Application of phase-shifted full-bridge soft-switch technology in suspension chopper

Suspension chopper is a high-power electrical equipment which controls the suspension state of maglev train. Its performance directly determines the stability and safety of maglev train. However, the traditional suspension chopper has the problem of high voltage spikes of IGBT and load, which poses a threat to the safe operation of high-speed maglev train. In order to solve this problem, this paper designs a phase-shifted full-bridge suspension chopper, which only adds an auxiliary circuit and four parallel capacitors. The soft-switch is realized by using the phase-shifted control signals, so as to reduce the voltage spikes. Compared with other voltage spike suppression methods, the method has the advantages of good suppression of voltage spikes, simple circuit structure, less use of components, and insensitive to component parameters. The performance of the designed circuit is simulated by ANSYS Simplorer, and verified by experimental test platform. The simulation and experimental results show that the phase-shifted full-bridge suspension chopper can greatly reduce voltage spikes of the load and IGBT.


Introduction
Maglev train is a new rail transportation tool that uses electromagnetic force to realize the active suspension of the train, and gets rid of the adhesion limitation, noise vibration, and rail wear of the traditional wheel-rail train.It has the advantages of high speed, safety, reliability, low maintenance cost, and green environmental protection. 1,2Suspension chopper is a high-power electrical equipment for vehicle suspension control, and its performance is crucial to the stability, reliability, and comfort of maglev vehicles.
At present, the practical suspension chopper mostly adopts hard-switch mode and IGBT switch tubes, which has the problems of large energy loss, large electromagnetic radiation, and high voltage spikes of load and IGBT.In order to improve the performance of suspension chopper, Wang et al. 3 designed a three-level double magnet system, Xiangyu et al. 4 designed an asymmetric three-level suspension chopper, and concluded that the three-level method can reduce the static ripple of the load current and improve the control accuracy.Huang 5 and Shi 6 designed the synovial control strategy and auto disturbance rejection control strategy respectively, which improved the response speed of the load current and the anti-interference ability of the system.Li et al., 7 Xu et al., 8 and Chen et al. 9 studied the application of PWM soft-switch in suspension chopper.By adding the auxiliary switch tube and the resonant circuit, the softswitch is realized, which reduces the switching loss and electromagnetic radiation.Long et al. 10 designed high temperature superconducting hybrid maglev system, and Wenlong 11 designed permanent magnet hybrid maglev system to replace the electromagnetic maglev system, greatly reducing the energy loss of the load electromagnet.
However, there are few studies on the problem of high voltage spikes of load and IGBT.Weifeng 12 pointed out that the zero-voltage PWM soft-switch technology can suppress the voltage spike problem to a certain extent.But the suppression effect of this circuit is not ideal, because the added auxiliary switch tube adopts the hard-switch mode and the added resonant circuit will increase the voltage oscillation.In the engineering practice of low-speed maglev train, the impact of voltage spikes are generally mitigated by absorbing resistance capacitance diode(RCD) circuit absorption or using redundant hardware devices.But the voltage spikes in high-speed maglev trains are large due to the high supply voltage, which makes the previous method unsatisfactory and the switching energy loss increases rapidly.So it is necessary to study new circuit topologies in order to find a method that can meet the control requirements and effectively suppress the voltage spikes.
The suspension chopper is a converter in essence, which has been researched a lot on the circuit structure, control mode and voltage spike suppression.Ko¨se and Aydemir 13 described the performance of full-bridge push-pull series power converter.The experimental results show that it is superior to diode dropper method and floating boost charger in protecting load, and superior to two-switch buck-boost converter in efficiency and dynamic response.Darvish Falehi 14 and Salari and Darvish Falehi 15 designed an asymmetric multi-level structure, which can generate a high step sinusoidal voltage by using few components.This method improves the stability of power transmission and reduces the cost.Paul Raj and Meenakshi Sundaram 16 proposed a single-phase cascaded Hbridge five-level inverter, which uses sinusoidal pulse width modulation technology to eliminate harmonic distortion.The system has the advantages of high power, high voltage capacity, low harmonics and low switching loss.Liu et al. 17 proposed a voltage spike suppression scheme that optimizes the laminated busbar structure and the absorption capacitor.The experimental results show that the scheme can suppress the voltage spike at about 60% before optimization.Tingting et al. 18 proposed an improved Y-source inverter, which introduced an absorption loop to optimize the topology, effectively improved the input current characteristics and reduced the bus voltage spike.Hongqi et al. 19 proposed a method of incorporating an improved RCD clamping link into the bus of converter, which can effectively control the voltage peak without affecting the performance of system.However, applying the above research results to the suspension chopper will make the circuit structure complicated, which is not conducive to maintaining the requirements of simple and high reliability of the suspension chopper.
Since the phase-shifted full-bridge (PSFB) softswitch converter was proposed, it has been rapidly developed and applied in occasions with high power, large output voltage and current changes because of its simple structure, convenient control and low power consumption.In this paper, combined with the working principle of the PSFB soft-switch converter and the characteristics of the suspension chopper, the PSFB suspension chopper is proposed.Aiming at the problems of narrow range of zero-voltage conditions and serious loss of duty cycle, an auxiliary circuit is designed to effectively suppress the voltage spikes, which provides a reference for improving the suspension chopper in engineering applications.Simulation and experimental results verify the ability of the circuit.
This paper has been organized as follows: After the introduction of the Section I and Section II analyzes the principle of PSFB suspension chopper in detail and the method of circuit parameters design.In Section III, the simulation and experimental verification of the designed circuit are carried out.The conclusion and final comments are shown in Section IV.

Principle of hard-switch suspension chopper
The load current of suspension chopper changes according to the control signals, thereby adjusting the electromagnetic force to stabilize the maglev train.The main circuit diagram of traditional suspension chopper is shown in Figure 1, where U DC is the supply voltage, VT1;VT4 are IGBT switches, D1;D4 are freewheeling diodes, R and L are the equivalent resistance and inductance of load, Ls is the stray inductance.Generally, the control signals of VT1 and VT2 are complementary, the signals of VT1 and VT4 are identical, and the signals of VT2 and VT3 are identical.When VT1 and VT4 turn on, the load current increases positively.
Taking the change of load current as an example, the waveform of hard-switch suspension chopper are analyzed as Figure 2, where PWM is the pulse control signal of the switch tubes, u RL is the load voltage, I 01 and I 02 are the maximum and minimum values of the load current when the suspension system is stable.
(1) In ½t 0 , t 1 time period: When t = t 0 , VT2 and VT3 turn on, i RL = I 01 , and u RL = À U DC , the load current decreases exponentially as shown as equation (1).
(2) In ½t 1 , T time period: At t 1 moment, VT1 and VT4 turn on, i RL = I 02 , and u RL = U DC , the load current increases according to equation (2).
R(e ÀR(TÀt 0 )=L À 1) The traditional hard-switch suspension chopper has the advantages of simple structure and easy implementation, but there are also a series of problems such as large switching loss, inductive switching, diode reverse recovery, and electromagnetic radiation and noise. 5

Principle of PSFB suspension chopper
The principle of PSFB converter is to realize soft-switch by parallel capacitor of switch tube.When the switch tube is about to turn off, the voltage of it rises from 0 because the voltage of parallel capacitor is 0. When the switch tube will turn on, the freewheeling diode conduction makes the parallel capacitor voltage drop to 0, achieving zero-voltage switching.The key to realize soft-switch of PSFB converter is to ensure that the four switch tubes can meet the conditions of zero-voltage switching.
Since the zero-voltage condition of the lag arm of the PSFB converter is realized by the oscillation of the load inductance, there are problems such as the narrow range of the zero-voltage condition and the serious loss of the duty cycle. 20In this regard, the realization range of the soft-switch can be widened by adding an auxiliary circuit.The main circuit diagram of the PSFB suspension chopper is shown in Figure 3      C3 are equal to U DC , the equivalent circuit diagram is shown in Figure 5. (2) In ½t 0 , t 1 time period: At t 0 moment, the advanced switch VT1 is turned off, the load current simultaneously charges C1 and discharges C2.The equivalent circuit diagram is shown in Figure 6.Since the voltage of capacitor C1 cannot be mutated, VT1 realizes zero-voltage switching.
At t 1 moment, the voltage of C1 rises to U DC , the voltage of C2 drops to 0, so the duration of this modal is given as equation ( 4), where C 12 is the value of C1 and C2.
During this period, due to the large load inductance of magnetic levitation electromagnet, it can be considered that the load current is approximately constant, as shown in equation ( 5).
At this time, the collector-gate voltage changes of VT1 and VT2 are expressed as equation (6).
(3) In ½t 1 , t 2 time period: D2 turn on at t 1 moment, clamping the voltage of VT2 at 0, then VT2 can achieve zero-voltage conduction.The equivalent circuit is shown in Figure 7.In order to ensure the zero-voltage conduction of VT2, the modal 2 must be completed within the dead time of VT2, so it is necessary to ensure t d(VT2) 5t 01 .
Since the angle corresponding to the ½t 0 , t 2 period is the phase difference, the duration of this modal is given as: where, d is the phase difference and the unit is rad, T PWM is the duration of a PWM cycle.In this period, the current of auxiliary inductor decreases according to the change rate of U DC =2L a .The load current decreases exponentially in the loops of VT2 and VT4, and the variation satisfies equation (8).
when t = t 1 , substituting i RL = i 0 into the above equation, we can get the decreases law of i RL is given by (4) In ½t 2 , t 3 time period: At t 2 moment, the advanced switch VT4 is turned off.The current of load and auxiliary charge C4 and discharge C3 simultaneously, and the load voltage drops to 0 and reverse increase.Since the voltage of C4 is 0 at t 2 time and the capacitor voltage cannot change abruptly, VT4 realizes zero-voltage turn off.The equivalent circuit is shown in Figure 8.
At t 3 moment, the voltage of VT4 rises to U DC , the voltage of VT3 drops to 0, and D3 naturally conduct.The duration of this modal is given as follow, where i a is the current of auxiliary inductor, C 34 is the value of C3 and C4.
During this period, the load works resonantly with C3 and C4 to obtain equation (11), where Q represents the charge of the capacitor and the unit is C.
Bring the current value at time t 2 into the above formula, the variation law of load current can be obtained as follow.
The voltage of VT3 and VT4 can be obtained as where v 1 = 1= ffiffiffiffiffiffiffiffiffiffiffiffiffi 2LC 34 p and the unit is rad=s, Z 1 = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi L=2C 34 p and the unit is O in the above two formulas.
(5) In ½t 3 , t 4 time period: D3 conduct at t 3 moment, the voltage of VT3 is clamped at 0 by C3, enabling VT3 to achieve zero-voltage turn on, and the equivalent circuit is shown in Figure 9.In order to ensure the zero-voltage conduction of VT3, the modal 4 must be completed within the dead time of VT3, so it is necessary to ensure t d(VT3) 5t 23 .
The conduction time of VT2 in one cycle corresponds to ½t 1 , t 4 , so the duration of this modal is given as follow, where D VT2 is the duty ratio of control signal for VT2.
During this period, the current of auxiliary inductor increases according to the change rate of U DC =2L a , the supply voltage is all applied to the load, and the following equation can be obtained.
Bring the current value at time t 3 into the formula above, the variation law of load current can be obtained as follow.
(6) In ½t 4 , t 5 time period: VT2 turn off at t 4 moment, and the current of load charge C2 and discharge C1, the equivalent circuit diagram is shown in Figure 10.Since the C2 voltage cannot be mutated, the voltage of VT2 is clamped at 0, and the VT2 realizes zero-voltage turn off.
The current of auxiliary inductor decreases rapidly under supply voltage.The voltage of C1 drops to 0, and the voltage of C2 rises to U DC at t 5 moment, so the duration of this modal is given as: During this period, it can be considered that the load current is approximately constant, as shown in equation (18).
(7) In ½t 5 , t 6 time period: VT1 turn on at t 5 moment.Since C1 voltage cannot change abruptly, the voltage of VT1 clamped at 0, enabling VT1 to realize zero-voltage turn on, the equivalent circuit is shown in Figure 11.In order to ensure the zerovoltage turn on of VT1, the modal 6 must be completed within the dead time of VT1, thus ensuring t d(VT1) 5t 45 .
Since the angle corresponding to the ½t 4 , t 6 period is the phase difference, the duration of this modal is given as: During this period, the current of auxiliary inductor increases according to the change rate of U DC =2L a .The load current decreases exponentially in the loops of VT1 and VT3, and the decreases law of i RL is given by (8) In ½t 6 , t 7 time period: VT3 turn off at t 6 moment, the voltage of VT3 is clamped at 0 by C3 to realize zero-voltage turn-off.The current of load charges C3 and discharges C4, the equivalent circuit diagram is shown in Figure 12.
At t 7 moment, the voltage of C3 rises to U DC , the voltage of C4 drops to 0 and D4 naturally conduct.The duration of this modal is given as equation (21).
In this period, the change law of load current is similar to that in ½t 2 , t 3 period, which satisfies equation (22).
(9) In ½t 7 , t 8 time period: VT4 turn on at t 7 moment, the voltage of VT4 is clamped at 0 to realize zerovoltage turn on, the equivalent circuit is shown in Figure 5.In order to ensure the zero-voltage turnon of VT4, the modal 8 must be completed within the dead time of VT4, thus ensuring t d(VT4) 5t 67 .
The conduction time of VT1 in one cycle corresponds to ½t 5 , t 8 , so the duration of this modal is given as follow, where D VT1 is the duty ratio of control signal for VT1.
In this period, the power supply voltage acts on the load, and the load current rises according to the following rule.
So far, the PSFB suspension chopper completes a full cycle of modal conversion, and enters the next cycle.

Design of circuit parameters
In order to realize the soft-switch of the PSFB suspension chopper, the dead time of the control signals and the parameters of the added components need to meet certain conditions.
Control signal.The dead time of signals has great influence on the performance of suspension chopper.The soft-switch cannot meet the implementation conditions if the dead time is too short.Conversely, it may cause waveform distortion, seriously reduce the output efficiency, and even adversely affect the stability of the chopper system if the dead time is too long. 21The load of the suspension chopper is a large inductance element, and the dead time setting of the control signal can be determined by equation (25). 21 where, t d is the dead time of control signal.The first term represents the dead time caused by IGBT, t d À off À max is the maximum turn off delay, t off À max is the maximum turn off drop time, and t d À on À max is the minimum turn on delay time.The second term represents the dead time caused by the driving circuit, t PDD À max is the maximum transmission delay, t PDD À min is the minimum transmission delay, and r represents the redundancy coefficient, generally 1.2-1.5.
Parallel capacitance.The selection of parallel capacitor parameters should meet the following conditions.
(i) In the dead time of IGBT, some modals should be completed in the dead time of IGBT, which prepares for the realization of IGBT zero-voltage turn on and turn off in the next modal.
(ii) The parallel capacitor charging and discharging of the lagging arm is completed by the load inductance, so the load inductance needs enough energy, which needs to meet the following formula.
(iii) The inductor and parallel capacitor form an oscillation circuit.In order to eliminate the influence of the oscillation circuit, it is necessary to make the dead time less than one-fourth times of the oscillation period, 22,23 namely to satisfy equation (28).
Auxiliary inductance.At steady state, the auxiliary capacitors C a1 and C a2 are voltage-sharing capacitors, and the voltage is U DC =2.According to the analysis of Hongqi et al., 19 the peak current of auxiliary inductor i a À max can be expressed as follow.
Under extremely light load conditions, the function of the auxiliary current is to complete the charging and discharging of the lag arm capacitance within the dead time, which needs to meet the following formula.
It can be obtained by simultaneous equations ( 29) and (30), and the auxiliary inductance needs to meet the following formula.
Ignoring the influence of the external capacitance on the auxiliary inductance, the upper formula can be simplified to the lower one.
Auxiliary capacitance.In the charging and discharging process of the lag arm, the auxiliary capacitors C a1 and C a2 are used as voltage sources.In order to ensure relatively stable voltage in this process, the oscillation period of the auxiliary circuit should be maintained at more than five times of the charging and discharging time, 24 which needs to meet the following formula.
where, C a is the value of C a1 and C a2 .

Simulation verification
This paper used ANSYS Simplorer to simulate the circuit designed.According to the actual situation of the suspension chopper, FF300R12KT3 type IGBT is selected.Other parameters are set as Table 1.
The simulation waveform of the load and VT1 of the traditional hard-switch suspension chopper are shown in Figures 13 and 14.The control signal setting  It can be seen from Figure 13 that the current increases when VT1(VT4) is on, and decreases when VT1(VT4) is off.In the moment of IGBT switching, the voltage of load oscillates violently under the action of stray inductance due to the large current change rate.The voltage spike of load reaches 944 V and the overshoot is 114.5%, which greatly exceeds the supply voltage.Figure 14 shows that when IGBT is switched off, the voltage spike of VT1 collector is about 926 V and the overshoot is 110.5%.
It can be seen from Figure 16 that the load current increases when VT1 and VT4 are connected together, the current remains constant When there is only one conduction, and the current decreases when both are turned off together.The current fluctuates at 0 due to the duty cycle of VT1 is set to be 50% in the simulation.The voltage spike of load is 648 V and the overshoot is 47.3% when VT4 is turn on.Compared to hard-switch suspension chopper, the peak drop rate is 68.2%.
Figure 17 shows that due to the switching cross-talk of VT4, there are two oscillations in the switching process of VT1, but the voltage spike of VT1 is about 695 V, which is 58% higher than the supply voltage overshoot, and the voltage spike is reduced by 52.5% when compared with the hard-switch suspension chopper.

Experimental verification
In order to test the suppression of voltage spikes by PSFB, a suspension chopper experimental verification platform is built, as shown in Figure 18.
Since the voltage spike and the supply voltage are approximately linear when the voltage spike does not exceed the short-circuit voltage of the switching tube, the power supply is set at a low potential level for experimental safety.Set the supply voltage U DC = 24V, the corresponding value L a = 78mH, C a = 12nF, and other parameters are consistent with the simulation parameters.
The experimental results of hard-switch suspension chopper are shown in Figures 19 and 20       Based on the principle and experimental results of the designed circuit, it can be seen that compared with the suppression methods such as adding RCD circuit absorption or using clamp circuit, which are often used in engineering, the PSFB circuit has great advantages.First of all, and most importantly, the PSFB circuit can reduce the voltage spikes from about 200% to about 40%, and the suppression effect has been greatly improved.Secondly, the common methods need to add RCD absorption circuit or clamping circuit to each IGBT.In comparison, the PSFB circuit only needs one auxiliary circuit and several parallel capacitors, and fewer components are used.Finally, the main circuit switch still uses the hard-switch mode when the aforementioned methods are used, and its switching loss is very large.However, the main switch of the PSFB circuit is the soft-switch mode, which can effectively reduce the energy loss while suppressing the voltage spikes.
Furthermore, in order to test the influence of component parameters on the performance of the PSFB circuit, experiments were performed on different values of the parallel capacitance, auxiliary inductance and auxiliary capacitance of the suspension chopper.The results are shown in Tables 2-4.
Table 2 shows that with the increase of parallel capacitance, the voltage of spikes load is almost constant, and the voltage spikes of VT1 has a small fluctuation.
Table 3 shows that with the increase of the auxiliary inductance, the voltage spikes of the load and VT1 are almost unchanged.
Table 4 shows that the voltage spikes of load and VT1 decrease slightly as the auxiliary capacitance increases.
It can be seen from the above results that the PSFB circuit can always suppress the voltage spikes at lower positions as the component parameters change.That is to say, the effect of the PSFB circuit is not sensitive to the value of the added components, which is very conducive to the selection of circuit components, and also makes the circuit always have a good effect even when

Conclusion
Aiming at the problem that the hard-switch suspension chopper in high-speed maglev train has large voltage spikes of load and IGBT, this paper proposes the PSFB suspension chopper.It only adds one auxiliary circuit and four parallel capacitors, using phase-shift control signals to make the four IGBT tubes achieve soft-switch sequential, which effectively reduces the voltage spikes.
Compared with the commonly used suppression methods such as adding RCD circuit to absorb or using clamping circuit, the PSFB circuit also has the advantages of using fewer components, effectively reducing energy loss and small influence of component parameters change on the suppression effect.The simulation and experimental results verify that the PSFB suspension chopper can reduce the voltage spikes of the load and IGBT to a lower value.Therefore, the PSFB circuit designed in this paper can provide a good reference for improving the suspension chopper system of high-speed maglev train.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
, where VT1 and VT2 constitute the lead arm, VT3 and VT4 constitute the lag arm.C1;C4 are capacitors in parallel with switch tubes, where C1 and C2, C3, and C4 have the same values.Auxiliary circuit composed of C a1 , C a2 , L a , D5, and D6, where C a1 and C a2 have the same value.The two switches of each arm are complementary to each other and leave a certain dead zone.There is a phase angle difference between the two arms.By adjusting the duty cycle of PWM control waveform and phase angle, the output voltage of load can be adjusted.The control signals, load voltage, and current waveform of the PSFB suspension chopper are shown in Figure 4, and the current flow of modals are shown in Figures 5-12 .

( 1 )
Before time t 0 , VT1 and VT4 are the conduction state, the voltage of C1 and C4 are 0. VT2 and VT3 are the cut-off state, the voltage of C2 and
. The red and green curves in the simulation results are the voltage and current of the load or VT1 respectively, the blue and brown curves are the drive signals of VT1 and VT4 respectively.
, and the experimental results of PSFB suspension chopper are shown in Figures21 and 22 . The yellow curve is the voltage of

Table 1 .
Parameters setting table for simulation.
of switch tubes for PSFB suspension chopper is shown in Figure15, and the waveform simulation results of load and VT1 are shown in Figures16 and 17

Table 3 .
Voltage spikes for different auxiliary inductors.

Table 4 .
Voltage spikes for different auxiliary capacitors.

Table 2 .
Voltage spikes for different parallel capacitors.