[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-272825-105":59,"doc-detail-272825-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","hybrid-symbolic-numeric-framework-for-power-system-modeling-and-analysis","Hybrid Symbolic-Numeric Framework for Power System Modeling and Analysis","","Hybrid symbolic-numeric framework reduces programming effort for power system differential-algebraic equation (DAE) modeling and simulation. It addresses limitations of existing open-source tools that require manual implementation of numerical equations, sparse Jacobians, and discontinuous components. The open-source Python library ANDES integrates a symbolic descriptive modeling layer with a numeric vector-based computation layer, enabling rapid assembly of DAE models from modular components. It supports discontinuous elements, transfer-function blocks, automatic generation of robust simulation code, and high-quality documentation. Case studies validate agreement with DSATools across power flow, time-domain simulation, and eigenvalue analysis.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/hybrid-symbolic-numeric-framework-for-power-system-modeling-and-analysis/272825/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/hybrid-symbolic-numeric-framework-for-power-system-modeling-and-analysis/272825.png","ImageObject",300,407,{"name":92,"@type":93},"eBook King","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does the paper target in power system DAE modeling and simulation?","Question",{"text":113,"@type":114},"It targets the high programming effort required by existing open-source tools to implement numerical equations, sparse Jacobians, and discontinuous components for DAE modeling and simulation.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the proposed hybrid symbolic-numeric framework work?",{"text":118,"@type":114},"It combines a symbolic layer for descriptive DAE modeling with a numeric layer for vector-based numerical computation, allowing DAE models to be built by mixing and matching modeling components.",{"name":120,"@type":111,"acceptedAnswer":121},"What validations are reported for the ANDES library?",{"text":122,"@type":114},"Case studies validate the library against DSATools for power flow, time-domain simulation, and eigenvalue analysis, including implementations of TGOV1, timing breakdowns for MATPOWER, and full eigenvalue analysis of Kundur’s system.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},272825,1789467777,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":41,"preview_page_count":4},962088006270,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Hybrid Symbolic-Numeric Framework for Power System Modeling and Analysis  \nHantao Cui , Member, IEEE, Fangxing Li, Fellow, IEEE, and Kevin Tomsovic, Fellow, IEEE  \nAbstract—With the recent proliferation ofopen-source packages for computing, power system differential-algebraic equation(DAE) modeling and simulation are being revisited to reduce the programming efforts. Existing open-source tools require manual efforts to develop code for numerical equations, sparse Jacobians, and discontinuous components. This paper proposesa hybrid symbolicnumeric framework, exemplified by an open-source Python-based library ANDES, which consists of a symbolic layer for descriptive modeling and a numeric layer for vector-based numerical computation. This method enables the implementation of DAE models by mixing and matching modeling components, through which models are described. In the framework, a rich set of discontinuous components and standard transfer function blocks are provided besides essential modeling elements for rapid modeling. ANDES can automatically generate robust and fast numerical simulation code, as well as and high-quality documentation. Case studies present a)two implementations ofturbine governor model TGOV1, b) power flow computation time break down for MATPOWER systems, c) validation of time-domain simulation with commercial software using three test systems with a variety ofmodels, and d)the full eigenvalue analysis for Kundur’s system. Validation shows that ANDES closely matches the commercial tool DSATools for power flow, time-domain simulation, and eigenvalue analysis.  \nIndex Terms—Power systems, open-source, DAE modeling, symbolic calculation, time-domain simulation, ANDES library.  \nI. INTRODUCTION  \nP OWER system modeling and transient simulation is a  \nwidely studied yet challenging topic. Digital computerbased simulation has been dominating in the industry and academia with both closed-source tools [1] and open-source tools[2]–[11]widely used. Although simulation software comes with a set of built-in models, users will likely need to customize models for new devices or control algorithms.  \nTo develop new models for simulation software is to implement the model equations in a program that can interact with the predefined software architecture. In general, there are two  \nManuscript received February 20, 2020; revised June 24, 2020 and July 30, 2020; accepted August 11, 2020 . Date of publication August 17, 2020; date of current version February 19, 2021 . This work was supported in part by the Engineering Research Center Program of the National Science Foundation and the Department of Energy under NSF Award EEC-1041877 and in part by the CURENT Industry Partnership Program. Paper no. TPWRS-00276-2020 .(Corresponding author: Fangxing Li.)  \nThe authors are with the Department of Electrical Engineering and Computer Science, The University of Tennessee, Knoxville, TN 37996 USA (e-mail: [hcui7@utk.edu](hcui7@utk.edu); fl[i6@utk.edu](i6@utk.edu); [tomsovic@utk.edu](tomsovic@utk.edu)) .  \nColor versions of one or more of the figures in this article are available online at [https://ieeexplore.ieee.org](https://ieeexplore.ieee.org).  \nDigital Object Identifier 10.1109/TPWRS.2020.3017019  \napproaches to implement user-defined models (UDMs): programmatically or through a graphical user interface (GUI) [12],[13], which is usually not available in open-source tools due to complexity and lack ofreturn. Still, open-source tools are crucial for scientific research, but they require programming proficiencyto develop new models on top of a deep understanding of the tool [14] .  \nTwo advanced UDM solutions exist in open-source tools: Dome cards [5] and the Function Mockup Unit (FMU) supportinGridDyn[8]. Dome cards are plain-textfiles containing model descriptions in the card protocol. Using a symbolic library under the hood, Dome uses cards to generate intermediate code that can be modified into final models. Although cards are flexible, they","cbCaigDcz8uMsZ6R","https://ap.wps.com/l/cbCaigDcz8uMsZ6R","pdf",2734459,12,"English","# I. INTRODUCTION\n## User-defined model implementation approaches\n## Hybrid symbolic-numeric method and ANDES contributions","[{\"question\":\"What problem does the paper target in power system DAE modeling and simulation?\",\"answer\":\"It targets the high programming effort required by existing open-source tools to implement numerical equations, sparse Jacobians, and discontinuous components for DAE modeling and simulation.\"},{\"question\":\"How does the proposed hybrid symbolic-numeric framework work?\",\"answer\":\"It combines a symbolic layer for descriptive DAE modeling with a numeric layer for vector-based numerical computation, allowing DAE models to be built by mixing and matching modeling components.\"},{\"question\":\"What validations are reported for the ANDES library?\",\"answer\":\"Case studies validate the library against DSATools for power flow, time-domain simulation, and eigenvalue analysis, including implementations of TGOV1, timing breakdowns for MATPOWER, and full eigenvalue analysis of Kundur’s system.\"}]","Hybrid Symbolic-Numeric Framework for Power System Modeling and Analysis | PDF"]