The transition phase from glow to streamer corona is of significant importance for the evaluation of leader discharges initiated from ultra-high voltage power transmission lines under thunderstorms. In order to study the condition required for streamer inception from a glow-corona generating wire, the continuity equations for electrons, positive ions and negative ions coupled with Poisson's equation are solved. The calculations are performed for a wire-cylinder coaxial configuration in one dimension. The analysis is performed by considering the generation of glow corona under a DC electric field, followed by the transition to a streamer-like ionization wave under a fast-changing electric field ramp. Thus, the critical rate of rise of the applied voltage on the wire surface required for streamer-like structures to initiate in the presence of a stable glow corona is evaluated for different radii and DC voltages.