## 1 Introduction
### Reference PD Pulses and Pulsating Noise Trains
#### 2.1.4 Noise Pulsating Signals  
Non-pulsating noises, such as broadcast disturbances, are limited to discrete bands. These disturbances can affect PD measuring instruments if the transmission frequency falls within the measurement frequency range of the PD measuring instrument. To mitigate this type of noise, band stop filters tuned to the frequencies where the disturbance occurs can be used. Wavelet filters can also be used to remove non-pulsating background noises. Pulsating background noises are pulse noises caused by power electronic components, such as HVDC thyristors or HVDC IGBT valves, etc., that can be mistaken for PD pulse waveforms. Noise rejection tools must operate in two steps. The first step is focused on rejecting the non-pulsating components of the background noise, for example, by means of band-rejection filters [14; 15] or wavelet filters [16; 17; 18], and the second step is removing pulsating components by means of pulse clustering tools [7; 19; 20]. An AI clustering tool will allow the classification of pulsating signals that have a similar pulse waveform based on their frequency components or on their temporal parameters. Table 4 shows an example of raw data acquisition in an HVDC converter plant. The raw data were filtered using an iterative wavelet filter to remove non-pulsating components of the noise. Consequently, only pulsating components (pulsating noise + PD pulses) remained after filtering out the non-pulsating components. Then, an AI PD clustering tool can be applied to separate different pulsating signals in such a way that pulsating noises and PD sources can be recognised by an AI PD recognition tool. Three different noise types are shown in Table 5 in the time and in the frequency domain (green signals), one coming from a wind plant, another from a PLC system in an MV grid, and the last one from a DC converter station. The impulsive components (red signals) remain after applying a wavelet filter. The resulting PRPD patterns after the filtering process are shown in the last column. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Time Domain** & **Frequency Domain** \\ \hline Raw data (PD pulse + global noise) & & \\ \hline Non-pulsating noise component & & \\ \hline Pulse components (Pulsating noise + PD pulses) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Non-pulsating noise component and pulsating component. The conventional double exponential (DE) function indicated in Equation (2) is typically used to emulate lightning impulses. Although it has steeper slopes at the front than at the tail, using this function the arbitrary behaviour of the slopes at the tail of PD pulses cannot be reproduced. Furthermore, the DE function is not appropriate to emulate PD pulses because at t = 0, the signal is not zero, which is not representative of a PD pulse waveform. \[i(t)=i_{peak}\cdot k\cdot\left(e^{\alpha\cdot t}-e^{-\beta\cdot t}\right) \tag{2}\]  
With the inverse double exponential (IDE) function defined by formula (3), it is possible to reproduce a pulse with any arbitrary front time T\({}_{1}\) for a selected tail time T\({}_{2}\) at half of the peak value. When using the IDE function, any pulse waveform with any slope and zero  
Figure 4: Representative PD pulse waveforms under HV stress. (**a**) PD pulse generated by moving particles in SF6 measured at 0.5 m with an antenna of 200 MHz. (**b**) PD pulse generated in a cavity of a cable system measured at 5 km with an HFCT sensor of 25 MHz. (**c**) PD pulse generated in a semiconductor junction measured at 1 m with an HFCT sensor of 25 MHz. \begin{table}
\begin{tabular}{c c c c} \hline
**Noise Examples** & **Time Domain (20 ms)** & **Frequency Domain** & **PRPD Pattern** \\ \hline Wind Plant & & & \\ \hline PLC in a MV grid & & & \\ DC converter & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Example of pulsating noises. tangent for t = 0 can be reproduced.