{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:35:50Z","timestamp":1765546550426,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T00:00:00Z","timestamp":1583107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["TBI-V-1-256-VBW-090"],"award-info":[{"award-number":["TBI-V-1-256-VBW-090"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>High-temperature fuel cells are one of the devices currently investigated for an integration into distributed power supply grids. Such distributed grids aim at the simultaneous production of thermal energy and electricity. To maximize the efficiency of fuel cell systems, it is reasonable to track the point of maximum electric power production and to operate the system in close vicinity to this point. However, variations of gas mass flows, especially the concentration of hydrogen contained in the anode gas, as well as variations of the internal temperature distribution in the fuel cell stack module lead to the fact that the maximum power point changes in dependence of the aforementioned phenomena. Therefore, this paper first proposes a real-time capable stochastic filter approach for the local identification of the electric power characteristic of the fuel cell. Second, based on this estimate, a maximum power point tracking procedure is derived. It is based on an iteration procedure under consideration of the estimation accuracy of the stochastic filter and adjusts the fuel cell\u2019s electric current so that optimal operating points are guaranteed. Numerical simulations, based on real measured data gathered at a test rig available at the Chair of Mechatronics at the University of Rostock, Germany, conclude this paper.<\/jats:p>","DOI":"10.3390\/a13030058","type":"journal-article","created":{"date-parts":[[2020,3,3]],"date-time":"2020-03-03T13:06:23Z","timestamp":1583240783000},"page":"58","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Kalman Filter-Based Online Identification of the Electric Power Characteristic of Solid Oxide Fuel Cells Aiming at Maximum Power Point Tracking"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1548-6547","authenticated-orcid":false,"given":"Andreas","family":"Rauh","sequence":"first","affiliation":[{"name":"Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8030-6963","authenticated-orcid":false,"given":"Wiebke","family":"Frenkel","sequence":"additional","affiliation":[{"name":"Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1160-8623","authenticated-orcid":false,"given":"Julia","family":"Kersten","sequence":"additional","affiliation":[{"name":"Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Huang, B., Qi, Y., and Murshed, A.K.M.M. (2013). Dynamic Modeling and Predictive Control in Solid Oxide Fuel Cells: First Principle and Data-based Approaches, John Wiley & Sons.","DOI":"10.1002\/9781118501054"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1016\/j.jprocont.2011.06.017","article-title":"Solid Oxide Fuel Cell: Perspective of Dynamic Modeling and Control","volume":"21","author":"Huang","year":"2011","journal-title":"J. Process Contr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.jpowsour.2005.09.010","article-title":"Control Strategy for a Solid Oxide Fuel Cell and Gas Turbine Hybrid System","volume":"158","author":"Stiller","year":"2006","journal-title":"J. Power Sourc."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dicks, A.L., and Rand, D.A.J. (2018). Fuel Cell Systems Explained, John Wiley & Sons.","DOI":"10.1002\/9781118706992"},{"key":"ref_5","unstructured":"Singhal, S.C., and Mizusaki, J. (2005). Non-Isothermal and Dynamic SOFC Voltage-Current Behavior. Solid Oxide Fuel Cells IX (SOFC-IX): Volume 1\u2014Cells, Stacks, and Systems, The Electrochemical Society."},{"key":"ref_6","unstructured":"(2020, March 02). PEM Fuel Cell. Available online: www.psenterprise.com\/sectors\/fuelcell."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pukrushpan, J., Stefanopoulou, A., and Peng, H. (2005). Control of Fuel Cell Power Systems: Principles, Modeling, Analysis and Feedback Design, Springer.","DOI":"10.1007\/978-1-4471-3792-4"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bove, R., and Ubertini, S. (2008). Modeling Solid Oxide Fuel Cells, Springer.","DOI":"10.1007\/978-1-4020-6995-6"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1093\/imamci\/dnu051","article-title":"Reliable Control of High-Temperature Fuel Cell Systems using Interval-Based Sliding Mode Techniques","volume":"33","author":"Rauh","year":"2016","journal-title":"IMA J. Math. Contr. Inform."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5208","DOI":"10.1109\/TIE.2015.2404811","article-title":"Interval-Based Sliding Mode Control Design for Solid Oxide Fuel Cells with State and Actuator Constraints","volume":"62","author":"Rauh","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","unstructured":"Rauh, A., Senkel, L., and Aschemann, H. (2015, January 24\u201326). Reliable Sliding Mode Approaches for the Temperature Control of Solid Oxide Fuel Cells with Input and Input Rate Constraints. Proceedings of the 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON 2015, St. Petersburg, Russia."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s11786-014-0205-x","article-title":"Interval Methods for the Implementation of Real-Time Capable Robust Controllers for Solid Oxide Fuel Cell Systems","volume":"8","author":"Rauh","year":"2014","journal-title":"Math. Comput. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Rauh, A., and Senkel, L. (2016). Interval Methods for Robust Sliding Mode Control Synthesis of High-Temperature Fuel Cells with State and Input Constraints. Variable-Structure Approaches: Analysis, Simulation, Robust Control and Estimation of Uncertain Dynamic Processes, Springer.","DOI":"10.1007\/978-3-319-31539-3_3"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"57","DOI":"10.3182\/20120620-3-DK-2025.00071","article-title":"Sensitivity-Based State and Parameter Estimation for Fuel Cell Systems","volume":"45","author":"Rauh","year":"2012","journal-title":"IFAC Proceedings Volumes"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Senkel, L., Rauh, A., and Aschemann, H. (2013, January 26\u201329). Experimental Validation of a Sensitivity-Based Observer for Solid Oxide Fuel Cell Systems. Proceedings of the 18th International Conference on Methods & Models in Automation & Robotics (MMAR), Mi\u0119dzyzdroje, Poland.","DOI":"10.1109\/MMAR.2013.6669897"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kunusch, C., Puleston, P., and Mayosky, M. (2012). Sliding-Mode Control of PEM Fuel Cells, Springer.","DOI":"10.1007\/978-1-4471-2431-3"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Frenkel, W., Rauh, A., Kersten, J., and Aschemann, H. (2020). Experiments-Based Comparison of Different Power Controllers for a Solid Oxide Fuel Cell Against Model Imperfections and Delay Phenomena. Algorithms, in press.","DOI":"10.3390\/a13040076"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1109\/TSTE.2017.2764266","article-title":"Framework of Maximum Power Extraction From Solar PV Panel Using Self Predictive Perturb and Observe Algorithm","volume":"9","author":"Kumar","year":"2018","journal-title":"IEEE Trans. Sustain. Energ."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, C., Chen, Y., Zhou, D., Liu, J., and Zeng, J. (2016). A High-Performance Adaptive Incremental Conductance MPPT Algorithm for Photovoltaic Systems. Energies, 9.","DOI":"10.3390\/en9040288"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2858","DOI":"10.1016\/j.corsci.2005.07.002","article-title":"A Hundred Years of Tafel\u2019s Equation: 1905\u20132005","volume":"47","author":"Burstein","year":"2005","journal-title":"Corrosion Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1515\/zpch-1905-5043","article-title":"\u00dcber die Polarisation bei kathodischer Wasserstoffentwicklung","volume":"50","author":"Tafel","year":"1905","journal-title":"Zeitschrift f\u00fcr physikalische Chemie"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Frenkel, W., Rauh, A., Kersten, J., and Aschemann, H. (2019, January 26\u201329). Optimization Techniques for the Design of Identification Procedures for the Electro-Chemical Dynamics of High-Temperature Fuel Cells. Proceedings of the 24th IEEE Intl. Conference on Methods and Models in Automation and Robotics (MMAR), Mi\u0119dzyzdroje, Poland.","DOI":"10.1109\/MMAR.2019.8864685"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Isermann, R., and M\u00fcnchhof, M. (2011). Identification of Dynamic Systems: An Introduction with Applications, Springer.","DOI":"10.1007\/978-3-540-78879-9"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A New Approach to Linear Filtering and Prediction Problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_25","unstructured":"Stengel, R. (1994). Optimal Control and Estimation, Dover Publications."},{"key":"ref_26","unstructured":"Anderson, B., and Moore, J. (2005). Optimal Filtering, Dover Publications."},{"key":"ref_27","unstructured":"Nocedal, J., and Wright, S. (2006). Numerical Optimization, Springer."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/3\/58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:03:23Z","timestamp":1760173403000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/3\/58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,2]]},"references-count":27,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["a13030058"],"URL":"https:\/\/doi.org\/10.3390\/a13030058","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2020,3,2]]}}}