[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124971-en":3,"doc-seo-124971-105":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},124971,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Physics-Informed Machine Learning for Power Grid Frequency Modeling","Power system operation depends on interacting technical, economic, and social factors, with renewable generation driven by weather and controllable by electricity markets, while load emerges from collective consumer behavior. Many relevant external drivers are only observed at coarse resolutions and the dependencies of the dynamic system parameters are often unknown. This work proposes a physics-informed machine learning framework that unifies stochastic differential equations and neural networks to build a probabilistic model of power grid frequency dynamics. The approach outperforms a daily-average baseline over 15 minutes, identifies time-dependent model parameters linked to external drivers, and generates synthetic series reproducing key statistical properties.","Physics-Informed Machine Learning for Power Grid Frequency Modeling  \nJohannes Kruse , 1,2 Eike Cramer ,3 Benjamin Schäfer ,4 and Dirk Witthaut1,2, * 1 Forschungszentrum Jülich, Institute for Energy and Climate Research (IEK-STE), Jülich 52428, Germany  \n2 Institute for Theoretical Physics, University of Cologne, Köln 50937, Germany 3 Forschungszentrum Jülich, Institute for Energy and Climate Research—Energy Systems Engineering (IEK-10),  \nJülich 52428, Germany  \n4 Institute for Automation and Applied Informatics, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen  \n76344, Germany  \n (Received 30 November 2022; revised 19 June 2023; accepted 18 August 2023; published 4 October 2023)  \nThe operation of power systems is affected by diverse technical, economic, and social factors. Social behavior determines load patterns, electricity markets regulate the generation, and weather-dependent renewables introduce power fluctuations. Thus, power system dynamics must be regarded as a nonautonomous system whose parameters vary strongly with time. However, the external driving factors are usually only available on coarse scales and the actual dependencies of the dynamic system parameters are generally unknown. Here, we propose a physics-informed machine learning model that bridges the gap between large-scale drivers and short-term dynamics ofthe power system. Integrating stochastic differential equations and artificial neural networks, we construct a probabilistic model of the power grid frequency dynamics in continental Europe. Its probabilistic prediction outperforms the daily average profile, which is an important benchmark, on a time horizon of 15 min. Using the integrated model, we identify and explain the parameters of the dynamical system from the data, which reveal their strong time-dependence and their relation to external drivers such as wind power feed-in and fast generation ramps. Finally, we generate synthetic time series from the model, which successfully reproduce central characteristics of the grid frequency such as their heavy-tailed distribution. All in all, our work emphasizes the importance of modeling power system dynamics as a stochastic nonautonomous system with both intrinsic dynamics and external drivers.  \nDOI: 10.1103/PRXEnergy.2.043003  \nI. INTRODUCTION  \nMitigation of climate change requires a comprehensive transformation of our economy and lifestyle, in particular the way we generate and utilize electric power [1,2] . Powerplants based on fossil fuels must be replaced by renewable sources such as wind and solar power, which are volatile and uncertain [3] . Various sectors are being integrated, for instance through electric heatpumps [4], introducing numerous new interdependencies and increasing system complexity. The electric power system is at the heart of this transformation. Hence, understanding risks and guaranteeing stability of the electric power system is critical amidst far-reaching challenges [5] .  \n* [d.witthaut@fz-juelich.de](d.witthaut@fz-juelich.de)  \nPublished by the American Physical Society under the terms of the Creative Commons Attribution 4 .0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.  \nPower system operation is determined by various technical, economic, and social influences and perturbations. Power generation from renewable sources is essentially determined by the weather [6,7], while the dispatch of conventional power plants is determined on various electricity markets [8] . Moreover, the load depends on the decisions and actions of millions of consumers [9] . As the power grid does not store electric energy, generation and load must be balanced at all times. On long time scales of hours, this is achieved by trading on electricity markets [10] . On short time scales of seconds and minutes, several layers of control reserves balance the grid, e.g., to counteract unfo","cbCailk4qBLM0LRW","https://ap.wps.com/l/cbCailk4qBLM0LRW","pdf",1917182,1,20,"English","en",105,"# Introduction\n## Modeling power system frequency dynamics as stochastic nonautonomous systems\n## Stochastic models and limitations of available driving data","[{\"question\":\"Why is power grid frequency dynamics difficult to model?\",\"answer\":\"It is shaped by many technical, economic, and social influences, and the external driving factors are usually available only at coarse scales while the true parameter dependencies are often unknown.\"},{\"question\":\"What is the main idea of the proposed method?\",\"answer\":\"The framework combines stochastic differential equations with artificial neural networks to create a probabilistic, physics-informed model linking large-scale drivers to short-term grid frequency dynamics.\"},{\"question\":\"How is the model evaluated and what does it achieve?\",\"answer\":\"Its probabilistic predictions outperform the daily average benchmark over a 15-minute horizon, and the integrated model allows identifying time-dependent parameters related to drivers such as wind feed-in and fast generation ramps.\"}]","Physics-Informed Machine Learning for Power Grid Frequency Modeling | PDF",1785895721,50,{"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},"physics-informed-machine-learning-for-power-grid-frequency-modeling","",{"@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/physics-informed-machine-learning-for-power-grid-frequency-modeling/124971/",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","2026-08-05",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 power grid frequency dynamics difficult to model?","Question",{"text":75,"@type":76},"It is shaped by many technical, economic, and social influences, and the external driving factors are usually available only at coarse scales while the true parameter dependencies are often unknown.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the main idea of the proposed method?",{"text":80,"@type":76},"The framework combines stochastic differential equations with artificial neural networks to create a probabilistic, physics-informed model linking large-scale drivers to short-term grid frequency dynamics.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the model evaluated and what does it achieve?",{"text":84,"@type":76},"Its probabilistic predictions outperform the daily average benchmark over a 15-minute horizon, and the integrated model allows identifying time-dependent parameters related to drivers such as wind feed-in and fast generation ramps.","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},[93,97,101,105,110,114,119,122,126,129,133],{"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":29,"slug":113},6,"Technology","technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":21,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":21,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":106,"slug":136},19,"General","general"]