Lyapunov stability analysis for self-excitation of induction generators

Based on Lyapunov stability theory, a holistic analysis approach is proposed for self-excited induction generator under no-load in the stationary reference frame with the transient mathematic model. Through analysis for initial transient states, a sufficient condition is fixed to be the limit cycle. The analytic formulas of the stator frequency, critical excitation capacitance and critical rotor speed are thus obtained. The self-excitation build-up can then be judged. Good agreement between measured values and calculated values verifies accuracy and validity of the critical analytic formulas, showing generality and engineering application value.