[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82471-en":3,"doc-seo-82471-105":29,"detail-sidebar-cat-0-en-105":90},{"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":13,"seo_description":14,"update_tm":27,"read_time":28},82471,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Small-Signal Stability of a Unified Single-Unit Infinite-Bus Swing-Equation Model for Generators and Inverters","A unified swing-equation model is developed for energy-conversion interfaces connected to an infinite bus, using generalized, equilibria-dependent inertia, damping, and synchronization constants. The formulation combines second-order active-power versus voltage-phasor-angle dynamics with network interconnection through power-flow equations. Unified parameterization links reduced-order models for synchronous generators, grid-following inverters with fast frequency response, and droop and virtual synchronous generator grid-forming inverters. Necessary and sufficient small-signal stability conditions for angle equilibria are derived.","Small-signal Stability of a Unified Single-unit Infinite-bus Swing-equation Model for Generators and Inverters  \nDebjyoti Chatterjee, Nathan Baeckeland, Bala Kameshwar Poolla, Gab-Su Seo, Brian Johnson, and Sairaj Dhople  \narXiv :2607 .00161v1 [ ee ss . SY] 30 Jun 2026  \nAbstract—We present a swing-equation model with generalized and equilibria-dependent inertia, damping, and synchronization constants for energy conversion interfaces with second-order active-power versus voltage-phasor-angle dynamics connected to an infinite bus. The model is unified in that prudent parameterization of the second-order angle-to-power transfer function aligns with reduced-order models for synchronous generators, grid-following inverters with fast frequency-response capability, and droop- and virtual synchronous generator-based gridforming inverters. Parametric necessary and sufficient conditions to examine small-signal stability of angle equilibria are derived from the unified swing-equation model.  \nIndex Terms—Grid-following inverter, grid-forming inverter, small-signal stability, swing equation, synchronous generator.  \nI. INTRODUCTION  \nSMALL-SIGNAL stability of angle equilibria  \nsingle-machine infinite-bus (SMIB) model is a  \nfor the  \nfounda-  \ntional tenet of power systems dynamics. While the setup is not remotely representative of complexity encountered in practice, the treatment sheds light on the interplay of power-flow equations and machine dynamics as they relate to an elementary notion of stability. Stability assessment has assumed increased importance with the changing resource mix on grids worldwide that now feature increasing numbers of grid-following (GFL) and grid-forming (GFM) inverterbased resources (IBRs) alongside synchronous generators (SGs) [1] . Networks with varying complexity—including elemental single-unit models—have been in focus; however, much of the recent work on swing-equation-type models and stability of the SMIB setup in the context of IBRs is unitspecific. The main contribution of this effort is to update the ubiquitous SMIB model to one that can acknowledge the dynamics of contemporary frequency-responsive power electronics alongside SGs while preserving a pathway to analytically examine small-signal stability.  \nWe study the quasi-steady-state dynamics of a controlledvoltage-source model for an energy-conversion interface connected to an infinite bus through an RL line. It is assumed  \nThis work was authored by the National Laboratory of the Rockies (NLR) for the U.S. Department of Energy (DOE), operated under Contract No. DE-AC36-08GO28308 . Funding provided in part by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy under the Solar Energy Technologies Office Award Number 38637 (UNIFI Consortium) and by the Laboratory Directed Research and Development (LDRD) Program at NLR. The views expressed do not necessarily represent those of the DOE or the U.S. Government. The U.S. Government retains, and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce this work for Government purposes. D. Chatterjee and B. Johnson are with the University of Texas at Austin; N. Baeckeland, B.K. Poolla, and G.-S. Seo are with the Power Systems Engineering Center of NLR; and S. Dhople is with the University of Minnesota.  \nto inject a nominal amount of (commanded) active power modulated by a linear frequency-versus-power relationship. A second-order transfer function is presumed for the active power versus voltage-phasor angle, and the network interconnection is modeled via power-flow equations. A second-orderswing-equation model that captures the small-signal angle dynamics emerges upon linearization about an equilibrium point. Unlike the classical swing equation for SGs, this version is generalized and sports equilibria-dependent inertia, damping, and synchronization co","cbCaiiEDimvyH5vh","https://ap.wps.com/l/cbCaiiEDimvyH5vh","pdf",1313941,1,7,"English","en",105,"# Introduction\n## Small-signal stability background\n# Unified swing-equation model\n## Dynamics and assumptions\n## Generalized equilibria-dependent parameters\n# Stability analysis\n## Routh–Hurwitz conditions\n## Equilibrium stability insights\n# Validation and results\n## Phase-portrait plots\n## Eigenvalue plots","[{\"question\":\"What unified swing-equation model is proposed in the document?\",\"answer\":\"The document proposes a swing-equation model with generalized and equilibria-dependent inertia, damping, and synchronization constants for interfaces connected to an infinite bus, capturing second-order active-power versus voltage-phasor-angle dynamics.\"},{\"question\":\"Which energy-conversion interfaces does the unified model encompass?\",\"answer\":\"It unifies reduced-order models for synchronous generators, grid-following inverters with fast frequency response, and grid-forming inverters based on droop and virtual synchronous generator concepts.\"},{\"question\":\"How are small-signal stability conditions for angle equilibria obtained?\",\"answer\":\"By applying the Routh–Hurwitz criterion to the unified swing-equation model, the document derives necessary and sufficient conditions on unit and network parameters to assess small-signal stability of angle equilibria.\"}]",1784180719,18,{"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":85,"head_meta":87,"extra_data":89,"updated_unix":27},"small-signal-stability-of-a-unified-single-unit-infinite-bus-swing-equation-model-for-generators-and-inverters","",{"@graph":35,"@context":84},[36,53,67],{"@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/small-signal-stability-of-a-unified-single-unit-infinite-bus-swing-equation-model-for-generators-and-inverters/82471/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What unified swing-equation model is proposed in the document?","Question",{"text":74,"@type":75},"The document proposes a swing-equation model with generalized and equilibria-dependent inertia, damping, and synchronization constants for interfaces connected to an infinite bus, capturing second-order active-power versus voltage-phasor-angle dynamics.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Which energy-conversion interfaces does the unified model encompass?",{"text":79,"@type":75},"It unifies reduced-order models for synchronous generators, grid-following inverters with fast frequency response, and grid-forming inverters based on droop and virtual synchronous generator concepts.",{"name":81,"@type":72,"acceptedAnswer":82},"How are small-signal stability conditions for angle equilibria obtained?",{"text":83,"@type":75},"By applying the Routh–Hurwitz criterion to the unified swing-equation model, the document derives necessary and sufficient conditions on unit and network parameters to assess small-signal stability of angle equilibria.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,118,121,126,129,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & 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