Research on aging parameters of XLPE cable based on isothermal relaxation current

The insulation of power cable deteriorates gradually with its service time,¹ especially in the situation of poor heat dissipation, water and dirty environment. As a result, it is important to evaluate its insulation status reasonably. At present, AC withstanding voltage test is the most widely adopted as a insulation evaluation method. However, this method is not only destructive to the cable but also difficult to evaluate the insulation status quantitatively. Oscillating wave test system (OWTS) is also applied to detect the fault in cable by analyzing the excited partial discharge,² but it cannot be used to diagnose the cable’s aging status, which is distributed in the cable.

In order to evaluate the cable’s aging status quantitatively, the research about its dielectric response characteristics is carried out in this paper. The dielectric response measurement, as a non-destructive method under low test voltage based on the monitoring the mobility of charge in insulator, attracts many researchers’ attention.^3–6 Right now, dielectric response mainly includes two methods, that are polarization/depolarization current (PDC) in time domain and frequency domain spectroscopy (FDS) in frequency domain.⁷ Compared with PDC, FDS is an AC method which need excessive power capacity due to the large capacitance of power cable. As a result, PDC current, especially isothermal relaxation current (IRC), is widely used in evaluating the aging status of power equipment.^8–10 

In 1973, Simmons proposed the theory of IRC to determine the trap parameters in insulation.¹¹ After that, many researchers developed this theory. Zhang et al combined the IRC theory with the space charge, and then proposed a model of isothermal surface potential decay (ISPD).¹² In this way, trap parameters can be used to determine the aging status of insulation material.¹³ 

Some researchers use other similar methods to determine trap parameters. Based on the pulsed electroacoustic (PEA) method, Chen et al applied trap depth and density to evaluate the insulation status of polymeric materials.¹⁴ In his opinion, charge decay shows different characteristics with different aging degree.¹⁵ And he proposes a trapping and de-trapping model based on two trapping levels.¹⁶ Dissado also studies the de-trapping mechanism by measuring the decay of space charge¹⁷ and considers most of shallow XLPE trap depth ranges 0.75–0.96 eV.¹⁸ By investigating electrically-induced mechanical change in polyethylene, Jones et al postulated the relationship among amorphous crystalline morphology, dielectric response and breakdown mechanism, which is worthy to be further studied.¹⁹ As can be concluded from the results of existing researches, it is helpful to propose a method for determining the trap depth of different polarization types based on IRC theory.

In this paper, an aging model based on IRC is proposed to reveal the relationship between different polarization traps and aging status. XLPE cable samples are aged under different temperature (120°C/140°C/160°C) and aging time. Then, we measure the IRC curve and use the trap model to calculate aging parameters of aged cables. The results indicate that the peak trap level of bulk polarization (type 1) remains stable and is regarded to be independent of aging degree. As the aging time increases, the peak trap level of amorphous crystalline relaxation (type 2) increases at low temperature (120°C) due to the breaking of molecular chain, while it decreases at high temperature (more than 140°C) due to the over cross-linking. The peak trap level of impurities interface relaxation (type 3) is highly influenced by aging temperature, which is the most sensitive to aging degree. Different insulation status can affect trap depth which is a quantificational aging parameter.

When applied in an electric field, different polarization types will appear in solid dielectric material, including electron polarization, deformation polarization, thermal ion polarization, orientation polarization and boundary/interfacial polarization, etc.

When a voltage U(t) is applied on a homogeneous dielectric material, a current through the test object can be expressed as equation (1).²⁰ 

Where, C₀ is the geometric capacitance and σ is the conductivity. ε₀ and ε_r represent the permittivity in vacuum and the relative permittivity, respectively. f(t) is the dielectric response function. For polarization and depolarization current method, as shown in Fig. 1, a dc voltage U(t) that changes as equation (1) is applied in a totally discharged insulation material.

T_c, which is from t = 0 to t₁, represents the polarization time, and T_d represents the depolarization time. Both the polarization and depolarization currents can be measured.²¹ At t = t₁, a dc voltage U(t) is removed while insulation material is short-circuited, and the depolarization current can be written as equation (3).

If we concentrate on depolarization part and temperature remains stable, charge accumulation in insulation material will dissipate with time and the current in this process is isothermal relaxation current. In order to study aging phenomena, polarization processes with longer cycle are researched since they contain more characteristics. Compared with other polarization, the boundary/interfacial polarization, which describes surface and space charge accumulation, has longest cycle, so it is a key to determine aging status.

For aged XLPE cable as Fig. 2 shows, extended Debye model can be used to explain polarization process. The polarization can be divided into bulk polarization (type 1), amorphous crystalline (type 2) and impurities interface polarization (type 3).²² Therefore, based on Debye theory, equation (3) can be written as equation (4).

Where, i₀ is conduction current. α_i represent 3 types of depolarization coefficients and τ_i is the corresponding time constant. As a result, by measuring the isothermal relaxation current and applying Levenberg – Marquardt algorithm,²³ parameters i₀, α_i and τ_i can be obtained.

According to Simmons’s theory, the electrons emit from trap should possess minimum detrapping level, so the trap depth is determined as equation (5).

Where, E_c is conduction band edge level and E_m is minimum detrapping level. k is Boltzmann constant and T is absolute temperature. v is attempt to escape frequency. For isothermal relaxation current, the relationship between IRC and t can determine trap parameters of defect solids, which is linearly proportional to trap level distribution N(E_m), shown as equation (6).

Where, e is element charge and A is electrode area. L is sample thickness and f₀(E) is a constant. Combining equation (4) with equation (6), we can turn them into equation (7).

It is apparent that the total current includes 3 types of relaxation components. Instead of using total current to calculate trap level distribution, we can make further efforts to study 3 relaxation components changing characteristics. Amorphous crystalline relaxation (type 2) comes from physical defects and impurities interface relaxation (type 3) comes from the cross-linking byproduct components such as cumyl alcohol, water, and acetophenone which is polar in nature.²⁴ The amorphous crystalline relaxation (type 2) and impurities interface relaxation (type 3) are highly affected by aging degree development. As a result, these types trap parameters should be further studied.

New YJV22-3×300-8.7/10kV XLPE cables are employed as test samples. The outer-sheath, steel tape, inner-sheath and filler of 10kV cable are removed. Only semiconductor layer, insulation and core remain for accelerated aging experiment. In this way, 16 single-core cables are prepared, which are 20 cm long and 300mm² in cross section. 120°C (4 cables), 140°C (4 cables) and 160°C (8 cables) are selected as aging temperature. Considering different aging rate, cables are aged with different time intervals. Time interval of cables at 120°C aging temperature are set as 20d, 30d, 40d and 50d, assigned as group I. Time interval of cables at 140°C aging temperature are set as 10d, 20d, 30d and 40d, assigned as group II. Time interval of cables at 160°C aging temperature are set as 10d, 15d, 20d and 25d, assigned as group III and group IV. Also an onsite 10kV cable running for 6 years in power system is measured as a reference.

Before IRC experiment, some treatments are carried out for each cable sample. As Fig. 3 shows, the insulation and semiconductor layer are stripped at one end whose length is 2.5cm. At the other end, only semiconductor layer is stripped. A dc voltage is applied at core and measuring terminal is connected to the semiconductor layer. To avoid the leakage current from the surface of insulation, the insulation part is wrapped with two copper rings. The two copper rings are grounded and fastened with insulating glue. In this way, the surface leakage current will flow into the ground through the copper rings, and the volume current will flow through the measuring terminal rather than the copper rings. In order to avoid residual charge in cable insulation, we short the core and semiconductor layer for 24h before IRC experiment.

In IRC experiment, the output voltage is 200V. The polarization and depolarization time are all set as 1000s. The testing temperature of our experiment is at room temperature, which is about 25 °C. Specific measurement circuit is shown as Fig. 4. Actually, if we applied this measuring method to on-site diagnosis, the cable has more aging interface which need higher voltage and longer time to reach steady state.

To eliminate the electromagnetic interference, we put samples into a grounded shielding box. Taking the fluctuation influence of power source into consideration, the first 10 seconds of depolarization current are neglected.

The cable IRC curves of different aging temperature and time are shown in Figs. 5–8 respectively. And the cable IRC curves of 6 years-old cable in power system is shown in Fig. 9.

From Figs. 5–8, as the aging time increases, the IRC curves become flatter while the steady current could be move forwards. Compared with different aged time, 10 days aged cables have the lowest steady current, which accords with insulation theory. As a reference, the IRC curves of 6 years-old cable in power system is shown in Fig. 9. The shape of this curve is similar to the curve of 10d/140°C aging cable.

It might not be ignored that other cables (20d/140°C, 30d/140°C, 15d/160°C and 20d/160°C aged cables) do not match all the judgment rules (such as decrease rate and steady current value). In addition, we could only qualitatively determine cable insulation status, which is not enough for on-site diagnosis. In order to solve these problems, trap parameters are used to quantitatively judge cable insulation in this paper.

From equation (4), the total IRC can be divided into 3 polarization types of current. According to equation (7), if the samples are the same size and measured at the same temperature, the trap level distribution N_i(E_m) is proportional to $exp(−t/τi)×t$⁠. For each depolarization type, the peak value of trap level distribution can be derived as equation (8) and shown as Fig. 10.

According to equation (5), because the measuring time is from 10s to 1000s, the measuring range of trap depth is from 0.75eV to 0.89eV. Trap around this level is usually considered as shallow traps. 3 types of relaxation correspond to 3 peak value and time constant, respectively, so we can use equation (5) to determine corresponding trap depth of each type.

In most cases, with the increase of cable aging degree, molecular chain of XLPE will be cross-linked and broken at the same time. The cross-linking byproduct components is generated from dicumyl peroxide (DCP). As a result, the amorphous crystalline relaxation (type 2) and impurities interface relaxation (type 3) are supposed to become stronger, which performed as the trap depth change.

In order to obtain the parameters α_i and τ_i, Levenberg – Marquardt algorithm is used to fit the IRC curves. Since there are 7 parameters to fit, uncertainties exist in the fitting process. Usually, R² (determination coefficient) and standard deviation are used as criteria to assess the fitting goodness. To get the optimal results, the R² is required to over 0.95. In this way, α_i and τ_i of all the samples can be calculated under the least uncertainties. Fig. 11 shows a typical comparison between measuring and fitting data, whose R² is 0.98047, over 0.95. At the same time, the standard deviation of this curve is 3.6272×10^-14.

According to equation (5), the peak trap level of each sample is calculated by the corresponding τ_i through 3 independent fitting processes and its standard deviation (SD) is also calculated, as shown in Tables I–IV, which is also as shown in Figs. 12–14. From the ratio of standard deviation to IRC results of all the aged samples, the fitting results is acceptable.

A cable running for 6 years in power system is measured at our laboratory as a reference. This cable sample comes from Beijing Power Company, which is in normal operation during its service time. This sample is removed from power system just because of need to increase the cross-section, not for insulation problem. Trap level of this cable in normal condition is calculated as Table V shows. From Figs. 12–14, it can be found that bulk polarization (type 1) remains stable and its peak trap level is around 0.76eV. Compared with the cable in normal condition, it can be inferred that trap level of bulk polarization (type 1) is independent of aging degree.

For amorphous crystalline relaxation (type 2), the peak trap level decreases with increasing aging time generally and the value is from 0.785eV to 0.82eV.

For amorphous crystalline relaxation (type 2), as shown in Fig. 15, trap level comes from irregular short molecular chain (A) as well as folding (B), circling (C), winding (D) molecular chain and even the linking between lamella. With the aging time increasing, molecular chain of XLPE will cross-link and break at the same time (Fig. 16), where the temperature is an influence factor, also mentioned by C. Kim.²⁵ Therefore, the trap level of type 2 is dependent on the crosslinking rate and fracture rate, which is closely related with the thermal aging temperature. For low aging temperature (120°C), trap level of amorphous crystalline relaxation increasing with aging time. And for high aging temperature (more than 140°C), XLPE is easily over cross-linked leading to trap level decreasing. The reason of this trend is that the melting temperature of PE is around 135°C and the decomposition temperature of DCP is 130∼140°C, so the higher temperature can accelerate crosslinking. This phenomenon is also proved by the DSC results of aged cable by Prof. Li.^26,27

Whereas, the trend of impurity interface relaxation (type 3) peak trap level is different from aging temperature. For cable under 140°C aging temperature, peak values of type 3 increase with aging time extending. But for cables aged under 160°C, the peak values of the first batch of cables seem like alternating decreasing in Fig. 14(a). In order to verify this downward tendency, trap level of the cables in group IV are measured, and the results agree with the first batch (cable group III), shown in Fig. 14(b).

The impurity interface relaxation (type 3) mainly comes from cross-linking byproduct components, salts and hydrated ions. Since the sample is only aged by high temperature, the results reflect chemical reaction of dicumyl peroxide (DCP) which mainly decomposes cumyl alcohol, acetophenone and a-methylstyrene.²⁸ The byproducts increase with aging degree, which can produce more traps and increase the deepth,²⁹ that agrees with the results aged under 140°C.

Compared with relatively low temperature (140°C), the higher temperature (160°C) is close to a-methylstyrene boiling point (165°C). During 160°C aging process, a-methylstyrene volatilize far faster, so the amount of byprodcuts shows downward trend and the trap level seems like alternating decreasing.

In this paper, XLPE cable samples aged with different temperature (120/140/160°C) and aging time interval. Then, their IRC curves are measured by a micro-current device and an aging model based on IRC has been proposed to calculate aging parameters of cable.

It can be concluded from the experiment results that IRC curves can reveal cable insulation status change. Usually, larger steady current and relatively flat curves follow with increasing aging degree. At the same time, those curves can only qualitatively determine the insulation status, and trap parameters is more suitable for quantitative judgment.

From the results of XLPE trap parameters, bulk polarization (type 1) remains stable and its peak trap level is around 0.76eV, so it is considered to be independent of aging degree. The peak trap level of amorphous crystalline relaxation (type 2), which is from 0.785eV to 0.82eV, increases at low temperature (120°C) due to the breaking of molecular chain and decreases at high temperature (more than 140°C) due to the over cross-linking. The peak trap level of impurities interface relaxation (type 3) is highly influenced by aging temperature, which is the most sensitive to aging degree.

In further research, more samples under different temperature and aging time should be measured by IRC. And if possible, this method can be used for on-site cable diagnosis.

The authors wish to thank the financial support of National Natural Science Foundation of China (51577150), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (51521065), Key Research and Development Program of Shaanxi Province (2018GY-001) and State Grid Headquarters Science and Technology Project (5226SX1600U9).