# Study on Reactive Power Compensation Strategies for Long Distance Submarine Cables Considering Electrothermal Coordination

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Electrical Calculation Model of HVAC Cables in Offshore Wind Farm

#### 2.1. Structure of Offshore Wind Power System

#### 2.2. Cable Design and Characteristics

^{2}three-core submarine cable are shown in Table 1.

#### 2.3. Lumped Parameter Model of Submarine Cables

_{1}and Y

_{2}represent equivalent susceptance of inductors installed at the sending and receiving ends of HVAC cable for compensation; V

_{s1}, V

_{r1}and I

_{s1}, I

_{r1}, respectively represent the voltage and current at sending and receiving ends of line; l is the length of the line; γ is the transmission coefficient of line; and Z

_{c}is the characteristic impedance of the line.

_{seg}= L/N, as shown in Figure 4. In Figure 4, V

_{1}, V

_{2}...V

_{n+1}and I

_{1}, I

_{2}...I

_{n+1}are respectively representing the voltage and current value of each PI equivalent circuit connection node from the sending end to the receiving end.

_{r}are the voltage values at sending and receiving ends respectively; I

_{S}and I

_{r}are respectively the input and output current values at sending and receiving ends; Q

_{S}, Q

_{r}, and Q

_{m}are for the reactive compensation power capacity at the sending end, receiving end, and middle line, respectively. According to Figure 5, the mathematical model in MATLAB for solving the line current distribution is shown as below. In this part, taking the reactive power compensation at 1/2 of long-distance submarine cables as an example to show the mathematic model.

_{0}, I

_{m}, and I

_{d}is the current of reactive power compensation equipment on the sending, middle line, and receiving end, respectively, I

_{y1}…I

_{yn}and I

_{z1}…I

_{zn}are respectively representing the current of admittance and impedance of PI equivalent circuit, cosφ

_{1}is the transmission power factors of the sending end of the submarine cable line, and i is the unit of imaginary number.

## 3. Impacts of Reactive Power Compensation on Current Distribution of for Long-Distance Submarine Cables

_{S}is the reactive power compensated at the sending end of the line, Var.

## 4. Thermal Calculation Model of Submarine Cables

_{c}is the conductor temperature, θ

_{a}is the environmental temperature of cable, θ

_{1}is the metal sheath temperature, θ

_{2}is the armor layer temperature, W

_{c}is the joule loss of conductor per unit length, W

_{d}is the dielectric loss of conductor insulation per unit length, T

_{1}is the thermal resistance between conductor and sheath, T

_{2}is the thermal resistance of the lining between sheath and armor, T

_{3}is the thermal resistance of the outer sheath of the cable, and T

_{4}refers to the thermal resistance between the cable surface and the surrounding medium. λ

_{1}is the ratio of the metal sheath loss to the conductor loss, and λ

_{2}is the ratio of the armor layer loss to the conductor loss.

_{s}is the skin effect factor; and Y

_{p}is the adjacent effect factor.

_{1}′ and eddy-current loss λ

_{1}″. The eddy-current loss is negligible for the three-core submarine cable. The calculation formula for the circulation loss λ

_{1}′ is as follows.

_{s}is the conductivity of the metal sheath material, Ω·m; A

_{s}is the cross-sectional area of the metal sheath, mm

^{2}; α

_{s}is the resistance temperature coefficient, 1/K; θ is the working temperature of conductor, °C; η is the ratio of the temperature of metal sheath to the temperature of conductor, were set as 0.7.

_{A}is the AC resistance of armor layer at the highest temperature, Ω/m; c is the distance between the conductor axis and the center of submarine cable, m; d

_{A}is the average diameter of the armor layer, m.

_{0}is the voltage to the ground, V; tanδ is the insulation loss factor under power frequency and working temperatures, here taken as $tan\delta =$0.0005, $w=2\mathsf{\pi}\mathrm{f}$.

_{T}is the thermal resistance coefficient of insulation, K·m/W; G is the geometric factor; and K is the shielding factor.

_{T}is the thermal resistance coefficient between sheath and armor, K·m/W.

_{T}is the thermal resistance coefficient of submarine cable outer sheath, K·m/W; t

_{3}is the thickness of outer sheath, m; D

_{a}′ is the outer diameter of the armor, m; and the calculation formula for the environmental thermal resistance T

_{4}depends on the laying environment, as shown below:

_{T}is the thermal resistance coefficient of soil, K·m/W; L is the buried depth of submarine cables, m, which is the distance between the cable axis and the ground surface; D

_{e}is the outside diameter of the cable, m; h is the coefficient of heat transfer on the cable surface, W/m

^{2}·K; Δθ

_{tr}is the temperature rise when the air temperature in the cable trench is higher than the surrounding air temperature, K; T

_{4a}, T

_{4b}, and T

_{4c}are, respectively, the air thermal resistance, the J-shape pipe thermal resistance, and the pipe external thermal resistance, which are between the cable surface and the inner surface of the pipe; U, V, and Y are constants related to laying conditions; θ

_{m}is the average temperature of medium between cables and pipelines, K; D

_{o}is the outer diameter of the pipe, m; D

_{d}is the pipe inner diameter, m; ρ

_{d}is the thermal resistance of J-shape pipe material, K·m/W; h

_{j}is the coefficient of heat transfer on the surface of the J-shape pipe, W/m

^{2}·K; Δθ is the temperature rise when the temperature of J-shape pipe is higher than the surrounding air temperature, K.

## 5. Reactive Power Compensation Analysis of Submarine Cables Based on Electrothermal Coordination

_{1}and cosφ

_{2}are the transmission power factors of the sending and receiving end of the submarine cable line, respectively; V

_{n}is the rated voltage of the line at 220 kV; I

_{line}is the current value in the submarine cable transmission line, A; I

_{rated}is the ampacity of each section of the line under different laying methods, A.

#### 5.1. Directly Buried Laying Method of Landing Section

#### 5.2. Cable Trench Laying Method in Landing Section

## 6. Conclusions

- (1)
- When the long-distance submarine cable is compensated for reactive power, not only the stability of the system should be maintained, but also the thermal limits of the submarine cable should be considered. The bottleneck of offshore wind farm output submarine cable ampacity appears in the landing section.
- (2)
- Conducting reactive compensation at sending end of the line can reduce the current at the receiving end. On the contrary, it can raise the current at the sending end of the line. The maximum current occurs at the sending or receiving end of the line depending on the capacity of reactive power compensation.
- (3)
- According to ETC, the current of long-distance submarine cable should be less than the ampacity under the condition of reactive power compensation. The cable trench laying method can improve the cable ampacity of landing section and thus reduce the capacity of reactive power compensation at sending end.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Simplified cross section of three-core submarine cable. 1–core conductor; 2–cross-linked polyethene (XLPE) insulation layer; 3–swelling tape; 4–metal sheath; 5–PE sheath; 6–filling layer and wrapping tape; 7–inner sheath; 8–armor layer; 9–outer serving; 10–fiber layer [28].

**Figure 4.**Segmentation of submarine cable into n sections for assessment of internal currents and voltages.

**Figure 6.**Current distribution of submarine cables under different load conditions without reactive power compensation.

**Figure 7.**Current distribution of submarine cables under full load with different reactive power compensation at the sending end.

**Figure 8.**Voltage distribution of submarine cables under full load with different reactive power compensation at the sending end.

**Figure 9.**Current distribution of submarine cables under full load with different reactive power compensation at the middle line.

**Figure 10.**Current distribution of long-distance submarine cables under reactive power compensation at different positions.

**Figure 11.**Output cable laying path for offshore wind farm. 1—J-shape pipe section; 2–seabed section; 3–mud flat section; 4–landing section; 5–offshore booster station platform; 6–onshore centralized control center.

**Figure 13.**Comparison of current distribution of submarine cables under reactive power compensation at the sending end with the full-line ampacity under directly buried laying in landing section.

**Figure 14.**Comparison of current distribution of submarine cables under reactive power compensation at mid-line with the full-line ampacity under directly buried laying in landing section.

**Figure 15.**Comparison of current distribution of 90 km submarine cables under reactive power compensation at the sending end with the full-line ampacity under trench laying in the landing section.

**Figure 16.**Comparison of current distribution of 104 km submarine cables under reactive power compensation at the sending end with the full-line ampacity under trench laying in the landing section.

Layer Number | Structure | Thickness/mm | Outer Radius of Structure/mm |
---|---|---|---|

1 | Core conductor | − | 13.3 |

2 | XLPE insulation | 27.0 | 43.7 |

3 | Swelling tape | 0.5 | 44.7 |

4 | Metal sheath | 3.5 | 48.2 |

5 | PE sheath | 3.3 | 51.5 |

6 | Filling layer | 0.6 | 112.15 |

7 | Inner sheath | 1 | 113.65 |

8 | Armored layer | 6.0 | 119.65 |

9 | Outer serving | 4.0 | 123.65 |

Parameters | Resistance Ω/km | Inductance mH/km | Conductance S/km | Capacitance µF/km |
---|---|---|---|---|

Value | 0.0488 | 0.43 | 2.11 × 10^{−8} | 0.1283 |

Material Parameters | Value |
---|---|

Thermal conductivity coefficient of soil at landing section (K·m/W) | 1.2 |

Thermal conductivity coefficient of soil at mud flat section (K·m/W) | 1 |

Thermal conductivity coefficient of soil at seabed section (K·m/W) | 0.83 |

J-shape pipe inner diameter (mm) | 468 |

J-shape pipe outer diameter (mm) | 508 |

Laying Environment | Environment Temperature °C | Laying Depth m | Thermal Resistance T_{4} | Ampacity A |
---|---|---|---|---|

J-shape pipe section | 55 | - | 0.16 | 620 |

Seabed section | 28.5 | 2.5 | 0.49 | 605 |

Mud flat section | 35 | 1 | 0.443 | 593 |

Landing section (directly buried) | 35 | 1 | 0.532 | 557 |

Landing section (cable trench) | 50 | 1 | 0.2766 | 582 |

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**MDPI and ACS Style**

Liu, G.; Fan, M.; Wang, P.; Zheng, M.
Study on Reactive Power Compensation Strategies for Long Distance Submarine Cables Considering Electrothermal Coordination. *J. Mar. Sci. Eng.* **2021**, *9*, 90.
https://doi.org/10.3390/jmse9010090

**AMA Style**

Liu G, Fan M, Wang P, Zheng M.
Study on Reactive Power Compensation Strategies for Long Distance Submarine Cables Considering Electrothermal Coordination. *Journal of Marine Science and Engineering*. 2021; 9(1):90.
https://doi.org/10.3390/jmse9010090

**Chicago/Turabian Style**

Liu, Gang, Mingming Fan, Pengyu Wang, and Ming Zheng.
2021. "Study on Reactive Power Compensation Strategies for Long Distance Submarine Cables Considering Electrothermal Coordination" *Journal of Marine Science and Engineering* 9, no. 1: 90.
https://doi.org/10.3390/jmse9010090