In this paper a simple technique required in the analysis of performance of short-shunt and long-shunt self-excited induction generators is presented. A novel procedure is used to obtain a second-degree polynomial for the operating frequency of a loaded generator, instead of the more complex ninth-degree polynomial which is normally used in such situations. Explicit analytical expressions for the frequency in terms of other parameters of operation are derived. Using these expressions no numerical solutions are required. The generator characteristics can be directly calculated. The results obtained from using the propose method were found to be almost identical with those obtained when numerical solution methods are applied to the ninth-degree polynomial of the frequency.