Purpose This paper aims to apply grey wolf optimizer (GWO) algorithm for steady state analysis of self-excited induction generators (SEIGs) supplying isolated loads. Design/methodology/approach Taking the equivalent circuit of SEIG, the impedances representing the stator, rotor and the connected load are reduced to a single loop impedance in terms of the unknown frequency, magnetizing reactance and core loss resistance for the given rotor speed. This loop impedance is taken as the objective function and minimized using GWO to solve for the unknown parameters. By including the value of the desired voltage as a constraint, the formulated objective function is also extended for estimating the required excitation capacitance. Findings The experimental results obtained on a three phase 415 V, 3.5 kW SEIG and the corresponding predetermined performance characteristics agree closely, thereby validating the proposed GWO method. Moreover, a comparative study of GWO with genetic algorithm and particle swarm optimization techniques reveals that GWO exhibits much quicker convergence of the objective function. Originality/value The important contributions of this paper are as follows: for the first time, GWO has been introduced for the SEIG performance predetermination and computation of the excitation capacitance for attaining the desired terminal voltage for the given load and speed; the predicted performance accuracy is improved by considering the variable core loss of the SEIG; and GWO does not require derivations of lengthy equations for calculating the SEIG performance.