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2016 China International Conference on Electricity Distribution (CICED 2016) Xi’an, 10-13 Aug, 2016 Multi Physical Field Coupling Calculation of Airflow Characteristics of SF6 Circuit Breaker Based on Actual Gas Model An Su, Xin Lin, Yalong Xia, Feiming Wang School of Electrical Engineering, Shenyang University of Technology, Shenyang, 110870, China Abstract—The Redlich-Kwong state equation of the real gas and the governing equations of the flow field were combined to solve the problem.The distribution of physical parameters of the interrupter was attained under the condition of the circuit breaker in small capacitive current interruption by analysis of the 126kV capacitor group SF6 gas circuit breaker arc extinguishing chamber in air flow field, which is according to enthalpy flow arc model and dynamic model of non-equilibrium arc energy built by microscopic parameters of plasma. The dielectric recovery characteristic curves in arc contacts after the arc extinguished were attained through the coupling calculation in the field of electric and gas flow. Calculation results show that: When the circuit breaker is opening the small capacitive current, the effect of breaking speed on arc burning time is very small and arc extinguished in advance. The arc gap conductivity is about 700S/m, and the thermal conductivity is about 1.1W/m·K at arc extinguishing time. The transient recovery voltage is always lower than that of the breakdown voltage, and the electric arc can successfully break without reburning. To make the short arcing time have a large arc distance, and the large nozzle should be open enough to be strong for the gas blowing condition, the optimum opening speed is 9.6m/s. Index Terms—Circuit breaker; Redlich-Kwong state equation; numerical calculation; gap breakdown margin I. INTRODUCTION SF6 gas circuit breaker parallel capacitor set special for capacitor group in the power system is used, the successful opening of capacitive small current is realized by using the SF6's strong electronegative and excellent thermo chemical properties, which can effectively inhibit the over voltage and reduce the critical wear rate[1]-[2]. Whether the SF6 breaker can successfully open is relative to the recovery speed of SF6 dielectric and voltage between contacts after the arc extinguishes, the process refers to the transition from conduction to insulation, including arc theory, plasma physics, electromagnetic field theory, fluid mechanics, thermodynamics and so on[3]-[4].The research on the coupling calculation of breaking characteristics is of great significance to the safety and stability of power CICED2016 Session 3 Paper No CP1234 system as well as the reliable operation of circuit breaker. The study on breaking performance of the circuit breaker is mainly divided into two aspects: test research and simulation research. Because of the long cycle and high cost, it is difficult to meet the actual requirements of the project, therefore accurate calculation of arc chamber pressure characteristics and dielectric recovery performance is vital to the design of circuit breaker[5]. Gas property is the basic data for calculating the breaking characteristics of SF6 circuit breakers, and accurate gas parameters are necessary to ensure the accuracy of the gas flow field[6].SF6 gas circuit breaker in high pressure has large molecules and is in transonic flow state during the breaking process with complex flow path. The solution to the gas flow field of the circuit breaker is the combination of the conservation equation and the gas state equation, during which the ideal gas state equation is used mostly, whereas the real gas state equation is seldom used[7]-[9].The ideal gas state equation ignores the molecular volume of gas, assuming there is no interaction force between the molecules, which is suitable for the calculation of small molecules, low pressure gas. The Redlich-Kwong state equation of the real gas considers the increasing effect of gas molecular volume on the dynamic pressure of the gas and the cohesion of intermolecular forces on reduction of gas pressure, it also considers the influence of temperature on molecular collision processes and ignores the molecular shape, polarity, and ensures the simplicity to improve the calculation accuracy, which is more suitable for the calculation on SF6 gas with macromolecules, non polarity, high pressure in circuit breaker[10]-[11]. In this paper, the Redlich-Kwong state equation of the actual gas was applied to the airflow field and electric field coupling calculation of SF6 126kV circuit breaker, based on the calculation on the distribution of electric field in the arc chamber, the non equilibrium state arc energy model was established, the distribution of physical parameters in the arc chamber of circuit breaker was calculated, and the breaking characteristics of circuit breakers were analyzed according to microscopic parameters of plasma and macroscopic parameters of gas. The research results not only provide a theoretical reference for the breaking characteristics Page1/7 2016 China International Conference on Electricity Distribution (CICED 2016) of circuit breakers but also have a certain guiding significance for the optimal design of circuit breakers. II. CALCULATION MODEL A. Research objects Fig. 1 is a diagram of the structure of the SF6 gas circuit breaker arc extinguishing chamber special for 126kV capacitor group. During the opening process, the main contact is separated from the arc contact, the current is transferred to the closed static and dynamic arc contact, and then the arc contact is separated to form arc. The rated gas pressure ,rated back-to-back capacitor bank breaking current circuit , arc contact distance and super-path of the circuit breaker are 0.7MPa, 1600A, 150mm, 50mm, respectively. The curves of the speed and route of the contact are showed in Fig.2. 1 3 2 4 5 Xi’an, 10-13 Aug, 2016 Kwong equation , high force coefficients in CR K are a function of the temperature T, which is superior to the ideal gas state equation and meets the actual Onnes equation highly. In the calculation of arc energy, Joule heating is considered without radiation heat transfer: I q E 2 J 2 / ( )2 / (5) A The relationship between the SF6 arc cross-section and the current is given by LESLIE S.FROST[12]-[13]: A l I/ pout F Where A is arc cross-sectional area; l is arc length; Pout is arc area downstream pressure; I is the current; is the conductivity, F is the enthalpy flow. In the equation of F = ρch / P , is the density, h is enthalpy, P is the pressure, c is the speed of sound, the relationship between speed of sound and temperature is as following: c 800 0. 164T 6 8 7 1 0 9 1-SF6;2-Static main contact;3-Large nozzle;4- -Movable main contact; 5-Air chamber;6-Static arc contact;7-Shield;8-Small nozzle;9-Movable arc contact;10-piston 12 行程/mm s/mm 8 Main contact trip 主触头行程 100 4 III. NUMERICAL CALCULATION 50 0 0 0.01 0.02 0.03 时间/s t/s 0.04 0.05 0.06 0 Fig. 2. The curve of speed and distance of circuit breaker B. mathematical model SF6 gas Redlich-Kwong equation of state is: P = RT a V - b T 1 / 2V V +b (1) Where P is the SF6 gas pressure; R is the gas constant; V is the gas volume, the constant a and b are based on the critical isotherms at the critical point. a = 0.42748 RTc R 2Tc2.5 b = 0.08664 Pc Pc (2) Where Tc is the critical gas pressure, Pc is the critical gas pressure. The formula(1) is deformed and expanded in the form of summation of series: RT 1 a 1 a V 1 b T bV 1 b T bV V V RT RTb a RTb 2 ab 2 3 V V V TV 2 TV 3 P RT V (3) 1 a 1 2 ab 1 V b 2 b T TR V T TR BR K b In the solution of the control equation, the parameters of the gas in different states f P, T were obtained by using two interpolation methods. 2 2 (8) f P,T - f Pi ,T 弧触头行程 Arc contact trip Speed of arc 弧触头速度 contact Speed of 主触头速度 main contact v/(m/s) 速度/(m/s) 150 a , T TR CR K b 2 ab T TR (4) A. Calculation of physical parameters of arc quenching chamber When the coupling numerical calculation was performed, the first kind of boundary condition was imposed on the moving arc contact and the moving main contact: 1 =1V, The first kind of boundary condition was the static main contact and the static arc contact with loading: 2 =0V[14]-[15]. The initial velocity of the gas is 0, the gas pressure is 0.7MPa, the initial temperature is 293K. The finite element volume method was used to discrete the mathematical model of the SF6 gas, the arc energy of arc contact was loaded by self programming, arc conductance was calculated simultaneously through the temperature and pressure in arc plasma area monitored by programs, the simulation process can be used to describe the dynamic development trend of arc during the opening of circuit breaker. Assuming the SF6 circuit breaker phases was 1/2π, the distribution of the physical property parameter in the arc extinguishing chamber under the unsteady flow were calculated under the average speed of arc contact is respectively 5.7m/s, 6.72m/s, 7.68m/s, 8.64m/s, 9.6m/s, when the capacitive small current was 1600A. Figure 3 shows the distribution of the physical parameters in the arc quenching chamber at different speed. (4) is the second and third force coefficient of Redlich CICED2016 Session 3 (7) f Pi ,T f P,T = i=0 i=0,i j f Pi ,T - f Pj ,T Fig. 1. Structure of arc quenching chamber 200 (6) Paper No CP1234 Page1/7 2016 China International Conference on Electricity Distribution (CICED 2016) (a)Electric field (b)Density Xi’an, 10-13 Aug, 2016 increases. However, the influence of breaking speed on arcing time is not obvious, the arcing time varies between 4.25ms and 4.33ms, and the range is not large. In the process of opening and breaking of the circuit breaker with the small 1600A capacitive current, there is a certain degree of advance quenching phenomenon in the process because of the lower arc energy and the smaller breaking current, in addition, due to the short arcing time, the large nozzle of circuit breaker has not yet opened in the process of opening the small current, therefore, the arc extinguishing ability of the circuit breaker is mainly determined by the pressure difference between chamber and the hollow tube when contact separates. Table.1 Arc parameters at different speeds Breaking Moment of Arcing Arc Extinguish speed (m/s) separation(ms) time(ms) distance(mm) 5.76 27.56 21 4.33 (c)Temperature (d)Pressure 6.72 23.62 4.28 27 7.68 20.67 4.25 32 8.64 18.37 4.3 37 9.6 16.53 4.27 41 B. Study on the dielectric recovery characteristic of circuit breaker According to the simulation model of the gas flow field and electric field of the fast grounding switch, the characteristic curve of dielectric recovery was calculated. In a slightly inhomogeneous electric field, the breakdown criterion of SF6 gas can be expressed by the following formula[16]: Ecrit =1.167 U b Ecrit / E1V (e)Conductivity (f)Thermal conductivity Fig. 3. Parameter distribution of arc extinguishing chamber at quenching moment It can be seen from the graph that at arc extinguishing time, arc gap conductivity is about 700S/m, and the thermal conductivity is about 1.1W/m·K. The greater the speed, the greater the pressure value in the upper reaches of the small nozzle, and the more the pressure difference between the upper and the lower reaches of the arc, with the greater gas blowing intensity at the moment of extinguishing, the convection heat transfer between air and electric arc is more obvious, and the arc energy diffusion is more adequate. When the circuit breaker breaking phase is 1/2π, the different parameters corresponding to the arc velocity are shown in table 1. According to the calculation results, it can be seen that the breaking speed directly affects the time of the arc contact and the distance of the arc extinguishing. With the increase of the breaking speed, the time of the contact shortens and the distance between the arc CICED2016 Session 3 Paper No CP1234 (9) Where Ecrit is the value of the critical breakdown electric field strength; U b is the Critical breakdown voltage; E1V is the electric field intensity distribution when the contact voltage is 1 V. When the electric field strength between contacts shows E > Ecrit , effective ionization coefficient γ>0, arc gap may be break down.The critical breakdown voltage distribution of arc extinguishing chamber is calculated in Figure 4. Fig. 4. Critical breakdown voltage distribution in arc extinguishing chamber Page1/7 2016 China International Conference on Electricity Distribution (CICED 2016) 62271-100:2008 IEC regulates the capacitor group circuit breakers of rated voltage 126kV, requirements of transient recovery voltage (TRV) are: uc 1.95 1.4 2 / 3 126kV 281kV (10) t 8.7ms The results through the calculation show that under different opening speed, the curves of the dielectric recovery characteristics of arc gap and transient recovery voltage changing with open distance were obtained in Fig.5, comparing the breaking voltage under different breaking angles and TRV under circuit breaker breaking with small capacitive current, it can be concluded that breakdown voltage of the breaks of circuit breaker is always higher than the value of transient recovery voltage, which can successfully break the arc without reburning. Fig.6 is curves of arc gap breakdown margin changing with open distance under different speeds in the process of breaking. Because the arc current is very small under short arcing times, the small current arc energy and arc radius are very small, as the influence of arc energy on the recovery of the post arc dielectric is relatively small, different breaking speeds mainly affect the electric field distribution at the moment of extinction and gas blowing intensity after large nozzle opening, thus affecting the dielectric recovery rate in short time after arc extinguishing and the value of the breakdown margin after large nozzle opening. the faster the speed, the faster the medium recovery rate after arc extinguishing, and the lower the breakdown margin of the large nozzle, the influence of the breaking speed on the early and late stage of the recovery of the medium is opposite. Considering the dielectric recovery characteristics of the circuit breaker, the short arcing time should have a large arc distance, and the large nozzle should be open enough to be strong for the gas blowing condition, so the optimum opening speed is 9.6m/s. 1500 5.76m/s 6.72m/s 7.68m/s 8.64m/s 9.6m/s TRV5.76m/s TRV6.72m/s TRV7.68m/s TRV8.64m/s TRV9.6m/s 电压/kV U/kV 1000 500 0 0 25 50 75 开距/mm k/mm 100 125 150 Fig. 5. Curve of the dielectric recovery characteristics in the opening process 5.76m/s 6.72m/s 7.68m/s 8.64m/s 9.6m/s 15 裕度 Margin IV CONCLUSION Based on the structure of the circuit breaker arc extinguishing chamber, the dielectric recovery characteristic of the capacitive small current breaking of the SF6 126kV circuit breaker was analyzed by the coupling calculation of electric field and flow field, and the following conclusions were drawn: (1) When the breaking phase was 1/2π under the condition of breaking 1600A small capacitive current, the average speed of the arc contact respectively 5.7m/s, 6.72m/s, 7.68m/s, 8.64m/s, 9.6m/s, corresponding to the burning arc time were 4.33ms, 4.28ms, 4.25ms, 4.3ms, 4.27ms. The effect of breaking speed on arc burning time is very small, but it has large effects on the circuit breaker pneumatic process and arc extinguishing time distance. Because of the low arc energy and the small breaking current, there exists arc extinguishing in advance in the process of breaking. (2) The arc gap conductivity is about 700S/m, and the thermal conductivity is about 1.1W/m·K at arc extinguishing time. With the greater speed, the convection heat transfer between air and electric arc is more obvious, and the arc energy diffusion is more adequate. (3) To make the short arcing time have a large arc distance, and the large nozzle should be open enough to be strong for the gas blowing condition, the optimum opening speed is 9.6m/s. REFERENCES [1] Lin Xin. Techniques of modern high voltage apparatus[M]. Beijing: Mechanical Press, 2011. [2] Liu Zhenya. Electric power and energy in China[M]. Beijing, China: China Electric Power Press, 2012.. [3] Schade E, Ragaller K. Dielectric recovery of an axially blown SF 6-Arc after current zero: part I-experimental investigations[J]. Plasma Science, IEEE Transactions on, 1982, 10(3): 141-153. [4] Zhong J Y, Lin X, He R T. The parallel computation simulation of the extinguishing arc performance in the self-extinguished SF (6) circuit breaker[J]. Proceedings of the CSEE , 2006, 26(20): 154-159(in Chinese) [5] Huang Shi, Cui Boyuan, Yao Sili, et al. Study on current tests of 145kV circuit breakers for capacitor bank current switching[J]. High Voltage Apparatus, 2012, 48(7): 66-70(in Chinese). [6] He Huiwen,Gu Dingxie,Zhou Peihong,et al. Simulating Calculation and Analysis on Time-to-crest of Switching Impulse for Test on Chinese UHV AC Pilot Project[J].High Voltage 20 10 5 0 0 Xi’an, 10-13 Aug, 2016 25 50 75 开距/mm k/mm 100 125 150 Fig. 6. Curve of breakdown margin changing with distance Engineering,2011,37(9):2156-2162 (in Chinese). [7] Lin Xin, Liu Kebin. Puffer Characteristic Calculation in Different Initial Gas Pressure and Operating Force of Self-Extinguishing SF6 Circuit Breaker[J]. Power System Technology, 2007, 40(10): 22-25. [8] Liu W D, Wu J Y, Huang Y L. Pressure Measurement in SF6 Circuit Breaker’s Nozzle in Heavy Current Interruption [J]. Proceedings of the CSEE,2010, 30(07): 131-136(in Chinese). [9] Ramming L, Aristizabal M. Cold characteristic development test CICED2016 Session 3 Paper No CP1234 Page1/7 2016 China International Conference on Electricity Distribution (CICED 2016) Xi’an, 10-13 Aug, 2016 of a new SF6 high voltage circuit breaker[C]//IEEE/PPES Transmission and Distribution Conference and Exposition, August, 2006, 1-3: 1263-1266. [10]JIN Lijun, DONG Xiao, YAN Shujia. Determin the break-brake speed of a half-self extinguish SF6 circuit breaker through analyzing the pressure characteristics of chamber[J]. High Voltage Engineering, 2013, 39(4): 776-781. [11]Han Xiaohong, Chen Guangming, Wang Qin, et al. A review on equations of state[J]. Natural Gas Chemical Industry, 2005, 30(5): 52-61. [12]RONG Mingzhe,YANG Qian,FAN Chunduo. SIMULATION OF THE PROCESS OF ARC ENERGY-EFFECT IN H.V. AUTO EXPANSION SF6 CIRCUIT BREAKER[J]. Chinese Society for Electrical Engineering, 24.2 (2004): 92-97(in Chinese). [13]Leslie S. Frost, Richard W. Liebermann, Composition and Transport Properties of SF6 and Their Use in a Simplified Enthalpy Flow Arc Model, Proceedings of the IEEE, 1971, 59(4): 474-485. [14]GU Ding-xie, ZHOU Pei-hong, DAI Min, et al. Comparison and Analyses on Over-voltage and Insulation Coordination of UHV AC Transmission System between China and Japan [J]. High Voltage Engineering,2009,35(6):1248-1253 (in Chinese) [15]Huang Daochun, Ruan Jiangjun, Liu Shoubao, et al. Potential distribution along UHV AC transmission line composite insulator and electric field distribution on the surface of grading ring[J]. High Voltage Engineering, 2010, 36(6): 1442-1447. [16]Zhibing LI, Xiaoang LI, Weijiang CHEN, et al. Impedance Characteristics of High-frequency Arc in Short SF6 Gap[J]. High Voltage Engineering, 2013, 39(006): 1411-1418(in Chinese). An Su was born in China in 1991. He is a master graduate student of Shenyang University of Technology. Currently, focuses on the research of high voltage and insulation test technology. E-mail:[email protected] Xin Lin was born in China in 1961. She is a professor and doctoral supervisor, research direction for high voltage and insulation technology, high voltage electrical appliances, intelligent electrical appliances, etc. CICED2016 Session 3 Paper No CP1234 Page1/7