# Research on Lifespan Prediction of Cross-Linked Polyethylene Material for XLPE Cables
## 1 Introduction
### Electrical Properties  
#### 2.3.1 Dielectric Frequency Spectrum Test  
Dielectric frequency spectrum testing can comprehensively reflect the electrical properties of the dielectric parameters, including polarization performance and loss performance. In this paper, the dielectric parameters, including complex dielectric permittivity (denoted as \(\varepsilon\)) and dielectric loss (denoted as tan \(\delta\)), of cross-linked polyethylene samples at different frequencies were measured by a broadband dielectric spectra scanner.  
An Alpha-A concept 80 broadband dielectric spectra scanner from Novecontrol Technologies was employed to measure the dielectric parameters. The measurement temperature was 20 \({}^{\circ}\)C, and the measurement frequency was set from \(10^{-2}\) Hz to \(10^{6}\) Hz.  
The results of dielectric parameters, including the complex dielectric permittivity \(\varepsilon\) and dielectric loss tan \(\delta\) of samples with different aging times, are shown in Figure 3. Moreover, as IEEE Standard 400.2-2013 [16] presented that the dielectric parameter at 0.1 Hz can characterize electrical properties  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multicolumn{8}{c}{**Hardness(Shore A)**} \\ \cline{2-10}  & \(a\) & \(b\) & \(c\) & \(d\) & \(e\) & \(f\) & \(A\) & \(a_{A}\) \\ \hline A\({}_{1}\) & 74.1 & 74.2 & 74.3 & 74.2 & 73.6 & 74.3 & 74.1 & 0.264 \\ A\({}_{2}\) & 73.9 & 74 & 74.2 & 74.1 & 74.3 & 74.1 & 74.1 & 0.141 \\ A\({}_{3}\) & 74.2 & 74.2 & 74.4 & 74.3 & 74.8 & 74 & 74.3 & 0.271 \\ A\({}_{4}\) & 74.1 & 74.3 & 74 & 74.4 & 74.6 & 74.5 & 74.3 & 0.232 \\ A\({}_{5}\) & 74.2 & 74.5 & 75.3 & 75.1 & 75.3 & 75.2 & 74.9 & 0.468 \\ A\({}_{6}\) & 75 & 74.4 & 74.6 & 75.4 & 74 & 75.4 & 74.8 & 0.566 \\ A\({}_{7}\) & 76.5 & 75.4 & 75.6 & 76.3 & 75.5 & 76.2 & 75.9 & 0.471 \\ A\({}_{8}\) & 75 & 75.7 & 77 & 75.2 & 75.2 & 75 & 75.5 & 0.770 \\ A\({}_{9}\) & 80.3 & 80.7 & 81.5 & 79.9 & 79.4 & 80.9 & 80.5 & 0.748 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Hardness test results of samples from Factory A.  
best, the specific dielectric values of the samples at a typical frequency point of 0.1 Hz are listed in Table 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Samples** & **Operating Time/Year** & \(\epsilon\) & **tan \(\delta\) (\(\times\)10\({}^{-2}\))** \\ \hline A\({}_{1}\) & 1 & 2.762 & 0.509 \\ A\({}_{2}\) & 2 & 2.815 & 0.514 \\ A\({}_{3}\) & 2.5 & 2.841 & 0.509 \\ A\({}_{4}\) & 3 & 2.85 & 1.488 \\ A\({}_{5}\) & 3.5 & 2.871 & 2.433 \\ A\({}_{6}\) & 5 & 2.875 & 3.844 \\ A\({}_{7}\) & 6 & 2.878 & 4.786 \\ A\({}_{8}\) & 7 & 2.882 & 7.056 \\ A\({}_{9}\) & 8 & 2.886 & 9.323 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Dielectric parameter of samples in different years at frequency of 0.1 Hz.  
Figure 3: Dielectric parameters of samples of different ages: (**a**) complex dielectric permittivity \(\epsilon\); (**b**) dielectric loss tan \(\delta\).  
According to the results obtained in Figure 3 and Table 4, both the dielectric permittivity \(\varepsilon\) and dielectric loss \(\tan\delta\) increase with the increase in operating time. To be specific, for samples aged for 2, 3, 6 and 8 years, the complex dielectric permittivity \(\varepsilon\) at 0.1 Hz increases by 1.92%, 3.19%, 4.20% and 4.49%, respectively, compared with samples aged for 1 year, and the dielectric loss \(\tan\delta\) increases by 0.01, 1.92, 8.4 and 17.31 times, respectively, compared with samples aged for 1 year. The reason for this may be that as the operating time increases, more macromolecular chains fracture and more polar impurities and defects appear in the material under oxidation reactions and thermal decomposition reactions, which, in turn, result in more free charge carriers gathering at the interface and defects. This will lead to an increase in interface polarization loss, along with an increase in dielectric permittivity \(\varepsilon\) and dielectric loss \(\tan\delta\).