{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T12:26:44Z","timestamp":1782736004507,"version":"3.54.5"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T00:00:00Z","timestamp":1521763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Basic Research Program (973 Program)","award":["2015CB251505"],"award-info":[{"award-number":["2015CB251505"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In recent years, coal-fired power plants contribute the biggest part of power generation in China. Challenges of energy conservation and emission reduction of the coal-fired power plant encountering with a rapid growth due to the rising proportion of renewable energy generation in total power generation. Energy saving power generation dispatch (ESPGD) based on power units sorting technology is a promising approach to meet the challenge. Therefore, it is crucial to establish a reasonable and feasible multi-index comprehensive evaluation (MICE) framework for assessing the performance of coal-fired power units accessed by the power grid. In this paper, a hierarchical multiple criteria evaluation system was established. Except for the typical economic and environmental indices, the evaluation system considering operational flexibility and power quality indices either. A hybrid comprehensive evaluation model was proposed to assess the unit operational performance. The model is an integration of grey relational analysis (GRA) with analytic hierarchy process (AHP) and a novel entropy-based method (abbreviate as BECC) which integrates bootstrap method and correlation coefficient (CC) into entropy principle to get the objective weight of indices. Then a case study on seven typical 600 megawatts coal-fired power units was carried out to illustrate the proposed evaluation model, and a weight sensitivity analysis was developed in addition. The results of the case study shows that unit 4 has the power generating priority over the rest ones, and unit 2 ranks last, with the lowest grey relational degree. The weight sensitivity analysis shows that the environmental factor has the biggest sensitivity coefficient. And the validation analysis of the developed BECC weight method shows that it is feasible for the MICE model, and it is stable with an ignorable uncertainty caused by the stochastic factor in the bootstrapping process. The elaborate analysis of the result reveals that it is feasible to rank power units with the proposed evaluation model. Furthermore, it is beneficial to synthesize the updated multiple criteria in optimizing the power generating priority of coal-fired power units.<\/jats:p>","DOI":"10.3390\/e20040215","type":"journal-article","created":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T08:34:53Z","timestamp":1521794093000},"page":"215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Comprehensive Evaluation of Coal-Fired Power Units Using Grey Relational Analysis and a Hybrid Entropy-Based Weighting Method"],"prefix":"10.3390","volume":"20","author":[{"given":"Dianfa","family":"Wu","sequence":"first","affiliation":[{"name":"National Research Center for Thermal Power Engineering and Technology, North China Electric Power University, Changping District, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ningling","family":"Wang","sequence":"additional","affiliation":[{"name":"National Research Center for Thermal Power Engineering and Technology, North China Electric Power University, Changping District, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiping","family":"Yang","sequence":"additional","affiliation":[{"name":"National Research Center for Thermal Power Engineering and Technology, North China Electric Power University, Changping District, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8535-5016","authenticated-orcid":false,"given":"Chengzhou","family":"Li","sequence":"additional","affiliation":[{"name":"National Research Center for Thermal Power Engineering and Technology, North China Electric Power University, Changping District, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongping","family":"Yang","sequence":"additional","affiliation":[{"name":"National Research Center for Thermal Power Engineering and Technology, North China Electric Power University, Changping District, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"ref_1","unstructured":"Council, C.E. (2017). Annual Development Report of China Electric Power Industry 2011, China Market Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.rser.2015.10.052","article-title":"Overall review of peak shaving for coal-fired power units in China","volume":"54","author":"Gu","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.enconman.2016.10.054","article-title":"Performance degradation diagnosis of thermal power plants: A method based on advanced exergy analysis","volume":"130","author":"Fu","year":"2016","journal-title":"Energy Convers. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1016\/j.enpol.2011.01.054","article-title":"Comprehensive evaluation of coal-fired power plants based on grey relational analysis and analytic hierarchy process","volume":"39","author":"Gang","year":"2011","journal-title":"Energy Policy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.enpol.2012.12.018","article-title":"Promoting energy-saving and environmentally friendly generation dispatching model in China: Phase development and case studies","volume":"57","author":"Ding","year":"2013","journal-title":"Energy Policy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1016\/j.rser.2014.11.037","article-title":"Energy-saving power generation dispatching in China: Regulations, pilot projects and policy recommendations\u2014A review","volume":"43","author":"Dong","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7346","DOI":"10.1016\/j.enpol.2010.08.011","article-title":"Evolution of China\u2019s power dispatch principle and the new energy saving power dispatch policy","volume":"38","author":"Gao","year":"2010","journal-title":"Energy Policy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.enpol.2015.03.016","article-title":"Energy-saving generation dispatch toward a sustainable electric power industry in China","volume":"83","author":"Zhong","year":"2015","journal-title":"Energy Policy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1016\/j.energy.2013.10.044","article-title":"A hybrid method of incorporating extended priority list into equal incremental principle for energy-saving generation dispatch of thermal power systems","volume":"64","author":"Cheng","year":"2014","journal-title":"Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.apenergy.2015.04.063","article-title":"Increasing thermal plant flexibility in a high renewables power system","volume":"154","author":"Kubik","year":"2015","journal-title":"Appl. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gonzalez-Salazar, M.A., Kirsten, T., and Prchlik, L. (2017). Review of the operational flexibility and emissions of gas- and coal-fired power plants in a future with growing renewables. Renew. Sustain. Energy Rev.","DOI":"10.1016\/j.rser.2017.05.278"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.ejor.2009.01.021","article-title":"PROMETHEE: A comprehensive literature review on methodologies and applications","volume":"200","author":"Behzadiana","year":"2010","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","first-page":"133","article-title":"Electre Methods","volume":"78","author":"Figueira","year":"2005","journal-title":"International"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.energy.2012.03.010","article-title":"An STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermal power plant location: A case study from India","volume":"42","author":"Choudhary","year":"2012","journal-title":"Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"642","DOI":"10.3390\/en10050642","article-title":"Determination of the Most Suitable Technology Transfer Strategy for Wind Turbines Using an Integrated AHP-TOPSIS Decision Model","volume":"10","author":"Dinmohammadi","year":"2017","journal-title":"Energies"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.trd.2017.03.001","article-title":"The application of the AHP-TOPSIS for evaluating ballast water treatment systems by ship operators","volume":"52","author":"Karahalios","year":"2017","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_17","first-page":"191","article-title":"Introduction grey system theory","volume":"1","author":"Deng","year":"1989","journal-title":"J. Grey Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"396","DOI":"10.3390\/e19080396","article-title":"A Fuzzy comprehensive evaluation method based on AHP and Entropy for landslide susceptibility map","volume":"19","author":"Zhao","year":"2017","journal-title":"Entropy"},{"key":"ref_19","first-page":"19","article-title":"How to Make a Decision: The Analytic Hierarchy Process","volume":"24","author":"Saaty","year":"1994","journal-title":"Eur. J. Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"404","DOI":"10.3390\/e18110404","article-title":"Decision-Making Model under Risk Assessment Based on Entropy","volume":"18","author":"Dong","year":"2016","journal-title":"Entropy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"53","DOI":"10.3390\/e12010053","article-title":"Imprecise Shannon\u2019s Entropy and Multi Attribute Decision Making","volume":"12","author":"Lotfi","year":"2010","journal-title":"Entropy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3017","DOI":"10.3390\/en6063017","article-title":"A Combined Fuzzy-AHP and Fuzzy-GRA Methodology for Hydrogen Energy Storage Method Selection in Turkey","volume":"6","author":"Gumus","year":"2013","journal-title":"Energies"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"697","DOI":"10.3390\/en9090697","article-title":"An Integrated Decision-Making Model for Transformer Condition Assessment Using Game Theory and Modified Evidence Combination Extended by D Numbers","volume":"9","author":"Sun","year":"2016","journal-title":"Energies"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.3390\/en4112002","article-title":"An Integrated Multi-Criteria Decision Making Model for Evaluating Wind Farm Performance","volume":"4","author":"Kang","year":"2011","journal-title":"Energies"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.3390\/en5041271","article-title":"An Integrated Performance Evaluation Model for the Photovoltaics Industry","volume":"5","author":"Lee","year":"2012","journal-title":"Energies"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"447","DOI":"10.3390\/en10040447","article-title":"Hybridising Human Judgment, AHP, Grey Theory, and Fuzzy Expert Systems for Candidate Well Selection in Fractured Reservoirs","volume":"10","author":"Zeng","year":"2017","journal-title":"Energies"},{"key":"ref_27","first-page":"404","article-title":"Comprehensive energy-saving evaluation of thermal power plants based on TOPSIS gray relational projection and the weight sensitivity analysis","volume":"35","author":"Guili","year":"2015","journal-title":"J. Chin. Soc. Power Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"270","DOI":"10.3390\/en9040270","article-title":"Optimal Siting of Charging Stations for Electric Vehicles Based on Fuzzy Delphi and Hybrid Multi-Criteria Decision Making Approaches from an Extended Sustainability Perspective","volume":"9","author":"Zhao","year":"2016","journal-title":"Energies"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S0377-2217(96)00049-5","article-title":"A probabilistic interpretation of the final rankings in AHP","volume":"96","author":"Rosenbloom","year":"1997","journal-title":"Eur. J. Oper. Res."},{"key":"ref_30","first-page":"14336","article-title":"Review of the main developments in the analytic hierarchy process","volume":"38","author":"Ishizaka","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1080\/03081070600687668","article-title":"Information entropy, rough entropy and knowledge granulation in incomplete information systems","volume":"35","author":"Liang","year":"2006","journal-title":"Int J. Gen. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1016\/j.apm.2009.09.022","article-title":"Weight determination for consistently ranking alternatives in multiple criteria decision analysis","volume":"34","author":"Kao","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1016\/0305-0548(94)00059-H","article-title":"Determining objective weights in multiple criteria problems: The critic method","volume":"22","author":"Diakoulaki","year":"1995","journal-title":"Comput. Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.mcm.2009.07.016","article-title":"Integration of correlations with standard deviations for determining attribute weights in multiple attribute decision making","volume":"51","author":"Wang","year":"2010","journal-title":"Math. Comput. Model."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"8445","DOI":"10.1016\/j.eswa.2010.05.034","article-title":"Effective weighting model based on the maximum deviation with uncertain information","volume":"37","author":"Lo","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.envsoft.2013.09.031","article-title":"A comprehensive evaluation of various sensitivity analysis methods: A case study with a hydrological model","volume":"51","author":"Gan","year":"2014","journal-title":"Environ. Model. Softw."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife, Springer.","DOI":"10.1214\/aos\/1176344552"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.chemolab.2012.10.007","article-title":"Bootstrap based confidence limits in principal component analysis\u2014A case study","volume":"120","author":"Babamoradi","year":"2013","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.stamet.2013.08.003","article-title":"Bootstrap\u2014An exploration","volume":"20","author":"Datta","year":"2014","journal-title":"Stat. Methodol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/4\/215\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:58:11Z","timestamp":1760194691000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/4\/215"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,23]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["e20040215"],"URL":"https:\/\/doi.org\/10.3390\/e20040215","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,23]]}}}