[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120404-en":3,"doc-seo-120404-105":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},120404,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Analysis of Machine Learning Models to Approximate the Optimal Power Flow Problem - Executive Summary","Executive summary of a master’s thesis in electrical engineering addressing how machine learning can approximate and speed up the optimal power flow (OPF) problem in sustainable smart grids. The work explains OPF as a nonlinear, non-convex optimization problem with power-flow equation constraints and operational limits, then reviews artificial neural networks and related deep-learning approaches for OPF. The study focuses on direct ANN mapping of OPF variables to predicted solutions and outlines how training data are generated to cover input operating ranges.","EXECUTIVE SUMMARY OF THE THESIS  \nAnalysis of machine learning models to approximate the optimal power flow problem  \nTESI MAGISTRALE IN ELECTRICAL ENGINEERING – Sustainable Smart Grids for Energy Transition  \nAUTHOR: Nicolas Pietri  \nADVISOR: Samuele Grillo  \nACADEMIC YEAR: 2022-2023  \n1. Introduction  \nThe energetic transition that we face involves to increase the use of the electrical network and so the use of tools which manage the power system as optimal power flow (OPF) . OPF problem is anonlinear, non-convex optimization problem that optimizes the operation of an electric power system by minimizing or maximizing an objective function within power flow equations constraints and operational limits. This problem is complex and computationally challenging. We investigated the use of machine learning techniques to solve it and speed up the process. We first investigated the OPF problem. Secondly, we defined artificial neural network (ANN) . Third we made a review of the use of machine learning and more specifically deep learning to solve the OPF problem. Fourth we designed an ANN to solve the OPF problem.  \n2. Optimal power flow  \nThe OPF problem was first presented in the 1960s by Carpentier [1] however it exists a wide range of  \napplications, challenges, and requirements for OPF. The initial problem can be stated as  \nmin 􀝂(􀝔) (1)  \nWhere x are the different variables of the power system that we want to include in the problem as active/reactive power, voltage magnitude/angle… and f(x) is the objective function to minimize. The problem is also subject to constraints:  \n􀝃 (􀝔) = 0 (2)  \nℎ (􀝔) ≤ 0 (3)  \nwhere g(x) are the equalities constraints and h(x) are the inequalities constraints and x are the variables of the power system. x, f(x), g(x), h(x) vary respectively according to the states variables we want to include, the objective function we want to minimize, the equalities and inequalities we want to fulfill. f(x) can be the active generation cost [3], the non-supplied demand [4], the load curtailment costs [5], the active power losses [5], the tap changers and capacitor units [6] . Theequalities g(x), and inequalities h(x) are related to the power flow equations and the operational limits. It exists an extensive number of possibilities to define x, f(x), g(x), h(x). This point explains that we can derive different types of OPFs. The solutions we decide to focus on are the AC OPF which respects the original power flow equations  \nand the AC network model, and DC OPF which is a linearized version of AC OPF. To solve the problem, there are several solving algorithms. The solutions obtained after solving the problem can be global, local or sub-optimal.  \n3. Artificial neural networks  \nAs its name suggests, artificial neural networks are based on neural network, the output of a neuron can be computed with a forward propagation as  \n􀯡  \n􀝕 = 􀝂 (∑􀯜 =0 􀝔􀯜 ∗ 􀝓􀯜 + 􀜾) (4)  \nwhere y is the output, x a vector of inputs and w the weights associated with b a bias and f an activation function. The principle of neural network is the addition of layers connected to eachother’s successively with several neurons in each layer and this is the increase of the number of layers and neurons which allows to solve higher complex problems such as OPF. According to the input x the neural network computes the output y, this output is then compared to the expected output and the weight and bias are then updated with backward propagation:  \n􀝓 􀯡+1 = 􀝓 􀯡 − η 􀰡􀯃􀰡(􀯪􀯪) (5)  \n􀜾 􀯡+1 = 􀜾 􀯡 − η 􀰡􀯃􀰡(􀯪􀯪) (6) With J(w) the loss error between the output predicted and the output expected, b the bias, w the weight, n the corresponding batch, η the learning rate. We can mention different activation function 􀝂, and loss error function J which implies a large scope of applications and ANN models.  \n4. State of the art of machine learning applied to the solving of optimal power flow  \nThere are different kinds of use of machine learning to solve the optimal power flow p","cbCaid17vfVW7mHI","https://ap.wps.com/l/cbCaid17vfVW7mHI","pdf",740419,1,7,"English","en",105,"# Introduction\n# Optimal power flow\n# Artificial neural networks\n# State of the art of machine learning applied to solving optimal power flow","[{\"question\":\"What is the optimal power flow (OPF) problem and why is it challenging?\",\"answer\":\"OPF is an optimization problem that minimizes or maximizes an objective function while satisfying power-flow equations and operational limits. It is nonlinear and non-convex, making it computationally demanding.\"},{\"question\":\"How do artificial neural networks (ANNs) work in this context?\",\"answer\":\"ANNs compute outputs through forward propagation using inputs, weights, biases, and activation functions. Training updates weights and biases via backpropagation to minimize prediction error.\"},{\"question\":\"What machine learning approach does the thesis focus on for OPF?\",\"answer\":\"The thesis emphasizes direct mapping of OPF variables to predicted OPF solutions using an ANN, training the model on input data and corresponding OPF outputs.\"}]","Analysis of Machine Learning Models to Approximate the Optimal Power Flow Problem - Executive Summary | PDF",1785729863,18,{"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},"analysis-of-machine-learning-models-to-approximate-the-optimal-power-flow-problem-executive-summary","",{"@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/analysis-of-machine-learning-models-to-approximate-the-optimal-power-flow-problem-executive-summary/120404/",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","2026-08-03",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},"What is the optimal power flow (OPF) problem and why is it challenging?","Question",{"text":75,"@type":76},"OPF is an optimization problem that minimizes or maximizes an objective function while satisfying power-flow equations and operational limits. It is nonlinear and non-convex, making it computationally demanding.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do artificial neural networks (ANNs) work in this context?",{"text":80,"@type":76},"ANNs compute outputs through forward propagation using inputs, weights, biases, and activation functions. Training updates weights and biases via backpropagation to minimize prediction error.",{"name":82,"@type":73,"acceptedAnswer":83},"What machine learning approach does the thesis focus on for OPF?",{"text":84,"@type":76},"The thesis emphasizes direct mapping of OPF variables to predicted OPF solutions using an ANN, training the model on input data and corresponding OPF outputs.","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},[93,97,101,105,110,115,119,122,127,130,134],{"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":113,"slug":114},6,"Technology",50,"technology",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},"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":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]