Modeling Subsea Cables for Offshore Wind Power at Hellenic Cables

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“Legal guidelines, Whitehouse obtained 5 minutes sign. Coil indicators too weak to relay. Attempt drive sluggish and common. I’ve put intermediate pulley. Reply by coils.”

Sound acquainted? The message above was despatched by means of the primary transatlantic telegraph cable between Newfoundland and Eire, method again in 1858. (“Whitehouse” refers back to the chief electrician of the Atlantic Telegraph Firm on the time, Wildman Whitehouse.) Quick ahead to 2014: The underside of the ocean is house to almost 300 communications cables, connecting nations and offering web communications world wide. Quick ahead once more: As of 2021, there are an estimated 1.3 million km of submarine cables (Determine 1) in service, starting from a brief 131 km cable between Eire and the U.Okay. to the 20,000 km cable that connects Asia with North America and South America. We all know what the world of submarine cables appears to be like like in the present day, however what in regards to the future?

Determine 1. Submarine cables hold the world related.

Transferring Wind Energy Offshore

The offshore wind (OFW) trade is without doubt one of the most quickly advancing sources of energy world wide. It is smart: Wind is stronger and extra constant over the open ocean than it’s on land. Some wind farms are able to powering 500,000 properties or extra. At present, Europe leads the market, making up nearly 80 % of OFW capability. Nevertheless, the worldwide demand for vitality is predicted to extend by 20 % in 10 years, with a big majority of that demand equipped by sustainable vitality sources like wind energy.

Offshore wind farms (Determine 2) are made up of networks of generators. These networks embody cables that join wind farms to the shore and provide electrical energy to our energy grid infrastructure (Determine 3). Many OFW farms are made up of grounded buildings, like monopiles and different varieties of bottom-fixed wind generators. The foundations for these buildings are costly to assemble and troublesome to put in in deep sea environments, because the cables should be buried within the seafloor. Set up and upkeep is simpler to perform in shallow waters.

Wind generators for offshore wind farms are beginning to be constructed additional out into the ocean. This creates a brand new want for well-designed subsea cables that may attain longer distances, survive in deeper waters, and higher join our world with sustainable energy.

The way forward for offshore wind lies in wind farms that float on ballasts and moorings, with the cables laid instantly on the seafloor. Floating wind farms are a fantastic resolution when wind farms located simply off the coast develop crowded. They will additionally reap the benefits of the larger and extra highly effective winds that happen additional out to sea. Floating wind farms are anticipated to develop extra well-liked over the subsequent decade. That is an particularly enticing choice for areas just like the Pacific Coast of the US and the Mediterranean, the place the shores are deeper, versus the shallow waters of the Atlantic Coast of the U.S., U.Okay., and Norway. One essential requirement of floating OFW farms is the set up of dynamic, high-capacity submarine cables which can be capable of successfully harness and ship the generated electrical energy to our shores.

Photo of dozens of wind power towers installed offshore.

Determine 2. Offshore wind farms are anticipated to assist meet rising calls for for sustainable vitality.

Picture by Ein Dahmer — Personal work. Licensed below CC BY-SA 4.0, through Wikimedia Commons

Design Elements for Resilient Subsea Cables

Ever skilled slower than typical web? Failure of a subsea cable could also be guilty. Cable failures of this sort are a standard — and costly — prevalence, whether or not from the harm of mechanical stress and pressure brought on by bedrock, fishing trawlers, anchors, and issues with the cable design itself. Because the offshore wind trade continues to develop, our have to develop energy cables that may safely and effectively join these farms to our energy grid grows as effectively.

Earlier than fixing or putting in a submarine cable, which may price billions of {dollars}, cable designers have to make sure that designs will carry out as meant in undersea circumstances. Immediately, that is usually completed with the assistance of computational electromagnetics modeling. To validate cable simulation outcomes, worldwide requirements are used, however these requirements haven’t been capable of sustain with current developments in computational energy and the simulation software program’s rising capabilities. Hellenic Cables, together with its subsidiary FULGOR, use the finite ingredient technique (FEM) to investigate their cable designs and examine them to experimental measurements, usually getting higher outcomes than what the worldwide requirements can supply.

Left photo shows a submarine cable with its layers remove revealing three inner cables; right image shows closeup of three inner cables, each surrounded by layers of metal and plastic for insulation, structure, and protection.

Determine 3. Examples of three-core (3C) submarine cables out there from Hellenic Cables.

Up to date Methodology for Calculating Cable Losses

The Worldwide Electrotechnical Fee (IEC) offers requirements for electrical cables, together with Commonplace 60287 1-1 for calculating cable losses and present rankings. One downside with the formulation utilized in Commonplace 60287 is that it overestimates cable losses — particularly the losses within the armor of three-core (3C) submarine cables. Cable designers are pressured to undertake a brand new methodology for performing these analyses, and the group at Hellenic Cables acknowledges this. “With a extra correct and sensible mannequin, vital optimization margins are anticipated,” says Dimitrios Chatzipetros, group chief of the Numerical Evaluation group at Hellenic Cables. The brand new methodology will allow engineers to scale back cable cross sections, thereby decreasing their prices, which is the paramount aim for cable manufacturing.

An electrical cable is a fancy gadget to mannequin. The geometric construction consists of three predominant energy cores which can be helically twisted with a selected lay size, and a whole bunch of further wires — display screen or armor wires — which can be twisted with a second or third lay size. This makes it troublesome to generate the mesh and clear up for the electromagnetic fields. “It is a tedious 3D downside with difficult materials properties, as a result of a number of the parts are ferromagnetic,” says Andreas Chrysochos, affiliate principal engineer within the R&D division of Hellenic Cables.

In recent times, FEM has made a large leap in terms of cable evaluation. The Hellenic Cables group first used FEM to mannequin a full cable part of round 30 to 40 meters in size. This turned out to be an enormous numerical problem that may solely realistically be solved on a supercomputer. By switching to periodic fashions with a periodic size equal to the cable’s cross pitch, the group lowered the issue from 40 meters all the way down to 2–4 meters. Then they launched short-twisted periodicity, which reduces the periodic size of the mannequin from meters to centimeters, making it a lot lighter to unravel. “The progress was great,” says Chrysochos. (Determine 4)

Though the enhancements that FEM brings to cable evaluation are nice, Hellenic Cables nonetheless must persuade its purchasers that their validated outcomes are extra sensible than these offered by the present IEC normal. Purchasers are sometimes already conscious of the truth that IEC 60287 overestimates cable losses, however outcomes visualization and comparability to precise measurements can construct confidence in venture stakeholders. (Determine 5)

Finite Ingredient Modeling of Cable Programs

Electromagnetic interference (EMI) presents a number of challenges in terms of designing cable methods — particularly the capacitive and inductive couplings between cable conductors and sheaths. For one, when calculating present rankings, engineers have to account for energy losses within the cable sheaths throughout regular operation. As well as, the overvoltages on cable sheaths have to be inside acceptable limits to fulfill typical well being and security requirements.

As Chrysochos et al. talk about in “Capacitive and Inductive Coupling in Cable Programs – Comparative Research between Calculation Strategies” (Ref. 3), there are three predominant approaches in terms of calculating these capacitive and inductive couplings. The primary is the complicated impedance technique (CIM), which calculates the cable system’s currents and voltages whereas neglecting its capacitive currents. This technique additionally assumes that the earth return path is represented by an equal conductor. One other frequent technique is electromagnetic transients program (EMT) software program, which can be utilized to investigate electromagnetic transients in energy methods utilizing each time- and frequency-domain fashions.

The third technique, FEM, is the muse of the COMSOL Multiphysics software program. The Hellenic Cables group used COMSOL Multiphysics and the add-on AC/DC Module to compute the electrical fields, currents, and potential distribution in conducting media. “The AC/DC Module and solvers behind it are very sturdy and environment friendly for most of these issues,” says Chrysochos.

The Hellenic Cables group in contrast the three strategies — CIM, EMT software program, and FEM (with COMSOL Multiphysics) — when analyzing an underground cable system with an 87/150 kV nominal voltage and 1000 mm2 cross part (Determine 6). They modeled the magnetic discipline and induced present density distributions in and across the cable system’s conductors, accounting for the bonding kind with an exterior electrical circuit. The outcomes between all three strategies present good settlement for the cable system for 3 totally different configurations: strong bonding, single-point bonding, and cross bonding (Determine 7). This demonstrates that FEM could be utilized to all varieties of cable configurations and installations when taking into consideration each capacitive and inductive coupling.

The Hellenic Cables group additionally used FEM to review thermal results in subsea cables, corresponding to HVAC submarine cables for offshore wind farms, as described in “Overview of the Accuracy of Single Core Equal Thermal Mannequin for Offshore Wind Farm Cables” (Ref. 4). The present IEC Commonplace 60287 1-1 features a thermal mannequin, and the group used FEM to determine its weak spots and enhance its accuracy. First, they validated the present IEC mannequin with finite ingredient evaluation. They discovered that the present requirements don’t account for the thermal affect of the cable system’s metallic display screen supplies, which implies that the temperature could be underestimated by as much as 8°C. Deriving analytical, correcting formulation primarily based on a number of FEM fashions, the group lowered this discrepancy to 1°C! Their evaluation additionally highlights vital discrepancies between the usual and the FEM mannequin, particularly when the corresponding sheath thickness is small, the sheath thermal conductivity is excessive, and the facility core is giant. This challenge is especially essential for OFW initiatives, because the cables concerned are anticipated to develop bigger and bigger.

Additional Analysis into Cable Designs

Along with learning inductive and capacitive coupling and thermal results, the Hellenic Cables group evaluated different features of cable system designs, together with losses, thermal resistance of surrounding soil, and grounding resistance, utilizing FEM and COMSOL Multiphysics. “Usually, COMSOL Multiphysics is far more person pleasant and environment friendly, corresponding to when introducing temperature-dependent losses within the cable, or when presenting semi-infinite soil and infinite ingredient domains. We discovered a number of methods to confirm what we already find out about cables, their thermal efficiency, and loss calculation,” says Chatzipetros.


The conductor measurement of a subsea or terrestrial cable impacts the price of the cable system. That is usually a vital facet of an offshore wind farm venture. To optimize the conductor measurement, designers want to have the ability to precisely decide the cable’s losses. To take action, they first turned to temperature. Currents induced in a cable’s magnetic sheaths yield further losses, which contribute to the temperature rise of the conductor.

When calculating cable losses, the present IEC normal doesn’t think about proximity results in sheath losses. If cable cores are in shut proximity (say, for a wind farm 3C cable), the accuracy of the loss calculation is lowered. Utilizing FEM, the Hellenic Cables group was capable of research how conductor proximity results affect losses generated in sheaths in submarine cables with lead-sheathed cores and a nonmagnetic armor. They then in contrast the IEC normal with the outcomes from the finite ingredient evaluation, which confirmed higher settlement with measured values from an experimental setup (Determine 8). This analysis was mentioned within the paper “Induced Losses in Non-Magnetically Armoured HVAC Windfarm Export Cables” (Ref. 5).

Thermal Resistance of Soil

Totally different soil sorts have totally different thermal insulating traits, which may severely restrict the quantity of warmth dissipated from the cable, thereby decreasing its current-carrying capability. Because of this bigger conductor sizes are wanted to transmit the identical quantity of energy in areas with extra thermally opposed soil, inflicting the cable’s price to extend.

Within the paper “Rigorous calculation of exterior thermal resistance in non-uniform soils” (Ref. 6), the Hellenic Cables group used FEM to calculate the efficient soil thermal resistance for various cable sorts and cable set up situations (Determine 9). First, they solved for the warmth switch downside below steady-state circumstances with arbitrary temperatures on the cable and soil surfaces. They then evaluated the efficient thermal resistance primarily based on the warmth dissipated by the cable floor into the encompassing soil.

Simulations have been carried out for 2 varieties of cables: a typical SL-type submarine cable with 87/150 kV, a 1000 mm2 cross part, and copper conductors, in addition to a typical terrestrial cable with 87/150 kV, a 1200 mm2 cross part, and aluminum conductors. The group analyzed three totally different cable set up situations (Determine 10).

The primary situation is when a cable is put in beneath a horizontal layer, corresponding to when sand waves are anticipated to step by step add to the seafloor’s preliminary stage after set up. The second is when a cable is put in inside a horizontal layer, which happens when the set up takes place in a area with horizontal directional drilling (HDD). The third situation is when a cable is put in inside a backfilled trench, typical for areas with unfavorable thermal habits, as a way to cut back the affect of the soil on the temperature rise of the cable. The numerical modeling outcomes show that FEM could be utilized to any materials or form of multilayer or backfilled soil, and that the tactic is appropriate with the present score methodology in IEC Commonplace 60287.

Grounding Resistance

The analysis of grounding resistance is essential to make sure the integrity and safe operation of cable sheath voltage limiters (SVLs) when topic to earth potential rise (EPR). With the intention to calculate grounding resistance, engineers have to know the soil resistivity for the issue at hand and have a sturdy calculation technique, like FEM.

The Hellenic Cables group used FEM to investigate soil resistivity for 2 websites: one in northern Germany and one in southern Greece. As described within the paper “Analysis of Grounding Resistance and Its Impact on Underground Cable Programs” (Ref. 7), they discovered that the obvious resistivity of the soil is a monotonic perform of distance, and {that a} two-layer soil mannequin is enough for his or her modeling downside (Determine 11). After discovering the resistivity, the group calculated the grounding resistance for a single-rod situation (as a way of validation). After that, they proceeded with a fancy grid, which is typical of cable joint pits present in OWFs. For each situations, they discovered the EPR on the substations and transition joint pit, in addition to the utmost voltage between the cable sheath and native earth (Determine 12). The outcomes exhibit that FEM is a extremely correct calculation technique for grounding resistance, as they present good settlement with each numerical knowledge from measurements and electromagnetic transient software program calculations (Determine 13).

A Vibrant and Windy Future

The Hellenic Cables group plans to proceed the essential work of additional enhancing the entire cable fashions they’ve developed. The group has additionally carried out analysis into HVDC cables, which contain XLPE insulation and voltage supply converter (VSC) expertise. HVDC cables could be extra price environment friendly for methods put in over lengthy distances.

Just like the wind used to energy offshore wind farms, electrical cable methods are throughout us. Regardless that we can not all the time see them, they’re working onerous to make sure we’ve got entry to a high-powered and well-connected world. Optimizing the designs of subsea and terrestrial cables is a vital a part of constructing a sustainable future.


  1. M. Hatlo, E. Olsen, R. Stølan, J. Karlstrand, “Correct analytic system for calculation of losses in three-core submarine cables,” Jicable, 2015.
  2. S. Sturm, A. Küchler, J. Paulus, R. Stølan, F. Berger, “3D-FEM modelling of losses in armoured submarine energy cables and comparability with measurements,” CIGRE Session 48, 2020.
  3. A.I. Chrysochos et al., “Capacitive and Inductive Coupling in Cable Programs – Comparative Research between Calculation Strategies”, tenth Worldwide Convention on Insulated Energy Cables, Jicable, 2019.
  4. D. Chatzipetros and J.A. Pilgrim, “Overview of the Accuracy of Single Core Equal Thermal Mannequin for Offshore Wind Farm Cables”, IEEE Transactions on Energy Supply, Vol. 33, No. 4, pp. 1913–1921, 2018.
  5. D. Chatzipetros and J.A. Pilgrim, “Induced Losses in Non-Magnetically Armoured HVAC Windfarm Export Cables”, IEEE Worldwide Convention on Excessive Voltage Engineering and Software (ICHVE), 2018.
  6. A.I. Chrysochos et al., “Rigorous calculation of exterior thermal resistance in non-uniform soils”, Cigré Session 48, 2020.
  7. A.I. Chrysochos et al., “Analysis of Grounding Resistance and Its Impact on Underground Cable Programs”, Mediterranean Convention on Energy Technology, Transmission , Distribution and Power Conversion, 2020.