1 Introduction Permanent magnet operating mechanisms are simple in structure, have few parts, and are highly reliable, making them very suitable for operating vacuum circuit breakers. Launched in the market in 1998, they have attracted widespread attention both domestically and internationally and have been successfully applied to medium-voltage vacuum circuit breakers. Currently, products with rated voltage levels of 12 kV, 17.5 kV, and 24 kV are available. Research on higher voltage level products has been ongoing, but no reports on their research and application have been found [1, 2]. High-voltage vacuum interrupters have a long travel distance and require high opening and closing speeds. For example, a 72.5 kV high-voltage vacuum interrupter requires a contact distance of approximately 50 mm and opening and closing speeds of 2.5 m/s and 1.8 m/s, respectively. Compared to the vacuum interrupter of a 12 kV medium-voltage circuit breaker, the contact distance is approximately six times and the opening and closing speeds are approximately twice as fast. Since the air gap reluctance is proportional to the air gap length, it is usually difficult for the moving iron core to obtain the mechanical force required for the breaking of a high-voltage vacuum interrupter at a long opening distance. This poses a considerable challenge to the use of a permanent magnet operating mechanism. This paper proposes a scheme for a permanent magnet operating mechanism for a 72.5kV high-voltage vacuum circuit breaker. Without significantly increasing the volume of the magnetic system, a magnetic shunt is set in the working air gap region of the trip coil, enabling the moving iron core to obtain sufficient mechanical force to drive its movement over a long stroke. Virtual tests were conducted through simulation, and the results show that its force output characteristics and speed characteristics meet the requirements. 2 Structure and Principle The electromagnetic system of the permanent magnet operating mechanism mainly consists of a moving iron core, a stationary iron core, a permanent magnet, a trip coil, and a closing coil. The permanent magnet and the trip and closing coils are respectively wound around the moving iron core and the transverse yoke, and between the moving iron core and the upper and lower side columns. When the moving iron core is in the closed or open position, the magnetic field of the permanent magnet mainly acts on the closed end of the moving iron core, generating an electromagnetic holding force sufficient to overcome the load reaction force from the vacuum interrupter and the mechanical transmission system, thus keeping the contacts open or closed. When the opening or closing coil is energized, the external magnetic field of the excitation coil cancels out the magnetic field of the permanent magnet. The electromagnetic holding force decreases as the excitation current increases. When the excitation current reaches the trigger value, the electromagnetic holding force is less than the load reaction force, and the moving iron core moves from one terminal position to the other, driving the contacts to move. The strength of the external magnetic field of the excitation coil on the moving iron core is inversely proportional to the air gap length of the magnetic circuit it links. The longer the air gap, the weaker the strength of the external magnetic field of the excitation coil on the moving iron core. To ensure that the electromagnet with a long stroke can obtain sufficient kinetic energy from the external magnetic field of the excitation coil in the initial stage of movement, this design sets a magnetic shunt made of magnetically conductive material in the working air gap region of the opening coil. Figure 1 shows a schematic diagram of the electromagnetic system of the permanent magnet operating mechanism with a magnetic shunt. After the introduction of the magnetic shunt, the magnetic flux entering the end face of the magnetic pole is divided into the main magnetic flux of the working air gap and the edge magnetic flux of the working air gap, and the electromagnetic attraction characteristics of the moving iron core tend to be flat [3]. In this way, the long-stroke electromagnet can also obtain enough energy from the external excitation magnetic field of the excitation coil to move in the initial stage of the opening movement. However, in the latter half of the movement and in the opening position, due to the presence of the magnetic shunt, the effect of the external magnetic field of the excitation coil and the magnetic field of the permanent magnet on the moving iron core will be greatly reduced, and the electromagnetic holding force will be reduced. [img=300,258]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/110-1.jpg[/img] The load forces of the vacuum interrupter and its mechanical transmission system mainly include: the self-closing force of the vacuum interrupter, the contact spring pressure, the closing electrodynamic force, and the gravity of the parts and the frictional force of their movement. Among these, the contact spring pressure and the closing electrodynamic force only play a role in the overtravel stage. Therefore, the load reaction force in the open position is much smaller than that in the closed position [4]. For a 72.5 kV vacuum circuit breaker, the load reaction force in the closed position is about 4000 N/phase; while the load reaction force in the open position is only about 200 N/phase. Although the magnetic shunt in the open position significantly reduces the electromagnetic holding force of the permanent magnet acting on the moving iron core, it is still sufficient to ensure that the contacts reliably break. In the closed position, the magnetic field of the permanent magnet needs to provide sufficient electromagnetic holding force to overcome the self-closing force from the vacuum interrupter and the load reaction force from the mechanical transmission system. Therefore, it is not advisable to set up a magnetic shunt in this position. Since the magnetic shunt of the working air gap weakens the electromagnetic holding force of the permanent magnet acting on the moving iron core in the open position, the load force that the external excitation magnetic field of the closing coil needs to overcome is relatively small in the initial stage of the closing motion. Although the magnetic circuit it links has a large working air gap, the moving iron core can still obtain the required kinetic energy. [b]3 Calculation Model and Calculation Equation of Magnetic Field[/b] The permanent magnet works by utilizing the remanence of the magnetic material. In the calculation, it can be equivalent to a surface current coil (number of turns N=1) with a constant magnetomotive force Ip wrapped on a magnetic conductor. After this treatment, the calculation problem of permanent magnetic field or magnetic circuit is reduced to the calculation problem of general magnetic field or magnetic circuit. All methods applicable to the calculation of DC electromagnetic system can be applied to the calculation of magnetic field or magnetic circuit of permanent magnet electromagnetic system. This paper uses the finite element method to numerically calculate the static magnetic field of the electromagnetic system of the permanent magnet operating mechanism. Because its magnetic field distribution has axisymmetry, cylindrical coordinates (r, θ, z) are used, with r representing the radial direction and z representing the axis of symmetry. Since the plane θ = 0 is the plane of symmetry, half of the field is taken as the computational domain. The computational domain Ω is shown in Figure 2 (the dotted line represents the boundary), and the vector magnetic potential A = 0 on the boundary surface. [img=324,71]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-1.jpg[/img] After the above processing, according to Maxwell's equations, a mathematical model for the vector magnetic potential A to be determined on the r-z plane in the cylindrical coordinate system can be derived, where μ is the permeability and J is the current density. [img=324,71]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-1.jpg[/img] The energy functional equivalent to the boundary value problem of equation (1) is [img=324,71]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-1.jpg[/img] The solution process involves discretizing the electromagnetic field, dividing the entire solution domain into E triangular elements and n nodes. The vector magnetic potential A of the constant magnetic field is thus discretized into the vector magnetic potentials of n nodes: A1, A2, ..., An. The energy functional of each element is differentiated with respect to A at each node, and the sum is set to zero, resulting in n linear equations. Substituting the known values ​​of A at the boundary nodes, the system of linear equations yields the A at the node in question. Since the permeability is related to the vector magnetic potential, the static magnetic field must be repeatedly calculated and the permeability corrected; several iterations are needed to obtain the vector magnetic potential A of the entire field. The magnetic induction intensity B at any point within a triangular element in the cylindrical coordinate system can be calculated using B = ∫ ... Using Maxwell's formula, the static attraction force exerted by the magnetic field on the moving iron core can be calculated. [align=center][img=336,44]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-2.jpg[/img][font=SimSun][size=3] [/size][/font][/align] Where n is the unit vector along the normal direction of the surface; S is the closed surface surrounding the moving iron core. [b]4 Dynamic Process Equations and Simulation[/b] The energy driving the moving iron core's movement comes from the electric field energy stored in the capacitor. The capacitor is pre-charged with a certain voltage. When operating, it releases energy to the excitation coil, thus converting the electric field energy into magnetic field energy, which is then converted into the mechanical energy of the moving iron core's movement. The switching process of an electromagnetic system is not in a steady state, but rather dynamic. Only by calculating the dynamic process can the structural parameters of the electromagnetic system and the electrical parameters of the capacitor be reasonably determined to ensure the reliable operation of the permanent magnet operating mechanism. 4.1 Dynamic Process Equations The permanent magnet operating mechanism has two coils, namely the closing coil and the opening coil. These two coils do not operate simultaneously; each constitutes an independent electromagnetic system. Although the expressions of their dynamic process equations are the same, the specific parameters are different. 4.1.1 Circuit Equations of the Excitation Coil Circuit The energy of the excitation coil is provided by the energy storage capacitor and its switching is controlled by power devices. Since the displacement of the moving iron core will change the magnetic field of the permanent magnet, the magnetic field of the permanent magnet is coupled with the magnetic field of the excitation coil. If eddy currents are not considered, the equivalent circuit of the excitation coil circuit is shown in Figure 3. If the forward voltage drop of the thyristor is neglected, the circuit equation for the coil circuit is [img=285,100]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-3.jpg[/img] where uC is the voltage across the capacitor; i is the current in the excitation coil; R is the resistance of the excitation coil; Ψ is the flux linkage of the excitation coil; L is the self-inductance of the excitation coil; M is the mutual inductance between the equivalent surface current coil of the permanent magnet and the excitation coil; and C is the capacitance of the capacitor. [img=264,114]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-4.jpg[/img] The initial conditions of the circuit are [img=282,66]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-5.jpg[/img] where U0 is the pre-charge voltage of the capacitor. From equations (4) and (5), we can derive [img=343,122]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-6.jpg[/img] 4.1.2 Equation of motion of the moving iron core During the motion of the moving iron core, the displacement equation of the moving part is [img=317,37]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-7.jpg[/img] where m(x) is the normalized mass of the moving part of the moving iron core; x is the displacement of the moving iron core; Ff(x) and Ff are the reaction forces related to the displacement and velocity of the moving part. 4.1.3 Attraction Equation Assuming the magnetic system is linear, the magnetic field energy is [img=346,130]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/111-9.jpg[/img][font=SimSun][size=3] [img=313,38]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/112-1.jpg[/img][/size][/font] 4.2 Simulation of Dynamic Process The above equations cannot be solved using rigorous analytical methods. This paper uses the SIMULINK toolbox of MATLAB to simulate the dynamic process equations. This not only obtains the time-domain solution of the dynamic process but also allows for convenient correction of the electrical parameters of the energy storage capacitor and excitation coil. Figure 4 shows the simulation model of the dynamic process. [img=318,218]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/112-2.jpg[/img] Figure 4 contains two subsystems, namely the electromagnetic attraction simulation model subsystem and the excitation current simulation model subsystem, which are the representations of equations (9) and (6) in SIMULINK, as shown in Figures 5 and 6. [img=325,250]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/112-3.jpg[/img][img=325,204]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/112-4.jpg[/img][align=left] Electromagnetic parameters required for simulation [img=162,37]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/112-5.jpg[/img] Functions of displacement x, which can be obtained before simulation using the finite element method or other magnetic field or magnetic circuit calculation methods. The load reaction characteristics and the reduced mass are also functions of displacement x, and are calculated before the simulation. These functions are represented by their respective sub-functions in the simulation model. When t = 0, the displacement of the moving iron core is 0; when the moving iron core is displaced to the terminal position, the simulation is terminated using the STOP module. Thus, the characteristic curves of the coil excitation current, capacitor discharge voltage, displacement and velocity of the moving part as a function of time or displacement can be obtained throughout the entire motion stroke of the moving iron core. [/align][align=left][b]5 Calculation Results and Analysis[/b] Figure 7 shows the field magnetic potential distribution diagram calculated when the excitation coil is not energized. In the closed position shown in Figure 7(a), the magnetic lines of force almost all pass through the end face of the moving iron core, generating a corresponding electromagnetic holding force; while in the open position shown in Figure 7(b), due to the magnetic shunt, part of the magnetic flux passes through the side of the moving iron core, and another part of the magnetic flux passes through the end face of the moving iron core. Therefore, the electromagnetic holding force in this position is much smaller than that in the closed position. The air gap reluctance is proportional to the air gap length. Therefore, the electromagnetic holding force of the permanent magnet acting on the end face of the moving iron core decreases as the air gap increases. Table 1 shows the calculated values ​​of the electromagnetic holding force of the permanent magnet acting on the closed end of the moving iron core under different air gaps. [Images: http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/112-6.jpg and http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/112-7.jpg] As can be seen from Table 1, the electromagnetic holding force changes very steeply near the terminal position of the open or closed circuit breaker. Near the closing position, as long as the working air gap length is no greater than 1.0 mm, it is sufficient to ensure reliable contact closure. Near the opening position, since the load reaction force of the vacuum interrupter and mechanical transmission system is only about 200 N/phase, although the electromagnetic holding force is greatly reduced by the magnetic shunt, it can still ensure reliable contact breaking. [img=347,158]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/113-1.jpg[/img] Figure 8 shows the magnetic potential distribution when the excitation coil is energized with a constant magnetomotive force. In the closing position shown in Figure 8(a), the magnetic field at the closed end of the moving iron core is weakened by the external magnetic field of the opening coil. Near the working air gap area of ​​the opening coil, the magnetic shunt reduces the air gap magnetic resistance and the leakage flux is less than when there is no magnetic shunt. The magnetic flux is concentrated on the outer end face and outer edge of the moving iron core. Under the influence of the external magnetomotive force applied to the trip coil, the electromagnetic force that keeps the moving iron core closed is canceled out, and the moving iron core tends to move towards the trip position. In the trip position shown in Figure 8(b), although the closing coil has a long working air gap and the magnetic field exerted by the external magnetomotive force on the closing coil end is weak, near the trip working air gap region, due to the presence of a magnetic shunt, a portion of the permanent magnet and the external magnetic field of the closing coil act on the side edge region of the moving iron core. The magnetic flux passing through the end face is relatively small, thus the electromagnetic force that keeps the moving iron core open is small, and the moving iron core tends to move towards the closed position. The simulation model established in this paper was used to simulate the design prototype, and its performance was evaluated based on the simulation results to allow for real-time correction of the electromagnetic parameters. Figure 9 shows the dynamic characteristics obtained from the simulation. [img=317,143]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/113-2.jpg[/img][img=317,189]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/113-3.jpg[/img][align=left] To enable the permanent magnet operating mechanism to obtain a large output mechanical force and operate quickly, the structural parameters and power supply parameters of the electromagnetic system should be reasonably designed and correctly selected. To ensure the excitation current reaches the required value, the pre-charge voltage U0 of the energy storage capacitor should be relatively high, and the capacitance C should also be relatively large. Simultaneously, during coil energization, to ensure the applied magnetic field of the excitation coil cancels out the magnetic field of the permanent magnet, the damping oscillation angular frequency of the discharge circuit should be reduced, which also requires a sufficiently large capacitance C. Both the opening and closing coils are equipped with an energy storage capacitor with a pre-charge voltage of 100 V and a capacitance of 0.1 F. [img=322,282]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/113-4.jpg[/img][img=322,290]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/113-5.jpg[/img][img=322,235]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zgdjgcxb/2001-12/113-6.jpg[/img] To ensure that the circuit breaker can complete a full O-C-O operation as required, the capacitor providing the tripping energy should be able to discharge continuously twice. The characteristic curves 1 and 3 shown in Figure 9 are the dynamic characteristics of the tripping capacitor when the pre-charge voltage is 100V and 90V, respectively. By comparing Figures 9(b), 9(c) and 9(d), it can be seen that since the pre-charge voltage across the capacitor has been reduced during the second discharge, the movement time of the moving iron core (mainly the contact time) increases slightly. However, the excitation current value of the tripping coil and the tripping speed value of the moving iron core are almost unchanged, which is sufficient to ensure reliable tripping. Comparing curves 1 and 3 in Figure 9(e), it can be seen that even if the pre-charge voltage of the capacitor is different, as long as the discharge can be maintained, the velocity displacement characteristics of the moving iron core are almost the same. As shown in the stroke speed characteristic curve of Figure 9(e), due to the magnetic shunt near the working air gap of the trip coil, the electromagnetic attraction characteristic of the moving iron core during the tripping motion is relatively flat. This makes the rate of increase of the tripping speed of the moving iron core steep at first and then slow down, which is beneficial to ensure that the contact moves according to the optimal tripping displacement characteristic curve. Conversely, since no magnetic shunt is set near the working air gap of the closing coil, the electromagnetic attraction characteristic of the moving iron core during the closing motion is steeper, resulting in a higher final closing speed, which helps to reduce pre-breakdown before closing. Under the same window area and fill factor, the thinner the wire diameter and the more coil turns, the greater the inductance and resistance of the coil circuit, the slower the increase of current and magnetic flux in the coil, and the longer the armature movement time. If the current in the coil cannot reach the trigger current, the armature will fail to move; conversely, if it can, the armature will not move. Therefore, reducing the number of coil turns helps to improve the tripping and closing speeds. [b]6 Conclusion[/b] This paper proposes a design scheme for a permanent magnet mechanism for a 72.5 kV high-voltage vacuum interrupter. By setting a magnetic shunt in the working air gap region of the trip coil, the armature can obtain sufficient kinetic energy even during a long stroke. Simulation and calculation results show that the permanent magnet operating mechanism designed in this way can meet the breaking requirements of the 72.5 kV vacuum interrupter. 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