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Electrical field simulation of 3 phase high voltage submarine power cables
Submarine Power Cables
A submarine power cable is a major transmission cable for carrying electric power below the surface of the water. These are called "submarine" because they usually carry electric power beneath salt water (arms of the ocean, seas, straits, etc.) but it is also possible to use submarine power cables beneath fresh water (large lakes and rivers). Examples of the latter exist that connect the mainland with large islands in the St. Lawrence River. The purpose of submarine power cables is to transport electric current at high voltage. The electric core is a concentric assembly of inner conductor, electric insulation and protective layers. The conductor is made from copper or aluminum wires, the latter material having a small but increasing market share. Conductor sizes less than 1200 mm2 are most common, but sizes over 2400mm2 have been made occasionally. For voltages, greater than 12 kV, the conductors are round in shape [1].
Cables are typically buried 1 m and exceptionally up to 10 m beneath the seabed to protect against trawl fishing, anchoring and other activities. The speed of burial is around 0.2km/h and is dependent on cable type and seabed conditions. Burial is not always possible, especially in rocky areas. Figure 1 shows the cross section of a 3-phase submarine cable. Figure 2 shows a typical submarine power cable system.
Figure 1 - cross section of a 3-phase submarine cable
CAD model of 3 phase submarine cable
The 3D model shown in Figure 3 was built in SolidWorks CAD. For the simulation of the submarine cable working in a real environment, we set up the simulation scenario where the cable is buried to 1.0 m beneath the seabed surface. The soil is assumed to be nonmagnetic. Figure 4 shows the simulation scenario of the cable. The table, Table 1, shown below contains major dimensions of simulated cable which are identical to real cable [2].
Table 1 - Dimensions of the submarine cable
| Thickness (mm) | Diameter (mm) | Note | |
| Conductor (Copper) | 29.8 | ||
| Insulator (XLPE) | 17.3 | 64.4 | Outer diameter |
| Sheath (Lead) | 2.3 | 69.0 | Outer diameter |
| Armour (Steel wire) | 5.0 | 172.8 | Outer diameter |
Figure 2 - 3D model of a 3 phase submarine cable
Figure 3 - Cabling scenario of the subsea cable used in simulation
Figure 4 - Geometrical model of the submarine cable for simulation
| Relative Permittivity | Conductivity (S/m) | |
| Conductor (Copper) | 1.0 | 58,000,000 |
| Insulator (XLPE) | 2.3 | 0.0 |
| Sheath (Lead) | 1.0 | 1,000,000 |
| Armour (Steel wire) | 1.0 | 1,100,00 |
| Sea bed | 25 | 0.25 |
Simulation Inputs and Results
The AC Electric Analysis allows users to analyze conduction currents due to time varying electric fields. Results generated by AC Electric Solver of EMS consist of Electric Field in V/m, Displacement Field in C/m^2, Current Density in Amps/m^2, Potential in Volts, Energy in Joules, Resistance in Ohms, Capacitance in Farads.
The AC Electric solver computes the electric fields excited by a Sinusoidal (or alternating) varying voltage or a Sinusoidal (or alternating) varying current.
Load restraint
Every core in the three-phase cable, comprising phases 1, 2 and 3 has 120° phase shift from each other. The magnitude of applied AC Voltage is 135kV at 50 Hz as operating frequency.
Table 3 - Applied voltages
| Conductors | AC Voltage (kV) | Phase shift (degree) |
| Core 1 | 135 | 0 |
| Core 2 | 135 | 120 |
| Core 3 | 135 | 240 |
Meshing
Figure 5 shows the mesh on a 3-phase cable. Meshing is a crucial step in any FEA simulation. EMS estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry and dimensions of the model, element size, mesh tolerance, and mesh control. In the early stages of design analysis where approximate results may suffice, you can specify a larger element size for a faster solution. For a more accurate solution, a smaller element size may be required.
We can control the mesh size from one body to another depending on its dimensions and its importance in the result by applying a mesh control. Applied mesh controls for this model are listed in table 4.
Table 4 - Mesh controls applied for this model
| Name | Mesh Size (mm) | Bodies/ components |
| Mesh control 1 | 5.00 | Conductors/Insulator/ Sheath / Armour |
| Mesh control 2 | 1.75 | Faces of conductors/ insulator/ Sheath/ Armour |
Figure 5- Meshed model of three- phase cable.
Electric Results
As mentioned above AC Electric solver generates the current distributions, E-field distributions and potential differences. In addition, any quantity that can be derived from the basic electromagnetic quantities can be analysed. Figure 6,7 shows the distribution of the electric field inside all cores of cable. Metallic sheaths in the cable create earthed shields for all cores, so the E-fields are seen to be strictly confined in each core and have a radially symmetric distribution within the dielectric XLPE. Consequently, no E-field is leaked from each core, giving rise to zero E-field outside the submarine cable. The electric field E attains its maximum value at the surface of the conductor and it is about 1.0969 e+7 V/m (about 1.0926e+7 V/m in [1]). Figure 8 shows the electric potential in the submarine cable.
Figure 7 - E field animation versus phase, vector plot
Figure 8 - Electric potential
Conclusion
Electromagnetic simulation using EMS can help engineers to design and size their high voltage submarine cable by optimizing geometrical properties and choosing right materials with low cost. Also, it can help to examine all possible breakdown voltage which can damage AC subsea cables. To read more about AC high voltage submarine cables and their effect on the marine ecosystem, visit our blog https://www.emworks.com/blog/high-voltage/3-phase-high-voltage-submarine-power-cables.
References
[1]: https://en.wikipedia.org/wiki/Submarine_power_cable[2]: “Electromagnetic Simulations of 135 kV Three-Phase Submarine Power Cables” by Dr Yi Huang, Department of Electrical Engineering & Electronics Liverpool, L69 3GJ UK retrieved from the following URL - https://corporate.vattenfall.se/globalassets/sverige/om-vattenfall/om-oss/var-verksamhet/vindkraft/kriegers-flak/14-mkb-bilaga-414-cmacs-electrom.pdf