Impact of Air Gap Defects on the Electrical and Mechanical Properties of a 320 kV Direct Current Gas Insulated Transmission Line Spacer

Abstract

Air gap defects inside a spacer reduce its insulation performance, resulting in stress concentration, partial discharge, and even flashover. If such gap defects are located at the interface between the insulation and conductor, a decrease in mechanical stress may occur. In this work, a finite element method-based simulation model is developed to analyze the influence of gap defects on the electrical and mechanical properties of a ±320 kV direct current gas insulated line (DC GIL) spacer. Present findings reveal that a radially distributed air gap produces a more significant effect on the electric field distribution, and an electric field strength 1.7 times greater than that of the maximum surface value is observed at the air gap. The axial distribution dominates the distortion of the surface stress by generating a stress concentration region in which the maximum stress of the air gap is twice the pressure in the surrounding area.

1. Introduction

With its advantages of low loss, large transmission capacity, and easy grid interconnection, high voltage direct current (HVDC) transmission is steadily influencing the future direction of modern power systems [1,2,3]. A GIL spacer offers unique advantages and is thus widely used to pass through partial areas with large vertical drops and poor meteorological conditions [4,5,6]. Among the components of a GIL, the insulation spacer is indispensable for tasks such as isolating the air chamber, electrical insulation, and mechanical support [7,8].

The GIL is filled with SF₆ gas [9] with a pressure of 0.45 MPa during operation. Obvious internal stress concentration may occur under the external stress load or around micro defects, which makes this region the weakest point of the spacer. However, bubbles and other defects can be inserted into the spacer as a result of imperfect manufacturing techniques or unstable equipment during production [10,11]. A micro defect can distort the electric field of the spacer [12,13], which leads to partial discharge or surface flashover. Compared to the AC spacer, the DC spacer offers relatively insufficient mechanical properties due to its flatter geometry. Accumulation of spatial charge under DC conditions further significantly reduces the flashover voltage of the DC spacer [14]. However, research thus far has focused mainly on charge accumulation and charge suppression and less on the influence of interior defects on the electrical or mechanical properties of DC spacers [1,14]. Therefore, the potential factors leading to a decline in mechanical and electrical performance under DC conditions need attention.

The specific stress on a spacer can be obtained in a mechanical water pressure test by arranging strain sensors on its surface to measure the stress at each position [15]. Measuring electric field intensity is more complex and mainly involves an electric field probe [16,17]. However, the probe will distort the electric field distribution, causing measurement errors. Other methods, such as dust mapping and electroluminescence [18], are also used, but it is difficult to obtain quantitative results by image reflection. It is also difficult to accurately analyze the mechanical stress and electric field intensity distribution by merely depending on experimentation. This issue can be overcome using the finite element method (FEM) [19,20]. According to the geometric structure, stress environment, and boundary conditions of the physical object, a simulation model can be developed to promote accurate and real-time analysis of the electrical and mechanical properties of an insulation spacer. One study [21] used the FEM method to simulate an insulation spacer under a hydrostatic test to determine the strain and stress distributions along the spacer surface. Another study examined the effect of adhering spherical conducting particles (with different sizes and locations) on the electric field distribution [22]. The group in [23] analyzed the electric field properties under two types of interface gaps via a 2D model. The literature [24] investigates the partial discharges raised by floating particles and nitrogen bubbles with different shapes and radii. All of these studies show the feasibility and applicability of the FEM. However, a more comprehensive spatial model including both electrical and mechanical properties should be constructed to investigate the field distortion.

Given the need for such a model, an FEM-based simulation model is constructed to investigate the electric field intensity and mechanical stress under various radially and axially distributed air gap defects. The variation in electric field intensity and stress versus radial or axial distance on the spacer surface is analyzed and discussed, and the corresponding functional relationship is established. Present findings reveal that a radial air gap influences the electric field distribution more significantly than an axially distributed air gap that dominates the surface stress deformation in different ways. The conclusions benefit a quantitative understanding of the impact of DC spacers on electrical and mechanical properties due to various air gap defects.

2. Simulation Model

2.1. Geometry

In this work, a defect spacer is researched to determine how an air gap impacts the GIL insulation performance. The FEM is used to achieve this purpose. Referring to previous work [25], the geometry is shown in Figure 1 and contains three types of material. The detailed material and geometric parameters are listed in

Table 1. Geometric and material parameters of the simulation model.

No.	Component	Geometry Parameter	Material	Material Parameter
1	Metal shell	Length: 52 cm Radius: 33 cm	Aluminum alloy	Relative permittivity: 1 × 107 Young modulus: 71 GPa Poisson’s ratio: 0.33 Density: 2700 kg/m3
2	Center conductor	Length: 52 cm Radius: 9.8 cm
3	Ground ring	Radius: 1 cm
4	Insulation spacer	Max thickness: 5 cm Radius: 27 cm	Epoxy resin	Relative permittivity: 4.95 Young modulus: 13 Gpa Poisson’s ratio: 0.36 Density: 2300 kg/m3
5	Air gap	Radius: 0.15 cm	Air	Relative permittivity: 1

.

2.2. Equation Derivation and Boundary Conditions

The insulation spacer in Figure 1 is operated at DC 320 kV. A DC voltage is preset at the center conductor (labeled 2 in Table 1), then the electric field intensity is generated and distributed along the upper and lower surfaces of the insulation spacer (labeled 4).

Given that the surface electric field intensity (E) is required to be less than 12 kV/mm under normal operation, making the monitor of this index is rather fundamental. In the simulation model, E can be also defined in terms of the negative potential φ:

$$E=-\nabla \phi$$

(1)

When the metal shell and ground ring are grounded (labeled 1 and 3 in Table 1), the potential in the region between them satisfies

$$\nabla \cdot (\nabla \phi )=0$$

(2)

The differential equations corresponding to the adjacent interfaces can be defined to describe transferred properties [26]. The subscript indicates each interface, n, is a normal vector, and ε is the relative permittivity. When the potential distribution in the computation regions is determined, the corresponding E can be naturally obtained via (1).

$$\begin{array}{l}{\phi }_1={\phi }_2\\ {\epsilon }_1\frac{\partial {\phi }_1}{\partial n}={\epsilon }_2\frac{\partial {\phi }_2}{\partial n}\end{array}$$

(3)

In addition to the necessary electrical performance, excellent mechanical performance is also required of a GIL insulation spacer because it always operates under a pressure of 0.45 MPa in a SF₆ atmosphere. To check the damage to the insulation spacer caused by the air gap, a 2.4-MPa pressure load is preset on the lower surface according to a hydrostatic test [20]. Once the external load is applied, all points inside the insulation spacer are in a state of stress balance.

During the simulation, the intersection between each spacer and the metal shell and between each spacer and the central conductor is set as a fixed constraint, and the upper surface and ground ring are treated as free boundaries. The epoxies filling the insulation spacer can be treated as isotropic materials, which means the Young moduli in all directions (G_xy, G_xz, G_yz) are the same:

$$G_{xy}=G_{xz}=G_{yz}$$

(4)

Finally, the stress boundary condition of the computation region Γ is obtained from the sum of boundary conditions of the external stress Γ_σ and internal deformation Γ_u:

$$\Gamma ={\Gamma }_{\sigma }+{\Gamma }_u$$

(5)

2.3. Performance Analysis with a Defect-Free Model

A total of 3,644,364 degrees of freedom were generated during the simulation. Figure 2 presents results of mesh generation of the simulation results. Figure 3 presents the distributions of the electric field intensity (modulus) and principal stress of the insulation spacer and its cross section without any defect. Figure 3b,d provide the cross profiles of Figure 3a,c, which are formed by rotating 360 degrees with the Z axis as the symmetry axis in Figure 3b,d.

Table 2. Electrical and mechanical performances of an insulation spacer without any defect.

Items	Emax (kV/mm)	Pmax (MPa)
Upper surface	2.929	14.365
Lower surface	3.427	25.632

shows the maximum electric field intensities and principal stresses (E_max and P_max) corresponding to the upper and lower surfaces of the insulation spacer. The electrical and mechanical performances of the defect-free model are sufficient for normal operation. To show how mechanical stress affects the spacers, Figure 4a describes the distribution of mechanical forces around the surface of the spacer, and Figure 4b presents the resulting shape of the spacer when conditioning the deformation caused by mechanical forces.

3. Impact on Model Performance of a Radially Distributed Air Gap Defect

3.1. Arrangement of the Air Gap Defect along the Radial Direction of the Insulation Spacer

In this section, the air gap is arranged inside the insulation spacer and has a radial distribution, as shown in Figure 5. The geometry of the air gap is simulated as a sphere with a radius of 3 mm. The air gap caused by the poor wetting operation is mostly spherical in the manufacturing process. Also, there is no uniform standard for the air gap shape caused by other faults, thus the simple sphere is utilized. In addition, the size of the air gap would not sharply alter the distribution of the electric field compared to that with diverse radii [24]. The size of the air gap generated in the manufacturing process is generally not too large, otherwise, it cannot pass the production inspection, while defects of too small a size cannot be observed. Therefore, a sphere with a radius of 3 mm is selected. Finally, ten equally spaced positions are distributed to install an air gap with similar distances between these positions and the upper and lower surfaces, The involved material parameter is permittivity, which is shown in Table 1. The distance between the center of the air gap and the conductor is defined as the radial distance X-dis and is in the unit mm.

The spacing between positions is 1 mm in Figure 5. The corresponding axial coordinate varies as a function of X-dis to ensure similar distances of the upper and lower surfaces of the insulation spacer. There is an intersection between the ground ring and the air gap marked 10. The geometry of this air gap can be altered at the interface, and the air gap can also be treated as a suspended contact defect (like a scratch on the surface). Ten simulations were sequentially carried out to analyze the distributions of electric field intensity and principal stress of the insulation spacer.

3.2. Impact on Electric Field Distribution

The electric field distribution and its maximum (E_max) on the air gap surface are tabulated in

Table 3. Electric field distribution and its maximum value on the air gap surface.

X-dis	11 mm	12 mm	13 mm	14 mm	15 mm
Emax
X-dis	16 mm	17 mm	18 mm	19 mm	20 mm
Emax

. The minimum electric field is 4.144 kV/mm, and the maximum appears at the start and end points of this distribution line. This range reflects the intersection of the spacer with the conductor and ground ring.

For each air gap, the electric field intensity on both ends is relatively low compared with that of the remaining region, and its maximum is always at the center. The air gap sharply increases around this position and causes a discharge breakdown once the electric field intensity is more than 3 kV/mm (the breakdown voltage of air) [23]. In this case, the accumulated discharge state gradually ages the epoxy materials and generates more charge carriers, which in turn promotes the discharge intensity. Consequently, once the air gap appears inside the insulation spacer, the maximum electric field strength on the air gap surface can lead to breakdown and trigger partial discharge regardless of its radial distance from the conductor. The discharge severity is positively related to the distance between the air gap and the conductor or grounding terminal, as illustrated by the points at 11 mm and 20 mm. The distorted air gap can be treated as a surface scratch defect when it intersects the ground ring. The distorted electric field intensity at 20 mm even exceeds 5.8 km/mm and is 1.2 times larger than that at 11 mm. This result reveals that the suspension discharge maintains a stronger intensity than that of the air gap discharge in the insulation spacer.

Figure 6 shows the distribution level along the surface and cross profile of the spacer when the air gap is treated as a surface scratch. The resulting maximum electric field intensity appears on the bottom surface and develops into the weakest point to form the defect in the insulation spacer. Figure 7 compares the E_max in the air gap with that on the upper and lower surfaces of the spacer and with that of a defect-free spacer. If the distance between the air gap and the upper and lower surfaces is sufficient, E_max for each surface is consistent with the defect-free state and is not affected by the air gap. The plot of E_max versus radial distance (X-dis) is fitted in Figure 7b to quantitatively analyze the distribution of E_max.

Table 4. Amplitude ratios of electric field intensity of the air gap for the upper and lower surfaces.

X-dis	11 mm	12 mm	13 mm	14 mm	15 mm
ke_upper	1.657	1.470	1.415	1.420	1.419
ke_lower	1.416	1.257	1.209	1.214	1.213
X-dis	16 mm	17 mm	18 mm	19 mm	20 mm
ke_upper	1.421	1.412	1.405	1.456	1.999
ke_lower	1.215	1.207	1.201	1.244	1.708

lists the resulting amplitude ratios of E_max corresponding to the air gap (E_{max_air}) and its upper and lower surfaces (E_{max_upperI} and E_{max_lower}) according to:

$$\begin{array}{l}{k}_{e\_upper}=E_{\max \_air}/E_{\max \_upper}\\ k_{e\_lower}=E_{\max \_air}/E_{\max \_lower}\end{array}$$

(6)

3.3. Impact on Mechanical Stress Distribution

The insulation spacer manufactured with epoxy material has a tensile stress failure threshold of 70 MPa, and the tensile stress at the bond between the spacer and the conductor is 25 MPa. Consequently, a lower mechanical stress amplitude is required to ensure safe operation [20]. Only the lower surface sustains the atmospheric pressure, so once the single-side compression is considered, mechanical stress concentration should be avoided as soon as possible. The distribution and maximum value (P_max) of the major principal stress on the air gap surface are shown in

Table 5. Mechanical stress distribution and maximum value on the air gap surface.

X-dis	11 mm	12 mm	13 mm	14 mm	15 mm
Pmax
X-dis	16 mm	17 mm	18 mm	19 mm	20 mm
Pmax

.

The observed variation is that P_max on the surface of the air gap decreases with increasing radial distance and gradually rises when it is close to the ground ring, similar to the electric field distribution. The distortion can still be observed at the air gap at a radial distance of 20 mm, corresponding to the scratch. The distribution of this scratch is presented in Figure 8, where P_max appears at the interface between the lower surface and the metal shell. The same phenomenon is also observed in the other nine cases. The lower surface is believed to be the boundary for sustaining the atmospheric pressure of 2.4 MPa. The generation of the air gap does not change the distribution of the surrounding area as sharply as the electric field intensity. Figure 9a further compares P_max on the air gap with that on the upper and lower surfaces of the spacer, with or without the preset defect. The curve of P_max on the air gap versus radial distance is then fitted in Figure 9b to highlight the radial distance dependence of the mechanical stress distribution.

The P_max on the upper and lower surfaces of a defect or a defect-free model is approximately uniform and much higher than that of the air gap. With the air gap, P_max on the upper surface varies because it is assigned as the free boundary. The impact of P_max on the maximum stress on the upper or lower surface is quantified as the following:

$$\{\begin{array}{l}{k}_{p\_upper}=P_{\max \_air}/P_{\max \_upper}\\ k_{p\_lower}=P_{\max \_air}/P_{\max \_lower}\end{array}$$

(7)

The results are listed in

Table 6. Amplitude ratio of mechanical stress of an air gap compared with the ratios for the upper and lower surfaces.

X-dis	11 mm	12 mm	13 mm	14 mm	15 mm
ke_upper	0.770	0.567	0.499	0.411	0.311
ke_lower	0.431	0.318	0.280	0.230	0.174
X-dis	16 mm	17 mm	18 mm	19 mm	20 mm
ke_upper	0.180	0.108	0.142	0.296	0.705
ke_lower	0.101	0.061	0.080	0.166	0.395

. As with Figure 8, the mechanical stress is concentrated in neither the air gap nor the inside region but is mainly distributed along the upper and lower surfaces, especially the intersection point.

4. Impact on Model Performance under an Axially Distributed Air Gap Defect

4.1. Arrangement of an Air Gap Defect along the Axial Direction of the Insulation Spacer

In the last section, a radially distributed air gap defect was studied to discuss the distortion of the electric field intensity and mechanical stress around the defect. The global maximum of the electrical indicator appeared near the interface between the central conductor and the insulation spacer. Thus, assigning the position at 11 mm as the radial coordinate, we next investigate distortions caused by an axially distributed air gap by changing the axial coordinate from 15 to 22 mm.

In contrast with the radial distribution, the first and last points of the axially distributed air gap form a surface scratch, and the corresponding geometry is determined by the interfaces of the upper and lower surfaces of the spacer. The generated surface scratch in Figure 10 is more representative than that of the suspended contact in Figure 5. Eight air gaps are arranged inside the insulation spacer, as shown in Figure 10.

4.2. Impact on Electric Field Distribution

The variation law implied by

Table 7. Electric field distribution and maximum value on the air gap surface.

X-dis	15 mm	16 mm	17 mm	18 mm
Emax
X-dis	19 mm	20 mm	21 mm	22 mm
Emax

is quite different from that in Table 3 because it involves growth first, then a decrease. The global maximum is near the center inside the insulation spacer because it is nearest to the interface between the insulation spacer and the energized conductor. Thus, we can conclude that the maximum electric field intensity on the air gap surface is positively correlated with the distance from the charged interface. Furthermore, the observed surface electric field intensity is greater than 3 kV/mm, regardless of how the air gap is distributed, indicating an easily triggered partial discharge.

Table 7 suggests that the electric field intensity is not sharply affected by the appearance of the surface scratch but reveals a minimum value along the distribution pass. Figure 11 further shows the electric field intensity distribution at two surface scratches.

The E_max values of an air gap corresponding to the upper and lower surfaces are compared for models with and without defects, similar to the analysis in Figure 7. The result differs from Figure 7 in that the electric field intensity of several points at the start or end position is lower than on the spacer surface. The distribution for the upper or lower surface of either the defect or defect-free model is not affected, which is the same as what is found in Figure 7. The relationship between E_max and axial distance is described via fitting analysis in Figure 12. Finally, Equation (6) is used to calculate the amplitude ratio of E_max corresponding to the air gap (E_{max_air}) and its upper or lower surface (E_{max_upper} or E_{max_lower}). These amplitude ratios are shown in

Table 8. Amplitude ratio of electric field intensity of an air gap compared with the ratios for the upper and lower surfaces.

X-dis	15 mm	16 mm	17 mm	18 mm
ke_upper	1.117	1.332	1.541	1.641
ke_lower	0.959	1.141	1.314	1.397
X-dis	19 mm	20 mm	21 mm	22 mm
ke_upper	1.626	1.431	1.109	1.220
ke_lower	1.386	1.229	0.950	1.044

. The biggest ratio is only 1.641 and much less than 1.999 in Table 4. Thus, the axially distributed air gap has less impact than the radial gap on the electric field intensity distribution.

4.3. Impact on Mechanical Stress Distribution

The mechanical stress distribution of an air gap is shown in

Table 9. Mechanical stress distribution and its maximum value on the air gap surface.

X-dis	15 mm	16 mm	17 mm	18 mm
Pmax
X-dis	19 mm	20 mm	21 mm	22 mm
Pmax

for various axial distances. Another trend can be found when this is compared with the radial distribution in Table 5. According to Table 9, the stress amplitude of the air gap surface is negatively related to the distance from the pressure side. The lower surface is assigned to be the pressure side (with an atmospheric pressure of 2.4 MPa); thus, a smaller axial distance means higher mechanical stress is generated on the surface of the air gap. Although another surface scratch appears at an axial distance of 22 mm, it is located (placed) on the upper surface, which is far away from the pressure side, causing minimum mechanical stress. Figure 13 shows the stress distribution of surface scratches. In the picture, the maximum stress on the entire spacer is also near the interface between the insulation spacer and the metal shell.

Figure 14 presents the mentioned law of decrease in P_max versus axial distance. When an air defect is inserted inside the insulation spacer, the mechanical stress of the upper surface varies with the changing axial distance and shows no functional relationship. In contrast, a functional relationship between the P_max of the air gap and axial distance is determined by the fitting analysis in Figure 14b, which establishes a general decay tendency.

The recorded P_max for the air gap at 18 mm is higher than at the last point (17 mm). This is attributed to the shorter distance from this point to the conductor than from other points. The same results are also obtained in Figure 9. Consequently, the stress on the air gap depends on the distance between the air gap and the pressure side or other interfaces (because these interfaces are also pressure boundaries and always sustain the local maximum of the mechanical stress). The pressure increases with decreasing distance.

Table 10. Electric field distribution and its maximum value on the air gap surface.

X-dis	15 mm	16 mm	17 mm	18 mm
ke_upper	0.729	0.608	0.592	0.672
ke_lower	0.479	0.421	0.393	0.468
X-dis	19 mm	20 mm	21 mm	22 mm
ke_upper	0.553	0.432	0.399	0.217
ke_lower	0.371	0.293	0.229	0.145

shows the amplitude ratio of P_max recorded for an air gap and upper and lower surfaces of the insulation spacer. The air gap defect only occurs on the lower surface of the insulation spacer, forming a surface scratch, and the mechanical stress at this time reaches half of that of the surface level. Thus, the air gap on the spacer surface leads to an obvious stress distortion, reducing the mechanical capacity of the defect insulation spacer by concentrating the surrounding stress at this point.

5. Conclusions

A radially distributed air gap does not affect the electric field intensity and stress distribution of the upper and lower surfaces. The electric field intensity of the radially distributed air gap is 1.2–1.7 times the maximum value on the spacer surface. In contrast, the maximum stress on the air gap is only 0.08–0.77 times that on its surface. Therefore, the air gap significantly affects the surrounding electric field distribution. A significant air gap discharge occurs when the electric field intensity is greater than 3 kV/mm, causing a breakdown and partial discharge.

For an axial air gap distribution, the electric field strength of the air gap surface grows with increasing distance from the surface. The maximum value (4.795 kV/mm) occurs near the center conductor, and the local electric field strength is minimum on the outer surface. However, the maximum stress (12.292 MPa) of the air gap occurs on the lower surface. Consequently, the radial air gap distribution contributes more significantly to the electric field distribution, whereas the axial distribution dominates the distortion of the surface stress in a different way.