[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-128805-105":59,"doc-detail-128805-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","a-comparative-analysis-of-machine-learning-based-power-flow-study-with-custom-made-open-source-python-codes","A Comparative Analysis of Machine Learning Based Power Flow Study with Custom Made Open Source Python Codes","","Power flow analysis determines steady-state operating conditions of power grids by solving nonlinear algebraic equations, traditionally using iterative numerical methods that can be computationally intensive, time/space expensive, and susceptible to convergence issues. This paper presents a comprehensive comparative analysis of multiple machine learning algorithms for solving power flow equations. Experiments on IEEE 3-bus and IEEE 118-bus networks are conducted using custom-developed, open-source Python codes, with performance evaluated using mean square error and related metrics, highlighting strengths and limitations.",{"@graph":69,"@context":122},[70,84,105],{"@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/a-comparative-analysis-of-machine-learning-based-power-flow-study-with-custom-made-open-source-python-codes/128805/",{"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/a-comparative-analysis-of-machine-learning-based-power-flow-study-with-custom-made-open-source-python-codes/128805.png","ImageObject",300,407,{"name":92,"@type":93},"Violet","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-18","2026-08-06",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why do traditional power flow methods face limitations?","Question",{"text":112,"@type":113},"They rely on iterative numerical techniques that can be computationally intensive and may suffer from convergence problems, including high time and space complexity due to Jacobian formation and matrix inversions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which machine learning algorithms are compared for power flow equation solving?",{"text":117,"@type":113},"The study compares Linear Regression, Decision Tree Regression, Random Forest, K-Nearest Neighbours, and Artificial Neural Networks, using the authors’ custom-developed Python codes.",{"name":119,"@type":110,"acceptedAnswer":120},"How is performance evaluated in the paper?",{"text":121,"@type":113},"Performance is discussed using mean square error (MSE) and the R² value as metrics, assessing strengths and weaknesses of each ML technique.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},128805,1786003594,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","A Comparative Analysis of Machine Learning Based Power Flow Study with Custom Made Open  \nSource Python Codes  \nBilal Ahmad  Power Systems Reseach Group Department of Electronic Engineering Royal Holloway University of London London, United Kingdom [bilal.ahmad.2023@live.rhul.ac.uk](bilal.ahmad.2023@live.rhul.ac.uk)  \nOnyemaNduka  Power Systems Reseach Group Department of Electronic Engineering Royal Holloway University of London London, United Kingdom [onyema.nduka@rhul.ac.uk](onyema.nduka@rhul.ac.uk)  \nAbstract— Power flow analysis is a cornerstone of power system planning and operation, involving the solution of nonlinear equations to determine the steady-state operating conditions of the power grid. Traditionally, these equations are solved using iterative methods, which, despite their accuracy, are computationally intensive, may not converge to the solution and involve high time and space complexity. The challenges above can be overcome using Machine Learning (ML). Consequently, in this paper, a comprehensive comparative analysis of different ML algorithms developed for solving the power flow equations are presented. Experimental simulations for IEEE 3-bus and IEEE 118-bus networks have been conducted using custom-developed, open-source Python codes and technical insights are highlighted.  \nKeywords—Machine Learning, Power Flow, Power System, Numerical techniques.  \nI. INTRODUCTION  \nPower flow analysis is a computational method which uses numerical technique to determine the steady state operating characteristics of a given power system. The line information and the bus information are required for the power flow analysis to determine the operating characteristics during steady state. A set of simultaneous nonlinear algebraic power equations are usually solved for unknown values for each bus depending on the type of the bus namely slack, PV and PQ bus. The power flow analysis requires modelling the components of the power system, developing the power flow equations and solving the developed equations using the numerical techniques. These numerical techniques can solve these nonlinear equations but have some disadvantages like convergence issues and time complexity issues. The solution of these equations is computationally very complex also since it includes the formation of Jacobian matrix and matrix inversions[1] .  \nDue to recent developments in modern power networks such as the integration of Renewable Energy Sources (RES) and the Low Carbon Technologies (LCT)[2-4], it becomes a difficult task to solve these simultaneous nonlinear equations. It can be inferred from the literature that various techniques have been applied to simplify the power flow solution. [5] discusses Newtons method for faster solution than Gauss Seidel. A probabilistic method of power flow was discussed in [6]. A fast Newton Raphson method using sparse technique and parallel programming was discussed in [7] . The advent of modern computational techniques, such as machine learning (ML), has greatly facilitated the prediction of power system values with high accuracy and precision. This approach eliminates the need to repeatedly solve complex equations, thereby reducing computational burden and removing the reliance on iterative processes. The application of machine  \nlearning algorithms in power systems has garnered significant attention in recent years. For example, ML has been employed to improve power quality [8], predict outages [9], and forecast power grid failures [10] . These studies highlight the growing role of ML in enhancing the efficiency and reliability of power system operations. One of the first papers published on power flow analysis was in 1999 which used neural network to predict the power flow [11] . An improved model was presented in [12]. A neural network model was used in [13] todo a similar analysis but for a DC power network. Since machine learning models gives predictions and not necessarily the actual solution, [14] discus","cbCaiq7RKRBFy6sG","https://ap.wps.com/l/cbCaiq7RKRBFy6sG","pdf",1881688,"English","# Introduction\n## Power flow formulation and challenges\n## Motivation for machine learning approaches\n# Mathematical Modeling\n## Power flow formulations\n## Nodal power equations\n# Dataset Preparation\n## Training data preparation\n# Results\n## IEEE 3-bus network results\n## IEEE 118-bus network results\n# Conclusions","[{\"question\":\"Why do traditional power flow methods face limitations?\",\"answer\":\"They rely on iterative numerical techniques that can be computationally intensive and may suffer from convergence problems, including high time and space complexity due to Jacobian formation and matrix inversions.\"},{\"question\":\"Which machine learning algorithms are compared for power flow equation solving?\",\"answer\":\"The study compares Linear Regression, Decision Tree Regression, Random Forest, K-Nearest Neighbours, and Artificial Neural Networks, using the authors’ custom-developed Python codes.\"},{\"question\":\"How is performance evaluated in the paper?\",\"answer\":\"Performance is discussed using mean square error (MSE) and the R² value as metrics, assessing strengths and weaknesses of each ML technique.\"}]","A Comparative Analysis of Machine Learning Based Power Flow Study with Custom Made Open Source Python Codes | PDF",15]