[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120645-en":3,"doc-seo-120645-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120645,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Inclusion of Frequency Nadir constraint in the Unit Commitment Problem of Small Power Systems Using Machine Learning","As renewable penetration rises, power systems face greater frequency instability after outages because reduced inertia makes frequency dynamics more vulnerable. To ensure tolerable frequency deviation under contingencies, this work integrates the non-linear frequency nadir constraint into the unit commitment formulation. A synthetic training dataset is generated, and machine learning models—logistic regression and support vector machine—are used to predict frequency nadir values. The approach is evaluated on the La Palma island power system against analytical linearized nadir formulations, achieving faster solution times while maintaining acceptable frequency response quality.","arXiv :2210 .01540v1 [ ee ss . SY] 4 Oct 2022  \nInclusion of Frequency Nadir constraint in the Unit Commitment Problem of Small Power Systems Using Machine Learning  \nMohammad Rajabdorri, Behzad Kazemtabrizi, Matthias Tro􀀋aes, Lukas Sigrist, Enrique Lobato  \nOctober 5, 2022  \nAbstract  \nAs the intention is to reduce the amount of thermal generation and to increase the share of clean energy, power systems are increasingly becom  \ning susceptible to frequency instability after outages due to reduced levels  \nof inertia. To address this issue frequency constraints are being included  \nin the scheduling process, which ensure a tolerable frequency deviation in  \ncase of any contingencies. In this paper, a method is proposed to integrate  \nthe non-linear frequency nadir constraint into the unit commitment prob  \nlem, using machine learning. First a synthetic training dataset is gener  \nated. Then two of the available classic machine learning methods, namely  \nlogistic regression and support vector machine, are proposed to predict  \nthe frequency nadir. To be able to compare the machine learning meth  \nods to traditional frequency constrained unit commitment approaches,  \nsimulations on the power system of La Palma island are carried out for  \nboth proposed methods as well as an analytical linearized formulation of  \nthe frequency nadir. Our results show that the unit commitment problem  \nwith a machine learning based frequency nadir constraint is solved con  \nsiderably faster than with the analytical formulation, while still achieving  \nan acceptable frequency response quality after outages.  \nNomenclature  \nData-Driven Approach  \n` (:) loss function y^ predicted label X set of all features Y set of all labels  \n􀀂 set of 􀀒 parameters  \n􀀒 coe􀀎cients in the linear model C regularization coe􀀎cient  \nf􀀒 (x) hypothesis function  \nFC set of feasible combinations Ki number of the steps M number of features m index of features N number of data samples n index of data samples x features of the dataset y labels of the dataset  \nFrequency Dynamics  \n􀀋; 􀀌 normalizing coe􀀎cients  \n􀀁f0crit critical rate of change of frequency  \n􀀁fnadcritir critical frequency nadir [Hz]  \n􀀁fscsrit critical steady state frequency [Hz]` index of the lost generator  \n􀀍j binary operator of a􀀎ne segments [2f0,1g]  \n􀀕j weight associated with breaking point j M base power of the unit [MW]  \naj breaking point D load damping factor [%/Hz] f (t) frequency [Hz]  \nf0 nominal frequency [Hz] H inertia [MW.s] J number of the breaking points  \nj breaking point index P` lost power [MW]  \nPe electrical power [MW] Pm mechanical power [MW] Tg delivery time of units [s]  \nz1 ; z2 auxiliaries for changing variables  \nUnit Commitment  \nI set of all generators  \nD maximum yearly thermal generation  \nPi maximum power output of generator i [MW]  \nRi maximum ramp-up of generator i [MW/h] Dt  demand at hour t  \nD  minimum yearly thermal generation  \nPi  minimum power output of generator i [MW] Ri  maximum ramp-down of generator i [MW/h] DT minimum down-time of generators [hours] gc generation costs [e]  \nI number of generators i index of generators  \nii alias index for generators p power generation variable [MW] r online reserve power variable [MW] s alias index for time intervals sg solar generation variable [MW] suc (:) start-up costs [e]  \nT set of all time intervalst index of time intervals  \nu commitment variable [2f0,1g]  \nUT minimum up-time of generators [hours] v start-up variable [2f0,1g] w shut-down variable [2f0,1g] wg wind generation variable [MW]  \n1 Introduction  \nThe share of renewable energy sources (RES) is growing steadily in power systems. It is essential to facilitate the growth of RES penetration to reduce the carbon emission from fossil fuel based generators. There are however some obstacles that limit the applicability of RES. RES are volatile in nature and forecasting them is subject to uncertainties. Hence, integrating them in the power system is challenging. Moreove","cbCaisihxWL5OdP1","https://ap.wps.com/l/cbCaisihxWL5OdP1","pdf",1291657,1,22,"English","en",105,"# 1 Introduction\n# Data-Driven Approach\n## Frequency Dynamics\n# Unit Commitment","[{\"question\":\"Why is frequency stability challenging in small power systems with high renewable penetration?\",\"answer\":\"Small systems like islands often suffer inertia scarcity, so outages can trigger stronger frequency volatility. Renewables are volatile and usually add limited inertia, making frequency stability harder to maintain during contingencies.\"},{\"question\":\"How does the proposed method incorporate the frequency nadir constraint into unit commitment?\",\"answer\":\"The work integrates the non-linear frequency nadir constraint into the unit commitment problem using machine learning. It generates a synthetic training dataset and trains models to predict frequency nadir values for use in the scheduling process.\"},{\"question\":\"What models are used to predict the frequency nadir, and how are they evaluated?\",\"answer\":\"Two classic machine learning methods are used: logistic regression and support vector machine. Simulations on the La Palma island system compare both ML-based approaches against traditional frequency-constrained unit commitment with an analytical linearized formulation of the nadir.\"}]","Inclusion of Frequency Nadir constraint in the Unit Commitment Problem of Small Power Systems Using Machine Learning | PDF",1785731151,55,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"inclusion-of-frequency-nadir-constraint-in-the-unit-commitment-problem-of-small-power-systems-using-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/inclusion-of-frequency-nadir-constraint-in-the-unit-commitment-problem-of-small-power-systems-using-machine-learning/120645/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is frequency stability challenging in small power systems with high renewable penetration?","Question",{"text":75,"@type":76},"Small systems like islands often suffer inertia scarcity, so outages can trigger stronger frequency volatility. Renewables are volatile and usually add limited inertia, making frequency stability harder to maintain during contingencies.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method incorporate the frequency nadir constraint into unit commitment?",{"text":80,"@type":76},"The work integrates the non-linear frequency nadir constraint into the unit commitment problem using machine learning. It generates a synthetic training dataset and trains models to predict frequency nadir values for use in the scheduling process.",{"name":82,"@type":73,"acceptedAnswer":83},"What models are used to predict the frequency nadir, and how are they evaluated?",{"text":84,"@type":76},"Two classic machine learning methods are used: logistic regression and support vector machine. Simulations on the La Palma island system compare both ML-based approaches against traditional frequency-constrained unit commitment with an analytical linearized formulation of the nadir.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]