Impact of electromagnetic losses in closed two-component magnetic shields on the ampacity of underground power cables

Progress In Electromagnetics Research, Vol. 135, 601–625, 2013 IMPACT OF ELECTROMAGNETIC LOSSES IN CLOSED TWO-COMPONENT MAGNETIC SHIELDS ON THE AMPACITY OF UNDERGROUND POWER CABLES Juan Carlos del Pino-L´opez1, *, Pedro Cruz-Romero1, and Luis Serrano-Iribarnegaray2 1Department of Electrical Engineering, University of Seville, Camino de los Descubrimientos s/n, Seville 41092, Spain 2Department of Electrical Engineering, Polytechnic University of Valencia, Camino de Vera, s/n, Valencia 46022, Spain Abstract—In this paper two typical arrangements of underground single-core high voltage three-phase power cables (flat and trefoil protected by PVC pipes) inside a closed shield of three different materials (low-carbon steel, non-oriented grain steel and aluminium) are analysed. The shield has two components: a U-shaped base and a flat plate (cover) located on top of the base. Whereas most of previous papers on this subject only dealt with the degree of mitigation obtained with each material, this paper, in addition to also addressing this issue, mainly focusses on the effect that electromagnetic losses induced in the shield have on the ampacity of the cable and the cost involved (material and losses). To obtain the numerical results, a high number of simulations by a well-known commercial finite element method software (COMSOL Multiphysics) have been performed. The results obtained in the numerous cases analysed are widely commented and the solutions that enable an important mitigation with no current derating and at a comparatively low cost are highlighted. 1. INTRODUCTION In the last decades several proposals have been published to mitigate the magnetic field (MF) generated by underground cables, undesirable in certain circumstances (proximity of dwellings, disruptive effects in sensitive equipment, etc.). In particular, one design that has raised a certain interest in the scientific community is the shield composed Received 23 November 2012, Accepted 26 December 2012, Scheduled 2 January 2013 * Corresponding author: Juan Carlos del Pino-Lopez (v[email protected]). 602 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray by two parts: a U-shape base and a flat plate (cover) located on top of the base, obtaining a closed shield. This design, proposed in [1] for ferromagnetic materials, has the advantage over previous closed shields of simplifying the laying procedure and the subsequent maintenance operations, keeping meanwhile the typical high MF mitigation of closed shields compared with open ones. Moreover, it does not require welding because each of the longitudinal sections of the shield (of about 1 m) has a conical shape so that it can be partially overlapped to the next one. This solution has been installed in several real lines in the last years. In [2] three applications in Italy are described (trefoil configuration at 132 and 380 kV), obtaining a shielding effectiveness SE (ratio between the non-mitigated field and the mitigated one in dB) greater than 25 dB. On the other hand, in [3] several experiments of installation of a similar ferromagnetic shield in a 150 kV line in Belgium are described, comprising both trefoil and flat configurations and different thicknesses. The SE obtained was around 26 dB. In this work the use of aluminium was also tested, obtaining a lower SE = 18 dB. Regarding the losses generated by this kind of shield, in [4] an indepth analysis is performed, comparing the losses dissipated by three types of material: two ferromagnetic materials of different magnetic permeabilities and aluminium. The main conclusion is that if losses must be limited aluminium is the best choice, provided that its lower mitigation compared with high-permeability material is enough. The importance of minimizing electromagnetic losses is associated to two important issues that must be taken into account. On one side, these losses can cause an additional temperature rise in the conductors, leading to a current reduction of the line. On the other side, these losses increase the operational cost of the line over all the years of operation. Therefore it is crucial to know how to reduce the induced losses into the screen in order to reduce both issues. To this end, in this paper we go a step further by performing an in-depth parametric analysis by means of 2-D finite element method (FEM) models, developed to show the influence of the geometrical parameters of the shield not only on the MF mitigation achieved, but also on the electromagnetic losses induced in the shield and their influence on the carrying capacity of the mitigated line. Furthermore, the economic cost of the shield is studied, taking into account both the material cost and the losses cost over all the years of operation. In this sense, three types of material are considered: a low-carbon steel, a non-oriented grain steel and aluminium. In order to analyse the worst situation (from the thermal point of view), either a flat or trefoil Progress In Electromagnetics Research, Vol. 135, 2013 603 configuration of the power cables will be considered installed into PVC pipes. 2. FEM MODEL The problem to be solved is rather complex, since there are two physics involved: an electromagnetic problem coupled to a thermal one. In addition, the complex geometrical shape of the screen requires the use of numerical techniques. In this situation the best choice is to use a FEM formulation for a suitable modelling of the system to be studied in order to compute either the mitigated MF [5–7] or the temperature of the power cables [7–9]. The mathematical models to be solved are described in the following sections. 2.1. Electromagnetic Problem The mitigated MF is computed by means of a FEM model based on the following assumptions: 1) The cables are straight and infinitely long, thereby rendering the problem 2-D. 2) All materials have constant electrical properties, with the exception of conductive materials (conductors and screen), whose electrical conductivity σ(θ) depends on temperature: σ(θ) = σ0 1 + α(θ−20) (1) where θis the unknown temperature and σ0and αare the conductivity and the temperature coefficient of the material at 20◦C, respectively. 3) The electrical conductivity of mother soil is ignored. 4) The phase currents are sinusoidal and balanced. In this situation, the equation to be solved can be described as ∇ × µ1 µ∇ × ~ A¶+jωσ ~ A=~ Je(2) where ~ Ais the magnetic vector potential, ωthe angular frequency, σthe conductivity, µthe permeability, and ~ Jethe external current density. To take into account the nonlinear behaviour of ferromagnetic materials, µwill be considered as a function of the flux density. 604 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray For better understanding, the shielding effectiveness of the shield is quantified in terms of the ratio between the resulting (root sum square) nonmitigated and mitigated MFs in dB: SE(x, y) = 20 ·log  ¯¯¯ ~ Bp(x, y)¯¯¯ ¯¯¯ ~ Bs(x, y)¯¯¯  (3) where ~ Bpis the MF generated by the power cables and ~ Bsthe mitigated field. The power losses generated in the cables and in the shield will be used as the heat input for the thermal problem. In particular, eddy current losses (Pe) can be calculated from the total current density ~ J as follows: Pe=Z~ J·~ J∗ σdS (4) On the other hand, the losses generated in nonlinear ferromagnetic materials are also considered. These losses can be conceptually separated into three loss components, known as the hysteresis Ph, classical eddy current Pe, and additional losses Pa[10]. Considering Steinmetz’s [11–13] and Bertotti’s [13, 14] equations, the total losses can be described as P=Ph+Pe+Pa=KhfaBb m+Pe+Kaf1.5B1.5 m(5) where Pecan be computed by (4), Bmis the maximum flux density, Khis the hysteresis loss coefficient, Kais the additional loss coefficient, and aand bare constants. The latter coefficients are obtained from information provided by the manufacturer. 2.2. Thermal Problem The starting assumptions for the thermal problem are as follows: 1) Since power cables are straight and infinitely long, the heat transfer problem can be formulated in 2D on the x-yplane. 2) The temperature gradient in the soil at great distance (25 m) from the cables is zero. 3) Power cables are buried in homogeneous soil. 4) All materials have constant thermal properties, including the thermal resistivity of the soil, since no moisture migration is considered. 5) The effect of radiation at the ground surface is neglected. 6) The soil temperature at a depth of 15 m is known (θs). Progress In Electromagnetics Research, Vol. 135, 2013 605 7) The heat flux at soil surface is transferred by convection, with known convection heat transfer coefficient (h) and temperature of the air (θa) [15]. 8) Heat radiation is present between the outer cable surface and the inner pipe surface, with known surface emissivity (ε) of the materials [15]. 9) The air region inside the plastic pipes is a closed system, so heat convection is present. The mass conservation, momentum conservation and energy conservation equations must be solved [8]. As a consequence, the associated steady-state heat conduction equation can be expressed [15] as ∂ ∂x µ1 ρ ∂θ ∂x¶+∂ ∂y µ1 ρ ∂θ ∂y ¶+q= 0 (6) where qis the heat source generated by the power cables and the shield (computed from the electromagnetic problem), θis the unknown temperature, and ρis the thermal resistivity of each material. The coupled electromagnetic-thermal problem is iteratively solved as there are temperature-sensitive elements, such as the electrical conductivity of the conductors and the shield, which must be continuously corrected for the newly calculated temperature. Figure 1. Underground phase conductors, screen and trench dimensions. 606 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray Table 1. Parameters of the power cable (copper) and pipes. Conductor diameter (mm) 30.2 DC Resistance of conductor (20◦C) (Ω/km) 0.0274 XLPE insulation thickness (mm) 18.25 Insulation thermal resistivity (K·m/W) 3.5 Copper sheath thickness (mm) 0.45 Copper sheath Section (mm2)95 PVC jacket thickness (mm) 3.2 Jacket thermal resistivity (K·m/W) 6 Cable external diameter (mm) 74 Copper thermal resistivity (K·m/W) 0.0025 Copper thermal coefficient α(◦C−1)0.00393 Pipe external diameter (mm) 160 PVC thermal resistivity (K·m/W) 6 Pipe internal diameter (mm) 140 PVC emissivity 0.9 3. CASE STUDY 1: POWER CABLES IN FLAT CONFIGURATION Two situations are discussed in this research. The first one concerns about a closed shield installed to mitigate the MF generated by a 132 kV underground three-phase power system placed in flat configuration, as shown in Fig. 1. Phase conductors are installed in PVC pipes having an external diameter of 160 mm, with a separation of wp= 25 cm, buried at a depth of dp= 1.25 m and have a crosssection of 630 mm2, with the electrical and thermal parameters shown in Table 1. Trench dimensions are wt= 1.1 m and dt= 1.6 m. On the other hand, the values of the thermal resistivity of the soil is ρs= 1.25 K·m/W, and the temperature of the soil at a depth of 15 m is θs= 10◦C. The convection heat transfer coefficient at soil surface Progress In Electromagnetics Research, Vol. 135, 2013 607 Figure 2. Relative permeability of the employed steels. is h= 25 W/m2·K and the air temperature θa= 25◦C. Finally, the surface emissivity of the outer cable surface and the inner duct surface (both are PVC) is ε= 0.9. In this situation, the ampacity of the line is about 809 A when there is no shield installed, in accordance with the IEC 60287 standard, since the permissible operating temperature is θm= 90◦C (cable insulation is XLPE). Therefore this value will be considered as the current flowing through the line in the parametric analysis. The shield is initially considered to have the following dimensions taken as a reference: a 3 mm thickness, a base width of about 660 mm, a height of 532 mm and the cover of 1040 mm. Once the power cables are installed into the shield, it is filled with cement mortar, which has a thermal resistivity of ρc= 0.83 K·m/W. Three materials are employed in the shield: aluminium (Al), a low-carbon steel (LCS) and a non-oriented grain steel (NOS). Their electrical and thermal parameters are shown in Table 2, which includes the coefficients needed to compute the hysteresis and additional losses by Equation (5) (data obtained from the manufacturer). Since both steels are nonlinear ferromagnetic materials, its relative permeability is a function of the flux density µr(B), as shown in Fig. 2. These materials have been selected since they can provide SE values higher than 0 dB in any point of the external area out of the shield (hence the MF has been reduced), as shows Fig. 3, where it is represented the SE field provided by the shield with each material. Also, Fig. 3 shows a remarkable efficiency obtained with NOS shield compared to aluminium and LCS shields. Regarding the relative position between the shield and the phase conductors, in the parametric analysis it will be assume that the shield is approximately centered with the power cables (the bottom of the shield is about 0.2 m away from the cables center), as shown in Fig. 1, although it is easier to lay them directly on the bottom of the shield. 608 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray Table 2. Parameters for the various materials used in the shield (20◦C). Material Density (kg/m3)σ(S/m) µr ρ (K·m/W) α(◦C−1) Aluminium 2700 38·1061 0.00625 0.004 Low carbon steel 7580 6.5·106µr(B) 0.0125 0.005 Non-oriented grain steel 7700 2.3·106µr(B) 0.03 0.005 Material Kha b Ka Aluminium − − − − Low carbon steel 0.045 1.15 1.35 0.0045 Non-oriented grain steel 0.0109 1.234 1.775 4.4·10−4 (a) (b) (c) Figure 3. SE field and iso-lines for shields made of (a) aluminium, (b) low carbon steel and (c) non-oriented grain steel. This is because in this situation the maximum temperature of the cables is the lowest possible without having a negative influence on the SE achieved with the three materials used, as shown in Fig. 4, where it is represented the evolution of the SE achieved at the point of interest situated at 1 m above ground surface (Fig. 1) and the maximum temperature of the cables when the separation from the bottom of the shield is increased. Progress In Electromagnetics Research, Vol. 135, 2013 609 Figure 4. Evolution of the SE (at 1 m above ground surface) and the maximum temperature of the cables with their separation from the bottom of the shield (3-mm thickness). Table 3. Evolution of the electromagnetic losses induced in the shield (3-mm thickness) with the distance between cables and the bottom of the shield for the three materials used. Aluminium Low carbon steel Non-oriented grain steel Distance (m) Pe (W/m) Ph (W/m)Pa (W/m)Pe (W/m)Ph (W/m)Pa (W/m) Pe (W/m) 0 36.52 18.15 6.20 52.25 16.61 4.32 49.91 0.05 19.91 14.83 4.92 37.87 9.06 1.16 22.86 0.1 11.05 10.72 3.34 24.15 7.19 0.96 14.64 0.2 9.21 10.31 3.17 22.62 7.14 0.96 13.99 0.3 12.41 13.27 4.25 30.42 12.72 1.47 24.39 As can be seen, the SE remains constant, or even increases, when power cables are separated from the bottom of the shield, while their temperature decreases. In particular, when aluminium is used, the temperature of the cables can even decrease below the maximum temperature of 90◦C. This way the effect on the ampacity of the line is minimum. This is partially caused by the lower electromagnetic losses that are induced in the shield when the conductors are farther from its bottom, as shown in Table 3, where each term of the induced losses decreases with higher distances and are minimum at about 0.2 m of separation. In this sense, it should be remarked that the induced losses on steel shields are more important than those on the aluminium shield for the same shield size, as will be seen again through the parametric analysis. In addition, when the shield is centered with the line, the 616 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray Figure 8(a) is computed considering that the current flowing through the line is equal to its ampacity (809 A), which is the most critical situation. But this current may vary being usually lower and hence modifying both the mitigation efficiency and the total cost associated with the shield. This is shown in Fig. 8(b) for the shield solutions that comply with a minimum SE of 26 dB (Table 6), where it is represented the evolution of SE and the total cost of the shield with the line current. As can be seen, when the line current is lower than 809 A the SE values of aluminium and LCS shields increase slightly, while it is worsened in NOS shields. In any case, the mitigation levels remain high. In addition, the total cost for the three materials diminishes with the current, since the induced electromagnetic losses do so. 3.3. Comparison with Open Shields From the previous section it can be concluded that an aluminium shield may be the best choice due to its balance between shielding effectiveness and cost. However, it may be of interest to compare this solution with others that are usually employed in underground power cables in flat configuration. In particular, an aluminium open shield in H-layout can provide important mitigation levels close to those of the closed shield [7]. This is shown in Fig. 9, where it is represented the evolution of the SE and the total cost of both shields for a range of thicknesses that have no effect on the ampacity of the line. It is easily observed that both solutions can provided similar results in terms of Figure 9. Evolution of the SE (at 1 m above ground surface) and the total cost of 100 m of shield with the thickness of the plates used in an aluminium closed shield (total scaling factor of 1.3) and a H-layout open shield (vertical plates of 1-m lenght separated by 1 m; horizontal plate of 0.9 m length and situated at 0.12 m above cables). Progress In Electromagnetics Research, Vol. 135, 2013 617 Figure 10. Underground power cables in trefoil configuration inside the shield. mitigation levels, but the closed shield is still cheaper than the H- layout, although the difference is not as remarkable as that observed in Fig. 8(a) when using NOS or LCS closed shields. So, the H-layout still is a solution of interest to be taken into account, specially when trench dimensions are restricted, since its width is only about 1 m, lower than that of the closed shield that is about 1.35 m. 4. CASE STUDY 2: POWER CABLES IN TREFOIL CONFIGURATION The second study included in this research is in relation with the same type of shield applied to the same 132 kV power line, but in this case the line is laid in trefoil configuration, as shown in Fig. 10. Again, phase conductors are installed into 160 mm PVC pipes, which are in contact. All the boundary conditions for the electromagnetic and thermal problems are identical to those used in the study case 1, but this leads to a new ampacity value for the line in trefoil configuration, which is about 765 A, value that is considered to be flowing through the line in the parametric analysis. For the rest, all dimensions and parameters of the system remain the same, except for the shield size taken as a reference, which in this case is initially considered to have a 3 mm thickness, a base width of 350 mm, a height of 340 mm and the cover is 560 mm wide. This way, the shield 618 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray (a) (b) (c) Figure 11. SE field and iso-lines for shields made of (a) aluminium, (b) low carbon steel and (c) non-oriented grain steel. is adjusted to the line size in order to simplify the laying process to ensure the trefoil configuration, as described in [1, 2]. A new parametric analysis is developed next using also aluminium (Al), a low carbon steel (LCS) and a non-oriented grain steel (NOS), with the electrical and thermal parameters shown in Table 2 and Fig. 2. Again, these materials have been selected since they can provide relevant mitigations levels (SE >0 dB) nearby the point of interest situated at 1 m above ground surface, especially in the case of NOS shield, as shown in Fig. 11. Regarding the relative position between the shield and the power cables, contrary to that observed in the case study 1, there are no significant differences in the SE and the temperature of the cables whether the shield is centered or not with them, since there are lower losses induced in the shield due to the compact configuration of the line (Fig. 10). So, in our analysis we will assume the conductors installed at the bottom of the shield due to the easiness to lay them. 4.1. Parametric Analysis 4.1.1. Influence of Shield Thickness and Size If only the shield thickness is varied, the SE and the maximum temperature on the phase conductors evolve as shown in Fig. 12(a). In this case, the worst mitigation results are presented for the aluminium shield, which barely reaches mitigations levels of 21 dB when using a thickness of 8 mm. In the same way, the LCS shield has poor mitigation Progress In Electromagnetics Research, Vol. 135, 2013 619 (a) (b) Figure 12. Evolution of the SE (at 1 m above ground surface) and the maximum temperature of the cables with (a) the thickness and (b) the size of the shield. levels if low thicknesses are used, but its SE improves when using values higher than 5 mm. On the contrary, the NOS shield is always able to reach values of SE far above 26 dB. Nevertheless, only when using aluminium it is possible not to overheat the power cables employing a greater thickness. So NOS shields, and particularly LCS shields, have to be carefully considered as they may cause an important current rating reduction of the power line. Therefore, it may be of interest to visualize the effects on the SE and the maximum temperature when a bigger shield is installed. This is shown in Fig. 12(b), where the thickness of the shield is fixed to 3 mm. It is clear that only the aluminium shield improves its SE with the shield size, while it worsens on both steels, especially on the NOS shield. Regarding the impact on the maximum temperature of the cables, it can be easily limited by slightly increasing the shield size when using aluminium or NOS, although it is also possible in LCS shields employing a much bigger shield. This is caused by the higher electromagnetic losses generated in the LCS shield, as shown in Table 7. 4.1.2. Influence of Shield Width and Height The influence of both the shield height and width are shown in Figs. 13(a) and 13(b) respectively, for a thickness of 3 mm. It is easily observed that both dimensions have similar effects on the SE provided by each material, where only the mitigation efficiency of the aluminium shield slightly improves while it remains constant for the LCS case and strongly decreases for the NOS shield. 620 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray Table 7. Total power losses induced in the shield (W/m) for various shield sizes. Total scaling factor Aluminium Low carbon steel Non-oriented grain steel 1 16.22 22.91 8.34 1.3 14.81 18.35 7.31 1.6 14.42 16.27 6.72 2 14.11 14.35 6.19 (a) (b) Figure 13. Evolution of the SE (at 1 m above ground surface) and the maximum temperature of the cables with (a) the height and (b) the width of the shield. So the only important advantage obtained from increasing one of these dimensions is that it helps us to limit the impact on the ampacity of the line, as can be seen in Figs. 13(a) and 13(b). However, each material has a different reaction to these actions. For example, it seems that aluminium shields reach lower temperatures faster when increasing the shield height instead of increasing its width. On the contrary, the temperature seems to diminish faster when increasing the width on LCS or NOS shields. This behaviour is related not only with the electromagnetic losses induced on each material (Table 8), but also with their thermal properties. 4.2. Shield Cost The economic analysis developed for this case study has been performed with the same data listed in the corresponding section of the Progress In Electromagnetics Research, Vol. 135, 2013 621 Table 8. Total power losses in the shield (W/m) for various shield widths. Width scaling factor Aluminium Low carbon steel Non-oriented grain steel 1 16.22 22.91 8.34 1.3 16.35 19.83 7.86 1.6 16.60 18.17 7.79 2 16.72 16.78 7.61 (a) (b) Figure 14. Evolution of the SE (at 1 m above ground surface) and the total cost of 100 m of shield (total scaling factor of 1.3) with (a) the thickness of the shield and (b) the current through the line. case study 1 (material and energy cost). However it is again necessary to select a particular size for the shield in order to avoid the current derating of the power line. In this sense, a shield size of 1.3 times the size taken as a reference is selected. This shield is supposed to be installed along a line length of 100 m. With these data, Fig. 14(a) shows the most important results when the shield thickness is increased. In particular the evolution of the SE and the total cost of the shield over 30 years of operation. It can be seen that the higher cost is obtained when using LCS to make the shield, which is about 1.6 times higher than the cost associated to the cheapest option (aluminium). Moreover, the shielding efficiency of both materials are very similar, so it is clear that LCS shields would be rejected. However, the cost of NOS shield is quite close to that of aluminium shield, especially at lower thickness, and they provide much higher efficiency levels than the aluminium. 622 Pino-L´opez, Cruz-Romero, and Serrano-Iribarnegaray Table 9. Total cost of different shields (euro) over 30 years as a function of the minimum mitigation requirements. SEmin (dB) Aluminium Low carbon steel Non-oriented grain steel 26 17,262 29,365 13,164 28 21,125 29,867 13,465 29.5 23,864 30,035 13,839 31 25,746 31,854 14,265 Considering all this, if a minimum SE of 26 dB is required, it would be necessary to choose the suitable thickness for each material to meet this constraint. In our case this leads to a NOS shield of 2.5 mm, a LCS shield of 7 mm and an aluminium shield of 9 mm. The total cost associated to these configurations is listed in Table 9, which also includes the total cost for other requirements of SE. As can be concluded, for any SEmin the best choice in this case is to use a NOS shield, since it complies with the mitigation requirements with the lowest cost possible. In any case, the total costs shown in Fig. 14(a) have been computed for a current flowing through the cables equal to its ampacity (765 A), which is the most critical situation. In fact, the current is usually lower. So this is considered in Fig. 14(b), where it is shown the influence of the current of the line in the mitigation efficiency and the cost of the shield when a SEmin = 26 dB is required. It is easily observed that, in general, the current through the cables has no important effects on both parameters, except for the case of LCS shields, whose SE can be lower than 26 dB if the current flowing through the line is about 700 A or less. But also, for this material the total cost of the shield decreases faster than the cost of the other materials when the current is lower. 5. CONCLUSIONS The shielding effectiveness of a closed two-component magnetic shield and the impact of the induced electromagnetic losses on the total shield cost and the ampacity of the power cables have been studied for two cases of an underground power line, installed in flat and trefoil configuration, both protected by PVC pipes. Three different materials for the shield have been considered in the study (aluminium, a low carbon steel and non oriented grain steel), which is performed by means of a FEM electromagnetic-thermal coupled model. Progress In Electromagnetics Research, Vol. 135, 2013 623 A parametric analysis has been developed for the selected configurations of the line, concluding that the geometrical parameters of the shield have significant effects not only on the shielding effectiveness, but also on the ampacity of the shielded line and the shield cost (including material and losses cost over the years of operation). Tables and curves with comparative data presented in this paper help to select the suitable dimensions of a shield to be placed in a particular situation, in order to obtain the best mitigation levels and the lowest impact on the current rating of the mitigated line. In this sense, it has to be noticed that, in general, a greater size of the shield leads to a lower impact on the current rating of the mitigated line, but this also leads to a lower mitigation efficiency when using steel. From all the materials considered to make the shield, this study concludes that aluminium provides significant mitigation levels with the lowest cost possible when shielding a line in flat configuration. Its mitigation efficiency is even close to that observed in other high efficiency open shields frequently used in lines laid in flat configuration, like the H-layout, but with a lower cost. However, if higher values of mitigation are needed, a non-oriented grain steel shield may be selected to be installed next to the line, but in this case the total cost of the shield is about twice of the aluminium. On the other hand, if the line is laid in trefoil formation, a shield made of non-oriented grain steel is the best choice, since it provides very high mitigation levels with a reasonable cost, which is similar to the total cost of aluminium shields. However, in this situation aluminium shields cannot provide such high mitigation levels as those of the non-oriented grain steel. Finally, in all the studied cases it is noticed that low carbon steel shields can provide significant mitigation levels when using a high value of thickness, but its cost is quite high compared to those of the other materials considered, which makes this material not to be best choice in any of the studied configurations. ACKNOWLEDGMENT This work has been supported by the Spanish Ministry of Science & Innovation under grant ENE2010-18867 and by the regional Government of Andaluc´ıa under grant P09-TEP-5170. REFERENCES 1. Maioli, P., E. Borghi, F. Donazzi, and S. 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