Abstract In this paper, a systematic method that predicts limit cycle oscillations in a hydroelectric system with governor deadband on the parameter plane is presented. A new technique for constructing limit cycle loci on this plane is also proposed. This approach is based on the characteristic equation as well as the describing function approximation and avoids the use of derivation and separation of stability equations. For each family of solution loci in the parameter plane, only two integrations are needed. The stability of the limit cycle can also be determined easily from the plane using the gradient approach. Finally, the proposed method is employed to investigate the influence that several variations in the modeling of a hydro system may have on the existence of limit cycles. The results from this study will shed some light on the selection of automatic generation control (AGC) parameters as a remedy for this phenomenon.