{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T08:10:34Z","timestamp":1773821434288,"version":"3.50.1"},"reference-count":83,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T00:00:00Z","timestamp":1601510400000},"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":["51977153, 51977161, 51577046"],"award-info":[{"award-number":["51977153, 51977161, 51577046"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"State Key Program of National Natural Science Foundation of China","award":["51637004"],"award-info":[{"award-number":["51637004"]}]},{"name":"Equipment research project in advance","award":["41402040301"],"award-info":[{"award-number":["41402040301"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Optimal Reactive Power Dispatch (ORPD) is the vital concern of network operators in the planning and management of electrical systems to reduce the real and reactive losses of the transmission and distribution system in order to augment the overall efficiency of the electrical network. The principle objective of the ORPD problem is to explore the best setting of decision variables such as rating of the shunt capacitors, output voltage of the generators and tap setting of the transformers in order to diminish the line loss, and improve the voltage profile index (VPI) and operating cost minimization of standard electrical systems while keeping the variables within the allowable limits. This research study demonstrates a compelling transformative approach for resolving ORPD problems faced by the operators through exploiting the strength of the meta-heuristic optimization model based on a new fractional swarming strategy, namely fractional order (FO)\u2013particle swarm optimization (PSO), with consideration of the entropy metric in the velocity update mechanism. To perceive ORPD for standard 30 and 57-bus networks, the complex nonlinear objective functions, including minimization of the system, VPI improvement and operating cost minimization, are constructed with emphasis on efficacy enhancement of the overall electrical system. Assessment of the results show that the proposed FO-PSO with entropy metric performs better than the other state of the art algorithms by means of improvement in VPI, operating cost and line loss minimization. The statistical outcomes in terms of quantile\u2013quantile illustrations, probability plots, cumulative distribution function, box plots, histograms and minimum fitness evaluation in a set of autonomous trials validate the capability of the proposed optimization scheme and exhibit sufficiency and also vigor in resolving ORPD problems.<\/jats:p>","DOI":"10.3390\/e22101112","type":"journal-article","created":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T09:04:12Z","timestamp":1601543052000},"page":"1112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A New Fractional Particle Swarm Optimization with Entropy Diversity Based Velocity for Reactive Power Planning"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9070-5407","authenticated-orcid":false,"given":"Muhammad Waleed","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock 22060, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasir","family":"Muhammad","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock 22060, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9953-822X","authenticated-orcid":false,"given":"Muhammad Asif Zahoor","family":"Raja","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock 22060, Pakistan"},{"name":"Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2488-8353","authenticated-orcid":false,"given":"Farman","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock 22060, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naveed Ishtiaq","family":"Chaudhary","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, International Islamic University, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yigang","family":"He","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,1]]},"reference":[{"key":"ref_1","first-page":"220","article-title":"Optimal power flow using differential evolution algorithm","volume":"91","author":"Abido","year":"2009","journal-title":"Electr. 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