THESIS TITLE: Solving Non – Linear Ode of Power Flow Mode Using Lie Symmetry Analysis

STUDENT’S NAME: Rhoda Machuma Mamuli

SUPERVISORS NAMES   

1. Vincent Marani
2. Micheal Oduor

ABSTRACT

Symmetry of a differential equation is a transformation that maps any solution to another
solution of the system. In Lie’s 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’, y”, y”’ ) = 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.