SOFT-SWITCHING BIDIRECTIONAL ISOLATED THREE-PHASE DC-DC CONVERTER WITH DUAL PHASE-SHIFT AND VARIABLE DUTY CYCLE

Herminio Miguel de Oliveira Filho, Demercil de Souza Oliveira Júnior, and Paulo Peixoto Praça

Energy Processing and Control Group – GPEC Electrical Engineering Department – DEE

Federal University of Ceará – UFC Fortaleza – CE – Brazil

herminio@dee.ufc.br, demercil@dee.ufc.br, paulopp@dee.ufc.br

Abstract – This paper presents the analysis, design, and experimental results for a soft-switching bidirectional isolated three-phase DC-DC converter with dual phase-shift and variable duty cycle. The topology uses three single H-bridges in the primary side and a three-phase inverter in the secondary side. The high frequency isolation is ensured by using three single-phase transformers connected in open delta-wye configuration. Variation of both phase shift angles between single H-bridge legs and/or primary and secondary side allows the power delivery control. This additional flexibility allows the system to maintain a low reactive power flow. The variable duty cycle is used to ensure a constant voltage bus and ZVS soft switching operation. A detailed analysis is presented considering a model based on fundamental components. Experimental results for a prototype are performed to validate the model used.

Keywords – Three-phase DC-DC converter, soft-

switching, phase shift.

I. INTRODUCTION

Research works regarding DC-DC converters have substantially increased in the last few years due to applications in hybrid electric vehicles, stand-alone systems used in renewable energy, DC distribution, and smart-grids. One of the most popular topologies is the ZVS (zero voltage switching) PS (phase-shift) PWM (pulse width modulation) full-bridge converter. However, for high power levels, the components suffer several stresses [1].

The troubleshooting of the previous converter was presented in 1988 by Prasad [2] and this paper introduced the concept of “Three-Phase DC-DC conversion”, which uses a three-phase inverter, a three-phase rectifier, and a high frequency isolation transformer. Thus, it is possible to reduce the components stress and also the transformer volume, with increase of the current and voltage ripple frequency in both input and output sides. Several solutions were developed aiming to improve the performance of the converter shown in [2], such as [1], [3], [4], and [5].

In 1991, De Donker [6] presented the first bidirectional three-phase DC-DC converter, known as Dual Active Bridge, which uses the leakage inductance and phase-shift (PS) concept to control the power delivery. Other bidirectional solutions were developed using PS e.g. [7], and employing resonant converters with such power delivery technique [8]. The work described in [9] shows that the power flow is controlled according to the switches operation.

This work presents a bidirectional version of the topology introduced in [3] without output inductor filter, which is shown in Fig. 1. The converter increases power rating by paralleling phases, not by paralleling multiple devices, and it decreases turn ratio due to a double output voltage by transformer open delta-wye connection. The possibility of direct and indirect power flow is achieved with dual phase-shift (DPS) [10]. Considering appropriate angles, it is possible to reduce the reactive content and reduce transformer volume. The duty cycle of the input bridge can be varied to regulate the input voltage and ensure ZVS over the entire operation range. A detailed analysis, design example are presented. In [11] are realized many simulations to validate the fundamental model. In this paper are presented experimental results.

Fig. 1. Proposed topology.

II. ANALYSIS OF THE FUNDAMENTAL MODEL

Conceptually, each phase of the converter can be viewed as an inductor (the transformer leakage inductance) driven at either terminal by a controlled square-wave voltage source. In order to simplify the analysis, the square-wave sources are replaced by their respective fundamental components and the output voltage is referred to the primary side. This model is identified as the synchronous-machine equivalent circuit and may present similar properties. Since all quantities are sinusoidal at a single frequency, a phasor analysis can be carried out [6]. The per-phase model of the proposed topology is presented in Fig. 2 and a dual phase-shift analysis is developed to obtain the power flow and commutation characteristics of the converter. The voltage sources use control angles α and θ, which correspond to the phase displacements of the secondary bridge and the primary bridge leg A2 with regard to the primary bridge leg A1, respectively.

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A. Power Delivery The input voltage magnitudes VA1 and VA2 both vary in

magnitude and phase with the duty cycle d, according to (1) and (2). ( )1 2

jA A iV V V d e γ= ⋅= (1)

Where

2

d πγ π ⋅= − + (2)

Fig. 2. Per-phase model of the dc-dc converter topology.

Vi(d) is obtained from the fundamental component of the leg midpoint with regard to capacitive bus midpoint. The fundamental equation is:

( ) ' ''2 2

dci

V v vV dπ π

+⋅⋅ ⋅

= (3)

Where ( ) ( ) ( )' 2sin 2 2 sin 4 1 sin 4v d dπ π π+ − + −⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦= (4)

( ) ( ) ( )'' 16 sin sin 4 sin 2v d d dπ π π π⋅ ⋅ ⋅ + ⋅ ⋅ − ⋅ ⋅= (5) The output voltage magnitude is given by

( ) ( )' 2 2 0.5 2o i i iV G V d G V G V= ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ (6) Where G is static gain between Vo’ and Vi. The current

phasor in steady-state is given by

( )0 '

1 2ˆ , ,2

j j jA A o

Ls L

V e V e V eI d

j f L

θ α

α θπ

⋅ − ⋅ − ⋅⋅ ⋅ ⋅ ⋅

= (7)

Where fs is the switching frequency. By substituting (1) and (6) in (7), the final expression for

the current phasor is obtained as:

( ) ( ) (1 ) 2ˆ , ,2

j j ji i

Ls L

V d e e G V eI d

j f L

γ θ α

α θπ

⋅ ⋅ − − ⋅ ⋅ ⋅⋅ ⋅ ⋅ ⋅

= (8)

The active and reactive power are given by (9) and (10), respectively. ( ) ( ) ( )*ˆ, , Re 2 , ,j

o i LP d G V e I dαα θ α θ⎡ ⎤= ⋅ ⋅ ⋅ ⋅⎣ ⎦ (9)

( ) ( ) ( )*ˆ, , Im 2 , ,jo i LQ d G V e I dαα θ α θ⎡ ⎤= ⋅ ⋅ ⋅ ⋅⎣ ⎦ (10)

According to previous equations, the characteristics for the active power (Po) and power factor (PF) of the converter varying angles θ and α can be obtained according to Fig. 3 and Fig. 4, respectively, considering that the duty cycle is 0.5. The highest active power values occur when θ and α tend to 180º and 90°, respectively. Besides, the highest values for PF occur when θ and α tend to 180° and 0°, respectively, where Po is approximately null.

Fig. 5 shows the profile of Po by varying angles θ and α for d=0.3. By decreasing the duty cycle, the maximum values of Po tend to occur at smaller values of α if compared with the previous case. It can be seen that the maximum value of Po, about 3.3, is less than that obtained in Fig. 3, which is 4.

When the duty cycle is not equal to 0.5, the phase current becomes asymmetrical, implying the increase of reactive power flow and the consequent reduction of the maximum power. The profile for power factor is shown in Fig. 6, and it can observed that the maximum PF is about 0.8. The maximum and minimum PF points are separated by values that vary in descending form.

Cases for duty cycle lager than 0.5 is not shown, but these cases, as d = 0.7, for example, presents results similar to those obtained for d=0.3, although Po and PF increase in the reverse direction.

Fig. 3. Active power (p.u.) for d=0.5.

Fig. 4. Power factor for d=0.5.

B. Switching Characterization The switching characterization for the proposed converter

is obtained from the time varying current analysis: ( ) ( )( ) 2 , , sinL Li t I d tω α θ ω ϕ⋅ ⋅ ⋅ −= ⋅ (11)

Where φ is the lag angle with regard to the voltage:

( )( )

ˆIm , ,arctan

ˆRe , ,L

L

I d

I d

α θϕ

α θ

⎡ ⎤⎣ ⎦⎡ ⎤⎣ ⎦

= (12)

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The condition to achieve zero voltage switching in the upper switch from input bridges lies in defining iL(0)=0. Applying this condition in (11) gives: ( )sin 0ϕ− = (13)

The static gain expression for the input upper switch boundary, which limits soft and hard switching regions, is obtained by substituting (12) in (13) and rearranging the resulting equation as:

( ) ( )cos 1 cos sin sin

2 cosi

ii

V dG

Vγ θ γ θ

α⋅ ⋅ − + ⋅⎡ ⎤⎣ ⎦

⋅ ⋅= (14)

Fig. 5. Active power (p.u.) for d=0.3.

Fig. 6. Active power (p.u.) for d=0.3.

The power at the input upper switch boundary is found by substituting (14) in (9).

To achieve zero voltage switching in the lower switch from input bridges is necessary defining iL(2πd)=0. Applying this condition in (11) gives: ( )sin 2 0dπ ϕ⋅ ⋅ − = (15)

The static gain expression for the input bridge boundary is obtained by substituting (12) in (16) and rearranging the resulting equation as:

( )( )2 cos sin tan 2

iii

i

V d A BGV dα α π

+⋅⋅ + ⋅ ⋅ ⋅

= (16)

Where: ( )cos 1 cos sin tan 2A dγ θ θ π⋅ − − ⋅ ⋅ ⋅⎡ ⎤⎣ ⎦= (17)

( ) ( )sin sin 1 cos tan 2B dγ θ θ π= ⋅ + − ⋅ ⋅ ⋅⎡ ⎤⎣ ⎦ (18) The power at the input upper switch boundary is found by

substituting (16) in (9). The condition to achieve zero voltage switching in the

output bridges is to find the value of ω.t=α so that iL(α)=0. Applying this condition in (11) gives: ( )sin 0α ϕ− = (19)

The static gain expression for the output bridge boundary is obtained by substituting (12) in (13) and rearranging the resulting equation as:

( )

2 cos sin tani

oi

V d C DGV α α α

+⋅⋅ + ⋅

= (20)

Where: [ ]cos 1 cos sin tanC γ θ θ α⋅ − − ⋅= (21)

( )sin sin 1 cos tanD γ θ θ α= ⋅ + − ⋅⎡ ⎤⎣ ⎦ (22) Analogously to the case of the input bridge switching

conditions, the power at the input bridge boundary is found substituting (20) in (9).

The graphs in Fig. 9 are plotted using (9) and varying static gain G, whose values are 0.5, 1.0, 1.5, and 2.0. It can be seen that, independent of the static gain, the ZVS region always lies between the boundaries, and primary upper and lower switches boundaries are similar. For other cases, only one bridge operates in ZVS mode. When θ and d equal 180° and 0.5, respectively, and with unity static gain, the converter behaves in ZVS mode for any value of α.

Fig. 9. Input and output bridge soft-switching boundary for d=0.5

and θ=-180º.

Fig. 10 presents the case where θ is adjusted to 120º, while the ZVS region occurs between the boundary curves. Decreasing θ eliminates the ZVS characteristic for unity static gain at low values of α (in this specific case, lower than -40º).

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↑output bridge boundary

ZVS region

hard-switching region

hard-switching region

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Fig. 10. Input and output bridge soft-switching boundary for d=0.5

and θ=-120º.

When duty cycle tends to extreme values (0 or 1), the switching characteristics are changed. The third analysis shown in Fig. 11 considers that the duty cycle is 0.3, while two regions exist. The first one is a ZVS region, which lies between the output bridge and the most internal input switch boundaries. The second region is composed by the remaining parts, where hard-switching is verified. When the duty cycle is higher than 0.5, the switching characteristics are similar to previous case with two regions, but they are inverted.

Fig. 11. Input and output bridge soft-switching boundary for d=0.3

and θ=-180º.

III. EXPERIMENTAL RESULTS

Fig. 12 shows the experimental prototype developed from the specifications proposed in Table I and its power circuit components are indicated in Table II. The values chosen are supposed to ensure that the converter presents the behavior of soft-switching and high power factor.

The FPGA Altera Cyclone® IV EP4CE22F17C6N was used to generate the triangular carrier and reference signals and, consequently, the dual phase shift signal. The value measured for α and θ is 28.3° and 180°, respectively.

First are shown results for the design example while after for static gain modified. Finally is presented the efficiency of the converter.

Fig. 12. Experimental prototype.

TABLE I Specifications for the design example

Input Voltage Vi 96V Output Voltage Vo 400V Output Power Po 4kW

Phase shift between primary and secondary sides α 28.5° Phase shift between primary side legs θ 180°

Duty cycle d 0.5 Switching frequency fs 20kHz

Efficiency η 95% TABLE II

Power circuit components used the design example Input electrolytic capacitor 6 x 100µF/400V

Input polypropylene capacitor 6 x 1µF/400V Output electrolytic capacitor 1 x 470µF/450V

Output polypropylene capacitor 3 x 470nF/630V

Transformer Core Magmattec MMT139T6325, NT = 28/15

Inductor Ld = 21,5µF, core Thornton NEE 42/21/20, NLd = 15

Primary Switches 12 x IRFP4321PbF Secondary Switches 6 x IRGP50B60PD

A. Experimental results for design example Fig. 13 shows the primary and secondary line voltages,

besides primary current when the converter is operating in buck mode. The maximum values for the voltages are, respectively, 96V and 400V, with a voltage ripple of 5V and 7V, respectively. The rms primary line current is 16.1A. The phase shift between primary and secondary sides can be seen by displacement of the voltage waveforms.

Three secondary line currents are shown in Fig. 14. Waveforms are symmetries and the DC level observed is less than 3%. Primary line currents do not present DC level due to use of series capacitors.

The switching characterizations for design example are shown in the next two Figures. All current through the switches in this paper are measure indirectly using the primary line current. The primary side is presented by Fig. 15 and secondary side by Fig. 16. Both cases show a ZVS switching, which is a behavior expected according to

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hard-switching region

hard-switching region

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← Lower input switchboundary

↑output bridge boundary ZVS region

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specifications from Table I and profile feature presented in Fig. 9 for = 28°.

Fig. 13. Secondary line voltage (leakage inductance plus inductor)

VLp (1 - 100V/div - 10µs/div), primary line voltage VLs (2 - 200V/div - 10µs/div), and primary line current ILp (3 - 50A/div -

10µs/div).

Fig. 14. Secondary line currents ILp (1 - 20A/div - 10µs/div).

Fig. 15. Results for -28.5°: Primary switch voltage VSp (1 –

100V/div - 5µs/div) and primary switch current ISp (2 – 5A/div - 5µs/div).

B. Switching characterization for static gain modified The waveforms shown in this section are obtained using

rated half voltage (Vi = 96V and Vo = 200V). According to Fig. 9, when α= -20° and the static gain

equals 1.5, the input bridge presents hard switching. The

experimental results presented in Fig. 17 and Fig. 18 validates this behavior.

Fig. 16. Results for -28.5°:Secondary switch voltage VSs (1 –

50V/div - 5µs/div) and secondary switch current ISs (2 – 10A/div - 5µs/div).

Fig. 17. Results for -20° and G = 1.5: Primary switch voltage VSp

(1 – 20V/div - 5µs/div) and primary switch current ISp (2 – 10A/div - 5µs/div).

Fig. 18. Results for -20° and G = 1.5: Secondary switch voltage VSs

(1 – 100V/div - 5µs/div) and secondary switch current ISs (2 – 10A/div - 5µs/div).

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C. Efficiency Fig. 19 presents the measured efficiency curve of the

converter as a function of the output power for buck mode. It has reach a final efficiency of 96.0% for output power equals 4033W, with a pick efficiency of 96.3%.

Fig. 19. Efficiency for design example for buck mode.

IV. CONCLUSION

This paper has presented a novel soft-switching bidirectional isolated three-phase DC-DC converter with dual phase shift and variable duty cycle. Through the equations and graphs generated from the fundamental model analysis, it is possible to obtain the optimum design specifications that ensure high power factor at rated condition and soft-switching.

The experimental results have validated the fundamental model, composed by power delivery and switch characterization. The efficiency is satisfactory, with a final value lager than 95%. Therefore the converter proposed can be an efficient solution for rated powers larger than the design example proposed in this paper.

Future works include a measured efficiency curve for the boost mode and an analysis of the dynamic model with a power flow control system.

ACKNOWLEDGEMENT

The authors acknowledge the CAPES and PPGEE/DEE/UFC for the financial support, and also the members of Group of Energy Processing and Control – GPEC/UFC for the friendship and overall support.

REFERENCES

[1] D. S. Oliveira Jr. and I. Barbi, “A Three-Phase ZVS PWM DC-DC Converter With Asymmetrical Duty Cycle Associated With a Three-Phase Version of the Hybridge Rectifier”, IEEE Transactions on Power Electronics, vol. 20, no. 2, pp. 354-360, March 2005.

[2] A. R. Prasad, P. D. Ziogas, and S. Manias, “Analysis and Design of a Three-phase Off-Line dc-dc Converter with High-Frequency Isolation”, in IEEE 1988 Industry

Applications Society Annual Meeting, vol. 1, pp 813-820, 1988.

[3] C. Liu, A. Johnson, and J. Lai, “A Novel Three-Phase High-Power Soft-Switched DC-DC Converter for Low-Voltage Fuel Cell Applications”, IEEE Transactions on Industry Applications, vol. 41, no. 6, pp. 1691-1697, November 2005.

[4] D. S. Oliveira Jr., F. L. M. Antunes, and C. E. A. Silva, “A Three-Phase ZVS PWM DC–DC Converter Associated with a Double-Wye Connected Rectifier, Delta Primary”, IEEE Transactions on Power Electronics, vol. 21, no. 6, pp. 354-360, November/December. 2006.

[5] C. Yoon, J. Kim, and S. Choi, “Multiphase DC–DC Converters Using a Boost-Half-Bridge Cell for High-Voltage and High-Power Applications”, IEEE Transactions on Power Electronics, vol. 26, no. 2, pp. 381-388, February 2011.

[6] R. W. A. A. de Doncker, D. M. Divan, and M. H. K. Kheraluwala, “A Three-phase Soft-Switched High-Power-Density DC-DC Converter for High-Power Applications”, IEEE Transactions on Industry Applications, vol. 27, no. 1, pp. 63-73, Jan/Feb. 1991.

[7] Z. Wang and H. Li, “A Soft Switching Three-phase Current-fed Bidirectional DC-DC Converter With High Efficiency Over a Wide Input Voltage Range”, IEEE Transactions on Power Electronics, vol. 27, no. 2, pp. 669-684, February 2012.

[8] R. Mirzahosseini and F. Tahami, “Phase-Shift Three-Phase Bidirectional Series Resonant DC/DC Converter”, IECON 2011 – 37th Annual Conference on IEEE IES, pp 1137-1143, 2011.

[9] H. Cha, “A New Bi-directional Three-phase Interleaved Isolated Converter with Active Clamp”, Applied Power Electronics Conference and Exposition – APEC, pp 1766-1772, 2009.

[10] H. Bai and C. Mi, “Eliminate Reative Power and Increase System Efficiency of Isolated Bidirectional Dual-Active-Bridge DC-DC Converters Using Novel Dual-Phase-Shift Control”, IEEE Transactions on Power Electronics, vol. 23, no. 6, pp. 2905-2914, Nov. 2008.

[11] H. M. Oliveira Filho, D. S. Oliveira Jr., C. E. A. Silva, F. L. Tofoli, “ZVS Bidirectional Isolated Three-Phase DC-DC Converter with Dual Phase-Shift and Variable Duty Cycle”, IIEE/IAS International Conference on ndustry Applications – Induscon, pp 1-8, 2012.

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