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Modeling and simulation of temperature distribution for planar cross-flow solid oxide fuel cell
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Energyonline Procedia 00 (2018) 000–000 Available onlineatat www.sciencedirect.com Available www.sciencedirect.com Energy Procedia 00 (2018) 000–000
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www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Energy Procedia 158 Energy Procedia 00(2019) (2017)1585–1590 000–000 www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Modeling and simulation of temperature distribution for planar ModelingTheand of temperature for planar 15thsimulation International Symposium on Districtdistribution Heating and Cooling cross-flow solid oxide fuel cell cross-flow solid oxide fuel cell Assessing the feasibility of using the heat demand-outdoor a Yuan-wu Xua, Xiao-long Wuaa, Hang Youaa, Tao Xueaa, Dong-qi Zhaoaa, Jian-hua Jiangaa, Yuan-wu Xu , Xiao-long Wufor , Hang You , Tao Xue , Jian-hua Jiang , a a,c,*Zhao temperature function aDeng long-term district heat demand forecast Zhong-hua , Xiao-wei Fu,bbDong-qi , Li Xi a a,c,* Zhong-hua Deng , Xiao-wei Fu , Li Xi *, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
School of Automation, Keya,b,c Laboratory of Education Ministry for aImage Processing and University of Science and a b Intelligent Control, Huazhong c c a School of Automation, Key Laboratory of Education Ministry for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan 430074, China b Technology, Wuhan and 430074, ChinaIndustrial System, Wuhan University of Science and Hubei Province Key Laboratory of Intelligent Information Processing Real-time a b IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Hubei Province Key Laboratory of Intelligent Information Processing Real-time Technology, Wuhan and 430065, ChinaIndustrial System, Wuhan University of Science and b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Technology, Wuhan China Research Institute of Huazhong University of Science &430065, Technology in Shenzhen, Shenzhen 518057, China c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France c Research Institute of Huazhong University of Science & Technology in Shenzhen, Shenzhen 518057, China a
I. Andrić
Abstract Abstract Abstract Solid oxide fuel cell is a device that can convert chemical energy directly into electricity. Its advantages, such as high efficiency, District heating networks are commonly addressed in the literature as into one electricity. of the mostItseffective solutions forhigh decreasing the Solid oxide fuelquiet cell is a device that flexibility, can convert chemical directly advantages, as low emission, operation, fuel bring aboutenergy the broad application prospect. However, it issuch difficult to efficiency, obtain the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat low emission, quiet operation, flexibility, the broad prospect. it isIndifficult to obtain the temperature distribution in the fuel existing planar bring cross about flow solid oxideapplication fuel cell through theHowever, experiment. this paper, a control sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, temperature distributiondifferential in the existing planar crossisflow solid oxide cellcross through experiment. paper, orient two-dimensional equation model established for a fuel planar flow the solid oxide fuel In cellthis based on athecontrol finite prolonging the investment return period. orient two-dimensional differential equation model is established for voltage a planarofcross flowcell solid oxide fuelfor cellthebased on Based the finite node method, and an iterative algorithm for calculating the real time the fuel is proposed model. on The main scope of this paper is to assessfor thecalculating feasibility the of using the heat demand outdoor function for heat demand node method, an iterative algorithm realtest time the– fuel cell temperature is thesimulation model. Based on the model, theand temperature distribution of the fuel cell in the andvoltage systemofconfiguration is proposed simulated.forThe results forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 the model, the model temperature distribution of the fuel cell in the test and system configuration simulated. Thecell, simulation results show that the can reflect the thermoelectric characteristics of the planar cross flow is solid oxide fuel especially the buildings thatmodel vary in construction period andcharacteristics typology. Three weather scenarios (low, medium, high) andespecially three district show that the canboth thecell. thermoelectric of the planar crossinflow solid oxide fuel cell, the temperature distribution ofreflect the fuel The SOFC temperature distribution modeling this paper is helpful for the development renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were temperature distribution of observers the fuel cell. SOFC temperature distribution modeling in this paper is helpful for the development of temperature distribution andThe design related control methods in later studies. compared with results from a dynamic heat demand model, previously developed and validated by the authors. of temperature distribution observers and design related control methods in later studies. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications Copyright © 2018 Elsevier Ltd. All rights reserved. error annual demand was lower However, after introducing renovation ©(the 2019 The Published by Elsevier Ltd.20% for all weather scenarios considered). Copyright ©inAuthors. 2018 Elsevier Ltd. Allresponsibility rights than reserved. Selection and peer-review under of the scientific committee of the 10th International Conference on Applied This is an open accessvalue article under theupCC license on (http://creativecommons.org/licenses/by-nc-nd/4.0/) scenarios, the error increased to BY-NC-ND 59.5% (depending the weather and renovation scenarios combination considered). th Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Peer-review under responsibility of the scientific committee of ICAE2018 –ofThe 10thupInternational Conference Applied Energy. The value of slope coefficient increased on average within the range 3.8% to 8% per decade, thatoncorresponds to the Energy (ICAE2018). decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Keywords: modeling, simulation, temperature distribution, planar cross flow solid oxide fuel cell; renovation scenarios considered). On the other hand, function intercept increased Keywords: modeling, simulation, temperature distribution, planar cross flow solid oxide fuel cell;for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-027-87557273; fax: +86-027-87557273. * Corresponding Tel.: +86-027-87557273; fax: +86-027-87557273. E-mail address:author. [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility the scientific Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.370
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Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
1. Introduction Solid Oxide Fuel Cell (SOFC) is a device that can convert chemical energy into electrical energy directly. It has many advantages such as high efficiency, low emission, noiseless, and a wide range of fuel sources. SOFC are widely used for power generation, especially in combined heat and power generation application [1,2,3]. Although SOFC technology has been developed greatly in recent years, there are still a series of issues to be solved to realize its application and commercialization widely [1]. Modeling analysis, efficiency optimization, system control and observer design is one of the most prominent obstacles [2]. In the SOFCs, a medium high temperature environment needs to be maintain for the electrochemical reaction. Excessively high temperature and temperature gradient result in large thermal stress to SOFC, which possibly causing failure of SOFC [3]. However, the characteristics of the SOFC are closely coupled with the thermal characteristics. The higher the temperature, the smaller the internal resistance, the greater the power generation capacity and the higher the output efficiency [4,5]. Therefore, thermal safety control and control-oriented SOFC temperature model is one of the focuses of SOFC research. Planar SOFC is divided into three types by gas flow directions: co-flow, counter-flow, and cross-flow. The gas flow in planar cross-flow SOFC has two dimension, Thus the model is more complex and computable. The SOFC model used in many control related literature is the lumped parameter [6]. A co-flow SOFC model is built and the model is verified and simulated in terms of electrical characteristics [7], and the temperature distribution observers is develop based on the model; In the paper [8], The maximum temperatures of the air at the outlet of the cell and the temperature of solid layers are modeled and simulated, but the internal temperature distribution of the cells was not modeled. In this paper, a control orient temperature distribution model for planar cross-flow SOFC is developed based on simplified first principles. Frist the finite node method is used to establish a two-dimensional model for planar cross-flow SOFC. An iterative algorithm for calculating the voltage of the cell is proposed. Then, the simulation of temperature distribution of SOFC was carried out based on the model using the test bench parameter. Finally, the theoretical analysis of the simulation results shows that the model can reflect the thermoelectric characteristics of the planar cross-flow SOFC, especially the temperature distribution. It should be pointed out that the SOFC temperature distribution modeling in this paper is used for the development of temperature distribution observers and design control methods in future studies. The modeling method draws on the principle of numerical simulation [9] and some simplifications are made. Therefore, the method of model develop is a bit different from the method of numerical simulation and features the characteristics of small calculation. 2. Modeling The principle and structure of planar cross-flow SOFC are shown in Fig. 1. As shown in Fig. 1(a), the connector is used for dividing the gas flow channel and collecting the current; the fuel flow channel and air flow channel provide a pathway for gas flow, the cathode air and anode fuel flow in two mutually perpendicular directions; The TPB (triple phase boundary, TPB) is the electrochemical reaction occurs area where the diffusion layer and the electrolyte are in contact. the fuel and air reach TPB through diffusion for electrochemical reaction. Since the cathode, the anode diffusion layer and the electrolyte are tightly combined, it is also called PEN (PositiveElectrolyte-Negative, PEN). As shown in Fig. 1(b), the gas molar fraction and temperature distribution in the planar cross-flow SOFC are distributed in two dimensions, so a 2D model is needed to accurately describe the temperature distribution of the cell. The finite node method is to discretization the continuum with finite nodes and uses the discrete results to approximate the continuum. In Fig. 2(a), the cell is divided into m*n nodes along the flow direction of air and fuel. In each node, it is assumed that all variables, such as gas molar fraction and temperature, are uniformly. The accuracy of the model will increase with the increase of m and n, but the complexity of the calculation will also increase. Taking into account both model accuracy and computational complexity, the value of m and n is set to 5, (m=n=5, 25 nodes). The node partitioning method has been able to obtain a sufficiently accurate temperature distribution, and the method of this paper does not depend on the specific number of divided nodes.
Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
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The model is composed of three parts, the conservation of mass, the conservation of energy and the equation of electrical properties, in Fig. 2(b). The energy conservation describes the temperature relationship within the node, the mass conservation describes the relationship of partial pressures in the node, and the electrical characteristic model describes the relationship between the voltage and the current.
Fig. 1. Principle and structure of planar cross-flow SOFC
Fig. 2. (a) Schematic of node division (b) Block diagram of SOFC node
2.1. Node modeling method All the models in the node are constructed according to the mass conservation, the energy conservation and the electric equivalent circuit, and the general formulas are shown in Table 1. Some reasonable assumptions are made for node modeling: The gas is ideal All parameters in the node are the same No pressure loss in node or cell
Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
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Uniform temperature and mole fraction in the node Gas and the SOFC is preheated above 873K. Table 1. Modeling formulas. gas Energy conservation
solid
Mass conservation
gas
Electric model
equivalent circuit
Cv , gas N chanal , gas
dTgas dt
Csolid solidVsolid
dxgas dt
H in (Tin, gas ) H out (Tgas ) hgas solid A1 (Tsolid Tgas ) Qreact
gas fuel , air
dTsolid hair solid A1 ( Tair Tsolid ) h fuel solid A1 ( Tfuel Tsolid ) dt neighbor T T k A2 i solid Qreact dx i
RTgas PVgas ,channal
(ngas ,in xin ngas ,out xgas rreact ) gas fuel , air
V Enernst Rohm I Vcon Vact
(1)
(2)
(3)
(4)
During SOFC power generation, the current of the fuel cell changes as the load changes. This is the most common operation mode for fuel cells. The current represents the total amount of electrochemical reactions in the stack and also reflects how much heat is generated in the reactor during the unit time. It is considered that the cell operates in the constant current mode and the voltage of all nodes is equal, corresponding to the following constraints:
I cell I node 0
(5)
Vcell Vnode
(6)
2.2. Iterative method The current value satisfying Eq. (5) is found by iteratively solving the SOFC voltage. This ensures that the SOFC cell current is maintained at the set value. The iterative method designed in this paper is shown in Fig. 3.
Fig. 3. Block diagram of iterative method
When the initial conditions are given and the SOFC current is given, the iterative process begins. First, use the gradient descent method to solve the cell voltage value, and based on the Eq. (6) the cell voltage value equals to the
Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
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voltage of each node; then for each node, use the gradient descent method to solve the node current. If the current sum of all the node is equal to the cell current, the iteration ends. 3. Simulation In this section, the input data from the test bench and system are taken as the input of the model, and the simulation results are compared and analyzed. Table 2. Modeling formulas. Parameter Length
Test bench variables
System variables
0.15m
Fuel flow
2NL/min/piece
Fuel flow
0.16NL/min/piece
Width
0.15m*0.15m
Air flow
3NL/min/piece
Air flow
10NL/min/piece
Connector thickness
0.001m
Fuel temperature
950K
950K
Fuel Channel height
0.001m
Air temperature
900K
Fuel temperature Air temperature
Air Channel height
0.002m
Pressure
~1.1bar
Pressure
~1.1bar
PEN thickness
0.0005m
Current
40A
Current
40A
900K
The fuel utilization FU and air excess ratio AR is calculated as follows:
FU
22.4 60 I cell 2 96485.3 Fin
(7)
AR
0.24 4 96485.3 Ain 22.4 60 I cell
(8)
Fin and Ain respectively indicate the fuel and air flow into fuel cell. The ratio of fuel utilization and air excess ratio is relatively small when the SOFC is operated in the test bench, and the fuel utilization and air excess are relatively large when operating in the system. There is a heating device in the test bench to maintain the temperature of the fuel cell, but in the system the fuel cell needs to rely on self-heating to maintain the temperature for the electrochemical reaction. The simulation parameters and input variables in the planar cross-flow SOFC test bench and system are shown in Table 2. The same simulation parameters are used in the test bench and the system: the SOFC has the same length, width and height. The fuel and air are preheated to 950K and 900K; in the test bench the fuel flow rate is 2 NL/min/piece, the air flow is 3 NL/min/piece, the current is 40A, equivalent to the fuel utilization rate of FU=13.9%, and the air excess ratio is AR=4.5; but in the system fuel flow rate is 0.8 NL/min/piece, air flow is 10 NL/min/piece, the current is 40A. the fuel utilization ratio is FU=34.8%, and the air excess ratio is AR=15. It can be seen that the utilization ratio of the system fuel is about 2.5 times of the test bench, and the system air excess ratio is about 3.3 times that of the test bench. In the system, this ratio may be greater. The actual system fuel utilization rate is about 2-5 times that of the system, and the air excess ratio is about 2-4 times that of the test. The test bench and system simulation results are shown in Fig. 4. The temperature is at the steady state: Under the test bench inputs, the temperature of the planar cross-flow SOFC increases with the air flow direction, and at the direction of hydrogen flow is also increased; the maximum temperature reaches 1090K and the minimum temperature is 1020K; Under the system inputs, the temperature of the planar cross-flow SOFC increases with the air flow direction, but at the direction of hydrogen flow decreased. The maximum temperature reaches 975K and the minimum temperature is 920K. In the system, higher fuel utilization is required to ensure less fuel is wasted. At the
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Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
same time, the excess air ratio is increased, so that the excess heat is taken away to maintain the stable operation of the system.
Fig. 4. The simulation results (a)test bench (b) system
4. Conclusion Based on the mass conservation, energy conservation and equation of electrical properties, a two-dimensional differential equation model for the planar cross flow SOFC is established in this paper. Along the flow direction of fuel and air, the 5 x 5 equal distance division of the 15cm x 15cm cross flow SOFC stack is carried out, and an iterative algorithm for calculating the real-time voltage of the SOFC is proposed in the model. The simulation of fuel cell temperature distribution in the test bench and the system is carried out based on the model. Through the simulation results, the model can reflect the temperature distribution of the SOFC. The SOFC temperature distribution modeling in this paper is helpful for the development of temperature distribution observers and design related control methods in later studies. Acknowledgements The authors would like to thank the support of the National Natural Science Foundation of China (61873323, 61573162), the Wuhan science and technology plan project (2018010401011292), the Hubei Province Natural and Science Foundation (2017CFB4165, 2016CFA037), open fund project of Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System (No. znxx2018ZD02) and Basic Research Project of Shenzhen (JCYJ20170307160923202, JCYJ20170818163921328). References [1] R.J. Braun, S.A. Klein, D.T. Reindl. Evaluation of system configurations for solid oxide fuel cell based micro-combined heat and power generators in residential applications. Journal of power sources. 2006 (158): 1290-1305. [2] J. H. Jiang, Xi Li, et al. Thermal management of an independent steam reformer for a solid oxide fuel cell with constrained generalized predictive control. International Journal of Hydrogen Energy. 2012(37): 12317-12331. [3] B. Huang, Y. Qi, et al. Solid oxide fuel cell: Perspective of dynamic modeling and control. Journal of Process Control, 2011, 21: 1426-1437. [4] Z. H. Deng, H. L. Cao, et al. Generalized predictive control for fractional order dynamic model of solid oxide fuel cell ouput power. Journal of Power Sources. 2010 (195): 8097-8103. [5] Lin Z, Xi L, Jiang J, et al. Dynamic modeling and analysis of a 5-kW solid oxide fuel cell system from the perspectives of cooperative control of thermal safety and high efficiency. International Journal of Hydrogen Energy, 2015, 40(1):456-476. [6] H. Xi, J. Sun, J. Chen. Estimation of spatial temperature distribution in co-flow planar solid oxide fuel cells. In: 2007 ASME international mechanical engineering congress and exposition, Seattle, Washington, USA; 2007. p. 1-10. [7] Cheng H, Jing S, Xu Y, et al. Control-oriented modeling analysis and optimization of planar solid oxide fuel cell system. International Journal of Hydrogen Energy, 2016, 41(47):22285-22304. [8] S. Campanari, P. Lora. Comparison of finite volume SOFC models for the simulation of a planar cell geometry. Fell Cells 2005; 5; 34-51. [9] Zhang, Y., Xia, C., & Meng, N. (2012). Simulation of sintering kinetics and microstructure evolution of composite solid oxide fuel cells electrodes. International Journal of Hydrogen Energy, 37(4), 3392-3402.
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Energyonline Procedia 00 (2018) 000–000 Available onlineatat www.sciencedirect.com Available www.sciencedirect.com Energy Procedia 00 (2018) 000–000
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www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Energy Procedia 158 Energy Procedia 00(2019) (2017)1585–1590 000–000 www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Modeling and simulation of temperature distribution for planar ModelingTheand of temperature for planar 15thsimulation International Symposium on Districtdistribution Heating and Cooling cross-flow solid oxide fuel cell cross-flow solid oxide fuel cell Assessing the feasibility of using the heat demand-outdoor a Yuan-wu Xua, Xiao-long Wuaa, Hang Youaa, Tao Xueaa, Dong-qi Zhaoaa, Jian-hua Jiangaa, Yuan-wu Xu , Xiao-long Wufor , Hang You , Tao Xue , Jian-hua Jiang , a a,c,*Zhao temperature function aDeng long-term district heat demand forecast Zhong-hua , Xiao-wei Fu,bbDong-qi , Li Xi a a,c,* Zhong-hua Deng , Xiao-wei Fu , Li Xi *, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
School of Automation, Keya,b,c Laboratory of Education Ministry for aImage Processing and University of Science and a b Intelligent Control, Huazhong c c a School of Automation, Key Laboratory of Education Ministry for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan 430074, China b Technology, Wuhan and 430074, ChinaIndustrial System, Wuhan University of Science and Hubei Province Key Laboratory of Intelligent Information Processing Real-time a b IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Hubei Province Key Laboratory of Intelligent Information Processing Real-time Technology, Wuhan and 430065, ChinaIndustrial System, Wuhan University of Science and b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Technology, Wuhan China Research Institute of Huazhong University of Science &430065, Technology in Shenzhen, Shenzhen 518057, China c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France c Research Institute of Huazhong University of Science & Technology in Shenzhen, Shenzhen 518057, China a
I. Andrić
Abstract Abstract Abstract Solid oxide fuel cell is a device that can convert chemical energy directly into electricity. Its advantages, such as high efficiency, District heating networks are commonly addressed in the literature as into one electricity. of the mostItseffective solutions forhigh decreasing the Solid oxide fuelquiet cell is a device that flexibility, can convert chemical directly advantages, as low emission, operation, fuel bring aboutenergy the broad application prospect. However, it issuch difficult to efficiency, obtain the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat low emission, quiet operation, flexibility, the broad prospect. it isIndifficult to obtain the temperature distribution in the fuel existing planar bring cross about flow solid oxideapplication fuel cell through theHowever, experiment. this paper, a control sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, temperature distributiondifferential in the existing planar crossisflow solid oxide cellcross through experiment. paper, orient two-dimensional equation model established for a fuel planar flow the solid oxide fuel In cellthis based on athecontrol finite prolonging the investment return period. orient two-dimensional differential equation model is established for voltage a planarofcross flowcell solid oxide fuelfor cellthebased on Based the finite node method, and an iterative algorithm for calculating the real time the fuel is proposed model. on The main scope of this paper is to assessfor thecalculating feasibility the of using the heat demand outdoor function for heat demand node method, an iterative algorithm realtest time the– fuel cell temperature is thesimulation model. Based on the model, theand temperature distribution of the fuel cell in the andvoltage systemofconfiguration is proposed simulated.forThe results forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 the model, the model temperature distribution of the fuel cell in the test and system configuration simulated. Thecell, simulation results show that the can reflect the thermoelectric characteristics of the planar cross flow is solid oxide fuel especially the buildings thatmodel vary in construction period andcharacteristics typology. Three weather scenarios (low, medium, high) andespecially three district show that the canboth thecell. thermoelectric of the planar crossinflow solid oxide fuel cell, the temperature distribution ofreflect the fuel The SOFC temperature distribution modeling this paper is helpful for the development renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were temperature distribution of observers the fuel cell. SOFC temperature distribution modeling in this paper is helpful for the development of temperature distribution andThe design related control methods in later studies. compared with results from a dynamic heat demand model, previously developed and validated by the authors. of temperature distribution observers and design related control methods in later studies. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications Copyright © 2018 Elsevier Ltd. All rights reserved. error annual demand was lower However, after introducing renovation ©(the 2019 The Published by Elsevier Ltd.20% for all weather scenarios considered). Copyright ©inAuthors. 2018 Elsevier Ltd. Allresponsibility rights than reserved. Selection and peer-review under of the scientific committee of the 10th International Conference on Applied This is an open accessvalue article under theupCC license on (http://creativecommons.org/licenses/by-nc-nd/4.0/) scenarios, the error increased to BY-NC-ND 59.5% (depending the weather and renovation scenarios combination considered). th Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Peer-review under responsibility of the scientific committee of ICAE2018 –ofThe 10thupInternational Conference Applied Energy. The value of slope coefficient increased on average within the range 3.8% to 8% per decade, thatoncorresponds to the Energy (ICAE2018). decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Keywords: modeling, simulation, temperature distribution, planar cross flow solid oxide fuel cell; renovation scenarios considered). On the other hand, function intercept increased Keywords: modeling, simulation, temperature distribution, planar cross flow solid oxide fuel cell;for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86-027-87557273; fax: +86-027-87557273. * Corresponding Tel.: +86-027-87557273; fax: +86-027-87557273. E-mail address:author. [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility the scientific Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.370
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Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
1. Introduction Solid Oxide Fuel Cell (SOFC) is a device that can convert chemical energy into electrical energy directly. It has many advantages such as high efficiency, low emission, noiseless, and a wide range of fuel sources. SOFC are widely used for power generation, especially in combined heat and power generation application [1,2,3]. Although SOFC technology has been developed greatly in recent years, there are still a series of issues to be solved to realize its application and commercialization widely [1]. Modeling analysis, efficiency optimization, system control and observer design is one of the most prominent obstacles [2]. In the SOFCs, a medium high temperature environment needs to be maintain for the electrochemical reaction. Excessively high temperature and temperature gradient result in large thermal stress to SOFC, which possibly causing failure of SOFC [3]. However, the characteristics of the SOFC are closely coupled with the thermal characteristics. The higher the temperature, the smaller the internal resistance, the greater the power generation capacity and the higher the output efficiency [4,5]. Therefore, thermal safety control and control-oriented SOFC temperature model is one of the focuses of SOFC research. Planar SOFC is divided into three types by gas flow directions: co-flow, counter-flow, and cross-flow. The gas flow in planar cross-flow SOFC has two dimension, Thus the model is more complex and computable. The SOFC model used in many control related literature is the lumped parameter [6]. A co-flow SOFC model is built and the model is verified and simulated in terms of electrical characteristics [7], and the temperature distribution observers is develop based on the model; In the paper [8], The maximum temperatures of the air at the outlet of the cell and the temperature of solid layers are modeled and simulated, but the internal temperature distribution of the cells was not modeled. In this paper, a control orient temperature distribution model for planar cross-flow SOFC is developed based on simplified first principles. Frist the finite node method is used to establish a two-dimensional model for planar cross-flow SOFC. An iterative algorithm for calculating the voltage of the cell is proposed. Then, the simulation of temperature distribution of SOFC was carried out based on the model using the test bench parameter. Finally, the theoretical analysis of the simulation results shows that the model can reflect the thermoelectric characteristics of the planar cross-flow SOFC, especially the temperature distribution. It should be pointed out that the SOFC temperature distribution modeling in this paper is used for the development of temperature distribution observers and design control methods in future studies. The modeling method draws on the principle of numerical simulation [9] and some simplifications are made. Therefore, the method of model develop is a bit different from the method of numerical simulation and features the characteristics of small calculation. 2. Modeling The principle and structure of planar cross-flow SOFC are shown in Fig. 1. As shown in Fig. 1(a), the connector is used for dividing the gas flow channel and collecting the current; the fuel flow channel and air flow channel provide a pathway for gas flow, the cathode air and anode fuel flow in two mutually perpendicular directions; The TPB (triple phase boundary, TPB) is the electrochemical reaction occurs area where the diffusion layer and the electrolyte are in contact. the fuel and air reach TPB through diffusion for electrochemical reaction. Since the cathode, the anode diffusion layer and the electrolyte are tightly combined, it is also called PEN (PositiveElectrolyte-Negative, PEN). As shown in Fig. 1(b), the gas molar fraction and temperature distribution in the planar cross-flow SOFC are distributed in two dimensions, so a 2D model is needed to accurately describe the temperature distribution of the cell. The finite node method is to discretization the continuum with finite nodes and uses the discrete results to approximate the continuum. In Fig. 2(a), the cell is divided into m*n nodes along the flow direction of air and fuel. In each node, it is assumed that all variables, such as gas molar fraction and temperature, are uniformly. The accuracy of the model will increase with the increase of m and n, but the complexity of the calculation will also increase. Taking into account both model accuracy and computational complexity, the value of m and n is set to 5, (m=n=5, 25 nodes). The node partitioning method has been able to obtain a sufficiently accurate temperature distribution, and the method of this paper does not depend on the specific number of divided nodes.
Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
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The model is composed of three parts, the conservation of mass, the conservation of energy and the equation of electrical properties, in Fig. 2(b). The energy conservation describes the temperature relationship within the node, the mass conservation describes the relationship of partial pressures in the node, and the electrical characteristic model describes the relationship between the voltage and the current.
Fig. 1. Principle and structure of planar cross-flow SOFC
Fig. 2. (a) Schematic of node division (b) Block diagram of SOFC node
2.1. Node modeling method All the models in the node are constructed according to the mass conservation, the energy conservation and the electric equivalent circuit, and the general formulas are shown in Table 1. Some reasonable assumptions are made for node modeling: The gas is ideal All parameters in the node are the same No pressure loss in node or cell
Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
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Uniform temperature and mole fraction in the node Gas and the SOFC is preheated above 873K. Table 1. Modeling formulas. gas Energy conservation
solid
Mass conservation
gas
Electric model
equivalent circuit
Cv , gas N chanal , gas
dTgas dt
Csolid solidVsolid
dxgas dt
H in (Tin, gas ) H out (Tgas ) hgas solid A1 (Tsolid Tgas ) Qreact
gas fuel , air
dTsolid hair solid A1 ( Tair Tsolid ) h fuel solid A1 ( Tfuel Tsolid ) dt neighbor T T k A2 i solid Qreact dx i
RTgas PVgas ,channal
(ngas ,in xin ngas ,out xgas rreact ) gas fuel , air
V Enernst Rohm I Vcon Vact
(1)
(2)
(3)
(4)
During SOFC power generation, the current of the fuel cell changes as the load changes. This is the most common operation mode for fuel cells. The current represents the total amount of electrochemical reactions in the stack and also reflects how much heat is generated in the reactor during the unit time. It is considered that the cell operates in the constant current mode and the voltage of all nodes is equal, corresponding to the following constraints:
I cell I node 0
(5)
Vcell Vnode
(6)
2.2. Iterative method The current value satisfying Eq. (5) is found by iteratively solving the SOFC voltage. This ensures that the SOFC cell current is maintained at the set value. The iterative method designed in this paper is shown in Fig. 3.
Fig. 3. Block diagram of iterative method
When the initial conditions are given and the SOFC current is given, the iterative process begins. First, use the gradient descent method to solve the cell voltage value, and based on the Eq. (6) the cell voltage value equals to the
Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
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voltage of each node; then for each node, use the gradient descent method to solve the node current. If the current sum of all the node is equal to the cell current, the iteration ends. 3. Simulation In this section, the input data from the test bench and system are taken as the input of the model, and the simulation results are compared and analyzed. Table 2. Modeling formulas. Parameter Length
Test bench variables
System variables
0.15m
Fuel flow
2NL/min/piece
Fuel flow
0.16NL/min/piece
Width
0.15m*0.15m
Air flow
3NL/min/piece
Air flow
10NL/min/piece
Connector thickness
0.001m
Fuel temperature
950K
950K
Fuel Channel height
0.001m
Air temperature
900K
Fuel temperature Air temperature
Air Channel height
0.002m
Pressure
~1.1bar
Pressure
~1.1bar
PEN thickness
0.0005m
Current
40A
Current
40A
900K
The fuel utilization FU and air excess ratio AR is calculated as follows:
FU
22.4 60 I cell 2 96485.3 Fin
(7)
AR
0.24 4 96485.3 Ain 22.4 60 I cell
(8)
Fin and Ain respectively indicate the fuel and air flow into fuel cell. The ratio of fuel utilization and air excess ratio is relatively small when the SOFC is operated in the test bench, and the fuel utilization and air excess are relatively large when operating in the system. There is a heating device in the test bench to maintain the temperature of the fuel cell, but in the system the fuel cell needs to rely on self-heating to maintain the temperature for the electrochemical reaction. The simulation parameters and input variables in the planar cross-flow SOFC test bench and system are shown in Table 2. The same simulation parameters are used in the test bench and the system: the SOFC has the same length, width and height. The fuel and air are preheated to 950K and 900K; in the test bench the fuel flow rate is 2 NL/min/piece, the air flow is 3 NL/min/piece, the current is 40A, equivalent to the fuel utilization rate of FU=13.9%, and the air excess ratio is AR=4.5; but in the system fuel flow rate is 0.8 NL/min/piece, air flow is 10 NL/min/piece, the current is 40A. the fuel utilization ratio is FU=34.8%, and the air excess ratio is AR=15. It can be seen that the utilization ratio of the system fuel is about 2.5 times of the test bench, and the system air excess ratio is about 3.3 times that of the test bench. In the system, this ratio may be greater. The actual system fuel utilization rate is about 2-5 times that of the system, and the air excess ratio is about 2-4 times that of the test. The test bench and system simulation results are shown in Fig. 4. The temperature is at the steady state: Under the test bench inputs, the temperature of the planar cross-flow SOFC increases with the air flow direction, and at the direction of hydrogen flow is also increased; the maximum temperature reaches 1090K and the minimum temperature is 1020K; Under the system inputs, the temperature of the planar cross-flow SOFC increases with the air flow direction, but at the direction of hydrogen flow decreased. The maximum temperature reaches 975K and the minimum temperature is 920K. In the system, higher fuel utilization is required to ensure less fuel is wasted. At the
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Yuan-wu Xu et al. / Energy Procedia 158 (2019) 1585–1590 Author name / Energy Procedia 00 (2018) 000–000
same time, the excess air ratio is increased, so that the excess heat is taken away to maintain the stable operation of the system.
Fig. 4. The simulation results (a)test bench (b) system
4. Conclusion Based on the mass conservation, energy conservation and equation of electrical properties, a two-dimensional differential equation model for the planar cross flow SOFC is established in this paper. Along the flow direction of fuel and air, the 5 x 5 equal distance division of the 15cm x 15cm cross flow SOFC stack is carried out, and an iterative algorithm for calculating the real-time voltage of the SOFC is proposed in the model. The simulation of fuel cell temperature distribution in the test bench and the system is carried out based on the model. Through the simulation results, the model can reflect the temperature distribution of the SOFC. The SOFC temperature distribution modeling in this paper is helpful for the development of temperature distribution observers and design related control methods in later studies. Acknowledgements The authors would like to thank the support of the National Natural Science Foundation of China (61873323, 61573162), the Wuhan science and technology plan project (2018010401011292), the Hubei Province Natural and Science Foundation (2017CFB4165, 2016CFA037), open fund project of Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System (No. znxx2018ZD02) and Basic Research Project of Shenzhen (JCYJ20170307160923202, JCYJ20170818163921328). References [1] R.J. Braun, S.A. Klein, D.T. Reindl. Evaluation of system configurations for solid oxide fuel cell based micro-combined heat and power generators in residential applications. Journal of power sources. 2006 (158): 1290-1305. [2] J. H. Jiang, Xi Li, et al. Thermal management of an independent steam reformer for a solid oxide fuel cell with constrained generalized predictive control. International Journal of Hydrogen Energy. 2012(37): 12317-12331. [3] B. Huang, Y. Qi, et al. Solid oxide fuel cell: Perspective of dynamic modeling and control. Journal of Process Control, 2011, 21: 1426-1437. [4] Z. H. Deng, H. L. Cao, et al. Generalized predictive control for fractional order dynamic model of solid oxide fuel cell ouput power. Journal of Power Sources. 2010 (195): 8097-8103. [5] Lin Z, Xi L, Jiang J, et al. Dynamic modeling and analysis of a 5-kW solid oxide fuel cell system from the perspectives of cooperative control of thermal safety and high efficiency. International Journal of Hydrogen Energy, 2015, 40(1):456-476. [6] H. Xi, J. Sun, J. Chen. Estimation of spatial temperature distribution in co-flow planar solid oxide fuel cells. In: 2007 ASME international mechanical engineering congress and exposition, Seattle, Washington, USA; 2007. p. 1-10. [7] Cheng H, Jing S, Xu Y, et al. Control-oriented modeling analysis and optimization of planar solid oxide fuel cell system. International Journal of Hydrogen Energy, 2016, 41(47):22285-22304. [8] S. Campanari, P. Lora. Comparison of finite volume SOFC models for the simulation of a planar cell geometry. Fell Cells 2005; 5; 34-51. [9] Zhang, Y., Xia, C., & Meng, N. (2012). Simulation of sintering kinetics and microstructure evolution of composite solid oxide fuel cells electrodes. International Journal of Hydrogen Energy, 37(4), 3392-3402.