Ordinary differential equations in the stability analysis to small disturbance of synchronous generator

• Grant number: 14/19425-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2014
• End date: November 30, 2015
• Field of knowledge: Engineering - Electrical Engineering - Power Systems
• Principal Investigator: Francisco Villarreal Alvarado
• Grantee: Hyago Ramom Martins Silva
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

Among the main classes of ordinary differential equations (ODEs), non homogeneous linear with constant coefficients are. The non homogeneous part is the functions of input (or forcing), these being the classic Dirac delta "function" (impulse function), the step function, ramp function (speed step) and the parable function (acceleration step) . In this Scientific Initiation Project (SIP), it is proposed the study of ODEs that model physical phenomena. Many of these phenomena are modeled by ODEs of second order or first order ODEs systems, such as electrical circuits formed by a series (or parallel) association of passive elements resistor, inductor and capacitor. This SIP should be studied equation oscillation of synchronous generator, which is a second order ODEs widely used to study the small signal stability of the electric power systems. The ODE considered will be solved analytically and numerically and after an analysis of the mathematical solution obtained must be done taking into account the expectations of the real problem. For analytical resolutions of the considered ODEs the Laplace transform techniques will be used in addition to usual methods for solving ODEs. The analytical solution must be implemented computationally to perform simulations and thus it is able to analyze the small signal stability of the electric power systems.