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Corrosion reaction kinetics and high‐temperature corrosion testing of contact element strips in ultra‐high voltage bushing based on the phase‐field method

Corrosion reaction kinetics and high‐temperature corrosion testing of contact element strips in... INTRODUCTIONWith the increase in transmission capacity, heat generation has become a key issue restricting the safe and stable operation of ultra‐high voltage (UHV) power transmission equipment. For the UHV power transmission equipment (UHV bushings), contact element strips are required to provide a current‐carrying connection between the long guide rods [1–3]. The contact elements undergo high‐temperature corrosion under long‐term current flow conditions, resulting in deterioration of contact resistance and electrical connection failure. The corrosion is a slow process. In addition, there is no test platform or operating data of the contact element strips under actual working conditions [4]. In recent years, discharge failures caused by an insufficient thermal margin of the structure or degradation of the electrical connection structure have occurred in the operation of ultra‐/extra‐high‐voltage bushing [5]. The overheating fault of the valve‐side bushing and wall bushing in China as of 2020 is shown in Figure 1. As can be seen from the figure, the surface of the contact elements changes from silver to black. Abnormal current‐carrying connection components account for 15.11% and 22% of the two types of bushing faults, respectively.1FIGUREOverheating failure of the bushing current‐carrying connection structureThe electrical contact corrosion process of current‐carrying structures is relatively complicated and affected by various factors, such as current intensity, chemical corrosion environment, and fretting wear. Scholars have carried out many experiments and theoretical studies on the corrosion mechanism of metal materials and SF6 decomposition after decades of development [6–9]. Holm et al. proposed the electrical contact model and continued to improve it [10, 11]. Through electron microscope observation, Trockels [12] suggested that the crack growth rate of aluminium alloys in corrosive environments is related to the hydrogen atoms released by the crack reaction. Eibech et al. [13] conducted a large number of SF6 decomposition experiments at temperatures higher than 200°C, obtained the annual decomposition rate of SF6 in different material containers, and measured the gas and solid products after the reaction. There has been no systematic research on the electrical contact characteristics of UHV actual current‐carrying connection structures. Moreover, there have been relatively few studies of the failure mechanism of current‐carrying structures under the synergistic effect of electrical stress, thermal stress, and the SF6 gas environment. In order to further reveal the overheating failure caused by contact elements, it is necessary to carry out research on the failure mechanism of the contact element strip used in UHV bushings.In this study, a two‐dimensional phase‐field model for high‐temperature corrosion was established to obtain the charge carrier concentration distribution in the film. Based on corrosion reaction kinetics, the influence of temperature, gas partial pressure, film thickness, and applied electric field on the growth rate of thin film was analyzed using the phase‐field method. At the same time, the contact elements strip commonly used in the bushing was the test object. A high‐temperature corrosion test was carried out in the SF6 atmosphere to simulate the high‐temperature corrosion caused by the uneven current carrying of the contact element strip under actual operating conditions. The energy spectrum analysis and morphology observation were carried out on the surface of the contact finger, which was similar to that of the faulty contact element strips. Combined with the simulation of temperature on the film growth rate, the surface corrosion characteristics of the contact area and the non‐contact area of the contact elements were qualitatively analyzed, and the corrosion mechanism of typical contact elements was further explained.FINITE ELEMENT PHASE‐FIELD METHOD AND MODEL CONSTRUCTIONReaction kinetics theoryIn the corrosive medium, a layer of surface film with different properties from the substrate will be formed on the metal, and the film will continue to grow under the action of the corrosive medium [14]. Since metal sulfides or fluorides are essentially ionic compounds, for stoichiometric ionic compounds, ion migration is explained by Schottky defects or Frenkel defects.The SF6 in the atmosphere diffuses to the interface between the gas and film (G–F interface), and physical adsorption occurs at the interface; that is1SF6(g)=SF6(ad.)\begin{equation}{\rm SF}_6(g) = {\rm SF}_6({\rm ad.})\end{equation}At the interface between the metal and film (M–F interface), the physically adsorbed molecules ionize to form cation vacancy and electron hole.2SF6ad.=MF2+VM′′+2hg+SF4\begin{equation}{\rm{S}}{{\rm{F}}_6}\left( {{\rm{ad}}{\rm{.}}} \right) = {\rm{M}}{{\rm{F}}_2} + {\rm V}^{\prime\prime}_{\rm{M}} + 2{{\rm{h}}^{\rm{g}}} + {\rm{S}}{{\rm{F}}_4}\end{equation}At the M–F interface, the cation vacancy and the electron hole recombine.3M2++VM′′=0\begin{equation}{\rm M}^{2 +} + {\rm V}^{\prime\prime}_{\rm{M}} = 0\end{equation}42′+2hg=0\begin{equation}{2^{\prime} + 2}{{\rm h}^{\rm{g}}} = 0\end{equation}Ideally, the migration of metal ion vacancies (VM′′${\rm V}_{\rm M}^{\prime\prime}$) can also be regarded as the migration of metal ions with equal flux in the opposite direction. Therefore, based on the Wagner model [15], ion vacancies (V") and electron holes (h·) can be used as carriers to establish a corresponding finite element phase‐field model.Based on different assumptions, scholars have proposed different mathematical models for the corrosion reaction kinetics of metal surfaces. In the model proposed by Williams, and Fromhold [16, 17], the oxidation rate limited by the thermal emission of electrons was simulated, and it was concluded that mass transport during corrosion depends heavily on the diffusion process. However, when the film thickness is in Debye length, or the interface reaction is the dominant mechanism, Wagner's law of parabola is violated. In particular, the electric field can modify the electron band profile and the defect structure of the oxide [18, 19]. The solution of the phase field is complex, which requires high convergence. In addition, it is difficult to obtain the physical parameters of the specific carriers in the film. Chen [20] used the per‐unit system of physical parameters for analysis and compared the phase‐field model with Wagner's theoretical model. Therefore, it is unrealistic to directly and accurately calculate the corrosion rate of the contact element strip in the SF6 gas through the corrosion kinetic model. Nevertheless, based on the Wagner theory and Chen's one‐dimensional phase‐field model, the analysis of the main factors that affect the corrosion rate is still effective for the study of the corrosion process of the contact element strip.Construction of finite element phase‐field modelDuring overheating failure in the current‐carrying structure of high‐voltage power transmission equipment, the most severely damaged place in the contact element strip is often the electrical contact area, whose surfaces are exposed to SF6 decomposition gas, thereby generating corrosion products. Aiming at the overheating corrosion of the contacts in SF6 gas, the reaction model includes three kinds of phase fields: gas, film, and metal. The carrier transport mechanisms in the three phase fields are unified in the form of equations, but there are significant numerical differences between the different phases. In order to unify the transport equations in different phase fields, two variables need to be introduced to represent the carrier transport and chemical reaction processes in time and space.In this model, two variables η(x,t) and ζ(x,t) are introduced to describe the spatial and temporal distribution of the phases, and the value range of η and ζ is determined to be (0,1). Then, η and ζ represent the local fractions of the metal and gas in the phase, respectively. They take the value of 1 in the phase field and otherwise take the value of 0. The schematic diagram of the two‐dimensional phase‐field model of metal high‐temperature corrosion is shown in Figure 2.2FIGURESchematic diagram of two‐dimensional phase‐field model for high‐temperature corrosion of metalFor the cation vacancy concentration, c1, and the electron hole concentration, c2, there are basic assumptions that conform to physical facts. First, cation vacancies are generated only at the G–F interface and participate in the corrosion reaction on the interface. They will not diffuse to the gas side. Second, cation vacancies will not penetrate the metal in a form other than chemical reactions. While the metal has excellent electrical conductivity, gas conductivity is poor, and the concentration of electron holes in the metal domain is much smaller than the concentration in the film. Regardless of whether the carrier transport reaches equilibrium at the G–F interface, the potential difference at the interface will always make the charge accumulate at the interface. As cation vacancies and electron holes have different activities in different phases, activity coefficients are introduced to characterize carriers’ activity.Based on the electrochemical potential of carriers during transport, the activity coefficient can be expressed as5f1x=[1+κGpζ][1+κMpη]\begin{equation}{f_1}\left( x \right){\rm{ = }}[1 + {\kappa _{\rm{G}}}p\left( \zeta \right)][1 + {\kappa _{\rm{M}}}p\left( \eta \right)]\end{equation}6f2x=1+κMpη1+Npζ\begin{equation}{f_2}\left( x \right) = \frac{{1 + {\kappa _{\rm{M}}}p\left( \eta \right)}}{{1 + Np\left( \zeta \right)}}\end{equation}where κG and κM are penalty factors for the gas field and the metal field, respectively, with values much larger than 1, representing almost no diffusion of cation vacancy into the gas phase and a small permeability to the solid side. p(η) and p(ζ) are common interpolation functions in the phase field. The value of N is much greater than 1 and is taken as 50, which means that the concentration of cation vacancy and electron hole in the gas is much higher than that in the film.When the rate of carrier consumption at the gas–film interface and the film–metal interface due to chemical reactions is much higher than the rate of carrier transport, the carrier concentration at both interfaces can be clamped to a concentration controlled by the chemical reaction equilibrium; that is, ci is a constant. Therefore, the flux at the gas–film interface satisfies two equations simultaneously.7JM+=DM+cM+x=MF−cM+x=GFx\begin{equation}{{\bm{J}}_{{{\rm{M}}^{ + }}}} = {D_{{{\rm{M}}^ + }}}\frac{{c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{MF}}}} \right. - c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.}}{x}\end{equation}8JM+=cM+x=GFdxdt\begin{equation}{{\bm{J}}_{{{\rm{M}}^{ +}}}} = c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.\frac{{{\rm{d}}x}}{{{\rm{d}}t}}\end{equation}In the formula, JM+ is cation diffusion flux/mol·m‐2·s‐1; DM+ is the cation diffusion coefficient/m2·s‐1; cM+|x=MF is the cation concentration at the metal–film interface /mol·m‐3; cM+|x=GF is the cation concentration on the metal–gas surface/mol·m‐3; and x is the thickness of the film/m.The two equations can be combined to obtain the following:9dxdt=kx⇒x2=2kt\begin{equation}\frac{{{\rm{d}}x}}{{dt}} = \frac{k}{x} \Rightarrow {x^2} = 2kt\end{equation}10k=DM+cM+x=MF−cM+x=GFcM+x=GF\begin{equation}k = {D_{{\rm{M + }}}}\frac{{c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{MF}}}} \right. - c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.}}{{c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.}}\end{equation}When the carrier concentration at the two interfaces is constant, k is a constant, and the film growth satisfies the parabolic law. However, in the actual carrier transport process, the k constant is related to the carrier conductivity, diffusion coefficient, and chemical reaction. So, the corrosion reaction rate cannot be simply viewed as a constant value.The transport of carriers in the film is essentially driven by the electrochemical potential gradient, causing the gas and metal to develop in the direction of entropy increase. The electrochemical potential of the carriers is expressed as11ξi=uiθ+kBTlnXi+zieφ\begin{equation}{\xi _i} = u_i^{{\theta}} + {k_{\rm{B}}}T\ln {X_i} + {z_i}e\varphi \end{equation}where uiθ$u_i^\theta $ is the standard chemical potential of carriers, Xi is the molar fraction of carriers, φ is the potential, and zi is the number of charges carried by the carriers.According to Fick's second law, the change of carrier concentration with time has a certain relationship with the divergence of carrier flux.12∂ci∂t=−∇×Ji\begin{equation}\frac{{\partial {c_i}}}{{\partial t}} = - \nabla \times {{\bm{J}}_i}\end{equation}13Ji=−υici∇ξi\begin{equation}{{\bm{J}}_i} = - {\upsilon _i}{c_i}\nabla {\xi _i}\end{equation}where Ji is the flux of carrier i, vi is the mobility of carrier i, and ξi${\xi _i}$ is electrochemical potential.The flux of carriers in the film is related to the diffusion and migration of carriers. The actual concentration and diffusion coefficient of different carriers are obviously different in different phases, so it is necessary to introduce a constructor function for adjustment to achieve unified expression of variables in different phases. The above equation is combined to obtain the expressions for the flux of cation vacancies and electron holes.14J1=−D1∗∇c1∗+υ1c1E\begin{equation}{{\bm{J}}_1} = - D_1^*\nabla c_1^* + {\upsilon _1}{c_1}{\bm{E}}\end{equation}15J2=−D2∗∇c2∗+υ2c2E\begin{equation}{{\bm{J}}_2} = - D_2^*\nabla c_2^* + {\upsilon _2}{c_2}{\bm{E}}\end{equation}In (14) and (15), E=−∇φ${\bm{E}} = - \nabla \varphi $ which satisfies Poisson's equation. c1∗$c_1^*$ and D1∗$D_1^*$ is the unified expression of c1 and D1 in different phases.16c1=c1∗/f1\begin{equation}{c_1} = c_1^*/{f_1}\end{equation}17D1=f1D1∗\begin{equation}{\rm{ }}{D_1} = {f_1}D_1^*\end{equation}18c2=c2∗f21+g0pη\begin{equation}{c_2} = \frac{{c_2^*}}{{{f_2}\left[ {1 + {g_0}p\left( \eta \right)} \right]}}\end{equation}19D2=f21+g0pηD2∗\begin{equation}{\rm{ }}{D_2} = {f_2}\left[ {1 + {g_0}p\left( \eta \right)} \right]D_2^*\end{equation}where f1 and f2 are constructor functions of c1 and c2, respectively.In the equation, as cation vacancies do not diffuse into the gas, in order to satisfy the condition of electroneutrality in the gas phase, it is necessary to construct a negative charge concentration c3 in the gas phase to neutralize the electronegativity of c2.20c3∗≡−c1∗t=0+12c2∗t=0\begin{equation}c_3^* \equiv - c_1^*\left| {_{t = 0}} \right. + \frac{1}{2}c_2^*\left| {_{t = 0}} \right.\end{equation}Migration‐diffusion expressions for solving variables in different phases are established. At the interface, carriers are continuously generated or compounded in the form of chemical reactions. From the perspective of phase‐field modelling, it is equivalent to the establishment of a reaction zone with a function at the G–F interface or M–F interface. The constructed reaction zone at the G–F interface or the M–F interface is21Λζ=ζ21−ζ2\begin{equation}{\Lambda _\zeta } = {\zeta ^2}{\left( {1 - \zeta } \right)^2}\end{equation}22Λη=η21−η2\begin{equation}{\Lambda _\eta } = {\eta ^2}{\left( {1 - \eta } \right)^2}\end{equation}In addition to diffusion and migration, the transport process of carriers includes chemical reactions (generation, recombination) in the interfacial region. Among them, the generation or recombination rates of carriers (c1) in the G–F interface and M–F interface can be expressed as23RIc1=Λζpx1/2kI−k′Ic1∗c2∗2\begin{equation}R_{\rm{I}}^{\left( {{c_1}} \right)} = {\Lambda _\zeta }\left( {p_x^{1/2}{k_{\rm{I}}} - {{k^{\prime}}_{\rm{I}}}c_1^*{{\left( {c_2^*} \right)}^2}} \right)\end{equation}24RIIc1=ΛηkIIc1∗c2∗2−kII′\begin{equation}R_{{\rm{II}}}^{\left( {{c_1}} \right)} = {\Lambda _\eta }\left( {k_{{\rm{II}}}}c_1^*{{\left( {c_2^*} \right)}^2} - k^{\prime}_{{\rm{II}}} \right)\end{equation}where I and II represent G–F interface and M–F interface, respectively. RI(c1) and RII(c2) are cation vacancy's reaction terms at G–F interface and M–F interface, respectively. kI and kII are the forward rate constants in G–F interface and M–F interface. kI′${k^{\prime}_{\rm{I}}}$ and kII′${k^{\prime}_{{\rm{II}}}}$ are the inverse rate constants in G–F interface and M–F interface. Arrows represent forward and reverse reactions.For the reaction term of c2 at the interface, the above equation can be re‐expressed as25RIc2=2RIc1\begin{equation}R_{\rm{I}}^{\left( {{c_2}} \right)} = 2 R_{\rm{I}}^{\left( {{c_1}} \right)}\end{equation}26RIIc2=2RIIc1\begin{equation}R_{{\rm{II}}}^{\left( {{c_2}} \right)}{\rm{ = 2}}R_{{\rm{II}}}^{\left( {{c_1}} \right)}\end{equation}When the reaction is in equilibrium, the electric field in the entire calculation field satisfies Gauss's law27∇×εrxε0Ex=∑icixNAzie+ρs\begin{equation}\nabla \times \left[ {{\varepsilon _{\rm{r}}}\left( x \right){\varepsilon _0}{\bm{E}}\left( x \right)} \right] = \sum_i {{c_i}\left( x \right)} {N_{\rm{A}}}{z_i}e + {\rho _{\rm{s}}}\end{equation}As the dielectric constants of materials in different phases are different, the relative dielectric constants of gas are regarded as 1 and those of metals as 1.0×106. In the paper, the relative dielectric constant of film εr = 4, so εr(x) can be expressed as28εrx=εr−1[1−pζ][1−pη]+1+106×pη\begin{equation}{\varepsilon _{\rm{r}}}\left( x \right){\rm{ = }}\left( {{\varepsilon _{\rm{r}}} - 1} \right)[1 - p\left( \zeta \right)][1 - p\left( \eta \right)] + 1 + {10^6} \times p\left( \eta \right)\end{equation}When the reaction is placed in the applied electric field E'. the carriers in the film will also be subjected to the applied electric field force.In summary, the solution equation is expressed as29∂c1∂t=Λζpx1/2kI−k′Ic1∗c2∗2I−ΛηkIIc1∗c2∗2−k′II+∇×D1∗∇c1∗−∇×D1c1z1E+E′∂c2∂t=2Λζpx1/2kI−k′Ic1∗c2∗2I−2ΛηkIIc1∗c2∗2−k′II+∇×D2∗∇c2∗−∇×D2c2z2E+E′\begin{eqnarray} \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} \def\eqcellsep{&}\begin{array}{l}\! \dfrac{{\partial {c_1}}}{{\partial t}} = {\Lambda _\zeta }\left( {p_x^{1/2}{k_{\rm{I}}} - {{k^{\prime}}_{\rm{I}}}c_1^*{{\left( {c_2^*} \right)}^2}_{\rm{I}}} \right) - {\Lambda _\eta }\left( {{k_{{\rm{II}}}}c_1^*{{\left( {c_2^*} \right)}^2} - {{k^{\prime}}_{{\rm{II}}}}} \right)\\[12pt] +\,\nabla \times \left( {D_1^*\nabla c_1^*} \right) - \nabla \times \left( {{D_1}{c_1}{z_1}\left( {{\bm{E}} + {\bm E}^{\prime}} \right)} \right) \end{array} \\[18pt] \def\eqcellsep{&}\begin{array}{l} \dfrac{{\partial {c_2}}}{{\partial t}} = 2{\Lambda _\zeta }\left( {p_x^{1/2}{k_{\rm{I}}} -\! {{k^{\prime}}_{\rm{I}}}c_1^*{{\left( {c_2^*} \right)}^2}_{\rm{I}}} \right) -\! 2{\Lambda _\eta }\left( {{k_{{\rm{II}}}}c_1^*{{\left( {c_2^*} \right)}^2}\! - {{k^{\prime}}_{{\rm{II}}}}} \right)\\[12pt] +\,\nabla \times \left( {D_2^*\nabla c_2^*} \right)\! - \nabla \times \left( {{D_2}{c_2}{z_2}\left( {{\bm{E}}{\rm{ + }}{\bm{E}}^{\prime}} \right)} \right) \end{array} \end{array} } \right.\hskip-10pt\nonumber\\[-4pt] \end{eqnarray}where z1 and z2 are the number of charges carried by cation vacancy and electron hole, respectively.We established a two‐dimensional phase‐field model for high‐temperature corrosion of metals, the transport and reaction of carriers in different phases can be described by a set of unified equations. The mathematical model is built based on the basic reaction, which is dominated by cation vacancy. This paper mainly discusses the mechanism by which cation vacancy dominates. The mechanism of action is similar when anions are dominant and anions and cations are co‐dominant.In this paper, the complete set of differential equations required for phase‐field calculation is established in the software COMSOL, which was not completed in previous studies. The calculation process is as follows in Figure 3:A two‐dimensional model of phase‐field is presented. In order to improve the convergence of the calculation, it is necessary to discretize the variable c (concentration) into a third‐order continuous and differentiable variable. The mesh division in the calculation area needs to be refined to suppress the numerical oscillation during the solution. The density of mesh division is 1/1000 (e.g. a model length of 10 μm corresponds to a grid cell size of 0.01 μm).The transport of diluted species (tds) module is used to establish the transport equations of anions, cations, and electrons in the calculation domain. The constant‐concentration boundary condition is applied at both ends of the two‐dimensional model, and a chemical‐reaction‐based boundary condition is applied at the middle section.The electrostatic field (es) module is used to solve the Poisson equation. In this paper, the boundary condition near the end of the metal side is set to ground, and the middle area is set to the space charge density. The charge density is set according to the transport of carriers in the tds module.The formulation of the fully coupled method is processed. The non‐linear method adopts the constant (Newton) method. The damping coefficient is 0.9, the maximum number of single‐step iterations is eight times, and the tolerance factor is set to 1. The electric field (E) and the concentration (ci) are transmitted as coupling variables in the tds module and the es module.3FIGUREFinite element phase‐field calculation process for metal corrosionThe initial carrier concentration distribution is shown in Figure 4. The generated cation vacancies exist in the oxide film, while the concentrations of cation vacancies in the metal phase and the gas phase are both zero. In order to meet the conditions of electrical neutralization, when the valence state of the cation vacancy is +2, the concentration of the cation vacancy in the gas phase is exactly one‐half of the electron hole concentration. The concentration of cation vacancy in the oxide film and the gas phase changes to zero.4FIGUREInitial concentration distribution of carrierSIMULATION RESULTS AND ANALYSISBased on the above phase‐field method, the carrier concentration, flux distribution, and preset charge distribution were obtained when computational domain length L =3 μm (film thickness of 2.8 μm). The computational domain includes the metal phase, the corrosion film, and the gas phase. The length of the computational domain is 3 μm (L =3 μm), where the thickness of the corrosion film is 2.8 μm. The carriers concentration was expressed in terms of relative concentration, c0*, and the diffusion coefficient, Di, was expressed in the form of Di* × D0. The magnitude of the binary sulfide ion diffusion coefficient was about 1.0 × 10−14 m2/s, so D0 was set to 1.0 × 10−14 m2/s, and the value of Di* was related to the carriers that affect transport processes. DM* took 1, and De* took 2000.It can be seen from Figure 5 that the electron holes in the film were affected by the diffusion in the concentration gradient, moving continuously from the gas side to the metal side along the film. Also, the electron holes fell rapidly in the M–F interface reaction zone. The cation vacancy concentration rose in the G–F interface reaction zone and then diffused along the growth direction of the film. Its concentration kept decreasing, especially in the reaction zone near the M–F interface, which quickly dropped to zero. When the reaction reached equilibrium, the cation vacancy flux was evenly distributed in the film and rapidly dropped to zero at the M–F interface.5FIGUREConcentration distribution and flux of carrier, charge density, and electric potential in the filmThere was an electric double layer at the G–F interface, while the inside of the film was electrically neutral. At the interface between film and gas, cation vacancies and electron holes were continuously generated on the gas. The diffusion coefficient of the electron hole was higher than that of the cation vacancy. During the carrier diffusion process, the negative charge density of the area near the gas side was higher than the positive charge density. So the charge accumulation inevitably occurred at the interface. Excessive positive charge density appeared on the side of the film, which led to the formation of an electric double layer. Similarly, at the M–F interface, owing to excessive positive charges, a small amount of charge would accumulate. In most areas of the film, the positive charge density was basically close to negative charge density. Thus, the potential difference was mainly concentrated at the electric double layer at the interface, and the reduction of the potential in the film was relatively gentle. The metal domain and the gas domain were electrically neutral, and the potential difference was zero.Influence of temperature on carrier distributionThe current‐carrying structure of the faulty bushing was disassembled to obtain the damage morphology of the contact elements strip. In order to further analyze the high‐temperature corrosion mechanism of the contact element strip, the carrier and flux distribution of the metal corrosion film under the influence of different overheating temperatures were simulated and calculated. As the diffusion coefficient of cation vacancy in the film was affected by temperature, the relationship between the diffusion coefficient and temperature can be expressed as30D=Dfe−QDRT\begin{equation}D = {D_{\rm{f}}}{{\rm{e}}^{ - \frac{{{Q_{\rm{D}}}}}{{RT}}}}\end{equation}In the formula, Df is the frequency factor/m2·s−1, and QD is the diffusion activation energy/J·mol−1.If the temperature of the matrix of metal on both sides of the contact was similar, the temperature rise relationship of the contact can be written as [21–23]:31Tm=U024L+T02\begin{equation}{T_{\rm{m}}} = \sqrt {\frac{{U_{\rm{0}}^2}}{{4L}} + T_0^2} \end{equation}where Tm is the temperature of the contact point, T0 is the temperature of the matrix, and U0 is potential differences.As the temperature increased, the diffusion coefficient of carriers would increase exponentially. Owing to the high temperature at the electrical contact point, the temperature of the contact point would be higher than the temperature of the matrix of metal. Therefore, the diffusion coefficients of cation vacancy varied greatly at different positions. First, to compare the difference in reaction kinetics at different temperatures, we calculated the carrier concentration distribution and flux changes under different diffusion coefficients; second, we set different temperatures for different positions of the two‐dimensional model to simulate the carrier distribution characteristics when there was a temperature difference between the contact point and the matrix of metal.Figure 6 presents the carrier concentration distribution in the film under steady‐state conditions with different cation vacancy diffusion coefficients. The figure components from (a) to (d) show the results for the diffusion coefficients of 1, 4, 7, and 12, in that order. Owing to the high concentration of carriers on the gas side, the concentration difference between the M–F interface and the G–F interface would promote the continuous transport of cation vacancies to the metal side until equilibrium was reached. With the increase in the cation vacancy diffusion coefficient, the diffusion capacity for cation vacancy to the gas side increased. The increased diffusion capacity would reduce the concentration gradient between the two interfaces, making the distribution in the film more uniform. Take a horizontal line segment starting from the metal side and ending at the gas side with the Y coordinate unchanged. Figure 7 shows the vacancy concentration and flux distribution under this path. It is apparent that the cation vacancy peak concentration at the G–F interface decreased with the increase in the vacancy diffusion coefficient, and that at the M–F interface, it increased slightly. At the same time, the carrier flux in the film increased as the cation transport capacity increased. After calculation, the film growth rate increased with the increase in the diffusion coefficient, but the slope of the growth rate gradually decreased. This was mainly because of the decrease in the concentration gradient on both sides of the diffusion coefficient, which in turn inhibited the diffusion of carriers.6FIGURETwo‐dimensional concentration distribution for different diffusion coefficients7FIGURECarrier distribution, flux distribution, and film growth rate under different diffusion coefficientsInfluence of gas partial pressure on carrier distributionIn order to analyze the influence of gas partial pressure on the change of carrier concentration in the film and the film growth rate, we modified the gas pressure in the phase‐field model. The cation vacancy concentration and its flux distribution when L = 3 μm were calculated by simulation, as shown in Figure 8. When the gas partial pressure was at the standard atmospheric pressure, the overall distribution of the cation vacancy concentration was low. As the gas partial pressure ratio increased sequentially by 1, 4, and 7, and 10 atmospheres, we observed an increase in the cation vacancy generation rate at the G–F interface, especially the peak concentration. However, the diffusion coefficient of carriers remained unchanged, and the concentration distribution of cation vacancies in the film showed an overall downward trend. After the calculation, the film growth rate increased with the increase of the gas pressure. When the air pressure rose 10‐fold, the film growth rate increased by 1.1 times. The effect of gas pressure on the growth rate is smaller than that of temperature. However, the increase in cation vacancy and electron hole concentration in turn inhibited the generation of carriers at the G–F interface. Therefore, as the gas partial pressure increased, the increase in carrier flux became smaller, and the film growth rate tended to be saturated.8FIGURECarrier distribution, flux distribution, and film growth rate under different gas pressuresInfluence of film thickness on carrier distributionBy changing the film thickness, the changes in the carrier concentration and the film growth rate under different film thicknesses were calculated. The phase‐field model calculated the cation vacancy concentration and flux distribution when L grew from 1 to 7 μm (value interval of 1.5 μm), as shown in Figure 9. As the film thickness increased, the difference in cation vacancy concentration between the M–F interface and the G–F interface increased. As the consumption of cation vacancies on the metal side was mainly related to the reaction rate, the reaction rate remained unchanged, and the change in the carrier concentration was relatively small. On the gas side, cation vacancies continued to be generated, and the increase in film thickness affected the diffusion of carriers, so the concentration rose significantly at the G–F interface. Through the calculation of the film growth rate, we found that the film growth rate decreased with the increase in the film thickness under the condition that the gas partial pressure and the diffusion coefficient remained unchanged. When the film thickness increased to a certain extent, the film growth rate and thickness satisfied the parabolic relationship, which is consistent with Wagner's theory and further proves the rationality of using the two‐dimensional phase‐field model.9FIGURECarrier, flux distribution, and film growth rate under different thicknessesInfluence of applied electric field on carrier distributionAccording to the electrical contact theory, the contact resistance is composed of film resistance and contraction resistance. In normal condition, the film resistance is negligible. However, when the corrosion film is formed, much attention needs to be paid on the film resistance due to poor electrical conductivity. A high electric field exists when a small voltage drop acts on a micron‐scale film. The previous simulation mainly considered the electromigration induced by the electrochemical potential during the formation of the corrosion film. On this basis, we introduced the electric field as a variable into the governing equations of phase‐field model, which was not considered in previous simulations. In order to analyze the influence of the applied electric field on the carrier concentration and the film growth rate, we kept other conditions unchanged and added the applied electric field of 0, ±0.07 kV/mm, ±0.2 kV/mm, and ±0.33 kV/mm in sequence. The cation vacancy concentration and its flux distribution under the positive and negative electric field are presented in Figure 10.10FIGURECarrier distribution, flux distribution, and film growth rate under different applied electric fieldsWith the increase in the positive applied electric field, the cation vacancy accelerated to migrate to the M–F interface. Owing to the limited reaction rate at the interface, under the dual effects of the electric‐field migration and the concentration gradient, positive charges began to accumulate on the metal side. The concentration of cation vacancy at the M–F interface rose and gradually produced a peak concentration. The occurrence of the peak concentration indicated that the influence of the applied electric field on the carrier migration could not be ignored. At the G–F interface, with successive increases in the intensity of the electric field, the cation vacancies concentration further decreased. On the contrary, when a negative electric field was applied, the positive charges were subjected to the force of the electric field opposite to the diffusion direction and were mainly concentrated on the gas side. The peak concentration of the cation vacancy at the G–F interface increased with the increase in the electric field. The positive charges accumulating at the M–F interface decreased.When the applied electric field existed, the distribution of carriers in the film was changed. The positive electric field promoted the migration of vacancies to the metal side, strengthened the flux of cation vacancies in the film, and enhanced accumulation of positive charges at the G–F interface, while the negative electric field had the opposite effect. Under the stable condition of corrosion reaction, the polarity of the applied electric field had an opposite effect on the growth rate of the corrosion film. Under the given physical parameters, when the electric field corresponds to −0.33 and 0.33 kV/mm, the growth rates of corrosion film increased from 7.9 to 8.6 nm/s. The applied electric field made the carrier distribution in the film tend to prevent the applied electric field. Owing to the limited reaction rate of the G–F interface, under the action of the positive electric field, the positive charge would accumulate on the gas side, weakening the electric double layer effect, and a negative electric field would strengthen the electric double layer at the interface. The growth rate of the G–F interface film increased with the increase in the electric field intensity, and the amplitude gradually became flat.HIGH‐TEMPERATURE CORROSION TESTFigure 11 shows the schematic structure of typical converter valve‐side bushings. The main structure includes an aluminium conductor or copper conductor, contact element strips, SF6, RIP cores, transformer oil, shielding, and a grounding flange. The contact element strips are installed in the transition area of current‐carrying conductors, which is the connection structure between the aluminium conductor and copper conductor. It is shown in blue in Figure 11 and bears the overall current. The path of the current at the plug‐in structure is shown by the red dashed line. Owing to the contact resistance, this position has a high degree of heat generation and is prone to degradation and corrosion with SF6 under overheating.11FIGUREThe schematic structure of typical converter valve‐side bushingsThe contact element strips deteriorate very slowly under normal working conditions. Due to the high cost of the time and experiments, it is necessary to design a high‐temperature corrosion accelerated test in order to simulate the overheating fault of the contact elements under the condition of uneven current carrying in the high‐voltage bushing. Therefore, we increase the test current to boost the heating power of the contact element strip and accelerate the corrosion reaction. The whole process of accelerated test is carried out under the current, and the electric field exists in the test.In order to obtain the higher contact temperature of the contact element strip, we selected the contact element strip used in the UHV bushing as the test object. The upper and lower electrodes were all made of aluminium. The lower electrode adopted the aluminium electrode with a T‐type slot, ensuring the stability of the contact elements. The contact element strip is LA‐CUD double‐tooth contact fingers, used in the electrical connection of high‐voltage bushings. The matrix of the contact element strip was copper, and its surface was plated with silver. The test platform and the structure of contact fingers are shown in Figure 12. Before the experiment, contact element strips were installed in parallel in the T‐type slot. Each contact element strip had four contact fingers, for a total of eight pieces. The DC current was 600 A, the ambient temperature was controlled at a constant temperature of 25°C, the experimental atmosphere was SF6, and the pressure was 2 atm. The test duration was 72 h. With the help of the auxiliary heating system, the electrode was kept at 100℃ to simulate the heating of the conductor. The current passed through the lower electrode and contact element strips and finally communicated with the upper electrode.12FIGUREHigh‐temperature corrosion test platform for contact element stripsDuring the test, the temperature of the contact element strip matrix and the contact voltage were measured in real time. We found that the temperature of the matrix was maintained at about 150°C. Because the contact area was squeezed by the upper electrode and the contact element strip and the overall structure size of the contact element were in the centimeter range, the contact temperature was difficult to measure directly. The contact temperature was estimated by using the V–T relationship that is widely used in electrical contact at present. In this experiment, the contact temperature will be significantly higher than the matrix temperature, possibly reaching to 500°C.Through the high‐temperature corrosion test on the contact element strips, the morphology of the experimental samples was analyzed. Figure 13 shows the corrosion morphology of the contact and the matrix of the contact element strip under the test. Obvious signs of overheating corrosion occurred in the contact area, as black products appeared on the surface. The matrix area began to turn yellow, but the surface was relatively flat. The characteristic peaks of Cu, F, S elements are high in the inner and edge of contact area, and the metal fluoride and sulfide is mainly concentrated in this area. The non‐contact area has only a very small amount of F and S elements. Thus, the corrosion degree of the contact area of contact element strips is much higher than that of the non‐contact area, accompanied by the formation of metal fluoride and sulfide. The corrosion appearance and corrosion products are similar to the sampling contacts in the faulty bushing, which can illustrate the effectiveness of accelerated testing.13FIGURECorrosion morphology and element analysis of contact element strips’ surfaceThe carrier distribution in the film was studied by simulating the temperature difference between the contact and the matrix. Different temperatures were set for each position on the metal side, and the temperature rose from 150°C to 500°C from bottom to top along the y‐axis. The upper end of the metal side represented the high‐temperature area of the contact, and the lower end represents the low‐temperature area of the matrix. Figure 14 shows the two‐dimensional distribution of carriers.14FIGURECarrier distribution characteristics under the high‐temperature difference between the contact and the matrixAs the temperature increased, the diffusion coefficient of cation vacancies in the film would increase exponentially. Therefore, the diffusion coefficient near the contact was much higher than that of the matrix. It can be seen that the cation vacancy distribution at the contact was more uniform, the peak concentration at the G–F interface gradually increased from the contact to the matrix, and the concentration at the M–F interface remained stable. This is consistent with the changed characteristics of the carrier distribution with the diffusion coefficient at a constant temperature. As the diffusion coefficient at the matrix was much smaller than the diffusion coefficient at the contact, even if the contact was completely stable, the matrix was still in a slow diffusion process, and the initial distribution was difficult to change in a short time.We calculated the film growth rate of the contact, the matrix, and the middle transition area, as shown in Figure 15. The carrier flux at the contact was much higher than the flux at the matrix. The growth rate at low temperature is orders of magnitude lower than that at high temperature. When parameters such as film thickness are given and the temperature is 150°C, the growth rate of the film is 20 nm/s. While the growth rate of the film is 517 nm/s in the contact position. Owing to the low temperature at the matrix, the film growth rate was extremely slow, close to zero; the temperature at the contact was high, the film growth rate was much higher than the matrix owing to the high diffusion coefficient. Combined with experimental analysis, when the contact element strips at the plug‐in structure are in poor contact, the temperature rise between the contact and the matrix will cause a significant difference in the growth rate of the corrosion film. The above analysis indicates that in UHV bushing, the contact area of the current‐carrying structure is the first to become the breakthrough point of the corrosion reaction, and the severity of corrosion is much higher than that of the non‐contact area.15FIGUREFilm growth rate at different positionsCONCLUSIONBased on the actual problems in engineering, the two‐dimensional phase‐field finite element model of corrosion reaction kinetics was established. The factors affecting the growth of the corrosion film of the contact were calculated. Meanwhile, the accelerated test was used to simulate the overheating corrosion state of contact element strips in the bushing. The following conclusions can be drawn:The coupling calculation analysis using COMSOL finite element software was successfully realized, which was not completed in previous studies. Temperature has the most obvious effect on the film growth rate. The influence of temperature on the growth rate increases exponentially. Under the given physical parameters, when the temperature from matrix to the contact area corresponds to 150°C and 500°C, the growth rates of corrosion film increased from 20 to 517 nm/s, which was 25 times the original. The corrosion rate tends to be stable with the increase of film thickness and gas pressure, but the two factors have opposite effects.The influence of the electric field was introduced into the equation of phase‐field model on the original basis. The polarity of the applied electric field has the opposite effect on the corrosion reaction. Compared with the negative electric field, the positive electric field increases the growth rate of the film. The growth rate increased by 8.5% between −0.33 and 0.33 kV/mm, and the increased amplitude decreases with the increase in the field strength. It can provide help for the next step in the study of the corrosion characteristics of contacts by AC and DC electric fields.The test results are similar to the faulty contacts, which can illustrate the effectiveness of accelerated testing. Obvious black traces appear in the contact area, accompanied by the formation of corrosion products. The characteristic peaks of Cu, F, S elements are high in the inner and edge of contact area. Combining the comparison of the film growth rate between the contact and the matrix at different temperatures, it shows that temperature rise caused by poor contact is the main cause of the failure of the electrical connection structure, and the contact area is the starting position of the corrosion. The difference of corrosion degree between the contact area and non‐contact area shows the rationality of the simulation calculation.This study is the first step in the research on the corrosion characteristics of the contact elements of the UHV bushing. Quantitative comparative analysis requires the design of a more precise and detailed experimental scheme, which will be the next step based on this study. And carriers corresponding to various corrosion reactions will be introduced into the phase field model in the next step of simulation calculation.ACKNOWLEDGEMENTSThe authors would like to appreciate State Key Laboratory of Electrical Insulation and Power Equipment in Xi'an Jiaotong University. This work is supported also by National Natural Science Foundation of China (NSFC: 52107163).CONFLICT OF INTERESTWe declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are openly available at http://doi.org/[doi].REFERENCESWang, Q., Yang, X., Tian, H., et al.: A novel dissipating heat structure of converter transformer RIP bushings based on 3‐D electromagnetic‐fluid‐thermal analysis. IEEE Trans. Dielectr. Electr. Insul. 24(3), 1938–1946 (2017)Israel, T., Schlegel, S., Gromann, S., et al.: Modelling of transient heating and softening behaviour of contact points during current pulses and short circuits. In: Holm Conference on Electrical Contacts. Milwaukee, 9–18 (2019)Yang, X., Yang, Z., Zhang, Y., et al.: Simulation analysis of electrical‐thermal‐fluid coupling property for supporting insulation in SF6 filled HVDC apparatus. IEEE Trans. Dielectr. Electr. Insul. 29(1), 69–76 (2022)Tian, H., Liu, P., Zhou, S., et al.: Research on the deterioration process of electrical contact structure inside the 500 kV converter transformer RIP bushings and its prediction strategy. IET Gener. Transmission Distrib. 13(12), 2391–2400 (2019)Zhou, A., Gao, L., et al.: Analysis and field‐repair of current overheating faults on dry type SF6 gas‐insulated valve side bushing in converter transformer. Power Syst. Technol. 42(5), 1401–1409 (2018)Ruppert, C., Runde, M.: Thermally induced mechanical degradation of contact spots in aluminum interfaces. IEEE Trans. Compon. Packag. Technol. 29(4), 833–840 (2006)Runde, M.: Inside the aluminum contact spot. In: 2019 IEEE Holm Conference on Electrical Contacts. Milwaukee. 1–8 (2019)Tang, J., Yang, D., Zeng, F., et al.: Research status of SF6 insulation equipment fault diagnosis method and technology based on decomposed components analysis. Trans. China Electrotechnical Soc. 31(020), 41–54 (2016)Zeng, F., Tang, J., Fan, Q., et al.: Decomposition characteristics of SF6 under thermal fault for temperatures below 400°C. IEEE Trans. Dielectr. Electr. Insul. 21(3), 995–1004 (2014)Kubler‐Riedinger, M., Bauchire, J.‐.M., Hong, D., et al.: Electrical and morphological investigations of electrical contacts used in low‐voltage circuit‐breakers. In: 2020 IEEE Holm Conference on Electrical Contacts and Intensive Course. San Antonio: IEEE, 115–122 (2020)Braunovic, M., Konchits, V.V. Myshkin, N.K.: Electrical Contacts Fundamentals, Applications and Technology. XU Liangjun, LU Na, LIN Xueyan, et al, translated. Beijing: China Machine Press, (2010)Trockels, I., Luetjering, G., Gysler, A.: Effect of frequency on fatigue crack propagation behavior of the aluminum alloys 6013 in corrosive environment. Mater. Sci. Forum. 217(222), 1599–1604 (1996)Eibech, R.E., Nears, W.H.: Sulfur Hexafluoride. 3rd Edition: Kirk‐Othmer Encyclopedia of Chemical Technology. (1980)Kofstad, P.: High Temperature Corrosion; Elsevier: London, (1988)Wagner, C.Z.: Phys. Chem. B 21, 25 (1933)Williams, E., Hayfield, P.: Vacancies and other point defects in metals and alloys. The Institute of Metals: London. 23(1), 131‐157 (1958)Fromhold, A.T.: Analysis of the Williams‐Hayfield Model for Oxidation kinetics. J. Electrochem. Soc. 153(3), B97–100 (2006)Yu, J.G., Rosso, K.M., Bruemmer, S.M.: Charge and ion transport in NiO and aspects of Ni oxidation from first principles. J. Phys. Chem. C 116, 1948–1954 (2012)Zhang, Z.F., Jung, K., Li, L., et al.: Kinetics aspects of initial stage thin γ‐Al2O3film formation on single crystalline β‐NiAl (110). J. Appl. Phys. 111, 034312 (2012)Cheng, T.L., Wen, Y.H., Hawk, J.A.: Diffuse‐interface modeling and multiscale‐relay simulation of metal oxidation kinetics‐with revisit on Wagner's theory. J. Phys. Chem. C 118(2), 1269–1284 (2014)Timsit, R.S.: On the evaluation of contact temperature from potential‐drop measurements. IEEE Trans. Compon., Hybrids, Manuf. Technol. CHMT‐6(1), pp. 115–121, Mar. (1983)Holm, R.: The influence of the Joule heat on constriction resistances in symmetric contacts. In: Electric Contacts: Theory and Application, Berlin, Germany: Springer, pp. 71–78 (1967)Gatzsche, M., Nils, L., Gromann, S., et al.: Evaluation of electric‐thermal performance of high‐power contact systems with the voltage‐temperature relation. IEEE Trans. Compon. Packag. Manuf. Technol. 7(3), 317–328 (2016) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "IET Generation, Transmission & Distribution" Wiley

Corrosion reaction kinetics and high‐temperature corrosion testing of contact element strips in ultra‐high voltage bushing based on the phase‐field method

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10.1049/gtd2.12487
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Abstract

INTRODUCTIONWith the increase in transmission capacity, heat generation has become a key issue restricting the safe and stable operation of ultra‐high voltage (UHV) power transmission equipment. For the UHV power transmission equipment (UHV bushings), contact element strips are required to provide a current‐carrying connection between the long guide rods [1–3]. The contact elements undergo high‐temperature corrosion under long‐term current flow conditions, resulting in deterioration of contact resistance and electrical connection failure. The corrosion is a slow process. In addition, there is no test platform or operating data of the contact element strips under actual working conditions [4]. In recent years, discharge failures caused by an insufficient thermal margin of the structure or degradation of the electrical connection structure have occurred in the operation of ultra‐/extra‐high‐voltage bushing [5]. The overheating fault of the valve‐side bushing and wall bushing in China as of 2020 is shown in Figure 1. As can be seen from the figure, the surface of the contact elements changes from silver to black. Abnormal current‐carrying connection components account for 15.11% and 22% of the two types of bushing faults, respectively.1FIGUREOverheating failure of the bushing current‐carrying connection structureThe electrical contact corrosion process of current‐carrying structures is relatively complicated and affected by various factors, such as current intensity, chemical corrosion environment, and fretting wear. Scholars have carried out many experiments and theoretical studies on the corrosion mechanism of metal materials and SF6 decomposition after decades of development [6–9]. Holm et al. proposed the electrical contact model and continued to improve it [10, 11]. Through electron microscope observation, Trockels [12] suggested that the crack growth rate of aluminium alloys in corrosive environments is related to the hydrogen atoms released by the crack reaction. Eibech et al. [13] conducted a large number of SF6 decomposition experiments at temperatures higher than 200°C, obtained the annual decomposition rate of SF6 in different material containers, and measured the gas and solid products after the reaction. There has been no systematic research on the electrical contact characteristics of UHV actual current‐carrying connection structures. Moreover, there have been relatively few studies of the failure mechanism of current‐carrying structures under the synergistic effect of electrical stress, thermal stress, and the SF6 gas environment. In order to further reveal the overheating failure caused by contact elements, it is necessary to carry out research on the failure mechanism of the contact element strip used in UHV bushings.In this study, a two‐dimensional phase‐field model for high‐temperature corrosion was established to obtain the charge carrier concentration distribution in the film. Based on corrosion reaction kinetics, the influence of temperature, gas partial pressure, film thickness, and applied electric field on the growth rate of thin film was analyzed using the phase‐field method. At the same time, the contact elements strip commonly used in the bushing was the test object. A high‐temperature corrosion test was carried out in the SF6 atmosphere to simulate the high‐temperature corrosion caused by the uneven current carrying of the contact element strip under actual operating conditions. The energy spectrum analysis and morphology observation were carried out on the surface of the contact finger, which was similar to that of the faulty contact element strips. Combined with the simulation of temperature on the film growth rate, the surface corrosion characteristics of the contact area and the non‐contact area of the contact elements were qualitatively analyzed, and the corrosion mechanism of typical contact elements was further explained.FINITE ELEMENT PHASE‐FIELD METHOD AND MODEL CONSTRUCTIONReaction kinetics theoryIn the corrosive medium, a layer of surface film with different properties from the substrate will be formed on the metal, and the film will continue to grow under the action of the corrosive medium [14]. Since metal sulfides or fluorides are essentially ionic compounds, for stoichiometric ionic compounds, ion migration is explained by Schottky defects or Frenkel defects.The SF6 in the atmosphere diffuses to the interface between the gas and film (G–F interface), and physical adsorption occurs at the interface; that is1SF6(g)=SF6(ad.)\begin{equation}{\rm SF}_6(g) = {\rm SF}_6({\rm ad.})\end{equation}At the interface between the metal and film (M–F interface), the physically adsorbed molecules ionize to form cation vacancy and electron hole.2SF6ad.=MF2+VM′′+2hg+SF4\begin{equation}{\rm{S}}{{\rm{F}}_6}\left( {{\rm{ad}}{\rm{.}}} \right) = {\rm{M}}{{\rm{F}}_2} + {\rm V}^{\prime\prime}_{\rm{M}} + 2{{\rm{h}}^{\rm{g}}} + {\rm{S}}{{\rm{F}}_4}\end{equation}At the M–F interface, the cation vacancy and the electron hole recombine.3M2++VM′′=0\begin{equation}{\rm M}^{2 +} + {\rm V}^{\prime\prime}_{\rm{M}} = 0\end{equation}42′+2hg=0\begin{equation}{2^{\prime} + 2}{{\rm h}^{\rm{g}}} = 0\end{equation}Ideally, the migration of metal ion vacancies (VM′′${\rm V}_{\rm M}^{\prime\prime}$) can also be regarded as the migration of metal ions with equal flux in the opposite direction. Therefore, based on the Wagner model [15], ion vacancies (V") and electron holes (h·) can be used as carriers to establish a corresponding finite element phase‐field model.Based on different assumptions, scholars have proposed different mathematical models for the corrosion reaction kinetics of metal surfaces. In the model proposed by Williams, and Fromhold [16, 17], the oxidation rate limited by the thermal emission of electrons was simulated, and it was concluded that mass transport during corrosion depends heavily on the diffusion process. However, when the film thickness is in Debye length, or the interface reaction is the dominant mechanism, Wagner's law of parabola is violated. In particular, the electric field can modify the electron band profile and the defect structure of the oxide [18, 19]. The solution of the phase field is complex, which requires high convergence. In addition, it is difficult to obtain the physical parameters of the specific carriers in the film. Chen [20] used the per‐unit system of physical parameters for analysis and compared the phase‐field model with Wagner's theoretical model. Therefore, it is unrealistic to directly and accurately calculate the corrosion rate of the contact element strip in the SF6 gas through the corrosion kinetic model. Nevertheless, based on the Wagner theory and Chen's one‐dimensional phase‐field model, the analysis of the main factors that affect the corrosion rate is still effective for the study of the corrosion process of the contact element strip.Construction of finite element phase‐field modelDuring overheating failure in the current‐carrying structure of high‐voltage power transmission equipment, the most severely damaged place in the contact element strip is often the electrical contact area, whose surfaces are exposed to SF6 decomposition gas, thereby generating corrosion products. Aiming at the overheating corrosion of the contacts in SF6 gas, the reaction model includes three kinds of phase fields: gas, film, and metal. The carrier transport mechanisms in the three phase fields are unified in the form of equations, but there are significant numerical differences between the different phases. In order to unify the transport equations in different phase fields, two variables need to be introduced to represent the carrier transport and chemical reaction processes in time and space.In this model, two variables η(x,t) and ζ(x,t) are introduced to describe the spatial and temporal distribution of the phases, and the value range of η and ζ is determined to be (0,1). Then, η and ζ represent the local fractions of the metal and gas in the phase, respectively. They take the value of 1 in the phase field and otherwise take the value of 0. The schematic diagram of the two‐dimensional phase‐field model of metal high‐temperature corrosion is shown in Figure 2.2FIGURESchematic diagram of two‐dimensional phase‐field model for high‐temperature corrosion of metalFor the cation vacancy concentration, c1, and the electron hole concentration, c2, there are basic assumptions that conform to physical facts. First, cation vacancies are generated only at the G–F interface and participate in the corrosion reaction on the interface. They will not diffuse to the gas side. Second, cation vacancies will not penetrate the metal in a form other than chemical reactions. While the metal has excellent electrical conductivity, gas conductivity is poor, and the concentration of electron holes in the metal domain is much smaller than the concentration in the film. Regardless of whether the carrier transport reaches equilibrium at the G–F interface, the potential difference at the interface will always make the charge accumulate at the interface. As cation vacancies and electron holes have different activities in different phases, activity coefficients are introduced to characterize carriers’ activity.Based on the electrochemical potential of carriers during transport, the activity coefficient can be expressed as5f1x=[1+κGpζ][1+κMpη]\begin{equation}{f_1}\left( x \right){\rm{ = }}[1 + {\kappa _{\rm{G}}}p\left( \zeta \right)][1 + {\kappa _{\rm{M}}}p\left( \eta \right)]\end{equation}6f2x=1+κMpη1+Npζ\begin{equation}{f_2}\left( x \right) = \frac{{1 + {\kappa _{\rm{M}}}p\left( \eta \right)}}{{1 + Np\left( \zeta \right)}}\end{equation}where κG and κM are penalty factors for the gas field and the metal field, respectively, with values much larger than 1, representing almost no diffusion of cation vacancy into the gas phase and a small permeability to the solid side. p(η) and p(ζ) are common interpolation functions in the phase field. The value of N is much greater than 1 and is taken as 50, which means that the concentration of cation vacancy and electron hole in the gas is much higher than that in the film.When the rate of carrier consumption at the gas–film interface and the film–metal interface due to chemical reactions is much higher than the rate of carrier transport, the carrier concentration at both interfaces can be clamped to a concentration controlled by the chemical reaction equilibrium; that is, ci is a constant. Therefore, the flux at the gas–film interface satisfies two equations simultaneously.7JM+=DM+cM+x=MF−cM+x=GFx\begin{equation}{{\bm{J}}_{{{\rm{M}}^{ + }}}} = {D_{{{\rm{M}}^ + }}}\frac{{c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{MF}}}} \right. - c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.}}{x}\end{equation}8JM+=cM+x=GFdxdt\begin{equation}{{\bm{J}}_{{{\rm{M}}^{ +}}}} = c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.\frac{{{\rm{d}}x}}{{{\rm{d}}t}}\end{equation}In the formula, JM+ is cation diffusion flux/mol·m‐2·s‐1; DM+ is the cation diffusion coefficient/m2·s‐1; cM+|x=MF is the cation concentration at the metal–film interface /mol·m‐3; cM+|x=GF is the cation concentration on the metal–gas surface/mol·m‐3; and x is the thickness of the film/m.The two equations can be combined to obtain the following:9dxdt=kx⇒x2=2kt\begin{equation}\frac{{{\rm{d}}x}}{{dt}} = \frac{k}{x} \Rightarrow {x^2} = 2kt\end{equation}10k=DM+cM+x=MF−cM+x=GFcM+x=GF\begin{equation}k = {D_{{\rm{M + }}}}\frac{{c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{MF}}}} \right. - c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.}}{{c_{{{\rm{M}}^ + }}\left| {_{x = {\rm{GF}}}} \right.}}\end{equation}When the carrier concentration at the two interfaces is constant, k is a constant, and the film growth satisfies the parabolic law. However, in the actual carrier transport process, the k constant is related to the carrier conductivity, diffusion coefficient, and chemical reaction. So, the corrosion reaction rate cannot be simply viewed as a constant value.The transport of carriers in the film is essentially driven by the electrochemical potential gradient, causing the gas and metal to develop in the direction of entropy increase. The electrochemical potential of the carriers is expressed as11ξi=uiθ+kBTlnXi+zieφ\begin{equation}{\xi _i} = u_i^{{\theta}} + {k_{\rm{B}}}T\ln {X_i} + {z_i}e\varphi \end{equation}where uiθ$u_i^\theta $ is the standard chemical potential of carriers, Xi is the molar fraction of carriers, φ is the potential, and zi is the number of charges carried by the carriers.According to Fick's second law, the change of carrier concentration with time has a certain relationship with the divergence of carrier flux.12∂ci∂t=−∇×Ji\begin{equation}\frac{{\partial {c_i}}}{{\partial t}} = - \nabla \times {{\bm{J}}_i}\end{equation}13Ji=−υici∇ξi\begin{equation}{{\bm{J}}_i} = - {\upsilon _i}{c_i}\nabla {\xi _i}\end{equation}where Ji is the flux of carrier i, vi is the mobility of carrier i, and ξi${\xi _i}$ is electrochemical potential.The flux of carriers in the film is related to the diffusion and migration of carriers. The actual concentration and diffusion coefficient of different carriers are obviously different in different phases, so it is necessary to introduce a constructor function for adjustment to achieve unified expression of variables in different phases. The above equation is combined to obtain the expressions for the flux of cation vacancies and electron holes.14J1=−D1∗∇c1∗+υ1c1E\begin{equation}{{\bm{J}}_1} = - D_1^*\nabla c_1^* + {\upsilon _1}{c_1}{\bm{E}}\end{equation}15J2=−D2∗∇c2∗+υ2c2E\begin{equation}{{\bm{J}}_2} = - D_2^*\nabla c_2^* + {\upsilon _2}{c_2}{\bm{E}}\end{equation}In (14) and (15), E=−∇φ${\bm{E}} = - \nabla \varphi $ which satisfies Poisson's equation. c1∗$c_1^*$ and D1∗$D_1^*$ is the unified expression of c1 and D1 in different phases.16c1=c1∗/f1\begin{equation}{c_1} = c_1^*/{f_1}\end{equation}17D1=f1D1∗\begin{equation}{\rm{ }}{D_1} = {f_1}D_1^*\end{equation}18c2=c2∗f21+g0pη\begin{equation}{c_2} = \frac{{c_2^*}}{{{f_2}\left[ {1 + {g_0}p\left( \eta \right)} \right]}}\end{equation}19D2=f21+g0pηD2∗\begin{equation}{\rm{ }}{D_2} = {f_2}\left[ {1 + {g_0}p\left( \eta \right)} \right]D_2^*\end{equation}where f1 and f2 are constructor functions of c1 and c2, respectively.In the equation, as cation vacancies do not diffuse into the gas, in order to satisfy the condition of electroneutrality in the gas phase, it is necessary to construct a negative charge concentration c3 in the gas phase to neutralize the electronegativity of c2.20c3∗≡−c1∗t=0+12c2∗t=0\begin{equation}c_3^* \equiv - c_1^*\left| {_{t = 0}} \right. + \frac{1}{2}c_2^*\left| {_{t = 0}} \right.\end{equation}Migration‐diffusion expressions for solving variables in different phases are established. At the interface, carriers are continuously generated or compounded in the form of chemical reactions. From the perspective of phase‐field modelling, it is equivalent to the establishment of a reaction zone with a function at the G–F interface or M–F interface. The constructed reaction zone at the G–F interface or the M–F interface is21Λζ=ζ21−ζ2\begin{equation}{\Lambda _\zeta } = {\zeta ^2}{\left( {1 - \zeta } \right)^2}\end{equation}22Λη=η21−η2\begin{equation}{\Lambda _\eta } = {\eta ^2}{\left( {1 - \eta } \right)^2}\end{equation}In addition to diffusion and migration, the transport process of carriers includes chemical reactions (generation, recombination) in the interfacial region. Among them, the generation or recombination rates of carriers (c1) in the G–F interface and M–F interface can be expressed as23RIc1=Λζpx1/2kI−k′Ic1∗c2∗2\begin{equation}R_{\rm{I}}^{\left( {{c_1}} \right)} = {\Lambda _\zeta }\left( {p_x^{1/2}{k_{\rm{I}}} - {{k^{\prime}}_{\rm{I}}}c_1^*{{\left( {c_2^*} \right)}^2}} \right)\end{equation}24RIIc1=ΛηkIIc1∗c2∗2−kII′\begin{equation}R_{{\rm{II}}}^{\left( {{c_1}} \right)} = {\Lambda _\eta }\left( {k_{{\rm{II}}}}c_1^*{{\left( {c_2^*} \right)}^2} - k^{\prime}_{{\rm{II}}} \right)\end{equation}where I and II represent G–F interface and M–F interface, respectively. RI(c1) and RII(c2) are cation vacancy's reaction terms at G–F interface and M–F interface, respectively. kI and kII are the forward rate constants in G–F interface and M–F interface. kI′${k^{\prime}_{\rm{I}}}$ and kII′${k^{\prime}_{{\rm{II}}}}$ are the inverse rate constants in G–F interface and M–F interface. Arrows represent forward and reverse reactions.For the reaction term of c2 at the interface, the above equation can be re‐expressed as25RIc2=2RIc1\begin{equation}R_{\rm{I}}^{\left( {{c_2}} \right)} = 2 R_{\rm{I}}^{\left( {{c_1}} \right)}\end{equation}26RIIc2=2RIIc1\begin{equation}R_{{\rm{II}}}^{\left( {{c_2}} \right)}{\rm{ = 2}}R_{{\rm{II}}}^{\left( {{c_1}} \right)}\end{equation}When the reaction is in equilibrium, the electric field in the entire calculation field satisfies Gauss's law27∇×εrxε0Ex=∑icixNAzie+ρs\begin{equation}\nabla \times \left[ {{\varepsilon _{\rm{r}}}\left( x \right){\varepsilon _0}{\bm{E}}\left( x \right)} \right] = \sum_i {{c_i}\left( x \right)} {N_{\rm{A}}}{z_i}e + {\rho _{\rm{s}}}\end{equation}As the dielectric constants of materials in different phases are different, the relative dielectric constants of gas are regarded as 1 and those of metals as 1.0×106. In the paper, the relative dielectric constant of film εr = 4, so εr(x) can be expressed as28εrx=εr−1[1−pζ][1−pη]+1+106×pη\begin{equation}{\varepsilon _{\rm{r}}}\left( x \right){\rm{ = }}\left( {{\varepsilon _{\rm{r}}} - 1} \right)[1 - p\left( \zeta \right)][1 - p\left( \eta \right)] + 1 + {10^6} \times p\left( \eta \right)\end{equation}When the reaction is placed in the applied electric field E'. the carriers in the film will also be subjected to the applied electric field force.In summary, the solution equation is expressed as29∂c1∂t=Λζpx1/2kI−k′Ic1∗c2∗2I−ΛηkIIc1∗c2∗2−k′II+∇×D1∗∇c1∗−∇×D1c1z1E+E′∂c2∂t=2Λζpx1/2kI−k′Ic1∗c2∗2I−2ΛηkIIc1∗c2∗2−k′II+∇×D2∗∇c2∗−∇×D2c2z2E+E′\begin{eqnarray} \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} \def\eqcellsep{&}\begin{array}{l}\! \dfrac{{\partial {c_1}}}{{\partial t}} = {\Lambda _\zeta }\left( {p_x^{1/2}{k_{\rm{I}}} - {{k^{\prime}}_{\rm{I}}}c_1^*{{\left( {c_2^*} \right)}^2}_{\rm{I}}} \right) - {\Lambda _\eta }\left( {{k_{{\rm{II}}}}c_1^*{{\left( {c_2^*} \right)}^2} - {{k^{\prime}}_{{\rm{II}}}}} \right)\\[12pt] +\,\nabla \times \left( {D_1^*\nabla c_1^*} \right) - \nabla \times \left( {{D_1}{c_1}{z_1}\left( {{\bm{E}} + {\bm E}^{\prime}} \right)} \right) \end{array} \\[18pt] \def\eqcellsep{&}\begin{array}{l} \dfrac{{\partial {c_2}}}{{\partial t}} = 2{\Lambda _\zeta }\left( {p_x^{1/2}{k_{\rm{I}}} -\! {{k^{\prime}}_{\rm{I}}}c_1^*{{\left( {c_2^*} \right)}^2}_{\rm{I}}} \right) -\! 2{\Lambda _\eta }\left( {{k_{{\rm{II}}}}c_1^*{{\left( {c_2^*} \right)}^2}\! - {{k^{\prime}}_{{\rm{II}}}}} \right)\\[12pt] +\,\nabla \times \left( {D_2^*\nabla c_2^*} \right)\! - \nabla \times \left( {{D_2}{c_2}{z_2}\left( {{\bm{E}}{\rm{ + }}{\bm{E}}^{\prime}} \right)} \right) \end{array} \end{array} } \right.\hskip-10pt\nonumber\\[-4pt] \end{eqnarray}where z1 and z2 are the number of charges carried by cation vacancy and electron hole, respectively.We established a two‐dimensional phase‐field model for high‐temperature corrosion of metals, the transport and reaction of carriers in different phases can be described by a set of unified equations. The mathematical model is built based on the basic reaction, which is dominated by cation vacancy. This paper mainly discusses the mechanism by which cation vacancy dominates. The mechanism of action is similar when anions are dominant and anions and cations are co‐dominant.In this paper, the complete set of differential equations required for phase‐field calculation is established in the software COMSOL, which was not completed in previous studies. The calculation process is as follows in Figure 3:A two‐dimensional model of phase‐field is presented. In order to improve the convergence of the calculation, it is necessary to discretize the variable c (concentration) into a third‐order continuous and differentiable variable. The mesh division in the calculation area needs to be refined to suppress the numerical oscillation during the solution. The density of mesh division is 1/1000 (e.g. a model length of 10 μm corresponds to a grid cell size of 0.01 μm).The transport of diluted species (tds) module is used to establish the transport equations of anions, cations, and electrons in the calculation domain. The constant‐concentration boundary condition is applied at both ends of the two‐dimensional model, and a chemical‐reaction‐based boundary condition is applied at the middle section.The electrostatic field (es) module is used to solve the Poisson equation. In this paper, the boundary condition near the end of the metal side is set to ground, and the middle area is set to the space charge density. The charge density is set according to the transport of carriers in the tds module.The formulation of the fully coupled method is processed. The non‐linear method adopts the constant (Newton) method. The damping coefficient is 0.9, the maximum number of single‐step iterations is eight times, and the tolerance factor is set to 1. The electric field (E) and the concentration (ci) are transmitted as coupling variables in the tds module and the es module.3FIGUREFinite element phase‐field calculation process for metal corrosionThe initial carrier concentration distribution is shown in Figure 4. The generated cation vacancies exist in the oxide film, while the concentrations of cation vacancies in the metal phase and the gas phase are both zero. In order to meet the conditions of electrical neutralization, when the valence state of the cation vacancy is +2, the concentration of the cation vacancy in the gas phase is exactly one‐half of the electron hole concentration. The concentration of cation vacancy in the oxide film and the gas phase changes to zero.4FIGUREInitial concentration distribution of carrierSIMULATION RESULTS AND ANALYSISBased on the above phase‐field method, the carrier concentration, flux distribution, and preset charge distribution were obtained when computational domain length L =3 μm (film thickness of 2.8 μm). The computational domain includes the metal phase, the corrosion film, and the gas phase. The length of the computational domain is 3 μm (L =3 μm), where the thickness of the corrosion film is 2.8 μm. The carriers concentration was expressed in terms of relative concentration, c0*, and the diffusion coefficient, Di, was expressed in the form of Di* × D0. The magnitude of the binary sulfide ion diffusion coefficient was about 1.0 × 10−14 m2/s, so D0 was set to 1.0 × 10−14 m2/s, and the value of Di* was related to the carriers that affect transport processes. DM* took 1, and De* took 2000.It can be seen from Figure 5 that the electron holes in the film were affected by the diffusion in the concentration gradient, moving continuously from the gas side to the metal side along the film. Also, the electron holes fell rapidly in the M–F interface reaction zone. The cation vacancy concentration rose in the G–F interface reaction zone and then diffused along the growth direction of the film. Its concentration kept decreasing, especially in the reaction zone near the M–F interface, which quickly dropped to zero. When the reaction reached equilibrium, the cation vacancy flux was evenly distributed in the film and rapidly dropped to zero at the M–F interface.5FIGUREConcentration distribution and flux of carrier, charge density, and electric potential in the filmThere was an electric double layer at the G–F interface, while the inside of the film was electrically neutral. At the interface between film and gas, cation vacancies and electron holes were continuously generated on the gas. The diffusion coefficient of the electron hole was higher than that of the cation vacancy. During the carrier diffusion process, the negative charge density of the area near the gas side was higher than the positive charge density. So the charge accumulation inevitably occurred at the interface. Excessive positive charge density appeared on the side of the film, which led to the formation of an electric double layer. Similarly, at the M–F interface, owing to excessive positive charges, a small amount of charge would accumulate. In most areas of the film, the positive charge density was basically close to negative charge density. Thus, the potential difference was mainly concentrated at the electric double layer at the interface, and the reduction of the potential in the film was relatively gentle. The metal domain and the gas domain were electrically neutral, and the potential difference was zero.Influence of temperature on carrier distributionThe current‐carrying structure of the faulty bushing was disassembled to obtain the damage morphology of the contact elements strip. In order to further analyze the high‐temperature corrosion mechanism of the contact element strip, the carrier and flux distribution of the metal corrosion film under the influence of different overheating temperatures were simulated and calculated. As the diffusion coefficient of cation vacancy in the film was affected by temperature, the relationship between the diffusion coefficient and temperature can be expressed as30D=Dfe−QDRT\begin{equation}D = {D_{\rm{f}}}{{\rm{e}}^{ - \frac{{{Q_{\rm{D}}}}}{{RT}}}}\end{equation}In the formula, Df is the frequency factor/m2·s−1, and QD is the diffusion activation energy/J·mol−1.If the temperature of the matrix of metal on both sides of the contact was similar, the temperature rise relationship of the contact can be written as [21–23]:31Tm=U024L+T02\begin{equation}{T_{\rm{m}}} = \sqrt {\frac{{U_{\rm{0}}^2}}{{4L}} + T_0^2} \end{equation}where Tm is the temperature of the contact point, T0 is the temperature of the matrix, and U0 is potential differences.As the temperature increased, the diffusion coefficient of carriers would increase exponentially. Owing to the high temperature at the electrical contact point, the temperature of the contact point would be higher than the temperature of the matrix of metal. Therefore, the diffusion coefficients of cation vacancy varied greatly at different positions. First, to compare the difference in reaction kinetics at different temperatures, we calculated the carrier concentration distribution and flux changes under different diffusion coefficients; second, we set different temperatures for different positions of the two‐dimensional model to simulate the carrier distribution characteristics when there was a temperature difference between the contact point and the matrix of metal.Figure 6 presents the carrier concentration distribution in the film under steady‐state conditions with different cation vacancy diffusion coefficients. The figure components from (a) to (d) show the results for the diffusion coefficients of 1, 4, 7, and 12, in that order. Owing to the high concentration of carriers on the gas side, the concentration difference between the M–F interface and the G–F interface would promote the continuous transport of cation vacancies to the metal side until equilibrium was reached. With the increase in the cation vacancy diffusion coefficient, the diffusion capacity for cation vacancy to the gas side increased. The increased diffusion capacity would reduce the concentration gradient between the two interfaces, making the distribution in the film more uniform. Take a horizontal line segment starting from the metal side and ending at the gas side with the Y coordinate unchanged. Figure 7 shows the vacancy concentration and flux distribution under this path. It is apparent that the cation vacancy peak concentration at the G–F interface decreased with the increase in the vacancy diffusion coefficient, and that at the M–F interface, it increased slightly. At the same time, the carrier flux in the film increased as the cation transport capacity increased. After calculation, the film growth rate increased with the increase in the diffusion coefficient, but the slope of the growth rate gradually decreased. This was mainly because of the decrease in the concentration gradient on both sides of the diffusion coefficient, which in turn inhibited the diffusion of carriers.6FIGURETwo‐dimensional concentration distribution for different diffusion coefficients7FIGURECarrier distribution, flux distribution, and film growth rate under different diffusion coefficientsInfluence of gas partial pressure on carrier distributionIn order to analyze the influence of gas partial pressure on the change of carrier concentration in the film and the film growth rate, we modified the gas pressure in the phase‐field model. The cation vacancy concentration and its flux distribution when L = 3 μm were calculated by simulation, as shown in Figure 8. When the gas partial pressure was at the standard atmospheric pressure, the overall distribution of the cation vacancy concentration was low. As the gas partial pressure ratio increased sequentially by 1, 4, and 7, and 10 atmospheres, we observed an increase in the cation vacancy generation rate at the G–F interface, especially the peak concentration. However, the diffusion coefficient of carriers remained unchanged, and the concentration distribution of cation vacancies in the film showed an overall downward trend. After the calculation, the film growth rate increased with the increase of the gas pressure. When the air pressure rose 10‐fold, the film growth rate increased by 1.1 times. The effect of gas pressure on the growth rate is smaller than that of temperature. However, the increase in cation vacancy and electron hole concentration in turn inhibited the generation of carriers at the G–F interface. Therefore, as the gas partial pressure increased, the increase in carrier flux became smaller, and the film growth rate tended to be saturated.8FIGURECarrier distribution, flux distribution, and film growth rate under different gas pressuresInfluence of film thickness on carrier distributionBy changing the film thickness, the changes in the carrier concentration and the film growth rate under different film thicknesses were calculated. The phase‐field model calculated the cation vacancy concentration and flux distribution when L grew from 1 to 7 μm (value interval of 1.5 μm), as shown in Figure 9. As the film thickness increased, the difference in cation vacancy concentration between the M–F interface and the G–F interface increased. As the consumption of cation vacancies on the metal side was mainly related to the reaction rate, the reaction rate remained unchanged, and the change in the carrier concentration was relatively small. On the gas side, cation vacancies continued to be generated, and the increase in film thickness affected the diffusion of carriers, so the concentration rose significantly at the G–F interface. Through the calculation of the film growth rate, we found that the film growth rate decreased with the increase in the film thickness under the condition that the gas partial pressure and the diffusion coefficient remained unchanged. When the film thickness increased to a certain extent, the film growth rate and thickness satisfied the parabolic relationship, which is consistent with Wagner's theory and further proves the rationality of using the two‐dimensional phase‐field model.9FIGURECarrier, flux distribution, and film growth rate under different thicknessesInfluence of applied electric field on carrier distributionAccording to the electrical contact theory, the contact resistance is composed of film resistance and contraction resistance. In normal condition, the film resistance is negligible. However, when the corrosion film is formed, much attention needs to be paid on the film resistance due to poor electrical conductivity. A high electric field exists when a small voltage drop acts on a micron‐scale film. The previous simulation mainly considered the electromigration induced by the electrochemical potential during the formation of the corrosion film. On this basis, we introduced the electric field as a variable into the governing equations of phase‐field model, which was not considered in previous simulations. In order to analyze the influence of the applied electric field on the carrier concentration and the film growth rate, we kept other conditions unchanged and added the applied electric field of 0, ±0.07 kV/mm, ±0.2 kV/mm, and ±0.33 kV/mm in sequence. The cation vacancy concentration and its flux distribution under the positive and negative electric field are presented in Figure 10.10FIGURECarrier distribution, flux distribution, and film growth rate under different applied electric fieldsWith the increase in the positive applied electric field, the cation vacancy accelerated to migrate to the M–F interface. Owing to the limited reaction rate at the interface, under the dual effects of the electric‐field migration and the concentration gradient, positive charges began to accumulate on the metal side. The concentration of cation vacancy at the M–F interface rose and gradually produced a peak concentration. The occurrence of the peak concentration indicated that the influence of the applied electric field on the carrier migration could not be ignored. At the G–F interface, with successive increases in the intensity of the electric field, the cation vacancies concentration further decreased. On the contrary, when a negative electric field was applied, the positive charges were subjected to the force of the electric field opposite to the diffusion direction and were mainly concentrated on the gas side. The peak concentration of the cation vacancy at the G–F interface increased with the increase in the electric field. The positive charges accumulating at the M–F interface decreased.When the applied electric field existed, the distribution of carriers in the film was changed. The positive electric field promoted the migration of vacancies to the metal side, strengthened the flux of cation vacancies in the film, and enhanced accumulation of positive charges at the G–F interface, while the negative electric field had the opposite effect. Under the stable condition of corrosion reaction, the polarity of the applied electric field had an opposite effect on the growth rate of the corrosion film. Under the given physical parameters, when the electric field corresponds to −0.33 and 0.33 kV/mm, the growth rates of corrosion film increased from 7.9 to 8.6 nm/s. The applied electric field made the carrier distribution in the film tend to prevent the applied electric field. Owing to the limited reaction rate of the G–F interface, under the action of the positive electric field, the positive charge would accumulate on the gas side, weakening the electric double layer effect, and a negative electric field would strengthen the electric double layer at the interface. The growth rate of the G–F interface film increased with the increase in the electric field intensity, and the amplitude gradually became flat.HIGH‐TEMPERATURE CORROSION TESTFigure 11 shows the schematic structure of typical converter valve‐side bushings. The main structure includes an aluminium conductor or copper conductor, contact element strips, SF6, RIP cores, transformer oil, shielding, and a grounding flange. The contact element strips are installed in the transition area of current‐carrying conductors, which is the connection structure between the aluminium conductor and copper conductor. It is shown in blue in Figure 11 and bears the overall current. The path of the current at the plug‐in structure is shown by the red dashed line. Owing to the contact resistance, this position has a high degree of heat generation and is prone to degradation and corrosion with SF6 under overheating.11FIGUREThe schematic structure of typical converter valve‐side bushingsThe contact element strips deteriorate very slowly under normal working conditions. Due to the high cost of the time and experiments, it is necessary to design a high‐temperature corrosion accelerated test in order to simulate the overheating fault of the contact elements under the condition of uneven current carrying in the high‐voltage bushing. Therefore, we increase the test current to boost the heating power of the contact element strip and accelerate the corrosion reaction. The whole process of accelerated test is carried out under the current, and the electric field exists in the test.In order to obtain the higher contact temperature of the contact element strip, we selected the contact element strip used in the UHV bushing as the test object. The upper and lower electrodes were all made of aluminium. The lower electrode adopted the aluminium electrode with a T‐type slot, ensuring the stability of the contact elements. The contact element strip is LA‐CUD double‐tooth contact fingers, used in the electrical connection of high‐voltage bushings. The matrix of the contact element strip was copper, and its surface was plated with silver. The test platform and the structure of contact fingers are shown in Figure 12. Before the experiment, contact element strips were installed in parallel in the T‐type slot. Each contact element strip had four contact fingers, for a total of eight pieces. The DC current was 600 A, the ambient temperature was controlled at a constant temperature of 25°C, the experimental atmosphere was SF6, and the pressure was 2 atm. The test duration was 72 h. With the help of the auxiliary heating system, the electrode was kept at 100℃ to simulate the heating of the conductor. The current passed through the lower electrode and contact element strips and finally communicated with the upper electrode.12FIGUREHigh‐temperature corrosion test platform for contact element stripsDuring the test, the temperature of the contact element strip matrix and the contact voltage were measured in real time. We found that the temperature of the matrix was maintained at about 150°C. Because the contact area was squeezed by the upper electrode and the contact element strip and the overall structure size of the contact element were in the centimeter range, the contact temperature was difficult to measure directly. The contact temperature was estimated by using the V–T relationship that is widely used in electrical contact at present. In this experiment, the contact temperature will be significantly higher than the matrix temperature, possibly reaching to 500°C.Through the high‐temperature corrosion test on the contact element strips, the morphology of the experimental samples was analyzed. Figure 13 shows the corrosion morphology of the contact and the matrix of the contact element strip under the test. Obvious signs of overheating corrosion occurred in the contact area, as black products appeared on the surface. The matrix area began to turn yellow, but the surface was relatively flat. The characteristic peaks of Cu, F, S elements are high in the inner and edge of contact area, and the metal fluoride and sulfide is mainly concentrated in this area. The non‐contact area has only a very small amount of F and S elements. Thus, the corrosion degree of the contact area of contact element strips is much higher than that of the non‐contact area, accompanied by the formation of metal fluoride and sulfide. The corrosion appearance and corrosion products are similar to the sampling contacts in the faulty bushing, which can illustrate the effectiveness of accelerated testing.13FIGURECorrosion morphology and element analysis of contact element strips’ surfaceThe carrier distribution in the film was studied by simulating the temperature difference between the contact and the matrix. Different temperatures were set for each position on the metal side, and the temperature rose from 150°C to 500°C from bottom to top along the y‐axis. The upper end of the metal side represented the high‐temperature area of the contact, and the lower end represents the low‐temperature area of the matrix. Figure 14 shows the two‐dimensional distribution of carriers.14FIGURECarrier distribution characteristics under the high‐temperature difference between the contact and the matrixAs the temperature increased, the diffusion coefficient of cation vacancies in the film would increase exponentially. Therefore, the diffusion coefficient near the contact was much higher than that of the matrix. It can be seen that the cation vacancy distribution at the contact was more uniform, the peak concentration at the G–F interface gradually increased from the contact to the matrix, and the concentration at the M–F interface remained stable. This is consistent with the changed characteristics of the carrier distribution with the diffusion coefficient at a constant temperature. As the diffusion coefficient at the matrix was much smaller than the diffusion coefficient at the contact, even if the contact was completely stable, the matrix was still in a slow diffusion process, and the initial distribution was difficult to change in a short time.We calculated the film growth rate of the contact, the matrix, and the middle transition area, as shown in Figure 15. The carrier flux at the contact was much higher than the flux at the matrix. The growth rate at low temperature is orders of magnitude lower than that at high temperature. When parameters such as film thickness are given and the temperature is 150°C, the growth rate of the film is 20 nm/s. While the growth rate of the film is 517 nm/s in the contact position. Owing to the low temperature at the matrix, the film growth rate was extremely slow, close to zero; the temperature at the contact was high, the film growth rate was much higher than the matrix owing to the high diffusion coefficient. Combined with experimental analysis, when the contact element strips at the plug‐in structure are in poor contact, the temperature rise between the contact and the matrix will cause a significant difference in the growth rate of the corrosion film. The above analysis indicates that in UHV bushing, the contact area of the current‐carrying structure is the first to become the breakthrough point of the corrosion reaction, and the severity of corrosion is much higher than that of the non‐contact area.15FIGUREFilm growth rate at different positionsCONCLUSIONBased on the actual problems in engineering, the two‐dimensional phase‐field finite element model of corrosion reaction kinetics was established. The factors affecting the growth of the corrosion film of the contact were calculated. Meanwhile, the accelerated test was used to simulate the overheating corrosion state of contact element strips in the bushing. The following conclusions can be drawn:The coupling calculation analysis using COMSOL finite element software was successfully realized, which was not completed in previous studies. Temperature has the most obvious effect on the film growth rate. The influence of temperature on the growth rate increases exponentially. Under the given physical parameters, when the temperature from matrix to the contact area corresponds to 150°C and 500°C, the growth rates of corrosion film increased from 20 to 517 nm/s, which was 25 times the original. The corrosion rate tends to be stable with the increase of film thickness and gas pressure, but the two factors have opposite effects.The influence of the electric field was introduced into the equation of phase‐field model on the original basis. The polarity of the applied electric field has the opposite effect on the corrosion reaction. Compared with the negative electric field, the positive electric field increases the growth rate of the film. The growth rate increased by 8.5% between −0.33 and 0.33 kV/mm, and the increased amplitude decreases with the increase in the field strength. It can provide help for the next step in the study of the corrosion characteristics of contacts by AC and DC electric fields.The test results are similar to the faulty contacts, which can illustrate the effectiveness of accelerated testing. Obvious black traces appear in the contact area, accompanied by the formation of corrosion products. The characteristic peaks of Cu, F, S elements are high in the inner and edge of contact area. Combining the comparison of the film growth rate between the contact and the matrix at different temperatures, it shows that temperature rise caused by poor contact is the main cause of the failure of the electrical connection structure, and the contact area is the starting position of the corrosion. The difference of corrosion degree between the contact area and non‐contact area shows the rationality of the simulation calculation.This study is the first step in the research on the corrosion characteristics of the contact elements of the UHV bushing. Quantitative comparative analysis requires the design of a more precise and detailed experimental scheme, which will be the next step based on this study. And carriers corresponding to various corrosion reactions will be introduced into the phase field model in the next step of simulation calculation.ACKNOWLEDGEMENTSThe authors would like to appreciate State Key Laboratory of Electrical Insulation and Power Equipment in Xi'an Jiaotong University. This work is supported also by National Natural Science Foundation of China (NSFC: 52107163).CONFLICT OF INTERESTWe declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are openly available at http://doi.org/[doi].REFERENCESWang, Q., Yang, X., Tian, H., et al.: A novel dissipating heat structure of converter transformer RIP bushings based on 3‐D electromagnetic‐fluid‐thermal analysis. IEEE Trans. Dielectr. Electr. Insul. 24(3), 1938–1946 (2017)Israel, T., Schlegel, S., Gromann, S., et al.: Modelling of transient heating and softening behaviour of contact points during current pulses and short circuits. 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"IET Generation, Transmission & Distribution"Wiley

Published: Aug 1, 2022

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