A Mathematical Method of Current-Carrying Capacity for Shore Power Cables in Port Microgrids
Abstract
:1. Introduction
2. Materials and Methods
2.1. Shore Power Cable Model
2.1.1. Simulation Model
2.1.2. Physical Model
2.2. Mathematical Algorithm for Ampacity Calculation of Shore Power Cable Using Heat Balance Equation
2.2.1. Thermal Circuit Model of Shore Power Cables
2.2.2. Newton–Raphson Method of Current-Carrying Capacity
2.2.3. Heat Balance Equation (HBE) and Solution for Shore Power Cables
2.3. Methodology of Mathematical Model for Current-Carrying Capacity
3. Results
3.1. Influence of Wind and Water Speed
3.2. Influence of Ambient Temperature
3.3. Effect of Solar Radiations
3.3.1. Laying in the Air
3.3.2. Laying Under Water
3.4. Influence of Exterior Thermal Resistance T4
3.4.1. Calculation of Exterior Thermal Resistance T4 When Laying in the Air
3.4.2. Calculation of Exterior Thermal Resistance T4 When Laying Under Water
4. Conclusions
5. Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Relative Dielectric Constant | Conductivity (S/m) | Specific Heat Capacity J/(kg·K) | Heat Conductivity W/(m·K) | Yang’s Modulus (GPa) | Poisson’s Ratio |
---|---|---|---|---|---|---|
Conductor | Tend to ∞ | 58 × 106 | 385 | 400 | 120 | 0.34 |
Insulation layer | 3 | Tends to 0 | 2300 | 0.2875 | 1.1 | 0.42 |
Conductor shied | 100 | 6 | 1005 | 0.2875 | 1.7 | 0.41 |
Filler | 1.6 | Tends to 0 | 1883 | 0.0169 | 1.1 | 0.44 |
Inner sheath | 3.6 | Tends to 0 | 2100 | 0.2 | 0.64 | 0.41 |
Aluminum sheath | Tends to ∞ | 38 × 106 | 871 | 273 | 70 | 0.33 |
Outer sheath | 3.5 | Tends to 0 | 2070 | 0.2 | 0.2 | 0.42 |
Radiation Intensity H (W/m2) | Wind Speed vair (m/s) | Current-Carrying Capacity Difference (A) | |
---|---|---|---|
0.001 m/s | 10 m/s | ||
0 | 334.6 | 409.7 | 75.1 |
200 | 309.4 | 388.5 | 79.1 |
400 | 280.8 | 366.0 | 85.2 |
600 | 249.2 | 342.0 | 92.8 |
800 | 212.7 | 316.3 | 103.6 |
1000 | 168.6 | 288.2 | 119.6 |
Radiation Intensity H (W/m2) | Ambient Temperature Tr ( °C) | Current-Carrying Capacity Difference (A) | |
---|---|---|---|
0 °C | 40 °C | ||
0 | 434.2 | 328.0 | 106.2 |
200 | 414.3 | 301.0 | 113.3 |
400 | 393.4 | 271.3 | 122.1 |
600 | 371.3 | 238.2 | 133.1 |
800 | 347.9 | 199.6 | 148.3 |
1000 | 322.6 | 151.5 | 171.1 |
Radiation Intensity H (W/m2) | Water Flow Velocity vwater (m/s) | Current-Carrying Capacity Difference (A) | |
---|---|---|---|
0.001 m/s | 10 m/s | ||
0 | 342.9 | 423.5 | 80.6 |
200 | 336.6 | 418.1 | 81.5 |
400 | 330.1 | 412.7 | 82.6 |
600 | 323.2 | 407.2 | 84 |
800 | 316.2 | 401.6 | 85.4 |
1000 | 309.2 | 396.0 | 86.8 |
Radiation Intensity H (W/m2) | Ambient Temperature Tr (°C) | Current-Carrying Capacity Difference (A) | |
---|---|---|---|
0 °C | 40 °C | ||
0 | 465.0 | 348.0 | 117.0 |
200 | 460.2 | 341.3 | 118.9 |
400 | 455.3 | 334.7 | 120.6 |
600 | 450.4 | 327.9 | 122.5 |
800 | 445.4 | 321.0 | 124.4 |
1000 | 440.3 | 313.9 | 126.4 |
Ambient Temperature Tr (°C) | Wind Speed Vair (m/s) | |||||
---|---|---|---|---|---|---|
0.001 | 0.05 | 1 | 4 | 7 | 10 | |
−20 | 0.813 | 0.580 | 0.268 | 0.158 | 0.125 | 0.107 |
−10 | 0.761 | 0.552 | 0.261 | 0.155 | 0.123 | 0.106 |
0 | 0.712 | 0.524 | 0.254 | 0.153 | 0.122 | 0.105 |
10 | 0.666 | 0.497 | 0.247 | 0.150 | 0.120 | 0.103 |
20 | 0.623 | 0.471 | 0.240 | 0.147 | 0.118 | 0.102 |
30 | 0.582 | 0.446 | 0.233 | 0.144 | 0.116 | 0.101 |
40 | 0.544 | 0.423 | 0.225 | 0.142 | 0.114 | 0.099 |
Ambient Temperature Tr (°C) | Water Flow Velocity Vwater (m/s) | |||||
---|---|---|---|---|---|---|
0.001 | 0.05 | 1 | 4 | 7 | 10 | |
−20 | 0.702 | 0.321 | 0.101 | 0.054 | 0.041 | 0.035 |
−10 | 0.662 | 0.312 | 0.099 | 0.053 | 0.041 | 0.035 |
0 | 0.623 | 0.302 | 0.098 | 0.053 | 0.041 | 0.035 |
10 | 0.587 | 0.292 | 0.097 | 0.053 | 0.041 | 0.035 |
20 | 0.552 | 0.283 | 0.096 | 0.052 | 0.041 | 0.035 |
30 | 0.519 | 0.273 | 0.095 | 0.052 | 0.040 | 0.034 |
40 | 0.488 | 0.263 | 0.094 | 0.052 | 0.040 | 0.034 |
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You, F.; Yusoh, M.A.T.M.; Nik Ali, N.H.; Yang, H. A Mathematical Method of Current-Carrying Capacity for Shore Power Cables in Port Microgrids. Electronics 2025, 14, 1749. https://doi.org/10.3390/electronics14091749
You F, Yusoh MATM, Nik Ali NH, Yang H. A Mathematical Method of Current-Carrying Capacity for Shore Power Cables in Port Microgrids. Electronics. 2025; 14(9):1749. https://doi.org/10.3390/electronics14091749
Chicago/Turabian StyleYou, Fei, Mohd Abdul Talib Mat Yusoh, Nik Hakimi Nik Ali, and Hao Yang. 2025. "A Mathematical Method of Current-Carrying Capacity for Shore Power Cables in Port Microgrids" Electronics 14, no. 9: 1749. https://doi.org/10.3390/electronics14091749
APA StyleYou, F., Yusoh, M. A. T. M., Nik Ali, N. H., & Yang, H. (2025). A Mathematical Method of Current-Carrying Capacity for Shore Power Cables in Port Microgrids. Electronics, 14(9), 1749. https://doi.org/10.3390/electronics14091749