Breakdown Field Strength of Lapped Kraft Paper, PPLP or Kapton in Liquid Nitrogen

IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 1 Breakdown Field Strength of Lapped Kraft Paper, PPLP or Kapton in Liquid Nitrogen Luhan Zu1, St´ephane Hol´e1∗, Nicolat Lallouet2, Georg Gamper3and Christian- ´ Eric Bruzek3 Abstract—Superconducting cables are good alternatives to transport electric power over long distances insofar as the insulation operates correctly at cryogenic temperatures. The breakdown electric field strength of various materials were tested in liquid nitrogen in a lapped configuration corresponding to a realistic geometry for the high voltage superconducting cable insulation. A specific sample holder was designed to perform several breakdown tests on the same sample without breaking testing conditions. It is shown that breakdown value is improved by increasing hydrostatic pressure and by reducing the gap between strips. It is also shown that the insulating structure still operates with little degradation after breakdowns although perforations are more destructive for PPLP and Kapton than for Kraft paper. Kapton presents a higher breakdown strength than PPLP itself higher than the one of Kraft paper though this latter material exhibits an interesting behavior under pressure due to its permeability to liquid nitrogen. Index Terms—Voltage breakdown, lapped insulation, liquid nitrogen, cryogenic tests, superconducting cables I. INTRODUCTION WITH the continual emergence of new technologies, the significance of energy issues has become increasingly pronounced [1]. As the transition towards greener energy progresses and the efficiency of energy supply improves, the demand for effective and safe power transmission technologies also increases. Since the discovery of superconductivity in mercury in 1911, over a century of development has matured the application of superconducting technologies in the field of power transmission [2]. With zero electric resistance in superconducting materials, superconducting cables made from these materials can significantly reduce energy losses during transmission and decrease the spatial occupancy in the soil [3], [4]. To understand the role of superconducting materials in modern power transmission lines, it is important to categorize them into low-temperature and high-temperature superconductors. Low-temperature superconductors (LTS), such as mercury (Hg) and niobium-titanium (NbTi alloy), exhibit superconductivity at extremely low temperatures and typically require liquid helium for cooling, except magnesium diboride (MgB2) which can operate in liquid hydrogen (20 K) and at a temperature up to 39 K [5]. High-temperature superconductors (HTS), including yttrium barium copper oxide (YBCO), are working in liquid nitrogen (77 K). 1LPEM, ESPCI Paris – PSL University, Sorbonne University, CNRS Paris – France 2Nexans France – Calais – France 3ASG Superconductor – Genova – Italy ∗Corresponding author: [email protected] Given these advancements, the European Union launched the SCARLET project in 2022, aiming to innovate in the field of superconducting power transmission lines [6]. The plan involves constructing a 500 MW, 25 kV direct current (DC) superconducting transmission network [7]. In addition to cooling requirements, the insulation characteristics of superconducting cables are critical for their performance in power transmission. Given the stringent environmental conditions required for superconducting materials, the study of superconducting cable insulation characteristics has always been a focal point. This includes aspects such as mechanical strength [8], space charge distribution [9], [10], thermal loads [11], aging [12], and dielectric strength [13]. Since the early 2000s, researchers have begun using materials such as Kraft paper [14], Polypropylene Laminated Paper (PPLP) [15] and Kapton [11] to create insulation layers for superconducting cables by wrapping them. This method effectively mitigates the impact of cable bending and accept differential shrinkage between metallic conductor and insulation material, thereby enhancing their stability. However, traditional studies of breakdown voltage often employed planar-layer testing methods [13], [16], [17], which did not account for the dimensions, structure and installation requirements of actual superconducting cables. It has also been shown in Ref. [4] that the lapping strengthens the insulation compared to liquid nitrogen alone. The intrinsic composite structure of the insulation must therefore be tested as a whole. To address this, materials are tested in the present study in a realistic operational geometry representative of superconducting cable insulation. This geometry inherently constitutes a composite structure, incorporating not only the raw material layers but also interstitial liquid nitrogen. The effective dielectric strength is thus a property of this composite system rather than of a stack of layers. Consequently, breakdown electric field strength is calculated by the voltage breakdown normalized by the nominal composite thickness, reflecting the actual insulation thickness under operational conditions as already been done for similar situations [18]. A testing system with an active internal structure was developed, allowing for continuous multipoint testing of the insulation layer of superconducting cables without breaking the testing conditions. Using this system, a comparative analysis of the dielectric strength of 3 insulating materials (Kraft paper, PPLP, and Kapton) in liquid nitrogen was conducted, leading to further insights. The three next sections present the samples, the experimental setup and testing procedure, and data analysis. Then experimental results are shown and discussed This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 2 before conclusion. II. SAMPLES The sample production method is identical to the actual processing technique used for the insulation layer of superconducting cables as shown in Figure 1. The insulation tape is directly wound onto the conductor using a winding machine, and because the tape moves at a uniform speed under a controlled tape tension, the spacing between tapes on the same layer is equal. The ends of the processed samples are secured using insulating adhesive tape. 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The sample assembly consists of lapped Kraft paper (120µm thick), polypropylene lapped paper (PPLP, 125-µm thick with 43% polypropylene), and lapped Kapton (50-µm thick). These insulating materials are configured in five layers, aligned butt to butt with a controlled gap, and wrapped over a 70cm-long 30-mm-diameter conductive steel tube, as depicted in Figure 2. Gaps filled with liquid nitrogen exist between the strips, creating a minimum of three insulation layers when two gaps coincide in the thickness. Notice that this structure is well representative to thicker structures due to the size of the nominal gap (of about 4 mm width) compared to the width of the tape (20-mm width). Therefore, the structure, mirroring actual cable structures, should have a great impact on the insulation efficiency since 3 to 5 layers of material are present from one point to another. However, since the same voltage is applied across cable insulation at any positions regardless the number of underlying strips or gaps, the insulation thickness is taken as the maximum number of strip layers thereafter, in other words 600 µm for Kraft paper, 625 µm for PPLP and 250 µm for Kapton. III. EXPERIMENTAL METHOD A. Experimental setup The samples are immersed in a cryostat filled with liquid nitrogen (LN2) at boiling point under various hydrostatic pressures up to 6 bar. To better test actual structures of superconducting cable insulation and to test multiple points without altering the operating environment, a movable test structure was designed, as sketched in Figure 3. The spark point consists of the intersection of two perpendicular (a) (b) (c) Fig. 2. Tested samples: (a) Kraft paper; (b) PPLP; (c) Kapton. The 20-mmwidth tapes are spaced away by 4-mm gaps. cylinders (see bottom inset in Figure 3), one from the inner conductor of the sample held to high voltage and the other from an outer rolling cylinder connected to ground through a resistor. This spark point can be displaced over more than 50 cm along the sample without breaking the testing conditions. A counter insulating cylinder is used to maintain the rolling cylinder connected to ground in good contact with the sample thanks to springs. FixedFixed Threaded rod Movable Sample Spark point Rolling cylinder Counter cylinder Counter cylinder 1 GΩ High Voltage Supply Insulating parts Conducting parts Spring Rolling cylinder (GND) Sample electrode (HV) Fig. 3. Schematic of the mechanism for adjusting the electrical breakdown point using a threaded rod. Bottom inset: Cut section along the dashed line. The sample is maintained in good contact with the rolling cylinder connected to ground thanks to springs and a counter insulating cylinder. This setup facilitates the assessment of superconducting cable insulation under realistic structure and cryogenic conditions, allowing for comprehensive and accurate evaluation of insulation performance. Figure 4a illustrates the detailed connection of the sample and grounding, highlighting the practical implementation of the testing structure. The movable structure is designed to fit inside a cryostat with a volume of approximately 100 L for testing, as shown in Figure 4c. The movable mechanism (see Figure 4b) is directly connected to the outside of the cryostat via a threaded rod controlled by a stepping motor. The voltage required for testing is supplied to the sample internal electrode through the bottom of the cryostat. An ISEG HPp-700-505 high voltage supply, which has a maximum output voltage of 70 kV, provides the necessary voltage and automatically switches This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 3 off when breakdown occurs. The entire testing process is automated by a computer, ensuring precise and repeatable testing conditions without manual intervention. 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Photography of the test equipment: (a) spark point; (b) moving spark point mechanism; (c) equipment under test. B. Electric field strength at spark point The two-perpendicular cylinder geometry generates a nonuniform electric field inside the sample due to the cylinder curvature. This was checked with a finite element analysis for a distance of 0.6 mm as the overall thickness of the insulation between the two perpendicular cylinders, the high voltage one of 30 mm in diameter and the grounded one of 20 mm diameter. The distance of 0.6 mm corresponds approximately to 5 layers of Kraft paper or PPLP and is much larger than 5 layers of Kapton thus corresponding to an even worst situation for this material in terms of electric field uniformity. Nevertheless, the results show that the effective testing area is well delimited (see Figure 5a) and that the amplitude variation of the Laplace electric field across the 0.6-mm distance does not exceed 1% of the average electric field amplitude for an uniform insulation (see Figure 5b). This shows that the electrode geometry, corresponding to two perpendicular cylinders, does not impair the measurement compared to other conventional geometries. C. Measurement protocols Once the sample inserted in the cryostat, air is first pushed away by gaseous nitrogen before filling the cryostat with liquid (a) HV HV Ground Ground (b) Electric field (kV/mm) 0 10 20 30 40 50 Fig. 5. Simulation of the electric field amplitude between the two perpendicular cylinders for HV = 30 kV: (a) view of the spark point extent; (b) elevation of the electric field amplitude across 600-µm distance between cylinders. nitrogen. At the beginning of the experiment, the spark point is positioned at the top of the system. When the targeted hydrostatic pressure is reached, the voltage is applied to the sample with a ramp of 200 V/s until breakdown. Then the spark point is displaced down by about 1.5 cm and a new voltage ramp is applied. When breakdown values are acquired, another pressure is adjusted and a new series of breakdown values is acquired. Up to 3 series can be acquired with this procedure without changing the sample and breaking the measurement conditions. Two different protocols were applied. In the first protocol, conditions are at atmospheric pressure (1 bar) plus 0 bar, plus 2 bar and plus 5 bar. The spark point is displaced after the occurrence of each breakdown. In the second protocol, the first and last conditions are at atmospheric pressure (1 bar) while the second condition is at higher pressure, either 2 or 3 bar depending on the material. This is to assess the influence of pressure cycles. The same spark point is also used several times before displacement in order to assess the insulating degradation due to a previous discharges. IV. ANALYSIS METHOD The data obtained from the experiments are analyzed using the two-parameter Weibull distribution [19]. The cumulative distribution function (CDF ) is defined as CDF = 1 −exp(−(V/α)β)(1) where Vis the breakdown value, (either voltage or electric field strength), αis the scale parameter, in other words the breakdown value at 63.2% probability, and βis the shape parameter, in other words the slope at which the breakdown value increases with respect to the probability in a Weibull diagram. Insofar as the scale parameter αgives the breakdown value at 63.2% probability, a high shape parameter βindicates a relatively stable breakdown value whereas a low shape parameter βindicates a spread of breakdown values. In the scope of high voltage insulation, it is preferable to assess the breakdown value at low probability. From (1), one has V=α×(−log(1 −CDF ))1/β ≈α×CDF1/β (2) This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 4 when CDF tends to 0. For instance, if α= 50 kV, then V(1%) = 20 kV for β= 5 and V(1%) = 31.5kV for β= 10. Both parameters are of great influence, therefore, when breakdown values are similar, materials with a higher shape parameter should be selected to ensure the stability of their electrical breakdown performance. Since CDF is unknown during the experiments, it has to be estimated [20]–[22]. The CDF is assumed evenly distributed over the data set with the beta inverse function or approximated for instance by Bernard law as CDF ≈i−0.3 n+ 0.4,(3) where iis the index of the breakdown value in ascending order, and nis the number of measurements in the set of breakdown values. Hence experimental values do not exactly follow the Weibull distribution but parameters αand βcan be retrieved from a linear fit in a plot showing log(−log(1−CDF )) versus log(V). The linear fit can include all measured values or the two central quartiles only. This latter reduced data set for the linear fit is interesting to get rid of extreme points because linear fits are very sensitive to these points which present at the same time larger CDF uncertainties. In such a way the linear fit is calculated only with the most accurate points in the Weibul distribution. In this study we restricted the extent of the two central quartiles from 30% to 70%, which corresponds to n= 12 measurements. It is also interesting to plot the 5%- 95% limits in the diagram to check the errors due to CDF estimation. All measured breakdown values shall be within these two limits to consider consistent estimations. Figure 6 shows the Weibull diagram for the 4 kinds of analysis in the case of PPLP at 1 bar in liquid nitrogen. The use of multiple estimation methods aims to assess the robustness of the Weibull parameters given the relatively small data set (about 12 breakdown value per condition) and the simplifications made to obtain the results. It can be seen that Weibull parameters obtained by Bernard approximation (figures 6c and 6d) are relatively closed to the ones obtained by inverse beta function (figures 6a and 6b). Taking into account only the central quartiles (figures 6b and 6d) instead of the complete data set (figures 6a and 6c) reduces both scale and shape parameters in this example. Another possibility for assessing αand βis to use the Maximum Likelihood Estimator (MLE) [20], [22] which maximize the product of the density function (DF) for each measured value Vi n Y i=1 DF(i) = n Y i=1 β ViVi αβ exp(−(Vi/α)β).(4) One advantage is that it is possible to estimate the pertinence of αand βparameters within a given confidence, for instance at 95%. Contrarily to the former 5%-95% limits on CDF, the 95% confidence on αand βindicates that the probability to be outside this domain of confidence is less than 5%. Notably, as MLE method maximizes the likelihood function directly, it is less influenced by extreme values compared to linearfitting-based methods that are very sensitive to low probability outliers. This distinction provides an alternative perspective (a) Method #1 1 1 11 2 2 22 5 5 55 10 10 1010 20 20 2020 40 40 4040 60 60 6060 90 90 9090 99 99 9999 CDF (%) CDF (%) β=6.32 (b) Method #2 β=6.22 (c) Method #3 α=85.8 α=85.8 β=6.30 (d) Method #4 α=82.6 α=82.6 β=6.20 20 20 20 20 50 50 50 50 100 100 100 100 200 200 200 200 α(kV/mm)α(kV/mm) Fig. 6. Various methods for the calculation of the Weibull parameters αand βon a PPLP sample in liquid nitrogen at atmospheric pressure. Cumulative density function CDF obtained by beta inverse function (a and b) or Bernard approximation (c and d). Linear fit (light blue) performed on the complete data set (a and c) or second and third quartiles (b and d). Green limits in (a-d) correspond to 5%-95% confidence on CDF estimation. on parameter estimation and helps to contextualize subtle differences observed among methods, especially in the shape parameter β. Figure 7 shows the estimation with MLE in the case of the data of PPLP at 1 bar in liquid nitrogen. Figure 7a is the Weibull graph and Figure 7b is the amplitude of the density function (DF)in (α, β)space and the 95%-confidence corresponding domain. Data points are here exactly on the Weibull law (Figure 7a) since it maximizes the probability of having a given CDF distribution which is thus no longer evenly distributed. Though scale parameter αis very similar to the ones obtained with the linear fit on the complete data set, the shape parameter βis significantly smaller. This is an illustration of the influence of extreme CDF values (even with only central quartiles) on the slope estimation. All estimation are nevertheless in the limit of the 95%-confidence domain (Figure 7b) which well encompasses all significant values of the density function DF . Although all methods produce well consistent results, it is interesting estimate their stability when one of the values is missing (leave-one-out method) [23]. Figure 8 shows the mean value and standard deviation for each method when one value of the data set is missing. It can be seen that the linear fit on the central quartiles exhibits a smaller deviation than other methods with this data set. However, it is more sensitive to breakdown value accuracy though the corresponding deviations remain negligible compared to the former ones. To ensure statistical accuracy, at least 12 breakdown values under the same conditions are performed. The results obtained from the 5 calculation methods as well as the min-max This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 5 (a) Method #5 1 2 5 10 20 40 60 90 99 CDF (%) α=85.9 β=5.84 20 50 50100 100 150200 α(kV/mm) α(kV/mm) (b) DF 2 4 6 8 10 β(unitless) 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95%95%95%95%95%95%95%95%95%95%95%95%95%95%95%95% 95% confidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limit confidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limit confidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence 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limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limit confidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limitconfidence limit confidence limit Fig. 7. Maximum likelihood estimation on a PPLP sample in liquid nitrogen at atmospheric pressure. (a) Weibull parameters αand β. The light blue line corresponds to the maximal probability and the green limits represent the 95%-confidence domain. (b) Density function in (α, β)space represented in false colors. Dark red stands for high probability and dark blue stands for nil probability. The white curve delimits the 95%-confidence domain. Method #1 #1 #2 #2 #3 #3 #4 #4 #5 #5 α(kV/mm) 81 82 83 84 85 86 87 88 β(unitless) 5 6 7 8 9 Fig. 8. Stability of the Weibull parameters αand βestimation on a PPLP sample in liquid nitrogen at atmospheric pressure. For each trial, one of the value is removed from the data set. Mean and standard deviation (blue), median and central quartiles (green), minimum and maximum (red) are then calculated. dispersion calculated from the leave-one-out method are provided in the results analysis in order to mitigate the bias only one method could provide. Since samples do not have the same overall thickness, the breakdown values used thereafter are the measured breakdown voltages divided by the thickness of 5 layers of insulating strips. This corresponds to the nominal breakdown electric field strength in the sample structure since the same voltage is applied all along the cable length whatever the real number of underlying strips or gaps. V. RESULTS AND DISCUSSION A. Effect of hydrostatic pressure The three types of insulating materials (Kraft paper, PPLP, and Kapton) were tested in boiling liquid nitrogen (LN2) at 1 bar, 3 bar and 6 bar absolute hydrostatic pressures. Data are given in Table I in the Annex. At 6 bar, Kraft paper and PPLP data are not taken into account as too many experiments issued with no breakdown at the maximum applicable voltage. The predicted breakdown field strength αincreases with hydrostatic pressure for all materials as shown in Figure 9 (precise data can be found in Table II in the Annex). This can be attributed to the reduction of the mean free path of charges with pressure, hence avalanche needs a higher electric field strength to be triggered. It is worth noting that the various methods lead to slightly different behaviors in the shape parameter β, highlighting the sensitivity of βparameter to extreme values. This reinforces the importance of considering multiple methods to put estimations into perspective. Method #1 Method #2 Method #3 Method #4 Method #5 α(kV/mm) 50 100 150 200 250 β(unitless) 2 4 6 8 10 12 14 16 18 Kraft paper Kraft paper 1 bar1 bar1 bar 1 bar1 bar1 bar 3 bar3 bar3 bar 3 bar3 bar3 bar PPLP PPLP Kapton Kapton 6 bar 6 bar Fig. 9. Effect of hydrostatic pressure of liquid nitrogen on Weibull parameter estimation. The five estimation methods are indicated and give similar trends. Corresponding numerical data are provided in Table II in the Annex. According to previous study [24], the dielectric strength of pure liquid nitrogen was also found to increase with pressure but tends to saturate above 2 bar. In the tested composite insulation structure, it can be reasonably assumed that local vapor bubbles formed near the breakdown points are constrained by the lapped structure of the insulation, limiting their growth and distribution. This effect could further extend the breakdown strengthening with hydrostatic pressure compared to that observed in pure liquid nitrogen. In addition, Kraft paper shows a large increase of the shape parameter βwith pressure while the ones of PPLP and Kapton remain relatively similar. This may be attributed to the fact that Kraft paper is more permeable to LN2 than PPLP and Kapton. Therefore LN2 can better penetrate inside Kraft paper with pressure and then further increases the insulation properties. This significant increase of the βparameter was visible with various Kraft paper samples made the same way. One curious consequence could be that though PPLP shows a slightly higher scale parameter αthan Kraft paper, it also This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 6 shows a much lower shape parameter βunder pressure. Counter intuitively, this suggests that PPLP is less suitable than Kraft paper when a low breakdown probability is required and high hydrostatic pressure conditions are met. However, Kapton remains better due to a much higher αparameter. B. Perforation analysis Images of each material layer are shown in Figure 10 at the position of a breakdown. Though qualitative, these images bring preliminary assumptions of the effect of breakdown on the material layers. Thermal imaging, gas diagnostics or time-resolved electrical measurements could be carried out in future work to provide more information. The perforation in Kraft Paper (Figure 10, top) corresponds to small holes directly through all layers. Black marks are clearly visible on the two outer layers suggesting paper burning, presumably due to a large temperature increase during the breakdown. In contrast, breakdown in PPLP (Figure 10, center) caused more significant damage to the outer layer, while the inner layer perforations appear as small holes with no black marks. As PPLP is partially impermeable due to the presence of polypropylene compared to Kraft paper, heat release during the breakdown has more time to vaporize liquid nitrogen. The resultant bubble punches one after another the PPLP layers without burning it. Because the outer layer is less constrained, the punching ends in an explosion. Outer layer Layer 2 Layer 3 Layer 4 Inner layer Kraft paperPPLPKapton 1 cm 1 cm 1 cm Inner electrode Inner electrode Inner electrode Fig. 10. Photography of penetration holes due to a breakdown in the different materials for each layer. An intermediate behavior is observed with Kapton since black mark are clearly detected as well as an explosion of the outer layer (Figure 10, bottom). A careful analysis of the images shows that holes are not perfectly aligned suggesting flashovers between layers. It can be deduced that Kapton breakdown occurs in different phases. First, the breakdown pinches one Kapton layer. This burns the layer surface, brings enough heat to vaporize liquid nitrogen, which then pinches all above layers and ends with explosion of the outer layer. C. Effect of the gap Two Kraft paper samples were made with different gaps between strips. The small-gap sample has 1-mm gaps whereas the normal-gap sample has 4-mm gaps. Figure 11 present the Weibull parameters of these two samples, before and after the application of a 5-bar hydrostatic pressure for 3 hours. Numeric data can be found in Table III in the Annex. Method #1 Method #2 Method #3 Method #4 Method #5 α(kV/mm) 60 65 70 75 80 β(unitless) 4 6 8 10 12 14 16 Small gapSmall gap Small gapSmall gap before 5 bar before 5 bar before 5 barbefore 5 bar after 5 bar after 5 bar after 5 barafter 5 bar Normal gapNormal gap Normal gapNormal gap Fig. 11. Effect of the gap between strips on Weibull parameter estimation for Kraft paper samples. Tests were made before and after applying 5 bar hydrostatic pressure. Corresponding numerical data are provided in Table III in the Annex. Before the application of the hydrostatic pressure, the smallgap sample exhibits a much larger scale parameter αthan the normal-gap sample. This can be explained by the fact that smaller gaps means more material and thus a higher dielectric strength. After the application of the hydrostatic pressure, the scale parameter of the small gap sample remains at a similar value whereas the one of the normal-gap sample increases almost to the value of the small-gap sample. This memory effect may be attributed to a better LN2 filling of gaps. Concerning the shape parameter β, both sample are similar before the application of the pressure. After the application of the pressure, the normal-gap sample remains similar contrary to the small-gap sample for which shape parameter shows an increase though this is less significant depending the calculation method being used and taking into account error bars. Finally, as expected, small gaps are better for the insulation. Unfortunately, a gap must remain for the cable flexibility though tests have recently been done with overlapped tape structures which still show reasonable flexibility. D. Effect of multiple breakdowns To test the effect of previous breakdowns on the insulating degradation, multiple breakdowns were done at the same point This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 7 for Kraft paper and PPLP, both with 4-mm gaps. In addition, tests were carried out before and after applying an hydrostatic pressure (5 bar for Kraft paper and 3 bar for PPLP). Results are presented in Figure 12 and numeric data can be found in Table IV in the Annex. Method #1 Method #2 Method #3 Method #4 Method #5 1st 1st 1st 1st 1st 1st 1st 1st 2nd 2nd 2nd 2nd 2nd 2nd 2nd 2nd 3rd 3rd 3rd 3rd 3rd 3rd 3rd 3rd α(kV/mm) 50 60 70 80 90 100 110 β(unitless) 0 2 4 6 8 10 12 Kraft paperKraft paper Kraft paperKraft paper before 3 bar before 3 bar after 3 bar after 3 bar before 5 bar before 5 bar after 5 bar after 5 bar PPLPPPLP PPLPPPLP Fig. 12. Effect of multiple breakdowns on Weibull parameter estimation for Kraft paper and PPLP samples. Tests were made before and after applying an hydrostatic pressure. Corresponding numerical data are provided in Table IV in the Annex. Method 2 and 4 are relatively noisy on the shape parameter βcompared to the others methods. Nonetheless, it can be seen that the breakdown value does not reduce too much after various breakdowns. One contribution for this behavior is LN2 which refills the holes after breakdowns. There is however also a contribution of the material since PPLP is still higher after 3 breakdowns. In the case of Kraft paper, a previous hydrostatic pressure stress improves the scale parameter αas seen previously, but it is not the case of PPLP which on the contrary reduced though remaining higher than Kraft paper. As to the shape parameter β, it seems not significantly affected by the series of breakdowns. VI. CONCLUSION In this study, it is demonstrated that measurements of DC breakdown voltage in cryogenic environments can gain accuracy and efficiency by using a moving breakdown point along the sample. First, test conditions are precisely maintained between measurements, second, realistic insulation structure can be studied. It was found that that Kraft paper exhibits a lower breakdown field strength αthan PPLP, itself lower than the one of Kapton. However, surprisingly, the shape parameter βof Kraft paper is larger than the one of PPLP under pressure suggesting to use Kraft paper instead of PPLP under pressure. This remains to be checked by other measurements to increase statistics. In addition, increasing the hydrostatic pressure substantially improves the insulation performance of the materials under test. The gain seems to be larger than the one in pure liquid nitrogen, probably due to an effect of the layers that constrain the bubble growth upon breakdown and thus extend the benefit of hydrostatic pressure. This assumption remains to be checked by other studies. As expected, gaps between strips should be reduced as much as possible to increase breakdown voltage while still providing cable flexibility. It is worth noting that liquid nitrogen allows the insulation to resist multiple breakdowns at the same point without degrading strongly the material voltage strength. ACKNOWLEDGMENT This project has received funding from the European Union’s Horizon Europe research and innovation program under grant agreement No 101075602. REFERENCES [1] P. Wirtz, M. Siemonsmeier, M. Sch¨onefeld, and A. 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[24] Stefan Fink and Volker Zwecker. 15 min dc breakdown tests with pressurized liquid nitrogen. Technical report, 2021. 37.06.02; LK 01. ANNEX Measured breakdown voltage are given in the following tables. To obtain the breakdown field strength, it is necessary to divide these values by 5×120 µm for Kraft paper, 5×125 µm for PPLP and 5×50 µm for Kapton. TABLE I BREAKDOWN VOLTAGES IN KILOVOLT (KV) FOR 5LAYERS OF MATERIAL IN LIQUID NITROGEN. Measured breakdown voltage (kV) Kraft paper PPLP Kapton Index 1 bar 3 bar 1 bar 3 bar 1 bar 3 bar 6 bar 1 41,4 57,4 50,8 54,6 44,4 36 33 2 38 54,2 59 46 34,8 45,8 54 3 36,8 50,6 44,2 52,8 38 49,6 60 4 33,6 55,8 51,8 70 34,2 46,4 61,2 5 35 59,6 45,8 54,6 32,4 58,2 48,6 6 51,2 62,2 36,8 55,6 32 43,4 52,2 7 41,2 52,8 45,2 62 42,2 55 66,8 8 55,8 57,2 52 65,4 45,8 45,6 51,8 9 44,8 62,4 45,8 44,2 41,6 52,2 44,8 10 53 52,4 70 68,6 31,6 48,8 48,8 11 51,8 60,8 42 61,4 33,2 39,4 60 12 47,4 62,8 56,6 na 30,2 43,6 54,6 In Tables II, III and IV, the Weibull parameters are determined by various methods. The cumulative density function CDF is obtained from the beta inverse function in methods #1 and #2, and from Bernard approximation in methods #3 and #4. Then Weibull parameters are obtained with the complete data set for methods #1 and #3 or with the two central quartiles for methods #2 and #4. Method #5 estimates Weibull parameters with the Maximum Likelihood Estimation (MLE). TABLE II WEIBULL PARAMETERS FOR THE 5ESTIMATION METHODS AND THE VARIOUS MATERIALS UNDER DIFFERENT PRESSURES. Estimation methods Conditions #1 #2 #3 #4 #5 α(kV/mm) Kraft 1 bar 79.0 80.2 79.0 80.2 78.8 Kraft 3 bar 98.8 99.3 98.8 99.3 98.7 PPLP 1 bar 85.8 82.6 85.8 82.6 85.9 PPLP 3 bar 98.3 98.4 98.3 98.4 98.0 Kapton 1 bar 156.5 155.2 156.5 155.2 156.2 Kapton 3 bar 198.8 194.4 198.8 194.4 198.7 Kapton 6 bar 228.2 227.7 228.2 227.7 225.8 β(unitless) Kraft 1 bar 6.33 4.16 6.31 4.14 6.86 Kraft 3 bar 14.83 10.74 14.78 10.69 16.53 PPLP 1 bar 6.32 6.22 6.30 6.20 5.84 PPLP 3 bar 7.31 5.85 7.28 5.82 8.19 Kapton 1 bar 7.18 4.53 7.16 4.51 7.43 Kapton 3 bar 8.29 9.34 8.26 9.30 8.49 Kapton 6 bar 6.00 6.27 5.98 6.25 7.57 TABLE III EFFECT OF THE GAP BETWEEN STRIPS ON WEIBULL PARAMETER ESTIMATION FOR KRAFT PAPER SAMPLES. Estimation methods Conditions #1 #2 #3 #4 #5 α(kV/mm) 1.5 mm before 5 bar 77.7 77.8 77.7 77.9 77.1 1.5 mm after 5 bar 79.6 77.1 79.6 77.1 79.5 4 mm before 5 bar 63.6 64.1 63.6 64.2 63.5 4 mm after 5 bar 74.3 77.3 74.3 77.3 73.8 β(unitless) 1.5 mm before 5 bar 6.00 4.59 5.99 4.57 7.06 1.5 mm after 5 bar 9.36 14.99 9.33 14.91 9.37 4 mm before 5 bar 7.14 5.11 7.11 5.08 9.16 4 mm after 5 bar 8.57 4.59 8.54 4.57 9.01 Luhan Zu Luhan Zu received the B.S. and M.S. degree in Instruments Science and Technology from Northwestern Polytechnical University, Xi’an, China, in 2019 and 2022. He is currently pursuing the Ph.D. in the Laboratory of Physics and Materials Studies in Paris, France. His current research interests include high voltage insulation performance test and liquid hydrogen test system design. This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION, DOI: 10.1109/TDEI.2025.3619463 9 TABLE IV EFFECT OF MULTIPLE BREAKDOWN ON WEIBULL PARAMETER DEGRADATION. Estimation methods Conditions #1 #2 #3 #4 #5 α(kV/mm) before 5 bar Kraft, 1st 63.6 64.1 63.6 64.2 63.5 Kraft, 2nd 61.2 62.3 61.2 62.3 61.1 Kraft, 3rd 61.5 59.1 61.5 59.1 61.5 α(kV/mm) after 5 bar Kraft, 1st 74.3 77.3 74.3 77.3 73.8 Kraft, 2nd 70.6 71.2 70.6 71.3 70.4 Kraft, 3rd 65.1 66.7 65.1 66.8 64.9 α(kV/mm) before 3 bar PPLP, 1st 96.1 95.7 96.1 95.8 96.0 PPLP, 2nd 94.1 106.3 94.1 106.4 93.1 PPLP, 3rd 90.3 81.8 90.3 81.8 90.2 α(kV/mm) after 3 bar PPLP, 1st 91.5 92.4 91.5 92.4 91.3 PPLP, 2nd 79.2 72.3 79.2 72.3 78.9 PPLP, 3rd 83.7 77.9 83.7 77.9 83.5 β(unitless) before 5 bar Kraft, 1st 8.57 4.59 8.54 4.57 9.01 Kraft, 2nd 8.76 6.41 8.73 6.38 9.79 Kraft, 3rd 10.53 23.08 10.50 22.97 9.72 β(unitless) after 5 bar Kraft, 1st 7.14 5.11 7.11 5.08 9.16 Kraft, 2nd 6.90 4.98 6.88 4.96 7.62 Kraft, 3rd 7.39 4.47 7.37 4.45 8.71 β(unitless) before 3 bar PPLP, 1st 8.18 4.89 8.15 4.86 8.42 PPLP, 2nd 4.09 1.86 4.08 1.85 5.24 PPLP, 3rd 4.62 7.72 4.61 7.68 4.82 β(unitless) after 3 bar PPLP, 1st 5.84 3.93 5.82 3.91 6.34 PPLP, 2nd 6.34 11.18 6.32 11.13 5.83 PPLP, 3rd 7.17 11.25 7.15 11.19 7.23 St´ ephane Hol´ estudied electronics and instrumentation at Paris 6 University (France). He received his PhD in 1996 and his Habilitation in 2007. Currently Professor at Sorbonne University (Paris, France), he has led the Instrumentation Group in LPEM at ESPCI (Paris, France) since 2007. His research topics include space charge measurements in solid and liquid materials and electromagnetic sensors. He has been coordinator of the Sensors, Instrumentation & Measurements master program at Sorbonne University since 2009. Nicolas Lallouet has 23 years of experience in superconductivity at Nexans. Since 2003 he has been responsible for the development of high-voltage and medium-voltage accessories for superconducting cable systems. He was also in charge during 10 years of developing HVDC cable system accessories for standard extruded cables. Previously, he was in charge of developing high-temperature superconducting tapes within Nexans. He has about 26 publications and 35 patents in the field of superconductivity. Georg Gamper completed his B.S. in Engineering Physics at the Politecnico di Torino and his M.S. in Physics and Nanotechnology at Denmark Technical University in 2021. After an internship at NKT Cables within the SuperLink-Project, he joined the Cryogenic laboratory of ASG Superconductors in 2022 and was assigned to the division dedicated to superconducting cables in 2023. Christian- ´ Eric Bruzek received a PHD and engineering diploma in material sciences at Lille University, France. He worked at ALSTOM in superconducting magnet division as technical manager before joining Nexans, where he managed “high-temperature superconducting tapes and Mineral Insulated Cable” division and then he directed the Material and Expertise division within the National Testing Laboratory (LNE). Back to Nexans, he was project director for advanced technical solutions at Nexans where he participated and led several national and international collaborative projects with universities and research institutes. For more than 10 years, he was also chairing of the French and International Superconductivity Standardization Committee NF90/IEC TC 90 Cigr´e. He is now employed as business development manager for power equipment at ASG Superconductors. He is particularly interested in hydrogen cooled cables for decarbonization, high-power cables for land and offshore grids and fault current limiters. He is also involved in the development of high current cable systems for several industrial applications. He is the author and co-author of over 100 peer-reviewed papers, technical brochures for Cigr´e, books and several patents. This is the accepted manuscript of the article by Luhan Zu et al. in IEEE Transactions on Dielectrics and Electrical Insulation, 2025 https://doi.org/10.1109/TDEI.2025.3619463 Distributed under the terms of the Creative Commons Attribution License (CC BY 4.0)