A Study of the Lyapunov Stability of an Self-Excited Induction Generator

The self-excited induction generators (SEIGs) can provide attractive renewable energy sources. Since it can be used in an open-loop fashion which includes no control closed-loop, its inherent stability can be counted on to allow operation over a wide range of operating conditions. Unlike classical arguments based on transient and steady-state analysis, it is proposed rigorous holistic analytical stability arguments based on the full nonlinear transient state-space model of a SEIG under two-phase stationary reference frame using dynamical systems theory. The conditions for critical transient stability of the unloaded SEIG are obtained in the sense of Lyapunov. Analytic formulas from the limit cycle conditions give the values of the range of capacitance, the range of rotor speed and the stator frequency for self-excitation. Analytic formulas from steady-state conditions give all the steady-state parameter and state values. Thus, the analytical results yield a set of simple and universal analytic formulas that can predict and evaluate the transient and steady-state stability characteristics of the SEIG. Good agreement between the experimental results and computed results validates the analytical results.