{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T04:45:24Z","timestamp":1770957924247,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T00:00:00Z","timestamp":1569888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Fund of Beijing Engineering Technology Research Center of Electric Vehicle Charging\/Battery Swap","award":["China Electric Power Research Institute."],"award-info":[{"award-number":["China Electric Power Research Institute."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The problem of electricity pricing for charging stations is a multi-objective mixed integer nonlinear programming. Existing algorithms have low efficiency in solving this problem. In this paper, a convex optimization algorithm is proposed to get the optimal solution quickly. Firstly, the model is transformed into a convex optimization problem by second-order conic relaxation and Karush\u2013Kuhn\u2013Tucker optimality conditions. Secondly, a polyhedral approximation method is applied to construct a mixed integer linear programming, which can be solved quickly by branch and bound method. Finally, the model is solved many times to obtain the Pareto front according to the scalarization basic theorem. Based on an IEEE 33-bus distribution network model, simulation results show that the proposed algorithm can obtain an exact global optimal solution quickly compared with the heuristic method.<\/jats:p>","DOI":"10.3390\/a12100208","type":"journal-article","created":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T11:11:16Z","timestamp":1569928276000},"page":"208","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Convex Optimization Algorithm for Electricity Pricing of Charging Stations"],"prefix":"10.3390","volume":"12","author":[{"given":"Jing","family":"Zhang","sequence":"first","affiliation":[{"name":"Beijing Engineering Technology Research Center of Electric Vehicle Charging\/Battery Swap, China Electric Power Research Institute Co., Ltd., Beijing 100192, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6775-1349","authenticated-orcid":false,"given":"Xiangpeng","family":"Zhan","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China"}]},{"given":"Taoyong","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Engineering Technology Research Center of Electric Vehicle Charging\/Battery Swap, China Electric Power Research Institute Co., Ltd., Beijing 100192, China"}]},{"given":"Linru","family":"Jiang","sequence":"additional","affiliation":[{"name":"Beijing Engineering Technology Research Center of Electric Vehicle Charging\/Battery Swap, China Electric Power Research Institute Co., Ltd., Beijing 100192, China"}]},{"given":"Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China"}]},{"given":"Yuanxing","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Engineering Technology Research Center of Electric Vehicle Charging\/Battery Swap, China Electric Power Research Institute Co., Ltd., Beijing 100192, China"}]},{"given":"Xiaohong","family":"Diao","sequence":"additional","affiliation":[{"name":"Beijing Engineering Technology Research Center of Electric Vehicle Charging\/Battery Swap, China Electric Power Research Institute Co., Ltd., Beijing 100192, China"}]},{"given":"Sining","family":"Han","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,1]]},"reference":[{"key":"ref_1","first-page":"23","article-title":"Research on electric vehicle orderly charging based on regional peak-valley time-of-use price","volume":"55","author":"He","year":"2018","journal-title":"Electr. 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