[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82295-en":3,"doc-seo-82295-105":30,"detail-sidebar-cat-0-en-105":83},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82295,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Inertia-Aware Optimal Power Flow Using PINN in IBR-Dominated Power Systems","Optimal Power Flow (OPF) is essential for secure and economical power-system operation, yet growing renewable penetration and reduced inertia make conventional optimization-based solvers increasingly difficult and slow, especially for large, low-inertia grids. A physics-informed neural network (PINN) framework is proposed to solve OPF in renewable energy–dominated, IBR-dominated systems. The model embeds a location-aware inertia constraint using system inertia strength tied to electrical distance, and simulation on a 6 GW test system achieves about 0.045% mean absolute error while ensuring physical-law and inertia-constraint compliance.","Inertia-Aware Optimal Power Flow Using PINNin IBR-Dominated Power Systems  \nMahyar Tofighi-Milani School of Electrical Engineering and Automation Aalto University Espoo, Finland Seyyed.tofighimilani@aalto.fi  \nSajjad Fattaheian-Dehkordi School of Engineering EPFL University Lausanne, Switzerland [sajjad.fattaheiandehkordi@epfl.ch](sajjad.fattaheiandehkordi@epfl.ch)  \nFranz Martin Rohrhofer Know-Center Research GmbH Graz, Austria [frohrhofer@know-center.at](frohrhofer@know-center.at)  \nMatti Lehtonen  \nSchool of Electrical Engineering and Automation Aalto University Espoo, Finland [matti.lehtonen@aalto.fi](matti.lehtonen@aalto.fi)  \nAbstract—The problem of Optimal Power Flow (OPF) is central to the secure and economic operation of modern power systems. However, increasing renewable energy penetration, and decreasing system inertia pose significant challenges to conventional optimization-based OPF solvers. While machine learning approaches have demonstrated substantial computational speed-ups, purely data-driven methods often suffer from data dependency, limited generalization, and lack of guaranteed physical feasibility. This paper suggests a physics-informed neural network (PINN) framework for solving the OPF problem in renewable energy– dominated, low-inertia power systems. In contrast to conventional OPF formulations, the model explicitly incorporates a location-aware inertia constraint based on the concept of system inertia strength, which accounts for the electrical distance between generation units and disturbance locations. Simulation results on a 6 GW test system demonstrate high accuracy. The mean absolute error (MAE) for both the training and testing datasets is approximately 0.045% of the total system capacity. The findings demonstrate that the proposed PINN framework is capable of producing highly accurate OPF solutions while ensuring compliance with both physical laws and inertia-related constraints. Overall, the findings highlight the potential of physics-informed learning to enable secure, efficient, and computationally scalable OPF for future low-inertia power systems.  \nKeywords—Frequency stability, IBR-dominated power systems, Inertia-constrained OPF, Low-inertia power systems, PINN, Virtual inertia.  \nNOMENCLATURE  \nCcon ,i / Cres ,i / CHRres,i  \n􀂂 / 􀂃 / 􀀪 Pcon ,i / Pres ,i  \n􀁄i , 􀁅i ,􀁊i  \n􀁎i ,􀁎iHR Pmiconn,i / Pmcoanx,i Prmesi,ni / Prmesa,xi  \nB, Bij  \n􀁔 , 􀁔i  \nPG / PD  \nThe cost of ith conventional unit / RES unit / RES headroom reserve  \nThe set of conventional units / RES units / lines Power generation of ith conventional / RES unit The cost coefficients of ith conventional unit Cost of ith RES and its headroom reserve Minimum / maximum limits of ith conventional unit  \nMinimum / maximum limits of ith RES unit Susceptance matrix of the system and its (i,j) element  \nAngle vector of the system and its ith element Power generation / demand vector  \nPG ,i  \nFl , Flmax l1 , l2 Hstr , Hmstirn  \nHG / HB  \nIHB / IPD  \nW  \nHR Hi  \nHREi  \n􀁗iHR  \n~~ ~~ ( j) ~~ ~~ ( j)ˆPG / P*GN  \nith element of PG  \nPower flow of line l and its maximum capacity Beginning and end bus of line l  \nStrength of system inertia and its minimum limit Inertia vector of generation / non-generation buses  \nOnes vector in the same dimension of HB / PD  \nBus weighting matrix  \nVirtual inertia from ith RES’s headroom reserve Headroom reserved energy of ith RESThe supporting time of ith RES in the case of imbalance occurrence  \nThe vector of predicted generations / real generations  \nNumber of training data  \nI. INTRODUCTION  \nT he Optimal Power Flow (OPF) problem plays a  \nfundamental role in the secure and economic  \noperation of modern power systems. It determines the optimal operating point of generation and network variables while satisfying physical laws and operational limits, enabling the objective of cost minimization [1], [2]. However, OPF is inherently nonlinear, and its complexity continues to grow with the expansion of network size, i","cbCaiuEvvghimJAB","https://ap.wps.com/l/cbCaiuEvvghimJAB","pdf",708278,3,1,6,"English","en",105,"# Introduction\n## Background on OPF and computational challenges\n## Machine learning approaches for OPF\n## Limitations of purely data-driven methods\n## Role of PINNs in power-system OPF","[{\"question\":\"What level of accuracy is reported on the 6 GW test system?\",\"answer\":\"Simulation results show a mean absolute error around 0.045% of total system capacity for both training and testing datasets.\"}]",1784179448,15,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"inertia-aware-optimal-power-flow-using-pinn-in-ibr-dominated-power-systems","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/inertia-aware-optimal-power-flow-using-pinn-in-ibr-dominated-power-systems/82295/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-22","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What level of accuracy is reported on the 6 GW test system?","Question",{"text":75,"@type":76},"Simulation results show a mean absolute error around 0.045% of total system capacity for both training and testing datasets.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,106,111,114,119,122,126],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":112,"slug":113},30,"research-report",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":98,"slug":129},19,"General","general"]