## 3 Results and Discussion
### Analysis of Typical Performances
#### 3.2.4 Space Charge Characteristics  
In DC transmission, space charge can accumulate in polyethylene. Excessive local charges can distort the local electric field and accelerate the insulation deterioration, thus reducing the reliability of the cable [51; 52]. Because the distribution of space charge accumulation is directly related to the weak parts of the insulating material, this paper focuses on the space charge accumulation characteristic. The test results are shown in Figure 11. The mean volume density of space charge by formula (3) was calculated to compare the accumulation of space charge more intuitively [36]:  
\[q\left(t;E_{p}\right)=\frac{1}{x_{1}-x_{0}}\int_{x_{0}}^{x_{1}}\left|q_{P}(x,t ;E_{P})\right|dx, \tag{3}\]  
where \(q(t;E_{p})\) is the mean volume density of space charge, \(x_{1}\) and \(x_{0}\) are the positions of the anode and cathode, respectively, \(t\) is the polarization time, \(E_{p}\) is the polarization field strength, and \(q_{p}(x,t;E_{p})\) represents the space charge density in the material. Figure 10: Anchoring effect of microcapsule in polyethylene. The accumulation of a positive space charge was observed in all samples. This may be mainly related to the DC bias pulse power supply and the errors of the test instruments. However, the trends of space charge accumulation are the same for many groups of test results, which does not affect the results analysis. In pure polyethylene with the original process, there was an obvious accumulation of heteropolar space charge near the electrode. With an increase in test time, the space charge peak (space charge packet) increased gradually, and migration to the interior of the sample and the mean volume density of the space charge increased gradually. The main sources of space charge in polyethylene are electrode injection and impurity ionization [50, 51]. Although polyethylene itself is a non-polar molecular structure, the polar impurities are introduced inevitably in the preparation process. In high electric fields, polar groups are ionized and decomposed, then attracted by electrodes and accumulated near the electrodes to form heteropolar charges. Moreover, due to the large mass of ionized products and the limitation of localized state in the dielectric, the migration rate of ions is slow, which makes it easy for ions to form charge packets. On the other hand, the electrodes can inject carriers, which move to the vicinity of their heteropolar electrodes to form heteropolar charge. In the movement process of the carrier, the repulsion force of the same polar charge packet can slow down the carrier motion. Then, the carrier is trapped by the charge trap near the charge packet, thus making the charge peak increase and move into the sample. It can be inferred that the charge trap depth of pure polyethylene with the original process is not large, so the carrier injected by the electrode has a greater probability of moving into the material. Compared with the original process, the accumulation of heteropolar charge near the electrode in the pure polyethylene with the modified process was significantly reduced. The charge accumulation  
Figure 11: Space charge accumulation characteristics of polyethylene. (**a**) Pure polyethylene with the original process. (**b**) Pure polyethylene with the modified process. (**c**) Microcapsule/polyethylene composite. (**d**) Mean volume density of space charge. (space charge peak) in the sample was not obvious. Moreover, the mean volume density of space charge was kept at a low level. The mobility of the carrier in the dielectric was not only related to the micro-parameters, such as charge traps, but also to the macro-parameters, such as volume resistivity. Its behavior determined the accumulation characteristics of space charges in the material [37; 51]. The volume resistivity of the pure polyethylene with the modified process clearly decreased (Section 3.2.2), so the barrier effect on carriers was reduced, that is, the it was easier for the charge to reach the electrode.