{"id":2241,"date":"2026-04-03T16:12:03","date_gmt":"2026-04-03T08:12:03","guid":{"rendered":"https:\/\/iweb20wp-b205b.url.tku.edu.tw\/jase\/?post_type=tkuisotope&#038;p=2241"},"modified":"2026-05-24T14:18:27","modified_gmt":"2026-05-24T06:18:27","slug":"nsga-ii-algorithm-based-wide-area-measurement-wams-allocation-with-considering-reliability","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=nsga-ii-algorithm-based-wide-area-measurement-wams-allocation-with-considering-reliability","title":{"rendered":"NSGA-II Algorithm-Based Wide Area Measurement (WAMS) Allocation with Considering Reliability"},"content":{"rendered":"\n<div class=\"wp-block-tkuwpbs5-bs5-row row article-info\">\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-3 align-self-start\">\n<p><i class=\"fa fa-folder\" aria-hidden=\"true\"><\/i>&nbsp;<a href=\"\/jase\/?page_id=2115\" data-type=\"page\" data-id=\"807\">2025<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-3 align-self-start\">\n<p><i class=\"fa fa-folder-open\" aria-hidden=\"true\"><\/i>&nbsp;<a href=\"\/jase\/?page_id=2223\" data-type=\"page\" data-id=\"1055\">Volume 28, Issue 2<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-6 align-self-start\">\n<div class=\"wp-block-tkuwpbs5-bs5-div dv_publish\" data-aos=\"normal\"><div class=\"wp-block-post-date\"><time datetime=\"2026-04-03T16:12:03+08:00\">2026-04-03<\/time><\/div><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-row row\">\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-5 align-self-start\">\n<div class=\"wp-block-tkuwpbs5-bs5-div au-ol\" data-aos=\"normal\">\n<p>Guimin Xu<sup>1<\/sup><a href=\"mailto:bingfeng71@126.com\"><i class=\"fa fa-envelope\"><\/i><\/a> and Zhengxiang Yang<sup>2<\/sup><\/p>\n\n\n\n<p style=\"font-size:14px\"><sup>1<\/sup>School of Physics and Mechanical &amp; Electrical Engineering, Hubei University of Education, Wuhan 430205, China<\/p>\n\n\n\n<p style=\"font-size:14px\"><sup>2<\/sup>School of intelligent manufacturing, Wuhan Technical College of Communications, Wuhan 430065, China)<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-div\" style=\"margin-top:var(--wp--preset--spacing--40)\" data-aos=\"normal\">\n<p>Received:&nbsp;June 8, 2023<br>Accepted:&nbsp;October 26, 2024<br>Publication Date:&nbsp;April 3, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-7 align-self-start clk=\u5716\u7247\"><img decoding=\"async\" src=\"\/jase\/wp-content\/uploads\/2026\/04\/28_02_16.jpg\" class=\"img-fluid img-fluid mx-auto d-block\" alt=\"\u4e0a\u50b3\u5716\u7247\">\n\n\n<p class=\"has-text-align-center img_caption\">Process that occurs in NSGA-II<\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><i class=\"fab fa-creative-commons\"><\/i>&nbsp;<strong>Copyright&nbsp;<\/strong>The Author(s). This is an open access article distributed under the terms of the&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\">Creative Commons Attribution&nbsp;License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n<p>Download Citation:\u00a0 <a href=\"\/jase\/wp-content\/uploads\/2026\/05\/V282.0016.bib\" data-type=\"attachment\" data-id=\"7179\" target=\"_blank\" rel=\"noreferrer noopener\">BibTeX <\/a>| <a rel=\"noreferrer noopener\" href=\"http:\/\/dx.doi.org\/10.6180\/jase.202502_28(2).0016\" target=\"_blank\">http:\/\/dx.doi.org\/10.6180\/jase.202502_28(2).0016<\/a>\u00a0\u00a0<\/p>\n\n\n\n<p class=\"btn btn-primary article-btn\"><a href=\"\/jase\/wp-content\/uploads\/2026\/04\/16_2023_0634_V28i2.pdf\" data-type=\"attachment\" data-id=\"2197\" target=\"_blank\" rel=\"noreferrer noopener\">Download PDF<\/a><\/p>\n\n\n\n<div style=\"height:24px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Today\u2019s power systems for various reasons, including linearization of equations of state estimation and improved speed control and protection systems, use Wide Area Measurement (WAMS). Due to their high cost, it is essential to optimize the number and placement of this equipment. The costs associated with deploying a Synchro phasor have evolved throughout time. The cost of upgrading a substation, which is far more than the cost of a single device, has emerged as the major expense component. When determining where to put phasor measuring units (PMUs), it\u2019s important to consider not only how many will need to be built at each substation but also how many will need to undergo upgrades to accommodate them. In this paper, the multi-functional locating of phasor measurement units has been done with goals such as the cost of investment and risk in power systems (reliability) by indicating the observability. Then the location of the phasor units was solved in the form of an optimization problem, using multi-objective optimization algorithm NSGA-II. In the end, the performance of the proposed method is examined on the 9-bus system.<\/p>\n\n\n\n<p><em>Keywords:&nbsp;Observability of Power Systems; Optimal PMU Allocation; Power System Reliability; Risk Cost; NSGA-II Algorithm<\/em><\/p>\n\n\n\n<div style=\"height:2rem\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-div ref_ol\" data-aos=\"normal\">\n<ol>\n<li>[1] A. P. S. Meliopoulos, G. J. Cokkinides, O. Wasynczuk, E. Coyle, M. Bell, C. Hoffmann, C. Nita-Rotaru, T. Downar, L. Tsoukalas, and R. Gao. \u201cPMU data characterization and application to stability monitoring\u201d. In: IEEE, 2006, 8\u2013pp.<\/li>\n<li>[2] S. Afzal, B. M. Ziapour, A. Shokri, H. Shakibi, and B. Sobhani, (2023) \u201cBuilding energy consumption prediction using multilayer perceptron neural network-assisted models; comparison of different optimization algorithms&#8221; Energy 282: 128446.<\/li>\n<li>[3] F. Aminifar, M. Fotuhi-Firuzabad, M. Shahidehpour, and A. Khodaei, (2010) \u201cProbabilistic multistage PMU placement in electric power systems&#8221; IEEE Transactions on Power Delivery 26: 841\u2013849.<\/li>\n<li>[4] M. Patel, S. Aivaliotis, and E. Ellen, (2010) \u201cReal-time application of synchrophasors for improving reliability&#8221; NERC report, Oct 1: 4.<\/li>\n<li>[5] V. Terzija, G. Valverde, D. Cai, P. Regulski, V. Madani, J. Fitch, S. Skok, M. M. Begovic, and A. Phadke, (2010) \u201cWide-area monitoring, protection, and control of future electric power networks&#8221; Proceedings of the IEEE 99: 80\u201393.<\/li>\n<li>[6] A. G. Phadke and J. S. Thorp. Synchronized phasor measurements and their applications. 1. Springer, 2008.<\/li>\n<li>[7] A. Khaleghi, M. O. Sadegh, and M. G. Ahsaee, (2018) \u201cPermanent Fault Location in Distribution System Using Phasor Measurement Units (PMU) in Phase Domain.&#8221; International Journal of Electrical Computer Engineering (2088-8708) 8:<\/li>\n<li>[8] C.-W. Liu and J. Thorp, (1995) \u201cApplication of synchronised phasor measurements to real-time transient stability prediction&#8221; IEE Proceedings-Generation, Transmission and Distribution 142: 355\u2013360.<\/li>\n<li>[9] T. T. Nguyen and V. L. Nguyen. \u201cApplication of widearea network of phasor measurements for secondary voltage control in power systems with FACTS controllers\u201d. In: IEEE, 2005, 2927\u20132934.<\/li>\n<li>[10] A. G. Phadke, (1993) \u201cSynchronized phasor measurements in power systems&#8221; IEEE Computer Applications in power 6: 10\u201315.<\/li>\n<li>[11] L. Wang, P. P. Gelberger, and N. Ramani. \u201cReliability assessment of the operational functions of a power system control center\u201d. In: IET, 1991, 229\u2013234.<\/li>\n<li>[12] M. S. Ghazizadeh and M. R. Aghamohammadi, (2023) \u201cA Deep Learning-Based Attack Detection Mechanism against Potential Cascading Failure Induced by Load Redistribution Attacks&#8221; IEEE Transactions on Smart Grid:<\/li>\n<li>[13] M. Zima, M. Larsson, P. Korba, C. Rehtanz, and G. Andersson, (2005) \u201cDesign aspects for wide-area monitoring and control systems&#8221; Proceedings of the IEEE 93: 980\u2013996.<\/li>\n<li>[14] Y. Wang, W. Li, J. Lu, and H. Liu, (2009) \u201cEvaluating multiple reliability indices of regional networks in wide area measurement system&#8221; Electric Power Systems Research 79: 1353\u20131359.<\/li>\n<li>[15] Y. Wang, W. Li, and J. Lu, (2010) \u201cReliability analysis of wide-area measurement system&#8221; IEEE Transactions on Power Delivery 25: 1483\u20131491.<\/li>\n<li>[16] F. Aminifar, M. Fotuhi-Firuzabad, M. Shahidehpour, and A. Khodaei, (2011) \u201cObservability enhancement by optimal PMU placement considering random power system outages&#8221; Energy Systems 2: 45\u201365.<\/li>\n<li>[17] F. Aminifar, M. Fotuhi-Firuzabad, M. Shahidehpour, and A. Khodaei, (2010) \u201cProbabilistic multistage PMU placement in electric power systems&#8221; IEEE Transactions on Power Delivery 26: 841\u2013849.<\/li>\n<li>[18] N. H. Abbasy and H. M. Ismail, (2009) \u201cA unified approach for the optimal PMU location for power system state estimation&#8221; IEEE Transactions on power systems 24: 806\u2013813.<\/li>\n<li>[19] F. Aminifar, A. Khodaei, M. Fotuhi-Firuzabad, and M. Shahidehpour, (2009) \u201cContingency-constrained PMU placement in power networks&#8221; IEEE Transactions on Power Systems 25: 516\u2013523.<\/li>\n<li>[20] C. Rakpenthai, S. Premrudeepreechacharn, S. Uatrongjit, and N. R. Watson, (2006) \u201cAn optimal PMU placement method against measurement loss and branch outage&#8221; IEEE transactions on power delivery 22: 101\u2013107.<\/li>\n<li>[21] S. Chakrabarti and E. Kyriakides, (2008) \u201cOptimal placement of phasor measurement units for power system observability&#8221; IEEE Transactions on power systems 23: 1433\u20131440.<\/li>\n<li>[22] K. Deb. Multi-objective optimisation using evolutionary algorithms: an introduction. Springer, 2011, 3\u201334.<\/li>\n<li>[23] J. B. A. London, S. A. R. Piereti, R. A. de Souza Benedito, and N. G. Bretas, (2009) \u201cRedundancy and observability analysis of conventional and PMU measurements&#8221; IEEE Transactions on Power Systems 24: 1629\u20131630.<\/li>\n<li>[24] F. Aminifar, C. Lucas, A. Khodaei, and M. FotuhiFiruzabad, (2009) \u201cOptimal placement of phasor measurement units using immunity genetic algorithm&#8221; IEEE Transactions on power delivery 24: 1014\u20131020.<\/li>\n<li>[25] F. Aminifar, M. Fotuhi-Firuzabad, and A. Safdarian, (2012) \u201cOptimal PMU placement based on probabilistic cost\/benefit analysis&#8221; IEEE Transactions on Power Systems 28: 566\u2013567.<\/li>\n<li>[26] D. Dua, S. Dambhare, R. K. Gajbhiye, and S. A. Soman, (2008) \u201cOptimal multistage scheduling of PMU placement: An ILP approach&#8221; IEEE Transactions on Power delivery 23: 1812\u20131820.<\/li>\n<li>[27] A. Khaleghi, M. O. Sadegh, M. Ghazizadeh-Ahsaee, and A. M. Rabori, (2018) \u201cTransient fault area location and fault classification for distribution systems based on wavelet transform and adaptive neuro-fuzzy inference system (ANFIS)&#8221; Advances in Electrical and Electronic Engineering 16: 155\u2013166.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"author":3,"template":"wp-custom-template-detail-4-aricles","meta":{"_uag_custom_page_level_css":""},"categories":[9,6,265],"tags":[310],"acf":[],"uagb_featured_image_src":[],"uagb_author_info":{"display_name":"\u6797\u923a\u6db5","author_link":"\/jase\/?author=3"},"uagb_comment_info":0,"uagb_excerpt":"&nbsp;Copyright&nbsp;The Author(s). This is an open access article distributed under the terms of the&nbsp;Creative Commons Attribution&nbsp;License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited. Download Citation:\u00a0 BibTeX | http:\/\/dx.doi.org\/10.6180\/jase.202502_28(2).0016\u00a0\u00a0 Download PDF Today\u2019s power systems for various reasons, including linearization of equations of&hellip;","_links":{"self":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope\/2241"}],"collection":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope"}],"about":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/types\/tkuisotope"}],"author":[{"embeddable":true,"href":"\/jase\/index.php?rest_route=\/wp\/v2\/users\/3"}],"wp:attachment":[{"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2241"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2241"},{"taxonomy":"post_tag","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}