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Thermal modelling and analysis for offshore submarine high‐voltage direct current cable crossings

2015; Institution of Engineering and Technology; Volume: 9; Issue: 16 Linguagem: Inglês

10.1049/iet-gtd.2015.0551

1751-8695

Ziyi Huang, James Pilgrim, P. L. Lewin, S.G. Swingler, G. Tzemis,

Electrical Fault Detection and Protection

IET Generation, Transmission & DistributionVolume 9, Issue 16 p. 2717-2723 Research ArticleFree Access Thermal modelling and analysis for offshore submarine high-voltage direct current cable crossings Ziyi Huang, Corresponding Author Ziyi Huang Uta.Huang@hotmail.com Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorJames A Pilgrim, James A Pilgrim Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorPaul Lewin, Paul Lewin Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorSteve Swingler, Steve Swingler Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorGregory Tzemis, Gregory Tzemis National Grid Plc, Warwick Technology Park, Warwick, UKSearch for more papers by this author Ziyi Huang, Corresponding Author Ziyi Huang Uta.Huang@hotmail.com Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorJames A Pilgrim, James A Pilgrim Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorPaul Lewin, Paul Lewin Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorSteve Swingler, Steve Swingler Tony Davies High Voltage Laboratory, University of Southampton, Hampshire, UKSearch for more papers by this authorGregory Tzemis, Gregory Tzemis National Grid Plc, Warwick Technology Park, Warwick, UKSearch for more papers by this author First published: 01 December 2015 https://doi.org/10.1049/iet-gtd.2015.0551Citations: 6AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract With an increasing number of offshore high-voltage direct current wind farm projects planned, submarine cable crossings become inevitable. It is important to accurately rate these circuits, because if high temperatures occur at crossing points, the cable may age prematurely. At present, the IEC60287-3-3 crossing rating method is inapplicable to such crossings due to a failure of the 'Image' theory, and it is challenging to carry out other analytical studies due to the difficulties in modelling the subsea thermal environment. As a solution, this study presents a new finite element analysis approach to study the thermal performance of submarine crossings under various continuous rating combinations and rock protection layer conditions, to provide guidelines for crossing operation. With focus on the free thermal convection mechanism within the rock layer, the significance of this mechanism is highlighted in a quantitative manner. It shows that when the free convection is preserved, the upper circuit can operate safely with its stand-alone rating regardless of the crossing; while the lower circuit may require a de-rating if its stand-alone rating is thermally limited. 1 Introduction Conventionally, the maximum power transmission capability of high voltage (HV) cable circuits is limited by thermal considerations. Thus, it requires an accurate cable current rating calculation to prevent thermal ageing or even damage to the cable insulation, before premature cable failure and significant costs for maintenance or replacement. When two HV cable circuits cross one another, the mutual heating can become significant and thus, de-rating is normally required to protect both circuits. At present, the only widely recognised analytical cable crossing rating method is IEC60287-3-3 [1] (refer to [2, 3] for more details), which assumes a plane isothermal ground surface to apply the Kennelly's hypothesis [4] (i.e. 'Image' theory). However, for submarine crossings which require a post-lay trapezoidal rock berm for protection against unexpected trawling, seabed scouring, etc., this method becomes inapplicable. As the installed rock berm generally has a thermal resistivity different from the seabed, applying the Image theory cannot provide an overall homogenous backfill environment for the following superposition calculation. In addition, the heat dissipation across the inclined rock berm side wall cannot be properly modelled by the Image theory. Although some papers [5] suggest a minimum 30 to 45 cm vertical separation is adequate to prevent the thermal interference, no comprehensive modelling study has been completed. Therefore, 3D finite element analysis (FEA) modelling method is adopted in this paper to evaluate the thermal performance of submarine crossings. It allows more realistic modelling of the thermal environment, as the principle of the modern FEA numerical modelling method is solving local partial differential equations at the nodes of automatically generated meshes [6]. Note that an alternative is the real time thermal rating system by means of fibre optic based distributed temperature sensing, but few practical cases exist at this time which would provide the necessary data. Some key contributions from this work include a development of analytical thermal resistivity calculation for unconsolidated rock protection layer with/without considering in-pore free water convection, and a quantitative study of this free convection mechanism under various rating strategies indicating its significant impact on cable crossing thermal performance. Thus, guidelines can be drawn for rating submarine crossings under different ambient thermal environments. The paper first presents the general principles of submarine cable protection design and relevant parameter calculations, as this information directly affects the model geometry and simulation result. Subsequently, the FEA modelling approach is concisely presented, including key aspects such as geometry layout, heat source definition, and boundary condition assignment. Finally, the thermal performance of four different crossing installations is evaluated, before drawing the final conclusion. 2 Submarine cable protection and heat transfer mechanism When installing submarine cables, proper mechanical protection is critical to prevent many months of downtime due to accidental cable damage (e.g. fishing and anchoring). The primary protection method in any submarine condition is sufficient burial, which is guided by the Burial Protection Index (BPI) [7] in terms of burial depth. As suggested, a minimum BPI = 1 against most hazards requires a burial depth between 0.5 and 2 m depending on the seabed conditions. However, when burial becomes impractical, remedial cable protection methods will be applied which include rock placement and concrete mattress covering. Protection by rock placement requires a rock berm installation over the submarine cable on the seabed. A typical rock berm cross section is trapezoidal with 0.5–1.5 m height, 5–12 m base width. The side slope can be either 1:4 or 1:3 [8]. Moreover, rope linked concrete slabs can be placed over the cable as an alternative measure. For crossing applications, the major vertical separator is the concrete mattress which can be inserted between the two crossing circuits. Typical commercial concrete mattress has a dimension of 150–450 mm thickness and maximum 10 m × 4 m plane area [5]. This information is used to design the model geometry in Section 3. Once the geometry is confirmed, it is important to accurately model the heat transfer mechanism through the porous rock berm. Due to its water filled unconsolidated nature, three heat transfer mechanisms may occur simultaneously: i. thermal conduction in the solid phase, liquid phase and across the solid-liquid interface; ii. thermal convection between solid phase and liquid phase; iii. thermal radiation from one internal solid wall to another. However, the thermal radiation effects are negligible for this study, because the maximum temperature is limited to 50°C for MI paper insulated cables [9]. Therefore, this paper will model the fundamental thermal conduction, and the pore-size related free convection. 2.1 Pure thermal conductivity of porous medium Several models exist for the calculation of the pure thermal conductivity, λc, of a two-phase porous system (i.e. solid phase λs, liquid phase, λf) with given volume fraction (i.e. solid phase porosity, ϕ). Examples in the literature include harmonic and arithmetic mean, Hashin and Shtrikman mean [10], Kunii and Smith Model [11], and Maxwell mixing law [12]. 2.1.1 Harmonic and arithmetic mean Similar to the resistance calculation in circuit theory, the harmonic and arithmetic mean is the simplest mixing law which gives the widest thermal conductivity range. With respect to the heat flow direction, arithmetic mean and harmonic mean are equivalent to two phases being thermally in parallel and in series respectively [9]. (1) 2.1.2 Hashin and Shtrikman mean Conversely, the Hashin and Shtrikman mean gives the narrowest thermal conductivity range from various two-phase composite moduli, which works for both liquid/solid system and gas/solid systems [10]. By assuming a pre-specified volume fraction, it has the expression as (2) 2.1.3 Kunii and Smith's model As a combination of harmonic mean and arithmetic mean, Kunii and Smith's model adds a series term to the solid phase for the heat transfer between solid grains through a stagnant fluid layer near to the grain contact points [11]. The expression is presented below (3) (4)where; εrock is a porosity dependent empirical parameter, and ε1 and ε2 are functions of λs/λf (values found in [11]), referring to the uniform cubic spheres packing (ϕ = 0.476) and tetrahedral packing (ϕ = 0.259) respectively. For porosity ϕ ≤ 0.259 or ϕ ≥ 0.476, εrock equals to ε1 or ε2 respectively. 2.1.4 Maxwell mixing law Although Maxwell's mixing law was initially applied for the effective electrical conductivity of a random dispersion of spherical inclusions in a continuous medium, it is expanded into thermal analysis through calculating the inclusion induced perturbed temperature field [9]. (5) 2.2 Effect of natural thermal convection Typical protective berm rocks are granite or basalt in sufficient sizes to resist movement under hydrodynamic loads, but not so large as to make the berm overly permeable [13]. Moreover subject to the rock ship fallpipe size (unless side dumping), an average rock diameter is found to be between 100 and 450 mm in practical designs [14]. To calculate the range of possible berm porosity due to different rock packing profiles, rocks are assumed to be spherical and equal in size and conforming to the two main packing profiles are illustrated in Fig. 1. Fig. 1Open in figure viewerPowerPoint Schematic illustration of rock packing profiles Note that based on the rock size and packing assumed in this work, the pores are interconnected allowing water to flow through the rock berm. Natural thermal convection is expected to occur and proved through Rayleigh Number calculation in Section 2.3. However, the strength of natural convection also depends on the location and local size of pore. For instance, not studied in this work, although a third packing profile (right-hand side of Fig. 1) can give a similar overall rock berm porosity, the free convection is largely limited as the pores are isolated in relatively small sizes. At present, only empirical calculations are available and widely adopted. As the rock berm structure satisfies Darcy's Law [15] which states that the flow through a porous medium is linearly proportional to the applied pressure gradient and inversely proportional to the fluid viscosity, the Rayleigh number (Ra) and Nusselt number (Nu) are used in this paper to quantify the natural thermal convection effect. In fluid mechanics, the dimensionless Rayleigh number is used to specify the convection onset state, Ra ≥ 4π2 in this paper [16]. For natural convection heat transfer from a horizontal cylinder embedded in a porous medium, the Rayleigh number, Ra, is calculated by [17] (6)where; αV is the fluid volumetric thermal expansion coefficient (K−1), Km the medium permeability, g the gravity acceleration (m.s−2), d the cylinder diameter (m) which is the cable outer diameter of 120 mm, vf the fluid kinematic viscosity (m2.s−1), βm the effective diffusivity of the saturated medium, and Δθ is the temperature difference between the cylinder surface and ambient (°C). Although (6) assumes unbounded porous medium for the 'Image' theory, the model still applies in this paper because the relatively thermally-resistive concrete mattress beneath the cable is equivalent to a thermal symmetric boundary which minimises the heat flux across it. Note that the above condition is valid only for unblocked rock berms with free thermal convection in the pores. As shown later in Section 2.3, the equivalent rock berm thermal conductivity with convection effect can reach as much as five times of the concrete mattress thermal conductivity. When analysing a pore-blocked rock berms pores in Chapter 4, (6) becomes invalid and thus not applied. Similarly, the Nusselt number is also dimensionless, representing the ratio of the thermal convection to conduction. According to [18], the Nusselt number, Nu, is calculated as an empirical function of Rayleigh number, Ra (7)Note that to calculate an overall equivalent thermal conductivity value including the convective effect, the pure thermal conductivity is multiplied by a factor of (1+Nu). 2.3 Rock berm thermal parameter calculation As stated in [19], assuming the average thermal conductivities for brine and rock are 0.6 W.m−1.K−1 and 1.86 W.m−1.K−1, the rock berm pure thermal conductivities are summarised in Table 1, for two packing profiles: compact tetrahedral packing (ϕ = 0.259) and loose cubic packing (ϕ = 0.476). Table 1. Summary of porous rock berm pure thermal conductivity calculation Method Thermal conductivity (W.m−1.K−1) Harmonic and arithmetic mean 1.20 ≤ λc ≤ 1.53 (compact) 0.93 ≤ λc ≤ 1.26 (loose) Hashin and Shtrikman mean 1.39 ≤ λc ≤ 1.47 (compact) 1.10 ≤ λc ≤ 1.18 (loose) Kunii and Smith's model Maxwell mixing law From Table 1, it is verified that the harmonic and arithmetic mean gives the widest conductivity range, while the Hashin and Shtrikman mean gives the narrowest. Considering all the results, a suitable conductivity range specified for this paper is 1.20 ≤ λc ≤ 1.47 (compact) and 0.99 ≤ λc ≤ 1.18 (loose). To consider the free convection through the Rayleigh number and Nusselt number, the supplementary data summarised in Table 2 are required. Table 2. Supplementary environment data Parameter Value Unit acceleration of gravity 9.8 m.s−2 average rock berm thickness 1.1 m rock permeability 10−8 m2 brine mass density 1025 kg.m−3 brine specific heat capacity 4020 J.kg−1.K−1 brine kinematic viscosity 1.83 × 10−6 m2.s−1 brine thermal expansion coefficient 109 × 10−6 K−1 brine thermal diffusivity 1.46 × 10−7 m2.s−1 average brine ambient temperature 4 °C average cable surface temperature 22 °C Note that the average cable surface temperature is calculated through a simple 1D thermal network under steady state, based on a maximum allowable cable conductor temperature of 50°C and the corresponding 3000 A thermal rating (i.e. cable parameter found in Table 3). For transient analysis, the cable surface temperature should be set as variable. Based on all the data provided, the Rayleigh number and Nusselt number calculated are 86 by (6) and 4.3 by (7). Note that as Ra = 86 ≥ 4π2, the free convection assumption in rock berm is supported. Considering the worst case, the modelled rock berm conductivity λrock equals to 0.99 W.m−1.K−1 without convection, and 5.25 W.m−1.K−1, that is, 0.99 × (1 + 4.3), with convection. Considering a thermal conductivity of 1 W.m−1.K−1 for the concrete mattress, the application of (6) is also supported. Please refer to [19] for more details and note that the equivalent 'conductivity' term represents the total net heat flow. Table 3. Analytical rating calculation for isolated cable Burial depth 0 m 0.5 m 2 m 5.25 W.m−1.K−1 rock berm 0.99 W.m−1.K−1 rock berm Thermal – limited rating, Ithermal [20] isolated 3033 2523 2656 2442 bundled – – 2374 2089 Electrical stress – limited rating, Istress [21] isolated 1945 1922 1994 1928 bundled – – 1881 1848 3 FEA modelling approach For FEA modelling, it is important to carefully specify the geometry, material properties, physical equations and boundary conditions. 3.1 Crossing installation As the seabed condition varies from case to case, four crossing installations are proposed and shown in Fig. 2 against most submarine hazards, which follow the protection design and specification in Section 2. Detailed sizing can be found in [19]. Fig. 2Open in figure viewerPowerPoint Illustration of offshore submarine cable crossing installationa Both cable circuits are originally buried (monopole)b Both cable circuits are originally buried (bipole)c Upper cable circuit is originally laid on seafloor (monopole)d Both cable circuits are originally laid on seafloor (monopole) Primarily, the cable design adopts 2500 mm2 copper conductor, 21 mm thick Mass impregnated paper insulation, and the external jacket diameter is 120 mm. An optimum crossing angle of 90° with theoretically minimised mutual heating is adopted, representing the most preferred design in practice. However, other crossing angles may be installed due to geographical constraints. In [6], the effect of crossing angle on rating calculation has been studied and the rating variation for some HV cables between 60° and 90° is as little as 1%. For Installation One and Two, some cable lengths away from the crossing point are not protected by the rock berm area. This is because only the cable part at the crossing is lifted up onto the seafloor, and the rest of the circuit remains fully buried which does not need extra protection. Note that the thermal resistivity is 3.5 K.m.W−1 for polymer (XLPE, PE), 6 K.m.W−1 for paper (MI), 0.7 K.m.W−1 for seabed backfill (no partial drying-out assumed), 1 K.m.W−1 for concrete mattress and considered negligible for metals. The maximum allowable cable conductor temperature is 50°C. 3.2 Heat source and boundary condition By assuming negligible dielectric leakage current loss in high-voltage direct current (HVDC) cables [20], the primary heat source is the conductor joule loss, Wc = I2R, which results from the conductor electrical resistance. In FEA models, this loss is deployed uniformly onto the conductor surface boundary. Externally, 4°C isothermal boundary is specified on the model upper surface B1 and bottom boundary B2 the same as ambient. According to Lewin et al. [22], an isothermal condition at 7 m depth is sufficient to give a well matched result with IEC60287. In this work, the 7 m depth model is also verified against 10 and 15 m depth models, which shows a maximum cable temperature variation between 7 m model and 15 m model less than 1°C. The thermal symmetry boundary is assigned to front side boundaries B3 and B4 in Fig. 1a to benefit from a geometric simplification. For side boundaries B5 and B6, the thermal insulating boundary is specified, provided that a 15 m half cable length in Fig. 2 sufficiently guarantees that the temperature gradient (i.e. longitudinal heat flux) at cable end is almost zero. The governing equation is (8)where; n is the unit vector normal to the surface, k the thermal conductivity (W.K−1.m−1), ∇ the gradient operator and θ is temperature (°C) Fig. 3. Fig. 3Open in figure viewerPowerPoint Half cable length determination 4 Thermal performance evaluation In this section, the FEA numerical modelling method is used to evaluate the thermal performance of submarine cable crossings under various rating combinations. Particularly, it aims to verify whether claims that a 30–40 cm vertical separation is sufficient to prevent the thermal interference and evaluate the impact of free in-pore thermal convection on the crossing thermal performance. Before conducting the evaluation, stand-alone cable ratings are firstly calculated, which are summarised in Table 3. Note that changing the equivalent rock berm thermal resistivity would only affect the rating for unburied cables (0 m), because all the other fully buried isolated cables (0.5, 2 m) do not require rock berm protection. The electrical stress-limited rating in Table 3 occurs exclusively in HVDC cables due to the dielectric field inversion. Under the inversion, the maximum dielectric electrical stress is found near the insulation screen and increases with an increasing cable rating. As the maximum dielectric strength is specified, it limits the maximum cable rating accordingly. In Table 3, the electrical stress-limited rating is calculated under an ideal operating voltage of 500 kV as an example. However, to maximise the transmission capacity in reality, the voltage level may be reduced to release the stress limit on rating [21]. Thus, the thermal-limited rating would still be applied. A combination of both ratings is designed to examine various operating options and summarised in Table 4 below. Table 4. Rating combinations and testing conditions Test One Two Three upper circuit (U) Ithermal Istress Istress lower circuit (L) Ithermal Istress Ithermal 4.1 Thermal-limited rating for both circuits and result As the most traditional combination, the thermal-limited rating is applied to both upper and lower circuits and free convection in rock berm pores is included. This represents the case where both circuits are thermal – limited, or originally stress-limited but operated under a reduced voltage level in practice. Detailed modelling results are presented in Table 5. Table 5. Maximum temperatures at the crossing point under test one Installation One Two Three Four Lower circuit burial depth 0.5 m 2 m 0.5 m 2 m 0.5 m 2 m Unburied rock berm conductivity circuit maximum temperature at crossing point (°C) 5.25 W.m−1.K−1 upper 38.5 23.2 41.7 31.2 50.2 49.6 49.7 lower 53.1 50.6 61.4 54.2 52.8 50.2 63.2 0.99 W.m−1.K−1 upper 62.2 49.8 86.7 60.9 52.6 50.4 54.0 lower 60.5 53.6 83.2 62.2 56.7 52.7 58.2 From Table 5, all the upper circuits can operate safely under the stand-alone ratings and no de-rating is required when free thermal convection is assumed within the rock berm. Especially for installation one and two, the upper circuit temperature is reduced to <42°C because the section at the crossing point is lifted up and thus benefits from a better upwards heat dissipation. For installation three and four, it seems that the thermal interference from the lower circuit is effectively minimised with <0.2°C temperature rise. However, all the lower circuits exceed their upper thermal limit of 50°C by up to 13°C, meaning that a de-rating is necessary to prevent thermal damage. Although increasing the vertical spacing does help to mitigate the thermal interference, the normal 30–45 cm separation is shown over optimistic. For instance, at least 200 cm vertical separation is required for installation one and three. In Fig. 4, sample longitudinal temperature distributions for all the four installations are plotted as an example, which refer to a 0.5 m lower circuit burial depth. Fig. 4Open in figure viewerPowerPoint Sample longitudinal temperature distribution According to Fig. 4, the lower circuit has an increased maximum temperature at the crossing point due to the thermal interference, and it gradually drops towards the cable end. For the upper circuit, the crossing point temperature can be either similar to or much lower than the cable end. This is because the surrounding thermal environment at the crossing point is locally changed due to various installations, while the stand-alone rating is always calculated at the cable ends. However, if the free thermal convection effect is omitted due to the blockage of rock berm pores, de-rating is required for both upper and lower circuits. The maximum temperatures for both circuits at the crossing point are increased by at least 10°C, except for installation three and four. This is because for the last two installations, the stand-alone thermal ratings of unburied upper circuits are calculated with a consideration of blocked rock berm protection. For installation one and two, the upper circuit can experience an even bigger temperature rise than the lower circuit because the blocked rock berm may sometimes have a higher equivalent thermal resistivity than seafloor backfill, depending on the materials filling the rock berm pores. Therefore, the significance of the rock berm pore blocking effect is highlighted. 4.2 Electric stress-limited rating for both circuits and result In the Section 4.2, the electrical stress-limited rating is applied to both upper and lower circuits with free convection in rock berm pores. It models the situation where both newly installed circuits are stress-limited under an increased voltage level. Table 6 below summarises the simulation results. Table 6. Maximum temperatures at the crossing point under test two Installation One Two Three Four Lower circuit burial depth 0.5 m 2 m 0.5 m 2 m 0.5 m 2 m Unburied rock berm conductivity circuit maximum temperature at crossing point (°C) 5.25 W.m−1.K−1 upper 21.6 21.2 26.8 25.1 21.2 20.9 20.9 lower 28.5 31.7 37.9 42.2 28.2 31.3 25.4 0.99 W.m−1.K−1 upper 31.9 30.7 50.4 46.4 29.7 29.0 30.7 lower 31.3 32.7 48.6 47.4 30.4 32.1 32.8 As shown in Table 6, both the upper and lower circuits can safely operate without exceeding any thermal limit under their stand-alone electrical stress-limited rating. Therefore, no de-rating is required. Moreover, it shows that, when free thermal convection is excluded in rock berm, both circuits suffer an increased maximum conductor temperature. By comparison, the impact is stronger on the upper circuit where the temperature rise is around 10°C. 4.3 Electric stress-limited/thermal-limited rating for upper/lower circuit and result In this section, the lower electrical stress-limited rating is applied to the upper circuit while the lower circuit remains a higher thermal-limited rating. Based on the implications from the previous two tests, it is interesting to examine whether the thermal interference can be removed by reducing the upper circuit rating only. Moreover, it refers to a common situation where a third party owns the thermal-limited lower circuit and does not wish to consent to any rating reduction on its asset. Test results are found in Table 7. Table 7. Maximum temperatures at the crossing point under test three Installation One Two Three Four Lower circuit burial depth 0.5 m 2 m 0.5 m 2 m 0.5 m 2 m Unburied rock berm conductivity circuit maximum temperature at crossing point (°C) 5.25 W.m−1.K−1 upper 22.2 21.4 28.3 25.5 21.6 21.1 21.6 lower 52.4 50.1 60.0 53.6 52.0 49.7 62.3 0.99 W.m−1.K−1 upper 34.1 31.5 56.0 47.9 31.4 29.6 32.4 lower 57.8 52.5 76.9 60.5 56.3 51.8 56.2 Comparing Table 7 with Table 5, it is interesting to find that with free thermal convection in rock berm pores, the lower circuit only has <1°C maximum temperature drop, even though the upper circuit heat generation is much lower (i.e. over 15°C temperature drop after applying the stress-limited rating). Without the free thermal convection, an average of 20°C drop in upper circuit only leads to an average of 2°C drop in lower circuit. Therefore, it is interesting to see how the condition of rock berm and concrete alone could affect the thermal profile of the lower circuit. 4.4 Thermal blocking effect evaluation In this test, a sensitivity analysis is designed to examine the thermal effect of the concrete mattress and rock berm on the lower circuit temperature rise. To isolate this thermal effect, installation one and two are chosen without installing the upper circuit. Results are presented in Table 8. Table 8. Thermal blocking effect test for concrete mattress and rock berm % temperature rise at crossing point above cable end Installation condition Installation one, % Installation two, % Lower cable burial depth 150 mm mattress 400 mm mattress 5.25 W.m−1.K−1 rock berm 0.99 W.m−1.K−1 rock berm 6.5 14.6 0.5 m x x 11.5 33 x x 11.5 22 x x 15 33.8 x x 1.4 3.1 2 m x x 2.5 8.3 x x 2.5 4.8 x x 3 8.5 x x Table 8 verifies that the condition of concrete mattress and rock berm does significantly contribute to an increased lower circuit temperature at the crossing point. For instance, the temperature rise can reach up to 33% for bundled bipole cables (i.e. Installation Two). Moreover, for shallow buried cable, it has been shown that excluding the free thermal convection in rock berm pores can result in 18% more temperature rise along with 150 mm mattress, and 11% more with 400 mm mattress. Conversely, a 250 mm mattress thickness increase will only result in 5% more temperature rise along with unblocked rock berms, and 3.5% with blocked ones. However, this effect is minimised for deeply buried circuits where most heat is supposed to dissipate more evenly into ambient in radial direction, rather than mainly drawn upwards by the ground boundary in a shallow buried situation. Therefore, adding more layers on top will not heavily affect the overall heat dissipation for deeply buried circuits. This explains why an exclusion of the free thermal convection causes a larger temperature rise in the upper circuit than the lower one in the three previous tests. 5 Conclusion For offshore submarine HVDC cable crossings, FEA modelling is the only available method at present to evaluate the thermal performance. Within the crossing, the upper circuit can normally operate with its stand-alone rating, while a de-rating of the lower circuit might be required depending on its original rating limiting factor (i.e. thermal or electrical) if free thermal convection can be assumed within the rock berm pores. Otherwise, de-rating for both circuits is required. More importantly, this work highlights the importance of free convection within rock berms as a heat transfer mechanism in quantitative manner. Depending on the local seabed conditions, if the pore spaces in the rock become blocked with fine material, the cable may suddenly experience a more onerous thermal environment (e.g. higher temperature rise caused by non-convective rock berm than thickened concrete mattress under Installation Two). This uncertainty will complicate the submarine crossing design and operation. 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Distrib., 1999, 146, (4), pp. 360– 364 (doi: 10.1049/ip-gtd:19990360) Citing Literature Volume9, Issue16December 2015Pages 2717-2723 FiguresReferencesRelatedInformation