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DC Converter
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Physics Procedia
Physics Procedia 24000–000 (2012) 139 – 148 Physics Procedia 00 (2011)
www.elsevier.com/locate/procedia
2012 International Conference on Applied Physics and Industrial Engineering
A Three-phase Dual Active Bridge Bidirectional ZVS DC/DC Converter Zhang Xuan1,Huang Shenghua1,Ning Guoyun2 1
College of Electrical & Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China 2 Dayu Electrical Technology Co., Ltd, Xiaogan, China
Abstract This paper discusses the detailed operations of a three-phase dual active bridge bidirectional zero-voltage switching (ZVS) DC/DC converter (TPDAB) which transfers a bidirectional power flow between a 12V net and a high voltage DC net. The converter is controlled by phase-shift-modulation (PSM) with a fixed duty cycle D=1/3. It features isolation, smoother drawing and injecting current from the 12V net, smaller capacitances, smaller switch current stress, ZVS over a wide range, high efficiency and a large power handling capability. The mathematic model is analyzed. The soft-switching principle is described and its ZVS criterias are derived. The simulation and experimental results are provided to verify the theoretical analysis. ©© 2011 Published by Elsevier B.V. Ltd. Selection and/orand/or peer-review under responsibility of ICAPIEof Organization Committee. 2011 Published by Elsevier Selection peer-review under responsibility [name organizer] Keywords:three-phase bidirectional dc/dc converter; zero-voltage switch (ZVS); phase-shift control
1.
Introduction
To mitigate rising oil prices and pollution concerns it is assumed that electric hybrid vehicles (HEVs) and electric vehicles (EVs) will be the trend in the near future. With the escalating need for electric power in future vehicles, there is an increasing requirement for bidirectional isolated DC/DC converters to transfer energy between different voltage levels, such as between the low voltage accessories and the high voltage drive train. For HEVs & EVs applications, the bidirectional dual active bridge DC/DC converter (DAB) is very attractive because of its features including zero-voltage switching, bidirectional power flow, low component stresses, and high-power density [1], [2], [3]. Besides, DAB is also widely used in applications of DC source distributed generators (DG) [4], uninterruptible power supplies (UPS) [5], bidirectional energy delivery between an energy storage system and a dc power system [6]-[7], power conversion system between an ac power system and a dc voltage source [8]-[9].
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of ICAPIE Organization Committee. doi:10.1016/j.phpro.2012.02.022
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[3] proposed a DAB based on a dual half-bridge topology. However, at higher power levels, the components face several stresses. As possible solutions, the parallelism of components or even converters can be applied. The former choice increases the complexity of the compromise between the circuit layout and the thermal design. Besides that, one should consider that the dynamic and static current sharing problem limits its application. The other alternative causes redundancy in the control circuits as well as in the number of power components and drivers, increasing the global cost and size of the equipment. For higher power level applications, [10] proposed a three-phase three-voltage bus DC/DC converter. However, the current changing rate at its low voltage accessory ports is large, which is negative for the accessories’ longevity. [11] proposed a three-phase current-fed dual active bridge bidirectional DC/DC converter (TPDAB), by interleaving three DABs proposed in [3]. Nevertheless, it is controlled by hybrid pulse-width-modulation (PWM) and phase-shift-modulation (PSM), the control is too complex and additional voltage measurement elements are required. This paper is made to discuss detailed operation of the TPDAB when it works with fixed duty cycle D=1/3, and is controlled by PSM alone. The total input current drawn from low voltage accessories, which is the sum of the currents of the coupling three input inductors, is almost a pure dc. Therefore, it can provide a more favorable operation condition for the low voltage accessories. The converter features isolation, smaller capacitances, smaller switch current stress, zero-voltage-switching (ZVS) over a wide range, high efficiency and a large power handling capability. The mathematic model and the power transfer characteristic are analyzed. The soft-switching principle is described and its criterias is derived. The simulation and experimental results verified the validity of the analysis. The paper is organized as follows. Section II gives an introduction of the topology and its key operating waveforms. In section III, the mathematic model is given. In section IV, the soft-switching principle is described and its criterias were given. In section V, the simulation results of a PSpice model and experimental results of prototype were provided to verify the theoretical analysis. 2.
Topology and Key operating Waveforms
Fig. 1 shows the TPDAB topology. The TPDAB is composed of three interleaving single-phase dual active bridge current source bidirectional DC/DC converters (DAB), and each phase output is 120 degree apart from each other. In this mode, the input current rating is increased by interleaving three phases, not by paralleling components, and the ripple frequency will be increased to three times the switching frequency and current ripple will be greatly reduced due to cancelling effects between each phase. The power flow of the TPDAB is controlled by the shifting phase between active bridges at low voltage side (LVS) and high voltage side (HVS). When energy flows from the 12V net side to the high voltage DC (HVDC) net side, the TPDAB works in boost mode, in which the driving pulses at LVS are ahead of that at HVS. On the contrary, when energy flows from the HVDC net side to the 12V net side, the TPDAB works in buck mode. The leakage inductances La~Lc of the high frequency transformer are acting as intermediate elements to store and transfer the power. The 12V net, the coupling three-phase input inductors L1~L3, and the switches S2, S4, S6 compose boost circuits. The duty cycles of the switches S1, S3, S5 are set at D, so the voltage V1 of capacitor C1 is boosted to 1/D times of Vin. The capacitors C1, C2 are used to handle high switching current ripple and maintain a nearly constant dc bus voltage. The stress of each switch of TPDAB converter is about one third of the single-phase topology, although the total stress is about the same for both converters since the number of switches is increased three times in TPDAB converter. The current stress of capacitors C1 and C2 of three-phase topology is much lower than that of the single-phase circuit therefore smaller capacitor could be used for three-phase topology and power density will be improved.
Zhang Xuan et al. / Physics Procedia 24 (2012) 139 – 148
Author name / Physics Procedia 00 (2011) 000–000
Figure 1. Toplogy of the three-phase dual active bridge bidirectional DC/DC converter
Fig. 2 show key operating waveforms of the converter in the boost mode: the three phase primary voltages Va2p, Vb2p and Vc2p in the top subplot; the secondary voltages Va3p, Vb3p and Vc3p, which are values reflected to the primary side, in the middle subplot; the three phase primary currents ILa, ILb and ILc, and the three phase input inductor currents IL1, IL2 and IL3 in the bottom plot. For the secondary voltages, it is defined that V2=VoutN, where N=Np/Ns is the turn ratio of the transformer. There is a phase difference of 120 degrees between A, B and C and a phase shift angleΦ between the primary and secondary voltages.
Figure 2. Key operating waveforms of the converter
3.
Mathematical Model
In order to simplify the analysis, it is assumed that the three phases of the converter are identical. At a time, only one upper switch or lower switch is on in the two three-phase bridges of both LVS and HVS, the voltage of the neutral points P and S on both sides of the transformer maintain fixed values, so it is reasonable to analyze the converter based on its single-phase operating waveforms and commutation processes. Ignoring the switching time and the dead time, for phase A, there are four main combinations of switching steps over a switching period of T, namely step I-IV, as indicated in Fig. 3. A brief description of each step is described as follows, where La represents the high frequency transformer leakage inductance, and ω represents the switching angular velocity.
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Figure 3. Simplified operating modes of the converter
A. StepⅠ(tⅠ
(1)
(2)
B. StepⅡ (tⅡ
2 2 V1 − V2 3 3
2 2 2π ( V1 − V2 ) 3 3 3 + V2φ I La (tⅢ ) = I La (tⅠ) + ω La ω La
(3)
(4)
C. StepⅢ (tⅢ
1 2 ΔV = − V1 − V2 3 3
2 2 2π 1 1 ( V1 − V2 ) (− V1 + V2 )φ 3 3 3 3 3 I La (tⅣ ) = I La (tⅠ) + + ω Ls ω Ls
(5)
(6)
D. StepⅣ (tⅣ
(7)
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I La (tⅤ ) = I La (tⅠ)
(8)
Due to the fact that the voltage applied to the primary side of the transformer is pure AC, the current should also be pure AC. Hence, the integration of the transformer current over a period is zero, i.e. I La (tⅠ) + I La (tⅡ ) I (t ) + I La (tⅢ ) 2π ( −φ) + φ + La Ⅱ 2 2 3 I La (tⅢ ) + I La (tⅣ ) I (t ) + I La (tⅤ ) 4π φ + La Ⅳ ( −φ) = 0 2 2 3
(9)
The current at the four switching points can be found from (2), (4), (6), (8) and (9), and is expressed in (10). Vφ (V − V2 )2π ⎧ − 2 − 1 ⎪ I La (tⅠ) = 3ω La 9ω La ⎪ ⎪ 2V1φ (V1 − V2 )2π (tⅡ ) − ⎪ I La= 3ω La 9ω La ⎪ (10) ⎨ 2 V ( V φ 2 1 − V2 )2π ⎪I = + (t ) ⎪ La Ⅲ 3ω La 9ω La ⎪ Vφ (V − V2 )2π ⎪ I (t ) = − 1 + 1 ⎪ La Ⅳ 3 L 9ω La ω a ⎩ Since it is assumed the three phases of the converter are balanced, there is La= Lb = Lc= Ls, where Ls is the leakage inductance of the transformer. The power transfer characteristic of the TPDAB can be derived as (11): T
Wo 3∫0 Va2 P I La dt 3V1V2 2 φ = = φ( − ) Po = ω Ls 9 4π T T
(11)
Po / (p.u.)
Figure 4 shows the output characteristics of the converter with different leakage inductance Ls. The converter output power Po is determined by the phase shift angleΦ. The maximum power occurs at 4π/9 for the curves, which are symmetrical to the vertical axis at 4π/9. As Ls increases, the maximum output power decreases.
Figure 4. Output characteristics of the converter
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4.
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Soft-swithching Principle and Criterias
The TPDAB is the three-phase derivation of the DAB. In [3], the soft-switching principle of the DAB topology was analyzed. ZVS was achieved due to the resonance of the switch parallel capacitances and the transformer leakage inductance. Similarly, with the switching time taken into account, the operating modes of the TPDAB can be redrawn more detailed as indicated in Fig.5. Over a switching period of T, there are 13 combinations of switching steps. The soft switching of each device in either direction of power flow is demonstrated by exploring the commutation process in boost mode. For the switches S1, S2, S7 and S8, their body diodes are represented as D1, D2, D7 and D8, their parasitic capacitances are represented as Cs1, Cs2, Cs7 and Cs8, the voltages across their source terminal and drain terminal are represented as VDS(S1), VDS(S2), VDS(S7) and VDS(S8), respectively. Step 1): (before t1): S1 and the body diode of S7 are conducting. Step 2): At t1, S1 is turned off. Cs1, Cs2 and La begin to resonate, making VDS(S2) fall from V1. Va2p also drops from 2V1/3. The rate of change depends on the magnitude of Ioff, which is the difference between ILa and IL1 at t2. Step 3): At t2, VDS(S2) attempts to overshoot the negative rail. D2 is therefore forward biased. During this period, S2 can be gated on at zero voltage. Step 4): From t3, ILa is less than IL1, so S2 begins to transfer current from D2. ILa keeps on decreasing until it is equal to 0 at t4. D7 is thereby still conducting until t4. Step 5): From t4 to t5, ILa begins to change polarity; therefore, current is commutated from D7 to S7. Step 6): At t5, S7 is gated to turn off. Cs7 and Cs8 begin to be charged and discharged, respectively. The rate of change of the voltage depends ILa on at t5. Step 7): At t6, when VDS(S8) attempts to overshoot the negative rail, D8 is forward biased. During this period, S8 can be gated on at any time at zero voltage. Step 8): At t7, S2 is gated off. Cs1, Cs2 and La begin to resonant again, making VDS(S1) discharge from V1. Va2p therefore increases from –V1/3. The rate of change now is decided primarily by the sum of the magnitude of ILa and IL1. Step 9): At t8, when VDS(S1) attempts to overshoot the positive rail, D1 is forward biased. ILa increases until it equals 0 at t9. During this period, S1 can be gated on at zero voltage. Step 10): From t9 to t10, ILa begins to change its polarity and continue to increase until it equals IL1. The current is commutated from D8 to S8. Step 11): From t10 to t11, IL1 begins to exceed IL1. The current is transferred from D1 to S1. Step 12): At t11, S8 is gated to turn off. Cs7 and Cs8 begin to be charged and discharged again. The charge/discharge rate depends mainly on the magnitude of ILa at t11. Step 13): At t12, when VDS(S3) attempts to overshoot the positive rail, D3 is forward biased. The circuit returns to the original steady state. During this period, S3 can be gated on any time at zero voltage.
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Figure 5. Detailed operating modes of the converter
From Fig. 5, it is clear that the conditions of soft switching in boost mode depend on the magnitude of ILa and IL1 at t1, t5, t7 and t11, respectively. This is summarized as: ⎧ I La (t1 ) < I L1 (t1 ) ⎪ ⎪ I La (t5 ) > 0 ⎨ ⎪ I La (t7 ) > I L1 (t7 ) ⎪⎩ I La (t11 ) < 0
(12)
The dc bias part IL1_DC of IL1 can be derived from (11), and is expressed in (13). = I L1_ DC
Po 3 3V2 2 φ φ( − ) = V1 3 ω Ls 9 4π
(13)
Over a switching period T, when S2 is on, the voltage across L1 is V1/3; when S1 is on, the voltage across L1 is 2V1/3, so the ac part IL1_AC of IL1 can be expressed in (14). V1π ⎧ ⎪ I L1_ AC (t1 ) = 9ω L ⎪ 1 ⎨ V π ⎪I (t ) = − 1 ⎪⎩ L1_ AC 7 9ω L1
(14)
Therefore, the values of IL1 at t1 and t7 are summarized as: ⎧ t1 ) ⎪ I L1 (= ⎪ ⎨ ⎪ I (= t ) ⎪⎩ L1 7
3V2 2 φ Vπ φ( − ) + 1 ω Ls 9 4π 9ω L1 3V2 2 φ Vπ φ( − ) − 1 ω Ls 9 4π 9ω L1
(15)
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By introducing an output voltage ratio M=V2/V1, the soft-switching criterias of the converter can be derived from (12) and (15), and is summarized as: ⎧ 2π − 3φ V2 8π 2 L1 + 4π 2 Ls M < = < ⎪ V1 8π 2 L1 − 27φ 2 L1 ⎨ 2π ⎪ 2 2 ⎩8π − 36φπ − 27φ > 0
(16)
The soft-switching region is shown by the shaded area in Fig. 6, where the horizontal axis is shift phase angleΦ, and the vertical axis is the output power Po in per-unit normalized by the maximum power for M =1. Curves showing the relationship between the output power and phase shift angle with different output voltage ratios (from 0.4 to 1.2) are also plotted. M=1.2 M=1.0 M=0.8 M=0.6 M=0.4
/ (°) Figure 6. Soft-switching area of the converter
From Fig. 6, it is clear that the soft switching region is the largest when M =1, and it narrows as the phase shift angle decreases, which makes the soft-switching difficult to achieve. 5.
Simulation Verification and Experimental Result
An OrCAD PSpice model rated at 2.4kW was built for converter simulation. In this model, the threephase circuits are identical and there is a phase difference of 120 degrees between them. The parameters of the converter are set as follows: L1=L2=L3=50μH, La=Lb=Lc=1μH, C1=C2=0.02F, R= 100Ω, the switching frequency fs is set at 20kHz, and the transformer turn ratio N=Np/Ns is set at 1/12. The phase shift angles Φ between the primary and secondary voltages of the three converters are the same. Fig. 7 shows the boost mode main waveforms for Φ=43.2º. In the figure, while only phase A voltage are shown, phase B and C voltages are exactly same except a 120 degrees’ phase difference. Fig. 8 shows the voltages VDS(S1) and VDS(S7) across the source and drain terminals of S1 and S7 for Φ=43.2º.
Figure 7. Key simulation waveforms of the converter
Zhang Xuan et al. / Physics Procedia 24 (2012) 139 – 148
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Figure 8. Voltage and current simulation waveforms of S1 and S7
From Fig. 8, it can be seen that the voltage of the 12V net was boosted to 36V, which is the voltage V1 of C1. The output voltage Vout of the HV net reached 210V. All the switches achieved ZVS in the softswitching area. A converter prototype rated at 500W was built to verify the analysis and modeling. 6 MOSFETs were used in both sides of the converter. A coupling three-phase inductor with five windings on the five legs was used as input inductor L1~L3. A three-phase transformer with its primary windings star connected was used to isolate the HVS and LVS. Three extra inductors were used to achieve the desired total leakage inductance value. Texas Instrument’s TMS320F2808 was used for real-time control. The control system hardware includes the DSP board, the isolated driving circuits, the isolated overvoltage and overcurrent detection circuits, CAN bus, RS232, USB and single-chip Ethernet communication circuits. A PC host program is designed for supervision. The switching frequency was set to 20kHz. An oscilloscope was used to record the waveforms. Fig. 9 shows waveforms of voltage Va2p, currents ILa and IL1. Fig. 10 shows the waveforms of voltage VDS(S1), VDS(S7) across the source and drain terminals of S1, S7, and currents IS1, IS7 which flows through S1, S7, respectively.
Figure 9. Key experimental waveforms of the converter
Figure 10. Voltage and current experimental waveforms of S1 and S7
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As shown in Fig. 10, it can be seen that the output voltage Vout of the HV net reached 302V. All the switches achieved ZVS in the soft-switching area. Further tests need to be done in buck mode and to test the efficiency of the converter. Conclusion
In this paper, a three-phase current-fed dual active bridge bidirectional dc-dc converter which can achieve ZVS in a large range is discussed. The mathematic model and the power transfer characteristic are analyzed. The soft-switching principle is described and its criterias is derived. The simulation and experimental results verified the validity of the proposed circuit. References [1]
R.W. De Doncker, D.M. Divan, and M. H. Kheraluwala, “A threephase soft-switched high power density DC/DC
converter for high power applications,” IEEE Trans. on Industry Applications, vol. 27, no. 1, Jan/Feb. 1991, pp. 63-73, doi: 10.1109/28.67533 [2]
M. H. Kheraluwala, R. W. Gascoigne, D. M. Divan, and E. D. Baumann, “Performance characterization of a high-power
dual active bridge dc-todc converter,” IEEE Trans. Ind. Appl., vol. 28, no. 6, Nov./Dec. 1992, pp. 1294–1301, doi: 10.1109/28.175280. [3]
Fang Z. Peng, Hui Li, Gui-jia Su, J. Lawler, “A New ZVS Bidirectional dc-dc Converter for Fuel Cell and Battery
Applications,” IEEE Transaction on Power Electronics, Vol. 19, No.1, Jan 2004, pp.54-65, doi:10.1109/TPEL.2003.820550. [4]
Jaehong Kim, Ilsu Jeong, Kwanghee Nam, “Asymmetric duty control of the dual-active-bridge DC/DC converter for
single-phase distributed generators,” Energy Conversion Congress and Exposition, 2009 (ECCE 2009), IEEE, Sept. 2009, pp. 75-82, doi: 10.1109/ECCE.2009.5316120. [5]
R. Morrison and M. G. Egan, “A new power-factor-corrected single-transformer UPS design,” IEEE Trans. Ind. Appl.,
vol. 36, no. 1, Jan./Feb. 2000, pp. 171-179, doi: 10.1109/28.821812. [6]
J. L. Duarte, M. Hendrix, and M. G. Simoes, “Three-port bidirectional converter for hybrid fuel cell systems,” IEEE
Trans. Power Electron., vol. 22, no. 2, Mar. 2007, pp. 480–487, doi: 10.1109/TPEL.2006.889928. [7]
H. M. Tao, A. Kotsopoulos, J. L. Duarte, and M. A. M. Hendrix, “Transformer-coupled multiport ZVS bidirectional dc-
dc converter with wide input range,” IEEE Trans. Power Electron., vol. 23, no. 2, Mar. 2008., pp. 771–781, doi: 10.1109/TPEL.2007.915129. [8]
S. Inoue and H. Akagi, “A bidirectional dc-dc converter for an energy storage system with galvanic isolation,” IEEE
Trans. Power Electron., vol. 22, no. 6, Nov. 2007, pp. 2299–2306, doi: 10.1109/TPEL.2007.909248. [9]
S. Inoue and H. Akagi, “A bidirectional isolated dc-dc converter as a core circuit of the next-generation medium-voltage
power conversion system,” IEEE Trans. Power Electron., vol. 22, no. 2, Mar. 2007, pp. 535–542, doi: 10.1109/TPEL.2006.889939. [10]
Lixin Tang, Gui-Jia Su. “Experimental Investigation of a Soft-switching Three-Phase Three-Voltage Bus DC/DC
Converter for Fuel Cell Vehicle Applications”. Power Electronics Specialists Conference, 2008 (PESC 2008), IEEE, June 2008, pp. 585-591, doi: 10.1109/PESC.2008.4591993. [11]
Zhan Wang and Hui Li, “Unified Modulation for Three-phase Current-fed Bidirectional DC-DC Converter Under Varied
Input Voltage,” Applied Power Electronics Conference and Exposition (APEC 2010) , IEEE Press, 21-25 Feb. 2010, pp. 807-812, doi: 10.1109/APEC.2010.5433575.
Physics Procedia
Physics Procedia 24000–000 (2012) 139 – 148 Physics Procedia 00 (2011)
www.elsevier.com/locate/procedia
2012 International Conference on Applied Physics and Industrial Engineering
A Three-phase Dual Active Bridge Bidirectional ZVS DC/DC Converter Zhang Xuan1,Huang Shenghua1,Ning Guoyun2 1
College of Electrical & Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China 2 Dayu Electrical Technology Co., Ltd, Xiaogan, China
Abstract This paper discusses the detailed operations of a three-phase dual active bridge bidirectional zero-voltage switching (ZVS) DC/DC converter (TPDAB) which transfers a bidirectional power flow between a 12V net and a high voltage DC net. The converter is controlled by phase-shift-modulation (PSM) with a fixed duty cycle D=1/3. It features isolation, smoother drawing and injecting current from the 12V net, smaller capacitances, smaller switch current stress, ZVS over a wide range, high efficiency and a large power handling capability. The mathematic model is analyzed. The soft-switching principle is described and its ZVS criterias are derived. The simulation and experimental results are provided to verify the theoretical analysis. ©© 2011 Published by Elsevier B.V. Ltd. Selection and/orand/or peer-review under responsibility of ICAPIEof Organization Committee. 2011 Published by Elsevier Selection peer-review under responsibility [name organizer] Keywords:three-phase bidirectional dc/dc converter; zero-voltage switch (ZVS); phase-shift control
1.
Introduction
To mitigate rising oil prices and pollution concerns it is assumed that electric hybrid vehicles (HEVs) and electric vehicles (EVs) will be the trend in the near future. With the escalating need for electric power in future vehicles, there is an increasing requirement for bidirectional isolated DC/DC converters to transfer energy between different voltage levels, such as between the low voltage accessories and the high voltage drive train. For HEVs & EVs applications, the bidirectional dual active bridge DC/DC converter (DAB) is very attractive because of its features including zero-voltage switching, bidirectional power flow, low component stresses, and high-power density [1], [2], [3]. Besides, DAB is also widely used in applications of DC source distributed generators (DG) [4], uninterruptible power supplies (UPS) [5], bidirectional energy delivery between an energy storage system and a dc power system [6]-[7], power conversion system between an ac power system and a dc voltage source [8]-[9].
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of ICAPIE Organization Committee. doi:10.1016/j.phpro.2012.02.022
140
Zhang Xuan et al. / Physics Procedia 24 (2012) 139 – 148
Author name / Physics Procedia 00 (2011) 000–000
[3] proposed a DAB based on a dual half-bridge topology. However, at higher power levels, the components face several stresses. As possible solutions, the parallelism of components or even converters can be applied. The former choice increases the complexity of the compromise between the circuit layout and the thermal design. Besides that, one should consider that the dynamic and static current sharing problem limits its application. The other alternative causes redundancy in the control circuits as well as in the number of power components and drivers, increasing the global cost and size of the equipment. For higher power level applications, [10] proposed a three-phase three-voltage bus DC/DC converter. However, the current changing rate at its low voltage accessory ports is large, which is negative for the accessories’ longevity. [11] proposed a three-phase current-fed dual active bridge bidirectional DC/DC converter (TPDAB), by interleaving three DABs proposed in [3]. Nevertheless, it is controlled by hybrid pulse-width-modulation (PWM) and phase-shift-modulation (PSM), the control is too complex and additional voltage measurement elements are required. This paper is made to discuss detailed operation of the TPDAB when it works with fixed duty cycle D=1/3, and is controlled by PSM alone. The total input current drawn from low voltage accessories, which is the sum of the currents of the coupling three input inductors, is almost a pure dc. Therefore, it can provide a more favorable operation condition for the low voltage accessories. The converter features isolation, smaller capacitances, smaller switch current stress, zero-voltage-switching (ZVS) over a wide range, high efficiency and a large power handling capability. The mathematic model and the power transfer characteristic are analyzed. The soft-switching principle is described and its criterias is derived. The simulation and experimental results verified the validity of the analysis. The paper is organized as follows. Section II gives an introduction of the topology and its key operating waveforms. In section III, the mathematic model is given. In section IV, the soft-switching principle is described and its criterias were given. In section V, the simulation results of a PSpice model and experimental results of prototype were provided to verify the theoretical analysis. 2.
Topology and Key operating Waveforms
Fig. 1 shows the TPDAB topology. The TPDAB is composed of three interleaving single-phase dual active bridge current source bidirectional DC/DC converters (DAB), and each phase output is 120 degree apart from each other. In this mode, the input current rating is increased by interleaving three phases, not by paralleling components, and the ripple frequency will be increased to three times the switching frequency and current ripple will be greatly reduced due to cancelling effects between each phase. The power flow of the TPDAB is controlled by the shifting phase between active bridges at low voltage side (LVS) and high voltage side (HVS). When energy flows from the 12V net side to the high voltage DC (HVDC) net side, the TPDAB works in boost mode, in which the driving pulses at LVS are ahead of that at HVS. On the contrary, when energy flows from the HVDC net side to the 12V net side, the TPDAB works in buck mode. The leakage inductances La~Lc of the high frequency transformer are acting as intermediate elements to store and transfer the power. The 12V net, the coupling three-phase input inductors L1~L3, and the switches S2, S4, S6 compose boost circuits. The duty cycles of the switches S1, S3, S5 are set at D, so the voltage V1 of capacitor C1 is boosted to 1/D times of Vin. The capacitors C1, C2 are used to handle high switching current ripple and maintain a nearly constant dc bus voltage. The stress of each switch of TPDAB converter is about one third of the single-phase topology, although the total stress is about the same for both converters since the number of switches is increased three times in TPDAB converter. The current stress of capacitors C1 and C2 of three-phase topology is much lower than that of the single-phase circuit therefore smaller capacitor could be used for three-phase topology and power density will be improved.
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Figure 1. Toplogy of the three-phase dual active bridge bidirectional DC/DC converter
Fig. 2 show key operating waveforms of the converter in the boost mode: the three phase primary voltages Va2p, Vb2p and Vc2p in the top subplot; the secondary voltages Va3p, Vb3p and Vc3p, which are values reflected to the primary side, in the middle subplot; the three phase primary currents ILa, ILb and ILc, and the three phase input inductor currents IL1, IL2 and IL3 in the bottom plot. For the secondary voltages, it is defined that V2=VoutN, where N=Np/Ns is the turn ratio of the transformer. There is a phase difference of 120 degrees between A, B and C and a phase shift angleΦ between the primary and secondary voltages.
Figure 2. Key operating waveforms of the converter
3.
Mathematical Model
In order to simplify the analysis, it is assumed that the three phases of the converter are identical. At a time, only one upper switch or lower switch is on in the two three-phase bridges of both LVS and HVS, the voltage of the neutral points P and S on both sides of the transformer maintain fixed values, so it is reasonable to analyze the converter based on its single-phase operating waveforms and commutation processes. Ignoring the switching time and the dead time, for phase A, there are four main combinations of switching steps over a switching period of T, namely step I-IV, as indicated in Fig. 3. A brief description of each step is described as follows, where La represents the high frequency transformer leakage inductance, and ω represents the switching angular velocity.
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Figure 3. Simplified operating modes of the converter
A. StepⅠ(tⅠ
(1)
(2)
B. StepⅡ (tⅡ
2 2 V1 − V2 3 3
2 2 2π ( V1 − V2 ) 3 3 3 + V2φ I La (tⅢ ) = I La (tⅠ) + ω La ω La
(3)
(4)
C. StepⅢ (tⅢ
1 2 ΔV = − V1 − V2 3 3
2 2 2π 1 1 ( V1 − V2 ) (− V1 + V2 )φ 3 3 3 3 3 I La (tⅣ ) = I La (tⅠ) + + ω Ls ω Ls
(5)
(6)
D. StepⅣ (tⅣ
(7)
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I La (tⅤ ) = I La (tⅠ)
(8)
Due to the fact that the voltage applied to the primary side of the transformer is pure AC, the current should also be pure AC. Hence, the integration of the transformer current over a period is zero, i.e. I La (tⅠ) + I La (tⅡ ) I (t ) + I La (tⅢ ) 2π ( −φ) + φ + La Ⅱ 2 2 3 I La (tⅢ ) + I La (tⅣ ) I (t ) + I La (tⅤ ) 4π φ + La Ⅳ ( −φ) = 0 2 2 3
(9)
The current at the four switching points can be found from (2), (4), (6), (8) and (9), and is expressed in (10). Vφ (V − V2 )2π ⎧ − 2 − 1 ⎪ I La (tⅠ) = 3ω La 9ω La ⎪ ⎪ 2V1φ (V1 − V2 )2π (tⅡ ) − ⎪ I La= 3ω La 9ω La ⎪ (10) ⎨ 2 V ( V φ 2 1 − V2 )2π ⎪I = + (t ) ⎪ La Ⅲ 3ω La 9ω La ⎪ Vφ (V − V2 )2π ⎪ I (t ) = − 1 + 1 ⎪ La Ⅳ 3 L 9ω La ω a ⎩ Since it is assumed the three phases of the converter are balanced, there is La= Lb = Lc= Ls, where Ls is the leakage inductance of the transformer. The power transfer characteristic of the TPDAB can be derived as (11): T
Wo 3∫0 Va2 P I La dt 3V1V2 2 φ = = φ( − ) Po = ω Ls 9 4π T T
(11)
Po / (p.u.)
Figure 4 shows the output characteristics of the converter with different leakage inductance Ls. The converter output power Po is determined by the phase shift angleΦ. The maximum power occurs at 4π/9 for the curves, which are symmetrical to the vertical axis at 4π/9. As Ls increases, the maximum output power decreases.
Figure 4. Output characteristics of the converter
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Soft-swithching Principle and Criterias
The TPDAB is the three-phase derivation of the DAB. In [3], the soft-switching principle of the DAB topology was analyzed. ZVS was achieved due to the resonance of the switch parallel capacitances and the transformer leakage inductance. Similarly, with the switching time taken into account, the operating modes of the TPDAB can be redrawn more detailed as indicated in Fig.5. Over a switching period of T, there are 13 combinations of switching steps. The soft switching of each device in either direction of power flow is demonstrated by exploring the commutation process in boost mode. For the switches S1, S2, S7 and S8, their body diodes are represented as D1, D2, D7 and D8, their parasitic capacitances are represented as Cs1, Cs2, Cs7 and Cs8, the voltages across their source terminal and drain terminal are represented as VDS(S1), VDS(S2), VDS(S7) and VDS(S8), respectively. Step 1): (before t1): S1 and the body diode of S7 are conducting. Step 2): At t1, S1 is turned off. Cs1, Cs2 and La begin to resonate, making VDS(S2) fall from V1. Va2p also drops from 2V1/3. The rate of change depends on the magnitude of Ioff, which is the difference between ILa and IL1 at t2. Step 3): At t2, VDS(S2) attempts to overshoot the negative rail. D2 is therefore forward biased. During this period, S2 can be gated on at zero voltage. Step 4): From t3, ILa is less than IL1, so S2 begins to transfer current from D2. ILa keeps on decreasing until it is equal to 0 at t4. D7 is thereby still conducting until t4. Step 5): From t4 to t5, ILa begins to change polarity; therefore, current is commutated from D7 to S7. Step 6): At t5, S7 is gated to turn off. Cs7 and Cs8 begin to be charged and discharged, respectively. The rate of change of the voltage depends ILa on at t5. Step 7): At t6, when VDS(S8) attempts to overshoot the negative rail, D8 is forward biased. During this period, S8 can be gated on at any time at zero voltage. Step 8): At t7, S2 is gated off. Cs1, Cs2 and La begin to resonant again, making VDS(S1) discharge from V1. Va2p therefore increases from –V1/3. The rate of change now is decided primarily by the sum of the magnitude of ILa and IL1. Step 9): At t8, when VDS(S1) attempts to overshoot the positive rail, D1 is forward biased. ILa increases until it equals 0 at t9. During this period, S1 can be gated on at zero voltage. Step 10): From t9 to t10, ILa begins to change its polarity and continue to increase until it equals IL1. The current is commutated from D8 to S8. Step 11): From t10 to t11, IL1 begins to exceed IL1. The current is transferred from D1 to S1. Step 12): At t11, S8 is gated to turn off. Cs7 and Cs8 begin to be charged and discharged again. The charge/discharge rate depends mainly on the magnitude of ILa at t11. Step 13): At t12, when VDS(S3) attempts to overshoot the positive rail, D3 is forward biased. The circuit returns to the original steady state. During this period, S3 can be gated on any time at zero voltage.
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Figure 5. Detailed operating modes of the converter
From Fig. 5, it is clear that the conditions of soft switching in boost mode depend on the magnitude of ILa and IL1 at t1, t5, t7 and t11, respectively. This is summarized as: ⎧ I La (t1 ) < I L1 (t1 ) ⎪ ⎪ I La (t5 ) > 0 ⎨ ⎪ I La (t7 ) > I L1 (t7 ) ⎪⎩ I La (t11 ) < 0
(12)
The dc bias part IL1_DC of IL1 can be derived from (11), and is expressed in (13). = I L1_ DC
Po 3 3V2 2 φ φ( − ) = V1 3 ω Ls 9 4π
(13)
Over a switching period T, when S2 is on, the voltage across L1 is V1/3; when S1 is on, the voltage across L1 is 2V1/3, so the ac part IL1_AC of IL1 can be expressed in (14). V1π ⎧ ⎪ I L1_ AC (t1 ) = 9ω L ⎪ 1 ⎨ V π ⎪I (t ) = − 1 ⎪⎩ L1_ AC 7 9ω L1
(14)
Therefore, the values of IL1 at t1 and t7 are summarized as: ⎧ t1 ) ⎪ I L1 (= ⎪ ⎨ ⎪ I (= t ) ⎪⎩ L1 7
3V2 2 φ Vπ φ( − ) + 1 ω Ls 9 4π 9ω L1 3V2 2 φ Vπ φ( − ) − 1 ω Ls 9 4π 9ω L1
(15)
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By introducing an output voltage ratio M=V2/V1, the soft-switching criterias of the converter can be derived from (12) and (15), and is summarized as: ⎧ 2π − 3φ V2 8π 2 L1 + 4π 2 Ls M < = < ⎪ V1 8π 2 L1 − 27φ 2 L1 ⎨ 2π ⎪ 2 2 ⎩8π − 36φπ − 27φ > 0
(16)
The soft-switching region is shown by the shaded area in Fig. 6, where the horizontal axis is shift phase angleΦ, and the vertical axis is the output power Po in per-unit normalized by the maximum power for M =1. Curves showing the relationship between the output power and phase shift angle with different output voltage ratios (from 0.4 to 1.2) are also plotted. M=1.2 M=1.0 M=0.8 M=0.6 M=0.4
/ (°) Figure 6. Soft-switching area of the converter
From Fig. 6, it is clear that the soft switching region is the largest when M =1, and it narrows as the phase shift angle decreases, which makes the soft-switching difficult to achieve. 5.
Simulation Verification and Experimental Result
An OrCAD PSpice model rated at 2.4kW was built for converter simulation. In this model, the threephase circuits are identical and there is a phase difference of 120 degrees between them. The parameters of the converter are set as follows: L1=L2=L3=50μH, La=Lb=Lc=1μH, C1=C2=0.02F, R= 100Ω, the switching frequency fs is set at 20kHz, and the transformer turn ratio N=Np/Ns is set at 1/12. The phase shift angles Φ between the primary and secondary voltages of the three converters are the same. Fig. 7 shows the boost mode main waveforms for Φ=43.2º. In the figure, while only phase A voltage are shown, phase B and C voltages are exactly same except a 120 degrees’ phase difference. Fig. 8 shows the voltages VDS(S1) and VDS(S7) across the source and drain terminals of S1 and S7 for Φ=43.2º.
Figure 7. Key simulation waveforms of the converter
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Figure 8. Voltage and current simulation waveforms of S1 and S7
From Fig. 8, it can be seen that the voltage of the 12V net was boosted to 36V, which is the voltage V1 of C1. The output voltage Vout of the HV net reached 210V. All the switches achieved ZVS in the softswitching area. A converter prototype rated at 500W was built to verify the analysis and modeling. 6 MOSFETs were used in both sides of the converter. A coupling three-phase inductor with five windings on the five legs was used as input inductor L1~L3. A three-phase transformer with its primary windings star connected was used to isolate the HVS and LVS. Three extra inductors were used to achieve the desired total leakage inductance value. Texas Instrument’s TMS320F2808 was used for real-time control. The control system hardware includes the DSP board, the isolated driving circuits, the isolated overvoltage and overcurrent detection circuits, CAN bus, RS232, USB and single-chip Ethernet communication circuits. A PC host program is designed for supervision. The switching frequency was set to 20kHz. An oscilloscope was used to record the waveforms. Fig. 9 shows waveforms of voltage Va2p, currents ILa and IL1. Fig. 10 shows the waveforms of voltage VDS(S1), VDS(S7) across the source and drain terminals of S1, S7, and currents IS1, IS7 which flows through S1, S7, respectively.
Figure 9. Key experimental waveforms of the converter
Figure 10. Voltage and current experimental waveforms of S1 and S7
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As shown in Fig. 10, it can be seen that the output voltage Vout of the HV net reached 302V. All the switches achieved ZVS in the soft-switching area. Further tests need to be done in buck mode and to test the efficiency of the converter. Conclusion
In this paper, a three-phase current-fed dual active bridge bidirectional dc-dc converter which can achieve ZVS in a large range is discussed. The mathematic model and the power transfer characteristic are analyzed. The soft-switching principle is described and its criterias is derived. The simulation and experimental results verified the validity of the proposed circuit. References [1]
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