A Novel Breaking Strategy for Reduced Response Time of Electromagnetic Contactor by Reverse Voltage Application

This paper proposes a novel breaking strategy for dramatically shortening the response time of a single, stable electromagnetic contactor. A reverse voltage was applied across the excitation coil to increase the decay velocity of the magnetic field in the iron core, leading to a dramatic reduction of the electromagnetic force when the contactor initiated the breaking process. The applied time of the reverse voltage was determined by numerical computation of circuit, magnetic field, and forces. The polarity of source voltage was overturned by controlling switching devices in the bridge drive circuit. A co-simulation coupling magnetic field, machinery, and circuit was carried out using Maxwell and Circuit Editor software. Experimental results are reported to demonstrate the effectiveness of the proposed breaking strategy for shortening the response time of an electromagnetic contactor.


Introduction
Electromagnetic contactors are widely used in power systems to switch the main circuit on and off, the performance of which directly affects the safety and stability of the power system and the controlled equipment [1][2][3][4].Numerous studies have examined the dynamic performance of contactors during both the making and breaking process.In [5], a new contactor modeling method that incorporates the back propagation neural network was proposed to map the complex nonlinear electromechanical coupling relation of the contactor.In [6], a nonlinear transient finite element analysis with strong circuit coupling was presented, discussing both current and voltage drive models.In [7,8], a closed-loop control strategy for contactors was proposed, which was based on measuring voltage and current signals; the strategy adopted Pulse Width Modulation (PWM) to flexibly modify the coil energization to effectively control the electromagnetic force.In addition, some sensorless schemes have been proposed to control the closure of contactors to reduce contact bounce [9][10][11].The current hysteresis-band control has also been employed to control the excitation coil current, which can reduce unnecessary energy consumption and ensure the reliable closure of contact during the holding process [12,13].As demonstrated by the above studies, the coil excitation current has a significant influence on the dynamic performance of contactors.
Until recently, research on the breaking process of contactors have concentrated on arc extinguishing to extend electrical life.In [14], a breaking strategy was proposed to minimize and balance the mass losses of the three-phase contacts by controlling the arcing phase angle.Wu et al. proposed a computation of arcing characteristics by utilizing electrical signals to achieve residual electrical endurance prediction of alternating current contactors [15].Meanwhile, a control method of closing the phase angle has also been proposed and was realized on a circuit breaker [16,17].However, an overlong breaking period is another significant problem that occurs in the breaking process of contactor, which is largely attributable to the freewheeling current in the excitation coil and the remanent flux density in the iron core [18].To solve this problem, some novel structures of contactors and breaking strategies have been proposed.Zhu et al. improved a permanent magnet (PM) actuator with two magnetic short circuit rings, equipped at the opening end of the armature, to largely decrease the holding force of the PM [19].In [20], a new structure with auxiliary making and breaking coils shortened the closing and opening time of actuators.In [21], a double-speed mechanism provided the necessary increase of contact separation speed without a significant increase of opening energy.In addition, an ironless Thomson actuator has been shown to be an effective solution to achieve the shortest opening delay possible [22].Several power semiconductor devices with high-speed, arcless interrupting characteristics and high reliability, such as integrated fate-commutated thyristors and gate turn-off thyristors, have been adopted to improve the breaking velocity of switchgear [23,24].However, the necessary structural improvements for the actuators are difficult to implement on manufactured products.In addition, a novel high-response electromagnetic actuator has been proposed for an electronic engraving system in [25], but it cannot be widely adopted in common systems.In [26], a flux-weakening control strategy to reduce the fluxes for holding forces has been proposed to shorten start-up time; however, it is only suitable for PM actuators.
This paper proposes a novel breaking strategy for shortening the response time of a single stable electromagnetic contactor.A reverse voltage is applied to eliminate remanent flux density in iron cores to accelerate contact opening.The applied time of the reverse voltage is determined by an accurate numerical calculation of the circuit, the magnetic field, and other forces to improve the breaking response speed as much as possible and prevent the contact from closing.The proposed breaking strategy and electromagnetic computation method of the applied time of reverse voltage are addressed in detail, and the dynamic breaking performance of contactor is investigated in depth.
This paper is organized as follows.In Section 2, the proposed breaking strategy is described, followed by electromagnetic computation and force analysis.Subsequently, simulations and experiments are described in Section 3. A co-simulation coupling magnetic field, machinery, and circuit was achieved via the use of Maxwell and Circuit Editor software.Experimental measurements were carried out on a prototype to verify the simulation model and the proposed strategy.Finally, conclusions are summarized in Section 4.

Novel Breaking Strategy
Figure 1 shows a single phase electromagnetic contactor, including an actuator, an insulator, and a vacuum tube.The making and breaking of the electromagnetic contactor were achieved via a controlled current in the single driving coil in the actuator.Once the control system of contactor received the breaking command, the power source was immediately cut off under the traditional breaking strategy.However, the electromagnetic contactor could not break instantly, as shown in Figure 2, because of the freewheeling current in the circuit as well as the remanent flux density in the iron cores.The response time of mechanical contact open was so long that the actuator could not complete the making and breaking of the high frequency.Therefore, the response time had to be shortened to improve the dynamic performance of the electromagnetic contactor.Applying a reverse voltage across the excitation coil is an effective approach to eliminate magnetic remanence in iron core to accelerate the opening of contact.When a reverse voltage is applied, the voltage equation of the control circuit can be written as where ψ is the flux linkage, -U1 is the applied reverse voltage, I is the current of coil, L and R are the inductance and resistance of excitation coil, respectively.After contact closes, the holding current in the excitation coil is expected to be as small as possible on the premise of ensuring the reliable closing of the moving iron core to reduce energy consumption.Furthermore, the smaller the holding current, the shorter the time required for current decline.Assuming that the holding current is kept as I0, the coil current under the reverse voltage can be expressed as  Applying a reverse voltage across the excitation coil is an effective approach to eliminate magnetic remanence in iron core to accelerate the opening of contact.When a reverse voltage is applied, the voltage equation of the control circuit can be written as where ψ is the flux linkage, -U1 is the applied reverse voltage, I is the current of coil, L and R are the inductance and resistance of excitation coil, respectively.After contact closes, the holding current in the excitation coil is expected to be as small as possible on the premise of ensuring the reliable closing of the moving iron core to reduce energy consumption.Furthermore, the smaller the holding current, the shorter the time required for current decline.Assuming that the holding current is kept as I0, the coil current under the reverse voltage can be expressed as Because of magnetic hysteresis, there was some remanent flux density in the iron core despite the disappearance of the excitation coil current.As a result, the movable iron core could move during the breaking procedure only when the electromagnetic force produced by the remanent flux density was less than the total anti-force.
Applying a reverse voltage across the excitation coil is an effective approach to eliminate magnetic remanence in iron core to accelerate the opening of contact.When a reverse voltage is applied, the voltage equation of the control circuit can be written as where ψ is the flux linkage, −U 1 is the applied reverse voltage, I is the current of coil, L and R are the inductance and resistance of excitation coil, respectively.After contact closes, the holding current in the excitation coil is expected to be as small as possible on the premise of ensuring the reliable closing of the moving iron core to reduce energy consumption.Furthermore, the smaller the holding current, the shorter the time required for current decline.Assuming that the holding current is kept as I 0 , the coil current under the reverse voltage can be expressed as Therefore, the coil current quickly decays and turns from positive to negative, which is helpful for opening contact quickly.However, the contact will close again if the negative current increases sufficiently.
Figure 3 shows the experimental results of the excitation coil current and the displacement of the movable iron core when a reverse voltage was continuously applied.A PWM signal was employed to adaptively control the excitation coil current in the holding period t 2 in Figure 3.In addition, the response time and the action time for breaking are indicated in Figure 3 as t 3 and t 4 , respectively.The sustained reverse voltage quickly overturned the direction of the coil current during the breaking procedure and then made the contact open.A back electromotive force was generated when the movable iron core moved towards the open position, which was proportional to the velocity of the movable iron core and led to an inflexion point in the current curve during t 4 .In contrast, the negative current continued to increase without control after contact opened and eventually made the contact close again after t 5 period, which was potentially damaging to the safety and stability of the contact.Consequently, the applied time of the reverse voltage should be determined accurately.Therefore, the coil current quickly decays and turns from positive to negative, which is helpful for opening contact quickly.However, the contact will close again if the negative current increases sufficiently.
Figure 3 shows the experimental results of the excitation coil current and the displacement of the movable iron core when a reverse voltage was continuously applied.A PWM signal was employed to adaptively control the excitation coil current in the holding period t2 in Figure 3.In addition, the response time and the action time for breaking are indicated in Figure 3 as t3 and t4, respectively.The sustained reverse voltage quickly overturned the direction of the coil current during the breaking procedure and then made the contact open.A back electromotive force was generated when the movable iron core moved towards the open position, which was proportional to the velocity of the movable iron core and led to an inflexion point in the current curve during t4.In contrast, the negative current continued to increase without control after contact opened and eventually made the contact close again after t5 period, which was potentially damaging to the safety and stability of the contact.Consequently, the applied time of the reverse voltage should be determined accurately.

Electromagnetic Computation and Force Analysis
The reverse voltage should be continuously applied across the excitation coil until the movable iron core starts to move.To make contact open, the electromagnetic force produced by the remanent flux density should be less than the total anti-force.According to Ampere's law and Maxwell force formula, the electromagnetic force can be expressed as where Sδ is the flux area, μ0 is the permeability of vacuum, N is the coil turns number, δ0 is the width of air gap, and M is the magnetization.Because iron cores are usually made of soft magnetic material and they are in a magnetic unsaturated state during holding process, the magnetization curve can be considered linear in this stage, i.e., the magnetization coefficient M can be regarded as a constant.The magnetic potential difference in the iron core can be ignored.In addition, the dispersion of the magnetic field between core columns can also be ignored because the air gap is sufficiently narrow.
In addition, the anti-force of electromagnetic actuator consists predominantly of the contact closing force, the forces of contact spring and return spring, the gravity of the movable parts, and the friction force between touched components [27], which can be written as

Electromagnetic Computation and Force Analysis
The reverse voltage should be continuously applied across the excitation coil until the movable iron core starts to move.To make contact open, the electromagnetic force produced by the remanent flux density should be less than the total anti-force.According to Ampere's law and Maxwell force formula, the electromagnetic force can be expressed as where S δ is the flux area, µ 0 is the permeability of vacuum, N is the coil turns number, δ 0 is the width of air gap, and M is the magnetization.Because iron cores are usually made of soft magnetic material and they are in a magnetic unsaturated state during holding process, the magnetization curve can be considered linear in this stage, i.e., the magnetization coefficient M can be regarded as a constant.
Energies 2019, 12, 789 5 of 12 The magnetic potential difference in the iron core can be ignored.In addition, the dispersion of the magnetic field between core columns can also be ignored because the air gap is sufficiently narrow.
In addition, the anti-force of electromagnetic actuator consists predominantly of the contact closing force, the forces of contact spring and return spring, the gravity of the movable parts, and the friction force between touched components [27], which can be written as where G is the gravity of movable parts; K 1 and K 2 are elastic coefficients of return spring and contact spring, respectively; x 1 and x 2 are the compression lengths of return spring and contact spring, respectively; and F z is the contact closing force.Therefore, the mechanical balance equation of the movable iron core can be expressed as Substituting Equations ( 2) to ( 5), one can have Finally, the applied time of the reverse voltage can be written as According to regulations, contactors need to work reliably under 85-110% of rated voltage.For this reason, the value of source voltage should be measured accurately and continuously.At the closed position, the PWM duty ratio is adaptively adjusted to keep the holding current constant when the source voltage fluctuates.The applied time of the reverse voltage is calculated online in a microcontroller to cut off the reverse voltage accurately when the source voltage fluctuates.In addition, the negative current is too small to cause significant Joule loss because the loading time of reverse voltage is very short.
The wear of the system, such as contact wear, has a comparatively small influence on the dynamic performance of contactor in the short term.Therefore, these influences can be ignored in the above calculation.In addition, a regular inspection of the mechanical structure and timely replacements of components can also decrease the influence of wear.
Mechanical or electrical parameters can change over time and can considerably affect the dynamic performance of the system.The applied time of the reverse voltage can vary within a certain range because it takes a relatively long time for the negative current to increase to make contact close again, as demonstrated by t 5 in Figure 3.However, a measurement of the negative current can prevent it from growing too large, cutting off the reverse voltage in time.

Simulation Results
A transient simulation model coupling magnetic field, machinery and circuit was established using Ansoft Maxwell and Circuit Editor software, as shown in Figure 4. LWinding1 represents the excitation coil that connects the actuator model; Rcoil and Llc are the inductance and the resistance of excitation coil, respectively.The main circuit includes three power sources, which were adopted to provide source voltages as well as the reverse voltage across the excitation coil during different procedures.Figure 5 shows the simulation results of the movable iron core displacement and the coil current with respect to time under different breaking strategies.Under the traditional breaking strategy, although the control system of contactor received a breaking command at 50 ms and the source voltage was disconnected simultaneously, the coil current decayed slowly and contacts remained closed.However, the current declined quickly and the movable iron core began to move promptly after the reverse voltage was applied.Therefore, the response time for the breaking of the electromagnetic contactor was greatly shortened.In addition, because the reverse voltage was accurately cut off when the movable iron core began to move, the negative current could not continuously increase.In addition, the movable iron core began to move before the excitation coil current dropped to zero because the simulation model did not consider magnetic hysteresis.Nevertheless, it still was able to verify the effectiveness of the proposed breaking strategy.Figure 6 shows the simulation results of the electromagnetic force and the anti-force under different breaking strategies.Under the traditional breaking strategy, the electromagnetic force declined slowly and was always greater than the anti-force.The anti-force remained constant because the contact remained closed.In contrast, the electromagnetic force declined rapidly under the proposed breaking strategy.The movable iron core began to move when the electromagnetic force Figure 5 shows the simulation results of the movable iron core displacement and the coil current with respect to time under different breaking strategies.Under the traditional breaking strategy, although the control system of contactor received a breaking command at 50 ms and the source voltage was disconnected simultaneously, the coil current decayed slowly and contacts remained closed.However, the current declined quickly and the movable iron core began to move promptly after the reverse voltage was applied.Therefore, the response time for the breaking of the electromagnetic contactor was greatly shortened.In addition, because the reverse voltage was accurately cut off when the movable iron core began to move, the negative current could not continuously increase.In addition, the movable iron core began to move before the excitation coil current dropped to zero because the simulation model did not consider magnetic hysteresis.Nevertheless, it still was able to verify the effectiveness of the proposed breaking strategy.Figure 5 shows the simulation results of the movable iron core displacement and the coil current with respect to time under different breaking strategies.Under the traditional breaking strategy, although the control system of contactor received a breaking command at 50 ms and the source voltage was disconnected simultaneously, the coil current decayed slowly and contacts remained closed.However, the current declined quickly and the movable iron core began to move promptly after the reverse voltage was applied.Therefore, the response time for the breaking of the electromagnetic contactor was greatly shortened.In addition, because the reverse voltage was accurately cut off when the movable iron core began to move, the negative current could not continuously increase.In addition, the movable iron core began to move before the excitation coil current dropped to zero because the simulation model did not consider magnetic hysteresis.Nevertheless, it still was able to verify the effectiveness of the proposed breaking strategy.Figure 6 shows the simulation results of the electromagnetic force and the anti-force under different breaking strategies.Under the traditional breaking strategy, the electromagnetic force declined slowly and was always greater than the anti-force.The anti-force remained constant because the contact remained closed.In contrast, the electromagnetic force declined rapidly under the proposed breaking strategy.The movable iron core began to move when the electromagnetic force Figure 6 shows the simulation results of the electromagnetic force and the anti-force under different breaking strategies.Under the traditional breaking strategy, the electromagnetic force declined slowly and was always greater than the anti-force.The anti-force remained constant because the contact remained closed.In contrast, the electromagnetic force declined rapidly under the proposed breaking strategy.The movable iron core began to move when the electromagnetic force was less than the anti-force.Furthermore, the electromagnetic force did not increase again because the reverse voltage was cut off in time.
Energies 2019, 12, x FOR PEER REVIEW 7 of 12 was less than the anti-force.Furthermore, the electromagnetic force did not increase again because the reverse voltage was cut off in time.
. Figure 7 shows the simulation results of magnetic flux density distributions at 70 ms under different breaking strategies.The contactor had entered the breaking process at that time because the breaking command was applied at 50 ms.In comparison with the traditional breaking strategy, the magnetic flux density in iron core declined more quickly when a reverse voltage was applied, which was down more than 99% at 70 ms.As a result, the electromagnetic force significantly decreased, which resulted in an obvious shortening of response time for breaking.

Control System
Figure 8 shows the control topology unit used to excite the electromagnetic actuator.Q1-Q5 are insulated gate bipolar transistors (IGBTs), which are used to switch the main circuit on or off.D1-D4 are the corresponding protection diodes for IGBTs.Q5 and R1 were used to charge the capacitor C1 to its rated voltage.When Q1 and Q3 were turned on, Q2 and Q4 were turned off, and the coil current flowed through loop1, which was composed of C1, Q1, Q3, R2, and the single drive coil, as shown in Figure 7 shows the simulation results of magnetic flux density distributions at 70 ms under different breaking strategies.The contactor had entered the breaking process at that time because the breaking command was applied at 50 ms.In comparison with the traditional breaking strategy, the magnetic flux density in iron core declined more quickly when a reverse voltage was applied, which was down more than 99% at 70 ms.As a result, the electromagnetic force significantly decreased, which resulted in an obvious shortening of response time for breaking.
Energies 2019, 12, x FOR PEER REVIEW 7 of 12 was less than the anti-force.Furthermore, the electromagnetic force did not increase again because the reverse voltage was cut off in time.
. Figure 7 shows the simulation results of magnetic flux density distributions at 70 ms under different breaking strategies.The contactor had entered the breaking process at that time because the breaking command was applied at 50 ms.In comparison with the traditional breaking strategy, the magnetic flux density in iron core declined more quickly when a reverse voltage was applied, which was down more than 99% at 70 ms.As a result, the electromagnetic force significantly decreased, which resulted in an obvious shortening of response time for breaking.

Control System
Figure 8 shows the control topology unit used to excite the electromagnetic actuator.Q1-Q5 are insulated gate bipolar transistors (IGBTs), which are used to switch the main circuit on or off.D1-D4 are the corresponding protection diodes for IGBTs.Q5 and R1 were used to charge the capacitor C1 to its rated voltage.When Q1 and Q3 were turned on, Q2 and Q4 were turned off, and the coil current flowed through loop1, which was composed of C1, Q1, Q3, R2, and the single drive coil, as shown in

Control System
Figure 8 shows the control topology unit used to excite the electromagnetic actuator.Q1-Q5 are insulated gate bipolar transistors (IGBTs), which are used to switch the main circuit on or off.D1-D4 are the corresponding protection diodes for IGBTs.Q5 and R1 were used to charge the capacitor C1 to its rated voltage.When Q1 and Q3 were turned on, Q2 and Q4 were turned off, and the coil current flowed through loop1, which was composed of C1, Q1, Q3, R2, and the single drive coil, as shown in Figure 8a.On the contrary, when Q2 and Q4 were turned on, Q1 and Q3 were turned off during breaking procedure.The coil current flowed through loop2, which was composed of C1, Q2, Q4, R2, and the single drive coil, as shown in Figure 8b.Therefore, it was convenient to overturn the polarity of the source voltage by controlling these switching elements in the drive circuit.The platform of the hardware circuit is shown in Figure 9.The system consists of a microcontroller unit TMS320F2812, a power supply, a rectifier filter circuit, a protection module, a current and voltage measuring circuit, a PWM drive circuit, and a switch control module.The digital signal processor (DSP) communicates with the upper monitor via a serial communication interface bus.In addition, the current transformer (CT) and the potential transformer (PT) are employed to convert high voltage signals to low voltage ones and feed the sampling data into the DSP for calculation.The main program flowchart of the breaking procedure is shown in Figure 10.The control system initiates and waits for the breaking command.After receiving the command, IGBTs are switched on or off to overturn the polarity of the source voltage.Subsequently, all the switching elements are switched off after a time delay, which is set in the program in advance.Consequently, the data are processed and transmitted to the upper monitor.Eventually, the software system will wait for the next command.The main program flowchart of the breaking procedure is shown in Figure 10.The control system initiates and waits for the breaking command.After receiving the command, IGBTs are switched on or off to overturn the polarity of the source voltage.Subsequently, all the switching elements are switched off after a time delay, which is set in the program in advance.Consequently, the data are processed and transmitted to the upper monitor.Eventually, the software system will wait for the next command.

Experimental Results
An experimental setup including a prototype of the single stable electromagnetic contactor, an intelligent control unit, a drive circuit, and some power supplies, was established to verify the The main program flowchart of the breaking procedure is shown in Figure 10.The control system initiates and waits for the breaking command.After receiving the command, IGBTs are switched on or off to overturn the polarity of the source voltage.Subsequently, all the switching elements are switched off after a time delay, which is set in the program in advance.Consequently, the data are processed and transmitted to the upper monitor.Eventually, the software system will wait for the next command.

Experimental Results
An experimental setup including a prototype of the single stable electromagnetic contactor, an intelligent control unit, a drive circuit, and some power supplies, was established to verify the

Experimental Results
An experimental setup including a prototype of the single stable electromagnetic contactor, an intelligent control unit, a drive circuit, and some power supplies, was established to verify the effectiveness of the proposed breaking strategy.Figure 11 shows the experimental results of the excitation coil current and the displacement of the movable iron core with and without the reverse voltage.The pulse width modulation was employed to keep the holding current both small and constant during the holding procedure.Under the traditional breaking strategy, the source voltage is cut off immediately when the microcontroller receives the breaking command.However, the response time for breaking is long, up to 94. shorten the electrical life of the contactor and damage the controlled system.In comparison with the traditional breaking strategy, the response time for contactor breaking is significantly reduced under the novel breaking strategy.The reverse voltage was applied across the excitation coil to increase the decay velocity of magnetic field in iron core.Consequently, the response time declined by 74%, from 94.8 ms to 24.6 ms.Furthermore, the reverse voltage was cut off accurately when the movable iron core began to move, as shown in Figure 11a, which verified the effectiveness of the computational method.
effectiveness of the proposed breaking strategy.Figure 11 shows the experimental results of the excitation coil current and the displacement of the movable iron core with and without the reverse voltage.The pulse width modulation was employed to keep the holding current both small and constant during the holding procedure.Under the traditional breaking strategy, the source voltage is cut off immediately when the microcontroller receives the breaking command.However, the response time for breaking is long, up to 94.8 ms.The contactor cannot open the main circuit in time, which may shorten the electrical life of the contactor and damage the controlled system.In comparison with the traditional breaking strategy, the response time for contactor breaking is significantly reduced under the novel breaking strategy.The reverse voltage was applied across the excitation coil to increase the decay velocity of magnetic field in iron core.Consequently, the response time declined by 74%, from 94.8 ms to 24.6 ms.Furthermore, the reverse voltage was cut off accurately when the movable iron core began to move, as shown in Figure 11a, which verified the effectiveness of the computational method.Table 1 indicates the experimental values of the reverse voltage, the maximum negative current, the response time, and the action time in the breaking procedure.The applied reverse voltage was −200 V and the maximum negative current only reached −0.17A, which led to reduced energy Table 1 indicates the experimental values of the reverse voltage, the maximum negative current, the response time, and the action time in the breaking procedure.The applied reverse voltage was −200 V and the maximum negative current only reached −0.17A, which led to reduced energy consumption.Under the traditional breaking strategy, the response time is almost six times longer than action time, which indicates that the breaking response considerably affects the dynamic performance of electromagnetic contactor.In addition to the response time, the action time was also greatly reduced, from 15.6 ms to 6.8 ms, which is beneficial for arc extinguishing.

Conclusions
This paper successfully proposes a novel breaking strategy for shortening the response time of electromagnetic contactors.A reverse voltage was employed to eliminate the magnetic remanence in an iron core to accelerate the opening of contacts.The applied time of the reverse voltage was determined by numerical computation of circuit, magnetic field, and forces.A novel drive circuit was designed to flexibly control the polarity of the source voltage.Simulation results of the proposed breaking strategy were obtained by co-simulation using Maxwell and Circuit Editor software.An experimental setup, including a prototype and a control system, was set up to verify the theoretical analyses and simulation results.It validated that the proposed breaking strategy can greatly shorten the response time to improve the performance of electromagnetic contactor significantly.This novel breaking strategy can be implemented in power systems in which the single stable electromagnetic contactor is widely used to frequently switch equipment on and off.

Figure 2 .
Figure 2. Experimental results of breaking procedure.(t0 is the response time for breaking, t1 is the moving time of the movable iron core).

Figure 2 .
Figure 2. Experimental results of breaking procedure.(t0 is the response time for breaking, t1 is the moving time of the movable iron core).

Figure 2 .
Figure 2. Experimental results of breaking procedure.(t 0 is the response time for breaking, t 1 is the moving time of the movable iron core).

Figure 3 .
Figure 3. Experimental results with sustained reverse voltage.(For the coil current, 1 A corresponds to 1 V; for the movable iron core displacement, 1 mm corresponds to 250 mV).

Figure 3 .
Figure 3. Experimental results with sustained reverse voltage.(For the coil current, 1 A corresponds to 1 V; for the movable iron core displacement, 1 mm corresponds to 250 mV).

Figure 5 .
Figure 5. Simulation results of coil current and displacement with and without the reverse voltage.The breaking command is applied at 50 ms.

Figure 5 .
Figure 5. Simulation results of coil current and displacement with and without the reverse voltage.The breaking command is applied at 50 ms.

Figure 5 .
Figure 5. Simulation results of coil current and displacement with and without the reverse voltage.The breaking command is applied at 50 ms.

Figure 6 .
Figure 6.Simulation results of electromagnetic force and anti-force.The breaking command is applied at 50 ms.

Figure 7 .
Figure 7. Simulation results of magnetic flux density distributions at ms under different breaking strategies.(a) With reverse voltage.(b) Without reverse voltage.

Figure 6 .
Figure 6.Simulation results of electromagnetic force and anti-force.The breaking command is applied at 50 ms.

Figure 6 .
Figure 6.Simulation results of electromagnetic force and anti-force.The breaking command is applied at 50 ms.

Figure 7 .
Figure 7. Simulation results of magnetic flux density distributions at 70 ms under different breaking strategies.(a) With reverse voltage.(b) Without reverse voltage.

Figure 7 .
Figure 7. Simulation results of magnetic flux density distributions at 70 ms under different breaking strategies.(a) With reverse voltage.(b) Without reverse voltage.

Energies 2019 , 12 Figure 8a .Figure 8 .
Figure 8a.On the contrary, when Q2 and Q4 were turned on, Q1 and Q3 were turned off during breaking procedure.The coil current flowed through loop2, which was composed of C1, Q2, Q4, R2, and the single drive coil, as shown in Figure8b.Therefore, it was convenient to overturn the polarity of the source voltage by controlling these switching elements in the drive circuit.

Figure 8 .
Figure 8.Control principle.(a) Making procedure.(b) Breaking procedure.The platform of the hardware circuit is shown in Figure9.The system consists of a microcontroller unit TMS320F2812, a power supply, a rectifier filter circuit, a protection module, a current and voltage measuring circuit, a PWM drive circuit, and a switch control module.The digital signal processor (DSP) communicates with the upper monitor via a serial communication In addition, the current transformer (CT) and the potential transformer (PT) are employed to convert high voltage signals to low voltage ones and feed the sampling data into the DSP for calculation.The main program flowchart of the breaking procedure is shown in Figure10.The control system initiates and waits for the breaking command.After receiving the command, IGBTs are switched on or off to overturn the polarity of the source voltage.Subsequently, all the switching elements are switched off after a time delay, which is set in the program in advance.Consequently, the data are processed and transmitted to the upper monitor.Eventually, the software system will wait for the next command.

Figure 11 .
Figure 11.Experimental results.(a) With reverse voltage.(b) Without reverse voltage.(For the coil current, 1 A corresponds to 1 V; for the movable iron core displacement, 1 mm corresponds to 250 mV.).

Figure 11 .
Figure 11.Experimental results.(a) With reverse voltage.(b) Without reverse voltage.(For the coil current, 1 A corresponds to 1 V; for the movable iron core displacement, 1 mm corresponds to 250 mV.).
8 ms.The contactor cannot open the main circuit in time, which may