# Study of Partial Discharge Inception Voltage in Inverter Fed Electric Motor Insulation Systems
## 2 Literature Review
### Pulse Width  
Generally speaking, researchers agree that a longer pulse width increases the probability of a starting electron occurring, as long as the applied voltage is maintained above the inception voltage. Once the ignition voltage is reached, if the pulse is maintained for a long time, there is more time to obtain a critical initial electron number, favouring PD  
Figure 5: Simplified sketch of the effect of rise time on PDIV. activity [48]. However, the effect of the pulse width on the measurement and definition of the PDIV is not so clear. Some authors state that the PDIV is not dependent on the pulse width as long as the rise time is sufficiently high [52]. [PERSON] et al. [52] concluded that there is no effect on the PDIV for unipolar 50 Hz and 300 ns rise time pulse in a range of 0.5-50 \(\upmu\)s pulse width. This is similar to in [54], where it is perceived as having an almost constant but slightly increasing effect on the PDIV with a pulse width for unipolar (positive and negative) 2.5 kHz and a 160 ns rise time pulse in a pulse width range of 40-100 \(\upmu\)s (duty rate 10-25%). The slight difference in the results is mainly related to the measurement uncertainty. At a lower pulse width, the variance of the results is higher, due to the higher impact of the firing electron delay. On the contrary, [PERSON] et al. [43] noticed a dependency of the PDIV on pulse width, with a 1000 ns rise time for unipolar waveform (1-100 kHz). They came to the conclusion that the PDIV is reduced with an increase in the pulse width (2-800 \(\upmu\)s), following, approximately, an inverse power law. The authors deduced that, for a defined rise time, the number of initial electrons was maintained for different pulse widths. For a longer pulse width, the electrons can be generated within a longer period (as long as the applied voltage is higher than the ignition voltage), and a lower applied voltage is enough to reach the necessary number of electrons to derive a PD. Therefore, the increase in the pulse width decreases the PDIV, with a smaller effect for longer pulse widths. Similar results are presented for formed wound samples [55] and plate-point analysis [56]. Considering lower rise times, [PERSON] et al. [43] also observed the same tendency that they observed for higher rise times (1000 ns) in the range of a 100-150 ns rise times. However, with a 70 ns rise time, [PERSON] et al. [57] identified an increasing effect of PDIV (9%), with a pulse width in the range of 1000-9000 \(\upmu\)s for unipolar 100 Hz waveforms. The authors explained that the increase in PDIV is mainly related to a decrease in the nonconduction duration (when the voltage is 0 V) over a period of time (9000 and 1000 \(\upmu\)s nonconducting duration for 1000 and 9000 \(\upmu\)s pulse widths, respectively). The application of the voltage generates the displacement of the surface charges, creating an electric field in opposition to the applied electric field and reducing the total electric field. During nonconduction periods, these charges are redistributed. When the nonconducting time slot is low compared to the exposure time, only a fraction of charges are redistributed, resulting in a charge accumulation, which decreases the total electric field. The PDIV can be defined at a higher voltage level (the case of 9000 \(\upmu\)s pulse width and 1000 \(\upmu\)s nonconducting duration). When the authors developed the same analysis with a 1 kHz waveform (pulse width 100-900 \(\upmu\)s), the influence of the pulse width on the PDIV was reduced. In these cases, the nonconducting duration was higher than the pulse width, leading to a lower influence of the charge accumulation between consequent pulse widths. This would agree with the results reported in [52; 54] as the nonconducting interval of the different pulses are high compared to the voltage exposure so that the resulting PDIV remains practically constant.