Analytic Calculation for Stator Frequency of Self-Excited Induction Generators With Routh Criterion

With regard to isolated self-excited induction generators (SEIGs) excited by capacitance parallel with load, the state-space transient mathematic model is derived based on the transient equivalent circuits of SEIG under the two-phase stationary reference frame. Thus the characteristic equation is obtained. The Routh table is attained according to the standard form in terms of descending order for complex operator s. Analysis for the system performed by the Routh Criterion gives the critical condition for the operation of loaded SEIG that there exists a line with all being zero. The derivation and analysis for the critical condition successively gives the analytic equation and analytic formulas of stator frequency in terms of capacitance, rotor speed and magnetizing induction. So the critical values of any one among the three parameters and stator frequency can be more easily attained under given the other two parameters. Good agreement between computed and theoretical results on the SEIG prototype verifies correctness and validity of theoretical analysis and the analytic formulas for loaded SEIG systems which are initiated through analysis by the Routh Criterion. The conclusion illustrates practicability of the approach in the paper and owes referenced values in engineering. So it is applicable to more complex systems.