In this paper, the comparative steady-state operating performance analysis algorithms of the stand-alone single-phase self-excited induction generator (SEIG) is presented on the basis of the two nodal admittance approaches using the per-unit frequency in addition to a new state variable de-fined by the per-unit slip frequency. The main significant features of the proposed operating circuit analysis with the per-unit slip frequency as a state variable are that the fast effective solution could be achieved with the simple mathematical computation effort. The operating performance results in the simulation of the single-phase SEIG evaluated by using the per-unit slip frequency state variable are compared with those obtained by using the per-unit frequency state variable. The comparative operating performance results provide the close agreements between two steady-state analysis performance algorithms based on the electro-mechanical equivalent circuit of the single-phase SEIG. In addition to these, the single-phase static VAR compensator; SVC composed of the thyristor controlled reactor; TCR in parallel with the fixed excitation capacitor; FC and the thyristor switched capacitor; TSC is ap-plied to regulate the generated terminal voltage of the single-phase SEIG loaded by a variable inductive passive load. The fixed gain PI controller is employed to adjust the equivalent variable excitation capacitor capacitance of the single-phase SVC.