SHENG Wangqun, LI Gang, LI Yanzhe, LI Baoxue, ZHAO Shanpeng
(1. China Railway First Survey and Design Institute Group Co., Ltd., Xi’an 710000, China；
2. School of Automation & Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China；
3. China Railway Lanzhou Group Co., Ltd., Jiayuguan Power Feed Section, Jiayuguan 735100, China)
Abstract：
The installed porcelain insulators on existing railway lines in China are prone to “snow flash” in winter. In order to prevent the occurrence of “snow flash” and improve the reliability of the insulators, a composite-porcelain insulator is designed. A multi-physics coupling simulation model is built based on numerical simulation methods of the electromagnetic field theory and computational fluid dynamics. Taking average electric field intensity on the surface of the insulator as the characteristic parameter of the electric field distortion degree and the snow crystal collision coefficient and distribution coefficient as the characteristic parameter of snow crystal deposition, the characteristics of snow crystal deposition under different wind speeds and wind direction angles and the electric field characteristics under two snow cover types are analyzed. The simulation results show that the average electric field intensity of composite-porcelain insulators is 10.4% and 13.8%, respectively, lower than that of porcelain insulators in vertical and horizontal wind snow covers, which can effectively reduce the degree of electric field distortion. The collision coefficient of snow crystals on the surface of the composite-porcelain insulator sheds is 16.0% higher than that of the porcelain insulator, and the collision coefficient of the trunk and the fittings are lower 20.2% and 11.9% than that of the porcelain insulator. There is almost no change in the distribution coefficient of the insulator sheds.
Key words：
porcelain cantilever insulator; snow flash; snow crystal deposition; electric field characteristics; simulation
The terrain along the existing railway lines in China is complex, and climate is changeable. The wind and snow areas are widely distributed[1-2]. Porcelain insulators are widely used in existing lines, which is easy to cause a lot of snow on the surface of the insulators in the wind and snow. The sheds of porcelain insulators have poor hydrophobicity, which makes snow and pollution dissolve and ionize. It will affect the reliability of railway power supply and the safety of train operation[3-4]. Therefore, an optimization plan is proposed for existing line porcelain insulators in the wind and snow areas to improve reliability of railway while being economical.
Insulator optimization mainly improves anti-contamination ability and electric field distortion by changing sheds structure and insulator material[5-8]. At present, the researches on insulator optimization mainly focus on combining the advantages of porcelain insulators and composite insulators from the perspective of materials[9], the influence of sheds spacing, extension and sheds inclination on electric field distribution and anti-contamination ability[10-12], effect of installing booster shed sheath[13-16]. However, the most studies are based on insulators for high and low voltage power lines, rather than data on catenary cantilever insulator in wind and snow environment. Moreover, the optimization based on electric field distribution and snow crystal deposition of cantilever insulator is not yet studied.
In view of “snow flash” problem, composite-porcelain insulator from sheds structure and materials is proposed. A multi-field and single-phase coupling finite element model of insulator is established by using electric field, flow field and particle tracking field. The electric field characteristics and snow crystal deposition characteristics of composite-porcelain insulators are analyzed, which provides optimization plan and theoretical basis for the porcelain insulators installed on existing lines.
The insulators installed on the existing railway lines in China are mainly porcelain insulators, and the QBG-25 type is mainly used in the heavily polluted sections. The railway line passes through the wind and snow section, and the flashover accident of the catenary insulator frequently occurs in the northern area. A composite-porcelain insulator is designed based on QBG-25 type porcelain insulator. The silicone rubber shed sheath is installed on the No.3 and No.7 sheds respectively under the premise that the original size remains unchanged. The design dimension of the composite-porcelain insulator is shown in Fig.1, and the full-scale model three-dimensional model is shown in Fig.2. The sheds are numbered sequentially from the high-voltage fitting to the low-voltage fitting.
Fig.1 Design dimension of insulator
Fig.2 Three dimensional model of insulator
Optimization of composite-porcelain insulator shows that porcelain material has good mechanical stability and service life, the composite shed sheath has good water hydrophobicity. When the snow on the surface of the insulator melts, it is not easy to form a continuous water film and electrolytic pollution layer. It is feasible and economical to install shed sheath on the installed porcelain insulator.
The electric field characteristics of insulators in snow environment are calculated and solved by the electromagnetic field equation. The snow crystal deposition characteristics in snow and strong wind environment are solved and calculated by the coupling of the flow field and the particle field. The Euler-Lagrangian calculation method is adopted. The air is regarded as the continuous phase and the particle trajectory is calculated.
In the flow field module, the air is regarded as an incompressible Newtonian fluid, and air fluid on the surface of the insulator is prone to bending considering the working conditions of the insulator under the action of wind. The model adopts the RANSk-εturbulence model[17]. The governing equations are
(1)
wherevis the fluid velocity (m·s-1);is the differential operator;vrefers to gradient operation ofv;·vrefers to divergence operation ofv;Iis the stress tensor (Pa);μTand μ are the turbulent dynamic viscosity and aerodynamic viscosity (Pa·s), respectively;ρis the air density (kg·m-3);Fis the volume force (N·m-3);kis the turbulent kinetic energy (m2·s-2) ;εis the turbulent dissipation rate (m2·s-3);Cμis the viscosity coefficient;σk,σε,Cε1,Cε2are the turbulence model parameters;pkis the turbulent energy term (W·m-3).
In the particle tracking field, the snow crystals are equivalent to spherical particles. The initial velocity of the snow crystals is the same as the velocity of the flow field and has turbulent diffusivity. Only the gravity and drag force of the snow crystals are considered in the particle tracking field. The governing equations are
(2)
wherempis the particle mass (kg);vpis the particle velocity (m·s-1);tis the particle movement time (s);Fg,FDare the gravity and drag force on the particle (N);ρPis the particle density (kg·m-3);gis the acceleration of gravity (m·s-2);τis the relaxation time (s);dis the particle diameter (m).
The creepage distance of QBG-25 type catenary insulator is 1 600 mm. The wavelength of the catenary power frequency AC is 6 000 km. It can be considered that the electric field of the insulator is stable at any instant, and the electrostatic field can be selected to simulate and analyze the electric field distribution of the insulator. The governing equations are
(3)
whereDis the electric flux density (C·m-3);Eis the electric field strength (V·m-1);ρis the charge density (C·m-3);φis the scalar potential function of the electrostatic field (V);·Drefers to divergence operation ofD;×Erefers to curl operation ofE;2is the Laplace operator;2φrefers to the divergence operation of the gradient operation ofφ;εis the dielectric constant (F·m-1).
In order to accurately calculate the simulation results of the snow crystal deposition characteristics of the insulators and the electric field characteristics under different snow types, the flow field particle field model and the electric field simulation model are established, respectively.
Considering the end effect of the insulator in the actual operating state, the composite-porcelain insulator model in Fig.2 is taken as the research object, and the wind tunnel model of the insulator is constructed in order to reduce the simulation calculation error as shown in Fig.3. The size of the wind tunnel model is larger than the height of the insulator structure. In this paper, the size of the wind tunnel model is set to 4 500 mm×4 500 mm×3 500 mm, which provides enough computational domain to simulate the development of turbulence. The insulator electric field model is a two-dimensional model, which is simplified from the perspective of engineering approximation. The high and low voltage fittings and sheds of insulator are regarded as axisymmetric, and the influence of the pillar, the cantilever positioning device and the catenary wire on the electric field potential distribution are ignored. The vertical snow cover electric field model is shown in the Fig.4, and the horizontal wind snow covered model is shown in the Fig.5.
Fig.3 Model of insulator in wind tunnel
Fig.4 Model of vertical snow cover electric field
Fig.5 Model of horizontal wind snow cover electric field
The insulator structure is discretized into a model composed of multiple elements which are connected by element nodes. The ideal assumption of the insulator structure is combined with the physical field governing equations and applied to each element in the structure to form a stiffness equation, which is solved by combined with boundary conditions. In the process of element solving, shape function interpolation and Gaussian numerical integration are introduced to solve the approximate solution of the state variables at each element node, and finally the approximate solution of the partial differential equation is obtained.
In the multi physical model of flow field particle tracking field and fluid-particle interaction, the wind tunnel model is imported and simulation calculation conditions are applied. According to the mathematical model and control equation of the flow field, the approximate solution of partial differential process of the flow field is solved first. Then, according to the mathematical model and control equation of particle tracking field combined with the calculation results of the flow field, the calculation results of multi physical coupling field are obtained, and the total number of snow crystal particles on the insulator surface and each part of the insulator are counted.
In the electric field, the model of vertical snow cover and model of horizontal wind snow cover are imported and simulation calculation conditions are applied. The complex permittivity is used to replace the permittivity. According to the electric field mathematical model and control equation, the approximate solution of partial differential equation of electric field is calculated, and the average electric field intensity of insulator and sheds is calculated.
Reasonable setting of boundary conditions is the key to improve simulation accuracy. To simulate the operating conditions of insulators under AC voltage, the boundary conditions are set as 1)-3).
1) Boundary conditions of electric field. 41 kV AC power frequency is applied to the high voltage fitting, and the low voltage fitting is grounded. There are two mechanisms for snow accumulation. (a) Snow accumulates vertically on the horizontally arranged insulators. (b) Snow accumulates on one side of the insulator due to strong horizontal wind. According to the Wieck snow test[18], the insulator surface snow is set to vertical snow cover type and horizontal wind snow covered, the vertical snow thickness on the surface of the insulator is set at 10 mm-60 mm in turn and the horizontal wind snow cover thickness is set at 1 mm-10 mm in turn. The transient solver is used to calculate the electric field distribution of the insulator. The physical constants of electric field dielectric are shown in Table 1.
2) Boundary conditions of the turbulent flow field. The turbulence is set as incompressible Newtonian fluid, and the airflow around the insulator will bend. The inlet and outlet of the insulator wind tunnel model are set as the velocity inlet and the pressure outlet, respectively. According to the empirical formula set the inlet turbulence intensityI=0.16(Re)-1/8and turbulence scalel=0.07De, whereReis the turbulent Reynolds number (dimensionless);Deis the average diameter of the insulator (mm). The outer wall of the wind tunnel is the sliding wall, and the insulator wall is the inner wall, which is set as a non-slip wall .
The existing line passes through wind and snow areas in the north. The wind speed is set to 10 m/s-30 m/s in the text. The wind direction angle is 0° perpendicular to the insulator axis. When the airflow is biased toward the high-voltage end fitting, the inclination angle is negative, and vice versa. The range of angle isβ∈[-60°,60°].
3) Boundary condition of particle tracking field. The snow crystal structure is determined by the external temperature and water vapor supersaturation. When the temperature is from -4 ℃ to -10 ℃, the snow crystal structure is columnar; when the temperature is from -10 ℃ to -22 ℃, the snow crystal structure is plate-shaped. When the temperature drops further, it becomes significant columnar again. The degree of water vapor supersaturation in the air will further affect the crystal structure. The snow crystal changes from hollow plate shape (when the supersaturation is 0.1 g·m-3) to hollow dendritic shape (when the supersaturation is 0.2 g·m-3), and becomes solid dendritic shape (when the supersaturation is 0.3 g·m-3). According to the three most common snow crystal structures, four types of snow crystals are set as 1 mm plate, 1 mm column, 4 mm hollow dendrites and 4 mm solid dendrites. The quality is calculated according to the snow crystal fitting formula, and the expression is
M=ADB,
(4)
whereAandBare the fitting coefficients of snow crystals;Mis the mass of snow crystals (mg);Dis the particle size of snow crystals. The correlation coefficients are shown in Table 2.
The snow crystals enter the wind tunnel vertically at the velocity of turbulent flow, and release 1 000 particles per second, including 550 plate particles, 300 columnar particles and 150 dendritic particles. The release time of snow crystals is 10 s.
The total number of snow crystals per unit volume exceeds tens of millions. In order to accurately describe the deposition amount, the collision coefficient and distribution coefficient are used as the characterizing parameters of the snow crystal deposition amount to describe the snow crystal deposition degree of the insulator and the snow crystal deposition distribution in each part of the insulator.The expression of collision coefficientλis
λ=Nt/N,
(5)
whereNtis the total number of snow crystals attached to the surface of the insulator;Nis the total number of snow crystals released.
The expression of distribution coefficient is
δ=Ni/Nt,
(6)
whereNiis the number of attached snow crystals corresponding to different parts on the surface of the insulator.
The transient solution calculation of the insulator multi-physical coupling field model is performed, the number of snow crystals on the surface of the insulator is counted, and the collision coefficient and distribution coefficient are used as the characterizing parameters to analyze the changes in the amount and distribution of snow crystals on the surface of the insulator. The simulation result of the insulator multi-physics coupling field is used to judge the influence of the installation of the sheath on the snow crystal deposition and distribution position. The electric field model of insulator is solved in steady state, and the electric field intensity of insulator surface with different snow thickness under two snow types is counted. The average electric field intensity of insulator and the average electric field intensity of sheds are taken as the characterization parameters to judge whether the installation of sheds is effective for insulator optimization.
There are several conditions for insulator snow flashover. Wet snow or compacted snow is adhered closely to the insulator surface. The length of evenly snow covers is about from 60% to 100% of the insulator dry arc length. Snow is too thick, and fills the entire gap between the sheds, thus bridging the dry arc distance between the sheds. Insulator surface pre pollution is diffused into the snow.
The snow flashover process starts from the leakage current of insulator surface and snow layer, and the current depends on the snow density, conductivity and liquid water content. The region with high current density in snow began to melt due to Joule heat, and remained stable after reaching from 50 mA to 100 mA.
The electrical accidents in heavy snow weather mainly occur on the insulators arranged in the horizontal direction, and the flashover process is shown in Fig.6.
Fig.6 Development process of snow flashover
According to the development process of flashover, the generation of leakage current further promotes the snow melting and causes flashover. The extension value of sheath is 110 mm. After installing the sheath, the snow cannot completely cover the sheds, and the sheath divides the snow into three parts, which reduces the possibility of flashover development. Hydrophobicity of the composite sheath ensures that the sheds cannot form a continuous water film after snow melting, thus reducing the probability of flashover.
Fig.7 shows the average electric length of insulator surface under vertical snow accumulation type, and Fig.8 shows the average electric field intensity of sheds.
Fig.7 Average electric field intensity of insulator
As shown in Fig.7, the average electric field intensity of the optimized composite-porcelain insulator is 10.4% lower than that of the unoptimized porcelain insulator, which effectively reduces the electric field distortion on the surface of the insulator. As shown in Fig.8, the optimized average field intensity along the surface of each shed under different snow thickness is significantly reduced. When the snow thickness is 40 mm, the average field intensity of the No.3 shed and No.7 shed decreases by 17.5% and 19.9%, respectively. The average field intensity of sheds on both sides of No.7 and No.3 sheds is also reduced.
Fig.8 Average electric field intensity of each shed
Fig.9 shows the average electric field intensity of insulators under the type of horizontal wind snow cover, and Fig.10 shows the average electric field intensity of insulator sheds.
Fig.9 Average electric field intensity of insulator
Fig.10 Average electric field intensity of each shed
As shown in Fig.9, after installing sheath on porcelain insulator, the average electric field intensity of the optimized composite-porcelain insulator is 13.8% lower than that of the unoptimized porcelain insulator. When the snow thickness is 10 mm, the average electric field intensity of the optimized composite-porcelain insulator is 15.9% lower than that of the unoptimized porcelain insulator. As shown in Fig.10, the optimized average field intensity along the surface of each shed under different snow thickness is significantly reduced. When the snow thickness is 10 mm, the average field intensity of the No.3 shed and No.7 shed decreases by 30.5% and 31.1%, respectively.
Since the electric field distribution along the surface of the insulator is different from that in the air gap, the insulator bears most of the electric field intensity, there is a normal electric field component perpendicular to the flashover path on the shortest flashover path, so the characteristic value of the electric field strength needs to be considered when extracting the electric field characteristics. The gas discharge starts from the region with the strongest electric field, but the randomness of the initial electron generation, the discharge start position is in a certain region near the maximum electric field intensity along the surface instead of a certain point. Snow accumulates distortion of the electric field distribution on the surface of the insulator. Especially in the snow melting stage, most of the voltage on the insulator is applied to a section of the air gap, and flashover occurs when the air gap breaks down. When snow completely covers the sheds, the electric field distribution on the surface of the shed is distorted, which will also cause local arcs on the snow surface to develop into a complete flashover.
Since the snow crystal particles are estimated to exceed 3.6 billion per unit of precipitation in 1 mm of snow, the computer cannot calculate accurately such huge data content. In the current snow test method, the development of snowflakes is starting from a snow crystal nucleus, spontaneous icing cannot be achieved. Therefore, in the test, ice crystal particles are injected as the growing crystal nucleus. It cannot be tested in a wind speed environment or used by collecting natural and clean snow for storage. Therefore, a coupling field of particle field interaction is established in the flow field. By calculating the adhesion of snow crystal particles on the surface of the insulator in a short period of time, the collision coefficient and distribution coefficient are obtained through the calculation formula to illustrate the change of snow crystal particles. The purpose is to analyze and compare the changes in the amount and distribution of snow crystal particles before and after the sheath is installed, and use the collision coefficient and the distribution coefficient to judge the influence of the sheath on the snow crystal deposition of the insulator.
The installation of the shed sheath increases the contact area of the wind, and the amount of snow crystal deposition on its surface changes accordingly. Therefore, it is of great significance for insulator optimization to analyze the deposition characteristics of insulator under different wind speed and wind direction by taking collision coefficient and distribution coefficient as characteristic parameters to characterize the amount of snow crystal deposition.
As shown in Fig.11, the collision coefficient of composite-porcelain insulator and porcelain insulator increase with the increase of wind speed. The increase of wind speed leads to the increase of drag force on the snow crystals, which intensifies the collision between the snow crystal and the surface of the insulator. When the wind speed is 30 m/s, the difference between the collision coefficients of the two insulators is the largest, and the collision coefficient of composite-porcelain insulator is 3.3% higher than that of porcelain insulator, which indicates that the installation of shed sheath has a negligible impact on the insulator contamination.
Fig.11 Relation between snow crystal collision coefficient and wind speed on insulator
Fig.12 is the static pressure distribution on the windward surface of the insulator. The color represents the size of the static pressure and reflects the intensity of the collision between the snow crystal particles and the surface of the insulator. The higher the static pressure, the more intense the collision between the snow crystals and insulator. Snow crystal particles mainly adhere to the windward surface of the insulator. The vortex on the leeward side of the insulator has little effect on the large particles, so the snow crystal deposition on the leeward side is close to zero. When the wind speed increases from 10 m/s to 30 m/s, the maximum surface static pressure of the porcelain insulator increases from 65.5 Pa to 584.5 Pa, and the maximum surface static pressure of the composite-porcelain insulator increases from 63.5 Pa to 552.9 Pa. The static pressure change range of the two insulators is similar, and the change trend of the collision coefficient of snow crystal particles is similar.
Fig.12 Distribution of static pressure on insulator surface
Fig.13 is the vector diagram of the surface velocity of the insulator. The color represents the air velocity on the surface of the insulator. The air flow has relative motion in contact with the insulator. Due to viscous shear force, the velocity of the thin fluid layer close to the insulator is reduced, which form a boundary layer. When snow crystal particles in the air are near the boundary layer, the shear force and gravity work together to deposit on the surface of the insulator. The wind speed increases, the boundary layer of insulator surface will separate and produce turbulence pulsation, which increases the possibility of snow crystal deposition on insulator surface.
Fig.13 Vector diagram of airflow velocity on insulator surface
The deposition amount and distribution position of snow crystals on insulator surface will be changed with the change of wind direction angle. It is necessary to analyze the snow crystal deposition characteristics of the insulators under different angles.
As shown in Fig.14, when the wind direction angleβ∈[-60°,60°], the collision coefficient of the two insulator snow crystals presents an “M” shape, and the collision coefficient increased first and then decreased with the increased of wind direction angle. When the angle is ±30°, the snow crystal collision coefficient of composite-porcelain insulator is the largest. When the wind direction angle is within ±30°, the vertical contact area between the airflow and the insulator gradually increases with wind direction angle gradually increases, resulting in increase of collision probability between the snow crystal and the insulator. The wind direction angle continues to increase at ±30°, the vertical contact area gradually decreases, causing the snow crystal collision coefficient to gradually decrease.
Fig.14 Relation between snow crystal collision coefficient and wind direction on insulator
Fig.15 is the distribution of static pressure on the windward surface of composite-porcelain insulator under different wind angles. Fig.16 is the vector diagram of airflow velocity of composite-porcelain insulator under different wind angles.
Fig.15 Distribution of static pressure on insulator surface under different wind angles
The vertical windward surface of the insulator gradually shifts to the side of the fitting with increase of wind direction angle. When the wind direction angle is 0°, the positive pressure is evenly distributed on the windward surface of the insulator. With the wind direction angle gradually increases, the positive pressure on the surface of the insulator is distributed on the windward side fitting and the surface of No.1 to No.3 and No.7 sheds. The air velocity vector on the surface of No.5 and No.8 to No.10 sheds is 0. No.3 and No.7 sheds act as a barrier to reduce the amount of snow on other sheds.
Fig.16 Vector diagram of airflow velocity on insulator surface under different wind angles
Fig.17 is the relation between snow crystal collision coefficient of composite-porcelain insulator and wind direction.
Fig.17 Relation between snow crystal collision coefficient and wind direction on insulator
The wind direction angle is within the range of ±30° in the same wind speed, the snow crystals collision coefficient of the shed increases with the increase of the wind direction angle. When the wind speed angle continues to increase, the wind direction angle ±30°is the turning point of the snow crystals collision coefficient of the shed, and the snow crystal collision coefficient shows a gradually decreasing trend with the wind direction angle continues to increase. Within the range of ±60°, the collision coefficient on the surface of the composite-porcelain insulator is increased by 16.0% than that of the porcelain insulator. When the wind angle is ±30°, the collision coefficient of shed on composite-porcelain insulator is 15.0% and 20.7% higher than that of porcelain insulator. In the range of ±60°, the collision coefficient of trunk and fitting on composite-porcelain insulator shows a downward trend with the increase of the wind direction angle. The collision coefficient of fitting on composite-porcelain insulator is 11.9% lower than that of porcelain insulator, and the collision coefficient of trunk is reduced by 20.2%.
Fig.18 is the relation between snow crystal distribution coefficient and wind direction on insulator shed. The wind direction angle has a direct effect on the distribution coefficient of snow crystals on the upper and lower surfaces of the shed. The amount of snow crystals deposited on the windward side of the shed is much larger than that on the leeward surface. The distribution coefficient of snow crystals on the shed edge gradually decreases and the distribution coefficient of snow crystals on the windward side of the shed gradually increases with the wind direction angle gradually increases. The change trend of the distribution coefficient of shed on composite-porcelain insulator is similar to that of porcelain insulator. The distribution coefficient of the windward side shed on composite-porcelain insulator is 2.8% higher than that of porcelain insulator, and the distribution coefficient of leeward side sheds on porcelain insulators is 3.4% lower than that of porcelain insulator. The distribution coefficient of composite-porcelain insulator is almost the same as that of porcelain insulator.
Fig.18 Relation between snow crystal distribution coefficient and wind direction on insulator shed
In this study, composite-porcelain insulator is the object of research interest. In snow environment, the average electric field intensity of composite-porcelain insulators is 10.4% and 13.8%, respectively, lower than that of porcelain insulators in vertical snow cover and horizontal snow cover, which can effectively reduce the degree of electric field distortion, and the electric field intensity of No.3 and No.7 sheds with sheaths is significantly reduced. The collision coefficient of porcelain insulators and composite-porcelain insulators gradually increases with the increase of wind speed. When the wind speed is 30 m/s, the collision coefficient on composite-porcelain insulator is 2.8% higher than that of porcelain insulator. The effect of installing shed sheath on the amount of snow crystal deposition is negligible. When the wind speed is the same, the collision coefficient of insulator surface presents an “M”-shaped distribution within the range of ±60°. The wind direction angle of ±30° is the turning point of snow crystal collision coefficient. The collision coefficient of composite-porcelain insulator first increases and then gradually decreases with the increase of wind direction angle. The surface collision coefficient of composite-porcelain insulator sheds is 16.0% higher than that of porcelain insulator, the collision coefficient of trunk is 20.2% lower than that of porcelain insulator, and the collision coefficient of fitting is 11.9% lower than that of porcelain insulator. The distribution coefficient of composite-porcelain insulator is almost the same as that of porcelain insulator. The results show that the electric field distortion of porcelain insulator can be effectively reduced by installing shed sheath, and the amount of snow crystal deposition does not increase significantly.
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