Investigation of Improved Thermal Dissipation of ±800 kV Converter Transformer Bushing Employing Nano-Hexagonal Boron Nitride Paper Using FEM

The heat dissipation factor of conventional epoxy impregnated paper bushings is a subject of concern due to the large quantities of power in a High Voltage Direct Current (HVDC) system. The present work deals with the selection of better insulation as a replacement to the conventional resin impregnated material employing nano-hexagonal-Boron Nitride and nano-hexagonal-Boron Nitride added with nano-cellulose-fiber. The bushing of the converter transformer is designed using the Finite Element Method (FEM), and the electrothermal analysis is performed at the loaded working condition. Besides, numerous optimization schemes are also presented for adapting the structure of the thermal conductor enclosed in the inner conductor. The electrothermal performances of the above materials with the optimized structure are compared and an advanced scheme is proposed. Further, the results obtained from the designed system are employed in the form of an Artificial Neural Network to simplify the process of thermal computation characterized by the selected scheme. The internal parameters of the neural network are tuned implementing a hybrid amalgamation of Particle Swarm optimization - Grey Wolf Optimiser and the performance is compared against the actual values. The supremacy of the implemented algorithm is justified by a comparative analysis with other well-established algorithms using various statistical parameters.


I. INTRODUCTION
S INCE the dawn of electrification about a century ago, the electricity demand has been soaring high. This places an inevitable call of expansion of transmission systems in terms of their capacity and voltage. In recent years, the power sector has shown an inclination towards High Voltage Direct Current (HVDC) transmission systems. In addition to the simpler mechanism in changing the direction of power flow, an HVDC system carries greater power per conductor and does not suffer from problems due to resonance [1], thereby making it a suitable selection for increasing the transmis-sion capacity over longer distances. The HVDC transmission system has shown lucid advantages over conventional transmission methods especially for longer distances and higher transmission capacities. At this point, it could be stated that the earlier race of electrification between the DC and AC systems is beginning to see the flip side of the coin.
In an HVDC system, bushings form as the essential equipment, and hence their stable operation is one of the main concerns for a power engineer. The converter transformer and the converter valves are the two of the most significant sections in the HVDC power transmission system, and the bushings act as a bridge by connecting them [2], [3]. The bushing allows the passage of high voltage conductors through the transformer tank and acts as an insulation medium [4]. To ensure an increase in transmission capability, the magnitude of current carried by the HVDC bushings has sailed high. The bushings implemented in HVDC transmission are broadly classified as resin-paper type and oil-paper type based on the nature of insulation. The resin-paper type of bushing bears remarkable heat resistance in addition to its exceptional mechanical properties. The main insulation material in a Resin Impregnated Paper bushing (RIP bushing) constitutes epoxy impregnated paper. The disadvantages of using epoxy in its purest form are its higher thermal expansion and inferior thermal conductivity. The large thermal expansion of the paper material in bushings has been the causing agent of most of the RIP bushing thermal failures. The issues related to the thermal consequences of the bushings have congested the operability and reliability of the equipment. To alleviate the former issue, authors in [5], carried out optimization of the design of the bushings. The design was devised in such a manner, that the heat carried out by the insulation medium was below the heat distortion temperature of the material. Earlier, there has been a numerous amount of work on the temperature field of electrical equipment. In one of the earliest attempts, researchers in [6] presented a numerical solution to coupled problems in electrical transformers. The work involved the utilization of Computational Fluid Dynamics (CFD) for solving the heat, fluid flow, and electromagnetic coupled design of a transformer. Further, in [7], the authors foretold the temperature profile of an HV SF 6 gas circuit breaker. The implemented methodology involved the usage of the commercial fluid dynamics tool ANSYS-CFX. The efficiency of computation was reported by successfully predicting the thermal behavior of the breaker at an elevated current. In [8], the effective replacement of oil-impregnated paper with the resin-impregnated paper was reported with the help of two-dimensional analysis of the temperature distribution. The work involved the development of a theoretical model for obtaining the thermal field distribution concerning the conductivity of the insulation. In [9], a UHV RIP bushing was considered for two-dimensional analysis of the temperature distribution with no consideration of radiation and convection aspects of heat. The work involved analysis of the thermal field by simplifying the process of radiation and convection using an empirical formula. Similarly, the authors provided the nominal operating environment for UHVDC wall bushings in [10]. The work optimized the design of the internal shield of an 1100 kV UHVDC wall bushing employing a nonlinear finite element model. Authors in [11]; considered the conduction and radiation effects of heat in determining the thermal distribution of the 400 kV bushings of converter transformer. The work included the development of a 3dimensional model implementing CFD and finite element analysis. An effective model with a tolerable difference of 10% in the maximum temperature was obtained, determining the suitability of the Finite Element Method (FEM). In a similar attempt, Wu et al. developed a numerical calculation model using ANSYS APDL for determining the static distribution of temperature in a 500 kV transformer bushing [12]. An electro-thermal analysis of a RIP bushings immersed in oil-SF 6 was performed in [13]. The work involved the usage of FEM for computing the heat losses due to the dielectric effect of the bushing capacitance. Tian et al. in [14] worked on analyzing the deterioration of electrical contact structure in a 500 kV converter transformer RIP bushings implementing a three-dimensional finite element model. The work involved analysis of the temperature distribution field at different rates of heating. The authors also proposed diagnostic strategies based on the simulation results thereby providing a reference for the prediction of faults. In particular, the FEM has attained a prominent place in analyzing the thermal behavior of complex systems. Work done by authors in [15] gives an account of the usage of FEM in solving complex geometries of that of transformers. In [16], the authors implemented FEM to model the thermal mechanism of OIP bushings of a power transformer. The thermal behavior of a 245 kV, 800 A bushing was analyzed at normal and overloaded operating points. In addition to the application of FEM, the modernday solutions of complex multiphysics problems have also witnessed the usage of optimization tools. Authors in [9] developed an interactive optimization process combining the multiphysics simulation with Particle Swarm Optimization (PSO).
The study on the analysis of thermal behavior of a converter transformer bushing would be incomplete without a brief on the behavior of the insulation material in its practical perspectives. It has been established that the conductivity is affected by the temperature [17]. For an effective reduction in temperature gradient between the outer and inner conductors, the thermal conductivity of RIP has to be increased. There are a few challenges that may arise while mixing polymers with nanoparticles. The incompatibility between nanoparticles and polymers and their inherent nature to form clusters leading to a depreciation of the desired effects are a few intricate concerns worth mentioning [18]. There have been studies proposing surface functionalization of nanoparticles implementing a suitable combination of coupling agents [19]. Functionalization is the introduction of organic polymers over the surface of nanoparticles that enables improvement in their electrical and mechanical properties [20]. The functionalization process alleviates the former difficulty by decreasing the affinity of nanoparticles to water, making it resemble the water-repelling nature of the polymers. The functionalization process also includes the adsorption of large molecules on the surface of the nanoparticles, thereby inducing their dispersion, thus, preventing their clustering or aggregation [20], [21]. Various researchers have worked on improving the thermal conductivity of the insulation material. thermal performance of epoxy material. In the same year, Wang et al. experimented on the in-plane thermal conductivity of a composite material of boron nitride and epoxy [23]. It was established that the boron nitride particles with larger sizes deliver higher thermal conductivity compared to the composites composed of smaller-sized particles. Moradi et al. experimented on improving the thermal conductivity at the same time maintaining the electrical insulation property of an epoxy-thiol material [24]. The difference in this work was the variation in the size of platelets typically in the order of 180µm. Many of the works have also reported on the implementation of nano-fillers in insulating materials. In [25], the authors prepared an electrically insulating and thermally conducting blend of a nano-paper using boron nitride sheets and cellulose nanofibre. The resulting blend provided an appreciable thermal conductivity of 2.4 W/mK showing an improvement of 94.4%. Besides, the resistivity of the material too was reported to be suitable for electrical insulation purposes. In one of the recent works, authors in [26] worked on improving the thermal conductivity of the epoxy RIP insulation material. The modification of the thermal properties was achieved by implementing hexagonal boron nitride flakes combined with nano-cellulose fiber to form a composite with RIP.
In this work, a three-dimensional model of an 800 kV converter transformer bushing is developed in the COMSOL Multiphysics environment. The model is solved using the electromagnetic, fluid, and thermal physics coupled methods. The distribution of temperature in the bushings on the nominal operation and overloaded condition has been analyzed. The insulation material implemented is composed of nano hexagonal boron nitride modified paper impregnated with epoxy resin as developed by Yang et al. in [17]. The main contributions of the work are enumerated below: 1) The analysis proposes nano-hexagonal-boron-nitride paper and nano-hexagonal-boron-nitride added with nano-cellulose modified epoxy resin as alternatives to the conventional epoxy material in bushings. 2) The work provides an optimized structure and number of heat conductors for the mitigation of thermal issues. 3) Artificial Neural Network-based system is modeled using Hybrid Particle Swarm Optimization -Grey Wolf Optimiser (HPSOGWO) for the prediction of thermal performance of the bushing at a given set of coordinates.
The obtained results are validated against the actual values. Besides, the comparison is also performed against the results using other well-established algorithms viz. the Grey Wolf Optimiser (GWO), Cuckoo Search (CS) algorithm, Teaching Learning Based Optimization (TLBO), Genetic Algorithm (GA), and unaltered PSO, GWO. The performances are compared based on their statistical performances with indices such as the standard deviation (σ d ), Mean Absolute Error (ϵ µ ), Root-mean squared error (ϵ α ) and Relative error (ϵ ρ ). The rest of the paper is divided as follows: Section II comprises the details on the model and the multiphysics environment followed by a simulation study in section III. The analysis of the electric field is presented in section IV. The optimization schemes for the heat conductors are presented in section V. Section VI details the validation procedure and comparison of the developed method with other possibilities. The computation scheme is validated with previous works in Section VII and the work is concluded in section VIII.

A. GEOMETRY
The three-dimensional model of the 800 kV bushing of the valve side of the converter transformer is depicted in Fig. 1. The conductors are the central components in the bushing. They are divided into inner and outer conductors. The bushing is composed of the inner conductor surrounded by the air gap further enclosed by the outer conductor. It is worth noting that the outer conductor does not carry current and is at equipotential balance with the inner conductor.
In addition, the bushings are composed of silicone rubber sheath for the weather shed, epoxy core surrounding the set of conductors, transformer oil, and SF 6 gas. The inner and outer diameters of the current-carrying conductor are 80 mm and 120 mm respectively and their length is 10517 mm. The outer conductor with a thickness of 12.5 mm encloses the inner conductor forming a tubular structure of 160 mm of outer diameter. The spacing between the inner and outer conductors consists of air as fluid, thereby reducing the thermal conductivity between the two conductors. The lower section of the bushing is present in the transformer tank and hence is surrounded by oil.

B. MATERIAL
The types of materials involved are subdivided into solids and fluids. The former type of materials include copper and alloy-based conductors and the fluids are in the form of air, SF 6 , and transformer oil. The properties of the fluid such as the thermal conductivity and the heat capacity are defined as the function of temperature. The thermal property of nanohexagonal Boron Nitride material as developed in [17] has been utilized in the present work as a replacement of epoxy impregnated material. The material implemented by the authors in the above work constitutes 0.5 µm nano-hexagonal Boron Nitride structured as lamellae with a thickness of up to 100 nm developed as per the industrial manufacturing process such as shaping, compressing, drying, and curing. The thermal conductivity of the material was reported to vary as per [17] as (1), Where κ f and κ 0 represent the thermal conductivity of the material with f % of additive and the thermal conductivity of conventional material respectively. The other type of material incorporated in the model is also developed in the same process by the authors in [26]. In the nano-hexagonal VOLUME V, YYYY Boron Nitride + nano cellulose fiber preparation process, the cellulose fiber is diluted to 2% with ions-free distilled water and added to the dried mixture of hexagonal-Boron Nitride flakes by the process of magnetic stirring at the rate of 500 rotations/minute. The formed mixture is then added to the primary pulp which is then shredded in the forms of sheets before compressing and drying. The properties of the above materials are employed to their best accuracy as a customized material in the library of the FEM analysis tool.

C. ELECTROTHERMAL MECHANISM
The governing equations describing the electric stress on the valve side bushings of the converter transformer are given as (2) -(4) [27], Wherein J denotes the current density, Q d denotes the charge density, σ denotes the conductivity, and V is the electric field. The thermal behavior of the bushing insulation has been developed implementing the phenomenon of conduction and convection. The heat flows from the core of the bushing to the gap between the core and the insulator by the process of convection and the flow from the conductor and the insulator condenser is by the phenomenon of conduction. As per the authors in [28], the heat transferred by radiation is too little to be considered. In general, the majority of heat is transferred by the mechanism of conduction, followed by convection. The mechanism of convection takes place in the fluids that surround the system or due to the presence of other fluids in the bushings. The equations that govern the mechanism of heat flow considering the above phenomena are given as (5), wherein q = −k∇T , Q represents the volumetric heat source in W/m 3 , q denotes the heat flux density in Wm, u represents the fluid velocity in m/s, k represents the thermal conductivity in W/(mK), ρ depicts the fluid density in kg/m 3 and T represents the temperature field. The heat sources are divided into those generated by the conductor and the heat loss from the insulating materials named Q C and Q I respectively. The heat sources are given as (6) and (7) [27], Where, I rms is the root mean square current through the conductor of length l m and area of cross-section a m 2 , γ s is the skin effect coefficient of the conductor, ρ C is the resistivity of the conductor (in Ω m), V C is the volume of the conductor, σ I is the conductivity of the insulating medium (in S/m) and E is the electric field (in V/m). The losses generated in the insulating materials due to the harmonics in the alternating current are comparably smaller and are neglected in the computation.

D. BOUNDARY CONDITIONS
The area enclosing the exterior of the bushing is arranged as an isothermal region with constant temperature (chosen to be the ambient temperature) [27]. The transformer oil employed in the model is set with the temperature profile as presented in IEEE International Standard -Bushings for DC application [29]. The flow in the system is analyzed using the laminar flow interface. The natural convection mechanism of heat transfer is considered in the interfacing boundary pairs of insulator core-oil and silicone sheath-ambient air. As per the authors in [3], with the oil temperature kept at 363.15 K at the lower base of the structure, a lower flow rate of 0.7 m/s is considered. For an ambient temperature up to 323.15 K, the flow rate of the air is considered at 0.9 m/s.

E. MESHING AND GRID INDEPENDENCE TEST
The mesh of finite elements is developed for the model. The element size is selected such that the results attained are accurate and the computational burden is lower. The agreement between the size of the mesh and the duration of computation is ensured by iterative variation of the mesh parameters. For each variation in the mesh parameters, the result is computed and is compared with the previous results. The process initiates with the finest possible mesh and continues to reduce the quality of the mesh. Once the results attained in the preceding stage bears a tolerable understanding with those of the current stage, the coarser mesh of the current stage is selected. As the geometry is huge, the number of mesh elements required for the accuracy of results is also large. A Mesh refinement study was incorporated, thereby attaining the most suitable mesh along with an agreement with computational effort. The adaptive refinement of mesh was implemented with a maximum of four refinements. The respective number of elements and the computational efficiency is presented in Fig. 2. Further tuning of mesh size led to an extensive increase in computation time and a minimal change in the results. A variation of about 0.05% was recorded with the fourth refinement. The implemented mesh bears 660164 tetrahedral, 244535 triangular, 88156 edge, and 3268 vertex elements generated in 165 s at a minimum element quality of 1.37×10 −5 . A curvature factor of 0.2 was considered with an elemental growth rate of 1.3. The finalized mesh is as shown in Fig. 3.

III. SIMULATION
The model described in the previous section is solved using finite element analysis. The initial temperature of the surrounding is kept at the ambient temperature of 293.15 K. A current of 755.80 A is applied through the inner conductor. The thermal parameters of the conductive oil and epoxy impregnated paper implemented in the simulation are obtained from [27]. The thermal dissipation of the insulation material is as depicted in Fig. 4. The plot is shown in central symmetry. As can be seen from the plot, the maximum temperature attained is 429.61 K. The thermal distortion temperature of the material is 393.15 K, and the maximum dissipation, in this case, is obtained to be nearly 36 K higher, leading to a thermal failure in the long run. On the analysis of the temperature distribution of the conductor, it has been observed to be non-uniform. The upper and lower ends of the conductor bear lower thermal strain owing to the better thermal conductivity of the insulation material in the axial direction. As explained earlier, the conventional epoxy material is replaced with two other materials. The thermal dissipation of the bushings on the use of nano-hexagonal-Boron Nitride paper is as shown in Fig. 5. The maximum temperature observed using nano-hexagonal-Boron Nitride in the bushings ranges to 411.61 K, which is lower than the previous case by a factor of 4.19%. Furthermore, thermal dissipation was also observed implementing nano-hexagonal-Boron Nitride+nano cellulose fiber modified paper in the bushings. The results are depicted in Fig. 6. A variation of 2.79% was observed compared to the epoxy impregnated paper. The maximum temperature attained is 417.61 K. The thermal distribution of nano-hexagonal Boron Nitride paper bushing is better as compared to the other two materials with the given ratings of supply. If the burden on the system were to increase, the maximum temperature may exceed the distortion temperature of the material leading to its failure. Upcoming sections detail the aspects of optimization in the internal structure of the conductors to modify the thermal dissipation of the entire structure.

IV. ANALYSIS OF ELECTRIC FIELD
The association between the thermal and electric field is in such a manner that a variation in thermal dissipation affects the electric field but the antithesis does not apply. The conductivity of the material determines the influence of the electric field on the material. As per the inferences in the past, the conductivity of insulation material varies owing to the unfolding of the thermal field leading to the distortion of electric field distribution [30]. The temperature field is coupled to the electric interface. The electric field distribution in the FEM model of the bushings is derived by implementing (4) and (8), Where ⃗ J represents the current, σ vt represents the volume conductivity concerning the temperature, and ⃗ E represents the electric field. To analyze the response of electrical conductivity of the material concerning the thermal field dissipation, the electric stress on the bushing is obtained. This section bears the electric field analysis of three cases implementing all the chosen materials as the core insulator of the bushings. It is worth noting at this point, that the thermal data is incorporated in the calculation process of the electric field combining the conductance characteristics of the respective insulation material. The variation of the electric field stress is analyzed in the axial as well as the in radial direction of the structure. All the calculations are performed considering the external temperature of the system at the ambient. The current through the inner conductors is maintained at the same magnitude as implemented in section III. The distribution of electric field (in kV/mm) in the radial length of the bushing is as shown in Fig. 7. The plot depicts that the electric field distribution of the bushing composed of epoxy VOLUME V, YYYY FIGURE 6. Thermal dissipation (in Kelvin) of bushing with nano-hexagonal-Boron Nitride+nano cellulose fibre modified paper impregnated paper bears the highest stress at the radial ends of the bushings. This is mainly because the temperature of the epoxy impregnated paper material is higher thereby affecting the electrical conductivity directly. With the implementation of modified materials namely the n-hBN and n-hBN+CNF the radial electric stress reduces towards the ends of the bushings. An appreciable reduction in electric stress by a factor of 10.14% has been recorded using n-hBN material. The electrical stress across the axial length of the bushing has been depicted in Fig. 8. The conventional epoxy impregnated paper bushing seems to perform comparably to the other two variants in the axial direction as can be seen from the plot. The maximum magnitude of electric stress of the n-hBN bushing is intermediate to that of the other two counterparts. In an overall insight, it could be inferred that the electric stress is comparatively well distributed with lower magnitude in the n-hBN+CNF impregnated paper bushings as compared to the other two materials.

V. OPTIMIZATION
Comparing the results in the previous section with the work done by Wang et al. in [5], it is observable that the improved thermal conductivity of the resin-impregnated paper has led to an efficient temperature distribution in the structure. This section highlights the additional optimized schemes developed for the structure of the bushings for additional benefit to the heat dissipation. The optimization design as proposed in [5] has been modified further to improve the  dissipation of heat. The new structure is developed in such a manner that the inner conductor houses a combination of thermally conductive oil surrounding heat conductors. The heat conductors primarily are made up of copper and run in correspondence with the inner conductor throughout the bushing. The conductive nature of the oil balances the heat dissipation across the entire length of the conductor. This, in turn, reduces the non-uniformity of temperature distribution across the cross-section of the inner conductor. The heat accumulated in the oil is then dissipated with the help of VOLUME V, YYYY heat conductors enveloped within the oil. In addition to heat conduction, the heat conductors also take a minimal part in conducting current through the bushing.
The thermal behavior of the bushing in the presence of internal heat conductors has been analyzed with different optimization schemes. Many of the configurations were tested and presented in the available literature. This work focuses on analyzing potential schemes suitable for efficient temperature distribution. The developed schemes are as shown in Fig. 9. The chosen schemes are further tuned in terms of their dimensions using the optimization module of the multiphysics solver. The model is created in the COMSOL environment including the mentioned physics in the previous sections. The radius of the heat conductors is chosen as the control variable with the temperature as the cost function. As a whole, the optimization problem to be solved here is the temperature profile of the design, by varying the shape of the heat conductors constrained under the desired upper and lower limits of the dimension. Several gradient-free optimization algorithms are present in the tool which are summarised in "The Optimization Module User's Guide -COMSOL Multiphysics" as, 1) Nelder -Mead: "A robust derivative-free, heuristic, simplex search algorithm, including a penalty method for constraint handling." 2) Coordinate search: "A method that searches for the optimum by successive sampling along the control variable axes, typically changing one control variable at a time. The thermal profile in Figs. 10 -21 depict the temperature distribution of the converter transformer bushings and the conductor separately. For comparison of the improved thermal characteristics, the temperature distribution of the bushings has been evaluated by implementing the conventional epoxy impregnated paper, n-hBN modified paper, and n-hBN+nano cellulose fiber paper respectively referred hereafter as material I, material II and material III. The temperature in scheme G has been observed to be suitable in terms of temperature distribution. As seen from Fig. 16, the maximum temperature in scheme G of the optimized structure is the lowest compared to all other schemes. The maximum temperature of the scheme I has been observed to be just higher than that of scheme G by a margin of 2.54%, giving rise to a bushing temperature of 399.19 K, 377.94 K, and 381.72 K for material I, material II and material III respectively. Schemes D, H, and B have shown comparative results in terms of the nearness of the maximum temperature with an increment of 3.98%, 4.74% and 5.22% respectively from the lowest obtained temperature of scheme G. The temperature in scheme D is obtained to be 404.76 K, 389.19 K, and 393.09 K respectively for material I, material II and material III. The proximity of the temperature distribution in these cases is due to the equal number of heat conductors within the inner conductor. As the number of heat conductors is increased in the system, the temperature shows to be increasing. This could be observed from the distribution plots of schemes J and K, which are near to each other in terms of temperature but are inferior to the thermal distribution as obtained from the preceding schemes. The temperature in schemes J and K are higher than that of G by a margin of 5.41% and 5.61% respectively. The maximum temperature of the bushings further increases to 6.75% in scheme E to the range of 415.55 K, 404.12 K, and 408.16 K respectively for material I, material II and material III. The worst temperature distribution has been observed with scheme A with a maximum of 426.24 K, 413.83 K, and 417.97 K for material I, material II and material III respectively. This scheme is analyzed to have a temperature rise of about 9.5% over the distribution of bushing implementing scheme G.
On a closer analysis of the thermal behavior implementing the optimization schemes, it has been observed that the temperature distribution is mainly affected by the volume of the thermal conductors and the heat conductive oil. Besides, it has been observed that the surface area of contact between the heat conductors and the oil also plays a role in the temperature distribution of the structure. Having said the aforementioned entities, a straight increase in the volume of the thermal conductive oil would not lead to an efficient temperature distribution as observed from Fig. 10. It is evident from the plot that the maximum temperature in scheme A is nearly 10% higher than that of the best-obtained scheme. Given that the volume of thermal conductive oil in scheme A is highest compared to other schemes, it is manifest that the temperature distribution is not efficient if the amount of oil is increased without a view of the heat conductors. The limitation to the increase of thermal conductive oil lies in the fact that the thermal capacitance of the oil is high, implying a higher stored temperature without a sufficient heat-carrying medium. With the insight of the above observation, the number of heat conductors must be increased to ensure efficient distribution of temperature in the overall structure. Analyzing the thermal profile of the schemes with more heat conductors, it is apparent that the temperature distribution improves with an increase in the number of heat conductors. The profile of schemes D, H, and B with four heat conductors confirms the proportionality of the number of heat conductors to the thermal distribution. To this point, it is apparent that the increment in heat conductors improves Suman Yadav et al.: Investigation of Improved Thermal Dissipation of ±800 kV Converter Transformer Bushing   FIGURE 9. Design schemes the thermal profile, but as the number of heat conductors increases further, the temperature profile tends to deteriorate. The case of scheme C with nine heat conductors tightly packed in the center coordinates of the conductor seems to have the worst performance after case A with an increase of about 9.33% from that of scheme G. Increase in the number of heat conductors from five to six as in the case of schemes J, K compared to E has increased the temperature by about 1.3% of that of the preceding. Assuming the constant volume of oil in the arrangement, if the volume of the heat conductors is increased, the thermal distribution would be efficient and the converse is also true. This leads to the conclusion that there must be an optimal agreement between the volume of conducting oil and the volume of the thermal conductors to provide an efficient thermal distribution. The agreement between the two volumes is due to the phenomenon of a heatcarrying "super high way" as described by the authors in [5]. The optimization schemes employed in the present work have been observed to be complying very well with the available literature.
Apart from the volumes of the oil and thermal conductors, the contact area of the heat-carrying oil with the thermal conductors also plays a prominent role in the conduction of heat. To verify the aforementioned statement, the shape of the thermal conductors employed in scheme G has further been analyzed by changing its dimension. The heat conductors were varied in their diameters in the range of [7.5-20 mm]. The distribution plot of the bushing has been depicted in Fig.  22 for each of the sizes. It can be seen that the variation in the contact area between the oil and heat conductors causes a variation in the thermal distribution of the bushings. The thermal distribution tends to improve from the smaller to the larger diameter of the heat conductor during the initial phase i.e. from 7.5 mm to 12.5 mm and deteriorate for diameters 15 mm to 20 mm. The maximum temperature attained with 12.5 mm diameter of heat conductors is 371.89 K which is 1.6% lower than the temperature distribution implementing heat FIGURE 10. Temperature distribution (in Kelvin) for scheme A of (a) Inner Conductor (b) Epoxy Impregnated Paper (c) n-hBN modified paper (d) n-hBN+nano cellulose modified paper conductors of 10 mm diameter. With the diameter of the heat conductors increased beyond 12.5 mm, say, for instance, 17.5 mm is 4.34% higher than that using 10 mm heat conductors. This variation in the temperature distribution is due to the significant role played by the surface contact area between oil and thermal conductors. Also, care must be taken such that the surface contact area must not interfere with the optimal configuration of the volumes of the oil and heat conductors.
To signify the nature of the material in thermal distribution the Figs. 10 -21 also depict the temperature profile of bushings with material I, material II and material III as stated earlier. From the distribution plots, it could be observed that the temperature distribution of the n-hBN (material II) VOLUME V, YYYY FIGURE 11. Temperature distribution (in Kelvin) for scheme B of (a) Inner Conductor (b) Epoxy Impregnated Paper (c) n-hBN modified paper (d) n-hBN+nano cellulose modified paper FIGURE 12. Temperature distribution (in Kelvin) for scheme C of (a) Inner Conductor (b) Epoxy Impregnated Paper (c) n-hBN modified paper (d) n-hBN+nano cellulose modified paper FIGURE 13. Temperature distribution (in Kelvin) for scheme D of (a) Inner Conductor (b) Epoxy Impregnated Paper (c) n-hBN modified paper (d) n-hBN+nano cellulose modified paper FIGURE 14. Temperature distribution (in Kelvin) for scheme E of (a) Inner Conductor (b) Epoxy Impregnated Paper (c) n-hBN modified paper (d) n-hBN+nano cellulose modified paper FIGURE 15. Temperature distribution (in Kelvin) for scheme F of (a) Inner Conductor (b) Epoxy Impregnated Paper (c) n-hBN modified paper (d) n-hBN+nano cellulose modified paper FIGURE 16. Temperature distribution (in Kelvin) for scheme G of (a) Inner Conductor (b) Epoxy Impregnated Paper (c) n-hBN modified paper (d) n-hBN+nano cellulose modified paper  bushing is appreciable concerning its conventional counterpart. Besides, material II also shows improved thermal performance compared to material III. The average variation in maximum temperatures using material II is observed to be respectively 3.53% and 0.99% lower than that of material I and material III.

A. ARTIFICIAL NEURAL NETWORK BASED PREDICTION
Artificial Neural Networks (ANNs) are one of the methods of computation and prediction which are inspired by the functioning process of the developed animal brain. The functioning process of an animal brain is quite sophisticated enabled by neurons as their basic functional units. The basic structure of a biological neural network bears billions of interconnected neurons processing information in correlation. The structure of a neuron is subdivided into four basic units namely the dendrites, cell bodies, axons, and the synapses [31]. In the biological neural system, the dendrites act as the receivers of the incoming information, and the axons act as a communicator between two neurons. As the name suggests the ANN is the artificial modeling of the biological neural networks. The motivation behind the development of ANN is designing an intelligent self-learning and functioning system or in other words developing a replica of the animal brain. Each of the neurons in an ANN is connected to other neurons present in the network thereby creating a vast information processing web. Once an artificial neuron receives a piece of information, it is transmitted to the connected neurons after processing. The entire network is composed of several layers with each of them consisting of several artificial neurons. Depending on the size of the data and the complexity of the problem the structure of an ANN is defined. The input data is received by the input layer acting as the dendrites of the ANN and the processed data are connected further to other neurons or the next layer. A typical structure of an ANN is as depicted in Fig. 23. In the figure, the hidden layers are shown enclosed within the green box and are three in number. The number of hidden layers defines the total number of layers in an ANN. Each of the layers consists of several neurons represented by cyan circles interconnected with other neurons of other layers with the help of connectors. These connectors define the significance of a neuron in information processing. The interconnection of neurons is defined with the help of numeric values called 'weights' representing each of the communication links between the neurons. These weights are determined in the method called 'Training'. The process of training involves feeding the ANN with inputs and their known outputs [32]. The output Ω k of the k th neuron out of t neurons present in the layer is given in [33] as (9), Wherein ρ represents the activation function, ι k represents the k th input with ϕ k as the weight, the term ψ represents the bias. The data to the developed neural network is fed from the thermal dissipation in the geometry of the bushing, A total of 500 of the coordinates and their respective thermal profile is taken. The network is then trained based on the data  neural network presents an average error of 4.58% which is acceptable as long as a conventional neural network is concerned. The performance of the neural network is improved by implementing a hybrid Particle Swarm optimization -Grey Wolf Optimiser (HPSOGWO) for determining the weights and biases of the ANN. Further, the performance of the implemented algorithm in terms of thermal dissipation was compared with those from networks tuned by numerous other well-established algorithms. The optimization methods are detailed in the upcoming sections.

B. A BRIEF ON HPSOGWO AND OTHER ALGORITHMS
To understand the combined behavior of the algorithms, the insights of each of the methods have been detailed here. To begin with, Particle Swarm Optimization is an optimization method that has evolved to be one of the widely used optimization schemes in solving engineering and science problems invariably. Developed in the mid-90s by social psychologist James Kennedy along with Russel C. Eberhart an electrical engineer. As the name suggests, the algorithm is inspired by the flocking behavior of birds or swarms of animals. Animals move in herds either for shelter or in search of food, the flocking of birds in search of food is defined as the objective of the flock. The flock is referred to as a swarm and every individual particle in the swarm is designated by the best position located by itself and its current position in the search area. The particles update their position after every iteration implementing the factor of velocity associated with the search process, given as (10), Λ n k+1 = βΛ n k + ϑ 1 r 1 π n k,pbest −π n k + ϑ 2 r 2 π n k,gbest −π n k (10) π n k+1 =π n k +Λ n k+1 (11) whereΛ denotes the velocity vector,π denotes the position vector,π n k,pbest is the self best location attained by the n th particle towards the end of k th iteration, β represents the inertial weight-parameter, ϑ 1 , ϑ 2 denote the optimization parameters with r 1 and r 2 denoting random numbers within the range [0,1]. The updated locations and velocities with a small possibility are discarded off and are replaced by a random location. The iteration halts with the attainment of optimal solution or on completion of the iteration count. With the inherent nature, the PSO algorithm tends to get trapped into local minima this is taken care of by implementing another advanced algorithm, the Grey Wolf Optimiser (GWO). Mirjalili et al., in their work in [34], developed an algorithm that derives its inspiration from the leadership hierarchy and hunting mechanism of the apex predator in the food chain namely the Grey Wolves. The leadership and hunting mechanisms of grey wolves are divided into four subcategories i.e the alpha, the beta, the delta, and the omega wolves. In terms of optimization algorithm, the alpha wolves denote the best solutions and are immediately followed by the beta and the delta wolves as the second and the third-best respectively. As per Muro et al., the hunting mechanism is executed by the pack of wolves in three distinct steps named tracking the prey, pursuing the prey followed by attacking the prey [35]. The mathematical model for encircling the prey influence by the hunting steps as developed in [34] is given by (12) and (13) as,λ During the execution of k th iteration,Π t (k) denotes the position of the target andΠ w (k) denotes the position of the grey wolves. The prey is characterised with the help of the vectorsT 1 andT 2 given as, Once the stage of encircling is attained, the wolves get set for thrusting the attack on the prey. The attacking phase is described mathematically as as (14) and (15) [34], The HPSOGWO algorithm implemented in this work is as developed in [36]. In the hybrid mechanism, the actual behavior of both methods is kept intact. This algorithm has performed successfully in solving various engineering problems. One of the recent works by G.K. Suman et al., implemented the HPSOGWO algorithm for solving problems related to optimization of renewables [37]. The exploration of PSO is supported by GWO by avoiding it from falling prey to local minima. This is enabled by migrating some particles of the swarm to positions that are updated by the GWO algorithm. The process flow of the hybrid optmisation is as given in Algorithm 1, Update the velocity and the position of particle 7: if rand(0,1)< prob then 8: Set GWO parameters 9: for small iteration count do 10: for small population count do The optimization commences with the PSO algorithm and continues with it till the generation of a possibility lesser than the user-defined rate. On attainment of certain possibilities lesser than the limit, the algorithm transitions to the GWO algorithm. The GWO then functions as explained above and presents with a modified position, the modified position is then updated to the particles in PSO which otherwise would have switched to a random position within the search space. Before termination, the process switches back to PSO and stops on completion of the iteration count.

1) Cuckoo Search Algorithm
Developed by Yang and Deb in 2010, the Cuckoo Search algorithm imitates the spawning mechanism of the cuckoo bird [38]. These birds lay their eggs down in the nests of other birds thereby compelling brood parasitism. The algorithm initiates with the population of cuckoos and a set of target nests suitable for breeding. Each of the cuckoos lays an egg at the rate of one at a time and deposits it in a host nest chosen at random. The eggs are the solutions to the optimization problem, and the best of the eggs with better solutions are assumed to be the ones dumped in the best nests. The best solutions so far would carry over to the next generation. The newer solutions are generated performing Lévy flights. This method provides random walks with the steps drawn using Lévy distribution and might help in broadening the search space [39]. Also, Lévy flights may well ensure avoidance of local minima. In the algorithm, there is a fair probability of the eggs being discovered by the host and is determined within the range of [0,1]. If the egg is discovered or in other words, the probability criterion is met, the nest is abandoned and a new nest is placed at a new location. The objective of this algorithm is to get rid of graver solutions and replace them with healthier ones. This method has well been used in solving numerous engineering problems and is established to provide promising solutions thereby forming an apt selection for comparative analysis.

2) Teaching Learning Based optimization
The past decade has been the peak time in the sphere of computational optimization. There have been numerous attempts in coming forward with an efficient algorithm for optimization. In one such attempt, a simple optimization tool with a lesser number of initialization parameters was developed by Rao et al. in [40]. This optimization algorithm derives its mechanism from the classroom process of teaching and learning. The entire process is characterized by two phases namely the "Teacher Phase" and the "Learner Phase". The first phase is marked with the initialization of population or in the terms of TLBO, the enrollment of learners in a particular course. The process of tutoring initiates with the objective of the teacher to develop the average value of the entire set of learners as per his abilities. The Teacher phase concludes with the attainment of mean values by the learners' population. The expertise attained by the learners in the teacher phase is refined in the second stage. The best learner from the earlier phase acts as a teacher and communicates with other learners in the population. The learners with a weaker solution or in other words less understanding of the subject improve themselves by interacting with the better learners. The previously accumulated solution with the learners in such a case is modified based on the best solutions from the teacher phase. The TLBO method has been established in literature to deal with problems related to numerous domains, the equipment related to electrical engineering is no exception. For further study on the TLBO algorithm concerning the optimization equations and related features, the readers, can refer to [41]. Consequently, it is one of the most appropriate selections for comparative analysis.

3) Genetic Algorithm
Famed as one of the very first population-based optimization algorithms developed in the history of computation, the Genetic Algorithm is inspired by Darwin's Theory of Evolution [42]. In simple terms, the theory of evolution could be referred to as the "survival of the fittest". A population is initiated with the algorithm evaluating the fitness of in-VOLUME V, YYYY dividuals of the population based on an expression referred to as an objective function. The solutions are referred to as the chromosomes with each parameter in the solution corresponding to a gene in the chromosome. The better chromosomes attain a chance of regeneration thereby producing newer offsprings or solutions. The regeneration can also be attained by 'crossover' or 'mutation'. The objective of the algorithm is the screening of unfit parent chromosomes from the search space allowing the fittest ones to reproduce. GA maintains the fittest solutions in each iteration and implements the same to improve unfit solutions thereby improving its reliability in achieving an optimal solution. The mutation operator changes the parameters of the solutions randomly to maintain diversity in the population thus increasing the ability of exploration. The algorithm is categorized into few stages namely the population initialization, selection of fittest solutions, recombination, and mutation. The process of generation and screening continues till the optimal solution is attained or the iteration count is completed. Being one of the earliest optimization algorithms, GA has found intense usage in solving numerous engineering optimization problems [43] with encouraging results.

VI. VALIDATION WITH ANN
The training of neural networks is a process in which the determined weights and biases lead to a minimal deviation between the actual and the network outputs. This process can be formulated as a minimization problem. The optimization tools described in the previous section are used to determine the weights and biases of the neural network or in other words, solve the minimization problem of the training process. In the HPSOGWO-ANN model, the hybrid optimization algorithm takes part in the minimization of errors of the neural network by defining the optimal weights and biases. For this problem, the objective is a function of the weight (ϕ) and bias (ψ). The objective function for the k th entity is defined in terms of the Root Mean Square Error (RMSE) comprising of N s samples as (17) [44], (17) wherein δ lm and γ lm represent the actual and the predicted values corresponding to the weight (ϕ) and bias (ψ), the term N n denotes the number of neurons. The defined objective function is minimized using the optimization methods presented in the previous section. The stopping criterion for the optimization algorithms is set on completion of the iteration count as presented in [41]. It is worth mentioning here that the error between the results of two successive generations can also be chosen as the convergence criterion. The process flow is as depicted in Fig. 25. The results produced by the network are compared with the actual ones by choosing 50 random test points in the design. The test points are as depicted in Fig. 26 colored in red. It is worth noting that the test points denoted in the figure are not to scale  Tables 1 and 2. For a better insight into the behavior of the implemented algorithms, the repeatability of the algorithms was also verified by analyzing the results obtained using the algorithms for 20 successive executions. The statistical parameters evaluated involves the standard deviation (σ d ), Mean Absolute Error (ϵ µ ), Root-mean squared Suman Yadav et al.: Investigation of Improved Thermal Dissipation of ±800 kV Converter Transformer Bushing   Where τ i denotes the value obtained during the i th out of N executions, τ a represents the actual value. The average values of the above statistical parameters are depicted in Table 3. Regarding the results in the table, it is evident that the performance of HPSOGWO-ANN is better than all the other implemented algorithms with a relative error (ϵ r ) of 0.0124. The relative error of the conventional LMA based ANN too proves to be promising at 0.0579 whereas its performance deteriorates concerning ϵ µ averaging at 19.09. The mean absolute error of the best method is found to be 4.3631. The GWO-ANN, TLBO-ANN, and GA-ANN perform well

VII. VALIDATION OF COMPUTATION SCHEME
This section analyses the effectiveness of the employed computation scheme. The case involved utilizing a heat pipe arrangement in the RIP-based valve-side bushing as presented by Chen et al. in [30]. The model developed in the COMSOL multiphysics environment is rated at ±800 kV and has an axial length of 14.5 m. The inner lining of the cylindrical current-carrying tube is attached with porous wicks for the removal of heat. The technical parameters of the developed model are as given in [30]. Similar to the present study, this case also involves the usage of the laminar flow model combined with heat transfer and DC module. The problem defined in the aforementioned case is reworked to employ the proposed computation scheme. For solving the temperature distribution field of the developed model, the external gas temperature is set at 323.15 K. The temperature distribution of the bushing under rated-current is obtained and is as depicted in Fig. 32. The analyzed condition involves the application of a current of 4500 A through the conductor with the temperature of the oil kept at 333.15 K.
There were two scenarios considered in the original work stated above, but for suitability study of the proposed method, the present work considers only one scenario. The employed scenario is marked by a condition wherein the heat pipe suggested in the work is turned off and a small current is allowed through the conductor. On analysis of the distribution plot in Fig. 32, the radial unevenness in the temperature of the bushing is observed. It was established that the presence of heat pipe helped in the even distribution of temperature with increased magnitudes of current. The results obtained from the above analysis are fed to the HPSOGWO-ANN scheme for the prediction of temperature. The temperatures at 5000 points across the axial length of the geometry were predicted and validated against the simulation results. The predicted values and their respective deviation have been depicted in Fig. 33. Besides, the temperature prediction has also been attained by implementing other schemes as presented in the previous section. The same test points were implemented for a fair comparison of the effectiveness of the algorithms. The comparative plot is depicted in Fig. 34. The deviation of the predicted values using each of the presented ANN schemes is given in Fig. 35. The deviation as presented in the plot depicts the nearness of the predicted values using the HPSOGWO-ANN scheme. The method produces an average deviation of 0.0013 K, thereby establishing its effectiveness over other schemes. With an average deviation of 0.129 GWO based ANN scheme produces the next best result. The worst performing scheme, with an average deviation of 2.344 is the GA-based ANN. The solutions attained implementing the HPSOGWO-ANN scheme are validated against the experimental results obtained from RIP-based valve-side bushing. The temperatures across the axial length of the geometry as obtained from the experimental setup are compared against the respective points in the simulated model. As many as sixteen test points were present in the model developed in [30]. The available test points are taken as the targeted measuring spot of temperature in the simulation model. The experimental and the simulated results are compared and are presented in Table 4. The pictorial representation of the comparison has also been depicted in Fig. 36 for a clear insight on the accuracy of the simulation scheme. The maximum deviation observed is about 2%, thereby assuring the effectiveness of the computation method.

VIII. CONCLUSION
The electrothermal behavior of a valve side bushing of a ±800 kV converter transformer is analyzed. With the use of conventional resin impregnated paper the maximum tem-VOLUME V, YYYY  perature of the bushings is found to be higher. The thermal conductivity of the core insulation material was increased by using n-hBN flakes as an additive to the conventional resin for the impregnation of paper insulation surrounding the conductor. The thermal dissipation was observed to be uniform across the geometry and lower in magnitude. Further, a novel optimization scheme was proposed in the shape of the heat conductors within the inner conductor of the bushing. The proposed scheme was chosen after analyzing twelve different schemes concerning the respective thermal stress exerted on the bushing core insulation. All the schemes were validated for the unmodified epoxy impregnated paper bushing and nano-hexagonal Boron Nitride was found to have improved The results produced by using the proposed computation scheme is found to be within a maximum deviation of 2% from the experimental values. The same is confirmed from the Table 4 and Fig. 36. The present study not only analyses the significance of using VOLUME V, YYYY n-hBN flakes in resin but also provides a novel dimension for the heat conductors thereby further improving the thermal profile. In addition, the HPSOGWOANN-based computation scheme would prove to be very effective in solving the thermal stress at a point in the geometry, thus, reducing the complexity and time consumption in computation. This method can suitably be implemented by design engineers before the fabrication of the bushing material to ensure a long-term, reliable bushing structure for converter transformers. It is worth noting that the incorporation of the developed system with relevant hardware would further enhance the horizon of analysis and broaden the scope which is one of the few limitations at the time of this work. Future works may include analysis of electric field distribution of the conductor and their performance in terms of electrical properties and usage of other forms of optimization methods for the mentioned problem.