Dual active bridge synchronous chopper control strategy ... - IEEE Xplore

www.ietdl.org Published in IET Electric Power Applications Received on 1st June 2013 Revised on 11th September 2013 Accepted on 16th October 2013 doi: 10.1049/iet-epa.2013.0181

ISSN 1751-8660

Dual active bridge synchronous chopper control strategy in electronic power transformer Rui Zhang1, Dan Wang1, Chengxiong Mao1, Jiming Lu1, Jiawei Yang1, Yang Yi1, Xun Chen2, Junfeng Zhang2 1

State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China 2 Power System Division, Electric Power Research Institute of Guangdong Power Grid Corporation, Guangzhou, People’s Republic of China E-mail: [email protected]

Abstract: The electronic power transformer (EPT) is a novel transmission and transformation device, which consists of a series connection of two voltage-source H-bridge converters and a DC–DC converter with high-frequency isolation transformer. When applied to microgrids, EPT will not only deliver energy to loads from the utility grid but also inject some amount of excess power into the utility grid. Hence, the capability of bidirectional power flow is important for EPT, which depends on the DC-link stage. The traditional synchronous chopper control for a dual active bridge (DAB) converter has some limitations in the application of bidirectional power flow area. This study proposes a novel synchronous chopper control strategy for the DAB converter to implement bi-direction power flow, details the basic principle and steady-state operation and presents the mathematical derivations. A three-phase three-stage circuit configuration of 10 kV/400 V bi-direction EPT system based on the novel control DAB converter is designed, and corresponding control schemes for the system are discussed. The performance of this EPT system is validated by the MATLAB/Simulink-based simulations and the laboratory prototype experiments.

1

Introduction

The electronic power transformer (EPT), also called solid-state transformer or power-electronic transformer (PET) [1–6], is a novel transmission and transformation device based on power electronics, which has been regarded as one of the ten most emerging technologies in 2011 by the Massachusetts Institute of Technology (MIT) technology review [5]. EPT is proposed to replace the conventional line-frequency power transformer by means of high-frequency transformer isolated AC–AC conversion technique. A significant advantage of EPT is that the magnitude and phase angle of voltages on both the primary side and the secondary side of EPT can be controlled in real time through power-electronic converters to achieve flexible regulation of the current and power, which makes it a possibility for EPT to provide many additional advantages such as reactive power compensation, voltage regulation, harmonic suppression, power factor correction, intelligent energy control and management, which traditional transformers cannot [6–8]. In the area of traction applications, an auto-balancing traction transformer has been proposed to solve the matching problem about the rated voltage and current of power electronic device with the power system [9], and a single-phase power electronic traction transformer has been developed, assembled, commissioned and successfully installed on locomotive [10, 11]. Various configurations for EPT were reported in [12–14], of which the AC–DC–DC–AC configuration is more IET Electr. Power Appl., 2014, Vol. 8, Iss. 3, pp. 89–97 doi: 10.1049/iet-epa.2013.0181

promising. The modularised subunit of EPT includes three main stages: a high-voltage stage (voltage-source H-bridge converter), a DC-link stage [DC–DC converter with high-frequency isolation transformer (HFIT)] and a low-voltage stage (voltage-source H-bridge converter). Fig. 1 shows the circuit diagram of a three-phase EPT, which connects to the 10 kV power grid with star-figuration, and provides 400 V line-to-line voltages to loads or sources with three-phase-four-wire connection. When the power is transferred to loads from the grid, the high-frequency AC–DC rectifier converts the 50 Hz, 10 kV AC-phase voltage to six individual 1.5 kV DC buses and the high-frequency DC–DC converter converts 1.5 kV DC bus voltage to 350 V, and then is inverted to a 50 Hz, 220 V AC voltage by the inverter. Nowadays, microgrids are becoming a reality in a scenario where renewable energy, distributed generation and distributed storage systems can be conjugated and integrated into the grid [5, 14, 15]. When applied to microgrids, EPT will not only deliver energy to loads from the utility grid but also inject some amount of excess power into the utility grid. Hence, the capability of bidirectional power flow is important for EPT, which depends on the DC-link stage. The LLC resonant converter and the dual-active-bridge (DAB) converter have received a lot of attention. The LLC resonant converter can handle a widely adjustable regulated output voltage by using frequency control, even when wide input voltage or output load variations are applied to the 89

& The Institution of Engineering and Technology 2014

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Fig. 1 Proposed 10 kV/400 V EPT

converter [16, 17]. The DAB topology is ideally suited for high-power galvanic isolated DC–DC conversion, because of the attractive features, such as low device and component stresses compared with resonant converters. The PI-based phase-shift control and PWM modulation method of the DAB converter are proposed in [18–21]. However, to achieve these closed-loop controls of DAB converter in EPT, both sides of the DC-voltages should be measured however, the high-DC-voltage measurement is expensive. Moreover, to achieve the phase-shift control, an auxiliary inductor is needed for each HFIT. The synchronous chopper control used in the DAB converter has been discussed in [8, 22, 23]. However, these references do not take the leakage inductance of HFIT into consideration. When the leakage inductance is considered, the 50% synchronous chopper has some limitations in the application. In this paper, the limitation of traditional synchronous chopper control for DAB converter is discussed, and a novel synchronous chopper control strategy is proposed to realise the bi-direction power flow for EPT while the DAB converter is working in an open-loop control. This paper details the basic principle and steady-state operation, and presents the mathematical derivations for this control strategy. It further investigates the influential factors of maximum current through the HFIT and the high DC-voltage, the design of the duty cycle and leakage inductance. The proposed novel synchronous chopper control for DAB converter used in EPT

bi-direction power flow is simulated and a prototype is built and tested. Experimental results verify the design and simulation.

2

Basic principle and design

The DAB converter has been proposed for high-power density and high-efficiency DC–DC converter applications. Fig. 2 shows the detailed circuit configuration of the DAB converter. It consists of two identical single-phase voltage source converters, and an HFIT with its leakage inductance. 2.1 DAB converter with synchronous chopper control Fig. 3a shows the voltages and current of the DAB converter with traditional synchronous chopper control. The uH and uL are defined as voltages of the primary and secondary sides of HFIT, respectively, is is the current of the leakage inductance of the secondary winding through the transformer. As shown in Fig. 3a, the waveform of is is in opposite phase with that of uH and uL during time t1–t2, and t3–t4, which means returning power to the source. The existence of reactive power may increase the peak current of is, therefore, larger sizes of HFIT and capacitances are required, which results in low-power density and high cost of the system. This paper proposes a novel synchronous chopper with a duty cycle less than 50%. Fig. 3b shows the synchronous

Fig. 2 Isolated DAB converter 90


IET Electr. Power Appl., 2014, Vol. 8, Iss. 3, pp. 89–97 doi: 10.1049/iet-epa.2013.0181

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Fig. 3 Waveforms and drive signals of the DAB converter a Waveforms with traditional synchronous chopper control b Drive signals of traditional synchronous chopper control c Drive signals of Novel synchronous chopper control

chopper drive signals for the H-bridges in DC-link stage, and Fig. 3c shows the novel synchronous chopper drive signals for bi-direction DAB converter. S1, S4, Q1 and Q4 are turned on during the first half cycle whereas S2, S3, Q2 and Q3 are turned on during the next half cycle. The free-wheeling diodes will conduct until the energy stored in the transformer leakage inductance drops to zero as shown in Fig. 4 during the duty cycle reduction. The current decreases to zero rapidly, which ensures that the current starts from zero to imply zero current switching and is in

phase with the voltage during the next cycle time. Hence, the proposed control method can decrease reactive power, decrease peak current, increase system efficiency and minimise the output capacitance. The design of duty cycle reduction depends on the parameters of output power, frequency, transformer leakage inductance and secondary side voltage of HFIT, which will be discussed later in this paper. Steady-state operations of the DAB converter are studied in detail in the following analysis. 2.2

Basic principle and steady-state operation

In this section, the steady-state operations of the DAB converter according to the novel synchronous chopper control are discussed. The design rules of duty ratio and leakage inductance are given. In the following analysis, the turns-ratio of the transformer is n, the switching frequency is f and the switching period is T. The duty cycle is based on half period, therefore, DT is the turn-on time during half period. Assuming that the power flows from the high-voltage stage to the low-voltage stage, (uH/n) is assumed to be larger than uL because of the leakage inductance. Different operation modes are illustrated in Fig. 4. Segment 1: [t0, t1] Switches S1 and S4 of the primary bridge and Q1 and Q4 of the secondary bridge are turned on. The current of the leakage inductor increases linearly from 0. Owing to the positive current in the inductor, M1 and M4 freewheel, and Q1 and Q4 do not conduct current. The current increment during interval [t0, t1] is DI =

(1/n)uH − uL DT Ls

(1)

hence, Fig. 4 Typical voltage and current waveforms with novel synchronous chopper control IET Electr. Power Appl., 2014, Vol. 8, Iss. 3, pp. 89–97 doi: 10.1049/iet-epa.2013.0181

i(t1 ) = Imax = DI =

(1/n)uH − uL DT Ls

(2)

91


www.ietdl.org Segment 2: [t1, t2] In this segment, switches S1 and S4 of the primary bridge and Q1 and Q4 of the secondary bridge are turned off. Diodes D2 and D3 freewheel because the current is positive. The primary voltage of the transformer is reversed, whereas the secondary voltage of the transformer maintains a positive value as M1 and M4 still conduct current. The leakage inductor current decrement during interval [t1, t2] is DI = −

(1/n)uH + uL D1 T Ls

i(t2 ) = i(t1 ) + DI = 0

(3) (4)

A similar analysis could be performed for the following segments because of the symmetry of operation. Segment 3: [t3, t4] Switches S2 and S3 of the primary bridge and Q2 and Q3 of the secondary bridge are turned on. The current decreases from 0 to the negative maximum, and switches M2 and M3 conduct current. Hence, the current increment in Ls in Segments 3 is DI =

−(1/n)uH + uL Ls

(5)

current is imax =

Po DuL

(12)

Equation (12) shows that the maximum current is proportional to the output power, and is inversely proportional to the duty cycle of the pulse. For a given output power, the maximum current is directly inversely proportional to the duty cycle of the pulse. Therefore, to achieve a lower maximum current, the duty cycle of the pulse needs to be chosen as large as possible. uH can be obtained by substituting (12) to (7) Ls f Po uH = n uL + 2 · D uL

(13)

Equation (13) shows that, for a given switching frequency, leakage inductance and a fixed low DC voltage uL, the DC voltage uH of the high-voltage side varies with duty ratio and the output power. For a given output power, the uH varies only with duty ratio. Therefore, to achieve a lower uH, the duty cycle of the pulse needs to be chosen as large as possible.

hence i(t4 ) = −Imax

−(1/n)uH + uL = DT Ls

2.3 (6)

Segment 4: [t4, t5] In this segment, switches S2 and S3 of the primary bridge and Q2 and Q3 of the secondary bridge are turned off. Diodes D1 and D4 freewheel because the current is negative. The current increases from i(t4) to zero. From the above analysis of the operation modes, the maximum current can be derived as follows imax

1 1 1 1 u + uL = D uH − uL = D fLs n fLs 1 n H

(7)

Design of the duty cycle

To obtain a smaller peak current and a lower high-voltage side DC voltage, the D needs to be set as large as possible. In any case, (D + D1) ≤ 50% should be ensured, so D has a boundary value to make (D + D1) = 50%. For a fixed Po the lowest maximum current is 1 P 2P o= o imax = u uL D + D1 L By substituting (14) to (7), we can obtain 2Po 1 1 u + uL = D uL fLs 1 n H

The average current of the leakage inductance in one half switching cycle can be derived from Fig. 4 1 imax DT + imax D1 T = D + D1 imax IL = T

(8)

(9)

therefore 1 P o D + D1 uL

(10)

2Po fLs uL (1/n)uH + uL

D1 =

uH − nuL D≪D uH + nuL

(11)

The effect of D1 may be ignored for (10), the maximum


(16)

The difference of (uH/n) and uL is few when compared with uL, therefore, (uH/n) is substituted by uL. We can obtain Po fLs u2L

(17)

The maximum value of D is 1 P fL D = − o2 s 2 uL

It can be obtained from (7) that

92

D1 =

D1 = imax =

(15)

hence,

Assuming that the load has a fixed resistance and the output power is Po, the average current is P IL = o VL

(14)

(18)

The maximum value of D decreases with the increase of the output power and leakage inductance. In the case of (D + D1) = 0.5, the system works at the optimal efficiency condition. IET Electr. Power Appl., 2014, Vol. 8, Iss. 3, pp. 89–97 doi: 10.1049/iet-epa.2013.0181

www.ietdl.org 2.4

Design of leakage inductance

Table 1 Parameters of the simulation the theory calculation and the prototype system

The leakage inductance is one of the most important parameters of HFIT. The design of leakage inductance for the DAB system needs to consider two aspects as follows. On one hand, it will affect the maximum current when the second harmonic AC components of DC voltages are taken into consideration. However, the voltages uCH, uCL consist of the DC component and the second harmonic AC component, and are defined as follows

uH = uH uL = uL

+ uH ac + uL ac dc dc

ac /n

+ uL

ac

Ps uHA uLA uHdc uLdc fH fdc

(19)

The total second harmonic AC component can be expressed as uac = uH

Parameters

(20)

fL LH LL CH CL N Ls D

Name

Value

rated power of the prototype system AC voltage of high-voltage stage AC voltage of low-voltage stage DC-bus voltage of high-voltage stage DC-bus voltage of low-voltage stage the switching frequency of high-voltage converter the switching frequency of DC–DC converter the switching frequency of low-voltage converter the inductance of high-voltage side the inductance of low-voltage side the capacitance of the primary side the capacitance of the secondary side the transformer ratio of HFIT the leakage inductance of HFIT the duty cycle

500 kW 5772 V 220 V 1500 V 350 V 1 kHz 1 kHz 4 kHz 20 mH 0.5 mH 640 μF 0.0224 F 4.28 16.33 μH 48%

hence, the maximum current is Imax =

(1/n)uH − uL + uac IL u + ac DT (21) DT = Ls Ls D + D1

Equation (21) shows that increasing the leakage inductance Ls will decrease the maximum current impact to the insulated gate bipolar transistors (IGBTs) and HFIT. On the other hand, increasing the leakage inductance Ls will increase the high-voltage side DC voltage as shown in (13). The design of leakage inductance needs to consider these two aspects which have opposite results. When the other parameters of the system have been designed, the leakage inductance is limited from (13) and (21) as follows u · DT ac , Ls Imax − I L / D + D1 u D2 · u L , H − uL · n f · Po

3 3.1

(22)

leakage inductance of the HFIT has been designed according to (22). 3.2

Control system configuration

A three-phase three-stage circuit configuration of 10 kV/ 400 V bi-direction EPT system based on the novel control DAB converter is designed, the corresponding control schemes for the system are discussed in the following analysis. 3.2.1 Control scheme of high-voltage stage: The high-voltage stage H-bridge converter devotes itself to regulating the mean DC voltage of ULdc at its reference voltage. A d − q-axes vector controller is used to regulate the input currents of the AC/DC rectifier, whereas the d-axis loop is used to regulate the DC bus voltage, and the q-axis loop to regulate the EPT reactive power generated [22–24], as shown in Fig. 5.

System and control Circuit configuration

The circuit configuration of the three-phase three-stage 10 kV/400 V bi-direction EPT (BEPT) system used in the following simulations and experiments is shown in Fig. 1. To reduce the system cost and improve reliability, a modular design is applied. Each three stages 962 V/220 V/ 30 kVA power electronics building block (PEBB) consists of a high-voltage power cell, an HFIT and a low-voltage power cell. Table 1 summarises the circuit constants of the PWM converters, and those of the bidirectional isolated DC/DC converters. A set of six cascade H-bridge PWM converters is equipped with an AC-link inductor LH (3.5%) in each phase at the front end to support an instantaneous-voltage difference. An AC-link inductor LL (5%) is at the low-voltage side for the same reason. On substituting the parameters of the system to the formula (17), the result of duty cycle reduction D1 is 0.8%. Considering the influence of dead-time and to obtain a safety margin in the system, D1 is set to 2%, hence, the duty cycle is set to 48%. The IET Electr. Power Appl., 2014, Vol. 8, Iss. 3, pp. 89–97 doi: 10.1049/iet-epa.2013.0181

Fig. 5 Control system for the rectifier in the high-voltage stage a Current reference generation b Current state feedback decoupling control 93


www.ietdl.org The voltage and current measurements in Fig. 5 are transferred into per-unit values firstly, and filters are introduced to decrease the influence of the harmonics components. A high performance phase locked loop (PLL), which tracks accurately the frequency and phase angle of the supply voltage UHABC, is applied. The controller works in synchronous rotating d−q coordinates and is synthesised on the basis of linear multivariable state feedback theory. The control law can be expressed as ⎧ KI ∗ ⎪ ⎪ U iHd − iHd − vLiHq + UHd = − K + ⎨ d P s ⎪ K ⎪ ⎩ Uq = − KP + I i∗Hq − iHq + vLiHd s

(23)

where L is the interface inductance between the rectifier and the power supply, UHd is the supply voltage of the rectifier and KP and KI are the proportion and integral gains. The voltage UHd intends to compensate the counter-effect of the input voltage of the rectifier and the gain ωL provides the decoupling terms. The reactive current reference value i∗Hq is set to zero to minimise the power rating of the rectifiers. The active current reference value i∗Hd is derived from the reference current signal generation block illustrated in Fig. 5a. The average of DC voltage of low-voltage stage is compared with its reference value, and the reference current component is obtained by a PI controller.

Fig. 8 Simulation results of the novel control strategy in EPT

3.2.2 Control scheme of the isolation stage: The isolation stage is responsible for galvanic isolation and active power transmission of EPT. The IGBTs of the DC-link stage are hard switched and open-loop synchronous PWM control with 48% duty cycle is applied in these simulations. Since the mean DC voltage of the low-voltage stage ULdc is regulated at its reference voltage, the active power flow of the DC-link stage depends on the behaviours of the mean DC voltage UHdc and the mean DC voltage of the high-voltage stage.

Fig. 6 Control strategy for the rectifier in the low-voltage stage

3.2.3 Control scheme of the low-voltage stage: The low-voltage stage H-bridge converter devotes itself to regulating the active power flow from the high-voltage stage to the low-voltage stage. The active power control mode is applied to control the power of the system. Another

Fig. 7 Simulation results for the DAB converters a Secondary side voltage of HFIT b Secondary side currents of HFIT c Primary side DC voltages d Secondary side DC voltages 94



www.ietdl.org d−q-axes vector controller is used to regulate the input currents of the AC/DC rectifier, which is almost the same with the scheme in Fig. 5b except that the active current reference value i∗Ld is a constant reference in Fig. 6.

4

Simulation results

SimPowerSystems Block Sets of MATLAB/SIMULINK have been used to verify the DAB converter with synchronous chopper control and the proposed controller for EPT. The three-phase three-stage configuration that is illustrated in Fig. 1 is used in the simulations and the main parameters for the EPT are shown in Table 1. The controllers illustrated in the aforementioned sections have been applied. 4.1 DAB converter with novel synchronous chopper control Fig. 7 shows the simulation waveforms of the DAB converter with novel synchronous chopper control used in the DC-link stage of the EPT. The waveform of uL is the voltage of the secondary side of the HFIT transformer. The DC voltages of uHdc and uLdc are well regulated at 1500 and 350 V, respectively, and the 100 Hz peak ripple component of uLdc is 5 V, which produces a 100 Hz harmonic AC current. The current decreases to zero rapidly during the duty cycle reduction produced by the novel synchronous chopper

control, which ensures the current in phase with the voltage to decrease the reactive power flow of the converter. 4.2

DAB converter with novel control used in BEPT

The novel synchronous chopper control proposed in this paper is to realise the bi-direction power flow for the EPT while the DAB converter is working in an open-loop control. Fig. 8 shows the waveforms of the BEPT to prove the bi-direction power flow. Before time t = 0.2 s, the waveform of iHABC is in phase with that of uHABC, whereas the waveform of iLabc is out of phase of 180° with that of uLabc. This indicates an active power of 500 kW delivering from high-voltage side to low-voltage side with no reactive power at both ends. After the time t = 0.25 s, the waveforms of iHABC and iLabc are reversed, hence, an active power of 500 kW is delivered from the low-voltage side to the high-voltage side. The direction of delivered power is changed in a time interval of 50 ms.

5

Experimental results

To test the control hardware and software beyond the numerical simulations, a three-stage PEBB circuit configuration of 962 V/220 V/30 kVA is designed and assembled. The high-stage AC voltage in the experiment is obtained from the 220 V grid voltage transformed through a voltage regulator firstly, and then boosted by a 1:5 dry type transformer. Owing to fact that the DC-bus voltage of the

Fig. 9 Experimental results a Basic waveforms of the DAB converter b Waveforms of 15 kW single-phase waveforms of BEPT IET Electr. Power Appl., 2014, Vol. 8, Iss. 3, pp. 89–97 doi: 10.1049/iet-epa.2013.0181

95


www.ietdl.org high-voltage stage of each PEBB is 1500 V, a 3.3 kV IGBT from Infineon Company has been chosen for the high-voltage converter. The typical operating frequency of FF200R33KF2C is 1 kHz, therefore, the frequency of HFIT is also set to 1 kHz. The DC-bus voltage of the low-voltage stage of each PEBB is 350 V, a 1.2 kV IGBT type of FF450R12ME has been chosen. The triangle-carrier frequency of the low-voltage converter is set as 4 kHz, which is also the typical operating frequency, to make the IGBTs work in the optimal condition. The controller for generating the gate drive signals is implemented by using the TI 320F28335 digital signal processing system. Fig. 9a shows the waveforms of the DAB converter used in EPT bi-direction power flow with the proposed novel synchronous chopper control, whose duty cycle is 48%. The DC voltages of uLdc, voltages of primary and secondary sides of HFIT and current of the secondary side of HFIT are shown, which indicates that there is no power returned to the source, hence the efficiency of power transfer maintains a high level. However, there is a strong second harmonic ripple of the current is, which is decided by both the two sides of the DC-bus voltages and the parameters of HFIT [25]. Fig. 9b shows experimental single-phase waveforms under the half-power (15 kW) delivered operation with the novel synchronous chopper control. The waveform of the low-voltage stage iLa is in phase with that of uLa, which indicates that an active power is delivered from the high-voltage stage to the low-voltage stage with no reactive power. The mean DC voltage of uLdc is well regulated at

350 V. The spurs emerging in the secondary voltage of HFIT are caused by the change of current direction. This spur will not deteriorate the system operation, but sometimes the frequent variation of voltage waveforms may bring electromagnetic interference [18]. Fig. 10 shows the experimental source waveforms uHa, iHa of high-voltage stage and uLa, iLa of low-voltage stage. The measurement of uHa connected to the oscilloscope is the voltage before the dry type transformer. In Fig. 10a, the waveform of the high-voltage stage iHa is in phase with that of uHa, whereas the waveform of the low-voltage stage iLa is in opposite phase with that of uLa. This indicates that an active power is delivered from the high-voltage stage to the low-voltage stage. In Fig. 10b, the phase relationship is reversed, and the active power is delivered from the low-voltage stage to the high-voltage stage with no reactive power. Fig. 10c shows the transient waveforms uLa, iLa of the low-voltage stage, in which the active current reference value i∗Ld is changed from 5 to −5 A. This figure is recorded by the Agilent oscilloscope. A 1000:7.07 voltage transformer is used since there is no isolation between the channels, and the actual output voltage is about 220 V. The experimental results show that the delivered power changes direction in a time of about one cycle. According to Fig. 10c, the amplitude of the voltage uLa is not equal as before when the direction of current is changed. This is due to the influence of the internal resistance of the voltage regulator used in the experiment. If the voltage is directly connected to the grid, the voltage will remain constant. The

Fig. 10 Experimental results a Waveforms of power flow from high-voltage stage to low-voltage stage b Waveforms of power flow from low-voltage stage to high-voltage stage c Waveforms of dynamic response under the change in reference current value 96



www.ietdl.org experimental results have verified the achievement of BEPT with the novel synchronous chopper controlled DAB converter.

6

Conclusions

This paper has made a detailed description of a novel synchronous chopper control strategy for the DAB converter to implement bi-direction power flow of EPT. It analyses the operation principles and various switching modes of the DAB converter, and derives the expressions of relations between voltage, current and power under the novel synchronous chopper control. A three-phase three-stages circuit configuration for the 10 kV/400 V BEPT system based on the DAB converter is designed and corresponding control schemes for the system are discussed. The high-voltage stage H-bridge converter devotes itself to regulating the mean DC voltage at its reference voltage, and the DC-link stage is responsible for galvanic isolation and bi-direction power transmission of EPT, whereas the low-voltage stage H-bridge converter regulates the power flow between the high-voltage stage and the low-voltage stage. The performance of this BEPT system is validated by the MATLAB/Simulink-based simulations, and one of the individual PEBBs has been constructed and tested to verify the effectiveness and viability in the laboratory.

7

Acknowledgments

This work was supported by the National Nature Science Foundation of China under Grant 51277083 and the National Basic Research Program of China (2009CB219702).

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