# Reference Power Cable Models for Floating Offshore Wind Applications

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology and Numerical Models

#### 2.1. Physical Power Cable Model

^{2}. The conductor is enclosed by a copper screen tied to the insulation layer made of cross-linked polyethylene (XLPE). XLPE insulation is preferred due to its favorable dielectric properties and high temperature resistance. Furthermore, XLPE has very good chemical and water resistance and provides very good protection against environmental degradation. Additionally, XLPE mechanical strength and low dielectric loss make it a durable and energy-efficient choice for insulation in dynamic power cable applications. The conductors are helically wound along the cable’s longitudinal axis and are separated by three filler bodies made of medium-density polyethylene (MDPE) to maintain the cable’s cross-section shape. The whole bundle is encapsulated in the inner sheath made of MDPE. The cable is protected by two cross-wound armor layers comprised of helically wound galvanized steel wires. The twist directions of the two layers are opposite to ensure the torsional balance of the cable. The 33 kV and 66 kV models use armor wire with a 3.15 mm diameter, and the 132 kV model uses armor wire with a 4.0 mm diameter. The armor layers are separated by thin bedding layers made of Polypyrrole.

#### 2.2. Numerical Model of the Dynamic Power Cable

#### 2.3. Mesh Sensitivity Study

#### 2.4. Local Analysis Results—Cable Cross-Section Properties

^{2}for the 33 kV cable, 152 kNm

^{2}for the 66 kV cable, and 250 kNm

^{2}for the 132 kV cable variant. The bending moment–curvature relation is obtained by gradually loading the cable to a target tension level and subsequently subjecting it to gradually increasing curvature. As shown in Figure 12, the relation between the bending moment and curvature is not linear anymore and shows approximately a bi-linear relation.

## 3. Case Study

#### 3.1. Environmental Conditions

#### 3.2. Global Response of the FOWT

#### 3.3. Extreme Loading Conditions

#### 3.4. Dynamic Simulations

#### 3.5. Fatigue Life Estimates

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Outer diameter, armor diameter, and conductor diameter for (

**a**) 33 kV, (

**b**) 66 kV, and (

**c**) 132 kV cable cross sections. Dimensions given in mm.

**Figure 3.**Definition of the reference systems used in UFLEX 2D for (

**a**) helical beam elements; (

**b**) shell elements (SINTEF [42]).

**Figure 4.**Modeled 66 kV cable cross-section: (

**a**) element types, red denotes beam elements, green denotes shell elements; (

**b**) computational mesh view.

**Figure 6.**Hysteretic behavior of curvature-bending moment for cases with different global mesh densities.

**Figure 8.**Close-up view of the armor wires discretization for (

**a**) very coarse, (

**b**) coarse, (

**c**) normal, and (

**d**) dense mesh variants.

**Figure 9.**Mesh sensitivity study results: (

**a**) effect of armor wire discretization on max. Von Mises stress; (

**b**) effect of armor wire discretization on max. contact pressure; (

**c**) effect of shell layers discretization on max. Von Mises stress; (

**d**) effect of shell layers discretization on max. contact pressure.

**Figure 10.**Axial force–axial strain relationships for three cable variants obtained from UFLEX simulations.

**Figure 11.**Torsion angle–torsion moment relationships for three cable variants obtained from UFLEX simulations: (

**a**) clockwise; (

**b**) anti-clockwise rotation. Applied axial tension, 50 kN.

**Figure 12.**Bending moment–curvature relationships for three cable variants obtained from UFLEX simulations at different tension levels: (

**a**) 33 kV, (

**b**) 66 kV, (

**c**) 132 kV cable model.

**Figure 13.**Definition of the FOWT–power cable system under consideration: (

**a**) front view, (

**b**) plan view. Dimensions are in m.

**Figure 14.**Surge RAO comparison for the considered OC3 FOWT setup without and with 66 kV power cable in a lazy wave configuration. Validation against FAST simulation results by Ramachandran et al. [55].

**Figure 15.**Sway RAO comparison for the considered OC3 FOWT setup without and with 66 kV power cable in a lazy wave configuration. Validation against FAST simulation results by Ramachandran et al. [55].

**Figure 16.**Heave RAO comparison for the considered OC3 FOWT setup without and with 66 kV power cable in a lazy wave configuration. Validation against FAST simulation results by Ramachandran et al. [55].

**Figure 17.**Roll RAO comparison for the considered OC3 FOWT setup without and with 66 kV power cable in a lazy wave configuration. Validation against FAST simulation results by Ramachandran et al. [55].

**Figure 18.**Pitch RAO comparison for the considered OC3 FOWT setup without and with 66 kV power cable in a lazy wave configuration. Validation against FAST simulation by Ramachandran et al. [55].

**Figure 19.**Stress factors for conductor and armor wires obtained from UFLEX simulations: (

**a**) stress versus applied curvature; (

**b**) stress versus applied tension.

**Figure 20.**Von Mises stress distribution in the cable cross-section under (

**a**) axial load of 1000 kN, (

**b**) bending curvature of 1 rad/m.

**Figure 22.**Power cable response under 50-year storm extreme condition: (

**a**) effective tension envelope, (

**b**) curvature envelope.

**Figure 23.**Comparison of: (

**a**) maximum curvature, (

**b**) maximum tension, (

**c**) curvature standard deviation, (

**d**) tension standard deviation experienced by the power cable under different ECs.

**Figure 24.**Envelopes of the cable’s vertical profile, curvature, and effective tension for EC1 and EC2.

**Figure 25.**Envelopes of the cable’s vertical profile, curvature, and effective tension for EC3 and EC4.

**Figure 26.**Envelopes of the cable’s vertical profile, curvature, and effective tension for EC5 and EC6.

No | Physical Model | Material | Layer Outer Diameter [mm] | Lay Angle [°] | ||
---|---|---|---|---|---|---|

33 kV | 66 kV | 132 kV | ||||

1 | Conductor | Copper | 29.90 | 29.90 | 29.90 | conductor bundle 10 |

2 | Conductor Screen | Copper tape | 33.90 | 33.90 | 33.90 | |

3 | Insulation | XLPE ^{1} | 53.90 | 57.70 | 64.30 | |

4 | Insulation Screen | Copper | 59.80 | 64.00 | 71.00 | |

5 | Conductor Sheath | MDPE ^{2} | 65.90 | 70.40 | 77.90 | |

6 | Filler | MDPE | 142.20 | 151.80 | 168.00 | 10 |

7 | Bedding | PPY ^{3} | 143.00 | 152.60 | 168.80 | - |

8 | Inner Sheath | MDPE | 151.00 | 160.70 | 176.60 | - |

9 | Armor (inner layer) | Steel | 157.30 | 167.00 | 184.60 | 13 |

10 | Bedding | PPY | 157.70 | 167.40 | 185.00 | - |

11 | Armor (outer layer) | Steel | 164.00 | 173.70 | 193.00 | 10 |

12 | Outer Sheath | HDPE ^{4} | 174.50 | 184.00 | 204.00 | - |

^{1}Cross-linked polyethylene,

^{2}Medium-density polyethylene,

^{3}Polypyrrole,

^{4}High-density polyethylene.

Material | Density [kg/m ^{3}] | Elasticity Modulus [MPa] | Poisson Ratio [-] | Friction Stiffness [MPa/mm] | Friction Coefficient [-] |
---|---|---|---|---|---|

Copper | 8890 | 112,200 | 0.34 | 1500 | 0.30 |

Steel | 7800 | 200,000 | 0.26 | 2000 | 0.20 |

XLPE | 925 | 1000 | 0.40 | 1200 | 0.25 |

MDPE | 956 | 1000 | 0.40 | 1200 | 0.46 |

HDPE | 980 | 1000 | 0.40 | 1500 | 0.10 |

PPY | 895 | 150 | 0.40 | 1500 | 0.10 |

No | Physical Model | Numerical Model | Element Type | Material |
---|---|---|---|---|

1 | Conductor | Conductor | Beam | Copper |

2 | Conductor Screen | |||

3 | Insulation | Insulation | Shell | XLPE |

4 | Insulation Screen | |||

5 | Conductor Sheath | Conductor Sheath | Shell | MDPE |

6 | Filler | Filler | Beam | MDPE |

7 | Bedding | Inner Sheath | Shell | MDPE |

8 | Inner Sheath | |||

9 | Armor (inner layer) | Armor Inner | Beam | Steel |

10 | Bedding | Bedding | Shell | PPY |

11 | Armor (outer layer) | Armor Outer | Beam | Steel |

12 | Outer Sheath | Outer Sheath | Shell | HDPE |

Mesh Variant | Very Coarse | Coarse | Normal | Dense |
---|---|---|---|---|

Numerical Model Layer | Number of Elements | |||

Conductor | 8 | 12 | 16 | 20 |

Insulation | 48 | 72 | 96 | 120 |

Conductor Sheath | 48 | 72 | 96 | 120 |

Filler | 44 | 66 | 88 | 110 |

Inner Sheath | 200 | 300 | 400 | 500 |

Armor Inner | 8 | 12 | 16 | 20 |

Bedding | 200 | 300 | 400 | 500 |

Armor Outer | 8 | 12 | 16 | 20 |

Outer Sheath | 200 | 300 | 400 | 500 |

Parameter | Unit | Value |
---|---|---|

OC3-Hywind FOWT specifications (Jonkman et al. [45]) | ||

Rotor diameter | m | 126 |

Hub height | m | 90 |

Spar platform draft | m | 120 |

Number of mooring lines | - | 3 |

Angle between mooring lines | deg | 120 |

Water depth | m | 200 |

Cut-in wind speed | m/s | 3 |

Rated wind speed | m/s | 11.4 |

Cut-out wind speed | m/s | 25 |

Properties of the power cable | ||

Voltage rating | kV | 66 |

Outer diameter | m | 0.184 |

Weight in air | N/m | 547 |

Drag coefficient normal | - | Re dependent |

Drag coefficient axial | - | 0.008 |

Added mass coefficient normal | - | 1.0 |

Added mass coefficient axial | - | 0.0 |

Properties of the power cable with buoyancy modules | ||

Outer diameter | m | 0.390 |

Weight in air | N/m | 948 |

Drag coefficient normal | - | Re dependent |

Drag coefficient axial | - | 0.35 |

Added mass coefficient normal | - | 1.00 |

Added mass coefficient axial | - | 0.50 |

Load Case | Wind Speed at the Hub Height [m/s] | Turbulence Intensity [-] | Significant Wave Height [m] | Peak Period [s] | Wind-Induced Current Speed [m/s] |
---|---|---|---|---|---|

EC1 | 5 | 0.224 | 2.10 | 9.74 | 0.11 |

EC2 | 10 | 0.157 | 2.88 | 9.98 | 0.22 |

EC3 | 14 | 0.138 | 3.62 | 10.29 | 0.31 |

EC4 | 18 | 0.127 | 4.44 | 10.66 | 0.39 |

EC5 | 22 | 0.121 | 5.32 | 11.06 | 0.48 |

EC6 | 25 | 0.117 | 6.02 | 11.38 | 0.55 |

EC50X | 37.44 | 0.0759 | 12.95 | 16.06 | 0.82 |

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## Share and Cite

**MDPI and ACS Style**

Janocha, M.J.; Ong, M.C.; Lee, C.F.; Chen, K.; Ye, N.
Reference Power Cable Models for Floating Offshore Wind Applications. *Sustainability* **2024**, *16*, 2899.
https://doi.org/10.3390/su16072899

**AMA Style**

Janocha MJ, Ong MC, Lee CF, Chen K, Ye N.
Reference Power Cable Models for Floating Offshore Wind Applications. *Sustainability*. 2024; 16(7):2899.
https://doi.org/10.3390/su16072899

**Chicago/Turabian Style**

Janocha, Marek Jan, Muk Chen Ong, Chern Fong Lee, Kai Chen, and Naiquan Ye.
2024. "Reference Power Cable Models for Floating Offshore Wind Applications" *Sustainability* 16, no. 7: 2899.
https://doi.org/10.3390/su16072899