Analysis of electrical performance and assessment of aging state for retired high-voltage cable accessory insulation

The cable accessories constitute a vulnerable element and are prone to failures in the operation of power transmission lines. To investigate the changes in the electrical performance and aging state of high-voltage cable accessories with different operating time, the volume resistivity, breakdown electric field, dielectric constant, and trap parameters of insulation samples taken from retired cable accessories were characterized. The results indicate that there is a certain correlation between the macroscopic dielectric characteristics of cable accessory insulation and its aging state. With the increase of operating time, the volume resistivity and breakdown electric field decrease, while the dielectric constant initially increases and then decreases. The trap distribution of cable accessory insulation can effectively reflect its aging state. With the increase of operating time, the trap energy levels of the accessory insulation become shallower, and the trap density increases. The trap results of the accessory insulation show good consistency with the resistivity and breakdown field strength. Clustering analysis is also used to classify the test data, and the results validate that the trap energy levels and trap density of the insulation samples have better correlation with the insulation aging state of cable accessories than macroscopic dielectric parameters.


Introduction
The rapid development of the Chinese economy has made higher demands on the transmission of electric power.High-voltage cables possess many advantages such as high transmission capacity, small occupied area, and high safety [1,2] .They can alleviate the issue of power resource shortages in certain regions.During the long-time operation, cable accessories are prone to faults, which can lead to power outages.Silicone rubber (SIR) and ethylene propylene diene monomer (EPDM) are the primary materials used in the production of cable accessories [3,4] .Parameters such as volume resistivity, dielectric constant, breakdown electric field, surface potential, and trap distribution serve as fundamental indicators for characterizing cable insulation conditions [5,6] .They enable the analysis and evaluation of the insulation performance and aging state of cables.
Currently, the cable body insulation, cross-linked polyethylene, has been sufficiently studied, but limited research has been found on the electrical performance and aging state of high-voltage cable accessory insulation, especially the retired ones [7,8] .Meanwhile, the accessory insulation configuration is more complex than cable body one, which is the most vulnerable area for insulating performance in high-voltage cable system [3] .The existing studies on accessory insulation mainly focus on few samples [4,8] and are short of statistical analysis and feature extraction.Considering the complicacy of accessory samples and operating environment, the artificial intelligence or machine learning should be applied to analyze the material and measurement data [9,10] .This study selected 21 SIR and 9 EPDM insulated cable accessories.The volume resistivity, breakdown electric field, dielectric constant, and trap distribution were characterized to explore the insulation condition and aging mechanism of cable accessories.Finally, clustering analysis was employed to extract the characteristic parameter of cable accessory insulation.Test results and analysis

Test platform and methods
The size of insulation samples from cable accessories is 45×45×1 mm 3 , as is shown in Figure 1(b).The volume resistivity was measured by Hioki SM-7110 based on the three-electrode method in Figure 1(e).The dielectric constant and breakdown strength were respectively measured using impedance analyzer and dielectric strength tester in Figure 1(c) and Figure 1(d).The surface charge and trap distribution were characterized by isothermal surface potential decay (ISPD) method in Figure 1(a).
The insulation sample was first charged by negative corona discharge using pin electrode.After charging saturation, the sample was moved under the Kelvin electrostatic probe (Trek6000B-6), and then the surface potential was measured and recorded by electrometer.The pin electrode tip and electrostatic probe are respectively 5 mm and 2 mm away from the upper surface of the sample.The charging voltage is -3 kV and the charging time is 180 s.The measurement time of the surface potential decay for each sample is about 4 hours.After surface potential test, the trap parameters were calculated based on isothermal decay theory.The corresponding equations are as follows [11] : Where ET is trap energy level, kB is Boltzmann constant, T is absolute temperature, vATE is trapped charge escape frequency (4.17×10 13 s -1 ), t is measurement time, L is the sample thickness, Qs is trap charge density, φs is surface potential.

Dielectric properties
The volume resistivity of cable accessory insulation mostly exceeds the China national standard requirement of 10 15 Ω•cm, but the resistivity of some cable accessories is below the national standard, which often encountered discharge faults caused by breakdown, poor sealing, or inadequate grounding.With the increase of operating time, the volume resistivity of accessory insulation demonstrates a downward trend.According to the measurement data, the cable accessory aging assessment range based on volume resistivity is provided in Table 1.
The measurement results of the breakdown electric field for cable accessory insulation show that the majority of breakdown strength values surpass the national standard requirement of 20 kV/mm.As a whole, the breakdown strength of some accessory insulation suffering breakdown is lower, around 18 kV/mm, and that of EPDM insulated accessory is higher.The values of breakdown strength range from 18 kV/mm to 33 kV/mm.With the increase of operating time, there is a downward trend in the breakdown electric field, although the overall change rule is not significant.Taking into account the available data, an aging assessment range for cable accessories based on the breakdown electric field is also provided in Table 1.The measurement results of the dielectric constant for cable accessories show that the majority of the accessory insulation has relative dielectric constants ranging from 2.5 to 3.5.Most cable accessories with dielectric constants greater than 3.5 have operating years within 8 years.The maximum dielectric constant is 4.5, and the overall aging level of this particular accessory, SIR insulated cable terminal, is quite profound.Other cable accessories with dielectric constants above 3.5 have often experienced faults such as breakdown, stress cone erosion, and discharges.The dielectric constant of cable accessory insulation exhibits an initial increase followed by a decline with increasing operating years, indicating that cable accessories are prone to faults and an increase in dielectric constant during the initial years of operation.After 10 years of operation, the dielectric constant tends to stabilize.Based on the available data, an aging assessment range for cable accessories based on dielectric constant is provided in Table 1.
The relationship between the volume resistivity of 27 cable accessories and the operating years is illustrated in Figure 2(a).From the graph, it is evident that, apart from a few samples with volume resistivity in the order of 10 17 Ω•cm, the majority of the samples exhibit volume resistivity around the order of 10 16 Ω•cm.As the operating time increases, there is a downward trend in the volume resistivity.The relationship between the breakdown electric field of cable accessory insulation and the operating time is depicted in Figure 2(b).It can be observed that the breakdown electric field of most samples is around 25 kV/mm, with minimal variation as the operating time increases.The relationship between the dielectric constant of cable accessory insulation and the operating time is shown in Figure 2(c).From the graph, the dielectric constant initially increases and then decreases with increasing operating time.Fig. 2. The relationship between dielectric parameters of cable accessories and operating time.

Trap distribution
The surface charge accumulation and dissipation behavior of insulation samples can be characterized by surface potential decay test [11] .The trap parameters, including trap energy level and trap density, are closely related with the defects inside the insulation sample.The results of surface potential decay and trap parameters in the insulation of cable accessories indicate that with increasing operating years, the surface potential decay of the accessory insulation accelerates.Both deep traps and shallow traps exhibit a trend of shallower trap energy level center, and trap density increases with the increase of operating years.Based on the available data, an aging assessment range for cable accessories based on trap parameters is provided in Table 2.The relationship between trap parameters and service life of cable accessories is shown in Figure 3, which shows the relationship between deep trap, shallow trap, deep trap density and shallow trap density and service life, respectively.It can be seen that regardless of deep traps or shallow traps, the trap energy levels of most samples become shallower with the increase of operating years, and the density of deep traps and shallow traps tends to increase with the increase of operating years.

Cluster analysis
The existing assessment of cable accessory status is typically based on the empirical conclusion drawn from a single parameter.However, the operation and aging of high voltage cables are affected by multiple aspects.Therefore, a new model is needed to comprehensively evaluate the aging parameters of cables.The goal of clustering is to group together data objects with similar characteristics, exploring valuable hidden information.It belongs to the category of unsupervised classification [12] .The K-means algorithm is a classic clustering algorithm known for its fast computation speed and effective clustering performance [13] , and its mathematical model can be stated as follows [10] .Given a dataset X of n data points represented as xi in d-dimensional space:  = { 1 ,  2 , … ,   },   ∈ R  (3) The mathematical formulation for K-means clustering is an optimization problem: minimize where  = { 1 ,  2 , … ,   } represents the set of K clusters, subject to the condition that each data point belongs to exactly one cluster; μi denotes the centroid of cluster Ci; ‖  −   ‖ 2 denotes the squared Euclidean distance between the data point xj and the centroid μi. Figure 4 presents the analysis results of the insulation parameters for cable accessory utilizing the K-means clustering algorithm.The red region in the diagram signifies cable aging, the gray area represents cable requiring attention, and the purple area indicates normal operational status.It can be seen from the figure that, in the two-dimensional clustering results concerning volume resistivity, breakdown electric field, and dielectric constant in relation to operational lifespan, data points do not concentrate within a specific region.This indicates that the clustering relationship between these three parameters and operational lifespan does not effectively reflect the aging status of cable accessory.Conversely, in the two-dimensional clustering results pertaining to trap density and trap levels, data points representing normal operation of cable accessory primarily cluster within the purple area, signifying the favorable status of the accessory.In comparison to other dielectric parameters, trap distribution can better reflect the insulation aging status of cable accessory.

Conclusions
There is a certain correlation between the macroscopic dielectric characteristics of cable accessory insulation and its aging state.As the operating time increases, the volume resistivity and breakdown electric field decrease, while the dielectric constant initially increases and then decreases.The potential decay and trap distribution of the accessory insulation can effectively reflect its aging state.With the increase of operating time, the trap energy levels of the cable accessory insulation become shallower, and the trap density increases.The trap analysis of the accessory insulation shows good consistency with the variations in resistivity and breakdown electric field.

Fig. 3 .
Fig. 3.The relationship between trap distribution of cable accessories and operating time.

Fig. 4 .
Fig. 4. Results of the clustering analysis of the insulation parameters for cable accessories.

Table 1 .
Aging assessment of cable accessories based on dielectric parameters.

Table 2 .
Aging assessment of cable accessories based on trap parameters.