulate the SOFC voltage across a capacitor by adjusting the SOFC power. A change in the capacitor voltage led to a change in the power supplied to an external load. When the fuel cell is capable of meeting a power demand, the surplus power recharges the capacitor. In this paper, a dynamic compartmental model based on first principles is developed to study dynamic behavior and control of a SOFC. This modeling approach is justifiable for this spatially distributed system, because the length of the tubular fuel cell is sufficiently short. The dynamic model accounts for diffusion processes, inherent impedance, transport (heat and mass transfer) processes, and electrochemical processes, as well as internal reforming/shifting reactions and potential losses, among others. Its simulation provides a quick insight into the dynamic behavior that one can expect from a typical tubular SOFC. Current, outlet voltage, and cell-tube temperature responses to step changes in fuel and air inlet conditions and an external load resistance are calculated using MATLAB Simulink. Simulation results show that inlet temperatures of the air and fuel feed streams strongly affect the dynamics of the fuel cell system. Two completely decentralized PI controllers
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are then implemented and simulated to study control of the fuel cell outlet voltage and cell-tube temperature. The remaining of this article is organized as follows. Section 2 presents a review of SOFC operating principles, and Section 3 describes the model development. Section 4 presents and discusses open-loop numerical simulation results. Section 5 focuses on input-output pairing/selection for an effective completely decentralized control and presents closed-loop results from completely decentralized PI control of the SOFC output voltage and temperature. Concluding remarks are presented in Section 6. 2. General Principle A solid oxide fuel cell (SOFC) uses a hard ceramic electrolyte and operates at temperatures up to 1000 °C. A mixture of zirconium oxide and calcium oxide forms a crystal lattice, although other oxide combinations have also been used as electrolytes. The crystal lattice allows oxide ions to pass through it to reach the anode surface, where the oxide ions combine with H+ ions and form water. The solid electrolyte is coated on both sides with specialized porous electrode materials. The anode consists of a metallic nickel- and Y2O3-stabilized ZrO2 skeleton, which inhibits sintering of the metal particles and provides a thermal expansion coefficient comparable to those of the other cell materials, thus limiting the buildup of stresses resulting from a difference in the coefficient of thermal expansion. The anode structure has a porosity of 20%-40% to facilitate mass transport of the reactant and product gases. The cathode material mostly used is strontium-doped lanthanum manganite (La1-xSrxMnO3, for x ) 0.10-0.15); its structure, such as that of the anode, is porous to permit rapid mass transport of the reactant and product gases. The cathode material has low levels of chemical reactivity with the electrolyte, which extends the lifetime of the material. However, it is a poor ionic conductor, so the electrochemically active reactions are limited to the triple-phase boundary (TPB), where the electrolyte, a gas, and an electrode meet. In other words, the TPB of a fuel cell is the area of contact between the three phases necessary for electrochemical (hydrogen oxidation and oxygen reduction) reactions at the electrode: an ion-conducting phase, an electronconducting phase, and a gas phase.35 The bigger the TPB area of a cell, the better the quality of the cell; a bigger TPB area allows the reactions to occur in more sites, thus maximizing current flow. Lanthanum strontium manganite also works well as a cathode at high temperatures, but its performance quickly decreases as operating temperature decreases to
