Ordinary differential equations and the power sensitivity model for the synchronous machine-infinite bus system

• Grant number: 14/19392-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): December 01, 2014
• Effective date (End): November 30, 2015
• Field of knowledge: Engineering - Electrical Engineering - Power Systems
• Principal Investigator: Francisco Villarreal Alvarado
• Grantee: Edson Fernandes Mendes Junior
• 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) are non homogeneous linear with constant coefficients. The part non homogeneous is about the functions of input (or forcing), these being the classic Dirac delta "function" (impulse function), the step function, ramp function (speed step) or 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 the power sensitivity model for the synchronous machine-infinite bus system, a model which is represented by a system of first order ODEs (system state equations) and widely used to study the small signal stability of the electric power systems. The system of EDOs considered will be solved analytically and numerically and after there will be done an analysis of the mathematical solution obtained taking into account the expectations of the real problem. For the analytical resolutions of the considered DOEs the Laplace transform techniques will be used in addition to usual methods for solving DOEs. 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.