1 Introduction

An important aspect for a nuclear power plant (NPP) life management about the long-term reliable operation is the condition monitoring (CM) of cable’s insulation and jacket [1]. The NPP has round about 1000–2000 km of low-voltage (LV) power and instrumentation and control (I&C) cables, and the integrity of these cables is of great importance to the normal operation generally, and in the case of a life extension of the NPP especially. Due to their location, these cables are exposed to humidity, radiation, vibration, chemical contact, mechanical bending and heating stresses, and hence are degraded over time. Therefore, the assessment of the condition, the process of aging and the degradation of the insulation of the cables are important. Taking into consideration the importance, a lot of work has been done in this regard, such as accelerated tests and types of tests to be undertaken [2,3,4].

As the insulation and jacket of LV cables are composed of polymer and it has been reported that the polymer material loses its functionality more due to the thermal stress than the radiation stress in the NPP environment. The thermal stress can be due to both self-heating (ohmic heating) and environmental temperature effect [5, 6] and can produce chemical and physical deterioration processes inside the material. In recent times, destructive methods have been used to determine the functionality of these cables, such as mechanical: elongation at break, indenter modulus [7, 8] and chemical: oxidation induction time, density, soluble fraction, infrared spectroscopy [9,10,11,12,13,14,15,16,17]. Due to the physicochemical changes, the primary purpose of the cable insulation (inner insulation and jacket), which is its electrical integrity, is affected by the perspective of polarization processes. Hence, the dielectric parameters and insulation characteristics are influenced. In the last few years, the methods used for the investigation of the effect of aging on the electrical properties are line resonance analysis (LIRA) [18], dielectric spectroscopy [19], time-domain reflectometry (TDR) and return voltage. Although these methods are nondestructive, the results reported by these methods are still not sufficient to state them as an effective online testing diagnostic tool. Besides, they also lack to report the conduction and the polarization processes which can be used to study the chemical changes happening inside the polymeric insulation due to thermal stress.

This paper has been focused to study the influence of thermal stress on the conduction and the polarization phenomenon in CSPE/XLPE insulation material used in the LV NPP power cable. The frequency-dependent dielectric parameters: capacitance, dissipation factor (tanδ) and resistivity, were measured for a wide range of frequency to detect the insulation state. The method has been implemented as a diagnostics method for the medium voltage cables used in NPP [20], while time-domain extended voltage response (EVR) technique was used to investigate the slow polarization processes in the LV NPP cable and hence reflecting the aging information. The methods have the advantage of being nondestructive, and the results showed that all the parameters measured were very helpful in studying the degradation of the polymeric insulation and jacket. The aging markers obtained from the measurements are a practical step forward towards the implementation of these methods as nondestructive methods for the CM of the LV cables in the NPP. Therefore, they can be used in the future to predict the remaining useful life of the cable insulation material, as has been suggested by the light water reactor sustainability program nondestructive evaluation (NDE) report [21].

The paper has been organized as follows: the composition of the cable and characteristics, accelerated thermal aging, measurement of capacitance, tanδ, and resistivity, and EVR setup have been presented in Sect. 2. In Sects. 3 and 4, the results of the measurements and discussion have been presented, respectively. A correlation between tanδ and EVR is established in Sect. 5, while the conclusion and discussion on future perspectives are presented in Sect. 6.

2 Experimental Work

2.1 Specimens

The LV power cable was composed of inner insulation as XLPE and the jacket CSPE (Hypalon®), Fig. 1. The cable consisted of a single tin-coated copper stranded conductor (diameter = 6.731 mm). The thickness of the insulation was 1.143 mm, while the jacket thickness was 0.762 mm. A short length of the insulation was removed from the conductor, and a short length of the jacket was removed from the insulation as per the guidelines of the International Atomic Energy Agency (IAEA) [1].

Fig. 1.
figure 1

Low-voltage power cable sample under investigation

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2.2 Thermal aging

A half-meter long cable specimens were placed in an air circulated oven for the accelerated thermal aging at a temperature of 120°C. The specimens were exposed to aging for a maximum period of 960 h, and after every 240 h, the cable specimens were withdrawn from the oven for the analysis. The aging hours were based on the Arrhenius relationship considering the activation energy of 1.23 eV, which were equivalent to 20, 40, 60 and 80 years of service time at 60°C [22]. In order to realize the actual behavior of the cable during field environments, the aging was carried out on the whole cable without removing the jacket and the insulation from the conductor.

2.3 Measurement of capacitance, tanδ and resistivity

The measurement of capacitance and resistivity represents the features of geometry and losses, respectively. Any degradation to the insulation geometry and resistance will result in the change of tanδ [20]. Since in every polymer insulation, the polar groups interact in a different way with adjacent molecules due to nonidentical structures. This results in a different dipolar response at each frequency [23]. This makes the study of tanδ at different frequencies suitable for the insulation diagnosis.

In this work, the measurement of capacitance, tanδ and resistivity was performed using an impedance analyzer over the frequency range 20 Hz–500 kHz, input voltage of 5 Vrms at a temperature of 25°C ± 2%. The electrodes and the cable sample were kept in the Faraday cage to avoid any external noises pickup. A wire braid was placed on the outer surface of the cable for the measurement of the output signal, while the conductor was used for the application of the input signal.

2.4 Extended voltage response

EVR is an extended version of the voltage response method and has been developed in recent times. The method has successfully been implemented on LV cables used in the distribution system and high-voltage cables and transformer insulations [24,25,26,27]. The method is very helpful in studying the slow dielectric polarization effect in the insulation in the time domain. The EVR measurement of the cable samples was carried out by subjecting each cable sample to a DC voltage of 1000 V for 4000 s, charging period. The voltage was applied between the conductor and the outer surface of the cable, Fig. 2. After the charging period, the cables were discharged for 2000 s. Two voltage slopes: decay \({S}_{\mathrm{d}}\) and return \({S}_{\mathrm{r}}\) voltages, were measured by the device which was connected to the computer.

Fig. 2.
figure 2

Extended voltage response timing diagram

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Figure 3 shows the setup of the EVR measurement. The \({S}_{\mathrm{d}}\) was measured after the disconnection of the supply voltage after the charging period, while the \({S}_{\mathrm{r}}\) was measured for 20 discharging times after short-circuiting. These discharging times gave a wide range of the slow polarization spectrum. The decay and return voltage slopes were calculated according to the following relationships:

Fig. 3.
figure 3

Measurement setup of extended voltage response

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$${S}_{\mathrm{d}}=\left({V}_{\mathrm{ch}/{\epsilon_{o}}}\right)\gamma $$
(1)
$${S}_{\mathrm{r}}=\left({V}_{ch}/{\epsilon }_{o}\right)\beta $$
(2)

Equation 1 shows that the decay voltage is related to the specific conductivity γ of the insulation, while Eq. 2 shows the relationship between the return voltage slope and the polarization conductivity β of the insulation. The test temperature and humidity were 25°C ± 2% and 25% ± 2%, respectively, for all the measurements. After the EVR measurements, the cable samples were discharged for five hours before the start of the next thermal cycle.

3 Experimental results

3.1 Capacitance, tanδ and resistivity of unaged and aged cable samples

Figure 4 shows the capacitance of the unaged and aged cable samples. Irrespective of the aging, the capacitance of the cable increased as the frequency was shifted to the lower values. After the first thermal cycle, the capacitance increased while no significant change was observed after the second thermal cycle. But after the third thermal cycle, it increased again and then decreased after the fourth thermal cycle. The overall impact of aging on the capacitance was reflected as an increase in its values.

Fig. 4.
figure 4

Capacitance versus frequency for different aging time

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Figure 5 shows the tanδ of the cable for the range of frequency under consideration. The tanδ started from a higher value at high frequency and then moved to a minimum value with the decrease in the frequency. After reaching the minimum value at a certain frequency, it started to increase as the frequency was further lowered. This behavior was observed for both the unaged and aged cable samples. The tanδ showed an interesting behavior with the change of frequency and the aging. The tanδ showed an increasing trend for a frequency range of 20Hz–50 kHz; while between 100 and 500 kHz, the tanδ values decreased after the first and the second thermal cycle. After, the third thermal cycle, a decrease in the values of the tanδ was observed in a frequency range of 10 and 100 kHz, whereas at all other frequencies the values of tanδ increased. After the fourth thermal cycle, the tanδ decreased between 10 and 500 kHz; however, an increase was observed for the 20 Hz–5 kHz, low-frequency range. The overall effect of the aging on the tanδ was shown as an increase in the values in the frequency range of 20 Hz to 5 kHz, but a decrease in the values between 10 and 500 kHz.

Fig. 5.
figure 5

tanδ versus frequency for different aging time

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The resistivity of the unaged and aged cable is shown in Fig. 6a; with decrease in frequency, the resistivity increased unrelatedly of the aging. After the first thermal cycle, a decrease in resistivity was observed between 20 Hz and 150 kHz, while it increased from 200 kHz up to 500 kHz. Similarly, after the second thermal cycle, the resistivity decreased between 20 Hz and 10 kHz, but an increase in the values was observed between 20 kHz and 500 kHz. A further decrease in the values of the resistivity was observed between 20 Hz–5 kHz and 150–500 kHz frequency ranges after the third thermal cycle, whereas an increase was detected between 10 and 100 kHz. After the fourth thermal cycle, between 10 and 500 kHz, the resistivity values increased while they decreased at all other frequencies. Figure 6b refers to the change of resistivity with respect to unaged cable at selected frequencies, i.e., 100 Hz, 500 Hz, 100 kHz, and 500 kHz.

Fig. 6.
figure 6

a Resistivity versus frequency for different aging time, b change of resistivity with aging time (h) at 100 Hz, 500 Hz, 100 kHz and 500 kHz

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3.2 EVR measurements

The results of EVR measurements are shown in Fig. 7. The change in the values of \({S}_{\mathrm{d}}\) with the aging time is shown in Fig. 7a. An increase in the values of \({S}_{\mathrm{d}}\) was observed with each aging cycle, while the \({S}_{\mathrm{r}}\) for the different aging cycles is plotted against the discharging times on a logarithm scale in Fig. 7b. It was observed that with an increase in the aging period, the \({S}_{\mathrm{r}}\) values decreased.

Fig. 7.
figure 7

EVR measurement a \({S}_{\mathrm{d}}\) versus aging hours, b \({S}_{\mathrm{r}}\) versus discharging time for different aging time

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4 Discussion

4.1 Capacitance, tanδ and resistivity

In an insulating material, the dielectric losses can be categorized into three main components, conduction losses (\({tan\delta }_{\mathrm{c}}\)), polarization losses (\({tan\delta }_{\mathrm{p}}\)) and partial discharge losses (\({tan\delta }_{\mathrm{PD}}\)), which can be shown as a summation of the total dissipation factor [28]:

$$tan\delta = {tan\delta }_{\mathrm{c}}+{tan\delta }_{\mathrm{p}}+{tan\delta }_{\mathrm{PD}}$$
(3)

At the low electric fields, the conduction and polarization losses are developing in contrast to partial discharge losses which are prominent in high electric fields. The measurements were carried under 5 Vrms electric field, which makes the conduction and polarization losses more of our interest. The conduction losses are due to the transportation of free mobile charge carriers such as ions or electrons, while the polarization is a more complex phenomenon because of several elementary processes. The main polarization mechanisms occurring in the insulation material are electronic, ionic, dipolar, interfacial and hopping polarization. The electronic polarization is very fast and is effective up to optical frequency, while the interfacial and the hopping polarizations are considered very slow polarizations. The dipolar polarization occurs up to MHz and some GHz, while ionic polarization takes place in the infrared region [29]. Since the frequency range under consideration is between 20 Hz and 1 MHz, the interfacial and dipolar polarization will be the subject of interest. Therefore, the tanδ values will help in better understanding the conduction and the polarization losses relating to the inside structural changes of the material. Moreover, the capacitance has a strong relationship with the polarization phenomenon; hence, the variation in capacitance values helps in understanding the production of the dipolar species.

The insulation material used in the cable in this study is XLPE, while the jacket material is CSPE. Both the materials are semicrystalline and are produced by the modification of the backbone of polyethylene [30, 31]. Chlorination and chlorosulfonation of polyethylene results in the formation of CSPE, while cross-linking the chains of polyethylene results in the formation of XLPE. Since each material is dielectric, any change in the material structure will affect the capacitance and the tanδ properties. Furthermore, we have seen that the results of capacitance, tanδ and resistivity have shown variation with different frequency range; thus, it is convenient to have the analysis into two blocks of the frequency range.

  1. (i)

    Frequency range: 20 Hz–50 kHz

It was observed that the tanδ values increased at a low-frequency range: 20 Hz–5 kHz, for all thermal cycles. Also, the capacitance values increased until the third thermal cycle in the frequency range; this shows that due to thermal stress morphological changes have happened inside the polymer matrix. This has resulted in the generation of dipolar products which leads to the production of electric dipole rotation and hence an increase in the interfacial polarization losses, which is also evident by the decrease in the resistivity of the material in the lower-frequency range. In XLPE and CSPE due to the thermal stress, in the presence of oxygen, chain scission and cross-linking reactions along with oxidation reactions take place both in the amorphous and crystalline regions. The chain scission reaction results in the breakage of polymer backbones, resulting in the generation of alkyl radicals, which are free radicals. These radicals either react with oxygen forming peroxy radicals alongside the generation of more free radicals or they react with each other through cross-linking [30]. With the application of the external electric field, these chemical species respond to the field. The increase in the values of tanδ could be attributed to the contribution of the alkyl and peroxy radicals, which are contributing to both interfacial and dipolar polarization losses.

The creation of new bonds because of more thermal stress has been depicted with a decrease in the values of capacitance after the fourth thermal cycle. Besides chain scission reaction, in polyethylene with more thermal stress the radicals cross-link with each other and they do not respond to the changing alternating field; hence resulting in the decrease in capacitance values. The further lowering of the values of resistivity and increasing values of tanδ after the fourth thermal cycle depicts the presence of chemical species, generated due to the radicals which are increasing the interfacial and dipolar polarization losses. This is possible as with more thermal stress, the alkyl radicals along with peroxy radicals can result in a chain of reaction where new free radicals are generated besides other chemical species such as ketones and hydroperoxides. The hydroperoxides with the ability to decompose result in the formation of new free radicals, which may contribute to the conduction losses and hence to the overall value of tanδ [30].

  1. (ii)

    Frequency range: 100–500 kHz

The change in the values of tanδ in the low-frequency range is more prominent as compared to the high-frequency range. Figure 8 shows the change of capacitance and tanδ values with reference to unaged samples at four different frequencies: 100 Hz, 500 Hz, 100 kHz and 500 kHz. The variation is higher at the lower frequencies in comparison with the higher frequencies, where the values have decreased with aging. It is possible that due to high thermal stress, the by-products created may have bound with the polyethylene end groups, this may have resulted in the decrease in small molecules, and hence, they do not respond to the high changing electric field and resulting in the decrease in tanδ values [32].

Fig. 8.
figure 8

Variation of a capacitance and b tanδ with aging at 100 Hz, 500 Hz, 10 kHz and 500 kHz. The variation is reported in relative value to that measured on an unaged sample

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Moreover, it was observed that the minimum value of tanδ shifted from a lower frequency; 200 Hz to a higher frequency; 500 Hz with aging, Fig. 9, which is due to the production of dipolar particles and free radicals.

Fig. 9.
figure 9

Shifting of minimum value of tanδ with aging

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4.2 EVR

Whenever a DC voltage is applied to an insulating material, the charging current is more prominent as compared to the leakage and the absorption current. The charging current contains three components: the first one is related to the intrinsic conductivity and is independent of the polarization, the second one is related to the very fast polarization processes because of the delta function, while the third one is related to all polarization processes during the voltage application [29]. In the EVR, when the material is separated from the voltage source, the charges accumulated on the electrodes are discharged in the insulation material; this results in the generation of decay voltage. While the return voltage arises after the shortening period, this results in the discharging of the free charges and the polarization processes inside the material begin to regress. Hence, the decay voltage is related to the specific conductivity of the material, while the return voltage is related to the polarization conductivity of the material, as expressed in Eqs. 1 and 2.

From the results of EVR measurements, the \({S}_{\mathrm{d}}\) increased with the aging time, which shows that due to thermal aging conductive paths have been created because of the structural changes happening inside the polymer matrix, which allows the accumulated electrode charge particles to occupy these paths which are at the low energy level. This also shows that the insulation resistance has decreased with aging, which has been observed for both CSPE and XLPE under thermal stress due to the separation of branch chains from the main chain resulting in the production of free radicals hence contributing to the leakage current [31,32,33].

Since the profile of \({S}_{\mathrm{r}}\) is developed due to the slow polarization processes which have high time constants or occur at very low frequencies, the decrease in the values of \({S}_{\mathrm{r}}\) with aging shows that the polarized particles, space charges, which have very high time constants and occur at very low frequencies, have decreased with aging, Fig. 10. Because CSPE and XLPE both are thermosets in nature, there is a phenomenon of cross-linking under the thermal stress which is associated with the type of materials as discussed in Sect. 4.1 [34]. The cross-linking is a three-dimensional network within the molecules and restricts the mobility of the charge transportation [35], making the molecules not to travel to the interface of the two insulation materials, i.e., CSPE and XLPE and which results in the decrease in space charge polarization; henceforth, a decrease in the values of \({S}_{\mathrm{r}}\) has been observed. It is interesting that in CSPE apart from cross-linking the phenomenon of dehydrochlorination happens under the thermal stress [36]. For the reason, the chlorine is separated from the main molecular chain of the polyethylene, this results in the decrease in dipoles, i.e., C–Cl bonds, and consequently, dielectric relaxation is decreased [37].

Fig. 10.
figure 10

\({S}_{\mathrm{r}}\) (V/sec) at 1-sec v/s aging time (h)

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5 Correlation between tanδ and \({{\varvec{S}}}_{{\varvec{d}}}\)

Figure 11 shows the correlation between the \({S}_{\mathrm{d}}\) and tanδ for the CSPE/XLPE-based cable specimen. The tanδ value has been taken at a low frequency of 100 Hz. The experimental results are correlated by linear regression. The quality of the fitting is quantified by the correlation coefficient R, which is very high for the case. This implies that the tanδ, particularly at 100 Hz and \({S}_{\mathrm{d}}\), is strongly correlated with each other. Figure 12 shows a strong trend of tanδ, \({S}_{\mathrm{d}}\) with aging time, making them strong aging markers.

Fig. 11.
figure 11

Correlation between \({S}_{\mathrm{d}}\) and tanδ at 100 Hz

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Fig. 12.
figure 12

Trending of tanδ and \({S}_{\mathrm{d}}\) with aging time in hours

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6 Conclusion

The effect on conduction and slow polarization charges in thermally aged CSPE/XLPE-based LV NPP power cables are studied in this paper. The tanδ at low frequencies shows the sign of degradation of the cable due to chain scission reactions also the \({S}_{\mathrm{d}}\) values obtained by the EVR give a good aging marker. The resistivity of the material at low frequencies also decreased, while the lowering of the \({S}_{\mathrm{r}}\) values shows that the slow polarization processes decay over with the passage of time due to the phenomenon of cross-linking, which is associated with polyethylene. The shifting of the minimum value of the tanδ towards higher frequency with aging shows the increase in interfacial and dipolar polarization losses besides the contribution of conduction losses due to the presence of free radicals. A strong correlation between the tanδ at 100 Hz, \({S}_{\mathrm{d}}\) and aging times has been observed. These results show that the electrical properties discussed in this paper can be used to assess the condition of the cable. The techniques are nondestructive and show the potential to be applied in the NPP for the online CM of the LV cables simply and effectively. The techniques also have the feature of being independent of the geometry of the cable. Further work is needed to be done to set the threshold values for the properties, which would help to determine the state of the cable and then predict the remaining life of it.