Modeling Subsea Cables for Offshore Wind Energy at Hellenic Cables

Up to date Methodology for Calculating Cable Losses

The Worldwide Electrotechnical Fee (IEC) supplies requirements for electrical cables, together with Normal 60287 1-1 for calculating cable losses and present scores. One drawback with the formulation utilized in Normal 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 staff at Hellenic Cables acknowledges this. “With a extra correct and practical mannequin, important optimization margins are anticipated,” says Dimitrios Chatzipetros, staff 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 objective for cable manufacturing.

An electrical cable is a fancy machine to mannequin. The geometric construction consists of three fundamental energy cores which can be helically twisted with a selected lay size, and tons of 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 resolve for the electromagnetic fields. “This can be a tedious 3D drawback with difficult materials properties, as a result of among the parts are ferromagnetic,” says Andreas Chrysochos, affiliate principal engineer within the R&D division of Hellenic Cables.

In recent times, FEM has made an enormous leap relating to cable evaluation. The Hellenic Cables staff 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 staff lowered the issue from 40 meters right 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 resolve. “The progress was super,” 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 practical than these supplied 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 undertaking stakeholders. (Determine 5)

Finite Aspect Modeling of Cable Programs

Electromagnetic interference (EMI) presents a number of challenges relating to designing cable techniques — particularly the capacitive and inductive couplings between cable conductors and sheaths. For one, when calculating present scores, 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 satisfy 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 fundamental approaches relating to calculating these capacitive and inductive couplings. The primary is the advanced 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 widespread technique is electromagnetic transients program (EMT) software program, which can be utilized to research electromagnetic transients in energy techniques utilizing each time- and frequency-domain fashions.

The third technique, FEM, is the muse of the COMSOL Multiphysics software program. The Hellenic Cables staff 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 strong and environment friendly for a majority of these issues,” says Chrysochos.

The Hellenic Cables staff 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 sort with an exterior electrical circuit. The outcomes between all three strategies present good settlement for the cable system for 3 totally different configurations: stable bonding, single-point bonding, and cross bonding (Determine 7). This demonstrates that FEM might be utilized to all forms of cable configurations and installations when making an allowance for each capacitive and inductive coupling.

The Hellenic Cables staff additionally used FEM to check thermal results in subsea cables, akin to HVAC submarine cables for offshore wind farms, as described in “Assessment of the Accuracy of Single Core Equal Thermal Mannequin for Offshore Wind Farm Cables” (Ref. 4). The present IEC Normal 60287 1-1 features a thermal mannequin, and the staff used FEM to determine its weak spots and enhance its accuracy. First, they validated the present IEC mannequin with finite factor 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 might be underestimated by as much as 8°C. Deriving analytical, correcting formulation based mostly on a number of FEM fashions, the staff lowered this discrepancy to 1°C! Their evaluation additionally highlights important 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 massive. 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 staff evaluated different features of cable system designs, together with losses, thermal resistance of surrounding soil, and grounding resistance, utilizing FEM and COMSOL Multiphysics. “Normally, COMSOL Multiphysics is rather more consumer pleasant and environment friendly, akin to when introducing temperature-dependent losses within the cable, or when presenting semi-infinite soil and infinite factor domains. We discovered a number of methods to confirm what we already learn about cables, their thermal efficiency, and loss calculation,” says Chatzipetros.

Losses

The conductor dimension of a subsea or terrestrial cable impacts the price of the cable system. That is typically a vital facet of an offshore wind farm undertaking. To optimize the conductor dimension, 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 staff was in a position to 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 factor 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

Completely different soil varieties 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 hostile soil, inflicting the cable’s value to extend.

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

Simulations had been carried out for 2 forms 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 staff analyzed three totally different cable set up situations (Determine 10).

The primary situation is when a cable is put in beneath a horizontal layer, akin to when sand waves are anticipated to regularly add to the seafloor’s preliminary degree 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 conduct, with a view to cut back the affect of the soil on the temperature rise of the cable. The numerical modeling outcomes show that FEM might be utilized to any materials or form of multilayer or backfilled soil, and that the strategy is suitable with the present ranking methodology in IEC Normal 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 a view to calculate grounding resistance, engineers have to know the soil resistivity for the issue at hand and have a strong calculation technique, like FEM.

The Hellenic Cables staff used FEM to research 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 drawback (Determine 11). After discovering the resistivity, the staff 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 show that FEM is a extremely correct calculation technique for grounding resistance, as they present good settlement with each numerical information from measurements and electromagnetic transient software program calculations (Determine 13).

A Vivid and Windy Future

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

Just like the wind used to energy offshore wind farms, electrical cable techniques are throughout us. Regardless that we can not at all times see them, they’re working arduous to make sure we now have 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.

References

1. M. Hatlo, E. Olsen, R. Stølan, J. Karlstrand, “Correct analytic components 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, “Assessment 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 Vitality Conversion, 2020.