Time Domain Transfer Function of the Induction Motor

Small signal stability of electrical machines at frequency domain has been shown by toque coefficients and eigenvalue of motional impedance matrix in state space form. The relation of damping, synchronizing and total synchronizing torque coefficients with the eigenvalue or the roots of the characteristic equation of the perturbed machine shows that the instability occurs at 2 different modes. Static mode represented by real root at over load condition, and dynamic mode represented by complex root at the condition when the total synchronizing coefficient exhibits zero value within the negative range of the damping torque coefficient. However, small signal instability details at time domain are not given in the literatures. This paper discusses with figures the time domain signals of the induction motor perturbation variables under hunting condition, and presents the differences observed between inverse Laplace transform and Fourier transform in time domain response, based on the transform of the transfer function from the frequency domain, The figures demonstrate and confirm the machine small signal stability performance given in frequency domain.