Multi-objective optimization of a solid oxide fuel cell-based integrated system to select the optimal closed thermodynamic cycle and heat coupling scheme simultaneously

Integrating thermodynamic cycles with SOFCs is an effective technology to make full use of energy, but the difficulty lies in selecting the optimum thermodynamic cycles and integration scheme. The performance of a thermodynamic cycle is directly determined by the working fluid and operating parameters, and the heat exchange network (HEN) synthesis scheme directly affects the heat coupling degree and the economic performance. Therefore, a multi-objective optimization model is proposed in this paper, where the working fluid and operating parameters of the closed cycle, as well as the HEN synthesis scheme are selected as decision variables, while the total exergy destruction (TED) and the total annual cost (TAC) are adopted as the objectives. To solve this complex problem, a solving strategy based on NSGA-II with two levels is proposed to obtain the Pareto Frontier of TED and TAC. Finally, a case is solved and three Pareto optimality are analyzed and compared.     

Analysis of total energy system based on solid oxide fuel cell for combined cooling and power applications

A total energy system (TES) incorporating a solid oxide fuel cell (SOFC) and an exhaust gas driven absorption chiller (AC) is presented to provide power, cooling and/or heating simultaneously. The purpose for using the absorption chiller is to recover the exhaust heat from the SOFC exhaust gas for enhancing the energy utilization efficiency of the TES. A steady-state mathematical model is developed to simulate the effects of different operating conditions of SOFC, such as the fuel utilization factor and average current density, on the performance of the TES by using the MATLAB softpackage. Parametric analysis shows that both electrical efficiency and total efficiency of the TES have maximum values with variation of the fuel utilization factor; while the cooling efficiency increases, the electrical efficiency and total efficiency decrease with increase in the current density of SOFC. The simulated results could provide useful knowledge for the design and optimization of the proposed total energy system.     

Performance assessment and optimization of an integrated solid oxide fuel cell-gas turbine cogeneration system

The combined solid oxide fuel cells and gas turbine (SOFC/GT) system is known to be a potential alternative for distributed power generation. In this paper, a novel SOFC/GT based cogeneration system, which integrated a transcritical carbon dioxide cycle (TRCC) with a LNG cold energy utilization system is proposed. A mathematical (zero-dimensional) model is developed to analyze the co-generation system performance from the perspective of thermodynamic (energy and exergy) and economic costs. The main parameters of the system are chosen to analyze their effects on thermodynamic performance. The results show that the current system can achieve 64.40% thermal efficiency and 62.13% exergy efficiency under given conditions, and can further improve efficiency through parameter optimization. Finally, the multi-objective optimization program using NSGA-II (Non-dominated Sorting Genetic Algorithm II) is used to obtain the optimal value of the system design parameters. In the multi-objective analysis, the thermodynamic efficiency and economic cost of the system are considered as objective functions. The optimization results show that the final optimized design selected from the Pareto front can achieve 63.08% thermal efficiency and 61.10% exergy efficiency, respectively.     

Thermodynamic modeling of an integrated biomass gasification and solid oxide fuel cell system

An integrated process of biomass gasification and solid oxide fuel cells (SOFC) is investigated using energy and exergy analyses. The performance of the system is assessed by calculating several parameters such as electrical efficiency, combined heat and power efficiency, power to heat ratio, exergy destruction ratio, and exergy efficiency. A performance comparison of power systems for different gasification agents is given by thermodynamic analysis. Exergy analysis is applied to investigate exergy destruction in components in the power systems. When using oxygen-enriched air as gasification agent, the gasifier reactor causes the greatest exergy destruction. About 29% of the chemical energy of the biomass is converted into net electric power, while about 17% of it is used to for producing hot water for district heating purposes. The total exergy efficiency of combined heat and power is 29%. For the case in which steam as the gasification agent, the highest exergy destruction lies in the air preheater due to the great temperature difference between the hot and cold side. The net electrical efficiency is about 40%. The exergy combined heat and power efficiency is above 36%, which is higher than that when air or oxygen-enriched air as gasification agent.     

Feedback control of solid oxide fuel cell spatial temperature variation

A high performance feedback controller has been developed to minimize SOFC spatial temperature variation following significant load perturbations. For thermal management, spatial temperature variation along SOFC cannot be avoided. However, results indicate that feedback control can be used to manipulate the fuel cell air flow and inlet fuel cell air temperature to maintain a nearly constant SOFC electrode electrolyte assembly temperature profile. For example temperature variations of less than 5 K are obtained for load perturbations of ±25% from nominal. These results are obtained using a centralized control strategy to regulate a distributed temperature profile and manage actuator interactions. The controller is based on H-infinity synthesis using a physical based dynamic model of a single co-flow SOFC repeat cell. The model of the fuel cell spatial temperature response needed for control synthesis was linearized and reduced from nonlinear model of the fuel cell assembly. A single 11 state feedback linear system tested in the full nonlinear model was found to be effective and stable over a wide fuel cell operating envelope (0.82-0.6 V). Overall, simulation of the advanced controller resulted in small and smooth monotonic temperature response to rapid and large load perturbations. This indicates that future SOFC systems can be designed and controlled to have superb load following characteristic with less than previously expected thermal stresses.     

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.     

Multi-loop control strategy of a solid oxide fuel cell and micro gas turbine hybrid system

Solid oxide fuel cell and micro gas turbine (SOFC/MGT) hybrid system is a promising distributed power technology. In order to ensure the system safe operation as well as long lifetime of the fuel cell, an effective control manner is expected to regulate the temperature and fuel utilization at the desired level, and track the desired power output. Thus, a multi-loop control strategy for the hybrid system is investigated in this paper. A mathematical model for the SOFC/MGT hybrid system is built firstly. Based on the mathematical model, control cycles are introduced and their design is discussed. Part load operation condition is employed to investigate the control strategies for the system. The dynamic modeling and control implementation are realized in the MATLAB/SIMULINK environment, and the simulation results show that it is feasible to build the multi-loop control methods for the SOFC/MGT hybrid system with regard to load disturbances.     

Analysis of a solid oxide fuel cell and a molten carbonate fuel cell integrated system with different configurations

A solid oxide fuel cell with internal reforming operation is run at partial fuel utilization; thus, the remaining fuel can be further used for producing additional power. In addition, the exhaust gas of a solid oxide fuel cell still contains carbon dioxide, which is the primary greenhouse gas, and identifying a way to utilize this carbon dioxide is important. Integrating the solid oxide fuel cell with the molten carbonate fuel cell is a potential solution for carbon dioxide utilization. In this study, the performance of the integrated fuel cell system is analyzed. The solid oxide fuel cell is the main power generator, and the molten carbonate fuel cell is regarded as a carbon dioxide concentrator that produces electricity as a by-product. Modeling of the solid oxide fuel cell and the molten carbonate fuel cell is based on one-dimensional mass balance, considering all cell voltage losses. Primary operating conditions of the integrated fuel cell system that affect the system efficiencies in terms of power generation and carbon dioxide utilization are studied, and the optimal operating parameters are identified based on these criteria. Various configurations of the integrated fuel cell system are proposed and compared to determine the suitable design of the integrated fuel cell system.     

Constrained model predictive control of a solid oxide fuel cell based on genetic optimization

Solid oxide fuel cells (SOFCs) are considered to be among the most important fuel cells. However, SOFCs present a challenging control problem owing to their slow dynamics, nonlinearity, and tight operating constraints. In this paper, we propose a model predictive control (MPC) strategy based on genetic optimization to solve the SOFC control problem. First, a support vector machine (SVM) model is identified to approximate the behavior of the SOFC system, then a specially designed genetic algorithm (GA) is employed to solve the resulting constrained nonlinear predictive control problem. A terminal cost is incorporated into the standard performance index to further enhance the control performance. Moreover, the GA is accelerated by improving the initial population based on the optimal control sequence obtained for the previous sampling period and a local controller. In addition, a dynamic constraint is also adopted in order to meet the requirements for the desired fuel utilization and control constraints. The measures to achieve offset-free properties are also discussed. Simulation results on an SOFC system illustrate that the proposed method can successfully deal with the control and control move constraints, and that a satisfactory closed-loop performance can be achieved.     

Thermodynamic assessment of solid oxide fuel cell system integrated with bioethanol purification unit

A solid oxide fuel cell system integrated with a distillation column (SOFC–DIS) has been proposed in this article. The integrated SOFC system consists of a distillation column, an EtOH/H₂O heater, an air heater, an anode preheater, a reformer, an SOFC stack and an afterburner. Bioethanol with 5 mol% ethanol was purified in a distillation column to obtain a desired concentration necessary for SOFC operation. The SOFC stack was operated under isothermal conditions. The heat generated from the stack and the afterburner was supplied to the reformer and three heaters. The net remaining heat from the SOFC system (Q_SOFC,Net) was then provided to the reboiler of the distillation column. The effects of fuel utilization and operating voltage on the net energy (Q_Net), which equals Q_SOFC,Net minus the distillation energy (Q_D), were examined. It was found that the system could become more energy sufficient when operating at lower fuel utilization or lower voltage but at the expense of less electricity produced. Moreover, it was found that there were some operating conditions, which yielded Q_Net of zero. At this point, the integrated system provides the maximum electrical power without requiring an additional heat source. The effects of ethanol concentration and ethanol recovery on the electrical performance at zero Q_Net for different fuel utilizations were investigated. With the appropriate operating conditions (e.g. C_EtOH = 41%, U_f = 80% and EtOH recovery = 80%), the overall electrical efficiency and power density are 33.3% (LHV) and 0.32 W cm⁻², respectively.     

Nonlinear model predictive control based on the moving horizon state estimation for the solid oxide fuel cell

As a nonlinear power generation device, the solid oxide fuel cell (SOFC) often operates under small window of operating conditions due to the constraints stemming from the environmental and safety considerations. The nonlinear model predictive control (NMPC) appears to be well suited control algorithm for this application. NMPC is a closed-loop feedback control scheme that predicts the open-loop optimal input based on the measurements and the setting trajectory. This work aims to develop a closed-loop feedback control strategy based on the NMPC controller for a planar SOFC. The current density, fuel and air molar flow rates are chosen as manipulated variables to control the output power, fuel utilization and temperature. The mole fraction and temperature of the exit gases are set as state variables, which can be estimated from the moving horizon estimation (MHE) method. The validation here is referred to robustness and stability of the controller, a typical case study has been conducted with the power output changes under constant fuel utilization and temperature. Simulation results show that the noise of the output is successfully filtered by the MHE. The NMPC controller works satisfactorily following the setting output trajectory.     

Predictive control of solid oxide fuel cell based on an improved Takagi-Sugeno fuzzy model

Thermal management of a solid oxide fuel cell (SOFC) stack essentially involves control of the temperature within a specific range in order to maintain good performance of the stack. In this paper, a nonlinear temperature predictive control algorithm based on an improved Takagi-Sugeon (T-S) fuzzy model is presented. The improved T-S fuzzy model can be identified by the training data and becomes a predictive model. The branch-and-bound method and the greedy algorithm are employed to set a discrete optimization and an initial upper boundary, respectively. Simulation results show the advantages of the model predictive control (MPC) based on the identified and improved T-S fuzzy model for an SOFC stack.     

From waste to electricity through integrated plasma gasification/fuel cell (IPGFC) system

The waste management is become a very crucial issue in many countries, due to the ever- increasing amount of waste material, both domiciliary and industrial, generated.The main strategies for the waste management are the increase of material recovery (MR), which can reduce the landfill disposal, the improvement of energy recovery (ER) from waste and the minimization of the environmental impact.These two last objectives can be achieved by introducing a novel technology for waste treatment based on a plasma torch gasification system integrated with a high efficiency energy conversion system, such as combined cycle power plant or high-temperature fuel cells.This work aims to evaluate the performance of an Integrated Plasma Gasification/Fuel Cell system (IPGFC) in order to establish its energy suitability and environmental feature.The performance analysis of this system has been carried out by using a numerical model properly defined and implemented in Aspen Plus™ code environment. The model is based on the combination of a thermochemical model of the plasma gasification unit, previously developed by the authors (the so-called EquiPlasmaJet model), and an electrochemical model for the SOFC fuel cell stack simulation.The EPJ model has been employed to predict the syngas composition and the energy balance of an RDF (Refuse Derived Fuel) plasma arc gasifier (that uses air as plasma gas), whereas the SOFC electrochemical model, that is a system-level model, has allowed to forecast the stack performance in terms of electrical power and efficiency.Results point out that the IPGFC system is able to produce a net power of 4.2 MW per kg of RDF with an electric efficiency of about 33%. This efficiency is high in comparison with those reached by conventional technologies based on RDF incineration (20%).     

Thermodynamic analysis of an integrated power generation system driven by solid oxide fuel cell

A new integrated power generation system driven by the solid oxide fuel cell (SOFC) is proposed to improve the conversion efficiency of conventional energy by using a Kalina cycle to recover the waste heat of exhaust from the SOFC-GT. The system using methane as main fuel consists an internal reforming SOFC, an after-burner, a gas turbine, preheaters, compressors and a Kalina cycle. The proposed system is simulated based on the developed mathematical models, and the overall system performance has been evaluated by the first and second law of thermodynamics. Exergy analysis is conducted to indicate the thermodynamic losses in each components. A parametric analysis is also carried out to examine the effects of some key thermodynamic parameters on the system performance. Results indicate that as compressor pressure ratio increases, SOFC electrical efficiency increases and there is an optimal compressor pressure ratio to reach the maximum overall electrical efficiency and exergy efficiency. It is also found that SOFC electrical efficiency, overall electrical efficiency and exergy efficiency can be improved by increasing air flow rate. Also, the largest exergy destruction occurs in the SOFC followed by the after-burner, the waste heat boiler, the gas turbine. The compressor pressure ratio and air flow rate have significant effects on the exergy destruction in some main components of system.     

Control-oriented modelling and analysis of a solid oxide fuel cell system

In this paper, a control-oriented model of a solid oxide fuel cell system is formulated and analyzed in detail. First, a lumped model based on first principle laws is formulated and tuned using experimental data coming from a real solid oxide fuel cell system test bench. The model calibration is carried out based on an optimization approach to minimize the error between the experimental data and the model one. To systematically analyze the system behavior, an equilibrium point analysis is formulated and developed. The analysis results show the maximum steady-state electrical power under each constant stack temperature. This will allow to appropriately select operation points during the system operation. Secondly, Lyapunov's theory is used to characterize the local stability of the equilibrium points. The results show that the equilibrium points are locally stable. Besides, comparison between the initial nonlinear model with the linearized model is performed to show the efficacy of the linearised model analysis. Finally, the frequency response of the linearized model is performed. This analysis provides key information about control system design in order to efficiently operate the solid oxide fuel cell system.     

Efficiency analyses of ethanol-fueled solid oxide fuel cell power system

In this study, the balance of plant (BOP) of an ethanol-fueled SOFC is analyzed using the GCTool software package developed by Argonne National Laboratory (ANL). The effects of the excess air ratio and fuel utilization on the electric and heat efficiencies of the SOFC are systematically examined for two reforming methods (steam reforming and auto-thermal reforming) and two flow sheets (BOP A and BOP B). In BOP A, the cathode off-gas is passed directly to the afterburner together with the unreacted fuel, and the hot flue gas exiting the burner is then used to provide the thermal energy required for the ethanol reforming process. In BOP B, the cathode off-gas is passed through a heat exchanger in order to heat the ethanol fuel prior to the reforming process, and is then flowed into the burner with the unreacted fuel. The results show that given an SOFC inlet temperature of 650 °C, a fuel utilization of 70.2% and excess air ratios of 4, 6 and 7, respectively, the overall system efficiency is equal to 74.9%, 72.3% and 71.0%. In general, the results presented in this study provide a useful starting point for the design and development of practical ethanol-fueled SOFC test systems.     

Design of a thermally integrated bioethanol-fueled solid oxide fuel cell system integrated with a distillation column

Solid oxide fuel cell systems integrated with a distillation column (SOFC-DIS) have been investigated in this study. The MER (maximum energy recovery) network for SOFC-DIS system under the base conditions (C_EtOH = 25%, EtOH recovery = 80%, V = 0.7 V, fuel utilization = 80%, T_SOFC = 1200 K) yields Q_Cmin = 73.4 and Q_Hmin = 0 kW. To enhance the performance of SOFC-DIS, utilization of internal useful heat sources from within the system (e.g. condenser duty and hot water from the bottom of the distillation column) and a cathode recirculation have been considered in this study. The utilization of condenser duty for preheating the incoming bioethanol and cathode recirculation for SOFC-DIS system were chosen and implemented to the SOFC-DIS (CondBio-CathRec). Different MER designs were investigated. The obtained MER network of CondBio-CathRec configuration shows the lower minimum cold utility (Q_Cmin) of 55.9 kW and total cost index than that of the base case. A heat exchanger loop and utility path were also investigated. It was found that eliminate the high temperature distillate heat exchanger can lower the total cost index. The recommended network is that the hot effluent gas is heat exchanged with the anode heat exchanger, the external reformer, the air heat exchanger, the distillate heat exchanger and the reboiler, respectively. The corresponding performances of this design are 40.8%, 54.3%, 0.221 W cm⁻² for overall electrical efficiency, Combine Heat and Power (CHP) efficiency and power density, respectively. The effect of operating conditions on composite curves on the design of heat exchanger network was investigated. The obtained composite curves can be divided into two groups: the threshold case and the pinch case. It was found that the pinch case which T_SOFC = 1173 K yields higher total cost index than the CondBio-CathRec at the base conditions. It was also found that the pinch case can become a threshold case by adjusting split fraction or operating at lower fuel utilization. The total cost index of the threshold cases is lower than that of the pinch case. Moreover, it was found that some conditions can give lower total cost index than that of the CondBio-CathRec at the base conditions.     

Small signal modelling and control of high gain coupled inductor boost inverter for solid oxide fuel cell based power generation system

Small signal model of high gain coupled inductor boost inverter is established in presented work. Developed small signal model is then integrated with the model of planar solid oxide fuel cell and simulation of complete system is realized using MATLAB/Simulink environment and compared with the already developed fuel cell-based power converters. Coupled inductor boost converter was chosen to achieve higher gain in dc link voltage by selecting the appropriate turn ratio. Small signal model for dc-dc and dc-ac stages is derived separately and accordingly control system is designed. Dual loop with feed forward control scheme for coupled inductor boost inverter resulted in good performance like stable dc link, fast transient response, low total harmonic distortion (THD) and input disturbance rejection. Mathematical analysis, simulation and hardware results prove the stability and reliability of the complete system.     

Multi-objective optimized operation of integrated energy system with hydrogen storage

In this paper, an integrated energy system (IES) consisting of wind turbine unit, photovoltaic cell unit, electrolytic hydrogen unit, fuel cell unit, and hydrogen storage unit is proposed, and the construction of multi objectives for day-ahead power dispatching of the IES considering both operation and environment cost is discussed. By adopting piecewise linearization method, the optimization variables are divided into 24 periods, and the day-ahead power dispatching optimization problem is transformed into a 24-h piecewise optimization problem. On the basis, a complete non-linear mixed integer dynamic scheduling optimization model is established. An improved non-dominated sorting genetic algorithm (NSGA-II) is applied to solving the model. In optimization process, an interactive strategy is adopted to solve the coordination between discretization of variables and restriction of switching times of electrolyzer. Optimization results show that, compared with the single objective of minimizing operating costs, the multi-objective optimization scheme can reduce carbon emissions by 3.5% with 2.8% increase of operating cost. Compared with the single objective of minimizing environmental, the multi-objective optimization scheme can reduce operating cost carbon by 5.12% with 2.6% increase of environmental cost.     

Performance assessment of a hybrid solid oxide and molten carbonate fuel cell system with compressed air energy storage under different power demands

As electricity demand can vary considerably and unpredictably, it is necessary to integrate energy storage with power generation systems. This study investigates a solid oxide and molten carbonate fuel cell system integrated with a gas turbine (GT) for power generation. The advanced adiabatic compressed air energy storage (AA-CAES) system is designed to enhance the system flexibility. Simulations of the proposed power system are performed to demonstrate the amount of power that can supply to the loads during normal and peak modes of operation under steady-state conditions. The pressure ratios of the GT and AA-CAES and the additional air feed are used to design the system and analyze the system performance. The results show that a small additional air feed to the GT is certainly required for the hybrid system. The GT pressure ratio of 2 provides a maximum benefit. The AA-CAES pressure ratio of 5 is recommended to spare some air in the storage and minimize storage volume. Moreover, implementation of the GT and AA-CAES into the integrated fuel cell system allows the system to cope with the variations in power demand.