# Numerical Study on Electromagnetic Coupled Heat Transfer and Ultrasonic Propagation in GIS Busbar Chamber

Authors: Wen-Rong Si; Chen-Zhao Fu; Zheng-Yong Hu; Bo Wang; Jian Yang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In the present paper, the electromagnetic coupled heat transfer and ultrasonic propagation in a 252 kV three-phase GIS busbar chamber were numerically studied by using the finite element method. The electromagnetic loss and distributions of SF6 gas velocity, temperature, and breakdown margin in the GIS busbar chamber were carefully analyzed, and the influences of SF6 gas velocity and temperature variations on ultrasonic propagation performances in the GIS chamber were discussed in detail. It is found that the SF6 gas breakdown margin in the GIS busbar chamber is mainly affected by the electric field intensity. WhenI = 3300 A and U = 1050 kV, the minimum SF6 gas breakdown margin in the GIS busbar chamber is 7.98 kV/mm, which is located at top of busbar conductor A, where the thermal breakdown risk is relatively high. Furthermore, it is noted that, when natural convection in GIS busbar chamber is weak, the influences of SF6 gas velocity and temperature variations on sound propagation would be insignificant. For this case, when acoustic propagation simulation is performed, the SF6 gas would be assumed to be stationary and its temperature would be set to the average gas temperature of natural convection in the GIS chamber, which would be beneficial to reduce the computational time and maintain the simulation accuracy as well.


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## Body

## 1. Introduction

Gas-insulated switchgear (GIS) is a high-voltage sealed switchgear that combines high-voltage electrical equipment together according to the main electrical connection, including circuit breakers, disconnectors, earthing switches, mutual inductors, busbars, and arresters. In recent years, GIS are widely used in power plants and power systems due to its advantages of small floor area, high operation reliability, and little interference from circumstance [1, 2]. However, there also exist many troubles during GIS operations, and the thermal failure is one of the most common failures due to its closed and compact structures [3].GIS busbar is a typical GIS component for power transmission, which is also one of the GIS components easy to appear thermal failures. Generally, the GIS busbar thermal failures include mechanical failures caused by thermal stress and insulation failures caused by temperature rise. Kang et al. [4] thought that, during busbar design, the impact of GIS internal insulation status on the busbar reliability and safety is greater than that of thermal stress. When serious insulation failure occurs in GIS, the equipment service life will be greatly shortened, and huge economic losses will be created due to long-term power failure of power grid. Therefore, in practical engineering, real-time detections of GIS operating temperature are required to ensure its operation reliability. Nowadays, it is a common method to diagnose overheating defects in conductors arranged in the GIS through temperature measurement on GIS shell [5]. However, there are some defects for this method, since the conductors inside GIS cannot be measured directly, the overheating defect would not be evaluated accurately. With development of computer technology, the temperature rise for GIS components can be predicted by using numerical simulation method. For example, Kim et al. [6] and Kim et al. [7] have proposed a magnetic-thermal coupling finite element method to predict the temperature rise of GIS busbar. In their studies, the loss obtained from electromagnetic analysis was adopted as the heat source to compute the temperature rise of busbar, and its feasibility was validated by the experiments. Zhong et al. [8] thought that the heat transfer of GIS busbar was mainly affected by the conductor electromagnetic loss, insulation heat loss, shell eddy current loss, contact resistance, skin effect, etc. According to the real heat transfer process of GIS busbar, a three-dimensional electromagnetic coupled heat transfer model was established, and the busbar temperature rise was numerically studied under variety influencing factors. Wu et al. [9] found that the bearing capacity and service life of GIS busbar were mainly determined by the temperature rise at contacts. A computational model for three-phase GIS busbar was established with finite element method, and the temperature rise at contacts was successfully predicted with considering of contact resistance. These studies showed that numerical simulation was an effective way to predict the temperature rise of GIS busbar. However, in these studies, the relationship between the temperature rise of busbar and thermal insulation failure was not discussed. The variations of SF6 gas insulation status in the GIS chamber under through-current condition were studied by Wu et al. [10]. In their study, the concept of gas breakdown margin was proposed, and the variations of SF6 gas breakdown margin were numerically studied with multiphysical coupling simulation method under different busbar working conditions. It showed that both the busbar through-current temperature rise and very fast transient phenomenon would lead to nonuniform distributions of local electric field intensity in the busbar, cause discharge, and make SF6 gas breakdown. However, in this study, the SF6 gas breakdown margin was only discussed in single-phase GIS busbar chamber, and the variations of SF6 gas breakdown margin in three-phase GIS busbar chamber were still unclear.When thermal insulation failure occurs, it would lead to GIS busbar discharge, which is usually related to various impact factors. For example, under the effects of through-current temperature rise, metal particles inside GIS chamber or external lightning impulse voltage, the breakdown discharge would occur in the busbar and lead to an insulation failure [11]. For practical applications, it is common to detect GIS discharges by measuring ultrasonic signals generated during GIS discharge process [12, 13]. However, for this method, the ultrasonic sensors are usually arranged on the outer surface of GIS shell, the ultrasonic signal detected by the sensor would be weak, and it would also be easily affected by external noise. Therefore, lots of researches were performed to improve the detection accuracy of ultrasonic signals. For example, based on Michelson interference principle, Zhou et al. [14] had developed a fiber-optic ultrasonic sensor system, and the detection performance for weak ultrasonic signals was experimentally studied. Xiao et al. [15] found that the interference of environmental noise could be effectively reduced with combined detection method for ultrasonic and ultrahigh frequency signals. With this method, the defect signals would be correctly identified, and the signal source would also be accurately located. Li et al. [16] had proposed an optical fiber acoustic emission sensor based on polarization interference, and its effectiveness for GIS discharge detection was verified by the experiments. Based on traditional piezoelectric transducer technology, Chen et al. [17] had developed a Fabry–Perot sensor for partial discharge ultrasonic signal detections. The experimental results showed that partial discharge ultrasonic signals for both broadband and narrowband modes could be properly detected by the sensor. Currently, it is popular to improve ultrasonic detection sensitivity by improving the performance of ultrasonic detection system, while the researches for ultrasonic propagation characteristics in the GIS are quite few. The partial discharge ultrasonic signal propagation in a GIS busbar chamber was numerically studied by Guo et al. [18]. They found that the ultrasonic signals would be reflected and refracted on the inner surface of GIS shell, and the ultrasonic signals would be significantly attenuated when they passed through insulator. The propagation path and attenuation characteristics of ultrasonic signals in the GIS chamber were also numerically studied by Xue et al. [19]. However, for these studies, the effects of SF6 gas velocity and temperature variations on ultrasonic signal propagation in the GIS chamber were unconcerned.Therefore, in the present paper, the electromagnetic coupled heat transfer and ultrasonic propagation in a 252 kV three-phase GIS busbar chamber were numerically studied by using finite element method. The electromagnetic loss and distributions of SF6 gas velocity, temperature, and breakdown margin in the GIS busbar chamber were carefully analyzed, and the influences of SF6 gas velocity and temperature variations on ultrasonic propagation performances in the GIS chamber were also discussed in detail. The present study would be helpful for further understanding electromagnetic coupled heat transfer and ultrasonic propagation in the GIS busbar chamber, and it would also be useful for the simplification of ultrasonic propagation computations.


## 2. Physical Model and Computational Methods

### 2.1. Physical Model and Geometric Parameters

In the present study, a 252 kV three-phase GIS busbar is selected for the investigation. Since the axial dimension of the busbar is much larger than its radial size, the busbar would be simplified as a two-dimensional model. The physical model and geometric dimensions for the three-phase GIS busbar are presented in Figure1. It shows that the busbar model is composed of GIS shell, busbar conductors and SF6 insulating gas. The GIS shell is made of aluminium, whose outer diameter is 59.6 cm and wall thickness is 0.8 cm. Three busbar conductors are arranged in a regular triangle in the busbar chamber. The inner diameter and outer diameter of the busbar conductor are 6 cm and 9 cm, respectively. The center of the busbar triangle is located on the center of busbar chamber cross section, and the center of the busbar conductor A is located on the y-axis (y = 14 cm). The frequency of alternating current in the busbar conductor is 50 Hz and the sinusoidal electric excitation phase difference between adjacent busbar conductors is 2π/3. High pressure SF6 insulating gas (0.35 MPa) is filled in the GIS chamber and busbar conductors. Typical physical properties of GIS shell, busbar conductor, and SF6 gas are presented in Table 1.Figure 1
Physical model and geometric dimensions for three-phase 252 kV GIS busbar.Table 1
Typical physical properties for different components of GIS busbar [20].
ComponentMaterialDensity (kg/m3)Thermal conductivity (W/(m·K))Heat capacity (J/(kg·K))Electrical conductivity (S/m)GIS shellAluminium27002389003.774 × 107Busbar conductorsAluminium alloy 60632700201900σ0 (T)Insulating gasSF6ρ (p, T)λ (T)cp (T)0(1)ρp,T=p×MconstT×Rconst,(2)cpT=−2×10−3×T2+2.4×T+123.4,(3)λT=λ0×TTenv1.5×Tenv+ST+S,(4)σ0=1ρAl1+αT−293.15,The variation of SF6 gas density with pressure and temperature is formulated as in equation (1). The variations of thermal conductivity and heat capacity for SF6 gas with pressure and temperature are formulated as in equations (2) and (3) [21]. The variation of electrical conductivity for busbar conductor with temperature is formulated as in equation (4).where T is the temperature, K; p is the pressure, Pa; Mconst is the molar mass of SF6 gas, g/mol; Rconst is the gas constant, J/(mol·K); λ0 is the thermal conductivity of SF6 gas at 0.1 MPa and W/(m·K); Tenv is the environmental temperature, K; S is the Sutherland constant of SF6 gas, K; ρAl is the electrical resistivity of busbar conductor at, Ω·m; and ɑ is the temperature effect coefficient.


### 2.2. Governing Equations and Computational Methods

In the present study, the electromagnetic effect, heat transfer, and SF6 gas flow in the GIS chamber are coupled for the simulations [22]. Firstly, the electromagnetic analysis is performed for the GIS busbar. When the busbar conductor is under sinusoidal electrical excitation, the frequency domain electromagnetic equations are formulated as follows:(5)−ω2γA⇀+jωσA⇀+∇×μ−1∇×A⇀=0,∇×A⇀=B⇀;E⇀=−jωA⇀;B⇀=μH⇀;J⇀=σE⇀,where A⇀ is the magnetic vector potential, Wb/m; B⇀ is the intensity of magnetization, T; E⇀ is the electric field intensity, N/C; H⇀ is the magnetic field intensity, A/m; J⇀ is the current density, A/m2; j is the imaginary unit; ω = 2πf is the phase angle, rad; f is the electrical excitation frequency, Hz; γ is the dielectric constant, F/M; μ is the magnetic permeability, H/m; σ is the electrical conductivity, S/m.Due to the effect of alternating current, the skin effect would appear in the busbar conductor and GIS shell, where the electric and magnetic fields are mainly concentrated near the surface of busbar conductor and GIS shell. In order to simplify simulations, the surface impedance boundary condition is usually adopted to formulate the relationship between electric and magnetic fields on the surface of busbar conductor and GIS shell [23], which are formulated as follows [20]:(6)μμ0rγ0γr−jσ/ωn⇀×H⇀+E⇀−n⟶−E⇀n⇀=n⇀⋅E⇀sn⇀−E⇀s,where E⇀s is the tangential component of electric field strength; n⇀ is the normal vector on conductor surfaces; μ0 is the relative permeability under vacuum condition, H/m; μr is the relative permeability; γ0 is the dielectric constant under vacuum condition, F/m; γr is the relative dielectric constant.The electromagnetic induction and heat conduction for busbar conductors and GIS shell are coupled as follows:(7)0=∇⋅λsolidT∇T+Qe,Qe=Qrh+Qml=12ReJ⇀⋅E⇀∗+12RejωB⇀⋅H⇀∗,where T is the temperature, K; Re is the real part of an imaginary number; Qe is the total electromagnetic loss density of busbar conductors or GIS shell; Qrh and Qml are the electrical loss density and magnetic loss density, respectively, W/m3; E⇀∗ and H⇀∗ are the conjugate complex numbers of E⇀ and H⇀; and λ solid (T) is the thermal conductivity of solid material, W/(m·K).The flow and heat transfer of SF6 gas in the GIS chamber would be regarded as turbulent natural convection heat transfer, and the governing equations are formulated as follows [24]:(8)∇v⇀=0,ρTv⇀⋅∇v⇀=−∇p+∇⋅μT+μt∇v⇀+∇v⇀T+1−βT−T0ρTg,ρTv⇀⋅∇T=∇⋅λTcpT+μtσT⋅∇T.The RANSk-ε turbulence model is adopted to simulate the turbulent flow of SF6 gas, which is formulated as follows:(9)k:ρTv⇀⋅∇k=∇⋅μT+μtσk⋅∇k+Pk−ρTε,ε:ρTv⇀⋅∇ε=∇⋅μT+μtσε⋅∇ε+cε1εkPk−cε2ρTε2k,where v⇀ is the velocity vector of SF6 gas, m/s; ρ (T) is the SF6 gas density, kg/m3; cp(T) is the heat capacity of SF6 gas, J/(kg·K); p is the pressure, Pa; μ (T) is the dynamic viscosity of SF6 gas, kg/(m·s); μt is the turbulent viscosity of SF6 gas, kg/(m·s); β is the volumetric expansion coefficient of SF6 gas; g is the gravitational acceleration, m/s2; λ (T) is the thermal conductivity of SF6 gas, W/(m·K); σT is the Prandtl number of SF6 gas in the heat transfer equation; k is the turbulent kinetic energy, m2/s2; ε is the turbulent dissipation rate, m2/s3; Pk is the turbulent shear generation term, kg/(m·s3); σk and σε are the Prandtl numbers in the k and ε equations, respectively; and cε1 and cε2 are the model constants in the k and ε equations, respectively.The heat transfer on the outer surface of busbar conductor is formulated as follows [25]:(10)λ1∂T∂r=h1T−Tf+σ1T4−J1−εc/εc.The heat transfer on the inner surface of GIS shell is formulated as follows:(11)λ2∂T∂r=h2T−Tf+σ1T4−J1−εk/εk.The heat transfer on the outer surface of GIS shell is considered as natural convection heat transfer with the air, which is formulated as follows:(12)λ2∂T∂r=h3T−Tenv,where λ1 and λ2 are the thermal conductivity of busbar conductor and GIS shell, respectively, W/(m·K); h1 and h2 are the convective heat transfer coefficients on the outer surface of busbar conductor and inner surface of GIS shell, respectively, W/(m2·K); h3 is the equivalent natural convective heat transfer coefficient on the outer surface of GIS shell, W/(m2·K); Tf is the SF6 gas temperature in the GIS chamber, K; εc and εk are the surface emissivity of busbar conductors and GIS shell, respectively; σ1 is the black body radiation constant, W/(m2·K4); and J is the effective radiation, W/m2.Due to the high temperature of hot spots, the breakdown discharge phenomenon would appear in the GIS chamber, and the instantaneous ultrasonic signal would also be generated. In the present study, the ultrasonic source is simulated using Gaussian pulse excitation [19], and the time-domain correlation for Gaussian pulse is formulated as follows:(13)Qt=Ae−π2f02t−tp2,where Q (t) is the time-domain signal of Gaussian pulse, m3/s; A is the intensity of ultrasonic source, m3/s; f0 is the pulse bandwidth, kHz; t is the time, s; tp is the propagation time as pulse reaches peak value, μs.The propagation process of ultrasonic signal in the GIS chamber can be presented through sound pressure variations. In order to consider the effect of SF6 gas flow on the ultrasonic propagation, the computational results of SF6 gas velocity and temperature should be coupled to the acoustic model with grid mapping method. The governing equations for sound propagations are formulated as follows:(14)∂ρs∂t+u⇀0⋅∇ρs+u⇀s⋅∇ρ0+ρs∇⋅u⇀0+ρ0∇⋅u⇀s=fp,∂u⇀s∂t+u⇀0⋅∇u⇀s+u⇀s⋅∇u⇀0+1ρ0∇ρs⋅u⇀0−ρsρ02∇p0=f⇀v,ρs=pscs2,where ρs is the SF6 gas density with acoustic interference, kg/m3; u⇀0 is the SF6 gas velocity vector after grid mapping, m/s; u⇀s is the ultrasonic velocity vector, m/s; ρ0 is the SF6 gas density after grid mapping, kg/m3; p0 is the SF6 gas pressure after grid mapping, Pa; ps is the sound pressure, Pa; cs is the ultrasonic propagation speed in SF6 gas, m/s; t is the time, s; fp is the source term related to the domain mass and pressure sources; and f⇀v is the source term related to the domain velocity and force sources.In the present study, the effect of SF6 gas flow on the ultrasonic propagation is mainly focused, and the ultrasonic attenuation caused by the solid wall is not considered. Therefore, the sound hard wall boundary condition was adopted in the solid walls, which is formulated as follows:(15)n⇀⋅u⇀0=0,n⇀⋅u⇀s=0,where n⇀ is the normal vector of solid wall surface.All the above governing equations are solved with commercial code Comsol Multiphysics 5.2, and the boundary settings are summarized in Table2. As for the electromagnetic, momentum, and heat transfer equations, the Mumps and Pardiso solvers are employed for the computations. When the iterative calculation residuals for all variables are less than 10−3, the computational results are considered to be convergent. As for transient ultrasonic propagation equations, the Mumps time-domain explicit solver is employed for the computations, where time step is set as 0.5 μs. When the iterative calculation residuals for all variables are less than 10−2, the computational results are considered to be convergent.Table 2
Boundary settings for simulations.
Boundary conditionFormulationSurface impedance boundaryμμ0rγ0γr−jσ/ωn⇀×H⇀+E⇀−n⟶−E⇀n⇀=n⇀⋅E⇀sn⇀−E⇀sNo slip velocity boundaryv⇀=0Heat flux conservation boundaryλ1∂T∂r=h1T−Tf+σ1T4−J1−εc/εc,λ2∂T∂r=h2T−Tf+σ1T4−J1−εk/εk,λ2∂T∂r=hT−Tenv,Sound hard wall boundaryn⇀⋅u⇀0=0,n⇀⋅u⇀s=0.


## 2.1. Physical Model and Geometric Parameters

In the present study, a 252 kV three-phase GIS busbar is selected for the investigation. Since the axial dimension of the busbar is much larger than its radial size, the busbar would be simplified as a two-dimensional model. The physical model and geometric dimensions for the three-phase GIS busbar are presented in Figure1. It shows that the busbar model is composed of GIS shell, busbar conductors and SF6 insulating gas. The GIS shell is made of aluminium, whose outer diameter is 59.6 cm and wall thickness is 0.8 cm. Three busbar conductors are arranged in a regular triangle in the busbar chamber. The inner diameter and outer diameter of the busbar conductor are 6 cm and 9 cm, respectively. The center of the busbar triangle is located on the center of busbar chamber cross section, and the center of the busbar conductor A is located on the y-axis (y = 14 cm). The frequency of alternating current in the busbar conductor is 50 Hz and the sinusoidal electric excitation phase difference between adjacent busbar conductors is 2π/3. High pressure SF6 insulating gas (0.35 MPa) is filled in the GIS chamber and busbar conductors. Typical physical properties of GIS shell, busbar conductor, and SF6 gas are presented in Table 1.Figure 1
Physical model and geometric dimensions for three-phase 252 kV GIS busbar.Table 1
Typical physical properties for different components of GIS busbar [20].
ComponentMaterialDensity (kg/m3)Thermal conductivity (W/(m·K))Heat capacity (J/(kg·K))Electrical conductivity (S/m)GIS shellAluminium27002389003.774 × 107Busbar conductorsAluminium alloy 60632700201900σ0 (T)Insulating gasSF6ρ (p, T)λ (T)cp (T)0(1)ρp,T=p×MconstT×Rconst,(2)cpT=−2×10−3×T2+2.4×T+123.4,(3)λT=λ0×TTenv1.5×Tenv+ST+S,(4)σ0=1ρAl1+αT−293.15,The variation of SF6 gas density with pressure and temperature is formulated as in equation (1). The variations of thermal conductivity and heat capacity for SF6 gas with pressure and temperature are formulated as in equations (2) and (3) [21]. The variation of electrical conductivity for busbar conductor with temperature is formulated as in equation (4).where T is the temperature, K; p is the pressure, Pa; Mconst is the molar mass of SF6 gas, g/mol; Rconst is the gas constant, J/(mol·K); λ0 is the thermal conductivity of SF6 gas at 0.1 MPa and W/(m·K); Tenv is the environmental temperature, K; S is the Sutherland constant of SF6 gas, K; ρAl is the electrical resistivity of busbar conductor at, Ω·m; and ɑ is the temperature effect coefficient.


## 2.2. Governing Equations and Computational Methods

In the present study, the electromagnetic effect, heat transfer, and SF6 gas flow in the GIS chamber are coupled for the simulations [22]. Firstly, the electromagnetic analysis is performed for the GIS busbar. When the busbar conductor is under sinusoidal electrical excitation, the frequency domain electromagnetic equations are formulated as follows:(5)−ω2γA⇀+jωσA⇀+∇×μ−1∇×A⇀=0,∇×A⇀=B⇀;E⇀=−jωA⇀;B⇀=μH⇀;J⇀=σE⇀,where A⇀ is the magnetic vector potential, Wb/m; B⇀ is the intensity of magnetization, T; E⇀ is the electric field intensity, N/C; H⇀ is the magnetic field intensity, A/m; J⇀ is the current density, A/m2; j is the imaginary unit; ω = 2πf is the phase angle, rad; f is the electrical excitation frequency, Hz; γ is the dielectric constant, F/M; μ is the magnetic permeability, H/m; σ is the electrical conductivity, S/m.Due to the effect of alternating current, the skin effect would appear in the busbar conductor and GIS shell, where the electric and magnetic fields are mainly concentrated near the surface of busbar conductor and GIS shell. In order to simplify simulations, the surface impedance boundary condition is usually adopted to formulate the relationship between electric and magnetic fields on the surface of busbar conductor and GIS shell [23], which are formulated as follows [20]:(6)μμ0rγ0γr−jσ/ωn⇀×H⇀+E⇀−n⟶−E⇀n⇀=n⇀⋅E⇀sn⇀−E⇀s,where E⇀s is the tangential component of electric field strength; n⇀ is the normal vector on conductor surfaces; μ0 is the relative permeability under vacuum condition, H/m; μr is the relative permeability; γ0 is the dielectric constant under vacuum condition, F/m; γr is the relative dielectric constant.The electromagnetic induction and heat conduction for busbar conductors and GIS shell are coupled as follows:(7)0=∇⋅λsolidT∇T+Qe,Qe=Qrh+Qml=12ReJ⇀⋅E⇀∗+12RejωB⇀⋅H⇀∗,where T is the temperature, K; Re is the real part of an imaginary number; Qe is the total electromagnetic loss density of busbar conductors or GIS shell; Qrh and Qml are the electrical loss density and magnetic loss density, respectively, W/m3; E⇀∗ and H⇀∗ are the conjugate complex numbers of E⇀ and H⇀; and λ solid (T) is the thermal conductivity of solid material, W/(m·K).The flow and heat transfer of SF6 gas in the GIS chamber would be regarded as turbulent natural convection heat transfer, and the governing equations are formulated as follows [24]:(8)∇v⇀=0,ρTv⇀⋅∇v⇀=−∇p+∇⋅μT+μt∇v⇀+∇v⇀T+1−βT−T0ρTg,ρTv⇀⋅∇T=∇⋅λTcpT+μtσT⋅∇T.The RANSk-ε turbulence model is adopted to simulate the turbulent flow of SF6 gas, which is formulated as follows:(9)k:ρTv⇀⋅∇k=∇⋅μT+μtσk⋅∇k+Pk−ρTε,ε:ρTv⇀⋅∇ε=∇⋅μT+μtσε⋅∇ε+cε1εkPk−cε2ρTε2k,where v⇀ is the velocity vector of SF6 gas, m/s; ρ (T) is the SF6 gas density, kg/m3; cp(T) is the heat capacity of SF6 gas, J/(kg·K); p is the pressure, Pa; μ (T) is the dynamic viscosity of SF6 gas, kg/(m·s); μt is the turbulent viscosity of SF6 gas, kg/(m·s); β is the volumetric expansion coefficient of SF6 gas; g is the gravitational acceleration, m/s2; λ (T) is the thermal conductivity of SF6 gas, W/(m·K); σT is the Prandtl number of SF6 gas in the heat transfer equation; k is the turbulent kinetic energy, m2/s2; ε is the turbulent dissipation rate, m2/s3; Pk is the turbulent shear generation term, kg/(m·s3); σk and σε are the Prandtl numbers in the k and ε equations, respectively; and cε1 and cε2 are the model constants in the k and ε equations, respectively.The heat transfer on the outer surface of busbar conductor is formulated as follows [25]:(10)λ1∂T∂r=h1T−Tf+σ1T4−J1−εc/εc.The heat transfer on the inner surface of GIS shell is formulated as follows:(11)λ2∂T∂r=h2T−Tf+σ1T4−J1−εk/εk.The heat transfer on the outer surface of GIS shell is considered as natural convection heat transfer with the air, which is formulated as follows:(12)λ2∂T∂r=h3T−Tenv,where λ1 and λ2 are the thermal conductivity of busbar conductor and GIS shell, respectively, W/(m·K); h1 and h2 are the convective heat transfer coefficients on the outer surface of busbar conductor and inner surface of GIS shell, respectively, W/(m2·K); h3 is the equivalent natural convective heat transfer coefficient on the outer surface of GIS shell, W/(m2·K); Tf is the SF6 gas temperature in the GIS chamber, K; εc and εk are the surface emissivity of busbar conductors and GIS shell, respectively; σ1 is the black body radiation constant, W/(m2·K4); and J is the effective radiation, W/m2.Due to the high temperature of hot spots, the breakdown discharge phenomenon would appear in the GIS chamber, and the instantaneous ultrasonic signal would also be generated. In the present study, the ultrasonic source is simulated using Gaussian pulse excitation [19], and the time-domain correlation for Gaussian pulse is formulated as follows:(13)Qt=Ae−π2f02t−tp2,where Q (t) is the time-domain signal of Gaussian pulse, m3/s; A is the intensity of ultrasonic source, m3/s; f0 is the pulse bandwidth, kHz; t is the time, s; tp is the propagation time as pulse reaches peak value, μs.The propagation process of ultrasonic signal in the GIS chamber can be presented through sound pressure variations. In order to consider the effect of SF6 gas flow on the ultrasonic propagation, the computational results of SF6 gas velocity and temperature should be coupled to the acoustic model with grid mapping method. The governing equations for sound propagations are formulated as follows:(14)∂ρs∂t+u⇀0⋅∇ρs+u⇀s⋅∇ρ0+ρs∇⋅u⇀0+ρ0∇⋅u⇀s=fp,∂u⇀s∂t+u⇀0⋅∇u⇀s+u⇀s⋅∇u⇀0+1ρ0∇ρs⋅u⇀0−ρsρ02∇p0=f⇀v,ρs=pscs2,where ρs is the SF6 gas density with acoustic interference, kg/m3; u⇀0 is the SF6 gas velocity vector after grid mapping, m/s; u⇀s is the ultrasonic velocity vector, m/s; ρ0 is the SF6 gas density after grid mapping, kg/m3; p0 is the SF6 gas pressure after grid mapping, Pa; ps is the sound pressure, Pa; cs is the ultrasonic propagation speed in SF6 gas, m/s; t is the time, s; fp is the source term related to the domain mass and pressure sources; and f⇀v is the source term related to the domain velocity and force sources.In the present study, the effect of SF6 gas flow on the ultrasonic propagation is mainly focused, and the ultrasonic attenuation caused by the solid wall is not considered. Therefore, the sound hard wall boundary condition was adopted in the solid walls, which is formulated as follows:(15)n⇀⋅u⇀0=0,n⇀⋅u⇀s=0,where n⇀ is the normal vector of solid wall surface.All the above governing equations are solved with commercial code Comsol Multiphysics 5.2, and the boundary settings are summarized in Table2. As for the electromagnetic, momentum, and heat transfer equations, the Mumps and Pardiso solvers are employed for the computations. When the iterative calculation residuals for all variables are less than 10−3, the computational results are considered to be convergent. As for transient ultrasonic propagation equations, the Mumps time-domain explicit solver is employed for the computations, where time step is set as 0.5 μs. When the iterative calculation residuals for all variables are less than 10−2, the computational results are considered to be convergent.Table 2
Boundary settings for simulations.
Boundary conditionFormulationSurface impedance boundaryμμ0rγ0γr−jσ/ωn⇀×H⇀+E⇀−n⟶−E⇀n⇀=n⇀⋅E⇀sn⇀−E⇀sNo slip velocity boundaryv⇀=0Heat flux conservation boundaryλ1∂T∂r=h1T−Tf+σ1T4−J1−εc/εc,λ2∂T∂r=h2T−Tf+σ1T4−J1−εk/εk,λ2∂T∂r=hT−Tenv,Sound hard wall boundaryn⇀⋅u⇀0=0,n⇀⋅u⇀s=0.


## 3. Grid Independence Test and Model Validations

### 3.1. Grid Independence Test

Firstly, the grid independence test for electromagnetic coupled heat and fluid flow model was performed. The computational grid for GIS busbar with test model is presented in Figure2. The unstructured grid is constructed for the computations, and the grid is intensified near the interfaces between solid and gas areas. The busbar current is set as 3300 A, and the current frequency is fixed at 50 Hz. Four sets of computational grids are adopted for the test. The total element numbers are 4688, 7204, 10064, and 14894, respectively. The maximum temperature (Tmax) and electromagnetic loss (Q) in GIS chamber with different computational grids are presented in Table 3. It shows that when the total element number changes from 10064 (Grid 3) to 14894 (Grid 4), the maximum temperature (Tmax) in the GIS chamber decreases by 0.02 K and the electromagnetic loss (Q) increases by 0.03 W/m3, respectively, where the deviations are 0.006% and 0.015%, respectively. Therefore, the Grid 3 with total element number of 10064 should be good enough for the test. For this grid, the minimum sizes of the grid element for Zone 1, Zone 2, and Zone 3 in the GIS chamber are 0.0054 m, 0.0045 m, and 0.0056 m, respectively. Therefore, the similar mesh settings to the Grid 3 (10064) is finally adopted for the subsequent electromagnetic coupled heat and fluid flow simulations.Figure 2
Computational grid for GIS busbar with electromagnetic coupled heat and fluid flow model.Table 3
The maximum temperature (Tmax) and electromagnetic loss (Q) in GIS chamber with different computational grids (I = 3300 A, f = 50 Hz).
GridRegionsMinimal grid size (m)Maximal grid size (m)Total grid numbersTmax (K)Q (W/m3)Grid 1Zone 10.01180.01554688336.25201.45Zone 20.00690.0155Zone 30.00710.0315Grid 2Zone 10.00870.01557204335.85202.74Zone 20.00500.0155Zone 30.00650.0277Grid 3Zone 10.00540.010610064335.67203.65Zone 20.00450.0080Zone 30.00560.0251Grid 4Zone 10.00440.007214894335.65203.68Zone 20.00360.0080Zone 30.00450.0170Then, the grid independence test for heat and fluid flow coupled acoustic propagation model was performed. The uniform unstructured grid is constructed for the computations. The ultrasonic frequency (f0) and wavelength (λ) are set as 80 kHz and 1.75 mm, respectively. Six sets of computational grids are adopted for the test. The total element numbers are 184292, 217458, 258700, 319300, 396292, and 486174, respectively, and the corresponding element sizes are 1.2 λ, 1.1 λ, 1 λ, 0.9 λ, 0.8 λ, and 0.7 λ, respectively. It is assumed that the ultrasonic signal source is located at the top point (0, 18.5 cm) of busbar conductor A and the ultrasonic receiving point (0, 28 cm) is located above busbar conductor A (see Figure 1). The variations of ultrasonic receiving time and sound pressure at ultrasonic receiving point with different computational grids are presented in Figure 3. It shows that, when the total element number changes from 319300 (Grid 4) to 396292 (Grid 5), the ultrasonic receiving time is almost unchanged (696 μs) and the sound pressure only increases by 0.63%. Meanwhile, as the total element number changes from 396292 (Grid 5) to 486174 (Grid 6), the ultrasonic receiving time is also almost unchanged (696 μs), and the sound pressure only increases by 0.08%.Figure 3
The variations of ultrasonic receiving time and sound pressure at ultrasonic receiving point with different computational grids (f0 = 80 kHz).Therefore, the Grid 4 with total element number of 319300 should be good enough for the test. For this grid, the element size is 1.575 mm (0.9λ). Therefore, similar grid settings to the Grid 4 (319300) is finally adopted for the subsequent heat and fluid flow coupled acoustic transport simulations.


### 3.2. Model Validations

Firstly, the computational model for electromagnetic coupled heat and fluid flow is validated. The electromagnetic coupled heat and fluid flow in a 252 kV three-phase GIS busbar chamber as reported in Ref. [24] was restudied in this section. The physical model and temperature test points for GIS busbar validation model are presented in Figure 4. It shows that the geometric dimensions for the validation model are the same to those as presented in Figure 1, while the physical parameters are different. For the validation model in Ref. [24], the busbar current is set as 3000 A, and the current frequency is set as 60 Hz. The pressure of SF6 insulating gas is set as 0.4 MPa. The emissivity of εc and εk are set as 0.1 and 0.85, respectively. The environmental air temperature is set as 289.35 K. Furthermore, typical physical properties of GIS shell, busbar conductor, and SF6 gas for the validation are presented in Table 4. The simulation and experimental results of temperature at different test points are presented in Table 5. It shows that the simulation results can agree well with the experimental results as reported in Ref. [24], where the maximum temperature deviation is 3.49 K and the average deviation is 2.1 K.Figure 4
Physical model and temperature test points for three-phase GIS busbar validation model [24].Table 4
Typical physical properties of different components for GIS busbar validation model [24].
ComponentMaterialThermal conductivity (W/(m·K))Heat capacity (J/(kg·K))Electrical conductivity (S/m)GIS shellAluminium alloy A5083P1209003.774 × 107Busbar conductorsAluminium alloy 60632019003.030 × 107Insulating gasSF6λ (T)cp (T)0λT=λ0×T/Tenv1.5×Tenv+S/T+S; cpT=−218.38+4.73×T−0.007×T2+5.67×10−6×T3−1.66×10−9×T4; where T is the temperature, K; λ0 is the thermal conductivity of SF6 at 0.1 MPa and W/(m·K); Tenv is the ambient temperature, K; and S is the Sutherland constant of SF6, K.Table 5
The simulation and experimental results of temperature for different test points.
Test point 1 (0, 18.5 cm)Test point 2 (−12.1 cm, −2.5 cm)Test point 3 (12.1 cm, −2.5 cm)Test point 4 (0, 29.8 cm)Test point 5 (0, 24 cm)T (K) (Exp. [24])336.05333.25335.45310.85328.25T (K) (simulation)336.85336.43336.39307.36326.14ΔT (K)0.803.180.943.492.11Then, the flow coupled acoustic propagation model was validated. The acoustic pulse propagation in a square area with stable flow inside [26] was restudied in this section. The physical model for the validation of flow coupled acoustic propagation is presented in Figure 5, where all the model parameters are dimensionless. The acoustic source is set at P (0, 0) with a Gaussian pulse excitation and the acoustic wave would propagate in the inner square area (6 × 6). The acoustic signal receiving point is set at P (2, 1). The outer layer around the inner square area is set as the acoustic absorption layer, where the acoustic wave would be completely absorbed. The fluid only flows along the X direction in the computational area (10 × 10). The dimensionless flow velocity and density of fluid are both set as 1, and the Mach number (Ma) is set as 0.5. The variation of the sound pressure with time at acoustic signal receiving point P (2, 1) is presented in Figure 6. It shows that the simulation results can agree well with the theoretical analysis results as reported in Ref. [26], where the maximum deviation of sound pressure is only 0.04%.Figure 5
Physical model for sound pulse propagation in a square area with stable flow inside [26].Figure 6
The variation of the sound pressure with time at acoustic signal receiving pointP (2, 1).


## 3.1. Grid Independence Test

Firstly, the grid independence test for electromagnetic coupled heat and fluid flow model was performed. The computational grid for GIS busbar with test model is presented in Figure2. The unstructured grid is constructed for the computations, and the grid is intensified near the interfaces between solid and gas areas. The busbar current is set as 3300 A, and the current frequency is fixed at 50 Hz. Four sets of computational grids are adopted for the test. The total element numbers are 4688, 7204, 10064, and 14894, respectively. The maximum temperature (Tmax) and electromagnetic loss (Q) in GIS chamber with different computational grids are presented in Table 3. It shows that when the total element number changes from 10064 (Grid 3) to 14894 (Grid 4), the maximum temperature (Tmax) in the GIS chamber decreases by 0.02 K and the electromagnetic loss (Q) increases by 0.03 W/m3, respectively, where the deviations are 0.006% and 0.015%, respectively. Therefore, the Grid 3 with total element number of 10064 should be good enough for the test. For this grid, the minimum sizes of the grid element for Zone 1, Zone 2, and Zone 3 in the GIS chamber are 0.0054 m, 0.0045 m, and 0.0056 m, respectively. Therefore, the similar mesh settings to the Grid 3 (10064) is finally adopted for the subsequent electromagnetic coupled heat and fluid flow simulations.Figure 2
Computational grid for GIS busbar with electromagnetic coupled heat and fluid flow model.Table 3
The maximum temperature (Tmax) and electromagnetic loss (Q) in GIS chamber with different computational grids (I = 3300 A, f = 50 Hz).
GridRegionsMinimal grid size (m)Maximal grid size (m)Total grid numbersTmax (K)Q (W/m3)Grid 1Zone 10.01180.01554688336.25201.45Zone 20.00690.0155Zone 30.00710.0315Grid 2Zone 10.00870.01557204335.85202.74Zone 20.00500.0155Zone 30.00650.0277Grid 3Zone 10.00540.010610064335.67203.65Zone 20.00450.0080Zone 30.00560.0251Grid 4Zone 10.00440.007214894335.65203.68Zone 20.00360.0080Zone 30.00450.0170Then, the grid independence test for heat and fluid flow coupled acoustic propagation model was performed. The uniform unstructured grid is constructed for the computations. The ultrasonic frequency (f0) and wavelength (λ) are set as 80 kHz and 1.75 mm, respectively. Six sets of computational grids are adopted for the test. The total element numbers are 184292, 217458, 258700, 319300, 396292, and 486174, respectively, and the corresponding element sizes are 1.2 λ, 1.1 λ, 1 λ, 0.9 λ, 0.8 λ, and 0.7 λ, respectively. It is assumed that the ultrasonic signal source is located at the top point (0, 18.5 cm) of busbar conductor A and the ultrasonic receiving point (0, 28 cm) is located above busbar conductor A (see Figure 1). The variations of ultrasonic receiving time and sound pressure at ultrasonic receiving point with different computational grids are presented in Figure 3. It shows that, when the total element number changes from 319300 (Grid 4) to 396292 (Grid 5), the ultrasonic receiving time is almost unchanged (696 μs) and the sound pressure only increases by 0.63%. Meanwhile, as the total element number changes from 396292 (Grid 5) to 486174 (Grid 6), the ultrasonic receiving time is also almost unchanged (696 μs), and the sound pressure only increases by 0.08%.Figure 3
The variations of ultrasonic receiving time and sound pressure at ultrasonic receiving point with different computational grids (f0 = 80 kHz).Therefore, the Grid 4 with total element number of 319300 should be good enough for the test. For this grid, the element size is 1.575 mm (0.9λ). Therefore, similar grid settings to the Grid 4 (319300) is finally adopted for the subsequent heat and fluid flow coupled acoustic transport simulations.


## 3.2. Model Validations

Firstly, the computational model for electromagnetic coupled heat and fluid flow is validated. The electromagnetic coupled heat and fluid flow in a 252 kV three-phase GIS busbar chamber as reported in Ref. [24] was restudied in this section. The physical model and temperature test points for GIS busbar validation model are presented in Figure 4. It shows that the geometric dimensions for the validation model are the same to those as presented in Figure 1, while the physical parameters are different. For the validation model in Ref. [24], the busbar current is set as 3000 A, and the current frequency is set as 60 Hz. The pressure of SF6 insulating gas is set as 0.4 MPa. The emissivity of εc and εk are set as 0.1 and 0.85, respectively. The environmental air temperature is set as 289.35 K. Furthermore, typical physical properties of GIS shell, busbar conductor, and SF6 gas for the validation are presented in Table 4. The simulation and experimental results of temperature at different test points are presented in Table 5. It shows that the simulation results can agree well with the experimental results as reported in Ref. [24], where the maximum temperature deviation is 3.49 K and the average deviation is 2.1 K.Figure 4
Physical model and temperature test points for three-phase GIS busbar validation model [24].Table 4
Typical physical properties of different components for GIS busbar validation model [24].
ComponentMaterialThermal conductivity (W/(m·K))Heat capacity (J/(kg·K))Electrical conductivity (S/m)GIS shellAluminium alloy A5083P1209003.774 × 107Busbar conductorsAluminium alloy 60632019003.030 × 107Insulating gasSF6λ (T)cp (T)0λT=λ0×T/Tenv1.5×Tenv+S/T+S; cpT=−218.38+4.73×T−0.007×T2+5.67×10−6×T3−1.66×10−9×T4; where T is the temperature, K; λ0 is the thermal conductivity of SF6 at 0.1 MPa and W/(m·K); Tenv is the ambient temperature, K; and S is the Sutherland constant of SF6, K.Table 5
The simulation and experimental results of temperature for different test points.
Test point 1 (0, 18.5 cm)Test point 2 (−12.1 cm, −2.5 cm)Test point 3 (12.1 cm, −2.5 cm)Test point 4 (0, 29.8 cm)Test point 5 (0, 24 cm)T (K) (Exp. [24])336.05333.25335.45310.85328.25T (K) (simulation)336.85336.43336.39307.36326.14ΔT (K)0.803.180.943.492.11Then, the flow coupled acoustic propagation model was validated. The acoustic pulse propagation in a square area with stable flow inside [26] was restudied in this section. The physical model for the validation of flow coupled acoustic propagation is presented in Figure 5, where all the model parameters are dimensionless. The acoustic source is set at P (0, 0) with a Gaussian pulse excitation and the acoustic wave would propagate in the inner square area (6 × 6). The acoustic signal receiving point is set at P (2, 1). The outer layer around the inner square area is set as the acoustic absorption layer, where the acoustic wave would be completely absorbed. The fluid only flows along the X direction in the computational area (10 × 10). The dimensionless flow velocity and density of fluid are both set as 1, and the Mach number (Ma) is set as 0.5. The variation of the sound pressure with time at acoustic signal receiving point P (2, 1) is presented in Figure 6. It shows that the simulation results can agree well with the theoretical analysis results as reported in Ref. [26], where the maximum deviation of sound pressure is only 0.04%.Figure 5
Physical model for sound pulse propagation in a square area with stable flow inside [26].Figure 6
The variation of the sound pressure with time at acoustic signal receiving pointP (2, 1).


## 4. Results and Discussion

### 4.1. Electromagnetic Coupled Heat Transfer and Breakdown Margin Analysis

Firstly, the current distribution and electromagnetic loss in three-phase GIS busbar chamber were analyzed. In the present study, the imbalance effect of three-phase current was not considered, where the current amplitude for three-phase busbar conductors are kept the same, and the phase difference is 120°. The current distributions in busbar conductors and GIS shell are presented in Figure7. It shows that, when high frequency alternating current is applied to busbar conductors, a variating magnetic field will be induced around the conductors and the induced current will be generated, which would lead to nonuniform current distribution on conductor cross section and result in skin effect. Due to the skin effect, the current in the busbar conductor will be concentrated on the outer surface of the conductor, and the effective resistance and electromagnetic loss for busbar conductors will increase. In addition, the magnetic field induced by one busbar conductor will also affect the current distributions in other conductors nearby. For example, due to the magnetic effect induced by busbar conductor B, the current in the busbar conductor A will concentrate toward to busbar conductor B and result in proximity effect. The proximity effect will further increase the nonuniform current distribution on busbar conductor cross section and increase electromagnetic loss of busbar conductors. Meanwhile, the induced current in the GIS shell will form a closed loop and generate eddy current loss inside. The variations of electromagnetic loss for busbar conductors and GIS shell with current are presented in Figure 8. It shows that the electromagnetic losses for three-phase busbar conductors are almost the same, which are much higher than the eddy current loss for GIS shell. As current increases, both electromagnetic losses for busbar conductors and GIS shell increase, while the increase rate for busbar conductors is much faster.Figure 7
Current distributions in busbar conductors and GIS shell (I = 3300 A).Figure 8
Variations of electromagnetic loss for busbar conductors and GIS shell with current.The temperature and SF6 gas velocity distributions in GIS busbar chamber are presented in Figure9. From Figure 9(a), it shows that the temperature of busbar conductor is high, and the temperature of GIS shell is relatively low. The SF6 gas temperature distribution in the GIS chamber is symmetry. The gas temperature on the upper surface of busbar conductors is relatively high, and the maximum gas temperature is 327.62 K, which is located on the top of busbar conductor A. The minimum gas temperature is 316.15 K, which is located at the bottom of GIS chamber. In addition, from Figure 9(b), it shows that SF6 gas convection mainly appears in the upper part of GIS chamber, where two large vortices are existed and the convection is relatively strong (the maximum velocity is 0.072 m/s). While in the central and bottom parts of the chamber, the SF6 gas velocity is relatively low and convection is weak.Figure 9
Temperature and SF6 gas velocity distributions in GIS busbar chamber (I = 3300 A). (a) Temperature. (b) SF6 gas velocity.
(a)(b)When GIS works in a severe outdoor environment, the lightning impulse impact on the GIS insulation performance is necessary to be considered. For practical engineering, the breakdown discharge tests with 1050 kV lightning impulse voltage are usually performed on 252 kV GIS equipment [27]. Therefore, in order to predict the breakdown discharge caused by overheating on the outer surface of busbar conductors, the breakdown margin (Em) of SF6 gas in the GIS busbar chamber under 1050 kV lightning impulse voltage is analyzed. The breakdown margin (Em) is defined as follows [10]:(16)Em=1.467ρT−E,where Em is the breakdown margin, kV/mm; ρ (T) is the SF6 gas density, kg/m3; and E is the local electric field intensity of SF6 gas, kV/mm.The electric field intensity and SF6 gas breakdown margin distributions in GIS busbar chamber are presented in Figure10. It shows that the distribution of SF6 gas breakdown margin in GIS busbar chamber is similar to the distribution of electric field intensity. In the areas between busbar conductor and GIS shell, the electric field intensity is large, and SF6 gas breakdown margin is small. While in the central region of GIS chamber, the electric field intensity is small, and the SF6 gas breakdown margin is large. It would indicate that the SF6 gas breakdown margin in the GIS busbar chamber is mainly affected by the electric field intensity and the effect of SF6 gas density is small. When I = 3300 A and U = 1050 kV, the minimum SF6 gas breakdown margin (Em,min) in the GIS busbar chamber is 7.98 kV/mm, which is located at top of busbar conductor A. At this place, the SF6 gas temperature is the highest (327.62 K), its density is the smallest and the electric field intensity is large. Therefore, the SF6 gas breakdown margin at top of busbar conductor A is small, its insulation performance is poor, and the thermal breakdown risk is relatively high.Figure 10
Electric field intensity and SF6 gas breakdown margin distributions in GIS busbar chamber (I = 3300 A, U = 1050 kV). (a) Electric field intensity. (b) Breakdown margin.
(a)(b)


### 4.2. The Effect of SF6 Gas Convection on Ultrasonic Propagation

Based on above analysis, it shows that the thermal breakdown risk at top of busbar conductor A in GIS busbar chamber is relatively high, which is marked as pointR (0, 18.5 cm). Therefore, in the present study, the point R is set as the ultrasonic source point when thermal breakdown happens in the GIS chamber (see Figure 11), and Gaussian pulse excitation is adopted to simulate the acoustic source (see Equation (13)). Meanwhile, 6 sensors were arranged in the GIS chamber to detect ultrasonic signal variations at different points. The specific locations for sensors in the GIS chamber are presented in Figure 11. For ultrasonic propagation simulations, the SF6 gas velocity, pressure, and temperature fields obtained from former computations should be mapped to the computational grid for sound simulations using grid mapping method at first, and then the sound pressure in the GIS chamber was computed. The sound pressure distributions in the GIS busbar chamber at different times are presented in Figure 12. It shows that the acoustic wave is a spherical wave. When the direct sound wave reaches the solid wall, it is reflected. Then, the reflected wave is mixed with the direct wave to form a composite wave. As time increases, the acoustic wave continuously diffuses and attenuates in the GIS chamber, and the sound pressure gradually decreases.Figure 11
Locations of ultrasonic source and sensors in GIS busbar chamber.Figure 12
Sound pressure distributions in GIS busbar chamber at different times. (a)t = 480 μs. (b) t = 960 μs. (c) t = 1920 μs. (d) t = 3840 μs.
(a)(b)(c)(d)In order to study the effects of SF6 gas velocity and temperature on the acoustic propagation in GIS chamber, the computational results of sound pressure using different computational models were compared and analyzed, including the fully coupled model, temperature coupled model, and uncoupled model. When the fully coupled model is used, both SF6 gas velocity and temperature distributions are coupled for sound pressure computations. When the temperature coupled model is adopted, the SF6 gas is assumed to be stationary (u = v = 0), and only SF6 gas temperature distribution is coupled for sound pressure computations. When the uncoupled model is adopted for sound pressure computations, the SF6 gas is assumed to be stationary (u = v = 0), and SF6 gas temperature is set to the average gas temperature of natural convection in the GIS chamber (Tf = Tf, ave = 321.45 K). The variations of maximum sound pressure and receiving time as acoustic signal arrives at different sensors under different computational models are presented in Table 6. It shows that, for different computational models, the receiving times as acoustic signal arrives at different sensors are same. This would indicate that, in the present study, the influences of SF6 gas velocity and temperature variations on sound propagation speed in the GIS chamber are quite small and the sound propagation time differences between different computational models should be less than the time step used for sound pressure computations Δt=0.5μs. Therefore, the sound propagation time difference between different computational models would be ignored. As for the variation of maximum sound pressure, it shows that the computational results obtained by the temperature coupled model and fully coupled model are quite close, where the maximum deviation is 0.09% and the average deviation is 0.06%. The difference of computational results obtained by the uncoupled model and fully coupled model are also small, where the maximum deviation is 1.95% and the average deviation is 1.84%. This means, in the present study, both the influences of SF6 gas velocity and temperature variations on sound pressure in the GIS chamber are insignificant. In our present study, the SF6 gas velocity of natural convection in GIS busbar chamber is relatively low (the maximum velocity is 0.072 m/s), and the temperature difference of SF6 gas is relatively small (the maximum temperature difference is 11.47 K). Therefore, the influences of SF6 gas velocity and temperature variations on sound propagation in the GIS chamber are insignificant. According to this reason, when the natural convection in the GIS busbar chamber is weak, the uncoupled model would be recommended for acoustic propagation computations in GIS busbar chamber, which would be beneficial to reduce the computational time and maintain the simulation accuracy as well.Table 6
The variations of maximum sound pressure and receiving time as acoustic signal arrive at different sensors under different computational models.
ParametersModelsSensor-1Sensor-2Sensor-3Sensor-4Sensor-5Sensor-6Pmax (Pa)Fully coupled model477.18230.72170.8397.9873.1925.60Temperature coupled model (u = v = 0, Tf = Tf, coupled)477.06230.67170.7297.8973.1225.61Uncoupled model (u = v = 0, Tf = Tf,ave = 321.45 K)486.02235.01173.9399.7374.5026.10t (μs)Fully coupled model125410.56962586.538404304.5Temperature coupled model (u = v = 0, Tf = Tf,coupled)125410.56962586.538404304.5Uncoupled model (u = v = 0, Tf = Tf, ave = 321.45 K)125410.56962586.538404304.5


## 4.1. Electromagnetic Coupled Heat Transfer and Breakdown Margin Analysis

Firstly, the current distribution and electromagnetic loss in three-phase GIS busbar chamber were analyzed. In the present study, the imbalance effect of three-phase current was not considered, where the current amplitude for three-phase busbar conductors are kept the same, and the phase difference is 120°. The current distributions in busbar conductors and GIS shell are presented in Figure7. It shows that, when high frequency alternating current is applied to busbar conductors, a variating magnetic field will be induced around the conductors and the induced current will be generated, which would lead to nonuniform current distribution on conductor cross section and result in skin effect. Due to the skin effect, the current in the busbar conductor will be concentrated on the outer surface of the conductor, and the effective resistance and electromagnetic loss for busbar conductors will increase. In addition, the magnetic field induced by one busbar conductor will also affect the current distributions in other conductors nearby. For example, due to the magnetic effect induced by busbar conductor B, the current in the busbar conductor A will concentrate toward to busbar conductor B and result in proximity effect. The proximity effect will further increase the nonuniform current distribution on busbar conductor cross section and increase electromagnetic loss of busbar conductors. Meanwhile, the induced current in the GIS shell will form a closed loop and generate eddy current loss inside. The variations of electromagnetic loss for busbar conductors and GIS shell with current are presented in Figure 8. It shows that the electromagnetic losses for three-phase busbar conductors are almost the same, which are much higher than the eddy current loss for GIS shell. As current increases, both electromagnetic losses for busbar conductors and GIS shell increase, while the increase rate for busbar conductors is much faster.Figure 7
Current distributions in busbar conductors and GIS shell (I = 3300 A).Figure 8
Variations of electromagnetic loss for busbar conductors and GIS shell with current.The temperature and SF6 gas velocity distributions in GIS busbar chamber are presented in Figure9. From Figure 9(a), it shows that the temperature of busbar conductor is high, and the temperature of GIS shell is relatively low. The SF6 gas temperature distribution in the GIS chamber is symmetry. The gas temperature on the upper surface of busbar conductors is relatively high, and the maximum gas temperature is 327.62 K, which is located on the top of busbar conductor A. The minimum gas temperature is 316.15 K, which is located at the bottom of GIS chamber. In addition, from Figure 9(b), it shows that SF6 gas convection mainly appears in the upper part of GIS chamber, where two large vortices are existed and the convection is relatively strong (the maximum velocity is 0.072 m/s). While in the central and bottom parts of the chamber, the SF6 gas velocity is relatively low and convection is weak.Figure 9
Temperature and SF6 gas velocity distributions in GIS busbar chamber (I = 3300 A). (a) Temperature. (b) SF6 gas velocity.
(a)(b)When GIS works in a severe outdoor environment, the lightning impulse impact on the GIS insulation performance is necessary to be considered. For practical engineering, the breakdown discharge tests with 1050 kV lightning impulse voltage are usually performed on 252 kV GIS equipment [27]. Therefore, in order to predict the breakdown discharge caused by overheating on the outer surface of busbar conductors, the breakdown margin (Em) of SF6 gas in the GIS busbar chamber under 1050 kV lightning impulse voltage is analyzed. The breakdown margin (Em) is defined as follows [10]:(16)Em=1.467ρT−E,where Em is the breakdown margin, kV/mm; ρ (T) is the SF6 gas density, kg/m3; and E is the local electric field intensity of SF6 gas, kV/mm.The electric field intensity and SF6 gas breakdown margin distributions in GIS busbar chamber are presented in Figure10. It shows that the distribution of SF6 gas breakdown margin in GIS busbar chamber is similar to the distribution of electric field intensity. In the areas between busbar conductor and GIS shell, the electric field intensity is large, and SF6 gas breakdown margin is small. While in the central region of GIS chamber, the electric field intensity is small, and the SF6 gas breakdown margin is large. It would indicate that the SF6 gas breakdown margin in the GIS busbar chamber is mainly affected by the electric field intensity and the effect of SF6 gas density is small. When I = 3300 A and U = 1050 kV, the minimum SF6 gas breakdown margin (Em,min) in the GIS busbar chamber is 7.98 kV/mm, which is located at top of busbar conductor A. At this place, the SF6 gas temperature is the highest (327.62 K), its density is the smallest and the electric field intensity is large. Therefore, the SF6 gas breakdown margin at top of busbar conductor A is small, its insulation performance is poor, and the thermal breakdown risk is relatively high.Figure 10
Electric field intensity and SF6 gas breakdown margin distributions in GIS busbar chamber (I = 3300 A, U = 1050 kV). (a) Electric field intensity. (b) Breakdown margin.
(a)(b)


## 4.2. The Effect of SF6 Gas Convection on Ultrasonic Propagation

Based on above analysis, it shows that the thermal breakdown risk at top of busbar conductor A in GIS busbar chamber is relatively high, which is marked as pointR (0, 18.5 cm). Therefore, in the present study, the point R is set as the ultrasonic source point when thermal breakdown happens in the GIS chamber (see Figure 11), and Gaussian pulse excitation is adopted to simulate the acoustic source (see Equation (13)). Meanwhile, 6 sensors were arranged in the GIS chamber to detect ultrasonic signal variations at different points. The specific locations for sensors in the GIS chamber are presented in Figure 11. For ultrasonic propagation simulations, the SF6 gas velocity, pressure, and temperature fields obtained from former computations should be mapped to the computational grid for sound simulations using grid mapping method at first, and then the sound pressure in the GIS chamber was computed. The sound pressure distributions in the GIS busbar chamber at different times are presented in Figure 12. It shows that the acoustic wave is a spherical wave. When the direct sound wave reaches the solid wall, it is reflected. Then, the reflected wave is mixed with the direct wave to form a composite wave. As time increases, the acoustic wave continuously diffuses and attenuates in the GIS chamber, and the sound pressure gradually decreases.Figure 11
Locations of ultrasonic source and sensors in GIS busbar chamber.Figure 12
Sound pressure distributions in GIS busbar chamber at different times. (a)t = 480 μs. (b) t = 960 μs. (c) t = 1920 μs. (d) t = 3840 μs.
(a)(b)(c)(d)In order to study the effects of SF6 gas velocity and temperature on the acoustic propagation in GIS chamber, the computational results of sound pressure using different computational models were compared and analyzed, including the fully coupled model, temperature coupled model, and uncoupled model. When the fully coupled model is used, both SF6 gas velocity and temperature distributions are coupled for sound pressure computations. When the temperature coupled model is adopted, the SF6 gas is assumed to be stationary (u = v = 0), and only SF6 gas temperature distribution is coupled for sound pressure computations. When the uncoupled model is adopted for sound pressure computations, the SF6 gas is assumed to be stationary (u = v = 0), and SF6 gas temperature is set to the average gas temperature of natural convection in the GIS chamber (Tf = Tf, ave = 321.45 K). The variations of maximum sound pressure and receiving time as acoustic signal arrives at different sensors under different computational models are presented in Table 6. It shows that, for different computational models, the receiving times as acoustic signal arrives at different sensors are same. This would indicate that, in the present study, the influences of SF6 gas velocity and temperature variations on sound propagation speed in the GIS chamber are quite small and the sound propagation time differences between different computational models should be less than the time step used for sound pressure computations Δt=0.5μs. Therefore, the sound propagation time difference between different computational models would be ignored. As for the variation of maximum sound pressure, it shows that the computational results obtained by the temperature coupled model and fully coupled model are quite close, where the maximum deviation is 0.09% and the average deviation is 0.06%. The difference of computational results obtained by the uncoupled model and fully coupled model are also small, where the maximum deviation is 1.95% and the average deviation is 1.84%. This means, in the present study, both the influences of SF6 gas velocity and temperature variations on sound pressure in the GIS chamber are insignificant. In our present study, the SF6 gas velocity of natural convection in GIS busbar chamber is relatively low (the maximum velocity is 0.072 m/s), and the temperature difference of SF6 gas is relatively small (the maximum temperature difference is 11.47 K). Therefore, the influences of SF6 gas velocity and temperature variations on sound propagation in the GIS chamber are insignificant. According to this reason, when the natural convection in the GIS busbar chamber is weak, the uncoupled model would be recommended for acoustic propagation computations in GIS busbar chamber, which would be beneficial to reduce the computational time and maintain the simulation accuracy as well.Table 6
The variations of maximum sound pressure and receiving time as acoustic signal arrive at different sensors under different computational models.
ParametersModelsSensor-1Sensor-2Sensor-3Sensor-4Sensor-5Sensor-6Pmax (Pa)Fully coupled model477.18230.72170.8397.9873.1925.60Temperature coupled model (u = v = 0, Tf = Tf, coupled)477.06230.67170.7297.8973.1225.61Uncoupled model (u = v = 0, Tf = Tf,ave = 321.45 K)486.02235.01173.9399.7374.5026.10t (μs)Fully coupled model125410.56962586.538404304.5Temperature coupled model (u = v = 0, Tf = Tf,coupled)125410.56962586.538404304.5Uncoupled model (u = v = 0, Tf = Tf, ave = 321.45 K)125410.56962586.538404304.5


## 5. Conclusions

In the present paper, the electromagnetic coupled heat transfer and ultrasonic propagation in a 252 kV three-phase GIS busbar chamber were numerically studied by using finite element method. The electromagnetic loss and distributions of SF6 gas velocity, temperature, and breakdown margin in the GIS busbar chamber were carefully analyzed, and the influences of SF6 gas velocity and temperature variations on ultrasonic propagation performances in the GIS chamber were also discussed in detail. The major findings are as follows:(1)
When high-frequency alternating current is applied to busbar conductors, the skin effect and proximity effect of three-phase GIS busbar conductors are remarkable, and the electromagnetic loss of busbar conductors are much higher than eddy current loss of GIS shell. The gas temperature on the upper surface of busbar conductors is relatively high, and the maximum gas temperature is 327.62 K atI = 3300 A, which is located on the top of busbar conductor A.(2)
The SF6 gas breakdown margin in the GIS busbar chamber is mainly affected by the electric field intensity, and the effect of SF6 gas density is small. WhenI = 3300 A and U = 1050 kV, the minimum SF6 gas breakdown margin (Em,min) in the GIS busbar chamber is 7.98 kV/mm, which is located at top of busbar conductor A. At this place, the SF6 gas temperature is the highest, its density is the smallest, and the electric field intensity is large. Therefore, the thermal breakdown risk at top of busbar conductor A is relatively high.(3)
In the present study, the SF6 gas velocity of natural convection in GIS busbar chamber is relatively low (the maximum velocity is 0.072 m/s), the temperature difference of SF6 gas is relatively small (the maximum temperature difference is 11.47 K), and the influences of SF6 gas velocity and temperature variations on sound propagation in the GIS chamber are insignificant. Therefore, when acoustic propagation simulation is performed at this case, the SF6 gas would be assumed to be stationary, and its temperature would be set to the average gas temperature of natural convection in the GIS chamber. This would be beneficial to reduce the computational time and maintain the simulation accuracy as well.



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*Source: 7836212-2022-03-10.xml*