Doubly fed induction machine state variables model and dynamic response

A state variables model in terms of d-q component displacements is deduced from linearized complex variable equations describing small-signal dynamic performance of the doubly fed induction machine. A state variables model in terms of magnitude and phase displacements of both stator and rotor voltages is deduced and studied. Transfer functions are also described. Study of the dynamics shows that the regions of instability are influenced by the variations of speed, of RMS value, and of phase angle of rotor applied voltage. This state variables model in polar coordinates eliminates the computations for the intermediate d-q components