# Study of Partial Discharge Inception Voltage in Inverter Fed Electric Motor Insulation Systems
## 2 Literature Review
### Switching Frequency
Finally, they concluded that the average amplitude of the overvoltage changed with the increase in the frequency, even maintaining the peak voltage. Thus, the probability of developing the PD is higher and the RPDIV can be detected in lower voltage levels at increasing voltage tests (generally used to determine PDIV and RPDIV). To summarise, the PDIV is not affected by the switching frequency, as it is defined when the first PD is developed. The RPDIV, however, is affected by the enhancement of free electrons due to charge accumulation at frequencies below 10 kHz, which decreases the RPDIV. Moreover, the overshoot average amplitude also increases the probability of developing the PD in switching frequencies up to 75-100 kHz. Finally, over 100 kHz, the RPDIV tends to stabilise. There is no agreement about the effect of the rise time on the PDIV in the literature. There are two main conclusions: (1) the PDIV is not affected by the rise time, but by the overshoot and its characteristics, which are enhanced at low rise times. (2) The PDIV is decreased with a decrease in the rise time when there is an absence or low overshoot. Referring to conclusion (1), several authors agree that the rise time does not affect the PDIV, but the overshoot resulting from the low rise time used in WBG devices is the main factor affecting the PDIV [26; 45; 52; 54; 46]. Therefore, different results are obtained depending on whether the PDIV definition is determined by selecting DC voltage or peak voltage (explained in Figure 2). The results reported in the literature for PDIV peak and PDIV DC are summarised in Figure 3. The PDIV values are normalised to the highest rise time (which is also the lowest overshoot) in each study. In Figure 3 the, peak and DC PDIV are collected depending on the rise time and overshoot percentage. Focusing on Figure 3a, it can be seen that, independent of the waveform and  
Figure 3: Bibliography results ([PERSON] et al. [45], [PERSON] et al. [26], and [PERSON] et al. [54]) of (**a**) PDIV peak vs. rise time; (**b**) PDIV DC vs. rise time; (**c**) PDIV peak vs. overshoot; (**d**) PDIV DC vs. overshoot. its polarity (bipolar or unipolar positive and negative), for a rise time above 20 ns, constant peak PDIV values were obtained. On the contrary, for lower rise times, there was a general increasing effect. For some researchers, this inflexion point was below 20 ns [45], whereas for others it was below 15 ns [26]. Moving to Figure 3b, the DC PDIV showed a similar effect but with a decreasing tendency. The change from a constant to an increasing/decreasing effect of the PDIV comes with a considerable increase in overvoltage. The relationship between the PDIV and the overshoot is depicted in Figure 3c,d. At low overshoots, there is no considerable effect on the peak and DC PDIV, as there is at high overshoots, which correspond to 7 ns [26], 20 ns, [45] and 80 ns [54] rise times. Figure 4 summarises the relationship between the peak and DC PDIV, depending on the overshoot. A linear relationship is evident. The difference between the peak and DC PDIV value increased with the waveform overshoot. After observing the impact of overshoot on the PDIV, [PERSON] et al. [31] proposed an extended volume-time theory based on the Streamer discharge mechanism, which deals with the generation probability of starting electrons considering temporal and spacing changes in electric field distribution (Section 2.2.4). With this theory, the PDIV can be discussed as the sum of starting electrons generated and is defined as the voltage level where the generation probability exceeds 50%. Accordingly, with surge voltages, the available starting electrons' quantity is the dominant factor used to define the PDIV. Several waveforms with rise times between 60 and 3000 ns and overshoot between 150% and 180% are analysed in [31] to validate the theory. It is worth mentioning that the highest overshoot corresponds to the lowest rise time, whereas the lowest overshoot corresponds to the highest rise time.