# Study of Partial Discharge Inception Voltage in Inverter Fed Electric Motor Insulation Systems
## 2 Literature Review
### Temperature
#### 2.1.2 Electrical Factors  
In the following sections, the effect of the main electrical waveform properties on the PDIV is discussed: waveform and polarity, frequency, rise time, and pulse width. The conditions necessary to develop PD activity are two key factors for the comprehension of the following sections: (1) the applied voltage must be higher than the ignition/inception voltage and (2) a free electron should be available [26] or a critical number of electrons should be reached [43]. It is worth mentioning that, when the following lines refer to a free electron, the Townsend discharge mechanism is considered. When a critical number of electrons is mentioned, the Streamer mechanism is considered. The differentiation is based on what the author of the corresponding article uses. More information regarding the Townsend and Streamer mechanisms is provided in Section 2.2.1. Waveform and Polarity  
The differences between the use of sinusoidal and square waveforms, either unipolar or bipolar, to define the PDIV of twisted pairs have been studied by different authors. It is worth mentioning that, in the studied cases, the PDIV is defined by increasing the voltage at a constant rate until the PD activity is detected. In [26], after observing PDIV experimental data for sinusoidal and bipolar square waveforms, it is concluded that only the peak value of the applied voltage is important for the definition of the PDIV, whereas the waveform does not affect the PDIV. It is explained that an error in the definition of the PDIV could arise when measuring using impulse bipolar voltages due to overshooting. Figure 2 depicts a situation where the peak voltage exceeds the ignition voltage (\(V_{\mathrm{inc}}\)) and the PD could happen in any voltage level of the overshoot, as long as there is a free electron available to start the avalanche. Two different cases are distinguished for the definition of PDIV. (1) If the peak voltage of the waveform is defined as PDIV, a higher value than the inception voltage could be considered, resulting in a positive error. (2) If the DC voltage is defined as the PDIV, as the DC voltage is lower than the ignition voltage, a negative error arises. The error in the definition of the PDIV considering either peak or DC voltage is enhanced with a larger overshoot. This could also happen in sinusoidal waveforms; the author remarks that, due to its low derivative at 50/60 Hz (generally used), this error could be neglected. The authors of [33,44] came to the same conclusion after measuring the PDIV for sinusoidal and repetitive impulse waveforms. In addition to the waveform, [PERSON] et al. [33] compared the PDIV for unipolar and bipolar square impulses. It was observed that the PDIV value measured using the unipolar waveform is around double that measured with the bipolar waveform, which also suggests that PDIV depends on the peak-to-peak value of the applied voltage. Finally, observing the influence of the polarity in the PDIV measurements using unipolar waveform, the author of [45] shows that the polarity has little impact on the PDIV measurements under unipolar voltages in twisted pairs. In fact, no polarity dependence is expected for twisted pairs because of the symmetry of the electrode configuration. It is of particular interest that, under a unipolar waveform, there is a considerable space charge (in the insulation bulk) and surface charge (in the insulation surface) accumulation compared to a bipolar waveform (either sinusoidal or square). [PERSON] et al. [33] exposed twisted pairs to unipolar and bipolar waveforms with a 0.5 PDIV voltage level at 50 Hz. The PDIV is measured at different exposure times (defined as the poling time). It is shown that, for a unipolar waveform, the PDIV value increases and then decreases. The increase in the PDIV at the initial stage is due to the surface charge accumulation. The accumulated charge generates an internal electric field in the opposite direction of the applied field.