**3. Results**

#### *3.1. Electrical Tree Degradation*

## 3.1.1. Tree Structure

The structure of electrical tree in polymer is related to certain combined factors: voltage waveform, temperature, and polymer fillers [36–38]. Table 1 shows the electrical tree structure distribution at 1 min. Figure 3 shows the electrical tree structures of the neat XLPE and polycyclic compound modified samples. Figure 3a,b show the compared electrical tree structures with −25 kV DC and +35 kV impulse voltages (the opposite polarity). Figure 3c,d show the compared electrical tree structures with −25 kV DC and −35 kV impulse voltages (the same polarity). The treeing times for both are 1 min for the convenience of comparison. In order to save space, only modified samples with a type A polycyclic compound were selected for comparison with neat XLPE samples. The electrical tree structures of XLPE-B and XLPE-C are shown in Figure A2 in our Appendix A. It can be seen that the electrical tree structures of neat XLPE samples are not affected by the temperature and the DC-impulse voltage waveform, which are branch trees. These results are consistent with the results in the literature [22], of which the electrical tree structures of PP samples are not affected by the DC-impulse voltage waveform at room temperature. After the addition of the polycyclic compound, the electrical tree structure changes, which are related to the polycyclic compound type. For XLPE-A samples, with −25 kV DC and +35 kV impulse voltage (the opposite polarity), the tree structures change to bush trees at 30 and 60 ◦C and it is double tree at 90 ◦C. With −25 kV DC and −35 kV impulse voltage (the same polarity), the tree structures change to bush trees at 30 ◦C. However, they are still branch trees at 60 and 90 ◦C. For XLPE-B and XLPE-C, the tree structures are double tree at 30 ◦C. However, they are still branch trees at 60 and 90 ◦C.


**Figure 3.** The electrical tree structures of the neat cross-linked polyethylene (XLPE) and XLPE−A composite.

#### 3.1.2. Electrical Treeing Characteristics with Opposite Polarity DC-Impulse Voltage

Figure 4 shows the electrical treeing characteristics of a representative electrical tree with opposite polarity DC-impulse voltage; Figure 4a is the relationship of the electrical tree length and the treeing time; Figure 4b is the relationship of the accumulated damage and the treeing time. The treeing voltage is +35 kV impulse superimposed −25 kV DC voltage, of which the impulse voltage polarity is opposite to the DC voltage polarity. The treeing time is 60 s, and the experimental temperatures are respectively 30, 60, and 90 ◦C. The electrical tree length of XLPE-A composite is 167 μm at 30 ◦C in 60 s and is reduced by 74.8% compared to the neat XLPE; the accumulated damage of XLPE-A is 0.5 × 10<sup>3</sup> pixels at 30 ◦C in 60 s and is reduced by 97.6% compared to the neat XLPE. The electrical tree length of XLPE-A is reduced by 69.9% at 60 ◦C in 60 s compared to the neat XLPE and the accumulated damage is reduced by 64%. At 90 ◦C, the electrical tree length of XLPE-A is reduced by 68.5% and the accumulated damage is reduced by 59.6%. For XLPE-B composites, the electrical tree length and accumulated damage are respectively reduced by 51.7% and 87.9% at 30 ◦C, 51.4% and 36.4% at 60 ◦C, and 50.3% and 31.6% at 90 ◦C in 60 s. For XLPE-C composites, the electrical tree length and accumulated damage is respectively reduced by 34.3% and 41.7% at 30 ◦C, 32.2% and 19.1% at 60 ◦C, and 30.8% and 26.3% at 90 ◦C. The experimental results reveal that the three type of polycyclic compounds all inhibit the length and accumulated damage of the electrical tree. Among them, the polycyclic compound A has the best effect, the type B is second, and the type C has the worst effect. It can be concluded that as the temperature increases, although the three polycyclic compounds still inhibit the growth of electrical trees, the effect of inhibition becomes weak.

**Figure 4.** Electrical treeing characteristics with opposite polarity DC-impulse voltage.

3.1.3. Electrical Treeing Characteristics with the Same Polarity DC-Impulse Voltage

Figure 5 shows the electrical treeing characteristics of a representative electrical tree with the same polarity DC-impulse voltage; Figure 5a is the relationship of the electrical tree length and the treeing time; Figure 5b is the relationship of the accumulated damage and the treeing time. The treeing voltage is −35 kV impulse superimposed −25 kV DC voltage, of which the impulse voltage polarity is the same as the DC voltage polarity. The electrical tree length of XLPE-A is 379 μm at 30 ◦C in 60 s and is reduced by 71.9% compared to the neat XLPE; The accumulated damage of XLPE-A is 9.1 × 10<sup>3</sup> pixels at 30 ◦C in 60 s and is reduced by 72.1% compared to the neat XLPE. The electrical tree length of XLPE-A is reduced by 57.3% at 60 ◦C in 60 s compared to the neat XLPE and the accumulated damage is reduced by 63.2%. At 90 ◦C, the electrical tree length of XLPE-A is reduced by 22.9% and the accumulated damage is reduced by 46.8%. For XLPE-B composites, the electrical tree length and accumulated damage are respectively reduced by 46.7% and 44.8% at 30 ◦C, 20.5% and 32.5% at 60 ◦C, and 14% and 29.1% at 90 ◦C. For XLPE-C composites, the electrical tree length and accumulated damage are respectively reduced by 31.9% and 26.4% at 30 ◦C, 23.8% and 16.9% at 60 ◦C, and 3% and 10.2% at 90 ◦C. The three polycyclic compounds all inhibit the growth of the electrical tree, and the polycyclic

compound A has the best effect, which is consistent with the results that have an opposite polarity DC-impulse voltage. The effect of temperature on the polycyclic compound is still the same as that with the opposite polarity. As the temperature increases, the suppression effect of the three polycyclic compounds becomes weak. It can be concluded that the suppression effect of the three types of polycyclic compounds with the same polarity is worse than with the opposite polarity.

**Figure 5.** Electrical treeing characteristics with the same polarity DC-impulse voltage.

#### *3.2. Trap Distribution and Carrier Mobility Behaviors*

There are many trap levels in the forbidden band of polymer materials. The formation of trap levels is complicated, and many factors affect the trap level, including molecular chain end groups, branches, amorphous regions and crystallization regions, polarizing groups, impurities, etc., as well as various physical chemistry effects that cause structural defects in materials [39]. After the polycyclic compound is added to the XLPE, the trap distribution and the carrier mobility behaviors change accordingly. In this section, the variation of the trap distribution and the carrier mobility behaviors of representative XLPE/polycyclic compounds at different temperatures are obtained, as shown in Figure 6. Figure 6(a1) compares the trap distribution behaviors of different samples at 30 ◦C. It can be seen that the trap distribution of the neat XLPE sample exhibits a *double peak* shape, for which a peak appears at a shallower trap level, and a peak appears at a deeper trap level. However, there is only one deep trap peak of the XLPE/polycyclic compound composites, indicating that the number of shallow traps is small. It can be seen from Table 2 that the deep trap depth of the neat XLPE sample is 0.88 eV at 30 ◦C. After adding the polycyclic compound, the deep trap depth is among 0.93 eV to 0.97 eV at 30 ◦C. It can be concluded that the deep trap level of the XLPE/polycyclic compounds composites increases, and the corresponding trap density increases, indicating that the addition of the polycyclic compounds introduces deep traps inside the XLPE sample. Among them, trap depth of the XLPE-A composite is the largest, XLPE-B is second largest, and trap depth of XLPE-C is the smallest. Figure 6(b1) compares the carrier mobility of different samples at 30 ◦C. The neat XLPE sample has a carrier mobility of 12.5 × 10−<sup>14</sup> m2V−1s−1, the XLPE-A has a carrier mobility of 0.5 × 10−<sup>14</sup> m2V−1s−1, the XLPE-B has a carrier mobility of 2 × 10−<sup>14</sup> m2V−1s−1, and the XLPE-C has a carrier mobility of 5.6 ×10−<sup>14</sup> m2V−1s−1. It is more difficult for charges to escape from deep traps than shallow traps [35]. After the polycyclic compound is added, the depth of the deep trap becomes larger, and the charge trapped by the deep trap is more difficult to transfer from the deep trap to the ground electrode, so that the carrier mobility of samples becomes smaller [11]. Figure 6(a2,a3) compare the trap distribution behaviors of different samples at 60 and 90 ◦C. The neat XLPE has a shallow trap depth of 0.85 eV and a deep trap depth of 0.91 eV at 60 ◦C. After adding A, B, and C polycyclic compounds, only deep traps are measured and the depths are 0.97, 0.94, and 0.93 eV, respectively. The neat XLPE has a shallow trap depth of 0.91 eV and a deep trap depth of 1 eV at 90 ◦C. After adding three types of polycyclic compounds, A, B, and C, the shallower trap depths are 0.98, 0.95, and 0.92 eV, respectively. The deeper trap depths are 1.02, 1.02 and 1.01 eV, respectively. Figure 6(b2,b3) compare the carrier mobility behaviors of different samples at 60 and 90 ◦C. The carrier mobility of XLPE is the largest, 24 × 10−<sup>14</sup> m2V−1s−<sup>1</sup> and 100 × <sup>10</sup>−14m2V−1s−1, respectively. The carrier mobility of XLPE-A is the smallest, 0.9375 × 10−<sup>14</sup> m2V−1s−<sup>1</sup> and 13.65 × 10−<sup>14</sup> m2V−1s−1, respectively. It can be concluded that the addition of the polycyclic compounds increases the trap depth and the corresponding trap density of the XLPE and reduces the carrier mobility. Among them, the XLPE-A composite has the deepest trap depth, trap density, and the smallest carrier mobility.


**Table 2.** Cross-linked polyethylene (XLPE) and its polycyclic compounds composites trap depth.

**Figure 6.** Trap distribution and carrier mobility behaviors of XLPE and its polycyclic compounds composites.
