Enhancement of the underground cable current capacity by using nano-dielectrics

In most underground power cables, cross ‐ linked polyethylene (XLPE) is utilized as the main insulating material, while polyvinyl chloride (PVC) is usually used as a nonmetallic sheath or jacketing for the cable. Accordingly, improving the electrical and thermal characteristics of these materials leads to an increase in cable dielectric strength, besides a rise in the current capacity of the underground power cables. Thus, enhancing the thermal characteristics of cable insulation is the goal of many research studies. In this regard, increasing the current capacity of underground power cables is an essential topic for electrical distribution and transmission networks

calculations carried out it is found that the use of nano-composite dielectrics reduces the temperature of the cable components by significant values.For example, the core temperature of the 33 kV cable is reduced by 15.6°C, while for the 66 kV cable, the cable core temperature is decreased by 12.6°C, and for 220 kV the conductor temperature is reduced from 71.3°C to 58.3°C when each cable is loaded by its rating.
cable capacity, polymer nano-composites, PVC, thermal and electrical properties, underground cables, XLPE

| INTRODUCTION
5][6] To achieve this, it is possible to use soil that can retain moisture for a long time, which reduces the soil's thermal resistance.For the cable insulating material, as well as the cable's nonmetallic sheath, it is required to modify their properties to reduce their thermal resistance and capacitance.One way to do this is to use nano-fillers with a prominent characteristic of expanded surface area that changes the polymer structure, which increases the atoms on the insulator surface, causing a reduction in the internal space charge. 7,8This helps to build up the electrical and thermal properties of the specific polymer.Many years ago, materials similar to cross-linked polyethylene (XLPE) and polyvinyl chloride (PVC) were commonly used as the main insulator in power cables and their nonmetallic sheath, respectively. 9The thermal, electrical, and electrochemical properties of some polymers are investigated by references. 10,113][14][15][16] The modifications on XLPE material by the use of silica (SiO 2 ) and clay nanoparticles were carried out to improve the cable dielectric characteristics.Moreover, Esa et al., 17 and Abdel-Gawad et al. 18 suggested methods for enhancing the dielectric properties of PVC by the use of chemically modified silica (i.e., silicon dioxide, abbreviated as SiO 2 ) nanoparticles.Recent research has been carried out using variant nanoparticles to reduce dielectric losses, enhancing dielectric strength and electric field distribution inside the nano-composites of power cables.Furthermore, studies of Thabet et al., 19 Gouda and Haiba, 20 and Thabet 21 have investigated the emerging nanotechnology applications in the electrical modern industry.It is noted that few studies 22,23 have investigated the effect of nano-materials on the current capacity of electric cables, especially when the cables are subjected to their dynamic loads.Some of the authors [24][25][26] have investigated the electric field distribution in the insulation of nano-composite materials; the influence of voids in the nano-composite insulation on the electrostatic field of 3-core power cables; and the experimental examination on dielectric losses and PDs patterns.The accelerated lifetime tests performed by Huber 27 proved that the service life of cables used in nuclear power plants can be increased from 40 to 60 years to 80 years by the use of combined nano-filler polymers.More details about the lifetime of cables insulated with nano-filler polymers are reported in Han and Wasserman, 28 Zhang et al., 29 Jonathan et al., 30 and Alshaketheep et al. 31 The method of preparing nano-dielectric materials varies depending on the structure of the dielectric material.For example, the preparation of the PE nanocomposites and PVC nano-composites is done using the SOL-GEL method, which is a technique using wet chemistry that is the process relies on using solvent. 16,18,20Otherwise, in the case of preparing XLPE nano-composites, the master batch method is used. 32,33he influences of nano-materials on the current capacity of underground power cables when subjected to a 100% load factor are the main purpose of this study.Experimental investigations and measurements of different nano-composite materials were carried out to select the most suitable nano-composites, which could be used as dielectrics for underground power cables to increase their current capacities.
Finally, it should be emphasized that this study aims to present a new method to increase the current capacity of underground power cables using nano-dielectrics, and the article included a study on the most important of the materials that can be used in this technique.Furthermore, calculations on underground cables current-carrying capacities using the tested materials as insulation are done.In addition, there was a gap in the previous study of the thermal performance of nano-dielectrics.For this reason, a lot of tests are done in the present study on PVC and XLPE with various nano-fillers having high thermal conductivity to reduce the nano-dielectrics thermal resistivity.The findings of this manuscript can be considered as an interesting contribution.

| SAMPLES PREPARATION
To study the impact of different nanoparticles on the electrical and thermal performance of PVC and XLPE dielectric materials, nanoparticles, such as Aluminum Oxide (i.e., Al 2 O 3 ), clay, SiO 2 , and Zinc dioxide (i.e., ZnO), are used to form PVC nano-composites, while Titanium dioxide (i.e., TiO 2 ), clay and ZnO fillers are utilized in the preparation of XLPE nano-composites.In addition, commercial PVC and XLPE pellets are used in the sample's preparation.They are obtained with the help of El-Sewedy Company, Egypt.Other nanoparticles, such as TiO 2 are received from Sigma Aldrich Chemicals P Ltd.The production of nano-composite polymers has been achieved by the use of the SOL-GEL fabrication method; the SOL-GEL technique aids in connection to the micro-structure of the required mixture materials.5][36] The SOL-GEL processing of the nanoparticles inside the polymer dissolved in nonaqueous or aqueous solution is the ideal procedure for the formation of interpenetrating networks between inorganic and organic moieties at the milder temperature in improving good compatibility and building strong interfacial interaction between two phases.This process has been used successfully to prepare nano-composites with nanoparticles in a range of polymer matrices.The organic-inorganic hybrid nanocomposites comprising of polymer and nanoparticles were synthesized through SOL-GEL technique at ambient temperature.Accordingly, the PVC nano-composites have been produced by using the Tetrahydrofuran as a solvent of polymer matrix.
The nano-composite XLPE samples have been produced by melt-mixing of XLPE pellets with nanoparticles without surfactants using a laboratory mixer with a high shear mixing blade called Metabo RWE1100 Rotary Drill/Mixer/Stirrer device that is used to mix the melted samples at a specified speed and time.The XLPE nano-composite is not soluble in typical solvents and was made into nano-composites by a melting technology process known as the master batch method.The XLPE samples have been produced by meltmixing of XLPE with nanoparticles (Clay, TiO 2 , and ZnO) without surfactants using a laboratory mixer with a high shear mixing blade called Metabo RWE1100 Rotary that is used to mix the melted samples at a specified speed and time.In detail after mixing the XLPE balls with nanoparticles at 135°C for about 15 min at a speed of 75 rpm, the mixture was left at a temperature of 55°C for 30 h.Then, it was blended at 140°C for 15 min at 30 rpm in a double roll's mixer.The samples were pressed for 25 min at 120°C under 150 bars by the use of an automatic hydraulic laboratory hot/cold press.The prepared samples are boiled for 3.5 h in water and left to be cooled gradually.
The penetration of the selected nanoparticles inside the polymer matrix occurs in the ultrasonic process by employing UP100H ultrasonic processor device, a vacuum drying oven is used for drying the prepared samples at 55-60°C for 20-22 h.After that, the prepared samples became ready for testing.For more information, the detailed preparation procedures were discussed previously by Abdel-Gawad et al., 16,18 Elsayed et al., 32 and Mansor et al. 33 A lot of samples are used for different tests that are done to investigate the nanomaterial's thermal and electrical properties.Sample photos of these materials and some that were damaged after testing are given in Figure 1.
The handling of the nanoparticles within the polymer, dispersed in a nonaqueous or aqueous solution, is the ideal procedure for the building of strong interfacial interactions between the polymers and nanofillers.This process has been used successfully in the preparation of nano-composites with variant nanoparticles in a range of polymer matrices.Several strategies are applied to the process of the formation of hybrid materials. 36Figures 2 and 3 illustrate scanning electron microscopy (SEM) measurements for variant nanoparticles in PVC and nanoparticles within XLPE, respectively.
The morphology of the SEM images for various nanoparticles within the PVC and XLPE matrix, given in Figures 2 and 3, showed that nanoparticles are well dispersed in the polymer matrix to some extent and there is not any accumulation or aggregation of nano-filler within the polymer matrix.An important observation is that the thickness of the nano-filler layers is still in the nano-size range (1-100 nm).This means that the samples are successfully prepared.

| MEASUREMENT OF ELECTRICAL AND THERMAL PROPERTIES OF NANO-COMPOSITES PVC AND XLPE
More than 80 samples of nano-composite PVC and XLPE materials (each side of every sample is 4 cm width and 2.5 mm thickness) were prepared.In this article, a lot of tests are conducted with numerous concentrations of ZnO, SiO 2 , TiO 2 , Al 2 O 3 , and clay nanoparticles.With the aim of obtaining the most appropriate concentration of nanoparticles in the dielectric materials to achieve the best results for both electrical and thermal properties, especially, the thermal resistivity test, so that it can contribute to increasing the current capacity of the underground cables.This was achieved in XLPE/ZnO 5 wt.% as well as PVC/ZnO 5 wt.%.This is because the Zinc dioxide nanoparticles have high thermal conductivity compared with the other nanoparticles.After carrying out many experiments, the nanocomposite dielectric materials given in Tables 1 and 2 are selected to study the impact of nano-composite dielectrics on the current capacities of underground power cables.This is because they have the appropriate electrical and thermal properties.

| Measurements of dielectric breakdown of the nano-composites XLPE and PVC samples
Dielectric breakdown measurements of the XLPE and PVC composites were performed by the use of AC, 50 Hz, 100 kV, 8 mA PHENIX Dielectric test set transformer.Each sample under the test was installed between two hemispheres' metallic electrodes and tested under a uniform field.The rate of voltage increase was 750 V/s.The AC voltage was increased until the breakdown of the sample occurred.According to IEC 62539, 37 the test is repeated five times for each sample under testing, and the average values are illustrated in Tables 1 and 2. The readings were taken directly from the instrument screen.

| Measurements of dielectric relative permittivity (ε r ) of nanocomposites XLPE and PVC samples
Agilent E4980A LCR meter was used for measuring the equivalent parallel capacitance (C p ) of the tested XLPE and PVC composites samples at power frequency and at room temperature, then the dielectric constant (ε r ) was calculated with the use of the relation given in Equation ( 1), according to IEC62631-2-1:2018. 38 where ε₀ = 8.854 × 10 −12 F/m, A represents the surface area of each sample face in m 2 , and t is the thickness of each tested sample in meters.The above-mentioned test was repeated five times for each sample and their average value is presented in Table 3.By the use of the Agilent  E4980A LCR meter, the influence of the stray capacities or the parasitic capacities can be omitted.

| Measurements of tan delta (dissipation factor) of nano-composites XLPE and PVC samples
The dissipation factor of each tested sample is measured directly according to IEC62631-2-1:2018 38 with the aid of an Agilent E4980A LCR meter with a dielectric sample holder at a frequency range of 20 Hz to 2 MHz at power frequency (50 Hz).The test results are illustrated in Tables 1 and 2. It is observed that tan delta (Tan δ) lessens with the use of nano-composite dielectrics compared with pure dielectrics.

| Thermal resistivity measurements
The test arrangement for measuring the thermal resistivity of the nano-composite XLPE and PVC samples as illustrated in Figure 4 comprised an auto-transformer to control the testing voltage, a programmable logic controller (PLC), and a series number of thermo-couples junction-K.These were positioned at several distances from the heat source to measure the temperature alongside the tested nano-composite XLPE and PVC samples.The specimen was positioned between two plates held at numerous temperatures.One of the plates was heated and the other was cooled with the aid of a water tube, as shown in Figure 4.Note that the platform shown in Figure 4 is complying with the ASTM C177 Standard. 39The heater was placed at the top of the tested sample, while the water tube was fed into the bottom.The heat flow is in the downward direction.The tested sample, the hot plate, the heater, the watercooling tube, and the cooling plate were completely thermally insulated from the surrounding environment.A heat flux transducer was employed to measure the heat flow within the specimen.The sensors for heat flux detection were thermocouples.The temperatures of the two plates were measured and recorded until they reached a constant value.After thermal equilibrium had been established, the thermal resistivity was calculated by the relation given in the below equation 39 : where ρ is the resistivity of the dielectric sample in °C.m/W,θ h and θ c are the hot face and cold face temperatures in °C, respectively.I, V , and t denote the heater current in Amperes, the supply voltage in volts, and the sample thickness in m, respectively.A is the sample surface area of each face, in m 2 .

| Measurements of volumetric specific heat of nano-composites XLPE and PVC samples
The specific heat capacity of the insulating material is the quantity of heat necessary to boost up the temperature of 1 kg of the material by 1°C.Good dielectric material usually has a high specific heat capacity due to it takes time to absorb more heat before it truly rises up to transfer the heat.
To determine the specific heat of nano-composite dielectric material the following relation can be used. 39 where C nano−composite is the volumetric specific heat of the nano-composite insulating materials in (J/m 3 .°C),C m represents the specific heat of the main insulating material in (J/Kg.°C),C n depicts the specific heat of the nano- material in (J/Kg.°C),γ m is the density of the insulating material, and γ n means nano-material density.Hence, the measurements of electrical and thermal properties of the nano-composite insulating materials are illustrated in Tables 1 and 2.
The measured values are done at 90°C for XLPE and at 55-60°C for PVC, which are considered as the operating temperatures of XLPE and PVC insulation thermoset and thermoplastic materials, respectively. 2As it is noticed in these tables most of the time, when nano-fillers are used, an increase in the dielectric constant and slight decreases in the loss tan δ are observed.Hence, this happened due to the nano-filler's nature.The obtained results illustrated in Tables 1 and 2 for thermal resistivity measurements are consistent with the commercial values of PVC and XLPE dielectrics according to IEC standards. 2he results obtained in Tables 1 and 2 for the XLPE nano-composite and PVC nano-composite samples are consistent with those reported by Abdel-Gawad et al., 18,40,41 and Abdelrahman Said et al. 42 in terms of improving the electrical properties.As for the thermal properties, they are consistent with what was stated in the Ebadi-Dehaghani et al., 43 Poostforush et al., 44 Han et al., 45 taking into account that the thermal properties of each of the nano-composites of XLPE and PVC materials have been investigated in the previous work rarely.Where Table 1 shows that the thermal resistivities of pure XLPE and their nanocomposite ranges from 1.65: 3.5°C.m/W,which correspond to thermal conductivity values of 0.286-0.61W/m.K for several nanoparticles loading (1-5 wt.%) at a temperature of 90°C.In addition, Table 2 shows that the thermal resistivities of pure PVC and their nano-composite ranges from 1.31: 6°C.m/W, which correspond to thermal conductivity values of 0.167-0.763W/m.K for numerous nano-particles loading (1-5 wt.%) at a temperature of 55: 60°C.It can be concluded that the thermal conductivity values in Tables 1 and 2 matched too with the previous research results as discussed in Ebadi-Dehaghani et al., 43 Poostforush et al., 44 Han et al. 45 It must be taken into consideration that the properties of nano-materials depend on many factors, such as chemical composition, strength of bonding, structure type, molecular weight of side groups, processing conditions, temperature, and so on.

| APPLICATION, RESULTS, AND DISCUSSION
To investigate the effect of nano-composites of XLPE and PVC materials as a dielectric and nonmetallic sheath, respectively, the parameters given in Tables 1 and 2 are used in the calculations which are performed on 220, 66, and 33 kV underground power cables.It is worth noting here that the importance of taking the PVC outer sheath into consideration lies not in its being insulation, but in the influence of its thermal resistance on the cable temperature rise, and thus the value of its current-carrying.

| Cable data and their surrounding soil properties
Details of the 220, 66, and 33 kV cables are illustrated in Table 3.The calculations are done in the case of a 100% load factor and the screen thickness is 2 mm.It is important to note that the core and screen materials and cable dimensions given in Table 3 are the same as those produced by companies according to the standard specifications and used in the electric power transmission and distribution networks.The only change made is the replacement of dielectric and jacketing with XLPE and PVC nano-materials.The surrounding soil specifications are given in Table 4.These specifications were measured using a similar technique to that proposed by Gouda et al. 46

| Impact of nano-composites XLPE and PVC materials on cable capacity at 100% load factor
It is known that the thermal resistivity of the cable dielectric is essential for cable current capacity; the thermal resistivity of XLPE/ZnO 5 wt.% nano-composite is the lowest of the XLPE nano-composites, as shown in Table 1.For that reason, in this article, it is used as the main insulation to be compared with cable current capacity isolated by pure XLPE.The current-carrying capacity of a buried power cable is usually determined by the formula of IEC 60287-1-3 standard 2 given in the below equation: In which, where T 2 represents the thermal resistance of the bedding between sheath and armor, °C.m/W, its value equals zero in this case according to IEC Publication 60287-1-3, 2 because it is considered as the metallic sheath thermal resistance.In the case of dry band formation, the following relation is used.
where ∆θ is defined as the difference between the conductor and ambient temperatures, n is the number of load carrying conductors for each phase, W d means the dielectric loss per unit length per phase, R ac depicts the conductor resistance per unit length in ohms per meter, T 1 , T 2 , T 3 , and T 4 represent the insulation bedding between sheath and armor, and jacket and surrounding soil thermal resistances, respectively, in (°C.m/W), λ 1 is the ratio between the losses in the metal sheath and the conductor losses, and λ 2 is the ratio of armor losses to conductor losses of the cable, ρ i , ρ ρ , b j , and ρ soil represent the specific thermal resistivities of the cable insulation, cable bedding, cable jacket, and the cable surrounding soil, respectively.Therefore, d c , D i , D s , Da, and D e represent the external diameter of the conductor, insulation, in addition to the screen, followed by armor, and finally the cable surface.S depicts the distance between the cables for the flat formation and L represents cable burial depth.∆θ x = (θ θ − x a ) represents the difference between the critical temperature and ambient temperature (°C) and ν means the ratio between the thermal resistivity of dry and moist areas.
The dielectric losses are calculated according to the following relation as in the below equation: where f is the supply frequency, δ tan means the loss factor, V o is the phase voltage, and finally, C represents the electrical capacitance, which is obtained as follows in the below equation: where ε is the insulator's relative permittivity, D i is the outer diameter of the insulator, and d c means the conductor diameter.The calculations are performed with the use of different nano-composite jacket materials.
Tables 5-7 illustrate the calculations of the current capacity of the 33, 66, and 220 kV underground power cables, respectively.In these tables, a comparison is made between the current capacities of the cables when using pure XLPE and when using XLPE/ZnO 5 wt.% nano-composites as main insulation.In both cases, different nano-composite jacket materials are used and the cable core temperature is fixed at 90°C with 25°C ambient temperature.
From the results given in Table 5, it is observed that for the cable of 33 kV rating, the use of ZnO/PVC nanocomposite as cable jacketing material and pure XLPE as cable insulation increased the cable current capacity by about 2.27% when wet sand was used as backfill soil and 1.06% when the backfill soil is replaced by dry sand.The use of PVC/ZnO nano-composites as jacket material and pure XLPE as insulation increases the current capacity of the 33 kV cable by 3.41% and 1.5% when wet and dry clay soils are used as backfill materials, respectively.It is observed also that the current capacity of the 33 kV cable has increased by 4.2% and 1.8% when wet and dry sands are used as backfill soils, respectively.In this case PVC/ ZnO 5 wt.% nano-composite is used as a jacket and XLPE/ZnO 5 wt.% is used as the main insulation.Finally, the cable capacity is increased by 6.2% and 2.4% with the use of XLPE/ZnO 5 wt.% as insulation and PVC/ZnO nano-composites as jacketing material when wet and dry clay soils are utilized as backfill soil surrounding the cable, respectively.Similar values of the cable current capacity increase are observed by the use of different nano-composite jacket materials.Table 6 shows that for the 66 kV cable rating, the use of XLPE as the main dielectric and PVC/ZnO nano-composites as the jacket material increases the cable current-carrying capacity by about 6.43% and 3.2% with the use of wet and dry sand as surrounding soils, respectively.When using wet and dried clay as backfill materials, the increase in the current-carrying capacity reaches 9.2% and 3.92%, respectively.When XLPE/ZnO 5 wt.% is used as the main dielectric, and the increase of the cable current reached 3.01% and 6.56% with dry and wet sand as backfill material, respectively.The increase in cable current reaches 9.6% and 4% when wet and dry clay are used as backfill materials, respectively.
Similar results are illustrated in Table 7 for the capacity of the 220 kV cable.The use of PVC/ZnO nanocomposites as jacket material and XLPE as main dielectric increases the cable current by 2.4% and 1.26% when wet and dry sandy soils are used as backfill materials respectively.The current capacity increases by 3.3% and 1.5% when wet and dry clay are used as backfill soils, respectively.When XLPE/ZnO 5 wt.% is used as the main dielectric material and ZnO/PVC nano-composites as the jacketing material, the current capacity increases by about 12.8% and 8.4% when wet and dry sandy soils, respectively, are used as backfill soils.Moreover, when XLPE/ZnO 5 wt.% is used as the main dielectric and wet and dry clay soils are utilized as back-fill material, the T A B L E 6 Maximum current capacity in (A) of 66 kV cable using pure and ZnO 5 wt.% cross-linked polyethylene (XLPE) as insulation.Finally, Tables 5-7 show that the cables buried in wet clay have the highest current values compared to cables buried in dry soils.The results shown in Tables 1 and 2 are interesting, as they illustrated that each of the XLPE and PVC nano-composites has a much lower thermal resistivity than the pure XLPE and PVC.It is worth noting here that some companies are on their way to producing cables insulated with nano-materials as prototype products.In this case, laboratory measurements will be conducted on them, and this may take some time.

| Temperature distribution map of the cable elements and their surrounding soil
The used steady state heat conduction of finite element method (FEM) for underground power cables problem description is governed by the below equation. 46

 
In the above equation, θ is the temperature at any point in the x and y plan, ρ is the medium thermal resistivity, and q depicts the heat generated by the cable losses per unit volume in W/m 3 and its calculation is done by using IEC 60287-1-3 equations. 2or every homogeneous region of a certain thermal conductivity as well as heat generation rate, the temperature at any point (x,y) in the region subject to particular boundary conditions can be achieved by solving Equation (12).The FEM utilizes the theory of the solution of Equation ( 12), namely θ (x,y) that lessens the functional 46 : The cable and its surrounding medium are divided into small triangles, forming a mesh, as illustrated in Figure 5 for flat and trefoil cable formations.The minimization of Equation ( 13) is done over the finite element mesh leading to a set of linear equations as presented in the below equation: where H represents the matrix of heat conductivity and θ means the temperature vector at the mesh nodes.In addition, b depicts the vector of heat generated at each node.Both vector b and matrix H are adapted to adjust the boundary conditions of the thermal circuit.The temperature distribution map of the cable elements and their surrounding soil is constructed by the use of the FEM and COMSOL multiphysics program. 47θ = .
a (15)   Hence, the soil surface is simulated as an isothermal boundary at ambient temperature, and it is expressed by Equation (15).
In Equation ( 15) θ a is the ambient temperature in °C.For each boundary side of the other three sides, the heat flux divergence in the direction normal on the boundary side mainly is equal to zero, and it is explained by the below equation: In which, n means an outward normal direction corresponding to the boundary side surface.
F I G U R E 5 Finite element meshes sample of (A) flat and (B) trefoil formation cables.Figures 6-9 illustrate the temperature distribution of the cable and its surrounding soil when different dielectrics are used for cable jacketing.Pure XLPE and XLPE/ZnO 5 wt.% materials are used as main dielectrics.Different soil types are used as back-fill materials surrounding the cable.The constant temperature boundary condition was considered for the modeling of heat transfer on the earth's surface.This is because the underground cables under study were buried at depths ranging between 1.8 and 1.2 m, as given in Table 3, which makes the impact of atmospheric changes negligible.To make the temperature distribution more clear, a zoom has been taken on the dimensions of Figures 6-9 for the purpose of clarification.In all cases given in Figures 6-9, each cable is loaded by its 100% load factor.
Figure 6A illustrates the temperature distribution of the 33 kV cable elements and its surrounding soil when pure XLPE as insulation and PVC as cable jacket are used.Figure 6B shows the temperature distribution of the same cable when XLPE ZnO 5 wt.% is employed for cable insulation and ZnO/PVC nano-composites is used for cable jackets.In the two figures dry clay soil is used as back-fill material.Comparing the two figures, it is clear that the use of nano-materials in cable insulation as well as in the outer jacket has reduced the conductor temperature by 12.6°C.
Similar maps of the temperature distribution for the 66 kV cable and its surrounding soil using pure XLPE as cable insulation and pure PVC as cable jacket is shown in Figure 7A.Further, Figure 7B illustrates the temperature F I G U R E 6 Finite maximum temperature distribution of the 33 kV cable elements in flat formation and its surrounding soil when using (A) pure cross-linked polyethylene (XLPE) as insulation and pure polyvinyl chloride (PVC) as cable jacket, and (B) XLPE/ZnO 5 wt.% for cable insulation and ZnO/PVC nano-composites for cable jackets, dry clay soil is used as back-fill material.
F I G U R E 7 Distribution of the maximum temperature of the elements 66 kV cable in flat formation and its surrounding soil when using (A) pure cross-linked polyethylene (XLPE) for cable insulation and pure polyvinyl chloride (PVC) for cable jacket, and (B) XLPE/ZnO 5 wt.% as insulation and Clay 2.5 wt.%/PVC nano-composite for cable jacket, the back-fill material is wet clay soil.distribution of the same cable when XLPE/ZnO 5 wt.% is used as the main insulation and Clay/PVC nanocomposite is employed for cable jacketing.In the two cases, the back-fill soil was wet clay material.Similar temperature maps of the 66 kV cable and its surrounding soil are shown in Figure 8 when using XLPE/ZnO 5 wt.% for cable insulation and Al 2 O 3 /PVC nano-composites for cable jacket as well as the back-fill materials are (a) wet sand soil and (b) wet clay soil, respectively.From Figures 7 and 8, it can be observed that by the use of nano-materials, a significant decrease in cable core temperature reaches 13.1°C (see Figure 7) and 12.5°C (see Figure 8).
To investigate the impact of the soil type on the temperature distribution of the 220 kV cable and its surrounding soil, the nano-composites containing XLPE/ ZnO 5 wt.% and SiO 2 1 wt.%PVC are used as the cable insulation and cable jacketing, respectively.Further, wet sand soil and wet clay soils are used as back-fill materials.The results of the temperature distribution are illustrated as shown in Figure 9A,B, respectively.It is observed that the use of wet clay as back-fill material surrounding the cable reduces the cable core temperature.This is due to clay retaining moisture, which leads to a decrease in its thermal resistivity compared to sand.
Maps of the temperature distribution for the 33 kV in trefoil configuration are shown in Figure 10.It can be observed from Figure 10A that an increase in cable core temperature by about 10.5°C, using XLPE as insulation and PVC as cable jacket, occurs when compared with the same cable in a flat configuration.When XLPE/ZnO 5 wt.% is used as the cable insulation and ZnO/PVC nano-composite is used as the cable jacketing, an increase in core temperature of about 17.3°C is observed when compared with the same cable in a flat configuration.The increase in temperature of the cable core of the trefoil configuration is expected due to thermal interference between the cable phases.
In terms of calculating the current capacity, the values calculated in this article in the case of using the two types of soil, whether dry or wet, agree with what was previously calculated in previous studies.However, in the case of using nano-insulating materials, the article is unique in that it is the first to address this topic, even if the innovation was in these calculations.It depends on reducing the thermal resistance values and thus increasing the thermal conductivity, which helps increase the rate of heat leakage resulting from losses in the cable and thus increases the current capacity of the cable.
From the previous tables, figures, and discussion, it is clear that the use of nano-dielectric materials leads to a decrease in the temperature of the cable conductor and thus an increase in the current capacity of the cable, regardless of the type of soil surrounding the cable, the cable configuration and its rated voltage.

| CONCLUSIONS
In this article, experimental measurements are carried out to investigate the electrical and thermal properties of nano XLPE and nano PVC to improve the underground power cables' performance.Based on the results of these measurements, theoretical analysis is carried out on actual cables with the aid of the heat balance of the cable's thermal model, and IEC 60287.Furthermore, the impact of using nano-composite dielectrics on underground power cable capacity has been investigated.Nano-fillers are used to enhance the XLPE and PVC materials, which are usually used as cable dielectric and nonmetallic sheath materials.
From the obtained results it can be concluded that the use of nano-dielectrics reduces the cable core temperature by significant values; for example, the core temperature of the 33 kV cable is lowered from 75.4°C to 59.8°C, while for the 66 kV cable, the cable core temperature is decreased from 73.1°C to 60.5°C and for 220 kV the conductor temperature is reduced from 71.3°C to 58.3°C.
The decrease in the temperatures of the core cables by using nano-composite dielectrics led to an increase in the current capacities of the underground cables in proportions depending on several factors; including the type of nano-dielectric material, the type of soil around the cable, cable configuration, and the operating voltage of the cable.For example, increases have occurred by 2.4%-6.2%,4%-9.6%, and 8.21%-15.7% in cases of 33, 66, and 220 kV cables, respectively.It is observed also that the use of nano-composite dielectrics reduces the cable component's temperature by significant values when the cable is loaded by its load rating.ORCID Mohamed M. F. Darwish http://orcid.org/0000-0001-9782-8813

F I G U R E 1
Samples photo of nano-composite materials before testing and some samples damaged after testing.F I G U R E 2 Scanning electron microscope (SEM) measurements for variant nanoparticles in polyvinyl chloride, listed as: (A) Clay/PVC nano-composites; (B) ZnO/PVC nano-composites; (C) SiO 2 /PVC nano-composites; and (D) Al 2 O 3 /PVC nano-composites.

F I G U R E 3
Scanning electron microscope (SEM) measurements for variant nanoparticles in cross-linked polyethylene (XLPE) should be listed as: (A) Clay/XLPE nano-composites; (B) TiO 2 /XLPE nano-composites; (C) ZnO/XLPE nano-composites; and (D) SiO 2 /XLPE nano-composites.T A B L E 1 Electrical and thermal properties of nano-composites cross-linked polyethylene (XLPE) materials at 50 Hz and 90°C.

F
I G U R E 4 Test arrangement of the thermal resistivity measurement, (A) test circuit outline, and (B) photo of the experimental test arrangement.

F I G U R E 8
Temperature distribution of the 66 kV cable elements in flat formation and the surrounding soil when using cross-linked polyethylene (XLPE)/ZnO 5 wt.% for cable insulation and Al 2 O 3 1 wt.%/polyvinyl chloride (PVC) nano-composites for cable jacket for: (A) wet sand soil and (B) wet clay soil.F I G U R E 9 Temperature distribution of the 220 kV cable-layers in flat formation and its surrounding soil when using cross-linked polyethylene (XLPE) ZnO 5 wt.% for cable insulation and SiO 2 1 wt.%/PVC polyvinyl chloride (PVC) nano-composites for cable jacket for: (A) wet sand soil and (B) wet clay soil.
Electrical and thermal properties of nano-composites polyvinyl chloride (PVC) materials at 50 Hz and 55-60°C.Details of the 220, 66, and 33 kV cables.
T A B L E 4 T A B L E 5 Maximum current capacity in (A) of 33 kV cable with the use of pure and ZnO 5 wt.% cross-linked polyethylene (XLPE) as insulation.
Maximum current capacity in (A) of 220 kV cable with the use of pure and ZnO 5 wt.% cross-linked polyethylene (XLPE) as insulation.