{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T03:08:15Z","timestamp":1784171295892,"version":"3.55.0"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,9,25]],"date-time":"2015-09-25T00:00:00Z","timestamp":1443139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the smart grid, large consumers can procure electricity energy from various power sources to meet their load demands. To maximize its profit, each large consumer needs to decide their energy procurement strategy under risks such as price fluctuations from the spot market and power quality issues. In this paper, an electric energy procurement decision-making model is studied for large consumers who can obtain their electric energy from the spot market, generation companies under bilateral contracts, the options market and self-production facilities in the smart grid. Considering the effect of unqualified electric energy, the profit model of large consumers is formulated. In order to measure the risks from the price fluctuations and power quality, the expected utility and entropy is employed. Consequently, the expected utility and entropy decision-making model is presented, which helps large consumers to minimize their expected profit of electricity procurement while properly limiting the volatility of this cost. Finally, a case study verifies the feasibility and effectiveness of the proposed model.<\/jats:p>","DOI":"10.3390\/e17106560","type":"journal-article","created":{"date-parts":[[2015,9,28]],"date-time":"2015-09-28T03:02:55Z","timestamp":1443409375000},"page":"6560-6575","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Expected Utility and Entropy-Based Decision-Making Model for Large Consumers in the Smart Grid"],"prefix":"10.3390","volume":"17","author":[{"given":"Bingtuan","family":"Gao","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Southeast University, Nanjing 210096, China"},{"name":"Jiangsu Key Laboratory of Smart Grid Technology and Equipment, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingjun","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Posts and Telecommunications, No. 9, Wenyuan Road, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"161","DOI":"10.14257\/ijca.2015.8.6.16","article-title":"Comparative Analysis of the Impacts on Operating Income of Power Grid Corporation after Implementing Straight-powered or Self-generation","volume":"8","author":"Zhao","year":"2015","journal-title":"Int. J. Control Autom."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1109\/TPWRS.2003.821474","article-title":"Bidding Strategies for Electricity Producers in a Competitive Electricity Marketplace","volume":"19","author":"Gountis","year":"2004","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0142-0615(00)00032-6","article-title":"Optimal Bidding Strategies for Competitive Generators and Large Consumers","volume":"23","author":"Wen","year":"2001","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1109\/TPWRS.2011.2112382","article-title":"Offering Strategies and Simulation of Multi-item Iterative Auctions of Energy Contracts","volume":"26","author":"Barroso","year":"2011","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1109\/TPWRS.2012.2212727","article-title":"Application of Information-Gap Decision Theory to Risk-Constrained Self-scheduling of GenCos","volume":"28","author":"Zareipour","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2105","DOI":"10.1109\/TPWRS.2007.907397","article-title":"Forward Contracting and Selling Price Determination for a Retailer","volume":"22","author":"Conejo","year":"2007","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.epsr.2008.06.003","article-title":"Optimal Selling Price and Energy Procurement Strategies for a Retailer in an Electricity Market","volume":"79","author":"Hatami","year":"2009","journal-title":"Electr. Power Syst. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.ijepes.2012.08.068","article-title":"Optimal Strategy Planning for a Retailer Considering Medium and Short-Term Decisions","volume":"45","author":"Nazari","year":"2013","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jiang, L., and Low, S. (2011, January 12\u201315). Multi-period Optimal Energy Procurement and Demand Response in Smart Grid with Uncertain Supply. Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, USA.","DOI":"10.1109\/CDC.2011.6161320"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1109\/TSG.2010.2078843","article-title":"Real-Time Demand Response Model","volume":"1","author":"Conejo","year":"2010","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1109\/TSG.2010.2055903","article-title":"Optimal Residential Load Control with Price Prediction in Real-Time Electricity Pricing Environments","volume":"1","year":"2010","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1049\/ip-gtd:20041252","article-title":"Energy Procurement for Large Consumers in Electricity Markets","volume":"152","author":"Conejo","year":"2005","journal-title":"IEE Proc. Gener. Transm. Distrib."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1049\/ip-gtd:20050466","article-title":"Risk-Constrained Electricity Procurement for a Large Consumer","volume":"153","author":"Conejo","year":"2006","journal-title":"IEE Proc. Gener. Transm. Distrib."},{"key":"ref_14","unstructured":"Yan, H., and Yan, H. (2000, January 23\u201327). Optimal Energy Purchases in Deregulated California Energy Markets. Proceedings of the 2000 IEEE Conference on Power Engineering Society Winter Meeting, Singapore, Singapore."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1109\/TPWRS.2006.879272","article-title":"Power Portfolio Optimization in Deregulated Electricity Markets with Risk Management","volume":"21","author":"Xu","year":"2006","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1109\/TPWRS.2007.895164","article-title":"A Stochastic Programming Approach to Electric Energy Procurement for Large Consumers","volume":"22","author":"Philpott","year":"2007","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.epsr.2009.08.006","article-title":"Multi-market Energy Procurement for a Large Consumer Using a Risk-Aversion Procedure","volume":"80","author":"Zare","year":"2010","journal-title":"Electr. Power Syst. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.enpol.2009.09.010","article-title":"Electricity Procurement for Large Consumers Based on Information Gap Decision Theory","volume":"38","author":"Zare","year":"2010","journal-title":"Energy Policy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1826","DOI":"10.1109\/TPWRS.2011.2112675","article-title":"Risk-Based Electricity Procurement for Large Consumers","volume":"26","author":"Zare","year":"2011","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2999","DOI":"10.1016\/j.energy.2010.03.036","article-title":"Demand Bidding Construction for a Large Consumer through a Hybrid IGDT-Probability Methodology","volume":"35","author":"Zare","year":"2010","journal-title":"Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.enpol.2003.10.004","article-title":"Distributed Generation: Definition, Benefits and Issues","volume":"33","author":"Pepermans","year":"2005","journal-title":"Energy Policy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/TPWRD.2003.809616","article-title":"Power Quality Analysis Using S-transform","volume":"18","author":"Dash","year":"2003","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.ejor.2004.01.031","article-title":"A Measure of Risk and a Decision-Making Model Based on Expected Utility and Entropy","volume":"164","author":"Yang","year":"2005","journal-title":"Eur. J. Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7499","DOI":"10.3390\/en7117499","article-title":"Game-Theoretic Energy Management for the Residential Users with Dischargeable Plug-in Electric Vehicles","volume":"7","author":"Gao","year":"2014","journal-title":"Energies"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1109\/TSG.2013.2296714","article-title":"Efficiency-Fairness Trade-off in Privacy-Preserving Autonomous Demand Side Management","volume":"5","author":"Baharlouei","year":"2014","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1080\/00036847200000017","article-title":"Entropy, Market Risk, and the Selection of Efficient Portfolios","volume":"4","author":"Philippatos","year":"1972","journal-title":"Appl. Econ."},{"key":"ref_27","first-page":"1279","article-title":"An Information-Entropy-Based Risk Measurement Method of Software Development Project","volume":"30","author":"Jiang","year":"2014","journal-title":"J. Inf. Sci. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1007\/s00780-005-0159-6","article-title":"Conditional and Dynamic Convex Risk Measures","volume":"9","author":"Detlefsen","year":"2005","journal-title":"Financ. Stoch."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1109\/TEM.2005.861803","article-title":"Entropy Methods for Joint Distributions in Decision Analysis","volume":"53","author":"Abbas","year":"2006","journal-title":"IEEE Trans. Eng. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1287\/opre.1040.0204","article-title":"Maximum Entropy Utility","volume":"54","author":"Abbas","year":"2006","journal-title":"Oper. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/TPWRS.2008.922625","article-title":"A Hybrid System-Econometric Model for Electricity Spot Prices: Considering Spike Sensitivity to Forced Outage Distributions","volume":"23","author":"Anderson","year":"2008","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1016\/j.cnsns.2008.04.020","article-title":"Study on Probability Distribution of Prices in Electricity Market: A Case Study of Zhejiang Province, China","volume":"14","author":"Zhou","year":"2009","journal-title":"Commun. Nonlinear Sci. Numer. Simul."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/6560\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:49:16Z","timestamp":1760215756000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/6560"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,25]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2015,10]]}},"alternative-id":["e17106560"],"URL":"https:\/\/doi.org\/10.3390\/e17106560","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,25]]}}}