# Electric Field & Voltage Distribution Along Non-Ceramic Insulators

*Porcelain and glass insulators have been used for over a hundred years and although these materials have proven themselves resistant to environmental ageing, their pollution performance has often been relatively poor due to hydrophilic surfaces. In recent decades, polymeric insulators have become more widely used because of the advantages they offer in terms of excellent hydrophobic surface properties under wet conditions. However, the bonds of polymeric materials are relatively weak in comparison to those of inorganic ceramic materials. Therefore, they are more susceptible to chemical changes under the various stressors encountered in service. These include electric stresses due to the operating voltage, corona and arc as well as environmental stresses such as contamination, UV and heat cycling. Under these stresses, the hydrophobicity of the shed surfaces on these insulators can be temporarily or even permanently lost resulting in worsened pollution performance.*

*Generally-speaking, the electric field distribution along a polymeric long rod is not so linear as that of a porcelain insulator string because there are no intermediate metallic parts. High electric field strength can cause corona on these insulators resulting in corona cutting, deterioration and ageing of the polymeric material. Therefore, controlling electric field strength along non-ceramic insulators is an important aspect of their design and also of the design of their grading devices. When installed on a power line, the tower geometry and nearby line end hardware and conductors will also affect electric field distribution around an insulator. Depending on voltage level, the magnitude of the electric field strength on the insulator’s surface may exceed recommended corona-related values. Grading rings are then used to modify the electric field distribution and reduce its maximum value. Given all these considerations, a three dimensional model should ideally be set up in order to evaluate electric field strength and voltage distribution near as well as along a non-ceramic insulator. This past INMR article by Dr. Weiguo Que of Axcelis Technologies and Professor Stephen Sebo of Ohio State University, discussed the specifics of just such a model. *

## Development of Insulator Computation Models

A typical 34.5 kV composite insulator has 12 weather sheds and a length of about 0.8 meters. By comparison, a typical 765 kV composite insulator has over 100 weather sheds and is nearly 5 meters long. Therefore, to obtain accurate results, considerably more elements have to be used for the electric field analysis of such a 765 kV insulator than is case for a unit designed for 34.5 kV. When using the boundary element method to calculate the electric field and voltage distribution along such insulators (EFVD), the greater the number of elements used, the more time is needed for computation. Therefore, in order to reduce calculation time when analyzing relatively long composite insulators, some simplifications of the insulator model are necessary.* *

A composite insulator, depending on design, can have up to four main components: the fiberglass reinforced (FRP) rod; the polymeric sheath on the rod; the polymeric weather sheds; and two metallic end fittings. To determine which component can be simplified with the least influence on the accuracy of the calculated results of EFVD, a 34.5 kV composite power line insulator was studied. The detailed geometry and dimensions of this 34.5 kV insulator are shown in Fig. 1.

The insulator, equipped with metallic fittings at both line and ground ends, is made of silicone rubber with a relative permittivity of 4.3 and a rod with a relative permittivity of 7.2. There are 12 weather sheds on the housing. The insulator is surrounded by air with a relative permittivity of 1.0. The top metal end fitting is taken as the ground electrode and the bottom electrode is connected to a steady voltage source of 1000 V for the purpose of calculations. The insulator is positioned vertically (but shown horizontally in Fig. 1 for convenience). Four simplified computation models are used for a step-by-step comparison process. In addition, a three dimensional “full” insulator model is set up as a reference for study of the EFVD. These five calculation models are shown in Fig. 2: (a) two electrodes only, (b) two electrodes and the fiberglass rod, (c) two electrodes, rod and sheath on the rod without weather sheds, (d) two electrodes, rod, sheath, two weather sheds at the each end of the insulator, and (e) the “full” 34.5 kV insulator.

As an example to show the element configuration, the “full” insulator model has 12,553 four-sided elements applied to the surface of boundaries and the interfaces of different media. The element configuration on the surface of the insulator is partially shown in Fig 3.

The equipotential contours around the five computation models are shown in Fig. 4. Again, the bottom electrode is energized, the top electrode grounded. The energizing voltage is 1000 V and the insulation distance between the two electrodes is 46 cm. Each number shown along the perimeters of the four contour plots is in centimeters. Case (a), no solid insulating material between the electrodes, shows that only some 20 per cent of the insulation distance sustains about 70 per cent of the applied voltage. The presence of the fiberglass rod changes the voltage distribution slightly, see Case (b).

The distribution of the equipotential contours for Case (c), with the sheath on the rod, is very close to Case (e), the “full” insulator model. The presence of the weather sheds changes the equipotential contours somewhat. If more accurate results of voltage distribution are needed near the line and ground end areas, the simplified insulator model with only two weather sheds at each end of the insulator, Case (d), can be used. Comparing Cases (d) and (e), the voltage distributions in the vicinity of the two weather sheds at the line end are very similar. Moreover, the positions of the equipotential lines for Cases (d) and (e) are very close to one another along the surface of the insulator’s sheath.

To see the comparison more clearly, the voltage distributions for Cases (d) and (e) along the calculation paths, shown as a dashed line in Fig. 4 (d) and (e), are shown in Fig. 5. Comparing Cases (d) and (e), the maximum difference between the voltages at the same point along the sheath surface of the insulator is only 1.2 per cent of the applied voltage. This indicates that the simplification introduced by Case (d) is acceptable for the calculation of the voltage distribution of the “full” insulator, Case (e), along the sheath surface.

The electric field strength magnitudes for Cases (d) and (e) along the paths defined on the surface of the sheath are also calculated for comparison, (see Figure 6.) The dips in the electric field strength plot of the insulator modeled with weather sheds are due to the calculation path passing through the weather shed material, which has a relative permittivity of 4.3. The electric field strength values in the vicinity of the two weather sheds at each end of the insulator are the same for Cases (d) and (e). There is a slight change in the electric field strength distribution near the other eight weather sheds shown by Case (e). The maximum electric field strength for Cases (d) and (e) are both the same, i.e.0.0256 kV_{p}/mm. This means that the electric field distribution of the insulator with the “full” number of weather sheds can be estimated through the simplified insulator model with a smaller number of weather sheds (e.g. only two) at each end of the insulator.

The conclusion which can be reached is that *a simplified insulator model with only a small number of weather sheds (shown in Fig. 2d), can be used to calculate the electric field and voltage distribution along the “full” insulator in service, with no significant influence on accuracy.* The number of weather sheds for the simplified insulator model can be decided simply by trial and error.

**Computation Model of 765 kV Composite Insulator**

The following discussion describes research related to determining the EFVD along typical 765 kV composite insulators when installed on a three-phase energized tower. The effects of tower configuration and other line components on EFVD are also analyzed. It is of practical interest to know the electric field strength distribution for a full-scale insulator under three-phase energization. A typical 765 kV composite insulator is used for this study, which is designed for four-sub-conductor bundles.

The detailed dimensions of the 765 kV insulator are shown in Fig. 7. Materials used are silicone rubber weather sheds and sheath, and FRP rod. There are over 100 weather sheds (large and small) on an actual 765 kV insulator. Based on the previous analysis, the calculation model for this full scale insulator can be simplified with only a small number of weather sheds (e.g. 10) at each end of the insulator in order to calculate the EFVD.

In order to reduce the electric field strength in the triple point region of the insulator, corona rings are applied at both line and ground ends of the insulator.

## Modeling of 765 kV Tower & Ground Plane

The simplified geometry and major dimensions of a typical 765 kV tower with four sub-conductor bundles are shown in Figure 8. The two ground wires are ignored in the calculations. The ground plane is modeled with a 50 m x 50 m large plane with zero potential. The number of elements used for the tower is 800 and for the ground plane 100.

A 3-D view of the entire 765 kV power line tower with four sub-conductor bundles, non-ceramic insulators, end fittings, and hardware is shown in Fig. 9.

(a) View of entire tower with four sub-conductor bundles.

(b) View of center phase conductor with insulators.

## Voltage & Electric Field Distributions Along Composite Insulator

The electric field and voltage distributions along the 765 kV composite insulator of the center phase have been studied on a typical 765 kV power line tower with four sub-conductor bundles. The instantaneous voltages applied to the three phase conductor system for the worst case – when there is maximum voltage across the center phase insulator – are as follows:

V_{left} = – 0.5 x V_{center} = – 0.5*624.6 = – 312.3 kV,

V_{center} =765 x √2/√3 = 624.6 kV (i.e., maximum value of the line-to-ground voltage)

V_{right} = – 0.5 x V_{center} = – 0.5*624.6 = – 312.3 kV.

There are some basic principles for showing the calculation results:

• In the following paragraphs, the voltages are expressed either in kV_{max} or in per cent values, referred to 624.6 kV_{max }, which is the actual applied voltage on the center phase insulator.

• The electric field strength is always expressed in kV_{max}/mm units.

• The insulation distances used in the figures are expressed either in cm units or in per cent values, referred to 436 cm as shown in Figs. 7 and 10.

• The calculation path on the surface of the insulator sheath (not along the leakage path) is identified as a straight dashed line as shown in Fig. 10.

The resulting per cent equipotential contours inside the tower window for a 765 kV non-ceramic insulator with four sub-conductor bundles are shown in Fig. 11.

It can be seen that the line end equipotential contours are greatly influenced by the line end hardware and the line end corona ring and that they are nearly parallel to the shed surface. The 10 weather sheds near the line end sustain about 35 per cent of the applied voltage while the 10 weather sheds near the ground end sustain about 12 per cent of the applied voltage.

Fig. 12 shows the actual voltage distribution in the worst case vs. per cent insulation distance at the surface of the insulator sheath with four sub-conductor bundles. The non-linear property of the voltage distribution along the non-ceramic insulator is clearly shown.

The electric field strength magnitude along the path defined on the surface of the insulator sheath is shown in Fig. 13. The maximum value of the electric field strength at the triple junction point is 1.586 kV_{max}/mm.

For a clearer view, the electric field strength distribution along the insulation distance near the line end fitting is shown in Fig. 14. The discontinuities in the magnitude of the electric field strength in Figs. 14 and 15 are the result of the calculation path, shown in Fig. 10, passing through the shed material. It can be seen that electric field strength is much higher at the junction region between the sheath and the shed than that at the middle part of the sheath region.

The electric field strength distribution along the insulation distance near the ground end fitting is shown in Fig. 15.

**Conclusions**

1. A simplified insulator model with only a small number of weather sheds at the line and ground ends can be used to calculate the electric field and voltage distribution along the “full” insulator in service with no significant influence on accuracy.

2. For a 765 kV tower with four sub-conductor bundles, studies (not shown here) prove that there is no significant difference between the EFVD along a composite insulator under single phase versus three phase energization. Therefore, the calculation model can be simplified further with the assumption of single phase energization.