# Study of Partial Discharge Inception Voltage in Inverter Fed Electric Motor Insulation Systems
## 2 Literature Review
### Switching Frequency
It is noticed that peak PDIV increases with high overshoot, similar to in the previously mentioned studies [26; 45; 54]. In this case, however, peak PDIV is further increased for lower rise times, despite having a similar overshoot of higher rise time waveforms. It can be said that not only does the overshoot level influence the peak PDIV, but also the rise time. For the same peak voltage level, the higher the rise time, the higher the discharge generation probability. The time the voltage is maintained above the inception value is higher, increasing the starting electron availability. Hence, the studies concluded that the PDIV increases with a decrease in rise time due to the characteristics in the time range of the inverter surge voltage. Moving to conclusion (2), several authors conducted PDIV measurements without or with an inconsiderable overshoot (<10%) in order to separate the impact of the rise time from the overshoot [43; 47]. [PERSON] et al. [47] showed that the PDIV (measured in peak) is reduced by 28% if a square unipolar positive voltage with a rise time of 150 ns is used instead of a 60 Hz sinusoidal waveform. Moreover, by decreasing the rise time from 150 ns to 60 ns, the PDIV is decreased by 21%. The study concluded that the AC PD test does not correctly evaluate the insulation capability of electrical apparatus subjected to  
Figure 4: Relationship between PDIV peak and DC as a function of the voltage overshoot based on the literature results ([PERSON] et al. [45], [PERSON] et al. [26], and [PERSON] et al. [54]). impulse voltage stress. Similarly, the authors of [43] stated that the DC PDIV decreases by 23-38% when the rise time of a unipolar waveform is decreased from 1000 ns to 150 ns. However, its influence is not so evident in the rise time range 100-150 ns. In [26], a low rise time bipolar square waveform without overshoot (150 ns and 1%, respectively) measuring the PDIV (measured in peak and DC) results were compared with sinusoidal waveform measurements; these were found to have a negligible difference. Hence, it supports using sinusoidal waveforms to test the winding insulation. To explain how the rise time influences PDIV, the authors of [43] observed, based on the extended volume-time theory, that for different rise times, the number of electrons (\(N_{0}\)) necessary for PD to happen is stable. For a fixed pulse width, with a shorter rise time, the electron generation can start earlier, as long as the applied voltage exceeds the inception voltage. However, it must also be considered as the initial electron generation rate in the air gap and the enamel surface, which depends on the electric field. As shown in [31], the electron generation rate from the air gap and enamel surface is increased with an increase in electric field intensity and as a result of applied voltage. Moreover, the author of [43] mentions that, under different rise times, the space charge influencing the electric field may be different and could influence the electron generation rate. Therefore, not only the rise time but also the electron generation rate are important factors for the PDIV in waveforms without overshoot. Based on the theoretical explanations provided by the authors of [43], a simplified schematic representation is depicted in Figure 5. For a fixed pulse width, two rise times are represented. For a lower rise time, the ignition voltage is reached earlier and electron generation starts earlier (\(t_{01}\)). The electrons have enough time to reach a critical value and develop the PD activity. On the contrary, for a higher rise time, in addition to a later electron generation starting (\(t_{0n}\)), the generation rate is slower and, therefore, by the time critical \(N_{0}\) is achieved, the applied voltage can be at a lower level than at inception, thereby avoiding PD, and the PDIV can be set to a higher voltage level. Overall, when the PDIV is measured with high overshoot, the main factor influencing it is the overshoot level rather than the rise time.