Francis turbines may experience cavitation surge phenomenon in the draft tube inducing large pressure fluctuations which can jeopardize the hydraulic system integrity. To predict this phenomenon, a one-dimensional draft tube model is derived from flow momentum and continuity equations including the convective terms that are not considered in the existing models. A parametric analysis of the draft tube model is carried out to investigate the influence of parameters on the cavitation surge onset identified by the hydraulic system stability. It is shown that convective terms have a stabilizing influence modifying stability limit prediction driven by the divergent geometry modelling of the draft tube.