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Temperature and electric field distribution of tri‐post insulator in DC‐GIL based on numerical multiphysics modelling

Temperature and electric field distribution of tri‐post insulator in DC‐GIL based on numerical... INTRODUCTIONDue to the advantages including large capacity, ease to be maintained, safety operation and space‐saving, gas‐insulated transmission lines (GIL) attract much attention in the past decades. Inside the GIL enclosure, high‐pressure gas such as SF6 and SF6/N2 mixture acts as the insulating medium, while the solid insulators are often designed as disc‐type, basin‐type and post‐type function as the supporters [1, 2]. With the development of high voltage direct current (HVDC) power systems, DC‐GIL attracts much attention. Thus, the operation characteristics of DC‐GIL should be investigated carefully.During long‐term operation, current up to several kiloamperes flows through the central conductor, and considerable Joule heat will consequently be generated. And the thermal gradient is established via heat conduction, convection and radiation inside the enclosure [3]. For the safe operation, standards have been suggested including the temperature rise for the conductor, insulator and enclosure [4]. Compared with the GIL in alternating current (AC) systems, different characteristics appear in the heat generation of the GIL in DC systems. Under the stress of DC, the heat generation due to eddy current can be neglected along with the heat generation in the enclosure. This would lead to different heat generation and thermal gradient distribution inside the enclosure. Besides, since the permittivity of the insulator varies slightly with temperature, the influence of thermal gradient on the electric field distribution of the GIL can be neglected under the stress of AC voltage. While the electric conductivity of the insulator, especially the volume electric conductivity, will increase nearly exponentially with increasing the temperature [5]. Thus, an obvious influence of thermal gradient on the electric field distribution of the insulator can be achieved [6]. Moreover, charge will accumulate on the insulator surface and affect the field distribution [7]. This acts as an important risk referring to flashover for the DC‐GIL during long‐term operation [8, 9]. It was reported that the thermal gradient would show an obvious influence on the surface charge accumulation characteristics which further affects the electric field distribution in an operating DC‐GIL [10]. Thus, the thermal gradient is one of the key issues in dealing with the insulation property of the DC‐GIL.Since it is difficult to obtain the spatial temperature distribution based on measurements, simulation is widely employed to deal with the temperature characteristics of the GIL and insulator. Rotational symmetry models were often applied to investigate the thermal gradient inside the vertically installed DC‐GIL with insulators [11, 12]. The thermal gradient of the insulator in a horizontally installed DC‐GIL is seldom involved, although it is widely applied in the transmission system. And 3D geometry model needs to be employed considering the temperature distribution characteristics in the horizontal GIL [13]. Besides, the operating conditions including the load current, ambient temperature, and gas pressure were reported to affect the thermal gradient of AC‐GILs [14], the influence on the DC‐GIL insulators needs to be revealed. Moreover, it is noted that the filler applied in the insulator would affect both the thermal and electric properties including the thermal conductivity, volume conductivity and surface conductivity [15, 16]. These parameters would affect the thermal gradient and electric field distribution characteristics of the DC‐GIL insulator under thermal–electric coupled fields. While parameters from different literature were often employed in the same simulation case in previous research. These parameters may be obtained based on the insulator sample with different kinds and fractions of fillers. This may cause inaccuracy in the simulation result.Here, the thermal gradient of a tri‐post type insulator inside a ±500 kV DC‐GIL was investigated. A 3D simulation model was established to deal with this horizontally installed GIL model. The thermal and electric parameters of the insulator were measured. Based on these parameters, the influence of operating conditions including ambient temperature, load current, and gas pressure on the thermal gradient characteristics was studied. The transient temperature rise under over‐load condition was studied as well. The electric field distribution of the insulator under the thermal‐electric coupled field was investigated. The conclusion in this paper will be beneficial in the design, operation and maintenance of DC‐GILs referring to the thermal and insulation property.SIMULATION METHODGeometry and parameterA ±500 kV DC‐GIL model was applied in this study and the geometry is illustrated in Figure 1. It should be noted that this GIL model is horizontally installed and a tri‐post type insulator is inside the GIL. The geometry, thermal and electrical parameters of the GIL are illustrated in Table 1.1FIGUREThe ±500 kV DC‐GIL with tri‐post insulator1TABLEThe parameters of the conductor and enclosureConductorEnclosureInner diameter (mm)100510Thickness (mm)208Density (kg/m3)26902660The density of the insulator was 2300 kg/m3 in this study. The thermal conductivity and specific heat capacity of the insulator at various temperatures were measured via the Transient Hot‐Wire (THW) method and Differential Scanning Calorimetry (DSC) method, respectively. The measured data with varying temperature is shown in Figure 2. And these data were fitted in the COMSOL Multiphysics software.2FIGUREThe thermal conductivity and specific heat capacity of the insulatorHeat generationCurrent flows through the aluminium conductor and Joule heat is generated as defined in (1),1P=I2R=I2LScondσAl$$\begin{equation}P{\rm{ = }}{I^2}R = \frac{{{I^2}L}}{{{S_{cond}}{\sigma _{{\rm{Al}}}}}}\end{equation}$$where P is the heating power, I is the load current, R is the resistivity of the conductor, L is the length of the conductor, Scond is the sectional area of the tubular conductor, σAl is the electric conductivity of the conductor. In this study, the conductivity varies with the temperature as illustrated in (2) [3, 14],2σAl(T)=σ201+0.004(T−293)$$\begin{equation}{\sigma _{{\rm{Al}}}}(T) = \frac{{{\sigma _{{\rm{20}}}}}}{{1 + 0.004(T - 293)}}\end{equation}$$where T is the temperature of the conductor and σ20 is the conductivity at 20°C (293 K).Heat transferThe heat generated from the central conductor will dissipate to the surrounding via conduction, convection and radiation. The heat conduction existing in the conductor, enclosure, gas and the insulator follows the equations below:3ρCp∂T∂t+∇·(q+qr)=Q$$\begin{equation}\rho {C_p}\frac{{\partial T}}{{\partial t}} + \nabla \cdot ({\bf{q}} + {{\bf{q}}_r}) = Q\end{equation}$$4q=−κ∇T$$\begin{equation}{\bf{q}} = - \kappa \nabla T\end{equation}$$where ρ is the density, Cp is the specific heat capacity, q is the heat flux due to conduction, qr is the heat flux due to radiation, κ is the thermal conductivity, Q represents the heat source for the conductor while it is zero for the enclosure, gas and insulator.Inside the enclosure pipe, heat will be transferred via radiation between the insulator and conductor, between the insulator and enclosure, between the conductor and enclosure. Besides, the radiation exists between the enclosure and the ambient surroundings. The radiation in this study follows the equation below,5ebT=n2σSBT4$$\begin{equation}{e_b}\left( T \right) = {n^2}{\sigma _{SB}}{T^4}\end{equation}$$6q=εG−ebT$$\begin{equation}q = \varepsilon \left[ {G - {e_b}\left( T \right)} \right]\end{equation}$$where eb(T) is the power radiated across all wavelengths, n is the refractive index, σSB is the Stefan‐Boltzmann constant, G is the incoming radiative heat flux, q is the net inward radiative heat flux and T is the surface temperature. ε is the surface emissivity which is 0.2, 0.93, 0.92 and 0.93 for the conductor, insulator, outside and inside surface of the enclosure, respectively [17].Navier–Stokes equations were applied to deal with the heat convection in this study as illustrated below referring to the conservation of mass (7), the conservation of energy (8), and the conservation of momentum (9).7∂ρ∂t+∇·(ρu)=0$$\begin{equation}\frac{{\partial \rho }}{{\partial t}} + \nabla \cdot (\rho {\bf{u}}) = 0\end{equation}$$8ρCp∂T∂t+u·∇T+∇·q=Q$$\begin{equation} \rho {C_p} \left(\frac{{\partial T}}{{\partial t}} + {\bf{u}} \cdot \nabla T \right) + \nabla \cdot {\bf{q}} = Q\end{equation}$$9ρ∂u∂t+ρu·∇u=∇·−pI+μ(∇u+(∇u)T)−23μ(∇·u)I+ρg$$\begin{eqnarray} && \rho \frac{{\partial {\bf{u}}}}{{\partial t}} + \rho {\bf{u}} \cdot \nabla {\bf{u}}\nonumber\\ && = \nabla \cdot \left[ { - p{\bf{I}} + \mu (\nabla {\bf{u}} + {{(\nabla {\bf{u}})}^T}) - \frac{2}{3}\mu (\nabla \cdot {\bf{u}}){\bf{I}}} \right] + \rho {\bf{g}}\end{eqnarray}$$Here, u is the velocity vector, p is the pressure, μ is the dynamic viscosity, g is the gravity vector and Q contains heat sources other than viscous heating.The thermal conductivity and the dynamic viscosity of the gas follow Sutherland's law [3, 14]. The relationship involving the gas pressure, density and temperature follows the ideal gas law.Flow modelThe GIL model can be considered as a horizontal arrangement cylinder from the view outside the enclosure pipe. And the space outside the GIL is considered infinite. In this way, the natural convection model outside the GIL can be selected.When dealing with the convection inside the enclosure, the central conductor is the heat source and the space referring to convection is finite. It can be regarded as a horizontally coaxial model with the central cylinder acting as the heat source. Since it is natural convection inside the enclosure, the dimensionless Grashof number (Gr) and Rayleigh number (Ra) can be used to determine whether turbulent flow model or laminar flow model should be applied to deal with the natural convection [18]. The calculation of Gr and Ra is defined as below:10Gr=gβ(Ts−T∞)Lc3v2$$\begin{equation}Gr = \frac{{g\beta ({T_s} - {T_\infty }){L_c}^3}}{{{v^2}}}\end{equation}$$11Ra=GrPr=gβ(Ts−T∞)Lc3v2Pr$$\begin{equation}Ra = GrPr = \frac{{g\beta ({T_s} - {T_\infty }){L_c}^3}}{{{v^2}}}Pr\end{equation}$$12β=−1ρρ∞−ρT∞−T$$\begin{equation}\beta = - \frac{1}{\rho }\frac{{{\rho _\infty } - \rho }}{{{T_\infty } - T}}\end{equation}$$where g is gravitational acceleration, β is the coefficient of volume expansion of SF6, Ts is the surface temperature of the conductor, T∞ is the temperature sufficiently far from the conductor surface and υ is the kinematic viscosity of SF6. Lc is the characteristic length of the geometry which is the gap between the conductor and the enclosure. Pr represents the Prandtl number which is 0.7.The calculated Gr and Ra fall into the range from 109 to 1010, which indicates a turbulent flow model inside the enclosure [19]. Since it is important to obtain the surface temperature of the insulator for further investigation of surface charge and field distribution, shear stress transport (SST) turbulent flow model was applied to deal with the flow motion considering its advantage in near‐wall treatment compared with the k‐ε model [20, 21]. The temperature distribution based on the laminar flow model was obtained as well. The surface temperature along the insulator surface involving the two kinds of flow models is illustrated in Figure 3.3FIGUREThe temperature difference along the insulator surface between different flow modelsAs indicated in the figure, a temperature difference exists between the results based on turbulent flow model and laminar flow model. Thus, in the analysis of stationary temperature distribution, the turbulent flow model was employed. When dealing with the transient temperature rise of the insulator and GIL, the laminar flow model was applied instead of turbulent flow model. Since a noteworthy reduction of memory and computing time consumption can be achieved, while the computing accuracy will not be disturbed too much. Besides, it is too slow with the SST model when conducting the simulation of transient temperature rise.Volume and surface conductivity of the insulatorInsulator samples with the thickness of 1 mm were applied in the measurement of electric conductivity. Three electrodes system was employed to measure the volume and surface conductivity. In the measurement of volume conductivity, the measurement was conducted in atmospheric pressure. Since both the electric field strength and temperature show obvious influence on the volume conductivity of the insulator [6], the volume conductivity at 20, 40 and 80°C was measured under the field strength of 2, 4 and 6 kV/mm, respectively. Besides, the surface conductivity shows different results in the conditions of SF6 gas and ambient air which may be due to the influence of moisture, while it varies slightly under different pressure in SF6 gas according to our previous measurement. Meanwhile, the surface conductivity varies obviously with the field strength while varies slightly with the temperature as reported [6]. Thus, the surface conductivity under different field strength was measured in SF6 gas of 0.5 MPa. The discrete data were fitted in the simulation to adapt to the continuous variation of temperature and electric field strength. The measured data of volume and surface conductivity is illustrated in Figure 4.4FIGUREThe measured volume and surface electric conductivity of the insulator sample. (a) Volume conductivity, (b) surface conductivityTEMPERATURE DISTRIBUTION OF THE GIL AND INSULATORA typical temperature distribution of the GIL was obtained as shown in Figure 5 under the load current of 5000 A, SF6 gas pressure of 0.5 MPa and ambient temperature of 20°C. Figure 5a is the temperature distribution of Cross‐section A, Figure 5b is the temperature distribution of Cross‐section B, and Figure 5c is the temperature distribution of Cross‐section C. Figure 5d illustrates the three cross‐sections referring to the GIL and insulator. Besides, the surface temperature distribution of the tri‐post insulator is shown in Figure 6.5FIGUREThe typical temperature distribution of the GIL. (a) The temperature distribution of Cross‐section A, (b) the temperature distribution of Cross‐section B, (c) the temperature distribution of Cross‐section C, and (d) the illustration of the cross‐sections6FIGUREThe typical temperature distribution of the insulator surfaceAs shown in Figure 5, a temperature difference of about 30°C is obtained between the conductor and the enclosure under this condition. The gas inside the enclosure pipe shows layered distribution instead of concentric distribution. This could attribute to the natural convection inside the pipe.The flow velocity distribution corresponding to Figure 5 is illustrated in Figure 7. As shown in Figure 7b, the gas is heated by the conductor and moves upwards to the enclosure. And then, the gas moves down along the inside surface of the enclosure. Finally, at the bottom of the enclosure, the gas moves upwards again to the conductor forming the flow circulation. During the flow moves from the top to the bottom, some of the gas directly moves towards the conductor before going down to the bottom. And during this flow circulation, the hot gas from the conductor is cooled. Since the conduction of the SF6 gas is very low, the heat transfer through convection dominates over the conduction. Thus, the gas temperature shows layered distribution in the vertical direction as indicated in Figure 5b.7FIGUREThe flow velocity distribution inside the GIL. (a) The flow velocity distribution of Cross‐section A, (b) the flow velocity distribution of Cross‐section B, and (c) the flow velocity distribution of Cross‐section COn the other hand, the temperature of the tri‐post insulator shows obvious concentric distribution as shown in Figure 5c compared with the gas. This could be due to the high thermal conductivity of the insulator compared with SF6 gas. The conductivity of the insulator is about 1 W/m/K, while the conductivity of SF6 at 0.5 MPa is 0.0136 to 0.0159 W/m/K in the temperature range from 30 to 60°C.Meanwhile, it can be observed that the temperature of the upper part is higher than the lower part of the insulator as shown in Figures 5c and 6. The temperature of the upper post is higher than the other two. And the temperature distribution is not standard concentric. This could attribute to the flow motion of SF6 gas. As shown in Figure 7c, the hot gas heated from the conductor flows upwards along the surface of the upper post to the top of the pipe. Then, the gas moves down along the pipe and is cooled. Some of the cooled gas moves to the bottom and then goes up, and some of the cooled gas moves directly to the insulator. Thus, the lower two posts show lower temperature compared with the upper post.Besides, the temperature difference among the posts is more obvious in the insulator surface as shown in Figure 6 compared with the temperature at the cross‐section as shown in Figure 5c. This is due to the fact that the surface temperature is strongly affected by the gas motion, while the inside temperature is dominated by the conduction through the insulator. Thus, although the gas temperature shows layered distribution, the insulator displays approximate concentric distribution as shown in Figure 5c.Moreover, it can be seen that the flow velocity is very low in most parts of the gas domain. High velocity can be observed near the upper part of the enclosure, near the upper part of the conductor, and the upper part of the symmetry plane as shown in Figure 7b. And the high‐velocity region is very thin compared with the low‐velocity region. Besides, from Figure 5a,b, it can be seen that obvious temperature difference can be observed between the conductor and the nearby gas, between the upper part of the enclosure and the nearby gas. Thus, the SST model is more proper compared with the k–ε model in dealing with the near‐wall region. According to our previous evaluation, more obviously discontinuous temperature distribution would appear in these regions with the k‐ε model. Meanwhile, the gas shows no obvious motion towards or away from the insulator as indicated in Figure 7a. Thus, the selection of the subsection length of the GIL model with an insulator at the middle location is reasonable in this investigation.THE INFLUENCE OF OPERATING CONDITIONS ON THE THERMAL GRADIENTAmbient temperatureThe influence of ambient temperature on the temperature distribution was studied. The load current was 5000 A and the gas pressure was 0.5 MPa. Ambient temperature of 0, 20 and 40°C was applied in the simulation of temperature. Besides, the electric field distribution was obtained under the influence of thermal gradient considering the temperature‐dependent electric conductivity of the insulator. DC high voltage of 500 kV was applied on the central conductor and the enclosure was grounded in the simulation of DC electric field strength.The temperature and electric field strength distribution of the insulator surface is shown in Figure 8 for different ambient temperature. As shown in this figure, with increasing the ambient temperature, the temperature of the whole insulator surface increases. And the electric field strength increases as well. The temperature of the upper post is higher than the other two posts regardless of the ambient temperature. While no obvious difference in electric field strength can be found among the three posts.8FIGUREThe temperature and electric field distribution of the insulator surface with different ambient temperatureTo investigate the influence of ambient temperature on the temperature and electric field distribution more quantitatively, the temperature and electric field strength along the insulator surface were abstracted. Since both temperature and field strength shows symmetric distribution, two curves were selected as indicated in Figure 9c. The surface temperature and electric field strength under different ambient temperature along Curve A and Curve B are illustrated in Figures 9a and 9b, respectively.9FIGUREThe temperature and electric field strength along Curve A and Curve B with different ambient temperature. (a) The temperature and field strength along Curve A, (b) the temperature and field strength along Curve B, and (c) the illustration of the two curvesAs shown in this figure, the surface temperature increases nearly linearly with increasing the ambient temperature. A temperature increase of 20°C can be achieved if the ambient temperature increases by 20°C. This could be due to the decrease in heat convection outside the pipe. The convection can be defined in (12).12−κe∂T∂n=h(Te−Ta)$$\begin{equation}{\rm{ - }}{\kappa _e}\frac{{\partial T}}{{\partial{n}}} = h({T_e} - {T_a})\end{equation}$$Here, κe is the thermal conductivity of the enclosure, n is the normal vector at the interface, h is the natural convection coefficient between the enclosure and the ambient air, Te and Ta are the temperatures of the enclosure and ambient air respectively. With increasing the ambient temperature, the convection coefficient varies little, thus the heat dissipation decreases nearly linearly. While the heat generation from the conductor varies slightly. Thus, the temperature increase of the entire GIL model nearly follows the variation of ambient temperature.It can be seen that a high electric field region appears in the middle part of the post, while the field strength near the conductor and the enclosure are low. The field strength of the three posts shows no obvious difference. The peak of the field strength appears in the middle of the post and slightly inwards as indicated in Figure 8. With increasing the ambient temperature, the field strength of the insulator surface increases obviously as shown in Figures 8 and 9. The peak of field strength increases from 3.94 to 4.33 kV/mm with increasing the temperature from 0 to 40°C. Besides, the peak moves towards the enclosure during this temperature variation as indicated in Figure 9. Thus, the influence of ambient temperature on the field and insulation property should be paid attention when dealing with the operating performance and design of DC‐GIL.Load currentThe influence of load current on the temperature distribution and electric field distribution was investigated. The gas pressure was 0.5 MPa and the ambient temperature was 20°C. And load current of 4000 and 5000 A was employed, respectively. The surface temperature and electric field strength distribution of the tri‐post insulator are illustrated in Figure 10.10FIGUREThe temperature and electric field distribution of the insulator surface with different load currentAs shown in this figure, higher temperature and higher electric field strength are achieved with higher load current. To quantitatively reveal the influence of load current on the temperature and electric field characteristics, the temperature and field strength along the two curves defined previously was obtained. The results are shown in Figure 11 corresponding to Curve A and Curve B, respectively.11FIGUREThe temperature and electric field strength along Curve A and Curve B with different load current. (a) The temperature and field strength along Curve A, and (b) the temperature and field strength along Curve BThe temperature near the conductor shows a more obvious increase with increasing the current compared with the region near the enclosure. This is quite different from the variation in Figure 9 that the temperature of the entire surface synchronously increases with increasing the ambient temperature. From 4000 to 5000 A, an increase of about 10°C is obtained at the conductor. While this temperature increase decreases to about 3°C at the grounded region. This is because the heat generation increases with increasing the load current. While the heat transfer including convection, conduction and radiation doesn't promote synchronously. And the convection outside the pipe varies slightly. Thus, the region near the heat source which is the conductor shows a more obvious temperature increase. Comparing the two figures in Figure 11, there is a more obvious temperature increase along Curve A compared with Curve B.The peak of the field strength increases from 4 to 4.11 with increasing the current from 4000 to 5000 A. This increase is less than that in the variation of ambient temperature since the temperature difference in this section is less obvious. And the location of the peak shows slight movement. While it can't be concluded that the insulation characteristics show no obvious difference just based on the slight variation of field distribution. It is known that the insulation property of the gas depends on the density. And the density distribution is affected by the temperature distribution in the pipe. Once dealing with the discharge characteristics along the gas/insulator interface in an operating GIL/GIS, the thermal gradient would affect the critical voltage or critical field strength due to the variation in gas density distribution [22, 23]. It was reported that the flashover voltage would decrease under the influence of thermal gradient due to the decrease of gas density at the high‐temperature conductor [24]. Thus, although there is a slight difference in field distribution under different load current, the insulation characteristics may perform an obvious difference in discharge characteristics due to the variation of gas density as the consequence of temperature variation.Gas pressureThe influence of SF6 gas pressure on the temperature and electric field distribution was studied. The load current was 5000 A, and the ambient temperature was 20°C. The gas pressure of 0.4, 0.5 and 0.6 MPa was applied in the simulation. The temperature distribution was obtained, and then the electric field characteristics were obtained based on the thermal gradient. The results are shown in Figure 12.12FIGUREThe temperature and electric field distribution of the insulator surface with different gas pressureThe temperature decreases with increasing pressure. To analyze the variation of temperature, the velocity characteristics were obtained for the cases of 0.4 and 0.6 MPa. The velocity distribution at the three cross‐sections corresponding to Figure 7 was illustrated in Figure 13. It can be found that the velocity under different pressure shows a slight difference. While increasing the pressure from 0.4 to 0.6 MPa, the density of SF6 gas increases from 25.2 to 38.9 kg/m3, and the specific heat capacity at constant pressure increases from 0.677 to 0.69 J/kg/K. Thus, the product of density and heat capacity which corresponds to the heat capacity per volume increases obviously. This leads to the promotion of heat convection in the pipe. Hence, the temperature decreases with increasing pressure.13FIGUREThe velocity distribution in the GIL with different gas pressure. (a) The flow velocity distribution of Cross‐section A, (b) the flow velocity distribution of Cross‐section B, and (c) the flow velocity distribution of Cross‐section CThe temperature and field strength along Curve A and Curve B are illustrated in Figure 14 for different gas pressure. A temperature decrease appears near the conductor with increasing pressure. And this temperature difference due to gas pressure decreases towards the enclosure. A decrease of 5°C is achieved by increasing the pressure from 0.4 to 0.5 MPa which is less obvious than that in the variation of ambient temperature and load current. Consequently, the electric field strength shows no obvious difference.14FIGURETemperature and electric field strength along Curve A (a) and Curve B (b) with different gas pressure. (a) The temperature and field strength along Curve A, and (b) the temperature and field strength along Curve BWhile it can't be concluded that the insulation characteristics aren't affected during this variation. Since the gas density increases with increasing pressure, the insulation property would be promoted. Besides, considering the influence of thermal gradient on the gas density distribution, the density distribution under each pressure should be concerned when dealing with the surface discharge characteristics. Thus, the investigation of gas density and electric field distribution under thermal gradient in different operating conditions would be beneficial in understanding the insulation characteristics of the DC‐GIL.Transient overloadThe transient temperature rise of the GIL and the insulator was investigated. The ambient temperature was 20°C, the load current was 5000 A and the gas pressure was 0.5 MPa in this simulation. The transient temperature distribution of the GIL at Cross‐section C is illustrated in Figure 15 as a typical example.15FIGUREThe transient temperature rise of the GIL and insulator under the load current of 5000 AAs shown in this figure, the temperature approaches the quasi‐steady state after about 8 h. The temperature rise at the conductor with increasing time is illustrated in Figure 16. It can be seen that the conductor temperature is about 60°C in the stationary state. And the temperature rise ΔT is about 40°C. After about 3.6 h, 80% of ΔT is achieved. After about 5.2 h, 90% of ΔT is achieved. And after 11 h, 98% of ΔT is achieved. Thus, after several hours the temperature distribution inside the pipe can be regarded as the stationary distribution.16FIGUREThe transient temperature rise of the conductor under the load current of 5000 AThis would be beneficial in the investigation of transient charge accumulation characteristics under thermal‐electric coupled fields. Since the charge accumulation would last for thousands of hours, and slight charge appears in the first couple of hours during the stress process [7, 11, 25]. Thus, the thermal gradient can be first established in the measurement or simulation. And then the investigation of transient charge accumulation can be conducted under the influence of stationary thermal gradient. In this way, the coupled thermal‐electric issue involving transient characteristics can be decoupled and transformed into the issue of transient charge accumulation under a stationary thermal gradient.Besides, the transient temperature rise in the overload condition was investigated. The gas pressure was 0.5 MPa and the ambient temperature was 40°C. A previous load process was employed before conducting the overload process. In the pre‐load process, the load current was 2500 A which is 50% of the load current in normal condition. After the temperature distribution reaches the stationary state, the current was increased to 5500 A which is 1.1 times the normal condition. The transient temperature rise during the overload process is illustrated in Figure 17.17FIGUREThe transient temperature rise of the GIL and the insulator under the overload conditionAs shown in this figure, the temperature distribution reaches the stationary state after several hours which is similar to the variation under the normal condition. The temperature variation of the conductor is illustrated in Figure 18 during this process.18FIGUREThe transient temperature rise of the conductor under the overload conditionIt can be found that the stationary temperature of the conductor is below 90°C. Thus, the temperature rise is lower than 60°C which meets the criterion of lower than 65°C. After about 2.4 h, 80% of the temperature rise is achieved. And after about 3.8 h, 90% of the temperature rise can be achieved. This is shorter than that in the normal condition as indicated in Figure 16. According to the previous discussion, this transient variation of temperature under the overload condition would affect insulation characteristics along the gas/solid interface involving the electric field distribution and gas density distribution.CONCLUSIONThe temperature distribution of the tri‐post insulator in a ±500 kV DC‐GIL was investigated based on the simulation method. And the influence of thermal gradient on the electric field distribution was discussed. The conclusions can be summarized as follows:A horizontally installed DC‐GIL model was employed and a 3D geometry model was applied in the simulation. The thermal conductivity, specific heat capacity, volume and surface electric conductivity of the insulator were measured and applied in the simulation. The temperature of the gas shows a layered distribution pattern due to convection. While the temperature of the insulator shows a radial distribution pattern due to its high thermal conductivity. And the temperature of the upper post is higher than the other two posts.With increasing the ambient temperature, the surface temperature increases nearly linearly following the variation of ambient temperature due to the suppression of convection outside the pipe. With increasing the load current, the temperature near the conductor which acts as the heat source shows an obvious increase. With increasing the gas pressure, the temperature decreases due to the promotion of convection.The electric field strength of the insulator increases if the temperature increases with varying operating conditions including ambient temperature, load current and gas pressure. And the peak of field strength moves towards the enclosure with increasing temperature. The variation in field strength is obvious with varying ambient temperature due to the obvious temperature difference.After about 5 h, 90% of the temperature rise can be achieved in normal and overload conditions, which is quite shorter than the transient charge accumulation process. Thus, the investigation of transient charge accumulation under thermal‐electric coupled fields can be conducted based on the stationary thermal gradient.Considering the influence of thermal gradient on the gas density and electric field distribution, the investigation of temperature characteristics of the DC‐GIL and the tri‐post insulator is necessary when dealing with the insulating performance under different operating conditions.AUTHOR CONTRIBUTIONSXiaolong Li: Data curation, Formal analysis, Funding acquisition, Investigation, Writing ‐ original draft; Mingde Wan: Methodology, Software, Visualization; Wen Wang: Validation, Writing ‐ review & editing; Zhenxin Geng: Formal analysis, Funding acquisition; Xin Lin: Project administration, Resources, Supervision.ACKNOWLEDGEMENTSThis work was supported by the National Natural Science Foundation of China (No. 51807122) and the Scientific Research Project of The Educational Department of Liaoning Province (No. LQGD2019003 and LJGD2019005).CONFLICT OF INTERESTThe authors declare no conflict of interest.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.REFERENCESDu, B.X., Liang, H.C., Li, J., et al.: Electrical field distribution along SF6/N2 filled DC‐GIS/GIL epoxy spacer. IEEE Trans. Dielectr. Electr. Insul. 25(04), 1202–1210 (2018)Chen, Y., Cui, B., Huang, C., et al.: Life test and prediction of insulator materials for UHV GIL. High Voltage Eng. 46(12), 4106–4112 (2020)Chen, G., Tu, Y., Wang, C., et al.: Analysis on temperature distribution and current‐carrying capacity of GIL filled with fluoronitriles‐CO₂ gas mixture. J. Electr. Eng. Technol. 13(06), 2402–2411 (2018)Koch, H.: Gas‐Insulated Transmission Lines, pp. 146–148, John Wiley & Sons, London, UK (2012)Okabe, S., Ueta, G., Nojima, K.: Resistance characteristics and electrification characteristics of GIS epoxy insulators under DC voltage. IEEE Trans. Dielectr. Electr. Insul. 21(03), 1260–1267 (2014)Zavattoni, L.: Conduction phenomena through gas and insulating solids in HVDC gas insulated substations, and consequences on electric field distribution. Ph.D. dissertation, Université de Grenoble, Grenoble, France (2014)Straumann, U., Schüller, M., Franck, C.M.: Theoretical investigation of HVDC disc spacer charging in SF6 gas insulated systems. IEEE Trans. Dielectr. Electr. Insul. 19(06), 2196–2205 (2012)Xing, Y., Wang, Z., Liu, L., et al.: Defects and failure types of solid insulation in gas insulated switchgear: In situ study and case analysis. High Voltage 7(1), 158–164 (2021)Xue, J., Chen, J., Dong, J., et al.: A novel sight for understanding surface charging phenomena on downsized HVDC GIL spacers with non‐uniform conductivity. Int. J. Elec. Power. 120, 105979 (2020)Winter, A., Kindersberger, J.: Transient field distribution in gas‐solid insulation systems under DC voltages. IEEE Trans. Dielectr. Electr. Insul. 21(01), 116–128 (2014)Yan, W., Li, C., Lei, Z., et al.: Surface charging on HVDC spacers considering time‐varying effect of temperature and electric fields. IEEE Trans. Dielectr. Electr. Insul. 26(04), 1316–1324 (2019)Liang, H.C., Du, B.X., Li, J.: Electric field regulation and parameter optimization of surface nonlinear conductivity spacer for 500 kV DC‐GIL. IEEE Trans. Dielectr. Electr. Insul. 27(04), 1330–1338 (2020)Niu, H., Chen, Z., Zhang, H., et al.: Multi‐physical coupling field study of 500 kV GIL: Simulation, characteristics, and analysis. IEEE Access 8, 131439–131448 (2020)Qiao, Y., Liang, R., Gao, P., et al.: Heat transfer analysis of different conditions for SF6/N2 gas‐insulated transmission lines. IEEE Trans. Power Delivery 36(02), 831–840 (2021)Du, B., Wang, M., Li, J., et al.: Temperature dependent surface charge and discharge behavior of epoxy/AlN nanocomposites. IEEE Trans. Dielectr. Electr. Insul. 25(04), 1300–1307 (2018)Zhang, Y., Tuo, R., Yang, W., et al.: Improved thermal and electrical properties of epoxy resin composites by dopamine and silane coupling agent modified hexagonal BN. Polym. Compos. 41(11), 4727–4739 (2020)Lienhard, H.I.V., Lienhard, H.V.: A Heat Transfer Textbook. 3rd ed., p. 528, Phlogiston Press, Cambridge, USA (2003)Yunus, A.C.: Heat Transfer: A Practical Approach, 2nd ed., pp. 465–466, Mcgraw‐Hill, New York, USA (2002)Kueh, T.H., Goldstein, R.J.: Correlating equations for natural convection heat transfer between horizontal circular cylinders. Int. J. Heat Mass Transfer 19(10), 1127–1134 (1976)COMSOL Inc.: CFD Module User's Guide, pp. 207–209, COMSOL, Burlington, USA (2019)Rebzani, N., Clavel, E., Marty, P., et al.: Numerical multiphysics modeling of temperature rises in gas insulated busbars. IEEE Trans. Dielectr. Electr. Insul. 23(05), 2579–2586 (2016)Hering, M., Speck, J., Gromann, S., et al.: Influence of gas temperature on the breakdown voltage in gas‐insulated systems. IEEE Trans. Dielectr. Electr. Insul. 24(01), 401–408 (2017)Lu, S., Zhang, L., Zhou, H., et al.: Effect of temperature on flashover voltage of epoxy column at power frequency. High Voltage Eng. 45(09), 2774–2781 (2019)Hisayasu, M., Ryoji, K.: Surface flashover characteristics of ceramic insulation in gases at 40°C‐700°C. IEEJ Trans. Fundam. Mater. 117(08), 832–838 (1997)Ma, G.M., Zhou, H.Y., Lu, S.J., et al.: Effect of material volume conductivity on surface charges accumulation on spacers under DC electro‐thermal coupling stress. IEEE Trans. Dielectr. Electr. Insul. 25(04), 1211–1220 (2018) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png IET Generation Transmission & Distribution Wiley

Temperature and electric field distribution of tri‐post insulator in DC‐GIL based on numerical multiphysics modelling

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© 2023 The Institution of Engineering and Technology.
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1751-8695
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10.1049/gtd2.12729
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Abstract

INTRODUCTIONDue to the advantages including large capacity, ease to be maintained, safety operation and space‐saving, gas‐insulated transmission lines (GIL) attract much attention in the past decades. Inside the GIL enclosure, high‐pressure gas such as SF6 and SF6/N2 mixture acts as the insulating medium, while the solid insulators are often designed as disc‐type, basin‐type and post‐type function as the supporters [1, 2]. With the development of high voltage direct current (HVDC) power systems, DC‐GIL attracts much attention. Thus, the operation characteristics of DC‐GIL should be investigated carefully.During long‐term operation, current up to several kiloamperes flows through the central conductor, and considerable Joule heat will consequently be generated. And the thermal gradient is established via heat conduction, convection and radiation inside the enclosure [3]. For the safe operation, standards have been suggested including the temperature rise for the conductor, insulator and enclosure [4]. Compared with the GIL in alternating current (AC) systems, different characteristics appear in the heat generation of the GIL in DC systems. Under the stress of DC, the heat generation due to eddy current can be neglected along with the heat generation in the enclosure. This would lead to different heat generation and thermal gradient distribution inside the enclosure. Besides, since the permittivity of the insulator varies slightly with temperature, the influence of thermal gradient on the electric field distribution of the GIL can be neglected under the stress of AC voltage. While the electric conductivity of the insulator, especially the volume electric conductivity, will increase nearly exponentially with increasing the temperature [5]. Thus, an obvious influence of thermal gradient on the electric field distribution of the insulator can be achieved [6]. Moreover, charge will accumulate on the insulator surface and affect the field distribution [7]. This acts as an important risk referring to flashover for the DC‐GIL during long‐term operation [8, 9]. It was reported that the thermal gradient would show an obvious influence on the surface charge accumulation characteristics which further affects the electric field distribution in an operating DC‐GIL [10]. Thus, the thermal gradient is one of the key issues in dealing with the insulation property of the DC‐GIL.Since it is difficult to obtain the spatial temperature distribution based on measurements, simulation is widely employed to deal with the temperature characteristics of the GIL and insulator. Rotational symmetry models were often applied to investigate the thermal gradient inside the vertically installed DC‐GIL with insulators [11, 12]. The thermal gradient of the insulator in a horizontally installed DC‐GIL is seldom involved, although it is widely applied in the transmission system. And 3D geometry model needs to be employed considering the temperature distribution characteristics in the horizontal GIL [13]. Besides, the operating conditions including the load current, ambient temperature, and gas pressure were reported to affect the thermal gradient of AC‐GILs [14], the influence on the DC‐GIL insulators needs to be revealed. Moreover, it is noted that the filler applied in the insulator would affect both the thermal and electric properties including the thermal conductivity, volume conductivity and surface conductivity [15, 16]. These parameters would affect the thermal gradient and electric field distribution characteristics of the DC‐GIL insulator under thermal–electric coupled fields. While parameters from different literature were often employed in the same simulation case in previous research. These parameters may be obtained based on the insulator sample with different kinds and fractions of fillers. This may cause inaccuracy in the simulation result.Here, the thermal gradient of a tri‐post type insulator inside a ±500 kV DC‐GIL was investigated. A 3D simulation model was established to deal with this horizontally installed GIL model. The thermal and electric parameters of the insulator were measured. Based on these parameters, the influence of operating conditions including ambient temperature, load current, and gas pressure on the thermal gradient characteristics was studied. The transient temperature rise under over‐load condition was studied as well. The electric field distribution of the insulator under the thermal‐electric coupled field was investigated. The conclusion in this paper will be beneficial in the design, operation and maintenance of DC‐GILs referring to the thermal and insulation property.SIMULATION METHODGeometry and parameterA ±500 kV DC‐GIL model was applied in this study and the geometry is illustrated in Figure 1. It should be noted that this GIL model is horizontally installed and a tri‐post type insulator is inside the GIL. The geometry, thermal and electrical parameters of the GIL are illustrated in Table 1.1FIGUREThe ±500 kV DC‐GIL with tri‐post insulator1TABLEThe parameters of the conductor and enclosureConductorEnclosureInner diameter (mm)100510Thickness (mm)208Density (kg/m3)26902660The density of the insulator was 2300 kg/m3 in this study. The thermal conductivity and specific heat capacity of the insulator at various temperatures were measured via the Transient Hot‐Wire (THW) method and Differential Scanning Calorimetry (DSC) method, respectively. The measured data with varying temperature is shown in Figure 2. And these data were fitted in the COMSOL Multiphysics software.2FIGUREThe thermal conductivity and specific heat capacity of the insulatorHeat generationCurrent flows through the aluminium conductor and Joule heat is generated as defined in (1),1P=I2R=I2LScondσAl$$\begin{equation}P{\rm{ = }}{I^2}R = \frac{{{I^2}L}}{{{S_{cond}}{\sigma _{{\rm{Al}}}}}}\end{equation}$$where P is the heating power, I is the load current, R is the resistivity of the conductor, L is the length of the conductor, Scond is the sectional area of the tubular conductor, σAl is the electric conductivity of the conductor. In this study, the conductivity varies with the temperature as illustrated in (2) [3, 14],2σAl(T)=σ201+0.004(T−293)$$\begin{equation}{\sigma _{{\rm{Al}}}}(T) = \frac{{{\sigma _{{\rm{20}}}}}}{{1 + 0.004(T - 293)}}\end{equation}$$where T is the temperature of the conductor and σ20 is the conductivity at 20°C (293 K).Heat transferThe heat generated from the central conductor will dissipate to the surrounding via conduction, convection and radiation. The heat conduction existing in the conductor, enclosure, gas and the insulator follows the equations below:3ρCp∂T∂t+∇·(q+qr)=Q$$\begin{equation}\rho {C_p}\frac{{\partial T}}{{\partial t}} + \nabla \cdot ({\bf{q}} + {{\bf{q}}_r}) = Q\end{equation}$$4q=−κ∇T$$\begin{equation}{\bf{q}} = - \kappa \nabla T\end{equation}$$where ρ is the density, Cp is the specific heat capacity, q is the heat flux due to conduction, qr is the heat flux due to radiation, κ is the thermal conductivity, Q represents the heat source for the conductor while it is zero for the enclosure, gas and insulator.Inside the enclosure pipe, heat will be transferred via radiation between the insulator and conductor, between the insulator and enclosure, between the conductor and enclosure. Besides, the radiation exists between the enclosure and the ambient surroundings. The radiation in this study follows the equation below,5ebT=n2σSBT4$$\begin{equation}{e_b}\left( T \right) = {n^2}{\sigma _{SB}}{T^4}\end{equation}$$6q=εG−ebT$$\begin{equation}q = \varepsilon \left[ {G - {e_b}\left( T \right)} \right]\end{equation}$$where eb(T) is the power radiated across all wavelengths, n is the refractive index, σSB is the Stefan‐Boltzmann constant, G is the incoming radiative heat flux, q is the net inward radiative heat flux and T is the surface temperature. ε is the surface emissivity which is 0.2, 0.93, 0.92 and 0.93 for the conductor, insulator, outside and inside surface of the enclosure, respectively [17].Navier–Stokes equations were applied to deal with the heat convection in this study as illustrated below referring to the conservation of mass (7), the conservation of energy (8), and the conservation of momentum (9).7∂ρ∂t+∇·(ρu)=0$$\begin{equation}\frac{{\partial \rho }}{{\partial t}} + \nabla \cdot (\rho {\bf{u}}) = 0\end{equation}$$8ρCp∂T∂t+u·∇T+∇·q=Q$$\begin{equation} \rho {C_p} \left(\frac{{\partial T}}{{\partial t}} + {\bf{u}} \cdot \nabla T \right) + \nabla \cdot {\bf{q}} = Q\end{equation}$$9ρ∂u∂t+ρu·∇u=∇·−pI+μ(∇u+(∇u)T)−23μ(∇·u)I+ρg$$\begin{eqnarray} && \rho \frac{{\partial {\bf{u}}}}{{\partial t}} + \rho {\bf{u}} \cdot \nabla {\bf{u}}\nonumber\\ && = \nabla \cdot \left[ { - p{\bf{I}} + \mu (\nabla {\bf{u}} + {{(\nabla {\bf{u}})}^T}) - \frac{2}{3}\mu (\nabla \cdot {\bf{u}}){\bf{I}}} \right] + \rho {\bf{g}}\end{eqnarray}$$Here, u is the velocity vector, p is the pressure, μ is the dynamic viscosity, g is the gravity vector and Q contains heat sources other than viscous heating.The thermal conductivity and the dynamic viscosity of the gas follow Sutherland's law [3, 14]. The relationship involving the gas pressure, density and temperature follows the ideal gas law.Flow modelThe GIL model can be considered as a horizontal arrangement cylinder from the view outside the enclosure pipe. And the space outside the GIL is considered infinite. In this way, the natural convection model outside the GIL can be selected.When dealing with the convection inside the enclosure, the central conductor is the heat source and the space referring to convection is finite. It can be regarded as a horizontally coaxial model with the central cylinder acting as the heat source. Since it is natural convection inside the enclosure, the dimensionless Grashof number (Gr) and Rayleigh number (Ra) can be used to determine whether turbulent flow model or laminar flow model should be applied to deal with the natural convection [18]. The calculation of Gr and Ra is defined as below:10Gr=gβ(Ts−T∞)Lc3v2$$\begin{equation}Gr = \frac{{g\beta ({T_s} - {T_\infty }){L_c}^3}}{{{v^2}}}\end{equation}$$11Ra=GrPr=gβ(Ts−T∞)Lc3v2Pr$$\begin{equation}Ra = GrPr = \frac{{g\beta ({T_s} - {T_\infty }){L_c}^3}}{{{v^2}}}Pr\end{equation}$$12β=−1ρρ∞−ρT∞−T$$\begin{equation}\beta = - \frac{1}{\rho }\frac{{{\rho _\infty } - \rho }}{{{T_\infty } - T}}\end{equation}$$where g is gravitational acceleration, β is the coefficient of volume expansion of SF6, Ts is the surface temperature of the conductor, T∞ is the temperature sufficiently far from the conductor surface and υ is the kinematic viscosity of SF6. Lc is the characteristic length of the geometry which is the gap between the conductor and the enclosure. Pr represents the Prandtl number which is 0.7.The calculated Gr and Ra fall into the range from 109 to 1010, which indicates a turbulent flow model inside the enclosure [19]. Since it is important to obtain the surface temperature of the insulator for further investigation of surface charge and field distribution, shear stress transport (SST) turbulent flow model was applied to deal with the flow motion considering its advantage in near‐wall treatment compared with the k‐ε model [20, 21]. The temperature distribution based on the laminar flow model was obtained as well. The surface temperature along the insulator surface involving the two kinds of flow models is illustrated in Figure 3.3FIGUREThe temperature difference along the insulator surface between different flow modelsAs indicated in the figure, a temperature difference exists between the results based on turbulent flow model and laminar flow model. Thus, in the analysis of stationary temperature distribution, the turbulent flow model was employed. When dealing with the transient temperature rise of the insulator and GIL, the laminar flow model was applied instead of turbulent flow model. Since a noteworthy reduction of memory and computing time consumption can be achieved, while the computing accuracy will not be disturbed too much. Besides, it is too slow with the SST model when conducting the simulation of transient temperature rise.Volume and surface conductivity of the insulatorInsulator samples with the thickness of 1 mm were applied in the measurement of electric conductivity. Three electrodes system was employed to measure the volume and surface conductivity. In the measurement of volume conductivity, the measurement was conducted in atmospheric pressure. Since both the electric field strength and temperature show obvious influence on the volume conductivity of the insulator [6], the volume conductivity at 20, 40 and 80°C was measured under the field strength of 2, 4 and 6 kV/mm, respectively. Besides, the surface conductivity shows different results in the conditions of SF6 gas and ambient air which may be due to the influence of moisture, while it varies slightly under different pressure in SF6 gas according to our previous measurement. Meanwhile, the surface conductivity varies obviously with the field strength while varies slightly with the temperature as reported [6]. Thus, the surface conductivity under different field strength was measured in SF6 gas of 0.5 MPa. The discrete data were fitted in the simulation to adapt to the continuous variation of temperature and electric field strength. The measured data of volume and surface conductivity is illustrated in Figure 4.4FIGUREThe measured volume and surface electric conductivity of the insulator sample. (a) Volume conductivity, (b) surface conductivityTEMPERATURE DISTRIBUTION OF THE GIL AND INSULATORA typical temperature distribution of the GIL was obtained as shown in Figure 5 under the load current of 5000 A, SF6 gas pressure of 0.5 MPa and ambient temperature of 20°C. Figure 5a is the temperature distribution of Cross‐section A, Figure 5b is the temperature distribution of Cross‐section B, and Figure 5c is the temperature distribution of Cross‐section C. Figure 5d illustrates the three cross‐sections referring to the GIL and insulator. Besides, the surface temperature distribution of the tri‐post insulator is shown in Figure 6.5FIGUREThe typical temperature distribution of the GIL. (a) The temperature distribution of Cross‐section A, (b) the temperature distribution of Cross‐section B, (c) the temperature distribution of Cross‐section C, and (d) the illustration of the cross‐sections6FIGUREThe typical temperature distribution of the insulator surfaceAs shown in Figure 5, a temperature difference of about 30°C is obtained between the conductor and the enclosure under this condition. The gas inside the enclosure pipe shows layered distribution instead of concentric distribution. This could attribute to the natural convection inside the pipe.The flow velocity distribution corresponding to Figure 5 is illustrated in Figure 7. As shown in Figure 7b, the gas is heated by the conductor and moves upwards to the enclosure. And then, the gas moves down along the inside surface of the enclosure. Finally, at the bottom of the enclosure, the gas moves upwards again to the conductor forming the flow circulation. During the flow moves from the top to the bottom, some of the gas directly moves towards the conductor before going down to the bottom. And during this flow circulation, the hot gas from the conductor is cooled. Since the conduction of the SF6 gas is very low, the heat transfer through convection dominates over the conduction. Thus, the gas temperature shows layered distribution in the vertical direction as indicated in Figure 5b.7FIGUREThe flow velocity distribution inside the GIL. (a) The flow velocity distribution of Cross‐section A, (b) the flow velocity distribution of Cross‐section B, and (c) the flow velocity distribution of Cross‐section COn the other hand, the temperature of the tri‐post insulator shows obvious concentric distribution as shown in Figure 5c compared with the gas. This could be due to the high thermal conductivity of the insulator compared with SF6 gas. The conductivity of the insulator is about 1 W/m/K, while the conductivity of SF6 at 0.5 MPa is 0.0136 to 0.0159 W/m/K in the temperature range from 30 to 60°C.Meanwhile, it can be observed that the temperature of the upper part is higher than the lower part of the insulator as shown in Figures 5c and 6. The temperature of the upper post is higher than the other two. And the temperature distribution is not standard concentric. This could attribute to the flow motion of SF6 gas. As shown in Figure 7c, the hot gas heated from the conductor flows upwards along the surface of the upper post to the top of the pipe. Then, the gas moves down along the pipe and is cooled. Some of the cooled gas moves to the bottom and then goes up, and some of the cooled gas moves directly to the insulator. Thus, the lower two posts show lower temperature compared with the upper post.Besides, the temperature difference among the posts is more obvious in the insulator surface as shown in Figure 6 compared with the temperature at the cross‐section as shown in Figure 5c. This is due to the fact that the surface temperature is strongly affected by the gas motion, while the inside temperature is dominated by the conduction through the insulator. Thus, although the gas temperature shows layered distribution, the insulator displays approximate concentric distribution as shown in Figure 5c.Moreover, it can be seen that the flow velocity is very low in most parts of the gas domain. High velocity can be observed near the upper part of the enclosure, near the upper part of the conductor, and the upper part of the symmetry plane as shown in Figure 7b. And the high‐velocity region is very thin compared with the low‐velocity region. Besides, from Figure 5a,b, it can be seen that obvious temperature difference can be observed between the conductor and the nearby gas, between the upper part of the enclosure and the nearby gas. Thus, the SST model is more proper compared with the k–ε model in dealing with the near‐wall region. According to our previous evaluation, more obviously discontinuous temperature distribution would appear in these regions with the k‐ε model. Meanwhile, the gas shows no obvious motion towards or away from the insulator as indicated in Figure 7a. Thus, the selection of the subsection length of the GIL model with an insulator at the middle location is reasonable in this investigation.THE INFLUENCE OF OPERATING CONDITIONS ON THE THERMAL GRADIENTAmbient temperatureThe influence of ambient temperature on the temperature distribution was studied. The load current was 5000 A and the gas pressure was 0.5 MPa. Ambient temperature of 0, 20 and 40°C was applied in the simulation of temperature. Besides, the electric field distribution was obtained under the influence of thermal gradient considering the temperature‐dependent electric conductivity of the insulator. DC high voltage of 500 kV was applied on the central conductor and the enclosure was grounded in the simulation of DC electric field strength.The temperature and electric field strength distribution of the insulator surface is shown in Figure 8 for different ambient temperature. As shown in this figure, with increasing the ambient temperature, the temperature of the whole insulator surface increases. And the electric field strength increases as well. The temperature of the upper post is higher than the other two posts regardless of the ambient temperature. While no obvious difference in electric field strength can be found among the three posts.8FIGUREThe temperature and electric field distribution of the insulator surface with different ambient temperatureTo investigate the influence of ambient temperature on the temperature and electric field distribution more quantitatively, the temperature and electric field strength along the insulator surface were abstracted. Since both temperature and field strength shows symmetric distribution, two curves were selected as indicated in Figure 9c. The surface temperature and electric field strength under different ambient temperature along Curve A and Curve B are illustrated in Figures 9a and 9b, respectively.9FIGUREThe temperature and electric field strength along Curve A and Curve B with different ambient temperature. (a) The temperature and field strength along Curve A, (b) the temperature and field strength along Curve B, and (c) the illustration of the two curvesAs shown in this figure, the surface temperature increases nearly linearly with increasing the ambient temperature. A temperature increase of 20°C can be achieved if the ambient temperature increases by 20°C. This could be due to the decrease in heat convection outside the pipe. The convection can be defined in (12).12−κe∂T∂n=h(Te−Ta)$$\begin{equation}{\rm{ - }}{\kappa _e}\frac{{\partial T}}{{\partial{n}}} = h({T_e} - {T_a})\end{equation}$$Here, κe is the thermal conductivity of the enclosure, n is the normal vector at the interface, h is the natural convection coefficient between the enclosure and the ambient air, Te and Ta are the temperatures of the enclosure and ambient air respectively. With increasing the ambient temperature, the convection coefficient varies little, thus the heat dissipation decreases nearly linearly. While the heat generation from the conductor varies slightly. Thus, the temperature increase of the entire GIL model nearly follows the variation of ambient temperature.It can be seen that a high electric field region appears in the middle part of the post, while the field strength near the conductor and the enclosure are low. The field strength of the three posts shows no obvious difference. The peak of the field strength appears in the middle of the post and slightly inwards as indicated in Figure 8. With increasing the ambient temperature, the field strength of the insulator surface increases obviously as shown in Figures 8 and 9. The peak of field strength increases from 3.94 to 4.33 kV/mm with increasing the temperature from 0 to 40°C. Besides, the peak moves towards the enclosure during this temperature variation as indicated in Figure 9. Thus, the influence of ambient temperature on the field and insulation property should be paid attention when dealing with the operating performance and design of DC‐GIL.Load currentThe influence of load current on the temperature distribution and electric field distribution was investigated. The gas pressure was 0.5 MPa and the ambient temperature was 20°C. And load current of 4000 and 5000 A was employed, respectively. The surface temperature and electric field strength distribution of the tri‐post insulator are illustrated in Figure 10.10FIGUREThe temperature and electric field distribution of the insulator surface with different load currentAs shown in this figure, higher temperature and higher electric field strength are achieved with higher load current. To quantitatively reveal the influence of load current on the temperature and electric field characteristics, the temperature and field strength along the two curves defined previously was obtained. The results are shown in Figure 11 corresponding to Curve A and Curve B, respectively.11FIGUREThe temperature and electric field strength along Curve A and Curve B with different load current. (a) The temperature and field strength along Curve A, and (b) the temperature and field strength along Curve BThe temperature near the conductor shows a more obvious increase with increasing the current compared with the region near the enclosure. This is quite different from the variation in Figure 9 that the temperature of the entire surface synchronously increases with increasing the ambient temperature. From 4000 to 5000 A, an increase of about 10°C is obtained at the conductor. While this temperature increase decreases to about 3°C at the grounded region. This is because the heat generation increases with increasing the load current. While the heat transfer including convection, conduction and radiation doesn't promote synchronously. And the convection outside the pipe varies slightly. Thus, the region near the heat source which is the conductor shows a more obvious temperature increase. Comparing the two figures in Figure 11, there is a more obvious temperature increase along Curve A compared with Curve B.The peak of the field strength increases from 4 to 4.11 with increasing the current from 4000 to 5000 A. This increase is less than that in the variation of ambient temperature since the temperature difference in this section is less obvious. And the location of the peak shows slight movement. While it can't be concluded that the insulation characteristics show no obvious difference just based on the slight variation of field distribution. It is known that the insulation property of the gas depends on the density. And the density distribution is affected by the temperature distribution in the pipe. Once dealing with the discharge characteristics along the gas/insulator interface in an operating GIL/GIS, the thermal gradient would affect the critical voltage or critical field strength due to the variation in gas density distribution [22, 23]. It was reported that the flashover voltage would decrease under the influence of thermal gradient due to the decrease of gas density at the high‐temperature conductor [24]. Thus, although there is a slight difference in field distribution under different load current, the insulation characteristics may perform an obvious difference in discharge characteristics due to the variation of gas density as the consequence of temperature variation.Gas pressureThe influence of SF6 gas pressure on the temperature and electric field distribution was studied. The load current was 5000 A, and the ambient temperature was 20°C. The gas pressure of 0.4, 0.5 and 0.6 MPa was applied in the simulation. The temperature distribution was obtained, and then the electric field characteristics were obtained based on the thermal gradient. The results are shown in Figure 12.12FIGUREThe temperature and electric field distribution of the insulator surface with different gas pressureThe temperature decreases with increasing pressure. To analyze the variation of temperature, the velocity characteristics were obtained for the cases of 0.4 and 0.6 MPa. The velocity distribution at the three cross‐sections corresponding to Figure 7 was illustrated in Figure 13. It can be found that the velocity under different pressure shows a slight difference. While increasing the pressure from 0.4 to 0.6 MPa, the density of SF6 gas increases from 25.2 to 38.9 kg/m3, and the specific heat capacity at constant pressure increases from 0.677 to 0.69 J/kg/K. Thus, the product of density and heat capacity which corresponds to the heat capacity per volume increases obviously. This leads to the promotion of heat convection in the pipe. Hence, the temperature decreases with increasing pressure.13FIGUREThe velocity distribution in the GIL with different gas pressure. (a) The flow velocity distribution of Cross‐section A, (b) the flow velocity distribution of Cross‐section B, and (c) the flow velocity distribution of Cross‐section CThe temperature and field strength along Curve A and Curve B are illustrated in Figure 14 for different gas pressure. A temperature decrease appears near the conductor with increasing pressure. And this temperature difference due to gas pressure decreases towards the enclosure. A decrease of 5°C is achieved by increasing the pressure from 0.4 to 0.5 MPa which is less obvious than that in the variation of ambient temperature and load current. Consequently, the electric field strength shows no obvious difference.14FIGURETemperature and electric field strength along Curve A (a) and Curve B (b) with different gas pressure. (a) The temperature and field strength along Curve A, and (b) the temperature and field strength along Curve BWhile it can't be concluded that the insulation characteristics aren't affected during this variation. Since the gas density increases with increasing pressure, the insulation property would be promoted. Besides, considering the influence of thermal gradient on the gas density distribution, the density distribution under each pressure should be concerned when dealing with the surface discharge characteristics. Thus, the investigation of gas density and electric field distribution under thermal gradient in different operating conditions would be beneficial in understanding the insulation characteristics of the DC‐GIL.Transient overloadThe transient temperature rise of the GIL and the insulator was investigated. The ambient temperature was 20°C, the load current was 5000 A and the gas pressure was 0.5 MPa in this simulation. The transient temperature distribution of the GIL at Cross‐section C is illustrated in Figure 15 as a typical example.15FIGUREThe transient temperature rise of the GIL and insulator under the load current of 5000 AAs shown in this figure, the temperature approaches the quasi‐steady state after about 8 h. The temperature rise at the conductor with increasing time is illustrated in Figure 16. It can be seen that the conductor temperature is about 60°C in the stationary state. And the temperature rise ΔT is about 40°C. After about 3.6 h, 80% of ΔT is achieved. After about 5.2 h, 90% of ΔT is achieved. And after 11 h, 98% of ΔT is achieved. Thus, after several hours the temperature distribution inside the pipe can be regarded as the stationary distribution.16FIGUREThe transient temperature rise of the conductor under the load current of 5000 AThis would be beneficial in the investigation of transient charge accumulation characteristics under thermal‐electric coupled fields. Since the charge accumulation would last for thousands of hours, and slight charge appears in the first couple of hours during the stress process [7, 11, 25]. Thus, the thermal gradient can be first established in the measurement or simulation. And then the investigation of transient charge accumulation can be conducted under the influence of stationary thermal gradient. In this way, the coupled thermal‐electric issue involving transient characteristics can be decoupled and transformed into the issue of transient charge accumulation under a stationary thermal gradient.Besides, the transient temperature rise in the overload condition was investigated. The gas pressure was 0.5 MPa and the ambient temperature was 40°C. A previous load process was employed before conducting the overload process. In the pre‐load process, the load current was 2500 A which is 50% of the load current in normal condition. After the temperature distribution reaches the stationary state, the current was increased to 5500 A which is 1.1 times the normal condition. The transient temperature rise during the overload process is illustrated in Figure 17.17FIGUREThe transient temperature rise of the GIL and the insulator under the overload conditionAs shown in this figure, the temperature distribution reaches the stationary state after several hours which is similar to the variation under the normal condition. The temperature variation of the conductor is illustrated in Figure 18 during this process.18FIGUREThe transient temperature rise of the conductor under the overload conditionIt can be found that the stationary temperature of the conductor is below 90°C. Thus, the temperature rise is lower than 60°C which meets the criterion of lower than 65°C. After about 2.4 h, 80% of the temperature rise is achieved. And after about 3.8 h, 90% of the temperature rise can be achieved. This is shorter than that in the normal condition as indicated in Figure 16. According to the previous discussion, this transient variation of temperature under the overload condition would affect insulation characteristics along the gas/solid interface involving the electric field distribution and gas density distribution.CONCLUSIONThe temperature distribution of the tri‐post insulator in a ±500 kV DC‐GIL was investigated based on the simulation method. And the influence of thermal gradient on the electric field distribution was discussed. The conclusions can be summarized as follows:A horizontally installed DC‐GIL model was employed and a 3D geometry model was applied in the simulation. The thermal conductivity, specific heat capacity, volume and surface electric conductivity of the insulator were measured and applied in the simulation. The temperature of the gas shows a layered distribution pattern due to convection. While the temperature of the insulator shows a radial distribution pattern due to its high thermal conductivity. And the temperature of the upper post is higher than the other two posts.With increasing the ambient temperature, the surface temperature increases nearly linearly following the variation of ambient temperature due to the suppression of convection outside the pipe. With increasing the load current, the temperature near the conductor which acts as the heat source shows an obvious increase. With increasing the gas pressure, the temperature decreases due to the promotion of convection.The electric field strength of the insulator increases if the temperature increases with varying operating conditions including ambient temperature, load current and gas pressure. And the peak of field strength moves towards the enclosure with increasing temperature. The variation in field strength is obvious with varying ambient temperature due to the obvious temperature difference.After about 5 h, 90% of the temperature rise can be achieved in normal and overload conditions, which is quite shorter than the transient charge accumulation process. Thus, the investigation of transient charge accumulation under thermal‐electric coupled fields can be conducted based on the stationary thermal gradient.Considering the influence of thermal gradient on the gas density and electric field distribution, the investigation of temperature characteristics of the DC‐GIL and the tri‐post insulator is necessary when dealing with the insulating performance under different operating conditions.AUTHOR CONTRIBUTIONSXiaolong Li: Data curation, Formal analysis, Funding acquisition, Investigation, Writing ‐ original draft; Mingde Wan: Methodology, Software, Visualization; Wen Wang: Validation, Writing ‐ review & editing; Zhenxin Geng: Formal analysis, Funding acquisition; Xin Lin: Project administration, Resources, Supervision.ACKNOWLEDGEMENTSThis work was supported by the National Natural Science Foundation of China (No. 51807122) and the Scientific Research Project of The Educational Department of Liaoning Province (No. LQGD2019003 and LJGD2019005).CONFLICT OF INTERESTThe authors declare no conflict of interest.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.REFERENCESDu, B.X., Liang, H.C., Li, J., et al.: Electrical field distribution along SF6/N2 filled DC‐GIS/GIL epoxy spacer. IEEE Trans. Dielectr. Electr. Insul. 25(04), 1202–1210 (2018)Chen, Y., Cui, B., Huang, C., et al.: Life test and prediction of insulator materials for UHV GIL. High Voltage Eng. 46(12), 4106–4112 (2020)Chen, G., Tu, Y., Wang, C., et al.: Analysis on temperature distribution and current‐carrying capacity of GIL filled with fluoronitriles‐CO₂ gas mixture. J. Electr. Eng. Technol. 13(06), 2402–2411 (2018)Koch, H.: Gas‐Insulated Transmission Lines, pp. 146–148, John Wiley & Sons, London, UK (2012)Okabe, S., Ueta, G., Nojima, K.: Resistance characteristics and electrification characteristics of GIS epoxy insulators under DC voltage. IEEE Trans. Dielectr. Electr. Insul. 21(03), 1260–1267 (2014)Zavattoni, L.: Conduction phenomena through gas and insulating solids in HVDC gas insulated substations, and consequences on electric field distribution. Ph.D. dissertation, Université de Grenoble, Grenoble, France (2014)Straumann, U., Schüller, M., Franck, C.M.: Theoretical investigation of HVDC disc spacer charging in SF6 gas insulated systems. IEEE Trans. Dielectr. Electr. Insul. 19(06), 2196–2205 (2012)Xing, Y., Wang, Z., Liu, L., et al.: Defects and failure types of solid insulation in gas insulated switchgear: In situ study and case analysis. High Voltage 7(1), 158–164 (2021)Xue, J., Chen, J., Dong, J., et al.: A novel sight for understanding surface charging phenomena on downsized HVDC GIL spacers with non‐uniform conductivity. Int. J. Elec. Power. 120, 105979 (2020)Winter, A., Kindersberger, J.: Transient field distribution in gas‐solid insulation systems under DC voltages. IEEE Trans. Dielectr. Electr. Insul. 21(01), 116–128 (2014)Yan, W., Li, C., Lei, Z., et al.: Surface charging on HVDC spacers considering time‐varying effect of temperature and electric fields. IEEE Trans. Dielectr. Electr. Insul. 26(04), 1316–1324 (2019)Liang, H.C., Du, B.X., Li, J.: Electric field regulation and parameter optimization of surface nonlinear conductivity spacer for 500 kV DC‐GIL. IEEE Trans. Dielectr. Electr. Insul. 27(04), 1330–1338 (2020)Niu, H., Chen, Z., Zhang, H., et al.: Multi‐physical coupling field study of 500 kV GIL: Simulation, characteristics, and analysis. IEEE Access 8, 131439–131448 (2020)Qiao, Y., Liang, R., Gao, P., et al.: Heat transfer analysis of different conditions for SF6/N2 gas‐insulated transmission lines. IEEE Trans. Power Delivery 36(02), 831–840 (2021)Du, B., Wang, M., Li, J., et al.: Temperature dependent surface charge and discharge behavior of epoxy/AlN nanocomposites. IEEE Trans. Dielectr. Electr. Insul. 25(04), 1300–1307 (2018)Zhang, Y., Tuo, R., Yang, W., et al.: Improved thermal and electrical properties of epoxy resin composites by dopamine and silane coupling agent modified hexagonal BN. Polym. Compos. 41(11), 4727–4739 (2020)Lienhard, H.I.V., Lienhard, H.V.: A Heat Transfer Textbook. 3rd ed., p. 528, Phlogiston Press, Cambridge, USA (2003)Yunus, A.C.: Heat Transfer: A Practical Approach, 2nd ed., pp. 465–466, Mcgraw‐Hill, New York, USA (2002)Kueh, T.H., Goldstein, R.J.: Correlating equations for natural convection heat transfer between horizontal circular cylinders. Int. J. Heat Mass Transfer 19(10), 1127–1134 (1976)COMSOL Inc.: CFD Module User's Guide, pp. 207–209, COMSOL, Burlington, USA (2019)Rebzani, N., Clavel, E., Marty, P., et al.: Numerical multiphysics modeling of temperature rises in gas insulated busbars. IEEE Trans. Dielectr. Electr. Insul. 23(05), 2579–2586 (2016)Hering, M., Speck, J., Gromann, S., et al.: Influence of gas temperature on the breakdown voltage in gas‐insulated systems. IEEE Trans. Dielectr. Electr. Insul. 24(01), 401–408 (2017)Lu, S., Zhang, L., Zhou, H., et al.: Effect of temperature on flashover voltage of epoxy column at power frequency. High Voltage Eng. 45(09), 2774–2781 (2019)Hisayasu, M., Ryoji, K.: Surface flashover characteristics of ceramic insulation in gases at 40°C‐700°C. IEEJ Trans. Fundam. Mater. 117(08), 832–838 (1997)Ma, G.M., Zhou, H.Y., Lu, S.J., et al.: Effect of material volume conductivity on surface charges accumulation on spacers under DC electro‐thermal coupling stress. IEEE Trans. Dielectr. Electr. Insul. 25(04), 1211–1220 (2018)

Journal

IET Generation Transmission & Distribution – Wiley

Published: Mar 1, 2023

Keywords: electrical installation; epoxy insulators; finite element analysis; gas insulated transmission lines; heat transfer; HVDC power transmission; SF 6 insulation

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