# Study of Partial Discharge Inception Voltage in Inverter Fed Electric Motor Insulation Systems
## 2 Literature Review
### Switching Frequency  
Different conclusions are obtained regarding the effect of the switching frequency on the inception voltage. On the one hand, in [26; 46] it is stated that, for a square waveform with constant rise time (8 ns), the PDIV is independent of the switching frequency in the range of 10-100 kHz as long as the real permittivity of the insulation material is as well. If real permittivity depends on the frequency, above a critical frequency, which depends on the material, the dipole orientation will not occur, resulting in a dielectric loss peak and a decrease in the real permittivity. This could increase the PDIV [38]. Moreover, the heat generated by dielectric losses could increase the temperature, reducing the air density and, therefore, the PDIV. As a result, in case the fundamental frequency and the harmonic distribution of the waveform are above the mentioned critical frequency, the PDIV could be affected by the switching frequency. [PERSON] et al. [47] came to the same conclusion. They detected that the PDIV slightly increases by about 6% with an increase in the frequency in the range of 1-10 kHz for a square waveform with a fixed rise time (100 ns) and duty cycle (tested at 0.2, 0.5, and 0.8 duty cycles). Nonetheless, they assumed that the effect of the frequency on the PDIV is negligible. [PERSON] et al. [37] did not perceive any effect of the frequency on PDIV in a range of 20-200 kHz for sinusoidal waveforms at different humidity conditions. On the other hand, several authors confirmed that the frequency (2-2000 Hz) can affect the PDIV if a repetitive waveform is considered, that is to say, RPDIV. In [48; 49], it is mentioned that the larger the frequency, the stronger the influence of charges left by the previous discharge (i.e., less time to relieve the charge). This could help the extraction of electrons, leading to the discharge occurring at a lower voltage level since the time lag (the time necessary to generate a free electron once the ignition voltage is reached) is reduced [50]. The increase in free electrons due to the charge accumulation is presented in discharges occurring in the same half-cycle (homo-discharges) [51]. The RPDIV follows the definition of homo-discharge, as subsequent PDs in the same half cycle are necessary. This is demonstrated in [52], where PD patterns are shown for 100 Hz and 1 kHz. For high frequency, charge promotes PD events reaching high PD magnitudes, whereas, at low frequency, the PD magnitudes are lower, especially in the positive flank, due to the absence of a charge. Additionally, [PERSON] et al. [19] conducted PD experiments under repetitive impulse voltages at higher voltage values than PDIV. The authors observed that, for higher frequencies, the PD activity was triggered earlier during the rising edge. It is concluded that this effect is caused by the charge accumulation left by the previous discharges, similar to [48; 49]. Similarly, in [28; 53], it is observed that, for unipolar PWM waveform, the RPDIV (defined by the peak-to-peak impulse voltage) decreases with an increase in the switching frequency in the range of 20-200 kHz, being stabilised at around 75-100 kHz. It is mentioned that, above 10 kHz, the memory effect can be considered perfect, so its effect at higher frequencies should be constant. Aside from the charge accumulation, these researchers studied two main factors to explain this effect, the relative permittivity of the insulation and the oscillation of the wave forms in the frequency range used. After measuring the relative permittivity at different frequencies, they concluded that its variation is not considerable enough to have an effect on the RPDIV. Alternatively, they examined the instantaneous frequency spectrum of the pulse. They found that the largest frequency content corresponds to the overvoltage and does not change for different switching frequencies. Consequently, they confirmed that the RPDIV is not dependent on the different instantaneous frequency contents of the applied voltage overvoltage.