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Modeling and control-oriented thermal characteristics under variable load of the solid oxide fuel cell

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Abstract

The performance of the solid oxide fuel cell (SOFC) is greatly influenced by its operating temperature. Therefore, making a profound study of the thermal characteristics inside the SOFC stack and maintaining the operating temperature within a reasonable range are the difficulties. This paper proposes a novel modeling and control strategy. Firstly, for studying the thermal characteristics of SOFC under variable load current and designing a more effective control schedule, the problem of SOFC temperature dynamic modeling is resolved by the beetle antennae search (BAS) optimizing–based back propagation (BP) neural network model (BAS-BP) innovatively. The simulation indicated that the mean absolute error (MAE), mean absolute percentage error (MAPE), and mean square error (MSE) of the designed BAS-BP algorithm are 19.14%, 24.51%, and 27.67% lower than those of the traditional BP model. The designed modeling method is armed with higher accuracy and faster convergence speed. Then, a sliding mode controller (SMC) based on the disturbance observer is represented in this paper, wherein the disturbance observer is first presented to predict disturbance functions, while the SMC realizes the tracking control of the SOFC node temperature by compensating for the observation error instead of ignoring it. It can be seen from the simulation that the proposed control strategy compared to the conventional proportional-integral-derivative (PID) controller achieves a 62.57%, 61.11%, and 6.27% reduction in MAE, MAPE, and MSE. The simulated results demonstrate that the presented strategy has better robustness to disturbances in addition to its validity in compensating for observation error, for the SOFC node temperature control.

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Abbreviations

F :

mole flow rate (mol s-1) or Faraday’s constants (96485 C mol-1)

V :

volume (m3) 

x :

mole fraction

r :

reaction rates term

I :

stack current (A)

R :

 universal gas constant (8.314 J mol-1 K-1)

C p :

 specific heat capacity (J mol-1K-1)

u f :

fuel utilization

T :

temperature (K)

U :

voltage (V)

v :

stoichiometric coefficient

ρmol :

molar density (mol m-3)

ρscs p :

106 J m-3 K-1

i :

i-th node

in :

input

ca :

cathode

an :

anode

ohm :

ohmic

act :

activation

con :

concentration

References

  1. Abdalla AM, Hossain S, Petra PM, Mostafa G, Abul AK (2020) Achievements and trends of solid oxide fuel cells in clean energy field: a perspective review. Front Energy. https://doi.org/10.1007/s11708-018-0546-2

    Article  Google Scholar 

  2. Bao C, Wang Y, Feng DL, Jiang ZY, Zhang XX (2018) Macroscopic modeling of solid oxide fuel cell (SOFC) and model-based control of SOFC and gas turbine hybrid system. Prog Energy Combust. https://doi.org/10.1016/j.pecs.2017.12.002

    Article  Google Scholar 

  3. Satyanand S (2021) Environmental energy harvesting techniques to power standalone IoT-equipped sensor and its application in 5G communication. Emerg Sci. https://doi.org/10.28991/esj-2021-SP1-08

  4. Balasubramanian R, Abishek A, Gobinath S, Jaivignesh K (2022) Alternative fuel: hydrogen and its thermodynamic behaviour. J Hum Earth Future. https://doi.org/10.28991/HEF-2022-03-02-05

  5. Xu YW, Wu XL, You H, Xue T, Zhao DQ, Jiang JH, Deng ZH, Fu XW, Li X (2019) Modeling and simulation of temperature distribution for planar cross-flow solid oxide fuel cell. Energy Procedia. https://doi.org/10.1016/j.egypro.2019.01.370

    Article  Google Scholar 

  6. Huo HB, Xu K, Cui LX, Zhang H, Xu JX, Kuang XH (2021) Temperature gradient control of the solid oxide fuel cell under variable load. ACS Omega. https://doi.org/10.1021/acsomega.1c01359

    Article  PubMed  PubMed Central  Google Scholar 

  7. Abbaker AO, Wang HP, Tian Y (2020) Voltage control of solid oxide fuel cell power plant based on intelligent proportional integral-adaptive sliding mode control with anti-windup compensator. T I Meas Control. https://doi.org/10.1177/0142331219867779

    Article  Google Scholar 

  8. Jurado F (2004) Modeling SOFC plants on the distribution system using modeling algorithms. J Power Sources. https://doi.org/10.1016/j.jpowsour.2003.11.035

    Article  Google Scholar 

  9. Huang B, Qi Y, Murshed M (2011) Solid oxide fuel cell: perspective of dynamic modeling and control. J Process Control. https://doi.org/10.1016/j.jprocont.2011.06.017

    Article  Google Scholar 

  10. Yang Y, Li X, Mou H, Li J (2009) Control-oriented thermal management of solid oxide fuel cells based on a modified Takagi-Sugeno fuzzy model. J Power Sources. https://doi.org/10.1016/j.jpowsour.2008.12.012

    Article  Google Scholar 

  11. Deng ZH, Cao HL, Li X, Jiang JH, Yang J, Qi Y (2010) Generalized predictive control for fractional order dynamic model of solid oxide fuel cell output power. J Power Sources. https://doi.org/10.1016/j.jpowsour.2010.07.053

    Article  Google Scholar 

  12. Arriagada J, Olausson P, Selimovic A (2002) Artificial neural network simulator for SOFC performance prediction. J Power Sources. https://doi.org/10.1016/S0378-7753(02)00314-2

    Article  Google Scholar 

  13. Razbani O, Assadi M (2014) Artificial neural network model of a short stack solid oxide fuel cell based on experimental data. J Power Sources. https://doi.org/10.1016/j.jpowsour.2013.08.018

    Article  Google Scholar 

  14. Shen C, Cao GY, Zhu XJ (2002) Nonlinear modeling of MCFC stack based on RBF neural networks modeling. Simul Model Pract TH. https://doi.org/10.1016/S1569-190X(02)00064-3

  15. Chen JW, Zhang HS, Weng SL (2017) Study on nonlinear identification SOFC temperature model based on particle swarm optimization-least-squares support vector regression. J Electrochem Energy. https://doi.org/10.1115/1.4036805

    Google Scholar 

  16. Tang YG, Bu CN, Liu MM, Zhang LL, Lian QS (2018) Application of ELM-Hammerstein model to the identification of solid oxide fuel cells. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2453-y

    Article  Google Scholar 

  17. Yuan P, Liu SF (2020) Transient analysis of a solid oxide fuel cell unit with reforming and water-shift reaction and the building of neural network model for rapid prediction in electrical and thermal performance. Int J Hydrogen Energy. https://doi.org/10.1016/j.ijhydene.2019.10.165

    Article  Google Scholar 

  18. Peng JX, Huang J, Wu XL, Xu YW, Chen HC, Li X (2021) Solid oxide fuel cell (SOFC) performance evaluation, fault diagnosis and health control: a review. J Power Sources. https://doi.org/10.1016/j.jpowsour.2021.230058

    Article  Google Scholar 

  19. ** H, Sun J, Chen J (2007) Estimation of spatial temperature distribution in co-flow planar solid oxide fuel cells. Proc IMECE. https://doi.org/10.1115/IMECE2007-43397

  20. Vijay P, Tadé MO (2012) An adaptive non-linear observer for the estimation of temperature distribution in the planar solid oxide fuel cell. J Process Control. https://doi.org/10.1016/j.jprocont.2012.11.007

    Article  Google Scholar 

  21. Vijay P, Tadé MO, Ahmed K, Utikar R, Pareek V (2014) Simultaneous estimation of states and inputs in a planar solid oxide fuel cell using nonlinear adaptive observer design. J Power Sources. https://doi.org/10.1016/j.jpowsour.2013.10.050

    Article  Google Scholar 

  22. Luo H, Yin Q, Wu GP, Li X (2015) A nonlinear Luenberger observer for the estimation of temperature distribution in a planar solid oxide fuel cell. Proc IEEE/CAC. https://doi.org/10.1109/CAC.2015.7382690

    Article  Google Scholar 

  23. Wu XD, Jiang JH, Zhang HB, Deng ZH, Li X, Li J (2018) Inner temperature distribution estimation based on unscented Kalman filter algorithm for planar solid oxide fuel cell stack. Proc IEEE/CAC. https://doi.org/10.1109/CAC.2018.8623191

    Article  Google Scholar 

  24. Lin PH, Hong CW (2009) Cold start dynamics and temperature sliding observer design of an automotive SOFC APU. J Power Sources. https://doi.org/10.1016/j.jpowsour.2008.11.043

    Article  Google Scholar 

  25. Wu XJ, Yang DN, Wang JH, Li X (2019) Temperature gradient control of a solid oxide fuel cell stack. J Power Source. https://doi.org/10.1016/j.jpowsour.2018.12.058

    Article  Google Scholar 

  26. Murshed AM, Huang B, Nandakumar K (2010) Estimation and control of solid oxide fuel cell system. Comput Che Eng. https://doi.org/10.1016/j.compchemeng.2009.06.018

    Article  Google Scholar 

  27. Qi YX, Mayken EA, Marcus T, Li TS, Andersson M (2019) Dynamic modelling and controlling strategy of polymer electrolyte fuel cells. Int J Hydrogen Energy. https://doi.org/10.1016/j.ijhydene.2019.09.178

    Article  Google Scholar 

  28. Wu XJ, Wang JH, Hao JQ, Li X (2018) Control of a solid oxide fuel cell stack based on unmodeled dynamic compensations. Int J Hydrogen Energy. https://doi.org/10.1016/j.ijhydene.2018.10.018

    Article  Google Scholar 

  29. Ławry´nczuk M, (2020) Constrained computationally efficient nonlinear predictive control of solid oxide fuel cell: tuning, feasibility and performance. ISA Trans. https://doi.org/10.1016/j.isatra.2019.10.009

    Article  PubMed  Google Scholar 

  30. Zhang L, Shi SY, Jiang JH, Wang F, **e HT, Chen H, Fu XW, Li X (2018) An optimization and fast load-oriented control for current-based solid oxide fuel cell system. J Solid State Electrochem. https://doi.org/10.1007/s10008-018-3996-x

    Article  Google Scholar 

  31. Jiang JH, Li X, Deng ZH, Yang J, Zhang YS, Li J (2012) Thermal management of an independent steam reformer for a solid oxide fuel cell with constrained generalized predictive control. Int J Hydrogen Energy. https://doi.org/10.1016/j.ijhydene.2012.05.119

    Article  Google Scholar 

  32. Chen JW, Hu ZC, Zhang HS (2022) A novel control scheme to mitigate temperature profile variation in a SOFC system. Energy Rep. https://doi.org/10.1016/j.egyr.2022.08.185

    Article  Google Scholar 

  33. Belkhier Y, Shaw RN, Bures M, Islam MD, Bajaj M, Albalawi F, Alqurashi A, Ghoneim SSM (2022) Robust interconnection and dam** assignment energy-based control for a permanent magnet synchronous motor using high order sliding mode approach and nonlinear observer. Energy Rep. https://doi.org/10.1016/j.egyr.2021.12.07523

    Article  Google Scholar 

  34. Belkhier Y, Achour A, Shaw RN, Ullah N, Chowdhury MS, Techato K (2021) Fuzzy supervisory passivity-based high order-sliding mode control approach for tidal turbine-based permanent magnet synchronous generator conversion system. Actuators. https://doi.org/10.3390/act10050092

    Article  Google Scholar 

  35. Belkhier Y, Achour A, Ullah N, N. Ahaw R, Farooq Z, Ullah A, Alased AAN, (2021) Intelligent energy-based modified super twisting algorithm and factional order PID control for performance improvement of PMSG dedicated to tidal power system. IEEE Access. https://doi.org/10.1109/ACCESS.2021.3072332

    Article  Google Scholar 

  36. Fardadi M, Mueller F, Jabbari F (2010) Feedback control of solid oxide fuel cell spatial temperature variation. J Power Sources. https://doi.org/10.1016/j.jpowsour.2009.12.111

    Article  Google Scholar 

  37. Khan AH, Cao XW, Li S, Vasilios NK, Liao LF (2020) BAS-ADAM: an ADAM based approach to improve the performance of beetle antennae search optimizer. Proc IEEE/CAC. https://doi.org/10.1109/JAS.2020.1003048

    Article  Google Scholar 

  38. Zhang JH, Chen DU, Shen GH, Sun ZQ, **a YQ (2021) Disturbance observer based adaptive fuzzy sliding mode control: a dynamic sliding surface approach. Automatica. https://doi.org/10.1016/j.automatica.2021.109606

    Article  Google Scholar 

  39. Huang J, Cao Y, Wang YW (2022) Adaptive proxy-based sliding mode control for a class of second-order nonlinear systems and its application to pneumatic muscle actuators. ISA Trans. https://doi.org/10.1016/j.isatra.2020.09.009

    Article  PubMed  Google Scholar 

  40. Zhang L, Jiang JH, Cheng H, Deng ZH, Li X (2015) Control s strategy for power management, efficiency-optimization and operating-safety of a 5-kW solid oxide fuel cell system. Electrochim Acta. https://doi.org/10.1016/j.electacta.2015.02.045

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Development of a Hybrid Power System for Ocean Ship** Ships (CB03N20), the Horizontal project (D-8006-21-0116), and the Shanghai Pujiang Program (18PJ1404200).

Funding

Development of a Hybrid Power System for Ocean Ship** Ships, CB03N20, Fan Liyun, Horizontal project, D-8006-21-0116, Xu **gxiang, Shanghai Pujiang Program, 18PJ1404200, Xu **gxiang

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Authors and Affiliations

  1. College of Power and Energy Engineering, Harbin Engineering University, Harbin, China

    Kui Xu, Chongchong Shen, Chao Xu & Liyun Fan

  2. College of Engineering Science and Technology, Shanghai Ocean University, Shanghai, China

    Haibo Huo, **gxiang Xu, **nghong Kuang & Lixiang Cui

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Xu, K., Shen, C., Xu, C. et al. Modeling and control-oriented thermal characteristics under variable load of the solid oxide fuel cell. J Solid State Electrochem 27, 2083–2099 (2023). https://doi.org/10.1007/s10008-023-05477-y

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