{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:12:54Z","timestamp":1760238774168,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electronics"],"abstract":"<jats:p>A bi-level operation scheduling of distribution system operator (DSO) and multi-microgrids (MMGs) considering both the wholesale market and retail market is presented in this paper. To this end, the upper-level optimization problem minimizes the total costs from DSO\u2019s point of view, while the profits of microgrids (MGs) are maximized in the lower-level optimization problem. Besides, a scenario-based stochastic programming framework using the heuristic moment matching (HMM) method is developed to tackle the uncertain nature of the problem. In this regard, the HMM technique is employed to model the scenario matrix with a reduced number of scenarios, which is effectively suitable to achieve the correlations among uncertainties. In order to solve the proposed non-linear bi-level model, Karush\u2013Kuhn\u2013Tucker (KKT) optimality conditions and linearization techniques are employed to transform the bi-level problem into a single-level mixed-integer linear programming (MILP) optimization problem. The effectiveness of the proposed model is demonstrated on a real-test MMG system.<\/jats:p>","DOI":"10.3390\/electronics9091441","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T11:22:43Z","timestamp":1599132163000},"page":"1441","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Bi-Level Operation Scheduling of Distribution Systems with Multi-Microgrids Considering Uncertainties"],"prefix":"10.3390","volume":"9","author":[{"given":"Saeid","family":"Esmaeili","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5505-3252","authenticated-orcid":false,"given":"Amjad","family":"Anvari-Moghaddam","sequence":"additional","affiliation":[{"name":"Department of Energy Technology, Aalborg University, 9220 Aalborg, Denmark"},{"name":"Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 5166616471, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6809-7660","authenticated-orcid":false,"given":"Erfan","family":"Azimi","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Babol Noshiravani University, Babol, Mazandaran 4714871167, Iran"}]},{"given":"Alireza","family":"Nateghi","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Shahid Beheshti University, Teheran 1684613114, Iran"}]},{"given":"Jo\u00e3o","family":"P. S. Catal\u00e3o","sequence":"additional","affiliation":[{"name":"Faculty of Engineering of the University of Porto and INESC TEC, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101628","DOI":"10.1016\/j.scs.2019.101628","article-title":"Retail market equilibrium and interactions among reconfigurable networked microgrids","volume":"49","author":"Esmaeili","year":"2019","journal-title":"Sustain. Cities Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/j.apenergy.2016.09.092","article-title":"Distributed EMPC of multiple microgrids for coordinated stochastic energy management","volume":"185","author":"Kou","year":"2017","journal-title":"Appl. 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