Design of an Anti-Corona Device for HVAC Substation Connectors

Citation: Larrea, A.M.; De La Hoz, M.; Etxegarai, A.; Mazon, A.J.; Aranzabal, I. Design of an Anti-Corona Device for HVAC Substation Connectors. Energies 2022, 15, 5781. https://doi.org/ 10.3390/en15165781 Academic Editors: Meng Huang, Yunxiao Zhang and Chenyuan Teng Received: 18 July 2022 Accepted: 4 August 2022 Published: 9 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article Design of an Anti-Corona Device for HVAC Substation Connectors Ane Miren Larrea , Manuel De La Hoz , Agurtzane Etxegarai , Angel Javier Mazon * and Itxaso Aranzabal Department of Electrical Engineering, Faculty of Engineering of Bilbao, University of the Basque Country UPV/EHU, 48013 Bilbao, Spain *Correspondence: javier[email protected] Abstract: One of the aspects to consider during high-voltage (HV) equipment design is the reduction in the probability of corona effect onset. Indeed, the corona effect is related to high electric field values beyond the equipment’s insulation levels and insulation strength, among other factors. This issue can be addressed during the design step, either by modifying the geometry of the electrical device or by including additional elements in the equipment structure to smooth out the voltage gradient along critical regions, such as anti-corona devices. The study of anti-corona devices for HV insulators is well documented, in contrast to substation connectors. Therefore, the present study proposed the design of a novel anti-corona device for HV substation connectors, including a method for the selection of its dimensions. This study shows that the relationship between the dimensional design variables and the critical electrical field on the connector is described by linear and rational functions. Thus, the design process times are cut down due to a reduction in the number of simulations required to run the assessment of the anti-corona device arrangement impact. Keywords: computer-aided manufacturing; connector; corona ring; electric fields; high voltage 1. Introduction The appearance of the corona effect is common in high-voltage (HV) overhead lines. The phenomenon corresponds to a discharge at the point where the electric field is greater than the disruptive strength of the insulation that surrounds the surface of the conductor and has several physical aspects, such as sound, luminance, and electromagnetic pulse waves that produce energy losses on the transmission system [ 1 ]. In the worst case, a corona effect could develop into an arc that causes the destruction of electric devices installed in overhead lines, such as insulators or connectors [2,3]. The study of the corona effect involves the calculation of the maximum electric field that insulation can withstand, which is a common step in the design of HV installations (e.g., substations) [ 4 ] and HV equipment (e.g., switchgear, insulators, connectors) [ 5 ]. The tools used in power system analysis studies generally include approximated modelling regarding the geometries of the transmission lines and towers [ 6 ]. However, in some specific geometries of insulators and connectors, a more detailed analysis is required [ 7 , 8 ]. In all cases, finite element analysis (FEA) is a valuable tool for calculating the electric field distribution. The electric field that is generated at the surface and around insulators and line connectors depends directly on the applied voltage and the geometry of the electrode. However, it is necessary to consider the environmental and insulation conditions to understand the corona effect completely [ 7 ]. Connectors are only subject to the line voltage, whereas in the case of insulators, one end is connected to the line voltage and the other end is grounded. The large difference in the voltage supported by the insulators causes an electric field gradient [ 9 ]. In contrast, for connectors, it is due to the smaller curvature in their geometry [10] since there is no voltage difference over them. The installation of anti-corona devices for insulators is well documented in the literature. In the case of insulating strings, Ilhan and Ozdemir [ 11 ] considered the electric Energies 2022,15, 5781. https://doi.org/10.3390/en15165781 https://www.mdpi.com/journal/energies Energies 2022,15, 5781 2 of 12 field surface of different points from the grading ring and the insulator string. Then, based on a sensitivity analysis, possible solutions were tested by considering the radio interference voltage produced by the configuration. Other authors applied optimisation methods [ 12 ]. However, these works did not show an evident solution to the location and size of the corona rings. Proposed optimisation algorithms are the bat flying algorithm [ 13 ], particle swarm optimisation [ 14 , 15 ], and surface response [ 16 ]. Generally, some minimum electrical field value is considered as an objective at a particularly critical point (e.g., the insulation triple point of an insulating string [ 17 ]) or along a characteristic line length (e.g., the periphery line of the insulating string [ 18 ]). Regarding the corona effect onset at substation connectors, Guiteras et al. [ 19 ] suggested installing shielding parts around the connectors or to cover them with a spherical cage under the same voltage. This solution reduces the electric field, and therefore, it can be used on systems operating under higher voltage. Nevertheless, for the specific problem conditions, the authors concluded that a redesign of the geometry of the connector is preferred. This approach is only valid for certain connectors since it may not be feasible for certain conductor arrangements. The redesign of the connectors also implies another kind of study for the connector (thermal, mechanical, etc.), and therefore, more industrial tests to be carried out. Three essential requirements are desirable in the design, manufacturing, and installation of corona rings. First, the rings must be simple to build. Second, the installation of the corona rings on site must be straightforward, involving a minimal number of steps. Consequently, in the present study, unconventional surfaces were not analysed, such as in Pattanadech et al. [ 20 ] and Liao et al. [ 21 ]. However, it could be a valid type of optimisation when applied to insulators [ 22 ]. Third, the point of attachment of the toroid is also relevant. Its position in space must be supported by some object to which it can be mechanically linked using an adjustment to achieve fixation [ 23 ]. For connectors, this means using their civil work support, if they have one, or fixing the rings on the conductors that enter the connector. The last option was considered for this work. Other time minimisation techniques in the test development are implemented in the modelling of anti-corona rings, such as the design of experiments (DOE) and analysis of variance (ANOVA) [ 16 ], in this case, for insulators. The limitation of this method lies in the fact that the relationships between the multiple factors considered must be linear [24]. The present study proposed the design of a novel anti-corona device, i.e., an anticorona ring, for HV substation connectors, including a method for ring dimension selection. The corona ring shape was mainly selected because it is easier to manufacture and maintain compared with spherical cages or other geometries. The applied method was focused on considering whether algorithmic expressions can be derived for the sizing of corona rings to reduce the analysis time in the design stage, as well as applying it to usual cases on substation connectors. It reduces the design process calculations by considering the relationship between the geometric dimensions of the corona rings and the value of the maximum surface electric field of the substation connector near the anti-corona ring. The objective was to reduce the number of trials to establish the possible relationship between design parameters, thus minimising the simulation resources required for an iterative optimisation process. The other advantage comes from the simulation of testing conditions using FEA. Although we considered the electrical field only at the connector surface, the connector geometry is challenging to model and must be done without any dimensional simplification (from a three-dimensional model to an axis-symmetry one, for instance). Any reduction in the numerical methods required speeds up the design process and increases the possibility of reduced testing. This paper is organised as follows. In the first part, geometrical details of the substation connectors, testing setup, and the anti-corona device arrangement are introduced. Thus, a numerical FEA model that was used to simulate standard HV laboratory conditions is presented, and the location of the maximum surface electric field is given. Based on previous results, in the second part, the specific positions of the corona rings near the Energies 2022,15, 5781 3 of 12 substation connectors under study that reduced the electric field are given. The results of several simulations to determine the effect of the proposed anti-corona ring’s geometrical factors on the electric field are presented. The last part offers information about the algebraic relationship between variables that diminish the design time, reduce the number of simulations, and consider the surface electric field as an indicator. The method can also be used on site to improve the location of the corona rings for standard conditions. 2. Description of the Connectors and the Testing Setup 2.1. Geometry of the Connectors and the Testing Setup The novel anti-corona device proposed in the present study was investigated for its application in specific aluminium connectors used in HV electrical substations. However, the arrangement is valid for any substation connector provided that a corona ring is installed in each of the connectors coupled through a substation connector following the design method introduced in Section 4. The connectors under study are shown in Figure 1, where their main dimensions are defined, including their length, width, height, and minimum radius. The dimensions of each connector are shown in Table 1. Energies 2022, 15, x FOR PEER REVIEW 3 of 12 This paper is organised as follows. In the first part, geometrical details of the substation connectors, testing setup, and the anti-corona device arrangement are introduced. Thus, a numerical FEA model that was used to simulate standard HV laboratory conditions is presented, and the location of the maximum surface electric field is given. Based on previous results, in the second part, the specific positions of the corona rings near the substation connectors under study that reduced the electric field are given. The results of several simulations to determine the effect of the proposed anti-corona ring’s geometrical factors on the electric field are presented. The last part offers information about the algebraic relationship between variables that diminish the design time, reduce the number of simulations, and consider the surface electric field as an indicator. The method can also be used on site to improve the location of the corona rings for standard conditions. 2. Description of the Connectors and the Testing Setup 2.1. Geometry of the Connectors and the Testing Setup The novel anti-corona device proposed in the present study was investigated for its application in specific aluminium connectors used in HV electrical substations. However, the arrangement is valid for any substation connector provided that a corona ring is installed in each of the connectors coupled through a substation connector following the design method introduced in Section 4. The connectors under study are shown in Figure 1, where their main dimensions are defined, including their length, width, height, and minimum radius. The dimensions of each connector are shown in Table 1. Figure 1. Geometry of connectors. Table 1. Geometrical dimensions of connectors. Connector Length (mm) Width (mm) Height (mm) Radius Min. (mm) Connector 1 470 470 100 6 Connector 2 585 270 95 3 Connector 3 240 120 230 4 In the present study, the investigation of the electric field around the connectors was based on the recreation of a laboratory testing setup, as shown in Figure 2. In the testing arrangement, several tubes allowed the connector to be suspended in the model, reflecting its possible installation in the substation, which would be the conventional assembly to be tested in the laboratory. Their diameters are the same as those used under standard installation requirements. One of the simplest and most effective solutions to reducing the electrical stress generated at the ends of the conductors in the test bench is to use corona-shielding systems (spheres and rings) at their ends [25] to prevent the electric field from increasing dramatically. Generally, these metal parts have a ring, spherical, or bowl shape [8]. Note that Figure 1. Geometry of connectors. Table 1. Geometrical dimensions of connectors. Connector Length (mm) Width (mm) Height (mm) Radius Min. (mm) Connector 1 470 470 100 6 Connector 2 585 270 95 3 Connector 3 240 120 230 4 In the present study, the investigation of the electric field around the connectors was based on the recreation of a laboratory testing setup, as shown in Figure 2. In the testing arrangement, several tubes allowed the connector to be suspended in the model, reflecting its possible installation in the substation, which would be the conventional assembly to be tested in the laboratory. Their diameters are the same as those used under standard installation requirements. One of the simplest and most effective solutions to reducing the electrical stress generated at the ends of the conductors in the test bench is to use corona-shielding systems (spheres and rings) at their ends [ 25 ] to prevent the electric field from increasing dramatically. Generally, these metal parts have a ring, spherical, or bowl shape [ 8 ]. Note that these elements are independent of the corona rings. The testing enclosure consisted of a box with dimensions 15 m × 15 m × 10 m and the arrangement was located at the centre, as shown in Figure 2. Energies 2022,15, 5781 4 of 12 Energies 2022, 15, x FOR PEER REVIEW 4 of 12 these elements are independent of the corona rings. The testing enclosure consisted of a box with dimensions 15 m × 15 m × 10 m and the arrangement was located at the centre, as shown in Figure 2. Figure 2. Modelled setup for the connectors. The box represents the testing room. 2.2. Configuration of the Simulation Tool The electric field of the connector was calculated with FEA. The assumptions considered were as follows. First, the FEA model simulation was carried out under HV laboratory conditions, according to normal pressure, temperature, and humidity, as established in standard IEC 61284 [26]. The FEA software tool of preference for this work was COMSOL Multiphysics. Second, when simulating a piece that is connected to conductors, its ends are exposed. That is, an infinite conductor cannot be defined. However, this had no impact when evaluating the piece, provided its length is considerably longer than the connector under analysis. Even so, a sphere covered the ends to avoid the maximum electric field of the whole assembly being found at the ends of the conductor, given its sharp geometry. The testing setup in Figure 2 was modelled in the FEA software. Then, the electric field was only analysed at its most critical point, i.e., the maximum values at each point of the connector surface were identified, omitting the fact that the voltage varied over time (the maximum value is at the peak of the sinusoidal wave). The simulation enclosure was grounded to define an appropriate environment. The rest of the pieces were connected to a line voltage of 450 kV peak as the reference. The characteristics of the mesh are a key factor when carrying out an analysis by means of FEA. To obtain precise results, the “very fine mesh” option in the meshing stage on COMSOL Multiphysics was selected. Other important characteristics related to the type of mesh used are described in Annex I. After defining meshing characteristics, a stationary study was carried out. Once the electric field on the connector was calculated, the point with the highest electric field value was obtained. 3. Geometry and Design of the Anti-Corona Device 3.1. Geometry of the Anti-Corona Device The electric field depends directly on the geometry of a power system element under voltage. Therefore, if the geometry of the element is varied, it has an impact on its electric field. To reduce the electric field of substation connectors, the present study proposed to include a ring around each conductor (Figure 3). In this way, it was possible to alter the geometry of the whole assembly (connector, rings, and conductors) and, in turn, the electric field. By attaching the rings to the conductors, a stable hold was allowed. Thus, a distance was kept between the ring and the connector, as defined by the designer. The ring Figure 2. Modelled setup for the connectors. The box represents the testing room. 2.2. Configuration of the Simulation Tool The electric field of the connector was calculated with FEA. The assumptions considered were as follows. First, the FEA model simulation was carried out under HV laboratory conditions, according to normal pressure, temperature, and humidity, as established in standard IEC 61284 [ 26 ]. The FEA software tool of preference for this work was COMSOL Multiphysics. Second, when simulating a piece that is connected to conductors, its ends are exposed. That is, an infinite conductor cannot be defined. However, this had no impact when evaluating the piece, provided its length is considerably longer than the connector under analysis. Even so, a sphere covered the ends to avoid the maximum electric field of the whole assembly being found at the ends of the conductor, given its sharp geometry. The testing setup in Figure 2was modelled in the FEA software. Then, the electric field was only analysed at its most critical point, i.e., the maximum values at each point of the connector surface were identified, omitting the fact that the voltage varied over time (the maximum value is at the peak of the sinusoidal wave). The simulation enclosure was grounded to define an appropriate environment. The rest of the pieces were connected to a line voltage of 450 kVpeak as the reference. The characteristics of the mesh are a key factor when carrying out an analysis by means of FEA. To obtain precise results, the “very fine mesh” option in the meshing stage on COMSOL Multiphysics was selected. Other important characteristics related to the type of mesh used are described in Annex I. After defining meshing characteristics, a stationary study was carried out. Once the electric field on the connector was calculated, the point with the highest electric field value was obtained. 3. Geometry and Design of the Anti-Corona Device 3.1. Geometry of the Anti-Corona Device The electric field depends directly on the geometry of a power system element under voltage. Therefore, if the geometry of the element is varied, it has an impact on its electric field. To reduce the electric field of substation connectors, the present study proposed to include a ring around each conductor (Figure 3). In this way, it was possible to alter the geometry of the whole assembly (connector, rings, and conductors) and, in turn, the electric field. By attaching the rings to the conductors, a stable hold was allowed. Thus, a distance was kept between the ring and the connector, as defined by the designer. The ring arrangement presented in this work allowed for a straightforward replacement of the rings if necessary and a perfect fastening at a distance from the piece as determined by the designer. In this way, the same connector could be used under different operation conditions by changing the geometry or distance of the rings instead of changing or Energies 2022,15, 5781 5 of 12 redesigning the connector. In addition, compared with spherical cages, rings are easier to manufacture and maintain. Energies 2022, 15, x FOR PEER REVIEW 5 of 12 arrangement presented in this work allowed for a straightforward replacement of the rings if necessary and a perfect fastening at a distance from the piece as determined by the designer. In this way, the same connector could be used under different operation conditions by changing the geometry or distance of the rings instead of changing or redesigning the connector. In addition, compared with spherical cages, rings are easier to manufacture and maintain. The design of the anti-corona device was classified according to the following parameters: thickness of the rings (A), inner diameter of the rings (Dint), and distance between the ring and the connector (dist), as identified in Figure 4. Figure 3. Connector with rings installed around the conductors. Figure 4. Design of individual rings installed around the conductors. 3.2. Modelling and Simulation of the Setup with the Anti-Corona Device The electric field of the connector was calculated with FEA again, but now for several cases that considered different parameter values. First, the testing setup in Figure 2 with the anti-corona device was modelled in the FEA software again. Then, the maximum electric field in the position found in Section 2.2 has been recorded. Two of the parameters were always constant and the last one was modified in order to find out the dependency with the maximum electric field on the connector surface. The simulation enclosure was grounded to define an appropriate environment. The rest of the pieces were connected to a line voltage of 450 kV peak as a reference, including the anti-corona device, since it was fixed to the cables of the setup. 4. Simulation Results 4.1. Simulation Results without the Anti-Corona Device The electric field at the surface of the connectors under study without any anti-corona device installed is shown in Figure 5. It can be observed that the maximum electric field value mostly occurred in the zone with the highest curvature. However, the normal vector from these critical surfaces was not always in the same direction as the axis of the tubes, as shown for connector 3 in Figure 5. Figure 3. Connector with rings installed around the conductors. The design of the anti-corona device was classified according to the following parameters: thickness of the rings (A), inner diameter of the rings (Dint), and distance between the ring and the connector (dist), as identified in Figure 4. Energies 2022, 15, x FOR PEER REVIEW 5 of 12 arrangement presented in this work allowed for a straightforward replacement of the rings if necessary and a perfect fastening at a distance from the piece as determined by the designer. In this way, the same connector could be used under different operation conditions by changing the geometry or distance of the rings instead of changing or redesigning the connector. In addition, compared with spherical cages, rings are easier to manufacture and maintain. The design of the anti-corona device was classified according to the following parameters: thickness of the rings (A), inner diameter of the rings (Dint), and distance between the ring and the connector (dist), as identified in Figure 4. Figure 3. Connector with rings installed around the conductors. Figure 4. Design of individual rings installed around the conductors. 3.2. Modelling and Simulation of the Setup with the Anti-Corona Device The electric field of the connector was calculated with FEA again, but now for several cases that considered different parameter values. First, the testing setup in Figure 2 with the anti-corona device was modelled in the FEA software again. Then, the maximum electric field in the position found in Section 2.2 has been recorded. Two of the parameters were always constant and the last one was modified in order to find out the dependency with the maximum electric field on the connector surface. The simulation enclosure was grounded to define an appropriate environment. The rest of the pieces were connected to a line voltage of 450 kV peak as a reference, including the anti-corona device, since it was fixed to the cables of the setup. 4. Simulation Results 4.1. Simulation Results without the Anti-Corona Device The electric field at the surface of the connectors under study without any anti-corona device installed is shown in Figure 5. It can be observed that the maximum electric field value mostly occurred in the zone with the highest curvature. However, the normal vector from these critical surfaces was not always in the same direction as the axis of the tubes, as shown for connector 3 in Figure 5. Figure 4. Design of individual rings installed around the conductors. 3.2. Modelling and Simulation of the Setup with the Anti-Corona Device The electric field of the connector was calculated with FEA again, but now for several cases that considered different parameter values. First, the testing setup in Figure 2with the anti-corona device was modelled in the FEA software again. Then, the maximum electric field in the position found in Section 2.2 has been recorded. Two of the parameters were always constant and the last one was modified in order to find out the dependency with the maximum electric field on the connector surface. The simulation enclosure was grounded to define an appropriate environment. The rest of the pieces were connected to a line voltage of 450 kV peak as a reference, including the anti-corona device, since it was fixed to the cables of the setup. 4. Simulation Results 4.1. Simulation Results without the Anti-Corona Device The electric field at the surface of the connectors under study without any anti-corona device installed is shown in Figure 5. It can be observed that the maximum electric field value mostly occurred in the zone with the highest curvature. However, the normal vector from these critical surfaces was not always in the same direction as the axis of the tubes, as shown for connector 3 in Figure 5. Energies 2022,15, 5781 6 of 12 Energies 2022, 15, x FOR PEER REVIEW 6 of 12 Figure 5. Electric field (kV/cm) at the connector surface. The maximum field values at the surface of the connectors without any ring were 45.2 kV/cm (connector 1), 46.5 kV/cm (connector 2), and 65.3 kV/cm (connector 3). The point of evaluation of the electric field for the simulations in Section 4.2 is indicated in Figure 5 by E bc . It coincided with the location of the maximum electric field E max , except in the study of connector 2. The proposed solution reduced the electric field magnitude in the closest points to the rings and the electric field vector must be almost parallel to the ring axis. Therefore, for connector 2, the point selected to analyse E bc was a point near the plane of the anti-corona device installation with an electric field value of 20.0 kV/cm. 4.2. Simulation Results with an Anti-Corona Device For the different configurations in Figure 3, several simulations were carried out by changing the ring parameters: thickness (A), inner diameter (Dint), and distance between the ring and the connector (dist). Figure 6 describes the maximum electric field value found at the connector surface under each specific parameter while keeping the others constant. It can be noted that for any configuration with anti-corona devices, the electric field was weaker than without the anti-corona devices, as indicated in Section 4.1, and the corona inception voltage was also reduced. (a) 5 10 15 20 25 30 35 40 45 15 35 55 75 95 E [kV/cm] A [mm] RING THICKNESS (A) Connector 1 Connector 2 Connector 3 Dint1= 100 mm dist1= 200 mm Dint2= 100 mm dist2= 250 mm Dint3=80mm dist3= 250 mm Figure 5. Electric field (kV/cm) at the connector surface. The maximum field values at the surface of the connectors without any ring were 45.2 kV/cm (connector 1), 46.5 kV/cm (connector 2), and 65.3 kV/cm (connector 3). The point of evaluation of the electric field for the simulations in Section 4.2 is indicated in Figure 5by E bc . It coincided with the location of the maximum electric field E max , except in the study of connector 2. The proposed solution reduced the electric field magnitude in the closest points to the rings and the electric field vector must be almost parallel to the ring axis. Therefore, for connector 2, the point selected to analyse E bc was a point near the plane of the anti-corona device installation with an electric field value of 20.0 kV/cm. 4.2. Simulation Results with an Anti-Corona Device For the different configurations in Figure 3, several simulations were carried out by changing the ring parameters: thickness (A), inner diameter (Dint), and distance between the ring and the connector (dist). Figure 6describes the maximum electric field value found at the connector surface under each specific parameter while keeping the others constant. It can be noted that for any configuration with anti-corona devices, the electric field was weaker than without the anti-corona devices, as indicated in Section 4.1, and the corona inception voltage was also reduced. Figure 6. Cont. Energies 2022,15, 5781 7 of 12 Figure 6. Electric field on the connector’s surface as a function of the ring dimensions: ( a ) ring thickness, (b) internal diameter, and (c) ring–connector distance. Even if the sweep range was modified for the different study cases, the tendency was similar for each parameter study. Depending on the electric field present at the installation point of the anti-corona device, the results of Figure 6allowed for deciding the dimensional characteristics of the anti-corona device as a first approximation. As observed in Figure 6a, the change in thickness of the ring (keeping its internal diameter constant) followed a downward linear trend. Analogously to the thickness, the increase in the internal diameter of the ring (Figure 6b) followed the same trend. Thus, the larger the internal diameter of the rings (keeping the rest of the parameters constant), the smaller the electric field. Finally, the variation of the distance between the ring and the connector in Figure 6c did not follow a linear trend, but a more complex trend. It was verified that the farther the rings were from the connector, the less influence they had on the electric field. Energies 2022,15, 5781 8 of 12 For a more accurate design, three fitting equations were extrapolated from Figure 6 based on the parameters analysed and the maximum electric field value. Equations (1)–(3) are intended for the selection of the corona ring dimensions. Equations (1) and (2) correspond to the relationships between the electric field E (kV/cm) and ring thickness A (mm) and between the electric field E (kV/cm) and the internal diameter of the ring Dint (mm) . Equation (3) relates the electric field E (kV/cm) and the distance between rings and connectors dist (mm). The value of R 2 for all the fittings was above 0.92. The constant values C1 to C6 according to the connector and equation are shown in Table 2. Emax =C1×A+C2 (1) Emax =C3×Dint +C4 (2) Emax =C5 √dist +C6 (3) Table 2. Constant values of Equations (1) to (3) for each connector. Connector C1 C2 C3 C4 C5 C6 Connector 1 −0.161 32.1 −0.103 37.3 −212 41.3 Connector 2 −0.138 16.8 −0.082 20.8 −376 36.9 Connector 3 −0.103 42.1 −0.074 47.3 −106 46.78 In Equations (1)–(3), the other parameters are kept constant, as specified in Table 2. A single fitted Equation (4) was deduced for the most general case, where all the parameters are described together. The constant values L1 to L4 for each connector are shown in Table 3. Emax =L1 +L2 ×A+L3 ×Dint +L4 √dist (4) Table 3. Constant values of Equation (4) for each connector. Connector L1 L2 L3 L4 Connector 1 56.8 −0.161 −0.103 −212 Connector 2 46.8 −0.138 −0.082 −376 Connector 3 56.2 −0.103 −0.074 −106 Equation (4) is useful for determining the electric field in a combination of the parameters that are not included in the studied cases, as long as the case considered is an interpolation. The distance between the rings and the connector (dist) is a key factor when studying the adequacy of an anti-corona device. If physical restrictions are disregarded, the closer the rings are to the piece, the smaller the electric field. In case the electric field value is not sufficiently low, the rings would have to be replaced by other rings of greater thickness or greater internal diameter. 5. Discussion Based on the configuration of a specific connector, it is possible to avoid the appearance of the corona effect by decreasing the value of the electric field at its surface. For this purpose, the present study proposed installing corona rings around each conductor linked by the connector. Under these conditions, the inception voltage increased, allowing for use of this equipment in applications with a higher electrical voltage. The geometry of the rings was defined by three parameters: thickness (A), internal diameter (Dint), and distance (dist), which can be calculated separately using Equations (1)–(3) for the connectors investigated in this study (Figure 1). The equations were verified for the connectors under study, which were subjected to a line voltage of 450 kV peak AC. The procedure can be generalised, and Energies 2022,15, 5781 9 of 12 thus, it can be applied to other connector designs at any voltage level. The generalised design methodology is introduced in the present paper. The paper presents other contributions, too. First, the maximum electric field under some conditions (e.g., connector 2) was not located in a favourable position for the anticorona ring to reduce its magnitude by a considerable percentage. The electric field reduction was strongly influenced by the separation between the anti-corona ring and the connector point under study. Hence, for very long connectors, the solution introduced in the present work could be impractical. Alternatively, the anti-corona ring can circumscribe the point where the electric field needs to be attenuated. However, the fixation of the ring should be further studied. Moreover, the design of the corona rings suggests the possibility of optimisation. Equation (4) gives a tentative objective function, where both economic and technical aspects should be considered. In any case, a sweep over each of the study cases is useful to analyse the behaviour of all the variables together, as shown in Figure 7. In each axis of Figure 7, one of the parameters involved in Equation (4) is represented. The electric field of each square has a colour that represents its value and corresponds to the case with the midpoint combination values. The hypersurface does not allow for inferring the behaviour of the design parameters analytically, but it does offer a global idea of the corona ring designs that should be considered by the designer. For instance, we could quickly establish areas with a limit value (e.g., 30 kV/cm) and discard those designs on the hypersurface. Energies 2022, 15, x FOR PEER REVIEW 9 of 12 linked by the connector. Under these conditions, the inception voltage increased, allowing for use of this equipment in applications with a higher electrical voltage. The geometry of the rings was defined by three parameters: thickness (A), internal diameter (Dint), and distance (dist), which can be calculated separately using Equations (1)–(3) for the connectors investigated in this study (Figure 1). The equations were verified for the connectors under study, which were subjected to a line voltage of 450 kVpeak AC. The procedure can be generalised, and thus, it can be applied to other connector designs at any voltage level. The generalised design methodology is introduced in the present paper. The paper presents other contributions, too. First, the maximum electric field under some conditions (e.g., connector 2) was not located in a favourable position for the anticorona ring to reduce its magnitude by a considerable percentage. The electric field reduction was strongly influenced by the separation between the anti-corona ring and the connector point under study. Hence, for very long connectors, the solution introduced in the present work could be impractical. Alternatively, the anti-corona ring can circumscribe the point where the electric field needs to be attenuated. However, the fixation of the ring should be further studied. Moreover, the design of the corona rings suggests the possibility of optimisation. Equation (4) gives a tentative objective function, where both economic and technical aspects should be considered. In any case, a sweep over each of the study cases is useful to analyse the behaviour of all the variables together, as shown in Figure 7. In each axis of Figure 7, one of the parameters involved in Equation (4) is represented. The electric field of each square has a colour that represents its value and corresponds to the case with the midpoint combination values. The hypersurface does not allow for inferring the behaviour of the design parameters analytically, but it does offer a global idea of the corona ring designs that should be considered by the designer. For instance, we could quickly establish areas with a limit value (e.g., 30 kV/cm) and discard those designs on the hypersurface. Figure 7. Electric field on connector 1 as a function of the ring dimensions: thickness (A), internal diameter (Dint), and ring–connector distance (dist), represented simultaneously. 6. Conclusions The installation of corona rings around a device to protect it, e.g., HV substation connectors, is a simple and effective way to avoid the appearance of the corona effect. The rings decrease the electric field at the critical points, and consequently, the probability of Figure 7. Electric field on connector 1 as a function of the ring dimensions: thickness (A), internal diameter (Dint), and ring–connector distance (dist), represented simultaneously. 6. Conclusions The installation of corona rings around a device to protect it, e.g., HV substation connectors, is a simple and effective way to avoid the appearance of the corona effect. The rings decrease the electric field at the critical points, and consequently, the probability of the corona effect occurring. The present study proposed a novel anti-corona device arrangement consisting of the installation of a corona ring per conductor coupled through substation connectors. This anti-corona device guaranteed a correct fixation and the corona effect onset was reduced. The design was studied for specific connectors used for the connection of four conductors under a line voltage of 450 kVpeak AC. The design of corona devices is a key factor when evaluating the electric field at a substation connector or in the case of substation repowering. Therefore, several simulations were carried out in the present work in order to determine the most adequate anti-corona