## 2 Materials and Methods
### Measurement Method  
This section presents information on the theoretical foundation of the measurement methods employed in experimental studies. Electrical discharges that occur only in a part of the insulating material between two electrodes are called partial discharges (PD) [35; 36]. PDs that occur in the gaps within the insulating materials are called internal PDs, and PDs that occur on the surface of the insulating materials are called surface PDs. The purpose of PD measurements is to detect PD events, measure their magnitudes, and evaluate the results by determining their location. The charge that creates a voltage change, as well as the resulting PD magnitude, is called PD amplitude (pC). PD amplitude is indicated by the symbol Q. The threshold voltage at which PD events start to occur is called the partial discharge inception voltage (PDIV). The equivalent circuit required to explain the PD measurements theoretically is presented in Figure 3[21]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **ABS** & **ASA** & **PETG** & **PLA** \\ \hline Nozzle diameter (mm) & 0.4 & 0.4 & 0.4 & 0.4 \\ \hline Layer height (mm) & 0.2 & 0.2 & 0.2 & 0.2 \\ \hline Sparse infill density (\%) & 100 & 100 & 100 & 100 \\ \hline Sparse infill pattern & Rectilinear & Rectilinear & Rectilinear & Rectilinear \\ \hline Nozzle temperature (\({}^{\circ}\)C) & 283 & 275 & 240 & 220 \\ \hline Build plate (\({}^{\circ}\)C) & 110 & 100 & 80 & 60 \\ \hline Chamber temperature (\({}^{\circ}\)C) & 53 & 53 & - & - \\ \hline Initial layer print speed (mm/s) & 50 & 50 & 50 & 50 \\ \hline Initial layer infill print speed (mm/s) & 105 & 105 & 105 & 105 \\ \hline Outer wall print speed (mm/s) & 200 & 200 & 200 & 200 \\ \hline Inner wall print speed (mm/s) & 300 & 300 & 300 & 300 \\ \hline Print cooling enable & No & Yes & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of 3D printing by the filament type. Figure 3: Partial discharge equivalent circuit. Here, the capacitance values are defined with the subscripts a, b, and c. C\({}_{\text{a}}\) indicates that the capacitance value belongs to the part of the insulator without defect, C\({}_{\text{b}}\) indicates the capacitance of the part outside the gap, and C\({}_{\text{c}}\) indicates the capacitance value of the gap. Tan\(\delta\) represents the ratio of the resistive (loss) component to the capacitive (stored energy) component of a dielectric material's impedance. It quantifies the energy lost as heat due to dielectric losses in an insulating material when subjected to an alternating electric field [37]. The parallel equivalent circuit and phasor diagram for this situation are shared in Figure 4 [21]. In the figure, R (\(\Omega\)) represents the resistance representing the insulation losses, C (F) the equivalent capacity of the insulating material, U (V) the applied voltage value, \(I_{\text{R}}\) (A) the current causing the dielectric loss, \(I_{\text{C}}\) (A) the current flowing through the capacitance, I (A) the total current, and \(\delta\) (\({}^{\circ}\)) the phase angle between \(I_{\text{C}}\) and \(I_{\text{R}}\). Using the equivalent circuit parameters and dielectric permittivity, the dielectric loss factor can be calculated as given in Equation (2). \[tan\delta=\frac{I_{R}}{I_{\text{C}}}=\frac{\frac{U}{K}}{U\cdot\omega\cdot C}= \frac{1}{\omega\cdot R\cdot C} \tag{2}\]  
Here tan\(\delta\) defines the dielectric loss factor and \(\omega\) (rad/s) defines the angular frequency. Accordingly, the losses occurring in the dielectric material can be calculated as given in Equation (3). \[P_{K}=\omega\cdot C\cdot U^{2} \tag{3}\]  
According to IEC-62631-2-1:2018 [38], tan\(\delta\) measurements are recommended to be conducted within a voltage range of 0.1 V to 2000 V. In this study, 2 kV was selected as a representative voltage from this range, and to broaden the analysis, measurements were also carried out at 4 kV.