**3. Results**

In this section, the main termination designs created and analyzed during the test stage are presented, as well as the optimized final termination design. The performance of the prototypes was evaluated by the distribution and maximum value of the calculated electric field.

#### *3.1. Intermediate Stages of the Termination Design*

Initially, the main intermediate stages of the termination design are shown in Figure 4.

**Figure 4.** Main intermediate stages of the termination design: (**a**) initial stress cone; (**b**) enhanced stress cone and corona ring inserted; (**c**) elongated stress cone with terminal away and (**d**) improvement in external shield and corona ring position.

Successive improvements were made between the initial design step and the final step, aiming to improve the electric field distribution and reduce the maximum electric field on the termination surface and in the air region around the termination. The initial stress relief configuration is shown in Figure 4a. In Figure 4b, the shape of the stress relief cone was modified, having been elongated, and a conductive material with a metal ring for improving the field distribution was applied to the shield termination on the outer surface of the cone. A corona ring was also added to the high-voltage electrode. In the Figure 4c configuration, the cone length was increased, the geometry was improved, and the corona ring position was modified. In Figure 4d, the portion of the stress cone in which the external shield ends was modified again, and the position of the corona ring was optimized.

In Figures 5 and 6, the potential distribution and maximum electric field around the termination are shown in the same order as the four intermediate stages presented in Figure 4.

**Figure 5.** *Cont*.

**Figure 5.** Potential distribution and electric field lines for the configurations of cable termination shown in Figure 4: (**a**) initial stress cone, (**b**) enhanced stress cone and corona ring inserted, (**c**) elongated stress cone with terminal away and (**d**) improvement in external shield and corona ring position.

As can be observed in Figure 5, a progressive change in the potential distribution was achieved due to modifications in the geometry. Moreover, as indicated in Figure 6, there was a progressive decrease of the maximum electric field in the air as the termination was being improved.

**Figure 6.** *Cont*.

**Figure 6.** Electric field distribution and position of its maximum value for the configurations of cable termination shown in Figure 4: (**a**) initial stress cone; (**b**) enhanced stress cone and corona ring inserted; (**c**) elongated stress cone with terminal away and (**d**) improvement in external shield and corona ring position.

#### *3.2. Final Termination Design*

In the final version of the proposed termination, a rubber-composed stress relief cone and a termination electrode with a round end were designed. Near the cone, the termination also had rubber sheds to prevent the formation of a superficial discharge. At the end of the termination itself, a sphere-shaped corona ring was used for decreasing the electric field enhancement at the cable end.

A drawing of the final termination design is shown in Figure 7.

**Figure 7.** Drawing of the proposed model geometry.

*Energies* **2019**, *12*, 3075

After the design definition, its dimensions were obtained, and an 2D-revolution form of the termination was drawn by using AutoCAD® computer-aided design software (2018 student version, AutoDesk, Inc., San Rafael, CA, USA). 3D drawing views of the designed termination are shown in Figure 8.

**Figure 8.** 3D drawing views of the designed termination.

Similar to the results regarding the intermediate versions of the termination, the potential and electric field distribution obtained for the final version of the termination are shown in Figure 9.

From the streamlines in Figure 9, field intensification points can be observed. They are located on the stress relief cone and at the torus-shaped electrode. As can be seen in Figure 9b, the maximum electric field achieved its minimum value for the last configuration. In addition, unlike in the initial design stages, the point of maximum external electric field in the final design is not in the region between the high-voltage terminal and stress cone, but on the external shield, away from the region susceptible to breakdown. This fact results in a better performance of the termination. In Table 2, the maximum electric field calculated for each of the presented termination designs are presented and compared.


**Table 2.** Maximum electric field calculated for the analyzed termination designs.

The results shown hereafter refer to the final termination design. The obtained result for the inner electric field on the termination is presented in the color plot in Figure 10.

**Figure 9.** (**a**) Potential distribution and (**b**) external electric field distribution for the final version of the proposed cable termination.

**Figure 10.** Electric field on the effective length end.

As shown in Figure 10, the maximum electric field is of the order of 800 kV/cm, exhibiting a reduction in the maximum electric field of 2.25 times when compared to the preliminary computer simulations shown in Figure 3.

As a way to verify the electric field distribution on the XLPE dielectric, the electric field was investigated over two paths of the insulation material. These paths are shown in Figure 11.

**Figure 11.** Paths for analysis of the electric field distribution.

In Figure 12, the distribution of the electric field over the points of Figure 11 is presented. Figure 12 curves represent the electric field decay along the insulating material radius. It is expected that a discharge must begin from a point where the field intensification is maximum. According to the standards, this point shall be inside the effective length of the cable, far enough from the external shield end.

**Figure 12.** Distribution of electric fields over the termination.

Figure 12 curves show that the maximum electric field occurs on the blue curve, inside the effective length of the cable, even though it is also observed that both curves are close. In addition, as shown in the figure, the maximum field in the XLPE decreases with radius, thus indicating that breakdown will begin next the conductor surface and occur inside the effective length.

In Figure 13, the reduction of the maximum electric field along the cable length is shown considering a line adjacent to the inner conductor. The electric field intensity starts decreasing at the point where the external shield ends, which occurs at about 1504 mm.

In order to check the termination performance against superficial discharges as well as corona and arc formation, the electric field at the rubber termination surface was analyzed. Therefore, the defined path is the one exhibited as a red line in Figure 14, which unites high-voltage and zero potentials.

The electric field strength along the red line highlighted in Figure 11 can be seen in Figure 15. The length count starts from the termination electrode and ends at the surface of the high-voltage electrode.

**Figure 13.** Electric field along the inner conductor length.

**Figure 14.** Outer path for external electric field analysis.

**Figure 15.** Simulated electric field along a path adjacent to the termination surface, highlighted in red in Figure 14.

The maximum electric field strength obtained on the termination surface was about 19 kV/cm near the stress relief cone. The effect of the insulating sheds can also be observed. The mean electric field throughout the superficial path is about 8.8 kV/cm.

#### **4. Summary and Conclusions**

The main contribution of this work is the proposition of a methodology that allows the design of adequate terminations that can withstand voltage tests and breakdown voltage tests in cables. Therefore, it was necessary to develop a termination that guaranteed that the greater electrical stress was applied to the internal insulation.

The optimized cable termination ensured that the electric field presented a greater probability of electrical breakdown inside the cable, in the cable part represented by the 3 m effective length. The achieved termination model minimized the probability of surface discharges and electrical breakdown between the high-voltage electrode and the external ground. In this context, the electric

field distribution in the air and termination surface was also analyzed. As shown in Figure 15, the proposed termination allows the control of the surface electric field.

The proposed methodology was tested using a 35 kV XLPE cable model. The designed termination model contained an additional insulator to avoid tangential discharges and increase creepage distance, a metal sphere at the end of the structure, and a ring-shaped electrode to improve the electric field distribution in the surrounding air. As a result, the average electric field throughout the superficial path was about 8.8 kV/cm, and the maximum electric field strength was about 19 kV/cm, near the stress relief cone surface.

From the analysis of the results obtained in the simulations, it was observed that the objective was reached, given that, when applying the termination created, dielectric breakdown is more likely to occur in the e ffective length (inner part) of the cable. The performed simulations showed that a termination with the proposed dimensions and materials decreased the probability of electrical discharge at the terminations of the cable to be tested. The proposed termination eliminated the field intensification at the termination of the cable.

The proposed methodology benefits from advanced simulations to perform initial tests and to avoid wasting resources with unsatisfactory termination models. A termination was e ffectively developed for the cable considered so that overvoltage tests could be performed. Furthermore, conventional materials were considered in the proposed design, which represents a potential cost reduction. Future research may be carried out by developing new models in search of an improved result. The proposed termination should be built to carry out experimental tests in relation to its functionality. This study may also contribute as a basis for future studies in the HVDC area, especially the ones related to cable terminations.

**Author Contributions:** Conceptualization, E.G.C., F.L.M.A., and A.F.A.; methodology, C.S.H.S.; software, F.L.M.A., A.F.A. and C.S.H.S.; formal analysis, F.L.M.A. and A.F.A.; resources, E.G.C. and G.R.S.L.; writing—original draft preparation, F.L.M.A., A.F.A. and C.S.H.S.; writing—review and editing, A.F.A., E.G.C. and C.S.H.S.; visualization, supervision, E.G.C. and G.R.S.L.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors acknowledge the UFCG Graduate Program for Electrical Engineering (COPELE), the Coordination of Improvement of Higher Education Personnel (CAPES), and the National Council for Scientific and Technological Development (CNPq) for granting scholarships.

**Conflicts of Interest:** The authors declare no conflict of interest.
