A Method for Calculating Grounding Current of AC Submarine Cable Armor Based on Load Current

Time: 2025-03-16 12:46:47 Source: Henan Province Jianyun Cable Co., Ltd.

Introduction

In high-voltage AC submarine cable systems, armor grounding current is a critical factor affecting cable safety, thermal performance, and insulation longevity. When load current flows through the cable core, it induces voltage in the armor layer via electromagnetic induction, forming a grounding current loop through the earth connection.

This study introduces a mathematical model based on Kirchhoff's Voltage Law (KVL) and electromagnetic induction law to calculate armor grounding current using Kramer's rule, eliminating the need for complex simulations. The Zhoushan-Ningbo 500 kV AC submarine cable project was used to verify the accuracy and feasibility of the method.

1. Mechanism of Armor Grounding Current Generation

When an AC submarine cable operates, the metal armor and sheath layer form a closed loop with the ground, creating induced voltage due to the magnetic field generated by the load current. This voltage drives the armor grounding current, leading to thermal stress and accelerated insulation aging if not properly managed.

2. Mathematical Model Based on Kirchhoff's Voltage Law (KVL)

Using KVL, the study establishes a six-equation system that describes the voltage and current relationship in the three-phase core, sheath, and armor layers.

The induced voltage $U$ from the load current $I$ is calculated as:

Usa=−2×10−7×jω×(Ialn⁡D1rs+Ibln⁡D2rs+Icln⁡D3rs)×LU_{sa} = - 2 \times 10^{-7} \times j \omega \times \left( I_a \ln \frac{D_1}{r_s} + I_b \ln \frac{D_2}{r_s} + I_c \ln \frac{D_3}{r_s} \right) \times L

where:

$I_a, I_b, I_c$ : Three-phase load current
$D_i$ : Distance between phases
$r_s$ : Radius of the sheath
$L$ : Cable length
$ω\omega$ : Angular frequency

3. Solving the Equation Using Kramer's Rule

By transforming the equations into a 6×6 matrix, the armor grounding current $I_{ka}$ can be calculated as:

Ika=Aka×IAI_{ka} = \frac{A_{ka} \times I}{A}

where:

$A_{ka}$ is the matrix determinant with the armor voltage
$A$ is the original system matrix

4. Experimental Validation: Zhoushan-Ningbo 500 kV Submarine Cable Project

Parameter	Value
Cable Length	16 km
Core Diameter	0.05 m
Sheath Diameter	0.134 m
Armor Diameter	0.17 m
Phase Distance	50 m
Ground Resistance	0.3 Ω

5. Results and Comparison

Method	Measured Current (A)	Kramer's Rule (A)	Error Rate
Experimental Data	88.48	87.90	0.6%
Numerical Simulation	88.45	87.90	0.7%

➡ Kramer's rule successfully achieved high accuracy, with an error margin of less than 1%, meeting the safety and precision requirements for high-voltage submarine cable systems.

6. Key Advantages of This Method

Parameter	Kramer's Rule Method	Numerical Simulation
Accuracy	High	High
Computational Speed	Fast	Slow
Resource Consumption	Low	High
Complexity	Low	High

7. Engineering Application and Recommendations

Real-time monitoring of armor grounding current for early fault detection.
Accurate evaluation of insulation aging and thermal stress.
Used as a design reference for grounding systems in future submarine cable projects.

8. Conclusion

The proposed method establishes a direct linear relationship between load current and armor grounding current through Kramer's rule.
The method eliminates the need for complex simulations, reduces computational time, and achieves high accuracy with an error rate of only 0.6%.
It has been successfully verified in the Zhoushan-Ningbo 500 kV submarine cable project and can be applied to other high-voltage AC submarine cable systems.

9. Keywords

AC Submarine Cable
Armor Grounding Current
Kramer's Rule Calculation
Electromagnetic Induction
Kirchhoff's Voltage Law (KVL)

10. References

Feng Zhi et al. (2024). A Method for Calculating Grounding Current of AC Submarine Cable Armor Based on Load Current. Wire & Cable, No.6, 2024. DOI: 10.16105/j.dxdl.1672-6901.202406007
GB/T 50217-2018 - Standard for Submarine Cable Design
IEC 60287 - Electric Cables Current Rating Standard