The impact of different air gap defects in polypropylene coaxial cables on electric field distortion

The internal cable will have different air gaps due to various physical influences, and partial discharge caused by air gap defects is the main cause of cable insulation aging. To avoid serious consequences caused by air gap defects, it is crucial to analyze the extent of the impact of early-stage air gaps on the electric field in the cable. In this paper, COMSOL Multiphysics software is used to build a three-dimensional model of the cable, and the insulation material is polypropylene. Different positions and sizes of air gap defects are designed in the model. The electric field distribution inside the cable is obtained through the finite element algorithm, and the degrees of distortion of the electric field under different air gap sizes, positions, and shapes are compared. The results show that the size of the air gap affects the change in the electric field. Air gaps closer to the copper core position produce greater electric field distortion. Additionally, air gaps with larger curvature also result in greater electric field distortion. Based on the conclusion of this study, the influence degree caused by different air gap defects can be determined and provide a basis for the analysis of such faults.


Introduction
Cross-linked polyethylene (XLPE) cables have been widely used in power grids due to their excellent insulation performance [1][2].However, they have the drawback of generating hazardous substances when decomposed.In this study, polypropylene (PP) material is utilized as the bulk insulation in highvoltage power transmission cables, benefiting from its high melting point and environmental friendliness.The discharge behavior in air gaps of this type of cable has been rarely studied, which is why this paper primarily investigates the effects produced by different types of air gaps on polypropylene material in coaxial cables.
Since its proposal in the 1940s to the present, finite element analysis (FEA) theory has been continuously developed and has become an important method for solving complex nonlinear problems and multiphysics coupling problems in mathematics, physics, and engineering [3][4].In [5], finite element analysis was used to study the influence of a single spherical air gap defect on the electric field intensity of high-voltage direct current cables under steady-state conditions.In [6], the influence of different defect types and water positions on electric field distribution was studied through experiments.The results showed that the shape and location of water had a significant influence on the electric field distribution, and the distortion caused by the defect type of water tree is the most serious, followed by the defect type of water film and water drop.In [7], simulations were conducted by altering the position, shape, size, and type of defects in insulating materials to systematically study their impact on electric and magnetic field distributions.In [8], a voltage distribution calculation model was established for the analysis of buffer layer discharge defects and the influencing factors were analyzed by using this model.The results showed that the white mark defect can quantify the probability of buffer layer discharge.In [9], the electric field situation was investigated when peeling off the entire external semiconductor layer on XLPE and partially peeling off the external semiconductor layer on XLPE.The results demonstrated a significant increase in the electric field.In [10], the influence of interface roughness defects and interface scratch defects was analyzed, and COMSOL software was used for finite element calculation and analysis.
The effects of air gap defects of different sizes, positions, and shapes on electric field distribution in cable insulation are studied in this paper.The results show that air gap defects of different sizes, positions, and shapes have different effects on electric field distortion.

Mathematical analysis method
The electric and magnetic field intensities in each mesh element are computed.The calculation process satisfies the following Maxwell equations as shown in Equation 1: In the equation, H represents magnetic field intensity, E represents electric field intensity, J represents conduction current density, ρ represents free charge density, and D represents electric displacement vector.

Establishing cable physical model
This paper utilizes the built-in model function of COMSOL Multiphysics software to establish a threedimensional model of polypropylene coaxial cable.The cable model mainly includes the insulation layer, metal armor layer, filling layer, and copper conductor, as shown in Figure 1.The innermost layer of the model is the copper conductor, followed by the filling layer on its outer side.The purpose of the filling layer is to provide a tighter fit to the cable core, hence it has a higher density.Otherwise, the gaps within the core would not be filled tightly.The outer side of the filling layer is the metallic armor layer.The outermost layer is the insulation layer.The cable 3D model diagram and grid division are shown in Figure 2. The innermost layer of the model is the copper conductor, with a diameter set at 30 mm.The layer adjacent to the conductor is the filling layer, with a relative permittivity set at 2.4 and a cylindrical diameter of 74.6 mm.Without proper filling, gaps in the cable core would compromise stability and reduce the cable's lifespan.The outside of the filling layer is the metallic armor layer, with a diameter set at 87.7 mm.Its purpose is to protect the cable from mechanical stress and enhance overall tensile strength.The outermost layer is the insulation layer, with a relative permittivity set at 3 and a diameter of 96.7 mm.
In this study, the COMSOL Multiphysics mesh partition module is used, with a total of 101,574 mesh elements and an average mesh quality of 0.6632, which basically meets the requirements of the mesh partition.

Air gap defect setting
Different sizes, shapes, and positions of air gap defects are set by using COMSOL Multiphysics, as shown in Figure 3.As shown in Figure 3, the air gap types of different sizes, shapes, and positions are set respectively.

Simulation results of different air gap sizes
In this study, when investigating air gap defects of different sizes, two defects with the same radial coordinates but different axial coordinates are established to simulate and analyze their respective results.(Left is the potential field, right is the electric field).
From Figure 4, the potential remains relatively unchanged.For larger air gaps, due to their larger spatial occupancy, the affected area around them is also larger.As a result, there are more regions with low electric field intensities surrounding larger air gaps.

Simulation results of different air gap shapes
In this study, unlike previous studies of different sizes, the same principle is applied to distribute two types of ellipsoidal air gap defects along different longitudinal positions in the same radial direction.In the physical field of the model, the two different-shaped ellipsoidal air gaps are oriented perpendicular and parallel to the magnetic field direction, respectively.The simulation results are shown in Figure 5. (Left is the potential field, right is the electric field).
From Figure 5, it can be observed that when the ellipsoid is oriented with its longer axis in the radial direction, the lower air gap has a smaller impact and is almost similar to the average electric field.However, for the ellipsoidal air gap oriented perpendicular to the magnetic field, a higher electric field intensity is observed within the air gap.From the electric field map, it can be seen that there are regions with electric field lower than the average value surrounding the air gap perpendicular to the magnetic field.

Simulation results of different air gap positions
In this study, for different air gap defect positions, three air gaps of the same size with different horizontal positions are established in the model.The distances of the three air gaps from the copper core are 2 mm, 15 mm, and 25 mm, respectively.The two air gaps with closer distances are distributed.(Left is the potential field, right is the electric field).
By referring to Figure 6, it can be observed that the placement of air gap defects has minimal impact on the potential, with variations that are even invisible to the naked eye.However, in terms of the electric field, the closer the air gap is to copper core, the greater the influence on the electric field is.In some regions surrounding the air gap, it is indicated that the electric field force experienced within the air gap is relatively stronger.

Radial curve analysis
This paper designs radial curves under three different circumstances, as shown in Figure 7.  From Figure (b), for air gaps oriented perpendicular to the magnetic field direction, the electric field distribution in the air gap is obviously distorted, with a magnitude of approximately 3.8*10 6 V/m.In this case, the degree of electric field distortion is small.On the other hand, for air gaps oriented parallel to the magnetic field direction, the magnitude of the distortion is relatively small, but the range of variation is larger.
It can be seen from Figure (c) that the air gap closest to the copper core has the greatest influence on the electric field distortion.There is a trend of decreasing electric field around each air gap, followed by a sharp increase, exceeding the range of average electric field values.

Conclusions
This paper mainly focuses on the simulation analysis of polypropylene coaxial cables.A comparison is made with the analysis results of normal cables, leading to the following conclusions: Firstly, when the air gap itself is larger, the change of the internal electric field will be more affected.On the other hand, air gaps with a smaller diameter exhibit a higher magnitude of electric field distortion but within a smaller range.
Secondly, the influence of air gaps on electric field distortion differs based on whether they are perpendicular or parallel to the magnetic field direction.Air gaps in the perpendicular direction show significantly higher amplitude of electric field distortion.
Thirdly, simulation results for air gaps at different positions show that the closer the air gap is to the position of the copper core, the more pronounced the electric field distortion it generates.

Figure 3 .
Figure 3. Types of air gap defects.

Figure 4 .
Figure 4. Air gap physical field distribution of different sizes.(Left is the potential field, right is the electric field).

Figure 5 .
Figure 5. Physical field changes caused by different ellipsoids.(Left is the potential field, right is the electric field).

Figure 6 .
Figure 6.The change of physical field caused by different positions of the air gap.(Left is the potential field, right is the electric field).

Figure 7 .
Figure 7. Radial effect of different sizes, shapes, and positions on the electric field.

Figure
Figure (a)  shows the electric field distribution.It can be observed that when crossing a larger air gap, the radial distortion of the electric field is longer.As for the interior of the air gap, the closer the copper conductor is, the stronger the electric field it generates.