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The electric field intensity (EFI) is important characteristic quantity for evaluating the internal insulation state of cable joints. Based on finite element method, this paper proposes two EFI research methods, field-circuit coupling method and equivalent circuit method. The average EFI of the inner surface of the outer semi-conducting shield can be calculated from the current in the measuring circuit. The relative error between these two methods is about 15%, which roughly proves the consistency of the two methods. Further practical application research enables online monitoring of cable joints.

In recent years, with the development of urban modernization, the unit capacity has been increasing, and the share of power cables in urban power supply has increased [

The electric field intensity (EFI) is important characteristic quantity for evaluating the internal insulation state of cable joints. When there is a defect in the insulation of the cable joint, the internal EFI distribution will change, and when the internal EFI exceeds the breakdown EFI, it will lead to the occurrence of partial discharge, and then accelerate the dielectric breakdown [

The source of the alternating electric field generated by power equipment is the charge on the metal surface of the power equipment. Due to the low frequency in the case of power frequency, with the exception of inductors and transformers, the effect of magnetic field changes with time in most power equipment can be ignored. In this case, the power frequency electric field is a quasi-static electric field, and the induced electric field is much smaller than the coulomb electric field. The field equation is

∇ × E ⇀ = 0 . (1)

∇ • D ⇀ = ρ . (2)

∇ • ( J ⇀ + ∂ D ⇀ / ∂ t ) = 0 . (3)

Auxiliary equations are

J ⇀ = γ E ⇀ . (4)

D ⇀ = ε E ⇀ . (5)

where E ⇀ is EFI vector, J ⇀ is conductive current density vector, D ⇀ is electric displacement vector, ρ is volume charge density, ε is the permittivity, γ is conductivity, t is time, ∇ is Nabla operator.

In the case of power frequency, the wavelength is 6000 km, which is much larger than the size of the conductor surface. Therefore, the phase difference between the electric field intensities between the points on the surface of the metal conductor can be ignored. If we are concerned about the EFI at point A on the surface of the conductor shown in

As shown in _{1}, capacitance C_{1} is the equivalent one between the slice and the outer conductor shield, capacitance C_{2} is the equivalent one between the high voltage conductor and the slice, u C 2 is voltage across capacitance C_{2}, i c 2 is the total current.

In the case of sinusoidal steady state, according to relationship of voltage and current of capacitance, we can calculate the average EFI of the inner surface of the slice from Equation (6) [

E = I / ( ω • ε • S ) . (6)

Among them, E is EFI on the inner surface of slice (V/m), ε for the permittivity (F/m), I is the total current (A) of the equivalent circuit in ^{2}), ω is angular frequency (rad/s).

The simulation model used in this paper is a three-dimensional 10 kV cable joint as shown in

As shown in

In addition, the model in this paper found that the meshing accuracy of the mesh near the slice has a greater impact on the calculation results, but the size of the slice is smaller than the entire model, so it is suitable to use local refinement. The method is divided to avoid the increase of calculation time caused by the overall mesh refinement and the limitation of memory and so on. Therefore, as shown in

Materials | Parameter and application | ||
---|---|---|---|

Relative permittivity | Conductivity (S/m) | Application | |

Copper | 1 | 5 .8 × 10 8 | Cable conductor |

XLPE | 2.3 | 1 × 10 − 15 | Main insulation |

Silicone Rubber | 4.3 | 2 .727 × 10 − 12 × e 9.796 × 10 − 6 × E | Joint insulation |

Semi-conducting material | 20 | 10 | Conductive layers and stress cone |

Insulation glue | 3.5 | 1 × 10 − 12 | Insulation gap |

applying multi-layer boundaries to the slice attachment area to refine the local grid and ensure the accuracy of the calculation without adding too much calculation time and computing memory.

When simulating the EFI of the inner surface of the outer semi-conducting shield of the 10 kV cable joint, two simulation calculation methods can be used to solve it.

One method is use the electrostatic field module of the finite element simulation software to calculate the capacitance between each part of _{11} is the capacitance evaluated between the grounded terminals and Terminal 1. This can be calculated by exciting Terminal 1. The capacitance between Terminals 1 and 2 would be C_{21}. This can be calculated once we have information about C_{11} and C_{22}. This means we would need to solve the model once again by exciting Terminal 2. By definition, C_{21} and C_{12} would be equal. This means that a three-terminal system will have six unique values of capacitance.

Through calculation, C_{12} (C_{1} in _{23} (C_{2} in _{1}, C_{2} and R, the measurement circuit can be formed.

The other method is to use the current field and circuit modules in the finite element simulation software, that is, the field-circuit coupling method to calculate the current through the measurement resistor, and then use Equation (6) to calculate the EFI of the inner surface of the slice corresponding to different power frequency voltage. It differs from the method described in part “4.1” in that the copper conductor is first processed with a power frequency voltage in current field, the shield is grounded, and the slice is connected to the circuit filed. In the circuit module, the slice voltage is set to the external I terminal 1, and a 1 MΩ measurement resistor is connected between the external I terminal 1 and the ground. Referring to the value of capacitor C_{1} in part “4.1” and comparing with resistor R, it can be calculated that almost all the current through the measuring circuit passes through resistor R. Therefore, in the case of applying a power frequency voltage to the copper conductor, it can be considered that the total current in the circuit is equal to the current on the measurement resistance, and the EFI of the inner surface of the slice is obtained using Equation (6).

The simulation calculations in this paper are mainly aimed at the EFI on the inner surface of the outer semi-conductive layer of the cable connector, and two different methods of field-circuit coupling and equivalent circuit are adopted to solve it.

Firstly, the simulation model is established, because the setting of the slice uses a three-dimensional model; in addition, the material parameters are set according to the physical properties of the 10 kV cable joint; then the boundary conditions and loads are applied, and the boundary conditions are selected from the effective voltage value as the calculated load. The final simulation results are obtained through the analysis and calculation of the proposed method. The results obtained by different methods are compared and analyzed.

Using the first equivalent circuit method described in part “3.2”, the capacitance matrix in the quasi-static electric field is solved to obtain the gap capacitance C_{1} in the established simulation model and the capacitance C_{2} between the semi-conducting layer outside the section, so as to form the measuring circuit with the measuring resistance R and obtain the total current in the circuit. In addition, for the field-circuit coupling method, the simulation model is first studied in the case of power frequency, and then “current through device R” can be obtained by global calculation of derived values. Since the current through the resistance R in the circuit is nearly equal to the total current in the circuit, the results calculated by the two methods are compared using the “current through the device R” in the field-circuit coupling and total current in equivalent circuit. With the change of power frequency voltage applied to copper conductor, the total current results calculated by the two methods are shown in

Using Equation (6), the average EFI of the inner surface of the outer semi-conducting shield can be calculated from the current in the measuring circuit. The comparison of the EFI calculated by the field-circuit coupling method

and the equivalent circuit method is shown in

・ In the case of power frequency, the relative error between the field-circuit coupling method and the equivalent circuit method is about 15%, which approximately proves the consistency of the two methods. Although the results are not sufficient to prove the correctness of the calculation method, if we can find more methods to calculate the EFI based on the experimental results, the correctness of the calculation method in this paper will be more fully verified.

・ For the actual 10 kV cable joint, the structure proposed in this article can be used to modify its structure, and the voltage drop information on the measured resistor can be transmitted to the “command center” through the transmission line. In this way, the measurement signal is obtained, and the change of the EFI is used to realize the measurement and monitoring of the EFI of the cable joint. Further practical application research enables online monitoring of cable joints.

This work was supported by the Science and Technology Project of China South Power Gird Co., Ltd. (GZHKJXM20180140).

The authors declare no conflicts of interest regarding the publication of this paper.

Zhang, R.X., Xiong, J., Wu, Z., Liao, L., Wu, M.Y., Du, G., Huang, X.Y., Jin, W.P., Li, H.M., Zhang, J., Cheng, W.L and Lu, B.X. (2020) Research on Simulation Methods of Electric Field Intensity on Surface of 10 kV Cable Joint. Energy and Power Engineering, 12, 37-45. https://doi.org/10.4236/epe.2020.124B004