System and method for calculating a parameter of water-trees in cross-linked polyethylene (XLPE) cables

Abstract

Aspects concern a method and system for calculating a parameter of water trees in a cross- linked polyethylene (XLPE) cable, the method comprising obtaining a segment of the XLPE cable having a thickness; measuring a length of one or more water trees on the segment; identifying a longest length from the measured one or more lengths; defining an area by using the water tree with the longest length as centre, and calculating a volume based on the defined area; comparing each of the measured length of the one or more water trees with a threshold; determining, from the one or more water trees, a number of water trees with the measured length above the threshold; and calculating a density parameter water trees in the segment based on the number of water trees with the measured length above the threshold, divided by the volume.

Description

SYSTEM AND METHOD FOR CALCULATING A PARAMETER OF WATERTREES IN CROSS-LINKED POLYETHYLENE (XLPE) CABLESTECHNICAL FIELD

[0001] The disclosure relates to a system and method for deriving or calculating a parameter of water- trees in a cross-linked polyethylene (XLPE) cable. In some embodiments, the parameter may be used for providing a health index and the estimation of the remaining useful life of the XLPE cable.BACKGROUND

[0002] The following discussion of the background is intended to facilitate an understanding of the present disclosure only, It should be appreciated that the discussion is not an acknowledgment or admission that any of the material referred to was published, known, or is part of the common general knowledge of the person skilled in the art in any jurisdiction as of the priority date of the disclosure.

[0003] Cross-linked polyethylene (XLPE) cables are critical assets for the safe and cost-effective operation of an electrical power grid. XLPE cables are widely used in urban power grids, and industrial power distribution systems, for power transmission and distribution due to their excellent electrical insulation properties, resistance to heat, and durability. However, over time, XLPE cables are subject to aging due to thermal, electrical, mechanical, and environmental stresses. Proper monitoring and maintenance of XLPE cables are crucial to ensuring reliable operation, minimizing failures, and optimizing replacement schedules.

[0004] Part of the monitoring process of XLPE cables includes the detection of defects. Defects of XLPE cables may include protrusions, voids, cracks, delamination, conductor shield interruptions, water trees, and electrical trees. In particular, the growth of water trees in cable insulation is a major aging factor for XLPE cables. The water trees can act as precursors for electrical trees, which lead to XLPE cable failure.

[0005] Currently, there is a lack of water-tree-based monitoring techniques to effectively estimate the health and remaining useful life of XLPE cables.

[0006] There exists a need to provide a parameter associated with water trees of XLPE cables, the parameter may be subsequently used for estimating a health index (HI) and the remaining useful life (RUL) of XLPE cables.SUMMARY

[0007] A technical solution, in the form of a system and a method for deriving a parameter of water trees in XLPE cables, is provided. The parameter may include a density parameter, the density parameter subsequently used to estimate a health index and remaining useful life of the cross-linked polyethylene (XLPE) cables. The derivation may be based on a statistical analysis of water tree results in XLPE cable insulation would be a practical method to assess the health index and remaining useful life of XLPE cable. In some embodiments, the present disclosure provides a method for calculating the health index of an XLPE power cable by accounting for water tree formation and other relevant operational factors. The health index (HI) serves as an indicator of the current condition of the cable. Additionally, the invention calculates the remaining useful life (RUL) of the cable based on the health index and historical degradation data. The health index serves as a metric for a condition of the cable, while the RUL provides an estimate of the cable's operational lifespan before it requires replacement or major refurbishment or repair. In some embodiments, the system and method may use a statistical analysis of water tree results in the XLPE to derive the HI and RUL.

[0008] The present disclosure provides a calculation method for the health index and remaining useful life of medium voltage XLPE cable based on a parameter, such as a density parameter of water trees in the XLPE cable. With a synergistic combination of the degree-of-outlier detection and the kernel probability density, the proposed calculation method based on the water tree provides condition-aware health index and remaining useful life, which ultimately facilitates informed decision-making for efficient asset maintenance of the medium XLPE cables.

[0009] According to an aspect of the present disclosure, there is provided a method for calculating a parameter of water trees in a cross-linked polyethylene (XLPE) cable, the method comprising obtaining a segment of the XLPE cable having a thickness; measuring a length of one or more water trees on the segment; identifying a longest length from the measured one or more lengths; defining an area by using the water tree with the longest length as centre, and calculating a volume based on the defined area and the thickness; comparing each of the measured length of the one or more water trees with a threshold; determining, from the one or more water trees, a number of water trees with the measured length above the threshold; and calculating a density parameter of water trees in the segment based on the number of water trees with the measured length above the threshold, divided by the volume

[0010] In one embodiment, the method further comprises calculating an average length of the measured one or more lengths.

[0011] In one embodiment, the method further comprises, determining, using the calculated density parameter, the longest length, and the average length as inputs, an outlier parameter, an age parameter, and / or a health index.

[0012] In one embodiment, the method further comprises, defining a plurality of age groups associated with the XLPE cable, and determining a median age of each of the plurality of age groups.

[0013] In one embodiment, the method further comprises modelling the outlier parameter as a degree of outlier, using a non-parametric probability density function.

[0014] In one embodiment, the non-parametric probability density function is a kernel density estimation function.

[0015] In one embodiment, the method further comprises estimating the age parameter based on the kernel density estimation function and the median age.

[0016] In one embodiment, the method further comprises calculating the health index using the estimated age parameter, the health index comprises a failure probability.

[0017] In one embodiment, the method further comprises calculating a remaining useful life (RUL) of the XLPE cable based on the estimated age parameter and a known end of life parameter.

[0018] In one embodiment, the method further comprises using a continuous probability distribution to model the failure probability.

[0019] Tn one embodiment, the continuous probability distribution is a Weibull cumulative distribution function.

[0020] In one embodiment, the method further comprises cutting the segment to a plurality of slices, each slice of the plurality of slices having a defined thickness.

[0021] According to another aspect of the present disclosure there is provided a system for calculating a parameter of water trees in a cross-linked polyethylene (XLPE) cable, the system comprises a processor, the processor configured to: receive a dataset comprising a water tree characteristic of a sample of the XLPE sample having a thickness, the water-tree characteristic comprising length measurements of one or more water trees on the segment; identify a longest length from the length measurements; define an area by using the water tree with the longestlength as center, and calculating a volume based on the defined area and the thickness; compare each of the measured length of the one or more water trees with a threshold; determine, from the one or more water trees, a number of water trees with the measured length above the threshold; and calculate a density parameter of water trees in the segment based on the number of water trees with the measured length above the threshold, divided by the volume.

[0022] In one embodiment, the processor is configured to calculate an average length of the measured one or more lengths.

[0023] In one embodiment, the processor is configured to determine, using the calculated density parameter, the longest length, and the average length as inputs, an outlier parameter, an age parameter, and / or a health index.

[0024] In one embodiment, the processor is configured to define a plurality of age groups associated with the XLPE cable and determine a median age of each of the plurality of age groups.

[0025] In one embodiment, the processor is configured to model the outlier parameter as probability or degree of outlier, using a non-parametric probability density function.

[0026] In one embodiment, the non-parametric probability density function is a kernel density estimation function.

[0027] In one embodiment, the processor is configured to estimate the age parameter based on the kernel density estimation function and the median age.

[0028] In one embodiment, the processor is configured to calculate the health index using the estimated age parameter, the health index comprises a failure probability.

[0029] In one embodiment, the processor is configured to calculate a remaining useful life (RUL) of the XLPE cable based on the estimated age parameter and a known end of life parameter.

[0030] In one embodiment, the processor is configured to use a continuous probability distribution to model the failure probability.

[0031] In one embodiment, the continuous probability distribution is a Weibull cumulative distribution function.

[0032] According to another aspect of the present disclosure, there is provided a method for calculating a parameter of water trees in a cross-linked polyethylene (XLPE) cable, the method comprising obtaining, using a cutting tool, a segment of the XLPE cable having a thickness;using an optical instrument, measuring a length of one or more water trees on the segment; identifying a longest length from the measured one or more lengths; defining an area by using the water tree with the longest length as a centre, and calculating a volume based on the defined area; comparing each of the measured length of the one or more water trees with a threshold; determining, from the one or more water trees, a number of water trees with the measured length above the threshold; and calculating a density parameter of water trees in the segment based on the number of water trees with the measured length above the threshold, divided by the volume. [VJP: This section will be further revised once the claims are approved.] BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The disclosure will be better understood with reference to the detailed description when considered in conjunction with the non-limiting examples and the accompanying drawings, in which:- FIG. 1A shows a cross-sectional view of an XLPE cable with various possible defects. - FIG. IB shows a magnified view of a water tree, an electrical tree, and a protrusion. - FIG. 2 is a flow chart of a method for deriving a parameter, such as a density parameter, of water trees in a XLPE cable.- FIG. 3 A to FIG. 3F shows various images of XLPE cables and measurements obtained by implementing the method for deriving the density parameter of water trees in an XLPE cable.- FIG. 4A shows a flow chart for calculating or deriving the density parameter based on the longest length measurement of a slice.- FIG. 4B illustrates a longest water tree length measurement among a number of slices. - FIG. 5A shows an example or illustration of the kernel density estimation function for the estimation of an equivalent age of a sample of XLPE cable.- FIG. 5B is an example of a Weibull cumulative distribution function for modeling a baseline curve for deriving a health index based on the density parameter.- FIG. 6A shows a flowchart of a method for the calculation of a health index (HI) and remaining useful life (RUL) based on the density parameter.- FIG. 6B shows an exemplary case of a table of water tree data and results generated based on applying the method of the present disclosure on medium voltage XLPE cables.- FIG. 7 is a schematic diagram of a system for obtaining water tree characteristics of a sample of a cross-linked polyethylene (XLPE) cable.DETAILED DESCRIPTION

[0034] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details and embodiments in which the disclosure may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the disclosure. Other embodiments may be utilized and structural, logical changes may be made without departing from the scope of the disclosure. The various embodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

[0035] Embodiments described in the context of one of the systems or methods are analogously valid for the other systems or methods.

[0036] Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments. Features that are described in the context of an embodiment may correspondingly be applicable to the other embodiments, even if not explicitly described in these other embodiments. Furthermore, additions and / or combinations and / or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0037] In the context of some embodiments, the articles “a”, “an” and “the” as used with regard to a feature or element include a reference to one or more of the features or elements.

[0038] Throughout the specification, unless the context requires otherwise, the word “comprise” or variations such as “comprises” or “comprising”, will be understood to imply the inclusion of a stated integer or group of integers but not the exclusion of any other integer or group of integers.

[0039] Throughout the specification, unless the context requires otherwise, the word “include” or variations such as “includes” or “including”, will be understood to imply the inclusion of a stated integer or group of integers but not the exclusion of any other integer or group of integers.

[0040] Throughout the specification, unless the context requires otherwise, the word “have” or variations such as “has” or “having”, will be understood to imply the inclusion of a stated integer or group of integers but not the exclusion of any other integer or group of integers.

[0041] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0042] As used herein, the term “water tree(s)” refers to microscopic tree-like patterns developed within an insulation material of an electrical power cable, such as a XLPE cable. Such microscopic tree-like patterns may be developed when the XLPE cable is exposed to moisture and electrical stress. Water trees may be a primary cause of cable insulation breakdown and may contribute significantly to the aging of XLPE cables. In the present disclosure, it was discovered that the more water trees existing in the insulation of a XLPE cable, the higher the probability of the water tree being converted to an electrical tree. Hence, the water tree density is proposed to characterize the water trees and for various purposes, including, but not limited to, the assessment of cable health.

[0043] As used herein, the term “server” or “processor” may include a single stand-alone computer, a single dedicated server, multiple dedicated servers, and / or a virtual server running on a larger network of servers and / or cloud-based service. The processor may include integrated circuit (IC) chips such as application specific integrated circuit (ASIC) chips.

[0044] As used herein, the term “module” refers to, or forms part of, or include an Application Specific Integrated Circuit (ASIC); an electrical / electronic circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor (shared, dedicated, or group) that executes code; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system-on-chip. The term module may include memory (shared, dedicated, or group) that stores code executed by the processor.

[0045] As used herein, the term “database” may include one or more data repositories to store data and access data from a single stand-alone computer, a data server, multiple dedicated data servers, a eloud-based service, and / or a virtual server running on a larger network of servers.

[0046] As used herein, the term “sensor” or “sensors” include hardware sensors, software sensors and combinations of hardware and software sensors.

[0047] In the following, embodiments will be described in detail.

[0048] FIG. 1A shows a cross-sectional view of an XLPE cable with various possible defects such as water trees 1, electrical trees 2, protrusions 3, voids 4, cracks 5, delamination 6, and conductor shield interruptions 7. These detects are typically formed on / in the insulation layer (material) of the XLPE cable. FIG. IB shows a magnified view of a water tree 1, an electrical tree 2, and a protrusion 3.

[0049] FIG. 2 is a flow chart of a method 100 for deriving a parameter, such as a density parameter, of water trees in a XLPE cable according to an aspect of the present disclosure. The XLPE cable may be a medium -voltage distribution cable or a high-voltage transmission cable.

[0050] The method 100 comprises the following steps of:

[0051] Step S 102: obtaining a segment of the XLPE cable, the segment having a thickness;

[0052] Step S 104: measuring a length of one or more water trees on the segment;

[0053] Step S 106: identifying a longest length from the measured one or more lengths;

[0054] Step S 108: defining an area by using the water tree with the longest length as a centre, and calculating a volume based on the defined area;

[0055] Step SI 10: comparing each of the measured length of the one or more water trees with a threshold;

[0056] Step S 112: determining, from the one or more water trees, a number of water trees with the measured length above the threshold; and

[0057] Step S 114: calculating the density parameter of each of the one or more water trees based on the number divided by the volume.

[0058] FIG. 3A to FIG. 3E shows various images of XLPE cables and measurements obtained by implementing the method 100 for deriving the density parameter of water trees in a XLPE cable.

[0059] Referring to Fig. 3A, a sample 302 of the XLPE cable may be obtained, according to step S102, using a cutting tool. The sample 302 may then be dissected until an insulation layer. As shown in FIG. 3B, a short insulation layer segment 304 of a defined length of the segment may then be cut. In some embodiments, the defined length of the segment may be in a range from 5 centimeters (cm) to 20 cm. In some embodiments, the defined length of the segment may be 10 cm.

[0060] The segment 304 may then be sliced.

[0061] As shown in FIG. 3C, a plurality of slices 306, each slice 306 being of a defined slice thickness, may be obtained. The plurality of slices may be sliced or cut by a precisioncutting or slicing instrument / tool, such as, but not limited to, a microtome. In some embodiments, the cutting or slicing tool may be a Leica™ microtome RM2235. In some embodiments, the short segment having a defined length of 10 cm may be sliced to 20 slices (as shown in FIG. 3C), each slice having a thickness of 0.2 millimetres (mm).

[0062] It is contemplated that the larger the number of slices (i.e. smaller thickness associated with each slice), the more accurate the measurement results may be. In some embodiments, the number of slices may be in a range of 10 to 50.

[0063] It is contemplated that the slice thickness is determined based on whether the water tree in each slice can be observed clearly by an optical instrument, such as a microscope. In some embodiments, the model of the optical instrument used may be the Leica™ microscope DM 750M. The optical instrument may be equipped with remote control communication hardware / software, and may be enabled to be remote controlled by a computer device, such as a small tablet or a smart mobile phone. In some embodiments, the range of this slice thickness can be set from 0.1 mm to 0.6 mm.

[0064] Each slice 306 may then be examined under the optical instrument. FIG. 3D shows the identification of a plurality of water trees 308 in the slice 306. The length measurements according to step S104 may be obtained for each of the plurality of water trees 308. FIG. 3D shows an example of a slice 306 marked slice no. 6 and a slice 306 marked slice no. 9. The length measurements may be manually obtained based on the settings of the optical instruction, such as the magnification power and ocular divisions.

[0065] From the length measurements, the longest length measurement 310 of the segment, may be obtained in accordance with step S 106. From FIG. 3D, it may be shown that the longest length measurement 310 is the water-tree marked with length 679.84 pm in slide no. 6. The average length Laves of the five longest water trees identified from all the slices 306 (i.e. from slices 1 to 20) may also be obtained.

[0066] In some embodiments, an average length may be obtained for all the length measurements across all the slices. In some embodiments, other statistical measures such as mode, median, may also be calculated or derived. Other known statistical measures may also be derived based on the measurements obtained.

[0067] In some embodiments, the percentage of the longest length and average length over an insulation thickness may be adopted as a normalization parameter, to account for the difference in insulation thickness of different voltage level cables. The reason is that once thewater tree length is over the 30% of the insulation thickness, the XLPE insulation has a high probability of breakdown. The longest length measurement of the water tree is one of the key parameters, and as many water trees exist in the one short XLPE insulation segment, only the longest length is unitary. Hence, the average length of the top five longest water tree length Laves is proposed to characterize the water tree to assess the cable health.

[0068] FIG. 3E shows a table, which may be implemented as a database, for data entry of measurements obtained for different brands (brands A, B, C, D, E) of XLPE cables, with known age in years and known cable length in metres.

[0069] In some embodiments, the preparation of the XLPE cable to obtain insulation layer slices 306 (also referred to as insulation slices), before measurements are obtained, may be performed manually. In some embodiments, the preparation of the XLPE cable to obtain its insulation layer may include the steps of cutting a short XLPE cable segment of around 1 metres (m) from the XLPE circuit. Dissecting the cable segment layer by layer to the insulation layer. Cutting one short segment of around 10 cm from the XLPE insulation layer. Cutting 20 microtome slices from the 10 cm length XLPE insulation segment, each slice with a thickness of 0.2 mm. According to a dyeing procedure, all 20 slices were dyed for further water tree measurements. After the XLPE dyeing slices were obtained, the water trees in all the slices may be observed by microscope. The water tree length and quantity in each slice would be recorded as described. FIG. 3F depicts the photos of an XLPE cable sample and various layers of XLPE cable sample at various stages of preparation, comprising an outer sheath 351, a steel tap armour 352, white binder tape 353, extruded bedding layer 354, white binder tape 355, filler 356, copper tape 357, semi-conductor insulation screen 358, insulation 359, copper conductor 360, slice before dyeing 361, and slice after dyeing 362.

[0070] FIG. 4A shows a flow chart 400 of calculating or deriving the density parameter based on the longest length measurement of a slice 308. It is appreciable that the longest length and water tree density measurements are obtained for each slice. After the measurements are obtained for each slice, the longest length among the segment (comprising the predetermined number of slices, for example, 20 slices) can be obtained. The longest length and maximum water tree density measurements obtained across all the slices are then used as water tree characteristic parameters for the specific cable segment.

[0071] In accordance with step S402, the longest length measurement of the water tree in each slice 308 may be obtained. The volume of the area may be defined by adjusting the watertree with the longest length measurement 310 to the center of the microscope’s field of view, with a magnification power of 10 times. The volume of the area may then be calculated and approximately equal to 1.2 mm x 0.62 mm x 0.2 mm = 0.148 mm3(step S404).

[0072] The number of water trees Nt with a length greater than the threshold of 20 pm may then be recorded in the area (step S406). The water tree density Dw, including the longest water tree, may be calculated based on the number Nt divided by the volume (step S408).

[0073] As illustrated in FIG. 4B, the longest water tree length among the 20 slices is 328.17 pm. Based on the microscope's field of view with a magnification of 10 times, the area is around 0.74 mm2, and the thickness of slice is around 0.2 mm. Hence, the volume of this area is around 0.148 mm3. The total number of water trees with length greater than 20 pm in that area is around 10. The water tree density is around 68 / mm3.

[0074] It may be appreciable that as the water tree density is equal to the quantity of water tree divided by the volume, the water tree density is dependent on the selection of the volume. For example, if there is only one water tree in one XLPE slice, and the volume could be selected as the whole slice or the half of slice or one-fourth of the slice. The water tree density would be greatly different if the volume selection is different. Therefore, in the present disclosure, the area including the longest water tree is selected to calculate the water tree density.

[0075] The output density parameter from the method 100 as described may be used for the determination of an outlier parameter, an age parameter, and / or a health index. In some embodiments, the longest length, and the average length may be used as input data for the determination of the outlier parameter, the age parameter, and / or the health index.

[0076] In some embodiments, the outlier parameter may be modelled as a degree of outlier using a non-parametric probability density function. In some embodiments, the non-parametric probability density function may be a kernel density estimation (KDE) function, which is a non-parametric way to estimate the probability density function of a random variable.

[0077] FIG. 5A shows an example or illustration of the kernel density estimation function for the estimation of an equivalent age of the sample 302. The KDF function may be mathematically expressed as Equation (1) as follows:i=n KDE< = — ) ——e A h J(nn / ,hV27T3 7i=lwherein KDEj is the estimated density at point xj n is the number of data points in the dataset. h is the bandwidth, which a smoothing parameter that controls the width of the kernel, andwhereinh√2π denotes the kernel function that is non-negative and integrates to 1.

[0078] The kernel function may be regarded as a Gaussian (normal) distribution centered at each data point, scaled by the bandwidth h.

[0079] In some embodiments, a plurality of groups may be defined, each of the plurality of group may be associated with an age range of the XLPE cable, may be defined. A KDE distribution may be generated for each group, and in some embodiments, the median age associated with each group may be determined for each of the plurality of age groups. In some embodiments, three groups may be defined as shown in FIG. 5A. The corresponding probabilistic distribution may be generated based on a first probability distribution 502 associated with the young asset group, a second probability distribution 504 associated with the mature asset group, and a third probability distribution 506 associated with the old asset group. Put in another way, the probability of an XLPE cable sample belonging to each group and the equivalent age can be calculated with the conditional probability on the estimated kernel density function of Equation (1). The probability density functions as depicted in FIG.5A may be utilized for the distribution of degree-of-outlier to correlate the XLPE cables' degree-of-outlier and its probability of belonging to different groups with inherently different failure probabilities. In the present disclosure, the probability density function for degree-of-outlier is derived based on the kernel density estimation (KDE).

[0080] In some embodiments, a degree of outlier D as a numerical indicator to find an abnormality may be defined based on the interquartile range and Tukey’s Fence, mathematically expressed in Equation (2) as follows:D = V. Max, ol] (2) wherein D is the result of the summation; Xi denotes the water tree variable, such as the longest length measurement 310, the average length, and the water density value of the ith cable segment; and Qi, so, Qi.os, and Qt,s are quantiles obtained based on, or considering all the data in the water tree database. Specifically, Qi, so is the median (50th percentile), Qi, 95 is the 95thpercentile, and Qi,s is the 5th percentile. If the data point's value distance to the median is larger than the distance between the lower fence (e.g., 5% quantile Qi, 5), and upper fence (e.g., 95% quantile Qi, 95), its degree of outlier will be larger than 1. Such modeling for degree-of-outlier includes the distance between monitoring and the medians, as well as the interquartile ranges that describe the spread of data.

[0081] Equation (2) may be used to measure the deviation of the water density value from the respective median value, while considering the range between the 5thand the 95thpercentiles. If the expression — is negative, the Max function would return a 0 value.<2SS_<25

[0082] The degree of outlier D and the KDE function may be used to estimate the equivalent age teqage- mathematically expressed in Equation (3), as follows.teqage ~ p 1 p 1 pf x\D + E / |P + ‘ z\D (3) wherein Ax, Ay. Azrepresent the median age of the three groups comprising x group (which corresponds to the young assets group), y group (which corresponds to the mature assets group), and z group (which corresponds to the old assets group) respectively, and wherein PX\D, Py\D, and PZ\D are the conditional probability values of the respective x group, y group, and z group. In summary, given the degree-of-outlier D from Equation (2), the probability of an XLPE cable belonging to each age group can be calculated with the conditional probability on the estimated kernel density function.

[0083] The RUL of the XLPE cable segment may be mathematically expressed in Equation (4), as follows:RUL — tend— teqage(4) wherein tendis the designed service life, which is typically a known value.

[0084] In some embodiments, the health index (HI) may be modelled as a probability of failure (POF) value having a normalized value between 0 and 1, mathematically expressed in Equation (5), as follows:'PoFlirm-PoF(Age), ift HIPoFeqage — tend limit (5)0, If teqage tend

[0085] In some embodiments, the HI ranges between 0 and 1 (where 1 is the best condition and 0 is the worst condition i.e., end of life). It is contemplated that the HI is an indicator to determine the sequence (priority) to perform maintenance. The RUL may be used to determinea period to perform maintenance, repair or replacement of the XLPE cables. As the HI is a quantified value, it may be easier to utilize for the asset management and investment planning of electric utilities.

[0086] In some embodiments, a continuous probability distribution may be used to model the failure probability and failure times. The continuous probability distribution may be a Weibull cumulative distribution function, shown in FIG. 5B, to model and provide a baseline curve for the HI.

[0087] FIG. 6A shows a flowchart of a method 600 for the calculation of HI and RUL based on the density parameter. In some embodiments, the method 600 may be implemented as executable software codes which, when executed by a processor, perform the steps of:

[0088] step S601: collecting or receiving water tree char acterization parameters comprising the longest length Lw, the average length Laves, and the water tree density Dw.

[0089] step S602: calculating the degree of outlier based on the collected water tree characterization parameters.

[0090] step S603: dividing the collected dataset comprising the water tree database into three groups based on the XLPE cable age. The three groups may be the young asset group, the mature asset group, and the old asset group as discussed.

[0091] step S604: calculating a probability density distribution of the degree of outlier in each group of the three groups based on the degree of outlier in each group, using the KDE function.

[0092] step S605: calculate the probability values PX\D, Py\D,anc> ^z|n °f the respective x group, y group, and z group.

[0093] step S606: calculate the equivalent age based on Equation (3).

[0094] step S607: calculate the RUL based on Equation (4).

[0095] step S608: calculate the health index based on Equation (5).

[0096] FIG. 6B shows an exemplary case of a table of water tree data and results generated based on applying the method steps on medium voltage XLPE cables. The medium voltage XLPE cables may be 6.6 Kilo-Volts (kV) XLPE cable, with measurements of the water trees of the segment and section of cables with different age group ranging from 0 to 40 years old (tend=40). The degree of outlier based on the water tree characteristics parameters may then be calculated based on the water tree characterization parameters;

[0097] Calculate the equivalent age based on the degree of outlier and RUL, based on, for example, Equation (3) and Equation (4).

[0098] Calculate the failure probability PoF based on the equivalent age and Weibull curve of XLPE cable, based on, for example. Equation (6) below.

[0099] In some embodiments, the expected or expectation of failure probability, denoted as PoF(Age), may be mathematically expressed as Equation (6) as follows. / tegageA^ PoF(Age) = 1 — e ' (6) wherein the expectation of failure probability PoF(Age) is calculated based on the equivalent age and Weibull curve of XLPE cable, β and η are shape parameter and scale parameter, which can be obtained by the curve fitting by using the age database failure and health cables.

[0100] By calculating the expected PoF(Age) the cable health can be quantitatively evaluated and the assets management can be effectively conducted. The lower the PoF(Age), then the healthier the XLPE cables.

[0101] FIG. 6B is a table depicting water tree results of medium voltage XLPE cables (with 22 kV and 6.6 kV power cables), based on a case study provided to demonstrate a commercial application of the invention. The 22 kV and 6.6 kV power cables may be a key part of the distribution power networks of a region or country. In the present disclosure, the XLPE power cables from the region or country with different age groups are taken as a research target. The water tree of these XLPE cables was measured and the corresponding character parameters of water trees are listed in FIG. 6B. From FIG. 6B, it could be known that with the cable age increasing, the longest water tree, average water tree, and water tree density have increased trending. Based on the water tree characterization parameters, the equivalent age and the RUL also can be obtained to evaluate the health status of the XLPE cables.

[0102] According to another aspect of the present disclosure, there is provided a system for deriving a parameter, such as a density parameter, of water trees in a cross-linked polyethylene (XLPE) cable, the system comprises a processor, the processor configured to receive a dataset, the dataset comprising water tree characteristics of a sample of the XLPE cable with a known thickness, the water-tree characteristics comprising length measurements of one or more water trees on the segment; identify a longest length from the length measurements; define an area by using the water tree with the longest length as centre, and calculating a volume based on the defined area; compare each of the measured length of the one or more water trees with athreshold; determine, from the one or more water trees, a number of water trees with the measured length above the threshold; and calculate the density parameter of each of the one or more water trees based on the number divided by the volume.

[0103] By separating the XLPE cables into different groups in different water tree conditions (and therefore different probability of failure), the corresponding probability density of degree-of-outlier for each group can be calculated.

[0104] Then, based on the probability density, the likelihood that the XLPE cables belong to each particular group can be determined. With the definitions of conditional probability, the estimated health condition (failure probability and physical age) can be calculated based on the Weibull function, given the certain monitored degree-of-outlier as condition D in conditional probability.

[0105] FIG. 7 is a schematic diagram of a system, which may be in the form of a server appar atus 700, for obtaining water tree char acteristic of a sample of a cross-linked polyethylene (XLPE) cable.

[0106] The server apparatus 700 may comprise a processor and a memory, the processor is capable of being configured to execute instructions stored in the memory to receive the water characteristics. In the embodiment illustrated in FIG. 7, the server apparatus may be a communications server apparatus. The communications server apparatus may be in the form of a server computer 700, the server computer 700 may be a single server, or have the functionality performed distributed across multiple server components.

[0107] In some embodiments, the server computer 700 includes a communication interface 702 (e.g. configured to receive data, i.e. length measurements of water trees, images of water trees, etc.). The communication interface 702 may include a transmitter module and / or a receiver module allowing the server apparatus 700 to communicate over a communications network. The communication interface 702 may include one or more user-interfaces configured to provide users for user control and may include, for example, one or more computing peripheral devices such as display monitors, computer keyboards and the like.

[0108] The server computer 700 may further include a processor in the form of processing unit 704 and a memory 706. The memory 706 may be used by the processing unit 704 to store, for example, data to be processed, such as the water characteristics data.

[0109] In some embodiments, the microscopic images of XLPE samples and water trees may be obtained from one or more image sensors or capturing devices 710. The obtainedmicroscopic images may then be sent to the server apparatus 700 (see arrow denoting data flow via wired / wireless) for processing to obtain the length measurements, the maximum length of all the water trees across all slices of the XLPE sample, the average length of the five (5) longest water trees. The density parameter may then be calculated in accordance with and the obtained and saved. In some embodiments, the processing may be based on known computer vision and image processing methods such as machine learning for recognition or identification of one or more water trees in the XLPE sample, and then fitting a bounding box around each identified water tree. The dimensions of the bounding box may provide the size in pixels, which may then be converted to the actual length of the water tree.

[0110] In some embodiments, the water tree characteristics of multiple samples of the XLPE cable may be stored in a database. The database may include a training dataset and a testing dataset for training an artificial intelligence or machine learning module for estimating and determining one or more of the water tree characteristics.

[0111] In some embodiments, the method 100, 600 and system 700 may be used in various applications, described as follows.

[0112] In some embodiments, the described method and system may be used in the context of a power utility cable maintenance for a large power distribution network using XLPE cables. In some embodiments, such large distribution networks may comprise extensive networks of XLPE-insulated cables that have been installed over the past decades. The utility may therefore face challenges in predicting the longevity of these cables and determining when to perform preventive maintenance. The method 100, 600 and system 700 of the present disclosure may be used to analyse the insulation quality of cables. By obtaining the length measurements of water trees and calculating the water tree density in a segment or slice of the XLPE cable, quantification of a level of insulation degradation may be achieved. The method calculates an equivalent age for each cable section based on degree of outliers in water tree results, accounting for variations in environmental conditions and cable usage. The health index (HI) can then be calculated by degree of outliers. The remaining useful life (RUL) is determined by comparing the equivalent age to the design service life.

[0113] Based on the RUL and HI obtained, XLPE cables showing lower HI and short RUL may be scheduled for replacement during planned outages, while cables in better condition are kept in service longer. In some embodiments, based on the RUL and HI, the system or method may be configured to provide alerts or notifications to asset managers when an unhealthy assetis identified. Such identification of unhealthy asset may be based on a comparison of the RUL and / or HI with one or more thresholds. The alerts and notifications may include, but are not limited to, audio notifications, visual notifications, email notifications, and messaging systembased notifications.

[0114] This may optimize maintenance budgets, prevents catastrophic failures, and extend cable lifespan. Therefore, the described method and system may lead to improved asset management with reduced outages and maintenance costs, and unnecessary replacements may be avoided.

[0115] In another embodiment, the present disclosure may be applied to an urban underground cable networks replacement planning. In one example there is a urban utility company that manages a vast network of underground XLPE cables. Over time, water treeing becomes a concern due to varying soil moisture and temperature conditions. Traditional methods of cable monitoring do not provide a clear' estimate of cable life. The present disclosure may be integrated with the existing monitoring and replacement system to measure water tree growth in cables located in different environments (e.g., wet vs. dry soil). The method identifies which cable sections are suffering from accelerated water tree growth through the analysis of statistical outliers. The RUL estimation guides the utility in creating a replacement plan, prioritizing cables nearing their equivalent end-of-life.

[0116] In general, the present disclosure seeks to provide a density parameter of water trees in a XLPE cable (generally found in the insulation layer of the XLPE cable), and the utilization of the density parameter for various purposes, including, but not limited to, assessing the health index and remaining useful life of medium voltage XLPE cable based on the water tree results. Various parameters of the water trees of the XLPE cables were required to be measured and recorded, and the degree-of-outlier of the water tree length as an indication of abnormality, and water tree density is analysed. According to the degree of outlier, the equivalent age and RUL of XLPE cables can then be obtained.

[0117] According to another aspect of the present disclosure there is provided a method for estimating the health condition of the medium XLPE cables. The method may comprise obtaining the characteristic of water tree(s) in an XLPE cable insulation; a condition monitoring of a degree-of-outlier mechanism for quantifying asset abnormal conditions; a kernel probability density function for estimating the probability density of the XLPE cable conditions. The characteristic of water tree(s), degree-of-outlier, and kernel probability densityfunction may be used for the estimation and derivation of a health index and equivalent physical age of the XLPE cable.

[0118] In some embodiments, the characteristic of water trees in XLPE cable insulation include the longest length measurement of the water trees, the average length of the top five water trees, and the water tree density. In some embodiments, a percentage of the longest water tree length and the average water tree length may be used to derive a normalized value.

[0119] In some embodiments, the condition monitoring degree-of-outlier mechanism may employ a statistical method to detect abnormal XLPE cable conditions.

[0120] In some embodiments, a kernel probability density function that uses non-parametric estimation techniques to model the distribution of XLPE cable conditions may be adopted.

[0121] In some embodiments, a module of determining the equivalent physical age of assets based on failure probability of the degree-of-outlier and the average of each age group.

[0122] In some embodiments, the module of determining the remaining useful life (RUL) is based on the equivalent age teqage, and the designed service life tend.

[0123] In some embodiments, the module further comprising a step of providing alerts or notifications to asset managers when an unhealthy asset is identified.

[0124] While the disclosure has been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims. The scope of the disclosure is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

CLAIMS1. A method for deriving a parameter of water trees in a cross-linked polyethylene (XLPE) cable, the method comprisingobtaining a segment of the XLPE cable having a thickness;measuring a length of one or more water trees on the segment;identifying a longest length from the measured one or more lengths;defining an area by using the water tree with the longest length as centre, and calculating a volume based on the defined area and the thickness;comparing each of the measured length of the one or more water trees with a threshold; determining, from the one or more water trees, a number of water trees with the measured length above the threshold; andderiving a density par ameter of water trees in the segment based on the number of water trees with the measured length above the threshold, divided by the volume.

2. The method according to claim 1, further comprises, calculating an average length of the measured one or more lengths.

3. The method according to claim 2, further comprises, determining, using the calculated density parameter, the longest length, and the average length as inputs, an outlier parameter, an age parameter, and / or a health index.

4. The method according to claim 3, further comprises, defining a plurality of age groups associated with the XLPE cable, and determining a median age of each of the plurality of age groups.

5. The method according to claim 3 or 4, further comprising, modelling the outlier parameter as a degree of outlier, using a non-parametric probability density function.

6. The method according to claim 5, wherein the non-parametric probability density function is a kernel density estimation function.

7. The method according to claim 6, further comprising estimating the age parameter based on the kernel density estimation function and the median age.

8. The method according to claim 7, further comprising calculating the health index using the estimated age parameter, the health index comprises a failure probability.

9. The method according to claim 7 or 8, further comprising calculating a remaining useful life (RUL) of the XLPE cable based on the estimated age parameter and a known end of life parameter.

10. The method according to claim 8 or 9, further comprises using a continuous probability distribution to model the failure probability.

11. The method according to claim 10, wherein the continuous probability distribution is a Weibull cumulative distribution function.

12. The method according to any one of the preceding claims, further comprises cutting the segment to a plurality of slices, each slice of the plurality of slices having a defined thickness.

13. The method according to claim 12, further comprises calculating a percentage value of the longest length and average length over the defined thickness.

14. A system for calculating a parameter of water trees in a cross-linked polyethylene (XLPE) cable, the system comprises a processor, the processor configured to:receive a dataset comprising a water tree characteristic of a segment of the XLPE cable having a thickness, the water-tree characteristic comprising length measurements of one or more water trees on the segment;identify a longest length from the length measurements;define an area by using the water tree with the longest length as center, and calculating a volume based on the defined area and the thickness;compare each of the measured length of the one or more water trees with a threshold; determine, from the one or more water trees, a number of water trees with the measured length above the threshold; andcalculate a density parameter of water trees in the segment based on the number of water trees with the measured length above the threshold, divided by the volume.

15. The system according to claim 14, wherein the processor is configured to calculate an average length of the measured one or more lengths.

16. The system according to claim 15, wherein the processor is configured to determine, using the calculated density parameter, the longest length, and the average length as inputs, an outlier parameter, an age parameter, and / or a health index.

17. The system according to claim 16, wherein the processor is configured to define a plurality of age groups associated with the XLPE cable and determine a median age of each of the plurality of age groups.

18. The system according to claim 15 or 16, wherein the processor is configured to model the outlier parameter as probability or degree of outlier, using a non-parametric probability density function.

19. The system according to claim 18, wherein the non-parametric probability density function is a kernel density estimation function.

20. The system according to claim 19, wherein the processor is configured to estimate the age parameter based on the kernel density estimation function and the median age.

21. The system according to claim 20, wherein the processor is configured to calculate the health index using the estimated age parameter, the health index comprises a failure probability.

22. The system according to claim 20 or 21, wherein the processor is configured to calculate a remaining useful life (RUL) of the XLPE cable based on the estimated age parameter and a known end of life parameter.

23. The system according to claim 21 or 22, wherein the processor is configured to use a continuous probability distribution to model the failure probability.

24. The system according to claim 23, wherein the continuous probability distribution is a Weibull cumulative distribution function.

25. The system according to any one of claims 14 to 24, wherein the segment is cut to a plurality of slices, each slice of the plurality of slices having a defined thickness.

26. The system according to claim 25, wherein the processor is configured to calculate a percentage value of the longest length and average length over the defined thickness.

27. A method for calculating a parameter of water trees in a cross-linked polyethylene (XLPE) cable, the method comprisingobtaining, using a cutting tool, a segment of the XLPE cable having a thickness; using an optical instrument,measuring a length of one or more water trees on the segment;identifying a longest length from the measured one or more lengths;defining an area by using the water tree with the longest length as a centre, and calculating a volume based on the defined area;comparing each of the measured length of the one or more water trees with a threshold; determining, from the one or more water trees, a number of water trees with the measured length above the threshold; andcalculating a density parameter of water trees in the segment based on the number of water trees with the measured length above the threshold, divided by the volume.

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