Investigation of ZVS Condition for Dual-Active-Bridge Converter using

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Abstract—This paper investigates the operation principle of Dual-Active-Bridge (DAB) converter using Dual-Phase-Shift modulation. All eight operation modes ...
Investigation of ZVS Condition for Dual-Active-Bridge Converter using Dual-Phase-Shift Modulation Nguyen Duy Dinh, Nguyen Duc Tuyen, Goro Fujita

Mohd Nabil Bin Muhtazaruddin

Shibaura Institute of Technology, Japan Email: [email protected]

Universiti Teknologi Malaysia Email: [email protected]

DC-Bus

Abstract— This paper investigates the operation principle of Dual-Active-Bridge (DAB) converter using Dual-Phase-Shift modulation. All eight operation modes are examined in order to find out the limitation for Zero Voltage Switch (ZVS) achievement. Some constraints are established to identify the ZVS region. Simulation results affirm that if the modulation is taken inside the region, lower switching dissipation could be attained. Especially, at the boundary of that region, the switching devices could obtain not only ZVS but also ZCS characteristic.

Wind turbine generator

AC DC

DC Solar PV Array

DC Loads

DC DC DC AC

Index Terms DPS, DAB, ZVS.

Grid

DC Battery

DC

I. I NTRODUCTION In hybrid renewable energy system, energy storage (e.g. battery, ultra-capacitor) plays a very important role. A typical configuration of such system can be seen in Fig.1. When the power from distributed generators (e.g. PV, wind turbine, etc.) fluctuates or intermits, of loads change, energy storage must compensate the variation to maintain the voltage of the common DC-bus at a reasonable value. In order to interface energy storage with that DC-bus, a bidirectional power converter usually be employed. Many researches have been conducted to deal with that converter in both isolated and non-isolated topologies [2]. For applications required galvanic isolation and high voltage gain ratios, the isolated bidirectional converter using high frequency transformer is preferred. Among many non-isolated topologies, Dual-Active-Bridge (DAB) [3] structure has been gained the most attention in recent years because of its inherent Zero Voltage Switching (ZVS) characteristic and high power density [4]. There are several switching methods for that DAB converter including Single-Phase-Shift (SPS), ExpandedPhase-Shift (EPS), Dual-Phase-Shift (DPS), and Triple-PhaseShift (TPS) modulation. Among those, DPS was claimed in [4] to be the most promising switching technique for DAB converter since it can improve overall efficiency and expand the ZVS operation range compared to SPS and EPS, and is easier to be implemented than TPS. The DPS modulation method uses two shift-angles which one for both two legs of each bridge and the other for two bridges. Depending on the relationship between that two shiftangles, there are several modes of operation. The operation principle, transmission power and soft switching condition of DAB converter using the DPS modulation were discussed in

DC

Ultracapacitor

Fig. 1.

DC AC

DC

AC Loads

DC

Typical configuration of Hybrid Renewable Energy System

[4], [5], [6], [7]. However, these publications are not consistent in the number of the converter’s operation modes. Paper [5] divides the operation of DAB with the DPS modulation by six modes, meanwhile it is classified by two modes and four modes in [6] and [7], respectively. Furthermore, the constraints for ZVS achievement are also not the same in these papers. In paper [3], there is only a simple condition for ZVS which is probably not enough to gain the ZVS characteristic for all switches. The constraint addressed in paper [5] on the other side is only for the specific examined modes in that study but all operation modes. Although paper [7] discusses this problem, it does not present any explicit restraints to achieve ZVS. This study investigates the DPS-DAB converter by analyzing all operation modes to find out ZVS condition and region for each mode. Its content is divided in five sections. Section II introduces the DAB converter and the DPS modulation method. Section III investigates the operation principle to derive some mathematic equations for identifying the transferred current. Section IV discusses the ZVS’s condition and its limitation. Simulation results will be shown in section V to validate the accuracy of previous investigation. Finally, section VI gives some conclusions.

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Vb Ψ + I0 ωL

I1 = ݅௕ᇱ

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There are eight switching states in mode 1. In the first state, S1 and S3 are ON that lead to short circuit in the primary side of the transformer meanwhile on the other bridge, since S4 and S3 are ON, energy stored in the transformer is transferred to DC-bus. If I0 is the initial current at the beginning of the first state, the current I1 at the end of this state can be determined by (1):

‫ݒ‬௕ᇱ

where ω is the switching frequency in rad/s. In the second state, the transformer is shorted in both sides, no energy is transferred and inductor current iL remains constant in this period. If I2 is the current at the end of second state, I2 can be calculated by (2). I2 =

ܵଶᇱ

Dual-Active-Bridge converter

0 (φ − Ψ) + I1 ωL

III. D ERIVATION OF E QUATIONS Typically, considering the mode 1 with following assumptions: • High frequency transformer does not saturate.  • Transition time of S1−4 and S1−4 , which are much smaller than switching period, can be neglected.  • Voltage drops on S1−4 and S1−4 are very small compared to the mean values of terminal voltages, Vs and Vb . • Voltages on energy storage and DC-bus remain constant during one switching cycle.

(2)

The secondary side of the transformer is shorted in the third state whereas the primary side is connected to Vs . Energy is stored into transformer as electromagnetic form, or in the other word, the equivalent inductor L is charged. (3) can be used to evaluate the current at the end of third state, I3 :

II. DAB CONVERTER WITH DPS MODULATION Power circuit of the DAB converter is illustrated in Fig.2.(a).  Switch S1−4 and S1−4 can be either MOSFET or IGBT. For simpler analyzing, high frequency transformer is replaced by its total leakage inductance L as depicted in Fig.2.(b). In this figure, vs ,is and vb , ib are the voltage and the current at terminals of storage and DC-bus, respectively; vbr1 and vbr2 are the output voltages of two active bridges; iL is the current flow through inductor L. The positive directions of electrical parameters are chosen as in Fig.2. And, Φ and Ψ are shifted-angles between two legs of each bridge and between two bridges, respectively. Because of the similar role of two legs of each bridge, only a half range of Φ (i.e. [0, π]) is concerned while a full range of Ψ (i.e. [0, 2π]) must be considered for bidirectional power transferring. Hence, eight operation modes of the converter can be occurred depending on the relationship between Φ and Ψ as illustrated in Fig.3. Fig.4 shows how these modes are located in Φ-Ψ graph.

(1)

Vs Ψ + I2 ωL

I3 =

(3)

In the fourth state, the primary side connects to V s while the secondary one joins to DC-bus. The electric energy not only charges into transformer but also transfers to DC-bus. The current at the end of fourth state, I4 , is calculated by (4): 

I4 =

Vs − Vb (π − Ψ − φ) + I3 ωL

(4)

Note that at equilibrium state, I4 = −I0 , solve (1), (2), (3), (4) for I0 : I0 = V

πVs . [(1 − K) φ − 2KΨ − (1 − K) π] 2ωL

(5)



where K = Vbs . The next four states act in the same manner as the previous four states in a reverse direction. Replace I0 calculated by (5) into (1), (2), (3): ⎧ I0 ⎪ ⎪ ⎨ I1 I2 ⎪ ⎪ ⎩ I3

= πC. [(1 − K) φ − 2KΨ − (1 − K) π] = πC. [(1 − K) φ − (1 − K) π] = πC. [(1 − K) φ − (1 − K) π] = πC. [(1 − K) φ + 2Ψ − (1 − K) π]

(6)

Vs where C = 2ωL Similarly, next seven modes are analyzed and Table I summarizes mathematic equations for all operation modes of the DPS-DAB converter.

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Mode 7: ʹɎ െ Ȳ ൑ Ԅ ൑ Ȳ െ Ɏ

Fig. 3.

Eight operation modes of DPS-DAB converter

IV. ZVS C ONDITION AND L IMITATION In the mode 1, at ωt = 0, and ωt = π, S1 and S4 make transition. If I0 ≤ 0, their body diode will conduct before the switches turn on. Thus, to realize ZVS for S1 and S4 , I0 must not be positive. Similarly, the following condition must be satisfied in order to have the ZVS characteristic of all switches: ⎧ I0 ≤ 0  (S1 , S4 ) ⎪ ⎪ ⎪ ⎪ ⎨ I1 ≥ 0 S  , S  1 4 (7) (S2 , S3 ) I2 ≤ 0  ⎪ ⎪ ⎪ ⎪ ⎩ I3 ≥ 0 S  , S  2

3

Solve (7) for Φ and Ψ: ⎧  1 (φ − π) ⎨ 2Ψ ≥ 1 − K 0 = (1 − K) (φ − π) ⎩ 2Ψ ≥ (1 − K) (φ − π)

(8)

If voltage gain ratio K = 1, all transistors will transit at zero voltage regardless of the values of both Φ and Ψ. When K = 1, the converter does not have ZVS at all. In the mode 2, the constraint (9) must be contented for ZVS of all switches:  

1 1 2Ψ ≥ 1 + K φ+ 1− K π (9) 2Ψ ≥ (1 + K) φ + (1 − K) π

TABLE I S UMMARY OF MATHEMATIC EQUATIONS OF DPS-DAB CONVERTER Mode 1: Ψ < φ < π − Ψ ⎧ I = πC. [(1 − K) φ − 2KΨ − (1 − K) π] 0 ⎪ ⎨ I1 = πC. [(1 − K) φ − (1 − K) π] I2 = πC. [(1 − K) φ − (1 − K) π] ⎪ ⎩ I3 = πC. [(1 − K) φ + 2Ψ − (1 − K) π] Is = CK.Ψ (2π − Ψ − 2φ) Mode 3: π − Ψ < φ < Ψ ⎧ I = πC. [(1 + K) φ − (1 + K) π] 0 ⎪ ⎨ I1 = πC. [(1 + K) φ − (1 + K) π] I2 = πC. [(1 + K) φ − 2KΨ − (1 − K) π] ⎪ ⎩ I3 = πC. [− (1 + K) φ + 2Ψ − (1 − K) π] Is = CK. (π − Ψ) (π + Ψ − 2φ) Mode 5: Ψ − π < φ < 2π − Ψ ⎧ I = πC. [(1 + K) φ + 2KΨ − (1 + 3K) π] 0 ⎪ ⎨ I1 = πC. [(1 + K) φ − (1 + K) π] I2 = πC. [(1 + K) φ − (1 + K) π] ⎪ ⎩ I3 = πC. [(1 + K) φ + 2Ψ − (3 + K) π] Is = CK. (Ψ − π) (Ψ + 2φ − 3π) Mode 7: π + φ < Ψ < 2π − φ ⎧ I = πC. [(1 − K) φ − (1 − K) π] 0 ⎪ ⎨ I1 = πC. [(1 − K) φ − (1 − K) π] I2 = πC. [(1 − K) φ + 2KΨ − (1 + 3K) π] ⎪ ⎩ I3 = πC. [− (1 − K) φ + 2Ψ − (3 + K) π] Is = CK. (2φ − Ψ) (2π − Ψ)

Mode 2: φ < Ψ < π − φ ⎧ I0 = πC. [(1 − K) φ − 2KΨ − (1 − K) π] ⎪ ⎪ ⎨ I1 = πC. [(1 + K) φ − 2KΨ − (1 − K) π]

I2 = πC. [− (1 + K) φ + 2Ψ − (1 − K) π]

⎪ I = πC. [(1 − K) φ + 2Ψ − (1 − K) π] ⎪ ⎩ I3 = CK. 2πΨ − 2Ψ2 − φ2 s Mode 4: π − φ < Ψ < φ ⎧ I0 = πC. [(1 + K) φ + 2KΨ − (1 + 3K) π] ⎪ ⎨ I1 = πC. [(1 + K) φ − (1 + K) π] I2 = πC. [(1 + K) φ − (1 + K) π]

⎪ ⎩ I3 = πC. [(1 + K) φ + 2Ψ − (3 + K) π] Is = CK. (Ψ − π) (Ψ + 2φ − 3π)

Mode 6: π + φ < Ψ < 2π − φ ⎧ I0 = πC. [(1 + K) φ + 2KΨ − (1 + 3K) π] ⎪ ⎪ ⎨ I1 = πC. [(1 − K) φ + 2KΨ − (1 + 3K) π] I2 = πC. [− (1 − K) φ + 2Ψ − (3 + K) π]

⎪ I = πC. [(1 ⎪  +2K) φ2+ 2Ψ − (3 + K) π] ⎩ 3 2 Is = CK. 2Ψ + φ − 6πΨ + 4π Mode 8: 2π − φ < Ψ < π + φ ⎧ I = πC. [(1 − K) φ − (1 − K) π] 0 ⎪ ⎨ I1 = πC. [(1 − K) φ − (1 − K) π] I2 = πC. [(1 + K) φ − (1 + K) π] ⎪ ⎩ I3 = πC. [(1 + K) φ − (1 + K) π] Is = −C.K (π − φ)

TABLE II C ONSTRAINTS FOR ZVS ACHIEVEMENT OF ALL SWITCHES Mode 1

Step-down (K < 1) -



2

3 4

Matching (K = 1)

1 2

Ψ ≥ [(1 + K) φ + (1 − K) π] Ψ ≤π−φ Ψ ≥ 12 [(1 + K) φ + (1 − K) π] Ψ ≥π−φ

-



5

6 7

-

8

-

1 2

Ψ ≤ [− (1 + K) φ + (3 + K) π] Ψ ≤π+φ Ψ ≤ 12 [− (1 + K) φ + (3 + K) π] Ψ ≥π+φ



Ψ≤φ Ψ≤π−φ Ψ≥φ Ψ≤π−φ Ψ≥φ Ψ≥π−φ Ψ≤φ Ψ≥π−φ

Ψ ≤ 2π − φ Ψ≤π+φ Ψ ≤ 2π − φ Ψ≥π+φ Ψ ≥ 2π − φ

Ψ≥π+φ

Ψ ≥ 2π − φ Ψ≤π+φ

Step-up (K > 1) -



-





Ψ ≥ 12 1 + Ψ≤π−φ

1 K

Ψ ≥ 12 1 + Ψ≥π−φ

1 K









φ+ 1−

Ψ ≤ 12 − 1 + Ψ≤π+φ

1 K

Ψ ≤ 12 − 1 + Ψ≥π+φ

1 K





φ+ 1−



1 K 1 K



φ+ 3+



φ+ 3+

π

π

1 K 1 K

π

π

-

(’-’ means: No ZVS for all switches but probably some)

In step-down mode, K < 1:     1 1 φ+ 1− π 1+ K K (10) Otherwise, in step-up mode, K ≥ 1:     1 1 2Ψ ≥ 1 + φ+ 1− π > (1 + K) φ + (1 − K) π K K (11) In matching mode, K = 1: 2Ψ ≥ (1 + K) φ + (1 − K) π >

Ψ≥φ

(12)

Table II summarizes constraints for ZVS achievement of all switches regarding boundary condition for each operation mode. Fig.4 illustrates the ZVS region of DAB converter using the DPS modulation in step-down mode. The ZVS feature for all transistors can be realized if the modulation is taken inside the shaded areas. From Table II, the shaded ZVS area only depends on the value of K regardless of switching frequency or construction of the high-frequency transformer. The smaller or bigger value of K is, the narrower ZVS region of the DPS modulation is obtained. When K equals to 1, the converter will always perform ZVS with every pair value of Φ and Ψ. It should be noted that although switching outside of the shaded

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Voltage and switch current wave form in mode 2

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areas achieve ZVS, it is not applicable for all transistors. V. S IMULATION R ESULTS The operation mode 2 is validated by the simulation. The voltage level of Energy Storage port and DC-bus are fixed at 200V and 100V, respectively. As a result, the voltage gain ratio at 0.5 is used in the simulations. The switching frequency is 50 kHz. The transformer has primary referred leakage inductance of 50μH. For a better evaluation of switching loss and the ZVS effect, power electronic devices used in the simulation are thermal modules of IRFP460 MOSFET manufactured by International Rectifier. Simulation results demonstrated in Fig.5 consist of four cases with the same bridge shift-angle and four phase-shift angles. Fig.5(a) presents the case when DPS is carried out in the boundary of the shaded areas in Fig.4. The current flow through S1 (IRFP460) is zero when it is switched on as well as switched off, hence the switch have both zero voltage and zero current (ZVS - ZCS) at commutation. In this case, the measured switching loss is about 3.14W. Fig.5(b) describes the DPS modulation inside the ZVS region. The current of S1 is negative at commutation, thus the switch achieves ZVS. The switching dissipation of 3.18W, which is 1.3% higher than the previous case, is measured. The result showed in Fig.5c is taken outside the ZVS region. Switching current is positive at the moment MOSFET turns on. The switching loss in this case is 3.36W, which is 7% higher than that in ZVS - ZCS circumstance. The result when taking DPS at the boundary between mode 1 and mode 2 is illustrated in Fig.5d. It is almost the same as seen in Fig.5c but the switching loss is at 4.13W, 31.5% higher than that in the ZVS - ZCS case. VI. C ONCLUSION This paper has investigated the operation principle of dual active bridge converter using dual phase shift modulation. Mathematic equations are constructed in order to assess the current transfer through the transformer and to evaluate the ZVS characteristic of the converter. Several constraints are established to limit the ZVS region. As affirmed by simulation, the DPS modulation taking inside the ZVS region will gain the ZVS feature, and as a result, the power dissipation is reduced. Especially, at the boundary of the region, the power electronic devices achieve both ZVS and ZCS characteristics, hence the switching loss is the lowest and the performance is the best. Recently, the DAB typed converter is high prospect in hybrid renewable energy system application. This research can be a reference for studies on modulation and controlling of DAB converter to get better performance. R EFERENCES [1] Wei Li, Joos. G., and Belanger.J., “Real-Time Simulation of a Wind Turbine Generator Coupled With a Battery Supercapacitor Energy Storage System”, Industrial Electronics, IEEE Transactions on , vol.57, no.4, pp.1137-1145, April 2010. [2] Tao.H., Kotsopoulos.A, and Duarte.J.L., Hendrix, M. A M, “Family of multiport bidirectional DC-DC converters”, Electric Power Applications, IEE Proceedings , vol.153, no.3, pp.451, 458, 1 May 2006.

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