{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T12:32:50Z","timestamp":1770726770464,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T00:00:00Z","timestamp":1770595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U24A20156"],"award-info":[{"award-number":["U24A20156"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Renewable intermittency forces electrolytic hydrogen systems to operate across multiple states, lowering efficiency. We design a thermodynamic cycle that recovers electrolysis waste heat and integrates it with an alkaline electrolyser. A detailed thermodynamic model of the hydrogen system and the heat-recovery loop is developed, and design and operating parameters are optimized to maximize overall exergy efficiency. To improve economic viability, heat-exchanger structural parameters are co-optimized. We further propose an optimal scheduling method for the heat-recovery system under fluctuating renewable supply. The method employs an interactive optimisation framework cantered on the temperature\u2013efficiency curve of alkaline electrolyser cells, jointly optimizing electrolyser current and working-fluid mass flow to enhance economic performance. A case study using real wind-farm data from Qinghai demonstrates that the proposed system with heat recovery significantly improves performance, increasing hydrogen production by up to 9% under wind scarcity compared to that of the system without heat recovery. These results confirm the practical viability of renewable-driven hydrogen production.<\/jats:p>","DOI":"10.3390\/e28020194","type":"journal-article","created":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T16:13:32Z","timestamp":1770653612000},"page":"194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Interactive Optimal Scheduling Method for Hydrogen Production System with Heat Recovery"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-8276-2858","authenticated-orcid":false,"given":"Shengchen","family":"Li","sequence":"first","affiliation":[{"name":"Qinghai Key Lab of Efficient Utilization of Clean Energy, School of Energy and Electrical Engineering, University of Qinghai, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenbin","family":"Wu","sequence":"additional","affiliation":[{"name":"Engineer School, Qinghai Institute of Technology, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenhang","family":"Wu","sequence":"additional","affiliation":[{"name":"Hubei Energy Group Ezhou Power Generation Co., Ltd., Ezhou 436032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linrui","family":"Ma","sequence":"additional","affiliation":[{"name":"Qinghai Key Lab of Efficient Utilization of Clean Energy, School of Energy and Electrical Engineering, University of Qinghai, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3429-3190","authenticated-orcid":false,"given":"Yang","family":"Si","sequence":"additional","affiliation":[{"name":"Qinghai Key Lab of Efficient Utilization of Clean Energy, School of Energy and Electrical Engineering, University of Qinghai, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,9]]},"reference":[{"key":"ref_1","unstructured":"IEA (2022). World Energy Outlook 2022, IEA."},{"key":"ref_2","first-page":"567","article-title":"Comprehensive review and prospect of the modeling of alkaline water electrolysis system for hydrogen production","volume":"44","author":"Li","year":"2022","journal-title":"Automot. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"118987","DOI":"10.1016\/j.apenergy.2022.118987","article-title":"A multiphysics model of the compactly-assembled industrial alkaline water electrolysis cell","volume":"314","author":"Huang","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mart\u00ednez-Rodr\u00edguez, A., and Ab\u00e1nades, A. (2020). Comparative analysis of energy and exergy performance of hydrogen production methods. Entropy, 22.","DOI":"10.3390\/e22111286"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"106489","DOI":"10.1016\/j.ijepes.2020.106489","article-title":"Optimal dispatching of power grid integrating wind-hydrogen systems","volume":"125","author":"Wei","year":"2021","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"120145","DOI":"10.1016\/j.apenergy.2022.120145","article-title":"A review of solid oxide steam-electrolysis cell systems: Thermodynamics and thermal integration","volume":"328","author":"Min","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yoo, Y., Lee, S.-Y., Seo, S.-H., Oh, S.-D., and Kwak, H.-Y. (2024). Energy, exergetic, and thermoeconomic analyses of hydrogen-fueled 1-kW proton-exchange membrane fuel cell. Entropy, 26.","DOI":"10.20944\/preprints202405.1080.v1"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27079","DOI":"10.1016\/j.ijhydene.2023.03.247","article-title":"Electrochemical performance study of proton exchange membrane electrolyser considering the effect of bubble coverage","volume":"48","author":"Xin","year":"2023","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.egyr.2023.04.208","article-title":"Low-carbon planning for park-level integrated energy system considering optimal construction time sequence and hydrogen energy facility","volume":"9","author":"Liu","year":"2023","journal-title":"Energy Rep."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1016\/j.egyr.2023.04.120","article-title":"An integrated demand response dispatch strategy for low-carbon energy supply park considering electricity\u2013hydrogen\u2013carbon coordination","volume":"9","author":"Bu","year":"2023","journal-title":"Energy Rep."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"87118","DOI":"10.1109\/ACCESS.2019.2924577","article-title":"Research on wind power accommodation for an electricity-heat-gas integrated microgrid system with power-to-gas","volume":"7","author":"Jiang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","first-page":"48","article-title":"Capacity configuration and optimal scheduling of a wind-photovoltaic-hydrogen-thermal virtual power plant based on a wide range power adaptation strategy for an alkaline electrolyser","volume":"50","author":"Liu","year":"2022","journal-title":"Power Syst. Prot. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.ijhydene.2024.05.264","article-title":"Computational predictions of hydrogen-assisted fatigue crack growth","volume":"72","author":"Cui","year":"2024","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"120413","DOI":"10.1016\/j.apenergy.2022.120413","article-title":"Exploration of the configuration and operation rule of the multi-electrolyzers hybrid system of large-scale alkaline water hydrogen production system","volume":"331","author":"Li","year":"2023","journal-title":"Appl. Energy"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ma, B., Zheng, J., Xian, Z., Wang, B., and Ma, H. (2024). Optimal operation strategy for wind\u2013photovoltaic power-based hydrogen production systems considering electrolyzer start-up characteristics. Processes, 12.","DOI":"10.3390\/pr12081756"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1016\/j.ijhydene.2020.10.019","article-title":"Multi-state techno-economic model for optimal dispatch of grid-connected hydrogen electrolysis systems operating under dynamic conditions","volume":"46","author":"Matute","year":"2021","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"9303","DOI":"10.1016\/j.ijhydene.2020.12.111","article-title":"Modeling alkaline water electrolysis for power-to-x applications: A scheduling approach","volume":"46","author":"Varela","year":"2021","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2662","DOI":"10.1109\/TSTE.2020.2970078","article-title":"Optimal planning for electricity-hydrogen integrated energy system considering power to hydrogen and heat and seasonal storage","volume":"11","author":"Pan","year":"2020","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"118091","DOI":"10.1016\/j.apenergy.2021.118091","article-title":"Optimal day-ahead dispatch of an alkaline electrolyser system concerning thermal\u2013electric properties and state-transitional dynamics","volume":"307","author":"Zheng","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"31108","DOI":"10.1016\/j.ijhydene.2021.07.016","article-title":"Valorisation of the waste heat given off in a system alkaline electrolyser\u2013photovoltaic array to improve hydrogen production performance: Case study Antofagasta, Chile","volume":"46","year":"2021","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"115697","DOI":"10.1016\/j.enconman.2022.115697","article-title":"Economic model predictive control for multi-energy system considering hydrogen-thermal-electric dynamics and waste heat recovery of MW-level alkaline electrolyser","volume":"265","author":"Huang","year":"2022","journal-title":"Energy Convers. Manag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"117622","DOI":"10.1016\/j.enconman.2023.117622","article-title":"Off-grid wind\/hydrogen systems with multi-electrolyzers: Optimized operational strategies","volume":"295","author":"Zheng","year":"2023","journal-title":"Energy Convers. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"56","DOI":"10.3390\/en16176132","article-title":"Operation Optimization of Wind\/Battery Storage\/Alkaline Electrolyzer System Considering Dynamic Hydrogen Production Efficiency","volume":"16","author":"Niu","year":"2023","journal-title":"Energies"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"86","DOI":"10.5293\/IJFMS.2017.10.1.086","article-title":"Numerical simulation on the performance of axial vane type gas-liquid separator with different guide vane structure","volume":"10","author":"Fan","year":"2017","journal-title":"Int. J. Fluid Mach. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4328","DOI":"10.1016\/j.ijhydene.2021.11.126","article-title":"Dynamic energy and mass balance model for an industrial alkaline water electrolyser plant process","volume":"47","author":"Sakas","year":"2022","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"230106","DOI":"10.1016\/j.jpowsour.2021.230106","article-title":"Numerical modeling and analysis of the temperature effect on the performance of an alkaline water electrolysis system","volume":"506","author":"Jang","year":"2021","journal-title":"J. Power Sources"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.jpowsour.2014.06.138","article-title":"Modeling an alkaline electrolysis cell through reduced-order and loss-estimate approaches","volume":"269","author":"Milewski","year":"2014","journal-title":"J. Power Sources"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.applthermaleng.2013.07.001","article-title":"Three-dimensional unsteady CFD simulations of a thermal storage tank performance for optimum design","volume":"60","author":"Ghorab","year":"2013","journal-title":"Appl. Therm. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"A216","DOI":"10.1149\/1.2137652","article-title":"Thermal-electrochemical modeling of a proton exchange membrane fuel cell","volume":"153","author":"Hwang","year":"2006","journal-title":"J. Electrochem. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Si, Y., Chen, L.J., Ma, L.R., Gao, M.Y., Ma, H.R., and Mei, S.W. (2021). Modeling the heat-hydrogen balance characteristic of hydrogen energy storage and cooperative dispatch of wind-hydrogen hybrid system. Front. Energy Res., 9.","DOI":"10.3389\/fenrg.2021.791829"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7338","DOI":"10.1016\/j.ijhydene.2008.09.051","article-title":"Thermal performance of a commercial alkaline water electrolyser: Experimental study and mathematical modeling","volume":"33","author":"Sanchis","year":"2008","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Shah, R.K., and Sekuli\u0107, D.P. (2003). Fundamentals of Heat Exchanger Design, John Wiley & Sons.","DOI":"10.1002\/9780470172605"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.enconman.2014.03.066","article-title":"Optimum configuration of shell-and-tube heat exchangers for the use in low-temperature organic Rankine cycles","volume":"83","author":"Walraven","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.matpr.2022.09.373","article-title":"Study on performance of working model of heat exchangers","volume":"80","author":"Singh","year":"2023","journal-title":"Mater. Today Proc."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"116399","DOI":"10.1016\/j.enconman.2022.116399","article-title":"Energy management strategy for a biogas plant in Anhui, China based on waste heat recovery and thermoeconomic analysis","volume":"273","author":"Lu","year":"2022","journal-title":"Energy Convers. Manag."},{"key":"ref_36","first-page":"60","article-title":"Thermoeconomic analysis of a gas turbine and cascaded CO2 combined cycle using thermal oil as an intermediate heat-transfer fluid","volume":"161","author":"Cao","year":"2018","journal-title":"Energy"},{"key":"ref_37","unstructured":"Turton, R., Bailie, R.C., Whiting, W.B., Shaeiwitz, J.A., and Bhattacharyya, D. (2012). Analysis, Synthesis, and Design of Chemical Processes, Prentice Hall. [4th ed.]."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"120765","DOI":"10.1016\/j.energy.2021.120765","article-title":"Low carbon district heating in China in 2025\u2014A district heating mode with low-grade waste heat as heat source","volume":"230","author":"Fu","year":"2021","journal-title":"Energy"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/2\/194\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T16:16:13Z","timestamp":1770653773000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/2\/194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,9]]},"references-count":38,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["e28020194"],"URL":"https:\/\/doi.org\/10.3390\/e28020194","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,9]]}}}