Solution of Linear Time Periodic Dynamical System with Appliction to Electrical Machines Using Chebyshev Polynomial Approch

AbstractThe magnetic field within electrical machines causes an interaction between the electrical and mechanical dynamics of the system. A unified rotor dynamic model can be developed combining the electrical dynamics and the mechanical dynamics. The electromagnetic behaviour of an electrical machine is a linear time-dependent model which is then easily coupled with a linear model for the mechanical dynamics. The developed coupled model is a linear time periodic system. This work uses the Chebyshev polynomial for solving LTP system. The solution to Mathieu equation is presented before solving dynamics of electrical machines. The Chebyshev polynomial method has been developed and tested for Mathieu equation. Later the method has been applied for electrical machine. The obtained results also compared with modified Runge-Kutta that is available in MATLABTM software package