Predictive control of SOFC based on a GA-RBF neural network model

Transients in a load have a significant impact on the performance and durability of a solid oxide fuel cell (SOFC) system. One of the main reasons is that the fuel utilization changes drastically due to the load change. Therefore, in order to guarantee the fuel utilization to operate within a safe range, a nonlinear model predictive control (MPC) method is proposed to control the stack terminal voltage as a proper constant in this paper. The nonlinear predictive controller is based on an improved radial basis function (RBF) neural network identification model. During the process of modeling, the genetic algorithm (GA) is used to optimize the parameters of RBF neural networks. And then a nonlinear predictive control algorithm is applied to track the voltage of the SOFC. Compared with the constant fuel utilization control method, the simulation results show that the nonlinear predictive control algorithm based on the GA-RBF model performs much better.     

Nonlinear dynamic modeling for a SOFC stack by using a Hammerstein model

Solid oxide fuel cell (SOFC) is a kind of nonlinear, multi-input–multi-output (MIMO) system that is hard to model by the traditional methodologies. For the purpose of dynamic simulation and control, this paper reports a dynamic modeling study of SOFC stack using a Hammerstein model. The static nonlinear part of the Hammerstein model is modeled by a radial basis function neural network (RBFNN), and the linear part is modeled by an autoregressive with exogenous input (ARX) model. To estimate the hidden centers, the radial basis function widths and the connection weights of the RBFNN, a new gradient descent algorithm is derived in the study. On the other hand, the least squares (LS) algorithm and Akaike Information Criteria (AIC) are used to estimate the parameters and the orders of the ARX model, respectively. The applicability of the proposed Hammerstein model in modeling the nonlinear dynamic properties of the SOFC is illustrated by the simulation. At the same time, the experimental comparisons between the Hammerstein model and the RBFNN model are provided which show a substantially better performance for the Hammerstein model. Furthermore, based on this Hammerstein model, some control schemes such as predictive control, robust control can be developed.     

Nonlinear model predictive control of SOFC based on a Hammerstein model

To protect solid oxide fuel cell (SOFC) stack and meet the voltage demand of DC type loads, two control loops are designed for controlling fuel utilization and output voltage, respectively. A Hammerstein model of the SOFC is first presented for developing effective control strategies, in which the nonlinear static part is approximated by a radial basis function neural network (RBFNN) and the linear dynamic part is modeled by an autoregressive with exogenous input (ARX) model. As we know, the output voltage of the SOFC changes with load variations. After a primary control loop is designed to keep the fuel utilization as a steady-state constant, a nonlinear model predictive control (MPC) based on the Hammerstein model is developed to control the output voltage of the SOFC. The performance of the MPC controller is compared with that of the PI controller developed in [Y.H. Li, S.S. Choi, S. Rajakaruna, An analysis of the control and operation of a solid oxide fuel-cell power plant in an isolated system, IEEE Trans. Energy Convers. 20 (2) (2005) 381–387]. Simulation results demonstrate the potential of the proposed Hammerstein model for application to the control of the SOFC, while the excellence of the nonlinear MPC controller for voltage control of the SOFC is proved.     

YSZ-based SOFC with modified electrode/electrolyte interfaces for operating at temperature lower than 650 °C

A NiO/Yttrium-stabilized zirconia (YSZ) transition layer and/or a SDC function layer were introduced into the anode/electrolyte and/or electrolyte/cathode interface to decrease the activation polarization resulted from the mass transfer at electrode/electrolyte interface. With a NiO/YSZ transition layer, the activation polarization simulated from I–V curves drops from 4.42 to 2.42 Ω cm² at 600 °C, about 45% less than that of cell I; with additional SDC function layer, no activation polarization is obviously observed. The cell performance was also remarkably improved with the introduction of both the transition layer and the SDC function layer. Peak power densities of 187 and 443 mW cm⁻² at 600 and 650 °C, respectively, were achieved for a single cell with both a transition layer and a function layer, with an increment of 87% and 95% compared to that of the cell without any structural improvement, and about 30% and 25% compared to that of the cell with only anode transition layer. The study by ac impedance spectroscopy technique also indicated that the interfacial polarization resistance, the main source of cell resistance, could be effectively reduced by interface improvement.     

Parameter identification of an SOFC model with an efficient,adaptive differential evolution algorithm

An efficient, adaptive differential evolution (DE) algorithm is proposed in which DE parameter adaptation is implemented. A ranking-based vector selection and crossover rate repairing technique are also presented. The method is referred to as IJADE (Improved Jingqiao Adaptive DE). To verify the performance of IJADE, the parameters of a simple SOFC electrochemical model that is used to control the output performance of an SOFC stack are identified and optimized. The SOFC electrochemical model is built to provide the simulated data. The results indicate that the proposed method is able to efficiently identify and optimize model parameters while showing good agreement with both simulated and experimental data. Additionally, when compared to other DE variants and other evolutionary algorithms, IJADE obtained better results in terms of the quality of the final solutions, robustness, and convergence speed.     

YSZ films fabricated by a spin smoothing technique and its application in solid oxide fuel cell

A dense single-layer YSZ film has been successfully fabricated by a spin smoothing method. Followed by a simplified slurry coating, an additional spin smoothing process was conducted to obtain a thinner and smoother film. By employment of high-viscosity slurry including high YSZ content, the film has a suitable thickness by a single coating cycle. With Sm_0.2Ce_0.8O_1.9 (SDC)-impregnated La_0.7Sr_0.3MnO₃ (LSM) cathode and porous NiO–YSZ anode, single solid oxide fuel cell (SOFC) based on an 8-μm-thick YSZ film was obtained. Open-circuit voltage (OCV) of the cell was 1.04 V at 800 °C, and maximum power densities were 676, 965 and 1420 mW cm⁻² at 700, 750 and 800 °C, respectively, using H₂ at a flow rate of 40 mL min⁻¹ as fuel and ambient air as oxidant. The power density could be increased to 1648 mW cm⁻² at 800 °C when the flow rate of H₂ was enhanced to 200 mL min⁻¹.     

A high-performance ammonia-fueled SOFC based on a YSZ thin-film electrolyte

Ammonia is a possible candidate as the fuel for solid oxide fuel cells (SOFCs). In this work, an anode-supported SOFC based on yttrium-stabled zircite (YSZ) thin-film electrolyte was fabricated by a simple dry-pressing process. Directly fueled by commercial liquefied ammonia, the single cell was tested at temperatures from 650 to 850 °C. The maximum power densities were 299 and 526 mW cm⁻² at 750 and 850 °C, respectively, only slightly lower than that fueled by hydrogen. Analysis of open current voltages (OCVs) of the cell indicated the oxidation of ammonia within a SOFC is a two-stage process. Impedance spectra showed the cell fueled by ammonia had the same electrolyte resistances as that fueled by hydrogen, but a little larger interfacial polarization resistances. Further, the performances of the cell were essentially determined by the interfacial resistances under 750 °C.     

Accelerated anode failure of a high temperature planar SOFC operated with reduced moisture and increased PH3 concentrations in coal syngas

Electrolyte supported SOFCs with Ni-YSZ/Ni-GDC bi-layer anodes were operated at 800 °C and 900 °C with 8% H₂O and 10-20 ppm of PH₃/syngas to reduce steam-related interference accelerate degradation. Cell power output degraded rapidly within the first 12 h, with even faster degradation at 900 °C. Nickel phosphide phases detected in the anode include Ni₃P, Ni₁₂P₅ and Ni₅P₂, while CePO₄ formed in the catalyst layer. Irrespective of the electrolyte component used, phosphorus penetrated to the anode-electrolyte interface in electrically loaded cells, as well as with Ni-GDC cells in coupon tests. In contaminated bi-layer anodes, phosphorus appeared to concentrate away from the surface, suggesting oxidation of PH₃ when steam rich environments were present.     

Deficiency of hydrogen production in commercialized planar Ni-YSZ/YSZ/LSM-YSZ steam electrolysis cells

Deficient, or non-linear hydrogen production is for the first time experimentally observed in large-scale planar Ni-YSZ/YSZ/LSM-YSZ steam electrolysis cells. The apparent coinciding of the concentration polarization and Faraday efficiency decrease at certain current density (?0.5Acm^?2 or -0.6Acm^?2 for selected steam content) indicates that steam starvation appears to affect the hydrogen production's linearity, which in essence the Ni/NiO redox process is believed to play a role in such normal SOEC operations. The SOEC survives 10h extreme polarization through electric conduction and oxygen vacancy transportation. Rational SOEC working mode is recommended accordingly. The present work is complementary for the general application of the Faraday's Law to estimate hydrogen production, and to further evaluate the SOEC's overall characteristics.     

基于径向基函数网络的热物性参数辨识

将径向基函数网络应用于热物性参数辨识，提出了完整的数学模型；数值模拟结果表明，此法具有相当的精确性，成功地克服了反问题中误差累积放大的弱点；结果很容易推广到多维或多热物性参数辩识的情形。     

Air plasma spray processing and electrochemical characterization of Cu-SDC coatings for use in solid oxide fuel cell anodes

Air plasma spraying has been used to produce porous composite anodes based on Ce_0.8Sm_0.2O_1.9 (SDC) and Cu for use in solid oxide fuel cells (SOFCs). Preliminarily, a range of plasma conditions has been examined for the production of composite coatings from pre-mixed SDC and CuO powders. Plasma gas compositions were varied to obtain a range of plasma temperatures. After reduction in H₂, coatings were characterized for composition and microstructure using EDX and SEM. As a result of these tests, symmetrical sintered electrolyte-supported anode-anode cells were fabricated by air plasma spraying of the anodes, followed by in situ reduction of the CuO to Cu. Full cells deposited on SS430 porous substrates were then produced in one integrated process. Fine CuO and SDC powders have been used to produce homogeneously mixed anode coatings with higher surface area microstructures, resulting in area-specific polarization resistances of 4.8 Ω cm² in impedance tests in hydrogen at 712 °C.     

The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data

The main objective of present study is to predict daily global solar radiation (GSR) on a horizontal surface, based on meteorological variables, using different artificial neural network (ANN) techniques. Daily mean air temperature, relative humidity, sunshine hours, evaporation, and wind speed values between 2002 and 2006 for Dezful city in Iran (32°16′N, 48°25′E), are used in this study. In order to consider the effect of each meteorological variable on daily GSR prediction, six following combinations of input variables are considered:

(I)

Day of the year, daily mean air temperature and relative humidity as inputs and daily GSR as output.

(II)

Day of the year, daily mean air temperature and sunshine hours as inputs and daily GSR as output.

(III)

Day of the year, daily mean air temperature, relative humidity and sunshine hours as inputs and daily GSR as output.

(IV)

Day of the year, daily mean air temperature, relative humidity, sunshine hours and evaporation as inputs and daily GSR as output.

(V)

Day of the year, daily mean air temperature, relative humidity, sunshine hours and wind speed as inputs and daily GSR as output.

(VI)

Day of the year, daily mean air temperature, relative humidity, sunshine hours, evaporation and wind speed as inputs and daily GSR as output.

Multi-layer perceptron (MLP) and radial basis function (RBF) neural networks are applied for daily GSR modeling based on six proposed combinations.The measured data between 2002 and 2005 are used to train the neural networks while the data for 214 days from 2006 are used as testing data.The comparison of obtained results from ANNs and different conventional GSR prediction (CGSRP) models shows very good improvements (i.e. the predicted values of best ANN model (MLP-V) has a mean absolute percentage error (MAPE) about 5.21% versus 10.02% for best CGSRP model (CGSRP 5)).     

SOFC anodes based on infiltration of tungsten bronzes

Several tungsten bronzes were investigated for use in solid oxide fuel cell (SOFC) anodes. Composite anodes were prepared by infiltration of the precursor salts into a porous yttria-stabilized zirconia (YSZ) scaffold to produce 40-wt% composites with bronze compositions of Na_0.8Nb_yW_1−yO_3−δ (y = 0, 0.3, 0.7, and 1), K_0.5WO_3−δ, Cs_0.2WO_3−δ, and Rb_0.2WO_3−δ. XRD data showed that the bronze structures were formed following reduction in humidified H₂ at 873 K but that the bronzes were partially reduced to metallic W above 1073 K. Composite conductivities as high as 130 S/cm were observed at 973 K for the Na_0.8WO_3−δ-YSZ composite but substitution of Nb significantly decreased the conductivity without increasing the temperature at which tungsten was reduced. The impedance of Na_0.8WO_3−δ-YSZ anodes in humidified H₂ at 973 K was greater than 1.0 Ω cm² but this decreased to approximately 0.3 Ω cm² upon the addition of 1-wt% Pd for catalytic purposes. The possible use of anodes based on tungsten bronzes is discussed.     

Proton conducting solid oxide fuel cells with layered PrBa0.5Sr0.5Co2O5+δ perovskite cathode

BaZr_0.1Ce_0.7Y_0.2O_3−δ (BZCY7) exhibits adequate protonic conductivity as well as sufficient chemical and thermal stability over a wide range of SOFC operating conditions, while layered perovskite PrBa_0.5Sr_0.5Co₂O_5+δ (PBSC) has advanced electrochemical properties. This research fully takes advantage of these advanced properties and develops a novel protonic ceramic membrane fuel cell (PCMFC) of Ni–BZCY7|BZCY7|PBSC. Experimental results show that the cell may achieve the open-circuit potential of 1.005 V, the maximal power density of 520 mW cm⁻², and a low electrode polarization resistance of 0.12 Ωcm² at 700 °C. Increasing operating temperature leads to the decrease of total cell resistance, among which electrolyte resistance becomes increasingly dominant over polarization resistance. The results also indicate that PBSC perovskite cathode is a good candidate for intermediate temperature PCMFC development, while the developed Ni–BZCY7|BZCY7|PBSC cell is a promising functional material system for SOFCs.     

Enhanced conductivity of SDC based nanocomposite electrolyte by spark plasma sintering

Recently, ceria-based nanocomposites have been considered as promising electrolyte candidates for low-temperature solid oxide fuel cells (LTSOFC) due to their dual-ion conduction and excellent performance. However, the densification of these composites remains a great concern since the relative low density of the composite electrolyte is suspected to deteriorate the durability of fuel cell. In the present study, the ionic conductivity of two kinds of SDC-based nanocomposite electrolytes processed by spark plasma sintering (SPS) method was investigated, and compared to that made by conventional cold pressing followed by sintering (normal processing way). The density of solid electrolyte can reach higher than 95% of the theoretical value after SPS processing, while the relative density of the electrolyte pellets by normal processing way can hardly approach 75%. The structure and morphology of the sintered pellets were characterized by XRD and SEM. The ionic conductivity of samples was measured by electrochemical impedance spectroscopy (EIS). The results showed that the ionic conductivity of the two kinds of electrolytes treated with SPS was significantly enhanced, compared with the electrolyte pellets processed through the conventional method. The profile of impedance curve of the electrolytes was altered as well. This study demonstrates that the conductivity of SDC based nanocomposite electrolyte can be further improved by adequate densification process.     

Electrode performance and analysis of reversible solid oxide fuel cells with proton conducting electrolyte of BaCe0.5Zr0.3Y0.2O3−δ

Reversible solid oxide fuel cells (R-SOFCs) are regarded as a promising solution to the discontinuity in electric energy, since they can generate electric powder as solid oxide fuel cells (SOFCs) at the time of electricity shortage, and store the electrical power as solid oxide electrolysis cells (SOECs) at the time of electricity over-plus. In this work, R-SOFCs with thin proton conducting electrolyte films of BaCe_0.5Zr_0.3Y_0.2O_3−δ were fabricated and their electro-performance was characterized with various reacting atmospheres. At 700 °C, the charging current (in SOFC mode) is 251 mA cm⁻² at 0.7 V, and the electrolysis current densities (in SOEC mode) reaches −830 mA cm⁻² at 1.5 V with 50% H₂O-air and H₂ as reacting gases, respectively. Their electrode performance was investigated by impedance spectra in discharging mode (SOFC mode), electrolysis mode (SOEC mode) and open circuit mode (OCV mode). The results show that impedance spectra have different shapes in all the three modes, implying different rate-limiting steps. In SOFC mode, the high frequency resistance (R_H) is 0.07 Ωcm² and low frequency resistances (R_L) are 0.37 Ωcm². While in SOEC mode, R_H is 0.15 Ωcm², twice of that in SOFC mode, and R_L is only 0.07 Ωcm², about 19% of that in SOFC mode. Moreover, the spectra under OCV conditions seems like a combination of those in SOEC mode and SOFC mode, since that R_H in OCV mode is about 0.13 Ωcm², close to R_H in SOEC mode, while R_L in OCV mode is 0.39 Ωcm², close to R_L in SOFC mode. The elementary steps for SOEC with proton conducting electrolyte were proposed to account for this phenomenon.     

Layered perovskite GdBaCoFeO5+x as cathode for intermediate-temperature solid oxide fuel cells

A layered perovskite oxide, GdBaCoFeO_5+x (GBCF), was investigated as a novel cathode for intermediate-temperature solid oxide fuel cells (IT-SOFCs). A laboratory-sized Sm_0.2Ce_0.8O_1.9 (SDC)-based tri-layer cell of NiO–SDC/SDC/GBCF was tested under intermediate-temperature conditions of 550–650 °C with humidified H₂ (∼3% H₂O) as a fuel and the static ambient air as oxidant. A maximal power density of 746 mW cm⁻² was achieved at 650 °C. The interfacial polarization resistance was as low as 0.42, 0.18 and 0.11 Ω cm² at 550, 600 and 650 °C, respectively. The experimental results indicate that the layered perovskite GBCF is a promising cathode candidate for IT-SOFCs.     

Enhancing oxygen reduction activity and CO2-tolerance of A-site-deficient BaCo0.7Fe0.3O3-δ cathode by surface-decoration with Pr6O11 particles

Sluggish oxygen reduction reaction (ORR) activity and poor CO₂-tolerance has been the long-standing limitations for the application of alkaline earth metal oxide cathode for solid oxide fuel cells (SOFCs). Here we report this situation can be ameliorated with a composite cathode based on Ba_0.9Co_0.7Fe_0.3O_3-δ (B90CF) by surface-decorated Pr₆O₁₁ (PO) particles. A halved polarization resistance is obtained by B90CF-15PO (PO of 15 wt%) cathode (0.033 Ω cm² at 700 °C) compared to blank B90CF, suggesting boosted oxygen reduction reaction activity owing to the accelerated oxygen surface exchange kinetics introduced by PO particles. PO protective layer also brings up desirable CO₂-tolerance for B90CF cathode due to the more stable fluorite cubic structure of PO and higher acidity of Pr³⁺/Pr⁴⁺ than Ba²⁺_, which ensures the stable operation of cells. This work demonstrates the positive potential of surface-decoration with PO in developing cathodes with high performance and CO₂-tolerance.     

Control of a solid oxide fuel cell stack based on unmodeled dynamic compensations

To guarantee solid oxide fuel cell (SOFC) safe operation, plenty control strategies have been developed to control stack temperature and voltage within a reasonable range. However, these control approaches ignore unmodeled dynamics of the SOFC system, which may lead to unsatisfactory control results, sometimes even make the system unstable. To overcome this challenge, a unique control strategy which considers unmodeled dynamic compensations of the SOFC system is proposed in this paper. A model of the SOFC system is firstly built, which includes a known linear model and an unmodeled nonlinear dynamic estimation. A nonlinear controller based on the unmodeled dynamic compensation is then developed to force the SOFC to track desired stack temperature and voltage. To evaluate the control performance, the proposed control method is compared with a traditional sliding mode controller. The simulation results show if the unmodeled dynamics have a small effect on the SOFC, both the sliding mode controller and the proposed controller can achieve a precise tracking. If the unmodeled dynamics have a great impact on the SOFC, the temperature and voltage can be well controlled with the proposed control strategy. However, in the sliding mode controller, the temperature and voltage trajectories deviate largely from the reference values.