{"id":3850,"date":"2023-12-05T06:42:03","date_gmt":"2023-12-05T06:42:03","guid":{"rendered":"https:\/\/sgs.kibu.ac.ke\/?p=3850"},"modified":"2025-11-21T04:52:56","modified_gmt":"2025-11-21T04:52:56","slug":"solving-non-linear-ode-of-power-flow-mode-using-lie-symmetry-analysis","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/sgs\/solving-non-linear-ode-of-power-flow-mode-using-lie-symmetry-analysis\/","title":{"rendered":"Solving Non \u2013 Linear Ode of Power Flow Mode Using Lie Symmetry Analysis"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"3850\" class=\"elementor elementor-3850\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5828c0b5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5828c0b5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5e819371\" data-id=\"5e819371\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-52dc1f07 elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"52dc1f07\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-4614975a\" data-id=\"4614975a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-5420579a\" data-id=\"5420579a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-36b9c00c elementor-section-height-min-height elementor-section-items-stretch elementor-section-boxed elementor-section-height-default\" data-id=\"36b9c00c\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-11a2d0d7\" data-id=\"11a2d0d7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-1caf4d9d elementor-section-height-min-height elementor-section-content-middle elementor-section-boxed elementor-section-height-default\" data-id=\"1caf4d9d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6898e520\" data-id=\"6898e520\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-34af1b92 elementor-widget elementor-widget-heading\" data-id=\"34af1b92\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Student\u2019s Name: <br>\nRhoda Machuma Mamuli<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-605b9ba4\" data-id=\"605b9ba4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6a9f4ec3 elementor-widget elementor-widget-heading\" data-id=\"6a9f4ec3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Supervisors:<br>\n1. Vincent Marani<br>\n2. Micheal Oduor<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-679fbac5\" data-id=\"679fbac5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c7df3de elementor-widget elementor-widget-heading\" data-id=\"c7df3de\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Master of Science Applied Mathematics<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1b163251 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1b163251\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-256a0dfc\" data-id=\"256a0dfc\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3087e8c3 elementor-widget elementor-widget-spacer\" data-id=\"3087e8c3\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-69d89e00\" data-id=\"69d89e00\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-206d1923 elementor-section-height-min-height elementor-section-boxed elementor-section-height-default\" data-id=\"206d1923\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-4f54013b\" data-id=\"4f54013b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5c0e4c12 elementor-widget elementor-widget-heading\" data-id=\"5c0e4c12\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">ABSTRACT<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1d16ec0 elementor-widget elementor-widget-text-editor\" data-id=\"1d16ec0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Symmetry of a differential equation is a transformation that maps any solution to another solution of the system. In Lie\u2019s framework such transformations are groups that depend on continuous parameters and consist of point transformations or point symmetries acting on the systems space of independent and dependent variables. Lie groups and its infinitesimal generators can be naturally prolonged to act on the space of independent variables. In this thesis, we present Lie symmetry analysis to solve a non-linear ordinary differential equation of an electric power flow model. The model is a nonlinear ODE of the form F (x, y, y\u2019, y\u201d, y\u201d\u2019 ) = 0. The model was developed to determine power loses over transmission lines. With the aid of the model, it is possible to determine current in transmission lines. Therefore, in our study we have used Lie Symmetry analysis approach to transform the equation by subjecting it to extension generators to obtain determining equations, to reduce the order of the equation to lower order and to find the general solution of the third order nonlinear ordinary differential equation. We exploited the use of prolongations, infinitesimal generators, variation of symmetries, adjoint symmetries, invariant transformation problems and integrating factors. The result is of great significance in the field of Mathematics, Engineering and Mechanics.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-43226030 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"43226030\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5fca3c3f\" data-id=\"5fca3c3f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Student\u2019s Name: Rhoda Machuma Mamuli Supervisors: 1. Vincent Marani 2. Micheal Oduor Master of Science Applied Mathematics ABSTRACT Symmetry of a differential equation is a transformation that maps any solution to another solution of the system. In Lie\u2019s framework such transformations are groups that depend on continuous parameters and consist of point transformations or point [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-3850","post","type-post","status-publish","format-standard","hentry","category-theses"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Solving Non \u2013 Linear Ode of Power Flow Mode Using Lie Symmetry Analysis - School of Graduate Studies<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kibu.ac.ke\/sgs\/solving-non-linear-ode-of-power-flow-mode-using-lie-symmetry-analysis\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solving Non \u2013 Linear Ode of Power Flow Mode Using Lie Symmetry Analysis - School of Graduate Studies\" \/>\n<meta property=\"og:description\" content=\"Student\u2019s Name: Rhoda Machuma Mamuli Supervisors: 1. Vincent Marani 2. Micheal Oduor Master of Science Applied Mathematics ABSTRACT Symmetry of a differential equation is a transformation that maps any solution to another solution of the system. 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Vincent Marani 2. Micheal Oduor Master of Science Applied Mathematics ABSTRACT Symmetry of a differential equation is a transformation that maps any solution to another solution of the system. 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