The conventional approach to detect partial discharges (PDs) relies on discrimination of PDs from the applied voltage, based on differences in their respective frequency contents. This is practically realised by means of a capacitive decoupling principle. However, due to the increased use of power electronic devices, voltages that appear in the system can contain high frequency components, which limit the possibility for the discrimination and make the use of the standard method for PD detection difficult or even impossible. It is therefore necessary to find other features of PDs that could be used in addition. One example is the statistical time distribution of PD appearance. In this study, the statistical time distribution of PD appearance was investigated for semi-square voltages with exponentially rising fronts. The test object was a needle in air, to which positive voltage waveforms with different rise times and voltage levels were applied. Voltages up to 10 kV with rise times of 60 Its 260 mu s were used. A conventional PD decoupling circuit followed by on-line signal processing was employed for the detection. To quantify the occurrence of PDs, a concept of "first discharge rate" was introduced and its dependence on steepness of the applied voltage was investigated. For most combinations of voltage level and rise time, a considerable number of PDs appeared during the voltage rise. This is important to consider when designing PD measurement techniques for semi-square voltages.