Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress

Layout of pre-moulded stress cones for elastomeric cable accessories is designed and optimized using computer calculations of electrical stress on the accessory. During installation, however, stress cones are expanded, thereby reducing thicknesses of the insulating rubber and also causing the semi-conductive deflectors to lose their original shape. Given this, electric field calculation for the original layout may no longer be accurate in describing the ‘expanded’ layout. This article, contributed to INMR by Thomas Klein, Stefan Zierhut and Eckhard Wendt of Strescon in Germany, proposed an approach to resolve this problem. The shapes of stress cones and the outline of surface contours were calculated using a method based on assuming that volume and length of the elastomeric part do not change considerably by expansion. Impact on electric field distribution was also discussed.


Introduction                                                                              

Use of stress control systems made from pre-moulded elastomeric materials is widely established in modern-day accessories for XLPE HV as well as EHV cables. Stress cones are made from insulating materials on the outside with embedded semi-conductive layers that are formed to create a field-control contour. Silicone elastomers have gained recognition in this field due to their superior manufacturing properties and outstanding dielectric and mechanical performance. It is common practice to determine the exact shape of the parts of the stress cone using computer-aided calculation of electric field distribution in the accessories.

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At joints and outdoor terminations, stress cones have to be installed on the cable with considerable expansion in a defined range. This expansion creates the surface pressure needed to withstand electric field stress in the interface between stress cone and cable surface. However, in expanding, the stress cone gets out of its original shape, wall thickness is reduced and deformation changes the outline of the semi-conductive surface. As such, the original electric field calculation is no longer applicable since field stress inside the stress cone and also on its surface can increase. This means that the installed accessory may perform worse than predicted by calculation.

These days, cable systems tend to higher voltages, often combined with comparatively less thickness of insulation. These cables therefore show increased electric field stress in the insulation that strains the field control system of the accessory. At the same time, use of large conductor cross sections is increasing, further raising electric field in outdoor terminations. Consequently, stress cones must be designed in an optimal way and it is essential to consider any effects relating to deformation. In order to arrive at a suitable approach to the problem of calculating the expanded outline of surface contours, some basic considerations have to be taken into account. Silicone elastomers are basically incompressible and experiments have shown that the length of a stress cone for a HV cable accessory does not change much by expansion during installation. Based on this, it can be assumed that volume of the elastomeric part as well as its length are not changed considerably by expansion. Given these boundary conditions, the new shape of an expanded elastomeric field control part can be calculated. These new surface contours and dimensions are then used in the electric field stress calculation. The original layout of the stress cone is then suitably modified to yield optimum performance after expansion.

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Deflector Function & Design

Fig. 1: Semi-conductive deflector (grounded electrode). stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 1: Semi-conductive deflector (grounded electrode).
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The electric field in the insulation of modern day polymeric HV cables can reach more than 16 kV/mm (long-term stress at U0 on inner semiconductor). Joints and terminations, used to connect cables, disrupt cylindrical field distribution of a coaxial cable. In order to avoid increases in electric field stress at cable connections or ends, deflectors are used. These deflectors (ground electrodes), as shown in Fig. 1, are made of semi-conductive rubber material and their defined outer shape serves to guarantee homogenous field distribution.

At cable terminations, with transition to air as the insulating medium, electric field stress has to be reduced in order to avoid discharges in the air that has considerably lower dielectric strength. That is why cable terminations use stress cones with a grounded electrode to manage the transition to air and the insulation of the cable ends. The general layout of a stress cone is shown in Fig. 2.

Fig. 2: Example of stress cone with integrated semi-conductive deflector for outdoor termination. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 2: Example of stress cone with integrated semi-conductive deflector for outdoor termination.
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Terminations for gas insulated switchgear (GIS) or ‘plug-in’ dry-type terminations work by the same principle but now there is a bushing insulator added, usually made of a cast resin that encloses the cable end with the stress cone. The same kind of stress cone is used in insulated joints on both cable ends. In addition, a HV electrode is applied, covering the connector for the conductor. The joint is completely covered with a grounded layer on the outside. All considerations in this article concerning stress cones are in principle also applicable for HV electrodes. The grading of the electrical stress for cable accessories with elastomeric stress cones is geometric-capacitive. The deflector is calculated in a way that the stress inside the material and along the interface to the cable is kept below some accepted maximum value, proven reliable based on long-term experience, and which depends on the materials used.

Stress Cone Expansion

The interface between stress cone and cable insulation is affected by quite a high tangential electric stress. To maintain control over this stress, the gap must not have any voids and the silicone material must enclose the cable with enough surface pressure. This is achieved by using a stress cone with a bore considerably smaller than the cable diameter over XLPE insulation. The expansion of the elastic silicone material during installation on the cable then creates the required surface pressure in the gap to the cable.

For plug-in or dry-type terminations, the interface on the outside of the stress cone to the inner wall of the bushing also has to be considered. But expansion rate and its range in this case is lower than for joints or fluid-filled terminations. The pressure between both interfaces – cable XLPE insulation to stress cones and stress cone to epoxy bushing – is created mainly by pressing the stress cone together with the cable into the conical bore of the epoxy bushing. To provide sufficient interface pressures during thermal movements, a spring mechanism applies axial force to the stress cone. Pre-moulded stress cones from silicone elastomers are produced in a certain number of sizes per voltage class and, because of high investment costs in moulds for these insulating parts, manufacturers prefer to offer as few different sizes as possible.

To design a consistent line of stress cones, maximum and minimum expansion allowed has to be defined and the shape of the part plays an important role in this regard. Greater wall thickness offers more pressure at a given expansion. Beyond that, minimum expansion depends on minimum required pressure inside the gap to the cable surface as well as on the shore hardness of the silicone elastomer being used. Softer materials require more expansion and vice versa. Maximum expansion, on the other hand, depends on the material’s elongation at break. For both values, the entire temperature range specified for the accessories has to be considered.

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Principle of Calculation

Silicone Compressibility

Experimental data suggest an elastic deformation for silicone elastomer gaskets of 10% at a pressure of 109 Pa (10,000 bar). The working pressure for elastomeric parts in HV cable accessories should be a factor of 1000 smaller, theoretically resulting in very small deformations on the magnitude of 100 ppm. This amount of compressibility is negligible. Another aspect is gaseous fractions in the elastomer parts, which would be of high compressibility. Silicone base materials are thoroughly de-gassed at time of delivery from the manufacturer. Moreover, the common two-component liquid silicone rubber (LSR) of the addition-curing type does not generate gaseous compounds during reaction. Because of this, stress control parts made from silicone elastomers do not normally contain dissolved gases. In any case, macroscopic bubbles, in any form, would normally render the parts useless for field control. Because of this, compressibility of silicone elastomer parts used these days can safely be neglected for the purpose of calculating stress cone deformation.

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Method of Calculation

Theoretical calculation of the expansion of tubes with applied inner pressure is highly complex, even without compressibility. For tubes with small wall thickness, some simplifications are applicable but this assumption does not strictly apply in this case. The Poisson’s ratio is the negative ratio of transverse to axial strain. Perfect incompressible materials have a Poisson’s ratio of exactly 0.5 if elastically deformed. Thus, the change in volume is zero (formula simplified):

calculation of the expansion of tubes with applied inner pressure stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4

Experimental results confirm that the change in length of stress cones for HV cable accessories is small, e.g. typically less than 1.5%. Based on the above and experimental findings, it can be assumed that the volume as well as length of an elastomeric part is not considerably changed by expansion. These assumptions allow for an analytical calculation of the problem. The area of every cross-section of the stress cone has to be constant. The rotation-symmetric design of the stress cone is not changed after expansion. Thereby, the inner radius is given (cable diameter) and the new outer radius is subsequently calculated with constant cross-sectional area. All other radii (e.g. of the conducting parts) are calculated accordingly.

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Relevance of Expansion Characteristic

A simple model of a cylinder is examined at 20% and 40% expansion. The following results, shown in Table 1, are obtained using the method of constant cross-section on the outline and for a typical radius inside the cylinder.

stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2018 09 14 at 15
Table 1: Dimensions of Expanded Cylindrical Body.
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Fig. 3: a) Cylinder with Di = 100 mm and Da = 200 mm without expansion b) Cylinder a) with 40% expansion. Di*= 140 mm, Da*= 222.7 mm stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 3: a) Cylinder with Di = 100 mm and Da = 200 mm without expansion b) Cylinder a) with 40% expansion. Di*= 140 mm, Da*= 222.7 mm.
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This example highlights two effects of expansion. Firstly, the thickness of the cylinder is reduced by 9.2% at 20% expansion and by 17.2% at 40% expansion. The impact on electric field stress on the surface of insulating parts will be shown below. Second, the movement of the red line (as shown in Fig. 3), having the identical distance to inner and outer diameter of the cylinder without expansion, shows deformation effects inside the cylinder caused by expansion. The line moves toward the inner diameter. Effect on electric field distribution is also shown below.

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Effect of Reduced Wall Thickness at Stress Cones

To ensure reliable operation of the accessory, a certain material thickness of the insulating component is necessary. This is important for stress cones of cable terminations and for joint bodies. Since a joint body is covered by a grounded semi-conductive layer, reduced material thickness could cause partial discharges or even puncture in the insulating rubber. Stress cones do not have a grounded layer outside but there is an interface to a second insulating component – oil in conventional fluid filled terminations or epoxy insulators in dry-type terminations. However, reduced material thickness is critical as well because electric field stress on the stress cone surface is thus increased. Even minor contamination during the installation process can lead to partial discharges. Fig. 4 shows the reduced material thickness of a stress cone with 30% expansion.

Fig. 4: 30% expansion of stress cone for outdoor terminations. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 4: 30% expansion of stress cone for outdoor terminations.
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Fig. 5: Electrical field stress on outer surface of stress cone in oil. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 5: Electrical field stress on outer surface of stress cone in oil.
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The diagram in Fig. 5 makes this clear. It shows the electric field stress on the outer surface of stress cone inside a fluid-filled outdoor termination. The calculated stress with the original material thickness of the stress cone shows stresses clearly below the limit (green line). With 30% expansion of the stress cone and equivalent reduction in material thickness, field stress on the stress cone surface (blue line) exceeds the limit by about 10%.

Effects of Deflector Deformations

Calculation of Deflector Shapes After Expansion

To evaluate a realistic stress cone design (as shown in Fig. 6), the contour of the earth deflector is separated into ‘layers’ of 0.1 mm thickness. For the deflector radius of each layer, the corresponding value after expansion is calculated. These values describe a new contour for the deflector, which then has to be transferred into the software for electric field calculation. Fig. 7 shows the comparison of the earth deflector with original and also with expanded shape.

Fig. 6: Typical layout of earth deflectors. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 6: Typical layout of earth deflectors.
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Fig. 7: Shape of earth deflector with and without expansion. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 7: Shape of earth deflector with and without expansion.
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For comparison of electric field distribution, the original contour is shifted parallel to the cable axis in such a way that its inner diameter is the same as the expanded layout. The software is then used to perform the electric field calculation. One possible way to put the output into graphs is to plot the electric stress alongside a relevant path, in this case the surface of the deflector or the gap between cable insulation and stress cone bore.

The same approach is used for the HV deflector or ‘middle electrode’ of an insulated joint body (see Fig. 8). This deflector encloses the connector of the conductor and is of a cylindrical form with rounded ‘tip’ at both ends. The contour of this is calculated to result in the lowest possible electric stress with the available distance to the grounded outer layer and to the earth deflectors.

stress cones stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 8: High voltage deflector (middle electrode) of joint body.
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Fig. 9: Shape of high voltage deflector ends with and without expansion. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 9: Shape of high voltage deflector ends with and without expansion.
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Impact of Deflector Deformation on Electric Field Stress

The following charts show the results of the calculation of the electric field of the previously shown deflectors in a stress cone and joint body. In case of an earth deflector, as shown in Fig. 10, the maximum field stress is not increased by deflector deformation as a result of expansion. There is just a shift in the position of the maximum. Another example of a HV deflector, shown in Fig. 11, is different. Here, the field stress maximum is increased by deflector deformation and exceeds the limit.

These results show that deflector deformation due to expansion causes changes in the electric field distribution. To overcome this problem, the shape of deflectors has to be designed in a way that they are optimized for deformation. Since a stress cone can be used for different cable dimensions and therefore expansion rate varies, exact optimization is not possible. Here ‘optimization’ means a design that minimizes any increase of electric field stress over the complete expansion range.

Fig. 10: Tangential electric field stress along interface XLPE insulation – stress cone with and without expansion. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 10: Tangential electric field stress along interface XLPE insulation – stress cone with and without expansion.
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Fig. 11: Field stress on surface of HV deflector with and without expansion. stress cones Impact of Stress Cone & Joint Body Expansion Rate on Electric Field Stress Screen Shot 2016 02 26 at 4
Fig. 11: Field stress on surface of HV deflector with and without expansion.
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