MOLDED case circuit breakers (MCCBs) are widely

Transcription

1 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 3, SEPTEMBER Analysis of the Interruption Process of Molded Case Circuit Breakers Xingwen Li, Degui Chen, Senior Member, IEEE, Yunfeng Wang, Qian Wang, and Yingsan Geng Abstract To the optimization design of molded case circuit breakers (MCCBs), it is important and necessary to simulate the interruption process and analyze the characteristics. A set of differential equations can describe the interactive coupled phenomena of electric circuit, electromagnetic field and mechanism motion system in MCCB. First, with virtual prototyping technology, the simulation model for the operation mechanism of MCCB can be built, and experiments have been carried out to verify its validity. Then, with the existence of electrodynamic repulsion force, the interruption process of the MCCB has been investigated with the influence of arc voltage, closing phase angle, prospective current, mechanism starting motion time and blow open force. It demonstrates the proposed method is effective and is capable of evaluating the new design of MCCB products. Index Terms Blow open force, circuit breaker, interruption process, repulsion force, virtual prototyping technology. I. INTRODUCTION MOLDED case circuit breakers (MCCBs) are widely used in low voltage electrical distribution systems, the breaking technique of which is based on current limitation. When a fault current comes, if the electrodynamic repulsive force exceeds the spring force, the contacts will separate first and the arc will appear. At the same time, a force, named blow open force, which is produced by a net pressure on the moving contact, will act on contacts and continue to accelerate the contacts apart from each other, together with the action of electrodynamic repulsion force. Then, the operation mechanism will begin to move after a short interval for the tripping process of release, and drive the moving contact to its final position. During the process, arc will elongate between contacts and enter the quenching chamber with the help of Lorentz force and/or gas dynamic force, which may lead to the rapid rise of arc voltage and allow the retention of the arc voltage at a sufficient value while absorbing the energy produced. It seems that the interruption process of MCCB is a very complicated and interactive coupled phenomena among electric circuit, electromagnetic field, and mechanism motion Manuscript received May 8, 2005; revised March 10, This work was supported by the National Natural Science Foundation of China under Grant This work was recommended for publication by Associate Editor J. McBride upon evaluation of the reviewers comments. X. Li, D. Chen, and Y. Geng are with the State Key Laboratory of Electrical Insulation and Power Equipment, Xi an Jiaotong University, Xi an , China ( jds20@mail.xjtu.edu.cn). Y. Wang is with Changshu Switches Manufacture, Ltd., Changshu , China. Q. Wang is with Applied Materials, Inc., Xi an , China. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TCAPT system. Especially, the motion status of the moving contact determines the interruption performance of MCCB to a great extent. Therefore, investigation on the interruption process is significant to analyze and design new MCCB products. Various experimental and theoretical papers reported the study of low voltage circuit breakers. Slepian proposed the method of arc quenching with splitter plates [1], which is still widely used in low voltage electric apparatus. Lindmayer analyzed the influence of contact material and chamber wall materials on the arc interruption process [2]. In literature [3], the influences of the properties of contact material, the configuration of arc chamber, and the arrangements of contact system on arc interruption characteristics were reviewed. McBride investigated the influence of gas flow and gas composition on the arc root mobility [4], and reviewed the arcing phenomena including arc column, arc root, arc electrode, arc motion, etc. in low voltage current limiting circuit breakers [5]. Takikawa [6] and Takeuchi [7] studied the distribution of temperature in the cross section of an arc column between separate contacts with spectroscopic detecting systems. Brdys studied the low voltage electric arc dynamics by magnetic diagnostics in a low voltage circuit breaker [8]. In our previous work, experimental investigation were carried out to analyze the influence of gassing material on the arc motion characteristics with the optical fiber measurement system and spectrum diagnostics system, on the other hand, 3-D magnetohydrodynamics (MHD) model of arc was developed to study the effects of the arc ignition location, venting size and gassing material on arc behavior [9], [10]. Karetta proposed a 3-D MHD model for arc chambers consisting of two arc runners and insulating walls [11]. With a 2-D model, Rachard [12] analyzed the influence of the magnetic force on the shape and displacement of the arc. Swierczynski developed a 3-D model to investigate the arc motion with the influence of external magnetic field, plasma composition, and transport properties [13]. Lindmayer simulated the process of arc-splitting between metal plates in low voltage arc chutes [14]. Without calculating the motion of operation mechanism simultaneously, i.e., neglecting the interaction between operation mechanism and moving contact, Stammberger simulated the temporal behavior of circuit breakers and motor starters [15]. The effects of the configuration of arc chamber and operation mechanism on the current limiting performance of MCCB were investigated in [16]. However, due to the complexity, studies of the interruption process of MCCB and the influence of relevant factors are less well carried out. This paper is devoted to model the whole interruption process of MCCB, and especially to analyze the motion status of moving contact. To one MCCB with the rated current 63 A, first, with commercial virtual prototyping design /$25.00 IEEE

2 376 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 3, SEPTEMBER 2007 Fig. 2. Calculation result of force variation with current and open angle. Fig. 1. Analysis model. software ADAMS, the basic simulation model of the operation mechanism was built, the validity of which also was verified experimentally. Then, based on the above basic model and adding the electrodynamic repulsion force acting on the moving contact, the model of the interruption process simulation can be developed by extending the software with self-written routines to solve the interactive coupled differential equations of electric circuit, electromagnetic field and operation mechanism system of MCCB. Finally, the effects of arc voltage, closing phase angle, prospective current, mechanism starting motion time, and blow open force on the interruption process of the MCCB were investigated, respectively. It demonstrates the proposed method is effective and is capable of evaluating the new design of MCCB products. II. ANALYSIS MODEL AND METHODS A. Analysis Model Fig. 1 shows the model of MCCB in ADAMS software and its corresponding operation mechanism schematic sketch. It can be seen that the mechanism consists of contact support f, linkage g and h, tripping device k, latch m, handle 1, and main spring 2. Contact force is provided by fixing a spring on rotation axis O. When the fault current comes, if the electrodynamic repulsion force exceeds the spring force acting on moving contact, contacts will begin to separate in advance before the mechanism moves, usually. Then, the moving contact continues to move around axis O with the influence of electrodynamic repulsion force, blow open force and contact spring. At the same time, once the release trips and make latch operate to unlock the tripping device. With the action of main spring, the tripping device will rotate clockwise around O. Then linkage h and g will drive the contact support to rotate around O until the moving contact and operation mechanism reach their final positions. It demonstrates that, in the interruption process, the motion status of moving contact mostly depends on the joint operation of electrodynamic repulsion force, blow open force, contact spring, and operation mechanism. B. Calculation Method for Electrodynamic Repulsion Force In literature [17], [18], with 3-D finite element nonlinear analysis, according to the equations among current-magnetic fieldrepulsion force and taking into account the ferromagnet, contact bridge model was introduced to simulate the current constriction between contacts, so Lorentz and Holm force acting on the moving contact can be combined to calculate. Coupled with circuit equations, the opening time of movable contact also can be obtained using iteration with the restriction of contact force. The arc column between contacts was modeled by a homogeneous solid conductor with constant electrical conductivity. To simulate the whole interruption process of MCCB, it is necessary to know the quantitative relation of electrodynamic repulsion force with the open angle of the moving contact and current values. Once the contact separates, Holm force will disappear, and only Lorentz force is involved. Then, according to the above mentioned method, within the whole range of open angle of moving contact and current, data grid for can be obtained with the variations of and. The calculation result is shown in Fig. 2, where and vary from 1 to 11 ka and from 10 to 40, respectively. In addition, to the MCCB, it is the opening torque that accelerates the moving contact, so the calculation result is the corresponding equivalent force acting on the far end of moving contact from the rotation axis. From the figure, it seems that there is less difference of the force value when the open angle is equal to 10 and 20.

3 LI et al.: INTERRUPTION PROCESS OF MOLDED CASE CIRCUIT BREAKERS 377 During the simulation of the interruption process, to certain open angle and current, interpolation method is used to get the corresponding force value. C. Calculation Method for Blow Open Force Apart from electrodynamic repulsion force, also, many researchers carried out some valuable works on blow open force. In [19], an experimental device was built to study the influence on the measured forces including electrodynamic repulsion force and blow open force of the contact material, the duration of the current pulse, the polarity of the electrodes, etc. In [20], the authors presented the results of theoretical and experimental investigation of the phenomena of electrical contact repulsion and its associated blow off characteristics at high currents. In [21], according to the relationship among gas pressure, arc temperature and arc electrical conductivity of regular stable arcs, the authors provided rough estimation of gas pressure values, assuming 70% of arc power is consumed for arc radiation. In literature [22], to investigate the blow open process of small size contactor, whose moving contact has vertical motion, Zhou proposed one formula to describe the blow open force acting on the moving contact, as shown in (1), where ( 70%) is the percentage of the electrical power that is converted into radiation, is the arc current, is the arc voltage, is the emission coefficient of the plasma at atmospheric pressure, is the cross section area of the arc chamber or the arc, is the contact gap, is the cross section area of contact surface and is 1 atm. It should be noted that W m is assigned to in the paper, according to the assumption that the plasma emission coefficient is only a function of plasma average pressure at an average plasma temperature of K [22] It should be noted that (1) still has certain limitation to calculate the blow open force precisely. In addition, 3-D MHD arc simulation together with the corresponding experiments seems one possible way to solve the problem. Typically, the blow open force is negligible. However, in the paper, to study the effect of blow open force on interruption process of MCCB theoretically, (1) is acceptable to evaluate the blow open force acting on the moving contact. D. Arc Voltage Definition and Electric Circuit Solution The characteristic of arc voltage is quite complex, which is mostly related to arc length and the process of arc-splitting between splitter plates. Fig. 3 shows one group of typical experimental arc current and voltage waveforms of the analyzed MCCB with 10 ka prospective short circuit current (effective value), which is provided by the capacitor bank circuit. The peak value of the arc voltage is 245 V. From the figure, neglecting the arc immobile period, the arc voltage can be defined by the following three stages (Fig. 4). 1) A time elapses between the start of the short circuit and the opening of the contacts, which depends on the relationship between the electrodynamic repulsion force and the initial contact force. (1) Fig. 3. Typical experimental curve of arc current and voltage of the MCCB. Fig. 4. Definition of the arc voltage. 2) The arc moves from the contacts and accelerates towards the splitter plates, and the arc voltage increases almost linearly. This is related to the arc running time. 3) The arc enters the splitter plates and remains there for a interval up to arc extinguishment, and the arc voltage almost maintains a constant value. In addition, means the total time for release and driving parts motion, called operation mechanism starting time. That is to say, at instant, the tripping device will be unlocked and the operation mechanism will begin to move. In paper [23], we presented a method for calculating the dynamic characteristics of a magnetic release in molded case circuit breaker. In the paper, only single-phase short circuit is considered. Therefore, the electric circuit equation can be expressed as (2), where and are inductance and resistance, respectively, is the effective value of source voltage and equal to 220 V, is the closing phase angle, is the arc current and is the arc voltage. can be described by the above-mentioned method. According to specified standard about the relationship between prospective current and power factor, together with, and can be solved. Then, with Runge Kutta method, the arc current value variation with time can be obtained. Here, it is assumed that the arc will extinguish just after the current goes through zero at the first time (2)

4 378 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 3, SEPTEMBER 2007 Fig. 5. Calculation method for simulation of interruption process. E. Simulation of the Interruption Process ADAMS program, used to mechanical dynamics simulation, can automatically build Lagrange motion functions with multiplier and their corresponding restriction functions for all rigid and flexible bodies in one system [24], as shown in (3) with where is kinetic energy, is the whole generalized coordinates of the system, is Lagrange multiplier, is generalized force, and is the number of the bodies. By solving the set of the differential equations and restriction functions, the motion and force parameters, such as displacement, velocity and acceleration, etc. of each body in the system can be evaluated through ADAMS. In the paper, coupled mechanism motion, electric circuit equation with electromagnetic field by embedding some self-programmed codes into ADAMS, the dynamic simulation of the interruption process of the MCCB has been implemented, as shown in Fig. 5 [25]. Through the interface provided by ADAMS, the open angle of the moving contact and the contact gap can be obtained. Together with the FEM calculation results for the electrodynamic force and circuit equation, codes have been programmed to evaluate the force at instant. Then, the calculated magnetic force and/or blow open force can be regarded as parameters of mechanism motion equations, as shown in (3). Therefore, the whole interruption process can be predicted by the bidirectional iteration process with time. III. SIMULATION AND EXPERIMENT ON THE OPERATION MECHANISM MOTION First, neglecting the effect of the electrodynamic repulsion force and blow open force, the model was built with reasonable restriction relationships based on the realistic MCCB, as shown in Fig. 1(a). Then, the operation mechanism motion can be well simulated. At the same time, in order to evaluate the value of friction coefficients, and verify the validity of simulation model, experiments were done by fixing an angular displacement sensor on axis O [Fig. 1(b)] under the case of free tripping (without load current). In the ADAMS software, we can assign reasonable friction coefficients on movable parts. According to our experience and some references from the ADAMS user guide, generally, the friction coefficients may be adjusted from 0.1 to 0.5 to be consistent with the experimental result. Fig. 6 shows the experimental (3) Fig. 6. Variation of angular displacement of contact support with time. TABLE I CALCULATION CONDITION and simulation results of the angular displacement of the contact support variation with the time. Therefore, based on the built model, the interruption process of the MCCB can be investigated in detail with the presence of self-programmed codes to couple the circuit, electromagnetic field and operation mechanism motion equations. IV. INFLUENCE OF SEVERAL FACTORS ON THE INTERRUPTION PROCESS A. Arc Voltage Characteristics First, we analyze the influence on the interruption process of, which is the arc running time and is mostly determined by the fault current, the configurations of arc chamber and current carrying conductors. The detailed calculation condition is shown in Table I. Fig. 7(a) and (b) show the calculation results of electrodynamic repulsion force, angular velocity of contact support and moving contact, arc current variation with time, when is equal to 4 ms and 2 ms, respectively. Fig. 7(c) shows arc current and voltage calculation results including the case of closing phase angle 30. From the calculation results, the following points can be obtained. 1) With the help of the electrodynamic repulsion force, the moving contact moves earlier than the contact support of the operation mechanism. 2) Just while the moving contact begin to move, the value of the electrodynamic repulsion force decreases sharply at point A [Fig. 7(a)], which results from the disappearance of the Holm force due to the current constriction between contacts.

5 LI et al.: INTERRUPTION PROCESS OF MOLDED CASE CIRCUIT BREAKERS 379 Fig. 8. Influence of the closing phase angle on the interruption process. Fig. 7. Influence of arc voltage on the interruption process. 3) At point B [Fig. 7(a)], the contact support catches up with the moving contact, and the angular velocity of the contact support has an obvious reduction due to the additional load from the moving contact. After that, the contact support will drive the moving contact with the same velocity. 4) Decreasing means the faster arc moving velocity, which results in more rapid rising of the arc voltage. Thus, the current limiting performance is stronger, which produces less electrodynamic repulsion force acting on moving contact yet. Correspondingly, the velocity of the operation mechanism will be reduced due to the higher load from the moving contact. In addition, increasing the peak value of the arc voltage, the similar influence may occur. B. Closing Phase Angle Based on the calculation condition as shown in Table I and 4 ms, Fig. 8(a) and (b) show the calculation results of arc current, electrodynamic repulsion force, angular velocity of contact support and moving contact variation with time, when is equal to 30 and 60, respectively. Fig. 7(c) also shows the arc current and voltage variation with time when is equal to 30. The following points can be seen from these results. 1) Increasing the closing phase angle, the is reduced and the peak value of the short circuit current occurs earlier. 2) Increasing the closing phase angle, because the current and the corresponding electrodynamic repulsion force drop more quickly, the trend of the backward motion of the moving contact becomes more obvious. From Fig. 8(b), the velocity of the moving contact begins to drop from point A until the contact support drives it to move with the same velocity at point B. C. Prospective Current The effects of prospective current on the interruption process may be studied with the assumption of the same and values of arc voltage. The detailed calculation condition is shown in Table II. Fig. 9(a) (c) show the calculation results of arc current, electrodynamic repulsion force, angular velocity of contact sup-

6 380 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 3, SEPTEMBER 2007 TABLE II CALCULATION CONDITION on the interrup- Fig. 10. Influence of the operation mechanism starting time t tion process. TABLE III CALCULATION CONDITION called over travel. The corresponding period of the angle is from point A to B [Fig. 9(a)]. After that, the contact support will drive the moving contact with the same velocity. 2) When is equal to 2.5 ka, the moving contact tries to open with the action of electrodynamic repulsion force at point A [Fig. 9(b)]. However, because the Holm force disappears once the contacts separate, the total force acting on the moving contact will decrease sharply, and the moving contact will move backward until the contact support begins to drive it at point B [Fig. 9(b)]. 3) When is equal to 10 ka, the produced electrodynamic repulsion force is large enough to accelerate the moving contact without the help of the contact support. In addition, if the prospective current is higher than 10 ka, the interruption process still can be estimated by the numerical method, and the result will be similar to the case of 10 ka except that the angular velocity of the moving contact will be higher due to the larger electrodynamic repulsion force acting on it. 4) A critical current value is related to decide whether the moving contact moves backward or not. Fig. 9. Influence of the prospective current on the interruption process. port and moving contact variation with time, when the effective value of prospective current is equal to 1, 2.5 and 10 ka, respectively. From the results, the following points can be seen. 1) When is equal to 1 ka, the electrodynamic repulsion force is so less that it could not overcome the contact force. Thus, the moving contact would not open in advance until the contact support moves over an angle D. Operation Mechanism Starting Time When the effective value of prospective current is equal to 4 ka, to different operation mechanism starting time, the calculation results of angular velocity of moving contact and contact support are shown in Fig. 10 under the condition shown in Table III. In addition, curve 2 presents the -coordination of point A [see Fig. 1(a)] on the moving contact when 9 ms. From Fig. 10, increasing, the moving contact begins to move backward at point A due to the gradual reduction of the current and the corresponding electrodynamic repulsion force, as well the action of the contact spring. At point B, the contact support will drive the moving contact with the same velocity.

7 LI et al.: INTERRUPTION PROCESS OF MOLDED CASE CIRCUIT BREAKERS 381 blow open force, the motion status of the moving contact differs obviously. The moving contact will move backward at a certain middle position and the maximum position, respectively. 4) In addition, during the interruption process, if the moving contact becomes to moves backward, and even contact weld may occur, it will produce serious accident. According to the above analysis, in order to improve the performance of MCCB products, it is important and necessary to take effective steps to avoid the possible contact falling back within its whole travel. Fig. 11. Influence of the blow open force on the interruption process. E. Blow Open Force To the case of 9 ms mentioned in Section IV-D, the influence of blow open force is investigated. Although the above-mentioned calculation method [see (1)] for blow open force is a little rough, it is available to carry out some interesting study of the influence of blow open force on the interruption process qualitatively. The calculation results are shown in Fig. 11, including equivalent total force, blow open force and electrodynamic repulsion force, current, angular velocity of moving contact and contact support, -coordination of point A [see Fig. 1(a)] variation with the time. From the results, these points can be drawn. 1) While the contacts separate, the value of electrodynamic repulsion force decreases, but the blow open force occurs, whose value is much higher than the electrodynamic repulsion force. Moreover, with the increase of arc gap, the blow open force decreases rapidly. 2) With the action of the electrodynamic repulsion force and blow open force, the moving contact may move to its maximum position. But, with the reduction of the above two forces, due to the action of contact spring and the immobile of the operation mechanism, the moving contact will move backward until the operation mechanism begin to move and the contact support drive it with the same velocity. 3) With regard to the calculation condition, compared with the results with and without the consideration of the V. CONCLUSION 1) With virtual prototype technology, the basic simulation model of the operation mechanism can be built, the validity of which also has been verified experimentally. Then, based on the basic model, the model of the interruption process simulation can be developed by extending the software with self-written routines to solve the interactive coupled differential equations of electric circuit, electromagnetic field, and mechanism motion system of MCCB. 2) The influence of arc voltage, closing phase angle, prospective current, operation mechanism starting time, and blow open force on the interruption process has been simulated and analyzed in detail. 3) The blow open force has a significant effect on the interruption process. It is necessary to investigate it further to get a better method to present it. 4) If the operation mechanism starting time is too late, the moving contact will fall backward, which has a great disadvantageous effect on the interruption performance. 5) The proposed method is effective and is capable of evaluating new designs and optimization designs of MCCB products. REFERENCES [1] J. Slepian, Theory of the deion circuit-breaker, Trans. AIEE, vol. 48, pp , Feb [2] M. Lindmayer, The influence of contact materials and chamber wall material on the migration and the splitting of the arc in extinction chamber, IEEE Tran. Parts, Hybrids, Packing, vol. PHP-9, no. 1, pp , Mar [3] P. G. Slade, Electrical Contacts Principles and Applications. New York: Marcel Dekker, [4] J. W. McBride, K. Pechrach, and P. M. Weaver, Arc motion and gas flow in current limiting circuit breakers operating with a low contact switching velocity, IEEE Trans. Compon. Packag. Technol., vol. 25, no. 3, pp , Sep [5] J. W. McBride, Review of arcing phenomena in low voltage current limiting circuit breakers, Proc. Inst. Elect. Eng., vol. 148, no. 1, pp. 1 7, [6] H. Takikawa and T. Sakakibara, Radiative aspects of the ablation stabilized arc in polyethylene tube, IEEE Trans. Plasma Sci., vol. 19, no. 5, pp , Oct [7] M. Takeuchi and T. Kubono, The spatial distributions of spectral intensity and temperature in the cross section of an arc column between separation Pd contacts, IEEE Trans. Comp., Packag., Manufact. Technol. A, vol. 21, no. 1, pp , Mar [8] C. Brdys, J. P. Toumazet, G. Velleaud, and S. Servant, Study of the low voltage electric breaking arc restrike by means of an inverse method, IEEE Trans Plasma Sci., vol. 27, no. 2, pp , Apr [9] X. Li, D. Chen, H. Liu, Y. Chen, and Z. Li, Imaging and spectrum diagnostics of air arc plasma characteristics, IEEE Trans. Plasma Sci., vol. 32, no. 6, pp , Dec

8 382 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 30, NO. 3, SEPTEMBER 2007 [10] X. Li, D. Chen, Q. Wang, and Z. Li, Simulation of the effects of several factors on arc plasma behavior in low voltage circuit breaker, Plasma Sci. Technol., vol. 7, no. 5, pp , Oct [11] F. Karetta and M. Lindmayer, Simulation of the gasdynamic and electromagnetic processed in low voltage switching arcs, in Proc. 42nd IEEE Holm Conf. Elect. Contacts, Chicago, IL, Sep , 1996, pp [12] H. Rachard, P. Chevrier, D. Henry, and D. Jeandel, Numerical study of coupled electromagnetic and aerothermodynamic phenomena in a circuit breaker electric arc, Int. J. Heat Mass Transf., vol. 42, no. 9, pp , May [13] B. Swierczynski, J. J. Gonzalea, P. Teulet, P. Freton, and A. Gleizes, Advance in low voltage circuit breaker modeling, J. Phys. D: Appl. Phys., vol. 37, pp , [14] M. Lindmayer, E. Marzahn, A. Mutzke, T. Ruther, and M. Springstubbe, The process of arc-splitting between metal plates in low voltage arc chutes, in Proc. 50th IEEE Holm Conf. Elect. Contacts, Seattle, WA, Sep , 2004, pp [15] H. Stammberger, H. Pursch, A. Zacharias, and P. Terhoeven, Simulation of the temporal behavior of circuit breakers and motor starter, in Proc. 50th IEEE Holm Conf. Elect. Contacts, Seattle, WA, Sep , 2004, pp [16] D. Chen, H. Liu, H. Sun, Q. Liu, and J. Zhang, Effect of magnetic field of arc chamber and operating mechanism on current limiting characteristics of low voltage circuit breakers, IEICE Trans. Electron., vol. E86-C, no. 6, pp , Jun [17] X. Li and D. Chen, 3-D finite element analysis and experimental investigation of electrodynamic repulsion force in molded case circuit breakers, IEEE Trans. Compon. Packag. Technol., vol. 28, no. 4, pp , Dec [18] S. Ito, Y. Takato, Y. Kawase, T. Ota, and H. Mori, Numerical analysis of electromagnetic forces in low voltage AC circuit breakers using 3-D finite element method taking into account eddy currents, IEEE Trans. Magn., vol. 34, no. 5, pp , Sep [19] D. Piccoz, P. Teste, R. Andlauer, T. Leblanc, and J. P. Chabrerie, The repulsion of electrical contacts crossed by short-circuit currents, in Proc. 45th IEEE Holm Conf. Elect. Contacts, Pittsburgh, PA, Oct. 4 6, 1999, pp [20] M. Bizjak, S. Kharin, and H. Nouri, Influence of vapour pressure on the dynamics of repylsion by contact blow-off, in Proc. 21st Conf. Electrical Contacts, Zurich, Switzerland, Sep. 9 12, 2002, pp [21] J. J. Shea, B. DeVault, and Y. Chien, Blow-open forces on doublebreaker contacts, IEEE Trans. Comp., Hybrids, Manufact. Techol., vol. 17, no. 1, pp , Mar [22] X. Zhou and P. Theisen, Investigation of arcing effects during contact blow open process, in Proc. 44th IEEE Holm Conf. Elect. Contacts, Arlington, VA, Oct , 1998, pp [23] H. Xiang, D. Chen, and X. Li, Investigation on the dynamic characteristics of a magnetic release in molded case circuit breaker, IEICE Trans. Electron., vol. E88-C, no. 8, pp , Aug [24] G. Wang, J. Zhang, and R. Ma, Virtual Prototype Technology and its Application on ADAMS. Xi an, China: Northwestern Polytech. Univ. Press, [25] X. Li, D. Chen, Z. Li, and W. Tong, Numerical analysis and experimental investigation of dynamic behavior of AC contactors concerning with the bounce of contact, IEICE Trans. Electron., vol. E87-C, no. 8, pp , Aug Degui Chen (SM 98) was born in Shanghai, China, in He graduated from Shanghai Jiaotong University, Shanghai, China in From 1983 to 1984, he was a Honorary Research Fellow at the University of Liverpool, Liverpool, U.K. Currently, he is a Professor at Xi an Jiaotong University, Xi an, China. He has published more than 150 papers in China and abroad. His research interests include low-voltage apparatus including switching arc model, arc movement, visual simulation of interrupting process, and electromagnetic phenomena. Dr. Chen is a Council Member of the China Electrotechnical Society (CES), Chairman of the Low Voltage Apparatus Committee of China, and the Director of the Expert Group, Chinese Low-voltage Apparatus Industry Association. Yunfeng Wang was born in Jiangsu, China, in He received the B.S. and M.S. degrees in electrical engineering from Xi an Jiaotong University, Xi an, China, in 2002 and 2005, respectively. He is currently an Electrical Engineer with Changshu Switches Manufacture, Ltd., Changshu, China. Qian Wang was born in Xi an, China, in She received the B.S. and M.S. degrees in electrical engineering from Xi an Jiaotong University, Xi an, China, in 2003 and 2006, respectively. She is currently a Mechanical Engineer with Applied Materials, Inc., Xi an. Yingsan Geng was born in Henan, China, in He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Xi an Jiaotong University, Xi an, China, in 1984, 1987, and 1997, respectively. He is now Director of the Department of Electric Machine and Apparatus, Xi an Jiaotong University. His research interests focus on the theory and application of electric apparatus. Xingwen Li was born in Shaanxi, China, in He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Xi an Jiaotong University, Xi an, China, in 1999, 2001, and 2006, respectively. He was a Visiting Scholar with the Department of Information Systems, Osaka University, Osaka, Japan, from 2001 to Currently, he is an Associate Professor at Xi an Jiaotong University, Xi an, China. His research interests focus on power equipment.