Comparative Study on the Ampacity of 500 kV Single-Core and Three-Core Submarine Cable

Submarine cable is an important equipment for data communication and power transmission in power systems, which has a complex laying environment. According to its structure, submarine cables can be divided into two types, single-core cables and three-core cables. In practical engineering, cable selection is crucial to ensure the safe and stable operation of the cable and reduce the cost. The present work compares the ampacity of 500 kV single-core cable and three-core cable with the same conductor cross-section area under certain laying conditions. And the temperature rise situation of the three-core cable and the single-core cable is compared under the application of the same current. The results reveals that the ampacity of the three-core cable is less than one-core cable under certain laying situations. And the maximum ampacity reduction of the three-core cable is 28.96%. Furthermore, the highest temperature rise point of the three-core cable is the air section of the J-tube, and the maximum temperature reaches 130.07°C.


Introduction
Submarine cable system is used to transmit electrical signal, electric power or internet data under the sea.It plays a key role in international communication, energy transmission and internet connection.With the increasing demand for internet and communication, submarine cable will tend to have higher transmission capacity in the future [1].
In the process of submarine cable selection, a comprehensive analysis of the cable must be conducted.The cable type must be selected according to different laying environments and ensure that the heat generated by the core conductor during current transmission does not damage the cable structure and affect the service life.Single-core submarine cable has a smaller outer diameter and lighter weight, so the cable manufacturing length can be unlimited by the cable reel and weight; single-core cable is easy to lay, but the overall construction time is longer because the three-phase cable is composed of three independent cable; single-core cable has a larger distance between phases, better heat dissipation, higher current carrying capacity under the same cross-section condition, and rarely occurs inter-phase short circuit.Three-core cable can effectively reduce the occupied area, but due to its own weight limitation, it is more suitable for short-distance laying.Three-core cable has three phases wrapped together, and the phases are insulated by insulation materials.If the insulation materials are damp or deteriorated, it is easy to cause inter-phase short circuit, but compared with single-core cable, it has lower cost and better economy [2].
The ampacity of a submarine cable refers to the current capability that the cable can withstand at the highest allowable operating temperature under specific laying methods and environmental conditions.When the current transmitted by the conductor exceeds the ampacity for a long time, it will cause the cable to be overloaded, resulting in the temperature of each layer exceeding its maximum allowable temperature, and thus shortening the service life of the cable.Therefore, accurately calculating the ampacity of submarine cable can help to select the cable type reasonably under different laying conditions, and achieve the minimization of engineering investment costs [3].
At present, the calculation methods of submarine cable ampacity are mainly divided into two categories: analytical calculation method and numerical calculation method [4].The analytical calculation method is the standard IEC-60287 [5] proposed by the International Electro-technical Commission for calculating the rated ampacity of power cable.By using the thermal circuit model in heat transfer, the calculation method for corresponding thermal resistance and losses in each part is provided, and the analytical calculation formula for calculating the core temperature is then derived.The numerical calculation method includes finite element method and difference method, which realizes the coupling calculation of multi-physical fields by computer technology, and can better simulate the actual laying situation of submarine cable [6][7].
As an important connection hub, how to reasonably select the cable type and cross-section, especially in the selection under various complex laying environments and methods that may occur between the offshore wind farms and onshore substations, is an important problem that many scholars are working hard to solve [8].Therefore, based on the standard IEC-60287, this paper calculates the ampacity of 500kV single-core cable and three-core cable with the same conductor cross-section area under different laying environments, compares the results of the two, analyzes the ampacity loss situation after changing from single-core submarine cable to three-core submarine cable under the same conditions, and investigates the temperature rise situation of the three-core submarine cable conductor under the same current condition through temperature field simulation, which provides some theoretical reference for the selection of submarine cable under different laying conditions in practical engineering applications.

Cable Samples and Calculation Parameters
The main structures of 500 kV single-core submarine cable and three-core submarine cable used in the present work include: conductor, conductor shield, insulation, insulation shield, metal sheath, optical fiber unit, armour, and outer sheath.The corresponding cable structure and size parameters are shown in figure 1

Analytical Method for Calculating Ampacity
Based on the standard IEC-60287 of ampacity calculation theory, the cable ampacity calculation formula is: where n is the number of cable cores, Wc is the conductor loss, R is the maximum operating temperature of the conductor unit length AC resistance, Wd is the insulation layer dielectric loss, λ1 is the metal sheath loss factor, λ2 is the armour layer loss factor, T1 is the insulation layer thermal resistance, T2 is the liner layer thermal resistance, T3 is the ourter sheath thermal resistance, T4 is the thermal resistance of the surrounding medium, θc is the core temperature of the cable, θ0 is the surrounding ambient temperature.The standard provides a calculation method for the thermal resistance, loss, and corresponding structural loss factor of different structures in cable.The calculation results are shown in table 2. The thermal resistance T4 of the surrounding medium is determined by the specific laying environment.Due to the complex laying environment of submarine cable, different laying environments can also result in different environmental temperatures and heat conduction boundary conditions.Therefore, when calculating the ampacity of submarine cable, it is necessary to calculate them separately based on different laying conditions.Submarine cable generally start from offshore booster stations and end at onshore terminals.Due to the constantly changing laying environment in the submarine cable system, it is necessary to divide them into different sections for calculation.In order to simplify the model, the present work selected four sections: J-tube section, submarine section, mudflat section and landing section for further calculation and analysis.The different environmental and temperature conditions in each region can also lead to changes in cable ampacity [9].
The laying environment in J-tube can be divided into three parts: the platform section, the air section, and the seawater section.The external environment of the platform section is air, and it is directiy exposed to sunlight.The external environment of the air section is air and is not exposed to sunlight.The external environment of the seawater section is seawater, which is assumed to be nonflowing [10].The convective heat transfer coefficient of air is 8W/(m 2 •K), and the environmental parameters under other laying conditions are shown in table 3.

Calculation and Simulation Results of 500kV Single-core Submarine Cable
Based on the standard IEC-60287, the ampacity of single-core submarine cable under different laying conditions is calculated by substituting the thermal parameters in table 2 into equation ( 1).The temperature of external environmental air θ0 is 40°C.When the cable is laid in seawater and soil, the environmental thermal resistance T4 under different laying conditions is calculated based on the environmental parameters in table 3, and then the cable ampacity is obtained.In the simulation, the convective heat transfer coefficients of the cable and the J-tube are both 8W/(m 2 •K).The current is continuously adjusted to make the cable core temperature reach 90℃, and the corresponding current value is recorded.Then, the conductor size is changed from 50 mm to 40 mm in diameter, and the same calculation and simulation are repeated.The final results are shown in table 5.

Calculation and Simulation Results of 500kV Three-core Submarine Cable
Based on the standard IEC-60287, the ampacity of three-core submarine cable under different laying conditions is calculated by substituting the thermal parameters in table 2 into equation ( 1).The temperature of external environmental air θ0 is 40°C.When the cable is laid in seawater and soil, the environmental thermal resistance T4 under different laying conditions is calculated based on the environmental parameters in table 3, and then the cable ampacity is obtained.In the simulation, the convective heat transfer coefficients of the cable and the J-tube are both 8W/(m 2 •K).The current is continuously adjusted to make the cable core temperature reach 90℃, and the corresponding current value is recorded.Then, the conductor size is changed from 50 mm to 40 mm in diameter, and the same calculation and simulation are repeated.The final results are shown in table 6.In order to explore the conductor temperature rise of 500kV three-core submarine cable relative to 500kV single-core submarine cable under the same conditions, the ampacity of the single-core submarine cable was used for the three-core submarine cable.The simulation results of the temperature field of the three core submarine cable are shown in table 7.

Comparative Analysis of Results
To investigate the impact of converting single-core cables to three-core cables on the cable ampacity.Under the same laying environment, compare the ampacity of three-core and single-core cables with conductor diameters of 50 mm, and obtain the loss of calculated and simulated ampacity.The results are shown in table 8.According to table 8, it indicated that under the same cross-sectional area, the ampacity of 500kV single-core to three-core cable will decrease.In the J-tube seawater section, the reduction in ampacity of the cable is the smallest.The calculated value of the ampacity decreased by 439.60A, a relative decrease of 24.14%, and the simulated value of the ampacity decreased by 412.67A, a relative decrease of 23.98%.In the J-tube air section, the ampacity of the cable decreases the most.The calculated value of the ampacity decreased by 483.67A, a relative decrease of 28.36%, and the simulated value of the ampacity decreased by 451.72A, a relative decrease of 28.69%.According to table 7, it can be concluded that under the same laying conditions, after replacing single-core submarine cable with three core submarine cable of the same cross-section, the highest temperature rise point is in the J-tube air section, and the highest temperature reaches 130.07℃; The lowest point of temperature rise is 109.61℃ in the seawater section of the J-tube.
Among six laying conditions of submarine cable, submarine section has the maximum ampacity because of the low ambient temperature and the best heat dissipation.On the contrary, J-tube air section has the worst condition of air flow and the lowest ampacity because of its J-tube wrapping.After changing from single-core to three core, the ampacity of 500 kV submarine cable with the same cross-sectional area will decrease.This is because the three core submarine cable are wrapped together, resulting in poor heat dissipation.However, three core submarine cable can reduce footprint and have lower costs than single-core submarine cable.Therefore, three-core cable are more suitable for power engineering with low current and short distance laying.

Conclusions
This paper applies the standard IEC-60287 to calculate the ampacity of 500 kV single-core and threecore cables with the same cross-sectional area conditions.By comparing the calculation results, this article examines the ampacity loss caused by replacing single-core submarine cables with three-core submarine cables under the same conditions.Through the temperature field simulation, this article also analyses the temperature rise of the three-core submarine cable conductors under the same current conditions.
1) Among the six different laying conditions of submarine cable, single-core submarine cable and three core submarine cable have the highest ampacity in the Submarine section.In the J-tube air section, the cable has the lowest ampacity.
2) The same cross-section of the single-core submarine cable to three-core submarine cable, the ampacity will be reduced, the maximum reduction of 28.69%;The highest point of temperature rise is in the J-tube air section, with the highest temperature reaching 130.07℃.
and table 1.
Figure 1.500kV submarine cable samples and structural drawings.

Table 2 .
Calculation results of ampacity parameters.

Table 3 .
[11]ng environment parameters.[11]TemperatureFieldSimulationModel and Parameters The temperature field simulation model of submarine cable is established based on the parameters in table1 and table 4. The laying environment of submarine cable is divided into three categories: air laying environment, J-tube laying environment, and seawater laying environment.According to different laying environments, change the boundary conditions and current values to obtain the distribution of cable temperature field under corresponding conditions.In the experiment, the temperature of the cable core was adjusted to 90℃ by adjusting the current size.At this point, the current value of the cable is the cable ampacity.

Table 5 .
Calculation and simulation results of single-core submarine cable ampacity.

Table 6 .
Calculation and simulation results of three-core submarine cable ampacity.

Table 7 .
Simulation results of three-core submarine temperature rise with the same section.

Table 8 .
Comparison of single-core and three-core cable ampacity results.