Submarine Power Cable Current Rating Calculations
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Current Rating Calculations
Submarine Cable Design
Bonding of Offshore Cable Systems
Modelling Submarine Cables
Armour Loss Calculations
Fundamentals
Landfall – Design and Modelling
Dynamic Ratings
J-tube – Design and Modelling
Seabed – Design and Modelling
2 K Criterion
Calculation Examples including Live Software Demo
• Submarine Installation
• J-tube Installation
Conclusions and Recommendations
Examples
ELEK Cable HV
Software
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for cable current rating
calculations.
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Suitable for any AC voltage and
HVDC cables.
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Complies with the IEC 60287
standards, the main authority for
cable rating calculations.
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Performs current rating
calculations for custom cables
under specific installation
conditions.
The accuracy of the calculations is validated
with CIGRE TB 880.
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IEC 60287 Current Rating Calculations
• The IEC Standard (60287) series provides analytical equations for
calculating cable current ratings.
• The IEC standards continue to be widely adopted because they:
• 1. Are adapted for common cable types and installation methods.
• 2. Are reasonably accurate, which leads to reliable, current ratings for
new and existing cable circuits.
• 3. Ensure consistency and comparability of current ratings determined
by different bidders, providers, or suppliers for stakeholders.
• The IEC standard calculations are somewhat complicated to
implement and ambiguous in parts.
9 parts to IEC 60287
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Submarine Power Cables Design
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Conductors:
– Usually copper. Some projects
use sections of Cu and Al.
– Deep water uses Aluminium for
its lighter weight during
installation and retrieval.
Insulation: XLPE for AC or DC is the
first choice.
Sheath: Around each core. Lead is
standard due to its flexibility.
Armour: Single or double layer (shore
landing sections). Provides strength
during installation and mechanical
protection during operation.
– Galvanised or stainless steel (nonmagnetic with low losses).
– SS grade 316 is recommended
over 304 but is very expensive.
Outer serving: Polypropylene yarn.
Dry design cables – Sheath is welded
separate lead (SL) or aluminium (SA).
Wet design – Sheath is replaced with
screen made of wires, tapes, or braid.
Cheaper & used for short lengths.
Lead sheath: The European Union's REACH
regulation classifies lead as a substance of Very High
Concern, potentially restricting future cable use.
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Bonding of Offshore HV Submarine Cables
Solidly Bonded HV AC Cables
For practical reasons, the metal layers (screen, sheath, and armour) in
offshore AC cables are solidly bonded.
30 kV Submarine Cable
The current rating is
920A at 90˚C
Sheath circulating
current: 85 A
Notes:
1. 3-core AC cables have lower electrical
losses than single-core cables.
2. Increasing conductor size has
diminishing benefits due to increased
sheath losses.
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Modelling Submarine Power Cables
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Requirements:
– Cable construction.
– Material properties.
– Layer dimensions.
Challenges:
– Incomplete information.
– Combined layers.
– Lay length factors unknown.
• Standard values: 1.01 for
cores, 1.05 for armour
– Back calculations required.
– Matching AC resistance.
– Custom layers.
– Material selection
(matching).
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Example of Modelling Submarine Cable
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Thermal Resistance of Fillers
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Three-core submarine cables
typically have an additional
jacket around each core.
An additional thermal resistance
between the sheath and the
armour (T2’) value is calculated
(not included in IEC 60287).
The dry thermal resistance of
the filler and armour bedding
must be used.
The water inside fillers with
voids is ignored.
Jacket around each
individual phase
conductor.
The thermal properties
of water-filled voids is
ignored.
The filler is assumed to
have uniform thermal
resistivity matching the
filler insulating material.
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Magnetic Armour Loss Considerations
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Magnetic armour wires will
electrically influence the skin
and proximity effects in the
cable conductors.
– IEC 60287 ignores this –
which is incorrect.
– CIGRE TB 880 proposes
multiplying factor of 1.5.
A multiplication factor of 1.5 is
applied to the circulating loss
factor for SL cables with
separate lead sheaths.
– May not always provide
conservative results [CIGRE
TB 908].
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Conductor AC resistance:
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Sheath circulating current loss
factor for separate lead sheath
cables:
Steel wire armour 1.5 x
multiplying factors
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Armour Loss Factor (λ2) Calculations
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Three core cables with non-magnetic wire armour λ2 = 0.
Reduction of armour losses due to sheath losses for SL cables.
Additional considerations according to CIGRE TB 908:
– Applicable for cables with a single armour of round metal wires.
– Suggests 1.5 x factor to conductor AC resistance is conservative.
– Considers the effect of magnetic armour on sheath eddy current losses.
– Considers lay direction of armour wires - Unilay or Contralay.
– Considers complex magnetic relative permeability of armour.
CIGRE TB 908 Implications
1. Conductor and sheath/screen losses considerably increase.
2. Armour losses significantly reduce.
3. Current rating improves significantly (typically by 10 %).
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Accurate Armour Loss Calculations
30 kV Submarine Array
Cable. 3 x 630 mm2
IEC/TB 880
with galvanised steel
wire armour.
TB 908
830 A
920 A
IEC/TB 880 Method
TB 908 Method
Difference (%)
Conductor loss
88.78 W/m
104.84 W/m
↑ 18.08
Sheath loss
14.45 W/m
19.105 W/m
↑ 32.214
Armour loss
37.34 W/m
7.77 W/m
↓ -79.19
Current rating
838.33 A
920.18 A
↑ 9.76
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Critical Sections for Cable Ampacity
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(1) Landfall, (2) J-tube, (3) Seabed.
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Landfall Sections – Design
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Open cut trench or HDD.
HDD is difficult in gravel-based
and rocky soils.
Typical burial depth 10 – 15 m.
TR of soil at landfall is higher
than at the seabed.
The ducts may be filled with
pumpable grout that does not
solidify over time.
Soil drying out above the water
table is a concern.
HDD ducts have a diameter of
1.5 – 2.5 times the cable OD.
Typically, the landfall area is the thermal
bottleneck for wind farm cable systems.
Limiting soil
dry out zone
Single-point bonding in the landfall
section can reduce losses by 20-25 %
Top image source: R. Spice, M. Hird, and J. Dix, "Dynamic cable rating with partial drying of soil," CIGRE Session Paper B1-11329, 2024.
Bottom image source: Olsen, E., Hovde, M., Pilgrim, J., & Williams, D. (2022). Single Point Bonding of 3-core Submarine Cables. CIGRE
Session 2022, B1 - Insulated Cables, PS2 / Future functionalities and applications, Paper ID 10961.
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Landfall Sections – Modelling
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Current rating () is substantially •
proportional to depth of burial
(d) and soil resistivity (ρ):
𝐼∝
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1
𝑙𝑛. 𝑑
Soil drying out at depths above
the water table.
1
𝐼∝
𝜌
Consider sections with buried
water-filled or air-filled ducts.
Water
-filled
Air/Solidfilled
Dry soil
zone
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Multiple export cables in pipe.
→ Requires FEM calculation.
Pipe
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Use calculated soil temperature
at significant depths (> 3 m):
Ducts
Meshing &
Temperature
Plot (ELEK
Software)
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Dynamic (Efficient) Ratings of Export Cables
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The export cable sizing can be
optimised by considering the
actual wind load generation.
Landfall export cables that are
deeply buried have a long
thermal time constant of
months or even years.
A multiple step dynamic rating
provides a method based on IEC
60287 and IEC 60853 to assess
the worst-case load event
during the cable life.
In a real-world example: rating
of deeply buried 220 kV export
cable increased by 8.4 %.
The long-term root mean square current (RMS) is
typically 50-70 % of the full load rating.
Several years of
wind data
K (τ)
Multi-step profile
(worst-case)
Cable temperature
response
T. Kvarts, I. Arana, R. Olsen, and P. Mortensen, "Systematic description of dynamic load for cables for offshore wind farms:
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Method and experience," 2016.
J/I-tube Sections – Design
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J-tube:
– Open-ended, J-shaped
section of metal pipe.
– Attached to an offshore unit.
– Bellmouth for cable entry.
Tube bends range between 1545 degrees.
Inner diameter should be not
less than 2.5 times cable OD.
Bending radius should not be
less than 20 times cable OD.
Multiple tubes should have
horizontal separation ≥ 1 m.
With bell mouths ≥ 2 m.
Image source: Elia Group
Tube can be made from
multiple sections with
vertical gaps to
facilitate air circulation
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J/I-tube Sections – Modelling
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An analytical approach is based
on heat transfer principles.
The hottest temperatures within
the J-tube are observed inside
the air-filled section.
Open to airflow at the top which
allows convective heat transfer.
Airflow is not circulating since
the tube is blocked at the
bottom due to the water.
Multiple cables
or a single cable
(heat sources)
are modelled.
Thermal model includes heat transfer by:
 Conduction inside/outside the tube.
 Convection inside/outside the tube.
 Radiation between cables and inner tube walls.
 Heat rise from solar radiation.
A new IEC standard for ampacity of cables in J-tubes is being prepared by WG 19.
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J-tube Sections – Factors Affecting Ampacity
Significant factors:
• Length of air-filled section.
• Ambient air temperature.
• Tube diameter. Small diameter
means higher ampacity.
• Solar radiation intensity.
• Wind speed.
Wind speed
Air-filled section length
Cables in separate J-tubes - 34 %
Cables combined in J tubes - 34.16 %
Major
Solar radiation
Standard values for sun-exposed area are 50% and
32%. The 50% assumes half-day shading, while 32% is
from Cress and Moltis's 1991 paper on risers.
Cables in separate J-tube - 9.37 %
Cables combined in a J-tube - 11.98 %
Minor
Cables in separate J-tubes - 14.61 %
Cables combined in a J-tube - 14.96 %
Moderate
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Seabed Sections – Design
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The cable can be buried during laying or
Direct burial in the seabed.
laid and then buried using a plough
Typical burial depth 1 – 4 m.
Nominal depth is 2 m.
At shore areas or places where
ploughing is not practical then
concrete mattresses or cable
covers are used.
At J-tube entries rock dumping
Exceptionally
is often adopted.
high and likely
TR tests are performed along caused by
organic content.
the cable route.
Typical soil resistivity at sea are
between 0.4 and 1.4 K.m/W.
Typical soil temperatures are
between 5 and 15 ℃ (Note).
Note: Seabed temperatures are highly variable and should be averaged using several years of data.
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Seabed Sections – Modelling
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Cables completely in water (natural or forced convection, varying salinity).
Cables partially buried in the seabed.
Cables fully buried under the seabed (standard IEC buried calculation).
Cables buried in ducts.
How does marine growth affect ampacity?
Water convection model
Partially-buried model
Marine growth model [BS 10009 (draft)]
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Underwater – Factors Affecting Ampacity
Typical ocean range
Dynamic cable systems:
Water velocity
𝐼 ∝ ΔΘ
Water temperature
Current rating () is
substantially proportional
to the difference
between conductor
temperature and ambient
temperature (Δϴ).
Tropical regions – 20-30 ℃, Temperate
regions – 5-20 ℃ (with seasonal variations)
Image (top-left) source: Prysmian
Ocean water range
Typical ocean water velocities – 0.1-2.5 m/s
Gulf Stream – 2.5 m/s, Deep ocean – 0.1 m/s
Salinity
Ocean water – 30-50 g/kg
Estuaries and inland seas – 0.5-30 g/kg
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Environmental Impact: The 2 K Criterion
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Guideline established by the
German Federal Agency for
Nature Conservation, requiring
that temperatures above a
buried submarine cable 200
mm below (or 300 mm1) the
seabed must not exceed 2 ℃ to
protect marine life.
2K criterion
Submarine cables cause local
temperature increases, affecting
benthic2 organisms. The burying
of cables can lead to
deoxygenation and the
formation of black spots on the
seabed, necessitating careful
cable design and installation.
(1)
(2)
(1) At rated current 2053 A,
the soil temperature
rises above 2 ℃ up to
0.17 m depth.
(2) To comply with the 2 K
criterion (such that soil
temperature is not
increased above 2 ℃
within 300 mm from
the seabed) the current
of the cables must be
reduced to 1579 A.
Footnote 1: This limit is even stricter in sensitive areas like the Wattenmeer National Park in Germany.
Footnote 2: Anything associated with or occurring on the bottom of a body of water, such as oceans, lakes, or rivers
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Calculation Examples
Now that we’ve explored the background, let’s model some examples!
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Submarine Installation
IN WATER
PARTIALLY BURIED
HVDC
INTER-ARRAY CABLE
WATER-FILLED DUCT
EXPORT CABLE
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J-tube Installation
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Conclusions and Recommendations
IEC 60287 is used for accurate ampacity calculations.
Submarine cable construction is complicated.
Solid sheath bonding is used for submarine cable systems.
The landfall is the most critical section (thermal bottleneck) of an offshore
wind farm.
• The J/I-tubes are another critical thermal bottleneck.
• The underwater sections have a higher rating but may be significantly
constrained by the 2 K criterion.
Recommendations:
1. Use the dynamic rating for deeply buried export cables by considering the
actual/predicted wind load data.
2. Use CIGRE TB 908 for accurate 3-core armour loss calculations that will
increase ratings by approximately 10 %.
3. Use the finite element method (FEM) for complicated installations including
multiple cable circuits inside pipes.
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