Research on Commutation and Coordination Control

energies Article

Research on Commutation and Coordination Control Strategy of Excitation Power Supply Based on Bidirectional Reduced Matrix Converter for Ion Accelerator Weizhang Song 1,2, *, Jiang Liu 1 , Xiangdong Sun 1 , Fenjun Wu 2 , Daqing Gao 2 and Youyun Wang 3 1 2 3

*

School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi, China; [email protected] (J.L.); [email protected] (X.S.) Institute of Modern Physics Chinese Academy of Sciences, Lanzhou 730000, China; [email protected] (F.W.); [email protected] (D.G.) State Key Laboratory of Large Electric Drive System and Equipment Technology, Tianshui, Gansu 741020, China; [email protected] Correspondence: [email protected]; Tel.: +86-150-290-29031

Received: 28 October 2018; Accepted: 26 November 2018; Published: 4 December 2018







Abstract: The contribution of this paper is putting forward a kind of ion accelerator magnet excitation power supply with bidirectional reduced matrix converter (BRMC) as well as a coordination control strategy with bipolar current space vector modulation strategy, which is utilized to realize bidirectional power flow for a BRMC system to solve problems such as low input power factor, large input current harmonics and no bidirectional energy in the conventional ion accelerator magnet excitation power supply. Meanwhile, a hybrid commutation strategy combining the simplified three-step commutation with zero vector commutation was proposed to solve the commutation problem for a matrix-type first stage in BRMC. The feasibility and effectiveness of the proposed strategy, which can achieve bidirectional energy flow and safer commutation, have been verified by the experimental results. Keywords: bidirectional reduced matrix converter; coordinated control strategy; hybrid commutation strategy; ion accelerator excitation power supply

1. Introduction Ion accelerators have been widely used in scientific research, medicine, aerospace, military and other fields. The output power range of accelerator magnet excitation power supplies ranges from several thousand watts to megawatts. Ion accelerator has broad application prospects in engineering physics and medical field, for which the key device is the excitation power supply. The new accelerator proposes higher criteria requirement for excitation power such as energy bidirectional flow, energy saving characteristics, sinusoidal input current, unit power factor and grid green pollution-free. Therefore, it is imperative to find a “green” and energy-saving excitation power supply with high regulation accuracy and fast dynamic response in order to solve the above-mentioned problems. The conventional topology used for this excitation power supplies are mainly Buck DC chopper converter, H bridge DC chopper topology, multi pulse rectifier and so on [1–4]. However, conventional ion accelerator magnet excitation power supplies have some disadvantages. These include low power factor, large harmonic pollution and the energy not being able tobe recovered [5,6]. At the same time, this kind of accelerator requires that the power supply have the function of energy feedback

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which can reclaim excess energy in the magnet to the grid. Then a “green” power supply with high power factor, sinusoidal input current and the function of energy feedback to overcome these aforementioned problems is necessary. Reference [7] proposed a dipole magnet power supply which can convert AC into DC based on phase-controlled rectifier with thyristor-technology. However, the problems of low power factor, large volume and low energy conversion efficiency still exist. Reference [8] proposed a multilevel voltage type rectifier + half bridge inverter + voltage doublers rectifier topology with great improvements on grid side performance, but this topology also has the disadvantages of more converter stages with low efficiency and complex close-loop control. In addition, these conventional excitation power supplies cannot realize bidirectional power flow. BRMC evolving from matrix converter (MC) is a new-type power electronic converters topology. Reference [9,10] indicated that Reduced Matrix Converter (RMC) system had excellent input and output performance involving unit power factor and sinusoidal input current; and it can achieve less conversion stage and higher power density. Therefore, the BRMC system is used as the magnet excitation power supply for ion accelerator in this paper. Meanwhile the paper also proposes a coordination control strategy with bipolar current space vector modulation strategy to realize bidirectional power flow without complex close-loop control and extra hardware circuits. It is known that commutation should be achieved without causing short circuits for the input phases and open circuits for the inductive load current, which will cause over current and voltage to destroy the devices in a matrix-type matrix. Reference [11] proposed a four-step commutation method based on the direction of output current. However, this method will cause the problem of commutation failure and short circuits when the direction information of small currents is wrongly judged. Reference [12] proposed a four-step commutation method based on input voltage of relative size, however, the disadvantages of this method are that the requirement of the voltage detection device is high, temperature drift and zero drift of the detection device can easily cause judgment mistakes, and a short-circuit would occur if there is a voltage reversal during the commutation. There are also other commutation strategies as presented in papers such as references [13,14]. But this paper puts forward a new hybrid commutation strategy combining simplified three-step commutation with zero vector commutation to solve an important problem for the reliable and safe operation of BRMC. The contribution of this paper is the proposition of a BRMC excitation power topology with bidirectional energy flow and its coordinated control method according to the requirement of the accelerator performance and the variation law of the exciting current. Meanwhile, in order to improve the reliability of BRMC, a more appropriate hybrid commutation strategy combining simplified three-step commutation with zero vector commutation is proposed according to the characteristics of BRMC modulation strategy and the actual situation of the load. Finally, an experimental prototype based on DSP + CPLD was built to verify the effectiveness of the proposed methods. This article is divided into 7 parts as follows: Section 1 gives a general account of the research background and problems that need to be solved. This paper outlines the improvements it makes on the basis of existing theories. Section 2 compares the proposed topology with the existing ones. Meanwhile, it highlights the advantages of BRMC, which is more suitable for ion accelerator power supplies. Section 3 introduces the coordinated modulation strategy presented in detail in this paper. It includes the B-C-SVM for the front stage and the coordination strategy of the latter stage to achieve bidirectional energy flow. Section 4 introduces the new hybrid commutation proposed in this paper. Sections 5 and 6 are to verify the effectiveness of the methods proposed in this paper and the experimental waveforms strongly proved their correctness. Section 7 is the conclusion of this paper. 2. Topology of BRMC There are two kinds of AC/DC converter topologies which can meet the aforementioned requirements for ion accelerator magnet excitation power supplies. One is the conventional converter consisting of PWM Rectifier Bridge + Dual Active Bridge (PRB-DAB) as shown in Figure 1a. Its schematic

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converter stage, a high frequency transformer and a controlled rectifier bridge. Comparing Figure 1b diagram2b, flow to is shown in Figure 1b. the The converter is the topology of BRMC as shown in Figure with Figure it is easy determine that stage can efficiently reduce the2a, three converter stage,ofa power high frequency transformer andother a controlled rectifier bridge. Comparing Figurestages 1b whose schematic diagram is shown in Figure 2b. It consists of three parts: a matrix converter stage, in PRB-DAB two stages in BRMC.that the converter stage can efficiently reduce the three stages with Figure 2b, to it is easy to determine a high frequency transformer and a controlled rectifier bridge. Comparing Figure 1b with Figure 2b,

in PRB-DAB to two stages in BRMC. it is easy to determine that the converter stage can efficiently reduce the three stages in PRB-DAB to two stages in BRMC.

(a) (a)

(b) (b) Figure 1. Conventional AC-DC converter:(a) Topology; (b) Schematic diagram. 1. Conventional AC-DC converter:(a) Topology; (b) (b) Schematic diagram. Figure Figure 1. Conventional AC-DC converter:(a) Topology; Schematic diagram.

(a) (a)

(b) Figure 2. Bidirectional reduced matrix(b) converter:(a) Topology; (b) Schematic diagram.

Figure 2. Bidirectional reduced matrix converter:(a) Topology; (b) Schematic diagram.

Comparing the two topologies, it can be found that BRMC leaves out the intermediate full Figure 2. Bidirectional matrix converter:(a) Topology; bridge inverter with energy reduced storage capacitor. Moreover, BRMC has lots(b) of Schematic advantagesdiagram. such as high Comparing the two topologies, it can be found that BRMC leaves out the intermediate efficiency and power density, electrical isolation, low cost and voltage regulation using a high-frequency full bridge inverter with the energy storage Moreover, BRMC has lots of advantages such as high transformer with small volumecapacitor. and low cost. Some results of the comparative of these two Comparing two topologies, it can be found that BRMC leaves out evaluation the intermediate full bridge topologies are compiled in Table 1. efficiency power density, electrical isolation, BRMC low cost regulationsuch using highinverter withand energy storage capacitor. Moreover, hasand lotsvoltage of advantages as ahigh

frequency transformer with small volume and low cost. Some of regulation the comparative efficiency and power density, electrical isolation, low cost andresults voltage using evaluation a highof these transformer two topologies aresmall compiled in Table 1. cost. Some results of the comparative evaluation frequency with volume and low of these two topologies are compiled in Table 1.

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Table 1. Comparisons of two topologies. Comparison Index

PRB-DAB

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High-frequency transformer Yes Power density Normal Table 1. Comparisons of two topologies. Converter stage 3 Comparison PRB-DAB Efficiency Index Normal Lifetimetransformer Normal High-frequency Yes Power density

BRMC Yes High 2 BRMC High Long Yes

Normal

3. Coordinated Control Strategy Converter for BRMC stage

High

3

controlEfficiency strategy

toNormal meet

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2 High performance

The BRMC coordinated is designed the requirement of ion Lifetime Normal accelerator magnet citation power supplies. The strategy of the BRMCLong rectifier stage adopts bipolar current space vector modulation (B-C-SVM), and its function is to convert three-phase alternating 3. Coordinated Control Strategy for BRMC current into a symmetrical and periodic square wave [15]. The latter controlled rectifier bridge should The with BRMCthe coordinated strategy designed to meet the performance requirement be synchronized BRMC control rectifier stageisto achieve bidirectional power flow. of ion accelerator magnet citation power supplies. The strategy of the BRMC rectifier stage adopts bipolar current vector modulation (B-C-SVM), and its function is to convert three-phase alternating 3.1. B-C-SVM forspace the BRMC Rectifier Stage current into a symmetrical and periodic square wave [15]. The latter controlled rectifier bridge should

bedivision synchronized with the BRMC rectifier in stage to achieve bidirectional power flow. Sector of B-C-SVM is shown Figure 3. The input voltages are divided into 6 sectors. In each sector, the mode of the phase with maximum amplitude is a constant, and the other two 3.1. B-C-SVM for the BRMC Rectifier Stage phases are modulated. In a conventional current source converter, two adjacent active vectors and Sector division of B-C-SVM is shown in Figure 3. The input voltages are divided into 6 sectors. one zero vector are enough to generate the desired output current. But for BRMC, it is necessary to In each sector, the mode of the phase with maximum amplitude is a constant, and the other two generate not onlyarethe desired three phase input current but also thetwo desired output wave current. phases modulated. In a conventional current source converter, adjacent active square vectors and one zero at vector arefive enough to generate the desired output current.vectors But for BRMC, it is necessary to In consequence, least vectors are needed: two adjacent to generate the positive part generate not only the desired three phase input current but also the desired output square wave of Iout ; two opposite vectors to generate the negative part of Iout and a zero vector to complete the current. In consequence, at least five vectors are needed: two adjacent vectors to generate the positive array [16,17]. Take the first sector as an example. Active vectors Iab ,aIzero zero vector Iaa composite ac and part of Iout; two opposite vectors to generate the negative part of Iout and vector to complete the vector Iref array in the first half switching period; Active vectors I , I and zero Iaa composite ca zero vector vector [16,17]. Take the first sector as an example. Active vectors Iabba , Iac and Iaa composite vector I ref in the first half switching period; Active vectors I ba , I ca and zero vector I aa composite vector vector −Iref in another first half period of switching period. The vector diagram is shown in Figure 4. ref in another first half period of switching period. The vector diagram is shown in Figure 4. Vector Vector Iref −I and −Iref have the same amplitude, but opposite direction and actuation duration (half the Iref and −Iref have the same amplitude, but opposite direction and actuation duration (half the switching switchingperiod). period).

Figure 3. Division of of input sectors. Energies 2018, 11, x FOR PEER REVIEW Figure 3. Division inputvoltage voltage sectors.

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dδ θin

dγ

Figure Space vector vector diagram. Figure 4. 4.Space diagram.

Suppose the three-phase input voltages are as follows:

usa = Ui cos(ωit )   usb = Ui cos(ωit − 2π 3)  u = U cos(ω t + 2π 3) i i  sc

(1)

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Suppose the three-phase input voltages are as follows:    usa = Ui cos(ωi t) usb = Ui cos(ωi t − 2π/3)   u = U cos(ω t + 2π/3) sc i i

(1)

where Ui is the phase voltage of grid side and ω i is the angular frequency of phase voltage. In order to get unit power factor on grid side, the phase current of grid side can be expressed as: 

   isa cos ωi t     is =  isb  = Iin  cos(ωi t − 2π/3)  isc cos(ωi t + 2π/3)

(2)

where Iin is the phase current amplitude on grid side. The reference current is composed by vectors (Iab, Iac and Iaa ) in first sector at the positive half period of the current. According to the rule of space vector synthesis shown in Figure 4, the action time of each vector can be derived as follows:  Ts   t x = ms sin(π/3 − θin ) 2 (3) ty = ms sin(θin ) T2s   t = (1 − d − d ) Ts γ 0 δ 2 Therefore, the duty cycle of each vector can be derived as:  2   dα = Ts tα = ms sin(π/3 − θin ) d β = T2 t β = ms sin(θin )   d = 1 s− d − d α 0 β

(4)

where ms is the modulation index and θ in is the angle of the oriented current vector. In order to obtain the unity power factor and considering that the phase error between the three-phase reference input current and the three-phase voltage is zero; θ in can be obtained in the first sector as: θin = ωi t + π/6 (5) It can be obtained from Equation (5) to (4) that:    dα = −ms cos(ωi t − 2π/3) d β = −ms cos(ωi t + 2π/3)   d = 1 − m cos(ω ) s 0 i

(6)

In order to facilitate calculation, the three-phase reference input phase current is defined as:    isa = cos(ωi t) isb = cos[(ωi t − 2π/3)]   i = cos[(ω t + 2π/3)] sc i

(7)

According to Equations (6)–(8), the duty cycle of the first sector can be calculated as:  d x = T2 t x = −ms isb     d = 2s t = −m i y s sc Ts y     d0 = 1 − d x − dy = 1 − ms isa

(8)

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The duty cycle formulas of the other 5 sectors are shown in Table 2. The output voltage in BRMC is the current in the high frequency transformer. In this case, the polarity of the adjacent vectors is changed to achieve square waveform. The effect brought by the alternation of this switching signal is compensated by the full bridge. Table 2. Duty cycle of each sector. Sectors

dx

dy

d0

1 2 3 4 5 6

−ms isb ms isa −ms isc ms isb −ms isa ms isc

−ms isc ms isb −ms isa ms isc −ms isb ms isa

1 − ms isa 1 + ms isc 1 − ms isb 1 + ms isa 1 − ms isc 1 + ms isb

Figure 5 shows the operating modes of BRMC rectifier stage when the active vectors work in the first sector. As aforementioned, one period is split into two equal periods. The primary voltage of the transformer is positive when Sap is normally turned on and is negative when San is normally turned on in the first sector. In the positive half period, the primary voltage of transformer is Uab as shown in Energies 2018, 11, x FOR PEER REVIEW 7 of 24 Figure 6, when the current operating mode is Uab as shown in Figure 5a. Similarly, the next primary voltages transformer are U and And they correspond to mode of Uac andUmode aa , respectively. switch Sanofnormally turned onac in theUnegative half period. The primary transformer voltages ,U Energies 2018, 11, x FOR PEER REVIEW 7 ofba24 ca of Uaa There is the in same form of the primary transformer voltage when the and UaaininFigure Figure5,6respectively. correspond to the mode Figure 5d–f, respectively. switch turnedon onininthe thenegative negative half period. primary transformer voltages switchSan Sannormally normally turned half period. TheThe primary transformer voltages Uba, UcaUba , Uca and in Figure 6 correspond to mode the mode in Figure respectively. aa Figure and UaaUin 6 correspond to the in Figure 5d–f,5d–f, respectively.

(a)

(b)

(a)

(b)

Lf Sap Sbp Scp

RL

Uca

LL

Lf

San Sbn Scn Uca Cf

(d)

(c)

Sap Sbp Scp Usa Usb Usc Usa Usb Usc

(d)

(c)

Cf

RL LL

San Sbn Scn

(e) (e)

(f) (f)

Figure 5. Operating mode of BRMC rectifier stage in the first sector (a) Mode of Uab; (b) Mode of Uac; Figure 5. Operating mode of BRMC rectifier stage in the first sector (a) Mode of Uab ; (b) Mode of Uac ; ba; (e) Mode ofstage Uca; (f) ofsector Uaa. (a) Mode of Uab; (b) Mode of Uac; (c)Figure Mode5.ofOperating Uaa; (d) Mode modeofofUBRMC rectifier in Mode the first (c) Mode of Uaa ; (d) Mode of Uba ; (e) Mode of Uca ; (f) Mode of Uaa . (c) Mode of Uaa; (d) Mode of Uba; (e) Mode of Uca; (f) Mode of Uaa.

Figure 6. Sequence diagram of BRMC output voltage. Figure 6. Sequence diagram of BRMC output voltage.

3.2. CoordinationStrategy of Controlled Rectifier Bridge 3.2. CoordinationStrategy of Controlled Rectifier Bridge Considering of the particularity of BRMC topology and the bidirectional power flow of the Considering of the particularity of BRMC topology and the bidirectional power flow of the magnet controlledrectifier rectifierbridge bridgeare aredifferent different energy forward magnetload, load,the thecontrol controlsignals signals of of the the controlled in in thethe energy forward

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3.2. CoordinationStrategy of Controlled Rectifier Bridge Considering of the particularity of BRMC topology and the bidirectional power flow of the magnet load, the control signals of the controlled rectifier bridge are different in the energy forward mode and the energy feedback mode. 3.2.1. Energy Forward Mode The principle waveforms of energy forward mode and energy feedback mode in the first sector are shown in Figure 7. The waveforms belong to three-phase voltage, switching state of the BRMC rectifier stage, primary voltage of transformer UPN , primary current of transformer IPN , drive signals of IGBT S1 and S4 , drive signals of IGBT S2 and S3 , output voltage U0 and output current I0 repectively. In the first sector, the control signals of the BRMC rectifier stage follow the upper part of the B-C-SVM. The primary voltage of the transformer is positive and the primary side current of the transformer is in phase with the voltage when switch Sap is normally turned on and Sbn , Scn , San are sequentially turned on in the phase A. Then the primary voltage of the transformer is negative and the primary side current of the transformer is in phase with the voltage when switch San is normally turned on and then Sbp , Scp , Sap are sequentially turned on with the opposite active vector. All other control signals of the controlled rectifier bridge are closed. Energies 2018, 11, x FOR PEER REVIEW

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ua ub uc u t

0

1

Sap

t

0 1

Sbn

t

0

Scn

1 0

San

t

1

t

0

Sbp1 t

0

Scp

1

t

0

UPN t

0

The primary current of transformer in energy forward mode

IPN 0

Switch signal

t

The primary current of transformer in energy feedback mode

1 0

t

0

t

0

t

S1 1 (S4) S2 1 (S3) U0 0

I0

The output current in energy forward mode

0

-I0

t t

The output current in energy feedback mode

Figure 7. 7. Principle of two twodifferent differentmodes modes in the sector. Figure Principlewaveforms waveforms of in the firstfirst sector.

As shown in Figure 8a, the input voltage and current present unit power factor and the output voltage and current are both positive. The system works in energy forward mode.

0

t

The output current in energy forward mode

I0

0

t

-I0

The output current in energy feedback mode

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Figure 7. Principle waveforms of two different modes in the first sector.

AsAs shown in Figure 8a,8a, thethe input voltage andand current present unit power factor andand thethe output shown in Figure input voltage current present unit power factor output voltage and current are both positive. The system works in energy forward mode. voltage and current are both positive. The system works in energy forward mode.

(a)

(b)

Figure 8. Voltage and current of input and output(a) Energy forward mode; (b) Energy feedback mode. Figure 8. Voltage and current of input and output(a) Energy forward mode; (b) Energy feedback 3.2.2. Energy mode. Feedback Mode

The symmetrical and periodic square wave signal of the BRMC first stage output is shown in Figure 5. The drive signals of the second stage of BRMC need to be coordinated with the output voltage signal of the first stage to realize the energy feedback function in feedback mode. Figure 7 shows the three-phase voltage in the first sector, switching state of the BRMC rectifier stage, primary voltage of transformer UPN , primary current of transformer IPN , drive signals of IGBT S1 and S4 , drive signals of IGBT S2 and S3 , output voltage U0 and output current I0 respectively. In energy feedback mode, the drive signals of the BRMC rectifier stage are the same as those in energy forward transmission mode. When the switching signal is turned on, switch tubes S1 and S4 turn on, and switch S2 and S3 turn off when the switching signal is turned off. Thus, the voltage and current of the primary side of the transformer are reversed, the output voltage is positive, the output current is negative, and the energy feedback is realized. As shown in Figure 8b, the input voltage and current present the opposite phase and the output voltage and current are positive and negative, respectively. The system is in energy feedback mode. The specific conduction rule of the switches is shown in Table 3. Table 3. Modulation rule of the positive primary voltage of the transformer. Normally Opened Switch

Sequential Switch

UPN

Switches of Controlled Rectifier Bridge

Energy forward

Sap

Sbn , Scn , San

uab , uac , uaa

S1 , S4

Energy feedback

San

Sbp , Scp , Sap

uba , uca , uaa

S2 , S3

Energy forward

Scn

Sap , Sbp , Scp

uac , ubc , ucc

S1 , S4

Energy feedback

Scp

San , Sbn , Scn

uca , ucb , ucc

S2 , S3

Energy forward

Sbp

Scn , San , Sbn

ubc , uba , ubb

S1 , S4

Energy feedback

Sbn

Scp , Sap , Sbp

ucb , uab , ubb

S2 , S3

Energy forward

San

Sbp , Scp , Sap

uba , uca , uaa

S1 , S4

Energy feedback

Sap

Sbn , Scn , San

uab , uac , uaa

S2 , S3

Energy forward

Scp

San , Sbn , Scn

uca , ucb , ucc

S1 , S4

Energy feedback

Scn

Sap , Sbp , Scp

uac , ubc , ucc

S2 , S3

Energy forward

Sbn

Scp , Sap , Sbp

ucb , uab , ubb

S1 , S4

Energy feedback

Sbp

Scn , San , Sbn

ubc , uba , ubb

S2 , S3

Sector 1

2

3

4

5

6

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The aforementioned control of switches (S1 , S2 , S3 and S4 ) is only related to the polarity of transformer primary voltage. As shown in Figure 6a, the positive transformer primary voltage is Uab in energy forward transmission mode. Also, the current flows through the parallel diode of this switch for the controlled rectifier bridge. So, S1 and S4 are opened as shown in Figure 6 when the system is in energy feedback mode. Current flows through the IGBT of the second stage of BRMC. Similarly, the negative transformer primary voltage is Uba shown in Figure 5d in energy forward transmission mode and S2 and S3 are opened energy Energies 2018, 11,inx FOR PEERfeedback REVIEW mode. Figure 9 shows two new operating modes under different 10 of 24 transformer primary voltage operating conditions.

(a)

(b)

Figure 9. Operating mode of BRMC in energy feedback mode: (a) Positive transformer primary voltage; Figure 9. Operating modeprimary of BRMC in energy feedback mode: (a) Positive transformer primary (b) Negative transformer voltage. voltage; (b) Negative transformer primary voltage.

3.2.3. Comparison between the Proposed Method and the Other Methods 3.2.3. Comparison between the Proposed Method and the Other Methods Reference [18] presented a bidirectional power flow control method based on two loops mode Reference [18] presented a bidirectional power control method basedbi-directional on two loopsDC-DC mode switching according to different duty cycle ratio for flow an interleaved three-level switching to different cycle ratio for ansystem, interleaved three-level bi-directional converter according for an application induty the energy storage but the regulator parametersDC-DC of two converter for be an the application the energy storage system, but the regulator parameters of two loops must same toinensure smoothly switching of power flow direction, which is loops at the must beperformance. the same to Reference ensure smoothly switching of power direction, which is atmethod the costwith of cost of [19] presented a voltage and flow current regulation control performance. Reference [19] a voltage and flow current regulation control method with afed twoa two-mode conversion for presented a bi-directional power solution in energy storage system by mode conversion for a bi-directional power flow solution in energy storage system fed by isolated AC-DC matrix converter, this bi-directional power flow function is realized byisolated using a AC-DC matrix converter, bi-directional function is realized using a closed mode mode conversion betweenthis a set-current and power DC-linkflow voltage control based onby a complex conversion between a set-currentcontrol and DC-link voltage control based on a complex closed loop system. loop system. The coordination is adopted in this paper for BRMC to make the energy flow in The control inisFigure adopted in thiscan paper for BRMC to make the energy flowaccording in both bothcoordination directions as shown 10, which be flexible switching between two modes directions as shown in energy Figure 10, which can be flexible switching between two modes to to the magnetic field requirements of the ion accelerator. It not only ensuresaccording the normal the magnetic field energy but requirements thethe ioninput accelerator. It not only ensures the normal operation of the accelerator, also ensuresofthat current harmonic is still small, which meets operation of the accelerator, butgrid. also ensures that the current harmonic still small, which the requirements of the power Furthermore, theinput proposed method can is realize bidirectional meets ofwithout the power grid. performance Furthermore,orthe proposed method can realize power the flowrequirements to save energy sacrificing adding complex close-loop control bidirectional power flow to save energy without sacrificing performance or adding closecompared with reference [18,19]. Moreover, this strategy is simple to implement, and complex is more reliable loop control application. compared with reference [18,19]. Moreover, this strategy is simple to implement, and is in practical more reliable in practical application.

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dδ θin

dγ

Figure The diagram coordinated control strategy. Figure 10.10. The diagram of of coordinated control strategy.

Hybrid Commutation Strategy BRMC 4. 4. Hybrid Commutation Strategy ofof BRMC Since BRMC evolved the basis the conventional matrix converter (MC), both them Since BRMC is is evolved onon the basis ofof the conventional matrix converter (MC), both ofof them follow the same commutation constraints, that is, the load cannot be in an open circuit due follow the same commutation constraints, that is, the load cannot be in an open circuit due toto itsits inductive nature and input phase cannot be in a short circuit. According to the B-C-SVM above, inductive nature and input phase cannot be in a short circuit. According to the B-C-SVM above, the the commutation problem andexchange the exchange of positive negative current vector both cause commutation problem and the of positive andand negative current vector cancan both cause voltage spike. Such as, one of the key technologies of BRMC is to ensure the safe commutation voltage spike. Such as, one of the key technologies of BRMC is to ensure the safe commutation forfor bidirectional switches realize stability input and output output BRMC rectifier bidirectional switches toto realize thethe stability ofof input and output asas thethe output of of thethe BRMC rectifier stage is high frequency AC symmetrical pulse and the current direction switch is very fast. Aiming stage is high frequency AC symmetrical pulse and the current direction switch is very fast. Aiming at the four-step four-step commutation commutationstrategy strategyofofvoltage voltageand andcurrent currentis is also at BRMC BRMC commutation commutation problems, problems, the also analyzed and improved. Then a hybrid commutation strategy combining three-step commutation analyzed and improved. Then a hybrid commutation strategy combining three-step commutation with zero vectors is proposed. with zero vectors is proposed. The BRMC topology adopts B-C-SVM strategy, and the positive and negative direction the The BRMC topology adopts B-C-SVM strategy, and the positive and negative direction ofof the primary side current of the transformer can be obtained by the current polarity switching signal, so primary side current of the transformer can be obtained by the current polarity switching signal, sothe current Comparedwith withthe thecurrent currentfour-step four-step commutation, the currentdirection directiondoesn’t doesn’tneed needto to be be detected. detected. Compared commutation, avoids the risk small current detection failure, ensures safety commutation process, it it avoids the risk ofof small current detection failure, ensures thethe safety of of thethe commutation process, and improves the reliable operation of BRMC. Considering that the turn-off time of the IGBT much and improves the reliable operation of BRMC. Considering that the turn-off time of the IGBT is is much longer than the turn-on time in practice, the two steps of the four-step commutation can be merged into longer than the turn-on time in practice, the two steps of the four-step commutation can be merged oneone step,step, which will reduce the time of the commutation and form aand three-step into which will reduce theinterval time interval of the commutation form acommutation. three-step Suppose that the S is normally turn-on, the current is switched from B to C, and ap that the Sap is normally turn-on, the current is switched from the commutation. Suppose B tocommutation C, and the process is shown inisFigure as shown Sbn+ represents the lower commutation process shown11. in Where Figure 11. Where in as Figure shown 12, in Figure 12, Sbn+ represents theswitch lowerof the B bridge arm bidirectional switch S and S represents the upper switch of the B bridge arm bn bn − switch of the B bridge arm bidirectional switch Sbn and Sbn− represents the upper switch of the B bridge bidirectional switch S . arm bidirectional switchbnSbn.

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12 of 24 11of of 24 21 12

(a) (a)

(b) (b)

Figure11. 11.Commutation Commutationprocess: process:(a) (a)Positive Positiveprocess; process;(b) (b)Negative Negativeprocess. process. Figure Figure 11. Commutation process: (a) Positive process; (b) Negative process.

Figure Figure12. 12. Topology Topologyof ofcommutation. commutation. Figure 12. Topology of commutation.

With above-mentioned commutation logic relation between the two phases, the commutation Withthethe above-mentioned commutation logic relation between the two phases, the processes of each phase can be deduced as in Figure 13. In each switching period, there is one normally With the above-mentioned commutation logic relation between the two phases, the commutation processes of each phase can be deduced as in Figure 13. In each switching period, there opened switch with three switches u u and u opened in turn at the contrary bridge arm. The commutation processes each phase cansbbe deduced Figure 13. In each switching period,bridge there6 sa, sc usa,as is one normally openedof switch with three switches usbin and usc opened in turn at the contrary bits shown Figure 12switch represent three sequential switch For example, Sap normally is one normally opened with three switches usa, usb andtubes. usc opened in turnFor at when the contrary bridge arm. The 6 in bits shown in Figure 12 represent three sequential switch tubes. example, when Sap turns on, 6 bits represent the switch state of S , S and S . Its order is S -S -S -S -S -S . arm. The 6 bits shown in Figure 12 represent three sequential switch tubes. For example, when S apan state an− cn+ cncn+ − bn of Sancn bn+ bn-S −bn+-S normally turns on, 6 bits represent the switch , Sbn and Scn. Itsan+ order is San+ -San− bn−-S 1normally represents that the corresponding switch is and turn turn turns on,that 6 bits thebidirectional switch state of Sswitch an, Sbn Scnon, . on, Itsand order isrepresents San+-San−-Sthe bn+-S bn−-Soff. cn+ Scn− . 1 represents therepresent corresponding bidirectional is turn and0 0represents the turn off. Take process as anan example, Sap+ and Sap are always turn-on. The 6-digit S cn−. 1the represents thatinthe corresponding bidirectional switch is turn on, 0 represents turn off. − Take thefirst firstsector sector inpositive positive process as example, Sap+ and Sap− areand always turn-on.the The 6-digit number state -S -Sbn+ -Scn− -S inItturn. It means San+ Take therepresents first sectorthe in switching positive process an-S example, S-Sap+ Sap− are turn-on. 6-digit an-S −bn+ cn+ cn −always bnand −-S number represents the switching state of ofasS San+ an+ an− -Sbn− -S cn+ in turn. means that The San+that and Sanand are turned-on and others are that Sbn+ and are number switching stateturned-off. of Similarly, San+-San−Similarly, -Sbn+ -Sbn−-S00-11-00 cn+represents -Scn− inrepresents turn. It means that Sare an+Sand anan- represents −S bn are S turned-on and the others are turned-off. 00-11-00 that Sbn+ and Sbn− turnedturned-on and others are turned-off. So the process of u converting to u is divided into three step. are turned-on and others are turned-off. Similarly, 00-11-00 represents that S bn+ and S bn− are turnedsa sb on and others are turned-off. So the process of usa converting to usb is divided into three step. The first The first step isare closing the SanThe Thestep second step is opening the and closing on and turned-off. So the process ofisuopening sa converting sb is Sdivided into three step.San+ Thedrive. first − drive. bn+ step is others closing the San− drive. second the Sto bn+udrive anddrive closing San+ drive. The third The step the is the opening theThe SThe drive. The process 110000 to 100000, thenand to 001000, step isisclosing San− drive. second iswhole opening the Sis bn+from drive and closing drive. The third bn− stepthird opening Sbn− drive. wholestep process is from 110000 to 100000, then toSan+ 001000, finally and finally to 001100. step is opening the Sbn− drive. The whole process is from 110000 to 100000, then to 001000, and finally to 001100. There are two types of transformer primary voltage spikes. One is “big spike” caused by currents to 001100. switching from one bridge arm to another bridge arm in the same pole vector. The other is “small spike” caused by current switching from positive to negative in one cycle. The three-step commutation can guarantee commutation safety of the same pole vector. But it has nothing to do with the big spike. The current has a large amount of changes from positive to negative. Therefore, in this paper, the zero vector commutation is proposed to ensure the safety commutation at current switch-over point between positive and negative currents. As shown in Figure 14a, the big spike of the transformer primary voltage exists when the transformer primary current doesn’t reduce to zero in the positive and negative switch-overas the zero vectors is too small in a cycle. In the respect of the big spike, this paper put forward a commutation method of increasing the action time of zero vectors. As shown in Figure 14b, the transformer primary current reduces to zero at the positive and negative switch-over point because of the longer

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action time of zero vectors. Thus, the current variation will be reduced at the positive and negative switch-over point. So, the larger the duty ratio of zero vectors is, the smaller the change of current is, Figure 13.voltage The switching and the2018, minimum spike is. logic diagram between input phase voltages. Energies 11, x FORthe PEER REVIEW 13 of 24

uscvoltage spikes. One is “big spike” caused by currents There are two types of transformer primary 00-00-11 switching from one bridge arm to another bridge arm in the same pole vector. The other is “small spike” caused by current switching from positive to negative in one cycle. The three-step 00-00-10 00-00-01 commutation can guarantee commutation safety of the same pole vector. But it has nothing to do 00-00-10 00-00-01 with the big spike. The current has a large amount of changes from positive to negative. Therefore, 01-00-00 10-00-00 u sa in this paper, the zero vector commutation is proposed to ensure the safety commutation at current 11-00-00 switch-over point between positive and negative currents. As shown in Figure 14a, the big spike of the transformer primary voltage exists when the transformer primary current doesn’t reduce to zero in the01-00-00 positive and negative switch-overas the 10-00-00 zero vectors is too small in a cycle. In the respect of the big spike, this paper put forward a 00-10-00 00-01-00 00-10-00 00-01-00 commutation method of increasing the actionu time of zero vectors. As shown in Figure 14b, the sb transformer primary current reduces to zero at00-11-00 the positive and negative switch-over point because of the longer action time of zero vectors. Thus, the current variation will be reduced at the positive Positive process Negative process and negative switch-over point. So, the larger the duty ratio of zero vectors is, the smaller the change Figure 13. The switching logic diagram between input phase voltages. of current is, and the minimum the voltage spike is. There are two types of transformer primary voltage spikes. One is “big spike” caused by currents switching from one bridge arm to another bridge arm in the same pole vector. The other is “small spike” caused by current switching from positive to negative in one cycle. The three-step commutation can guarantee commutation safety of the same pole vector. But it has nothing to do with the big spike. The current has a large amount of changes from positive to negative. Therefore, in this paper, the zero vector commutation is proposed to ensure the safety commutation at current switch-over point between positive and negative currents. As shown in Figure 14a, the big spike of the transformer primary voltage exists when the transformer primary current doesn’t reduce to zero in the positive and negative switch-overas the zero vectors is too small in a cycle. In the respect of the big spike, this paper put forward a commutation method of increasing the action time of zero vectors. As shown in Figure 14b, the transformer primary current reduces to zero at the positive and negative switch-over point because of the longer action time of zero vectors. Thus, the current variation will be reduced at the positive and negative switch-over point. So, the larger the duty ratio of zero vectors is, the smaller the change of current is, and the minimum the voltage spike is. Drives

Sap Sbn

Scn

(a)

San

Sbp

San Scp

Drives

Sap

Sap Sbn

Scn

San

Sbp

(b) T /2

San Scp

Sap

Ts/2 s Ts t Ts t Upn Uab Upn Uac Figure 14. Schematic diagram of the zero vector commutation: (a) Before the zero vector commutation; Uab U ac (b)Schematic After the zero vector commutation. Figure 14. diagram of the zero vector commutation: (a) Before U Uaa the zero vector commutation; aa 0 0 (b) After the zero vector commutation Uaa t Uaa t mentioned The comparisonBig between the hybrid commutation method and the other methods spike spike out. Reference in literatures are carried a two-step commutation method based Uba Uca [20] introduced No Uba Uca I pn current direction I pn on field-programmable gate array in which the output was needed. However, Not reduced to 0

Reduced to 0

the measurement and implementation hardware are complex and expensive. Reference [21] proposed an improved 0four-step commutation method based0 on the traditional four-step commutation. t converter, t It simplifies the first and fourth steps and raises the effective working time of matrix

(a)

(b)

Figure 14. Schematic diagram of the zero vector commutation: (a) Before the zero vector commutation;

measurement and implementation hardware are complex and expensive. Reference [21] proposed an improved four-step commutation method based on the traditional four-step commutation. It simplifies the first and fourth steps and raises the effective working time of matrix converter, but a four-step commutation board is needed. Therefore, a hybrid commutation method combining threeEnergies 2018, 11, 3396 13 of 21 step commutation with zero vector commutation is proposed in this paper. Among them, the threestep commutation guarantees commutation safety for the same pole vector while the zero vector but a four-step commutation board is needed. Therefore, a hybrid commutation method combining commutation guarantees commutation safety for the positive and negative switch-over point. As for three-step commutation with zero vector commutation is proposed in this paper. Among them, the particularity ofcommutation BRMC, the existence of positive and switching saves the the three-step guarantees commutation safety for the negative same pole vector while thesignals zero vector measurement of output current. Meanwhile, compared theswitch-over four-step commutation, the commutation guarantees commutation safety for the positive andwith negative point. As for the particularity of BRMC, the existence of positive and negative switching signals saves the measurement of commutation introduced in this paper reduces commutation time. Finally, on the premise of safe outputwith current. compared with the four-step commutation, commutation introduced commutation theMeanwhile, same polarity, a zero vector commutation is the proposed to reduce the voltage in this paper reduces commutation time. Finally, on the premise of safe commutation with the spike at the positive and negative switching points. Thus, this hybrid commutation scheme same polarity, a zero vector commutation is proposed to reduce the voltage spike at the positive and combining three-step commutation with zerocommutation vectors is used tocombining ensure safe commutation. negative switching points. Thus, this hybrid scheme three-step commutation with zero vectors is used to ensure safe commutation.

5. Implementation and Prototype of BRMC System 5. Implementation and Prototype of BRMC System

To verify the feasibility of the proposed strategy, a simulation was performed based using the To verify the feasibility of the proposed strategy, a simulation was performed based using the MATLAB/Simulink environment, a BRMC experimental prototype as shown in15 Figure 15 MATLAB/Simulink environment, a BRMC experimental prototype waswas builtbuilt as shown in Figure and the block of this experimental isshown shown Figure and thediagram block diagram of this experimentalsystem system is in in Figure 16. 16.

Figure Experimental prototype. Figure 15.15.Experimental prototype.

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16. The block diagramof ofBRMC BRMC magnet power supply system. FigureFigure 16. The block diagram magnet power supply system.

6. Simulation and Experimental Verification

6. Simulation and Experimental Verification

The simulation and experimental parameters are shown in Table 4.

The simulation and experimental parameters are shown in Table 4. Table 4. Parameters.

Table 4. Parameters

Parameters. Values

Input Voltage

ParametersInput filter

Output filter Switching frequency Input Voltage

Input filter

Load

6.1. Validation of the New Commutation Output filter Strategy

100 V/50 Hz 1.41 mH, Values 6 uF 10 mH, 450 uF 5 kHz 100 V/50 Hz 10 Ω, 10 mH

1.41 mH, 6 uF

10 mH, 450 uF

The interval time for each step commutation is set to 2 us according to the data manual of the Switching frequency 5 kHz used IGBT SK60GM123. The three-step commutation algorithm is the main commutation strategy, Load Ω, 10asmH and the simulation and experimental results and analyses are10 shown follows. Figures 17 and 18 show the simulation and experimental driving waveforms of the four-step commutation and the three-step commutation 6.1. Validation of the New Commutation Strategy when Sbn switches to Scn in the positive half period. The experimental results are in agreement with the simulation results, therefore it can be found that Thethe interval time for eachis step commutation set to 2 ussaves according to than the data manual of the commutation interval 2 us and the three-stepis commutation more time the four-step used IGBT SK60GM123. The three-step algorithm is theand main commutation strategy, commutation. Three-step commutationcommutation is used in the following simulation experiments. Figures 19 andexperimental 20 show the simulation experimental waveforms thefollows. output voltage, current, and the simulation and resultsand and analyses are shownofas primary voltage and current of the transformer. Comparing Figures 19 and 20 with Figures 19 and 20, Figures 17 and 18 show the simulation and experimental driving waveforms of the four-step the results show that the big spike still exists and small spikes are eliminated as a result of vectors commutation and the three-step commutation when Sbn switches to Scn in the positive half period. The switching after using the three-step commutation. This proves that the three-step commutation can experimental results are spike in agreement with the simulation results, therefore it can be found that the eliminate the small of the vector switchover. commutationAtinterval is 2and usnegative and theswitching three-step commutation savesgreatly, more and timethethan the four-step the positive point, the current changes multi-step commutation algorithm cannot completely eliminate the voltage spike since the three-step commutation. Three-step commutation is used in the following simulation and experiments. commutation algorithm is semi-forced commutation. In order to eliminate this big spike by using the zero vectors commutation, the operating time of zero vector at positive and negative switch-over point is increased. It is the three-step commutation with zero vector mixed commutation strategy that first reduces the primary current of the transformer to zero and then uses three-step commutation. Figures 21 and 22 show the simulation and experimental waveform contrast before and after changing the action time of zero vectors. It can be found in Figures 21 and 22 that the primary current of transformer has reduced to 0 relative to small action time of the zero vector shown in Figures 21

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Energies 11,increasing x FOR PEER action REVIEWtime of the zero vector. The safe commutation is realized when 16 of 24 and 22 2018, when the 2 2 positive and negative switching has no big spike. 1 1

Sbn−

Sbn−

0

0

-1 2

-1 2

Scn+

1

Scn+

1

0

0

2

2

Sbn+

1

Sbn+

1

0

0

-1 2

-1 2

Scn−

1

Scn−

1

0

0

-1 5.586

5.587

5.588

5.589 5.59 t (5us/div)

5.591

5.592

-1 5.593 0.0475

0.0475

0.0475

0.0475 t (5us/div)

-3

x 10

(a)

0.0475

0.0475

0.0475

(b)

(a) (b) Figure 17. Commutation driving simulation diagram: (a) Four-step commutation; (b) Three-step commutation. Figure 17. Commutation driving simulation diagram: (a) Four-step commutation; (b) Three-step commutation. Figure 17. Commutation driving simulation diagram: (a) Four-step commutation; (b) Three-step commutation.

(1us/div)

Sbn-

Sbn-

(5V/div)

(5V/div)

Scn+

Scn+

(5V/div)

(5V/div)

Sbn+

Sbn+

(5V/div)

(5V/div)

Scn-

Scn-

(5V/div)

(5V/div)

(1us/div)

(a)

(b)

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Figure 18. Commutation driving experiment diagram: (a) Four-step commutation; (b) Three-step commutation. (a) (b) Figure 18. Commutation driving experiment diagram: (a) Four-step commutation; (b) Three-step commutation. Output voltage

Output voltage

30

Output voltage and cureent

Output voltage and cureent

30 Figure 18. Commutation driving experiment diagram: (a) Four-step commutation; (b) Three-step Figures 19 and 20 show the simulation and experimental waveforms of the output voltage, 15 commutation. 15

Primary voltage of transformer

Primary voltage of transformer

current, primary voltage Output andcurrent current of the transformer. Comparing FiguresOutput 19bcurrent and 20b with Figures 0 19aFigures and 20a,19 theand results show that the big spike still exists and small spikes are eliminated as a result Big spike 0 No small spike 20 show and experimental waveforms of the output voltage, 150 Big spike the simulation Small spike 150 of vectors switching after using the three-step commutation. This proves that the three-step current, primary voltage and current of the transformer. Comparing Figures 19b and 20b with Figures 0 commutation can eliminate the small spike of the vector switchover. 0 20a, the results show that the big spike still exists and small spikes are eliminated as a result 19a and

Primary current of transformer

Primary current of transformer

of vectors switching after using the three-step commutation. This proves that the three-step -150 -150 3 commutation can eliminate the small spike of the vector switchover. 3 0 -3

0

-3 0.0304

0.0305

0.0306

0.0307

0.0308

0.0309

0.031

0.0311

0.8

1

1.2

1.4

t(s)

t(s)

(a)

(b)

Figure 19. Simulation waveform contrast before and after the three-step commutation: (a) Before Figure 19. Simulation waveform contrast before and after the three-step commutation: (a) Before commutation; (b) After commutation. commutation; (b) After commutation.

Output voltage Big spike Small spike

(10V/div) Output

Output voltage Big spike

No small spike

(10V/div) Output

*10 -3

t(s)

t(s)

(a)

(b)

Figure 19. Simulation waveform contrast before and after the three-step commutation: (a) Before Energies 2018, 11, 3396 (b) After commutation. commutation;

16 of 21

Output voltage

Output voltage

(10V/div) Output current

Big spike Small spike

(100us/div)

Big spike

No small spike

(10V/div) Output current

(1A/div)

(1A/div)

Primary voltage of transformer

Primary voltage of transformer

(50V/div)

(50V/div)

Primary current of transformer

Primary current of transformer

(5A/div)

(2A/div)

(100us/div)

(a)

(b)

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Figure 20. Experimental waveform contrast before and after the three-step commutation: (a) Before

Energies 2018, 20. 11, xExperimental FOR PEER REVIEW 18 of 24 Figure waveform contrast before and after the three-step commutation: (a) Before commutation; (b) After commutation. No big spike

Big spike commutation; (b) After commutation.

150

Primary voltage of transformer

Primary Primary Primary Primary Duty cycleDuty cycle current of current of voltage of voltage of of zero of zero transformer transformer transformer transformer vector vector

150

Duty cycle of zero vector

Primary current of transformer

0 At0 the positive and negative switching point, the current changes greatly, and the multi-step commutation algorithm cannot completely eliminate the voltage spike since the three-step -150 -150 Not reduced to 0 Reduced toby 0 using the commutation algorithm is semi-forced commutation. In order to eliminate this big spike 3 3 zero vectors commutation, the operating time of zero vector at positive and negative switch-over 0 0 point is increased. It is the three-step commutation with zero vector mixed commutation strategy that -3 -3 and then uses three-step commutation. first reduces the primary current of the transformer to zero 2 2 Figures 21 and 22 show the simulation and experimental waveform contrast before and after 1 1 in Figures 21b and 22b that the primary changing the action time of zero vectors. It can be found 0 current0 of transformer has reduced to 0 relative to small action time of the zero vector shown in -1 -1 0.0236 0.024 0.0241 0.0242 time 0.0243 of the zero0.0238 0.0239The 0.024 0.0242 0.0243 is 0.0244 0.0245 Figures 21a and0.0237 22a 0.0238 when0.0239 increasing action vector. safe0.0241 commutation realized t(s) t(s) when the positive and negative switching has no big spike. (a) (b)

(a)

(b)

Figure 21. Simulation waveform contrasts of different zero vector: (a) Small zero vector; (b) Big zero vector. Figure 21. Simulation waveform contrasts of different zero vector: (a) Small zero vector; (b) Big Figure 21. Simulation waveform contrasts of different zero vector: (a) Small zero vector; (b) Big zero zero vector. vector. Big spike

Primary voltage of transformer

Primary voltage of transformer

No big spike

(50V/div) Primary current of transformer

Not reduced to 0

(50us/div)

(a)

(50V/div)

Reduced to 0

Primary current of transformer

(5A/div)

(2A/div)

Duty cycle of zero vector (2V/div)

Duty cycle of zero vector (2V/div)

(50us/div)

(b)

Figure 22. Experimental(a) waveform contrasts of different zero vector: (a) (b) Small zero vector; (b) Big Figure 22. Experimental waveform contrasts of different zero vector: (a) Small zero vector; (b) Big zero vector. zero vector. Figure 22.ofExperimental contrasts of different zero vector: (a) Small zero vector; (b) Big 6.2. Validation Bidirectionalwaveform Energy Flow zero vector. 6.2. Validation of Bidirectional Energy Flow

6.2.1. Energy Forward Mode 6.2. Validation of Bidirectional Energy Flow 6.2.1. Energy 23 Forward Figures and 24Mode show simulation and experimental waveforms of BRMC in energy forward modeFigures at 5 kHz switching frequency. Seenand fromexperimental Figures 23 and 24, the input phase in current is in phase and 24 Mode show simulation waveforms of BRMC energy forward 6.2.1. Energy23 Forward mode at 5 kHz switching frequency. Seen from Figures 23a and 24a, the input phase current is in 23 and 24 show simulation experimental waveforms of BRMC in23b energy forward phaseFigures with input voltage resulting in highand power factor. It can be seen from Figures and 24b that mode at 5 kHz frequency. Seen Figures 23asame and 24a, phase in the system gets switching a stable output voltage andfrom current. At the time,the theinput polarity of current voltage is and phase with input voltage resulting in high power factor. It can be seen from Figures 23b and 24b that current on the primary side of the transformer is consistent. This shows that energy is transmitted the system gets stable voltage and current. the At the same time, polarity of voltage and from the grid to athe load.output It’s convenient to observe waveforms, thethe input current and output

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ua

1000 50

-6012 -1208 124

Primary Primary voltage of voltage of transformer transformer

5 5 200 0

4 200 0

0.01

0.02

0.03

-200 0.01

0.02

0.03

0.04

0.05

t(s)

(a)

0.04

0.05

t(s)

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

(a)

-200 0 0.0335

-200 0.0335

Current(*10)

Voltage

Current(*10)

Voltage

2000

0 200

0

0 10

100

80

-200 0 0

100

15050

ia(*4)

Primary voltage Primary voltage Output and current of and current of current transformer transformer

A phase A phase Output input voltage Output input voltage current and current current and current

120 60 0 120 -60 60 -120 0

Output Output Output voltage current voltage

with input voltage resulting in high power factor. It can be seen from Figures 23 and 24 that the system gets a stable output voltage and current. At the same time, the polarity of voltage and current on the primary side of the transformer is consistent. This shows that energy is transmitted from the grid to the load. It’s convenient to observe the waveforms, the input current and output current in simulation is magnified 4 and 10 times respectively. However, Figure 25 shows the harmonic magnitude of the input phase current at different switching frequency separately, obtained using a power analyzer. Figure 25a shows the input phase current THD at 4 kHz switching frequency and is 4.57%, which is higher than the THD at 5 kHz switching frequency. But this THD value is also lower than THD = 5% with the supply-side criterion in my country. The fifth harmonic, the eleventh harmonic, and the thirteenth harmonic of the input phase current are 0.0369, 0.1115, and 0.0630, respectively. Figure 25b shows the input phase current THD at 5 kHz switching frequency and is 3.71%. The fifth harmonic, the eleventh harmonic, and the thirteenth harmonic of the input phase current are 0.0319, 0.0790, and 0.0506, respectively. Energies 2018, 11, x FOR PEER REVIEW 19 of 24 Figure 26 shows a harmonic comparison using a relative value at different switching frequency. Comparing the fifthPEER harmonic, the eleventh harmonic, and the thirteenth harmonic in the two conditions, Energies 2018, 11, x FOR REVIEW 19 of 24 it can be seen that the higher frequency enables the system to get a lower THD. ua 150 iswitching (*4) a

0.0336

0.0337

0.0338

0.034

0.0339

0.0341

0.0342

0.0343

0.0344

t(s) 0.0336

0.0337

0.0338

(b)

0.0339

0.034

0.0341

0.0342

0.0343

0.0344

t(s)

(b)

Figure 23. Simulation waveform of energy forward mode at 5 kHz switching frequency: (a) Input Figure 23. waveform4of energy at 5and kHzcurrent switching frequency: (a) Input voltage andSimulation current (magnified times); (b)forward Primarymode voltage (magnified 10 times) of Figure 23. Simulation waveform of energy forward mode at 5 kHz switching frequency: (a) Input voltage and current (magnified 4 times); (b) Primary voltage and current (magnified 10 times) transformer. voltage and current (magnified 4 times); (b) Primary voltage and current (magnified 10 times) of of transformer. transformer. A phase input voltage A phase (50V/div) input A phase voltage input (50V/div) current A phase (10A/div) input current Output

Output voltage Output (20V/div) voltage Output (20V/div) current (5A/div) Output current Primary (5A/div) current of

(10A/div) current Output (5A/div) current Primary voltage of (5A/div)

transformer

(10ms/div)

(a)

(10ms/div)

Primary (200V/div)

voltage of transformer

(200V/div)

(100us/div)

(b)

(100us/div)

transformer Primary (5A/div) current of Primary transformer voltage of (5A/div) transformer Primary (200V/div) voltage of transformer

(200V/div)

(a) waveform of energy forward mode at 5 kHz switching (b) frequency: (a) Input Figure 24. Experimental Figure 24. Experimental waveform of energy forward mode at 5 kHz switching frequency: (a) Input voltage and current; (b) Primary voltage and current of transformer. voltage and current; (b) Primary voltage and current of transformer. Figure 24. Experimental waveform of energy forward mode at 5 kHz switching frequency: (a) Input voltage and current; voltage and current of transformer. However, Figure (b) 25 Primary shows the harmonic magnitude of the input phase current at different switching frequency separately, obtained using a power analyzer. Figure 25a shows the input phase However, Figure 25 shows the harmonic magnitude of the input phase current at different current THD at 4 kHz switching frequency and is 4.57%, which is higher than the THD at 5 kHz switching frequency separately, obtained using a power analyzer. Figure 25a shows the input phase switching frequency. But this THD value is also lower than THD = 5% with the supply-side criterion current THD at 4 kHz switching frequency and is 4.57%, which is higher than the THD at 5 kHz in my country. The fifth harmonic, the eleventh harmonic, and the thirteenth harmonic of the input switching frequency. But this THD value is also lower than THD = 5% with the supply-side criterion phase current are 0.0369, 0.1115, and 0.0630, respectively. Figure 25b shows the input phase current

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(a)

(b)

Figure 25. Harmonic analysis of input current under different switching frequency: (a) 4 kHz switching frequency; (b) 5 kHz switching frequency.

(a)

(b)

Figure 26 shows a harmonic comparison using a relative value at different switching frequency. Figure 25. Harmonic analysis of input current under different switching frequency: (a) 4 kHz switching Comparing fifth harmonic, eleventh and the thirteenth harmonic the two Figure 25. the Harmonic analysis ofthe input currentharmonic, under different switching frequency: (a) 4 in kHz frequency; (b) 5 kHz switching frequency. conditions, can be seen higher switching switchingitfrequency; (b) 5that kHzthe switching frequency. frequency enables the system to get a lower THD. FFT Figure 26I(n),pu(%) shows a harmonic comparison using a relative value at different switching frequency. 3.5 Comparing the fifth harmonic, the eleventh harmonic, and the thirteenth harmonic in the two 4kHz Towards 100% conditions, it3can be seen that the higher switching frequency enables the system to get a lower THD. 5kHz 2.5

3.5

2

3 1.5 2.5

1

2 0.5 1.5

0 1

1 0.5 0

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Harnomic order n Figure 26.26. Harmonic comparison inin different frequency. Figure Harmonic comparison different frequency.

6.2.2. Energy Feedback 2 3 4Mode 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 6.2.2. Energy1Feedback Mode In general simulations, energy feedback modes can be easily realized. But in actual experiments, In general simulations, energy feedback modes can be easily realized. But in actual experiments, due to the limited experimental no comparison larger inductances can frequency. meet the experimental requirements. Figureconditions, 26. Harmonic in different due to the limited experimental conditions, no larger inductances can meet the experimental In this paper, the method of a rectifier power series connection is used to simulate the energy in requirements. In this paper, the method of a rectifier power series connection is used to simulate the the accelerator, so as to verify the function of bidirectional BRMC energy feedback mode. The experimental 6.2.2. Energy Feedback Mode energy in the accelerator, so as to verify the function of bidirectional BRMC energy feedback mode. verification is carried out with the input voltage of 100 V. TheInexperimental verification is carried outmodes with the voltage of 100But V. in actual experiments, general simulations, energy feedback caninput be easily realized. Figures 27 and 28 show the simulation and experimental waveform in energy forward mode. 27 andexperimental 28 show the conditions, simulation and experimental waveform in energy forward mode. due toFigures the limited no larger inductances can meet the experimental Seen from Figures 27 and 28, the input phase voltage and current keep the same frequency and Seen from Figures andthe 28a,method the input voltage and current keep theissame requirements. In this27a paper, of aphase rectifier power series connection usedfrequency to simulateand thean an 180◦ phase difference. It can be seen from Figures 27 and 28 that the input current keeps its 180° phase difference. It seen the from Figures and 28c that theenergy input feedback current keeps energy in the accelerator, so can as tobeverify function of 27c bidirectional BRMC mode.its sinusoidal characteristics and the total harmonic is less than 5%. The system gets a good performance sinusoidal characteristics and totalout harmonic is input less than 5%. The system The experimental verification is the carried with the voltage of 100 V. gets a good performance at the grid-side. Figures 27 and 28 shows that the voltage on the load side stays positive and the at the grid-side. 27bthe and 28b showsand thatexperimental the voltage on the loadinside staysforward positivemode. and the Figures 27 andFigures 28 show simulation waveform energy current is negative. Meanwhile, the voltage and current of primary side of the transformer get the current negative. voltage current primary side the transformer getanthe Seen fromisFigures 27a Meanwhile, and 28a, the the input phaseand voltage andof current keep theofsame frequency and opposite polarity. The above conclusions show that the proposed method achieves the function of 180° phase difference. It can be seen from Figures 27c and 28c that the input current keeps its energy feedback. sinusoidal characteristics and the total harmonic is less than 5%. The system gets a good performance at the grid-side. Figures 27b and 28b shows that the voltage on the load side stays positive and the current is negative. Meanwhile, the voltage and current of primary side of the transformer get the

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ua

100

Output voltage

ia(*10)

60 0 120 60 60 -120 0

ua ia(*10)

Output Output current voltage

A phase A phase Outputinput voltage input voltage current and current and current

opposite polarity. The above conclusions show that the proposed method achieves the function of energy feedback. opposite polarity. Energies 2018, 11, 3396 The above conclusions show that the proposed method achieves the function 19 of of 21 energy feedback. 120

060 -120 -1.25 0 -2.5 -1.25 200 -2.5 0 200

Primary voltage Primary voltage Output and and current of current of current transformer transformer

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Current(*20)

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Fundamental (50Hz) = 1.35 , THD= 4.02% 2

Magnitude(A)Magnitude(A)

1.8 1.6 2 1.4 1.8 1.2 1.6 1 1.4 0.8 1.2 0.6 1 0.4 0.8 0.2 0.6 0 0.4 0

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(c) Figure 27. Simulation waveforms of energy feedback mode: (a) Input voltage and current (magnified Figure 27. Simulation of energy mode: (a) voltage and current (magnified 10 times); (b) Primarywaveforms voltage and currentfeedback of transformer; (c) Input Harmonic analysis of input current Figure 27. Simulation waveforms of energy feedback mode: (a) Input voltage and current (magnified 10 times); (b) (magnified 20 Primary times). voltage and current of transformer; (c) Harmonic analysis of input current 10 times); (b) Primary voltage and current of transformer; (c) Harmonic analysis of input current (magnified 20 times). (magnified 20 times). A phase input voltage A phase (50V/div) input Avoltage phase input (50V/div) current A phase (2A/div) input current Output

Output voltage Output (50V/div) voltage Output (50V/div) current (5A/div) Output Primary current voltage of (5A/div)

(2A/div) current (2A/div) Output Primary current voltage of (2A/div)

transformer Primary (200V/div) voltage of Primary transformer

current of (200V/div)

transformer Primary (200V/div)

(10ms/div)

(100us/div)

voltage of transformer

(a)

(b)

(200V/div)

(10ms/div)

(100us/div)

(5A/div)

(b)

Magnitude(A) Magnitude(A)

(a)

transformer Primary (5A/div) current of transformer

Harmonic order

(c)

Harmonic order

(c) mode: (a) Input voltage and current; (b) Primary Figure 28. Experimental waveform of energy feedback voltage and current of transformer; (c) Harmonic analysis of input current.

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Figure 28. Experimental waveform of energy feedback mode: (a) Input voltage and current; (b) Primary Energies 2018, 11,voltage 3396 and current of transformer; (c) Harmonic analysis of input current.

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6.3. Dynamic Experiment 6.3. Dynamic Experiment Figure 29 shows the dynamic simulation and experimental waveforms of input voltage, current, Figure 29 shows the dynamic andatexperimental waveforms input voltage, current, output current and primary currentsimulation of transform a reference current jumpoffrom 1A to 1.5 A. From output current and primary current of transform at a reference current jump from 1 A to 1.5 A. the result, it can be seen that the output current can track the change of the reference with a jump From1the result, it and can be that the output current can trackofthe change ofalso thechange reference with jump from A to 1.5 A, theseen input current and primary current transform with thea jump from 1 A to 1.5 A, and the input current and primary current of transform also change with the jump of the reference. The input current is sinusoidal before and after the change of the output reference. of the reference. The input current is sinusoidal before and after the change of the output reference. 30 15 0 -15 -30

A phase input voltage and current

ua

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ia(*10)

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3 Output current

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Figure 29. Dynamic waveform of input voltage, current, output current and primary current of Figure 29. at Dynamic waveform input voltage, current and primary transform a reference current of jump from 1A to current, 1.5 A: (a)output simulation waveform (inputcurrent current of is transform reference current jumpwaveform. from 1A to 1.5 A: (a) simulation waveform (input current is magnified at 10atimes); (b) experimental magnified 10 times); (b) experimental waveform.

7. Conclusions 7. Conclusions The contribution of this paper is to present a coordination control strategy based on bipolar current vector modulation and itsa hybrid commutation strategy based for bidirectional Thespace contribution of this paperstrategy is to present coordination control strategy on bipolar reducedspace matrix-type power supplyand in ion system. Thestrategy expression duty cycle current vector exciting modulation strategy its accelerator hybrid commutation for of bidirectional of the BRMC rectifierexciting stage ispower deduced and the schematic diagram of coordination control and the reduced matrix-type supply in ion accelerator system. The expression of duty cycle switch state table are given. experimental prototype with DSP +ofCPLD controller as theand control of the BRMC rectifier stage isAn deduced and the schematic diagram coordination control the core is state designed built. The experimentalprototype results verify effectiveness and feasibility of the switch tableand are given. An experimental withthe DSP + CPLD controller as the control coordinated control andexperimental the new commutation strategy. The proposed solves core is designed andstrategy built. The results verify the effectiveness andscheme feasibility of the problems of the largestrategy harmonic pollution the power grid and theThe challenges recovering energy coordinated control and the newofcommutation strategy. proposed scheme the solves the of the ion accelerator, furthermore, safer commutation is achieved for industrial application. Thus, problems of the large harmonic pollution of the power grid and the challenges recovering the energy it can alsoaccelerator, be applied furthermore, to charging piles, and is other placesfor where bidirectional energy flow of the ion safer elevators commutation achieved industrial application. Thus, it is needed. can also be applied to charging piles, elevators and other places where bidirectional energy flow is needed. Author Contributions: writing—original draft preparation and writing—review and editing, W.S and J.L; supervision, X.S. Author Contributions: writing—original draft preparation and writing—review and editing, W.S and J.L; Funding: This supervision, X.S.research was funded by National Natural Science Foundation of China (51877176). Shaanxi international exchange and cooperation project (2017KW-035). Shaanxi Provincial Education Department of ServiceThis Local Specialwas Plan Project State Key Laboratory of Large Electric Drive Shaanxi System Funding: research funded by (18JC024). National Natural Science Foundation of China (51877176). (SKLLDJ022016008). Research funding forproject Xi’an University of Technology (2016CX034). international exchange and cooperation (2017KW-035). Shaanxi Provincial Education Department of Service Special Project (18JC024). Key Laboratory of Large Electric Drive System ConflictsLocal of Interest: ThePlan authors declare no conflictState of interest. (SKLLDJ022016008). Research funding for Xi’an University of Technology (2016CX034).

References Conflicts of Interest: The authors declare no conflict of interest. 1.

Furukawa, T.; Shirai, T.; Inaniwa, T.; Sato, S.; Takeshita, E.; Mizushima, K.; Hara, Y.; Noda, K.; Kakutani, N.;

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