[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82205-en":3,"doc-seo-82205-105":29,"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":20,"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":13,"seo_description":14,"update_tm":27,"read_time":28},82205,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Power Flow Feasibility Assessment Using Variational Graph Autoencoders","Data-driven accelerators for power flow calculations using graph neural networks have gained attention, yet little work addresses whether the obtained solution is feasible under the governing power flow equations. This paper introduces a Variational Graph Autoencoder (VGAE) that detects power flow solution feasibility on the IEEE 118-bus case, enabling validation of outputs from AI-driven solvers. The approach targets distinctions between feasibility and algorithmic convergence failures, which traditional solvers reveal but regressors may miss.","Power Flow Feasibility Assessment Using Variational Graph Autoencoders  \nFerran Bohigas-Daranas Hamid Latif-Martinez Eduardo Prieto-Araujo  \nCITCEAUPC Barcelona, Spain 0009-0001-6477-6591  \nBNNUPC Barcelona,Spain 0000-0001-6006-3175  \nCITCEAUPC Barcelona, Spain 0000-0003-4349-5923  \nPere Barlet-Ros  \nBNNUPC, Hypergraph Barcelona,Spain 0000-0001-7837-0886  \nOriol Gomis-Bellmunt  \nCITCEAUPC Barcelona, Spain 0000-0002-9507-8278  \narXiv :2607 .09 122v 1 [ cs .LG] 10 Jul 2026  \nAbstract—Data-driven methods, including graph neural networks, have been studied for accelerating power flow calculations in recent years, but very little attention has been paid to the solution feasibility, which can be obtained by traditional solvers. This paper presents a Variational Graph Autoencoder (VGAE) that detects the power flow solution feasibility, using the IEEE 118-bus case, to assess the validity of the solutions provided by AI-driven solvers.  \nIndex Terms—Power Flow, Graph Neural Networks, Variational Graph Autoencoder, Variational Autoencoder, feasibility, convergence, saddle-node bifurcation, Newton–Raphson.  \nI. INTRODUCTION  \nSteady-state analysis of electric power networks relies on the solution of a system of nonlinear algebraic equations known as the Power Flow (PF) equations, by using a set of nonlinear equality constraints encoding Kirchhoff’s laws.  \nIn practice, the PF problem is solved by iterative algorithms, such as Newton–Raphson (NR) [1], whose convergence is not guaranteed, even when mathematical research has been carried out to improve the results [2], and new methods have been proposed, such as holomorphic embedding (HELM) [3] for power flow calculation. Power system operators frequently encounter cases in which a solver fails to converge, and the fundamental question arises: does the problem admit no solution (infeasibility), or did the algorithm simply fail to find one (non-convergence)?  \nThe terms feasibility and convergence are frequently confused in the power systems literature, yet they refer to fundamentally distinct mathematical properties. Feasibility is a property of a problem: it concerns the existence of a solution satisfying all governing equations and constraints. Convergence is a property of an algorithm: it concerns whether an iterative procedure finds that solution.  \nThis distinction carries critical operational consequences. An infeasible PF indicates that the system has surpassed  \nThe research has been funded by projects Daedalos(Horizon Europe research grant agreement No 101172829), GRAPHS4SEC (grant PCI2023- 145974-2 funded by MICIU/AEI/10.13039/501100011033) and BLOSSOMS (grant PID2024-158530OB-I00, by MI-CIU/AEI/10.13039/501100011033/ and ERDF/EU) . The work of P.Barlet, O.Gomis-Bellmunt and E.Prieto-Araujo was supported by the Agncia de Gesti d’Ajuts Universitaris i de Recerca (AGAUR) through the ICREA Acadmia programme, and by the Departament de Recerca i Universitats of the Generalitat de Catalunya. E. Prieto-Araujo is a member of the Serra H´unter Programme.  \nits voltage stability margin. Convergence failure, by contrast, may simply require better initialization, rescaling, or a more robust algorithm. Misdiagnosis leads to either unnecessary load curtailment or, more dangerously, to false confidence ina solution that was never actually found.  \nThis problem can be still more dangerous when using AI or data-driven methods, which provide a regression solution that does not consider the feasibility. Prior work has focused solely on the regression solution [4][5], neglecting problem feasibility; only Li et al. [6] have proposed a Graph Attention Network (GAT) architecture to predict power flow convergence using supervised learning.  \nThis paper proposes a fast and reliable method to assess the feasibility of the PF problem by using a VGAE architecture based on Message Passing Neural Networks (MPNNs) .  \nThe remainder of this paper is organized as follows. Section II presents the PF problem, its f","cbCain9mVY5F4rVW","https://ap.wps.com/l/cbCain9mVY5F4rVW","pdf",292730,1,5,"English","en",105,"# Introduction\n## Power Flow: feasibility vs convergence\n# Power Flow: feasibility and convergence\n## Problem formulation\n## Saddle-node bifurcation and feasibility boundary","[{\"question\":\"What problem does the paper target in AI-based power flow solvers?\",\"answer\":\"It targets the risk that AI-driven regression models can output results without verifying feasibility under the actual power flow equations, leading to misdiagnosis when solvers should be non-feasible rather than merely non-convergent.\"},{\"question\":\"How does the paper distinguish feasibility from convergence?\",\"answer\":\"Feasibility is a property of the PF problem, i.e., whether a solution satisfying all equations and constraints exists. Convergence is a property of an iterative algorithm, i.e., whether the algorithm finds such a solution.\"},{\"question\":\"What method does the paper propose to assess feasibility?\",\"answer\":\"The paper proposes a Variational Graph Autoencoder (VGAE) based on message passing neural networks to detect the feasibility of the power flow solution, using the IEEE 118-bus case to evaluate validity.\"}]",1784178798,13,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"power-flow-feasibility-assessment-using-variational-graph-autoencoders","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/power-flow-feasibility-assessment-using-variational-graph-autoencoders/82205/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper target in AI-based power flow solvers?","Question",{"text":75,"@type":76},"It targets the risk that AI-driven regression models can output results without verifying feasibility under the actual power flow equations, leading to misdiagnosis when solvers should be non-feasible rather than merely non-convergent.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper distinguish feasibility from convergence?",{"text":80,"@type":76},"Feasibility is a property of the PF problem, i.e., whether a solution satisfying all equations and constraints exists. Convergence is a property of an iterative algorithm, i.e., whether the algorithm finds such a solution.",{"name":82,"@type":73,"acceptedAnswer":83},"What method does the paper propose to assess feasibility?",{"text":84,"@type":76},"The paper proposes a Variational Graph Autoencoder (VGAE) based on message passing neural networks to detect the feasibility of the power flow solution, using the IEEE 118-bus case to evaluate validity.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":21,"slug":137},19,"General","general"]