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Modelica based modelling and control design of counter-flow SOFC system considering temperature distribution

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  • Xia, Lei
  • Wu, Jiafeng
  • Khosravi, Ali
  • Sun, Li

Abstract

In this study, a counter-flow methane reforming solid oxide fuel cell (MR-SOFC) system is proposed. Based on the response data of the system, a nonlinear least squares (NLS) identification method is used to identify the state space model, and a Kalman filter-based model prediction control (KF-MPC) is developed in SIMULINK. Finally, the co-simulation framework of Modelica/SIMULINK is developed to investigate the control performance of KF-MPC. The results show that the tracking accuracy and speed for the KF-MPC system are superior to those of proportional-integral-derivative (PID) in large-scale load changes and load fluctuations. The shortest settling time (tst) for net output power (Pnet) is 15s, which is only 24.19% of that of the PID in large-scale load changes. During load fluctuations, the maximum value of the root mean square error (RMSE) for Pnet in KF-MPC is 0.0372 kW, lower than that of PID (0.0948 kW) and only 39.23% of it. The tst in the KF-MPC system is 7s, much lower than the 285s in PID, at the step change of SOFC cathode inlet temperature (Tin). A large overshoot of Tin occurs in the PID system, and its RMSE (2.23 K) is higher than that (0.42 K) of the KF-MPC system. The maximum temperature gradient (max|ΔTPEN|) of the SOFC in the KF-MPC system is 19.94 K/cm, smaller than that of the PID. The temperature change rate of each node of the SOFC in the KF-MPC system is significantly smoother and the system operates more reliably during the control process.

Suggested Citation

  • Xia, Lei & Wu, Jiafeng & Khosravi, Ali & Sun, Li, 2025. "Modelica based modelling and control design of counter-flow SOFC system considering temperature distribution," Energy, Elsevier, vol. 331(C).
  • Handle: RePEc:eee:energy:v:331:y:2025:i:c:s0360544225026532
    DOI: 10.1016/j.energy.2025.137011
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    1. Fan, Liyuan & Li, Chao'en & van Biert, Lindert & Zhou, Shou-Han & Tabish, Asif Nadeem & Mokhov, Anatoli & Aravind, Purushothaman Vellayani & Cai, Weiwei, 2022. "Advances on methane reforming in solid oxide fuel cells," Renewable and Sustainable Energy Reviews, Elsevier, vol. 166(C).
    2. Shrestha, Anil & Mustafa, Andy Ali & Htike, Myo Myo & You, Vithyea & Kakinaka, Makoto, 2022. "Evolution of energy mix in emerging countries: Modern renewable energy, traditional renewable energy, and non-renewable energy," Renewable Energy, Elsevier, vol. 199(C), pages 419-432.
    3. Wang, Chen & Xia, Mengli & Wang, Piao & Xu, Junjie, 2022. "Renewable energy output, energy efficiency and cleaner energy: Evidence from non-parametric approach for emerging seven economies," Renewable Energy, Elsevier, vol. 198(C), pages 91-99.
    4. Wang, Zhiwen & Xiong, Wei & Ting, David S.-K. & Carriveau, Rupp & Wang, Zuwen, 2016. "Conventional and advanced exergy analyses of an underwater compressed air energy storage system," Applied Energy, Elsevier, vol. 180(C), pages 810-822.
    5. Kandepu, Rambabu & Imsland, Lars & Foss, Bjarne A. & Stiller, Christoph & Thorud, Bjørn & Bolland, Olav, 2007. "Modeling and control of a SOFC-GT-based autonomous power system," Energy, Elsevier, vol. 32(4), pages 406-417.
    6. Wang, Erlei & Xia, Jiangying & Li, Jia & Sun, Xianke & Li, Hao, 2022. "Parameters exploration of SOFC for dynamic simulation using adaptive chaotic grey wolf optimization algorithm," Energy, Elsevier, vol. 261(PA).
    7. Lu, Yisha & Hu, Yaozhong & Qiao, Yan & Yuan, Minjuan & Xu, Wei, 2024. "Sparse least squares via fractional function group fractional function penalty for the identification of nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Li, Bohan & Wang, Chaoyang & Liu, Ming & Fan, Jianlin & Yan, Junjie, 2023. "Transient performance analysis of a solid oxide fuel cell during power regulations with different control strategies based on a 3D dynamic model," Renewable Energy, Elsevier, vol. 218(C).
    9. Fardadi, Mahshid & McLarty, Dustin F. & Jabbari, Faryar, 2016. "Investigation of thermal control for different SOFC flow geometries," Applied Energy, Elsevier, vol. 178(C), pages 43-55.
    10. Zeng, Zezhi & Qian, Yuping & Zhang, Yangjun & Hao, Changkun & Dan, Dan & Zhuge, Weilin, 2020. "A review of heat transfer and thermal management methods for temperature gradient reduction in solid oxide fuel cell (SOFC) stacks," Applied Energy, Elsevier, vol. 280(C).
    11. Yang, Sheng & Liu, Yiran & Yu, Yingao & Liu, Zhiqiang & Deng, Chengwei & Xie, Nan, 2024. "Thermodynamic and parametric analyses of a zero-carbon emission SOFC-based CCHP system using LNG cold energy," Energy, Elsevier, vol. 307(C).
    12. Hajimolana, S.A. & Tonekabonimoghadam, S.M. & Hussain, M.A. & Chakrabarti, M.H. & Jayakumar, N.S. & Hashim, M.A., 2013. "Thermal stress management of a solid oxide fuel cell using neural network predictive control," Energy, Elsevier, vol. 62(C), pages 320-329.
    13. Orlando Corigliano & Leonardo Pagnotta & Petronilla Fragiacomo, 2022. "On the Technology of Solid Oxide Fuel Cell (SOFC) Energy Systems for Stationary Power Generation: A Review," Sustainability, MDPI, vol. 14(22), pages 1-73, November.
    14. Chen, Jinwei & Hu, Zhenchao & Lu, Jinzhi & Zhang, Huisheng & Weng, Shilie, 2022. "A novel control strategy with an anode variable geometry ejector for a SOFC-GT hybrid system," Energy, Elsevier, vol. 261(PA).
    15. Guk, Erdogan & Venkatesan, Vijay & Babar, Shumaila & Jackson, Lisa & Kim, Jung-Sik, 2019. "Parameters and their impacts on the temperature distribution and thermal gradient of solid oxide fuel cell," Applied Energy, Elsevier, vol. 241(C), pages 164-173.
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