A new simplified approach for the steady state analysis of self-excited induction generators employing the concepts of co-ordinate geometry

A methodology for the steady state analysis of self-excited induction generators (SEIGs) is proposed employing an approach using simple co-ordinate geometry. The equivalent circuit of the SEIG is taken and its three complex admittances, Y̅₁, Y̅₂ and Y̅₃, are considered. Using the nodal analysis of the circuit and considering the nature of the parameters involved for ensuring self-excitation of the induction machine, it is shown that a triangle can be obtained by plotting Y̅₁, Y̅₂ and Y̅₃ in the complex plane. Utilizing the well-known properties of the triangle, in a few steps, a simple equation is derived for the per unit (pu) speed, in terms of pu frequency, real part of Y̅₁ and rotor resistance. This, consequently, leads to another simple expression for the calculation of the magnetizing reactance and further processing of the performance analysis of SEIG. Thus, this proposed method does not require advanced techniques or complex calculations. The analytical results arrived at are compared with those calculated using the popularly adopted genetic algorithm technique and recently evolved binary search method and also with the values obtained experimentally on a 3-phase, 3.75 kW, 230 V delta-connected induction machine run as an SEIG. A very close agreement is seen between these three sets of results.