Modified Dual Active Bridge Bidirectional dc-dc

Converter with Optimal Efficiency

Hamid Daneshpajooh, Alireza Bakhshai, Praveen Jain

ePower Center, ECE Department

Queen’s University

Kingston, ON, Canada

Abstract—In this paper a modified dual active bridge (DAB)

topology with a new modulation technique is proposed for

bidirectional dc-dc conversion that not only improves the soft

switching range of the converter but also highly reduces the

large current ripples at low voltage side. Phase shift and duty

cycles of active bridges on two sides, (d1, d2, θ), are used to

control the converter in order to extend the soft switching range

against wide range of operating voltages on both ports and also

to maximize the efficiency. The converter operation is analyzed

and the soft switching conditions are extracted. For an aero

space application it is shown that with a proper converter design

the soft switching zones in control space can cover full power

range against the wide voltage range required by standards. The

extraction of optimal trajectories of control parameter values

(d1opt, d2opt, θopt), for maximum efficiency are also discusses and

an implementation method for the controller is proposed.

Precise simulated model of the converter is developed to verify

the analytic results and fine tune the design. A 2KW, 250 KHz

prototype is also implemented to verify the results in practice.

I. INTRODUCTION

Bidirectional dc-dc converters are growingly used in many energy systems especially in renewable applications, such as hybrid/electric vehicles or uninterruptable/auxiliary power supplies. They are also considered for more specific modern high power density converters as in more-electric aircrafts. Light weight and compact size along with unified bidirectional converter structure are key features requested for those applications, especially in aerospace. Usually batteries or ultra capacitors are used as energy storage component of the system and placed at the low voltage port of bidirectional converter. They are usually made at low voltages for better reliability and lower cost. The other port is usually at higher voltage (a few hundred volts) and connected to the system that is to be served by the energy system. High switching frequency is required to reduce the size and weight of the converters, but to avoid high switching losses, soft switching techniques should be employed. Compared to hard switched converters, these techniques also improve other quality factors of the converter such as EMI and switching noises. Among the bidirectional soft switched converters, dual active bridge (DAB) introduced in [1] and [2] is one of the most common choices for medium to high power isolated bidirectional dc-dc converters (Fig. 1). Phase shift modulation (PSM) control is used in most of

previous works but the soft switching range of the converter is limited to a narrow range of operating dc voltages (VA and VB) and for relatively higher power levels in the power range of the converter. The reason is that with a single controlling variable (phase shift) only one parameter (transferred power) can be controlled and no control is left to keep the converter in soft switching mode when other system parameters (VA or VB) are changed. So newer modulation techniques with more degrees of freedom are further improved as in [3] and [4] employing phase shift plus duty cycle control to compensate the wide voltages variations and improve soft switching performance. The DAB converter suffers from another problem that is due to the voltage source operation of its LV side bridge (named side A in Fig. 1). The dc bus current ripples in any voltage fed bridge topology are relatively high, but it will be too much when bus voltage is low and power is high. In other words, the amount of ripple in the iA current is very high that requires a filter with high current rating to smooth the bus dc current. Note that batteries and ultra capacitors require smooth charge/discharge current for longer life time and better efficiency. To avoid this problem current fed type converters are used, usually by inserting a large series inductance between the bridge and the dc bus. But with these arrangements, extra active or passive auxiliary elements are necessary for voltage clamping and to achieve soft switching. Besides these auxiliary switches may operate in hard switching mode in some switching instances making them even less efficient [5, 6]. When minimum number of switches and less power rating is desired, dual half bridge (DHB), presented in [7] may also be used. In DHB phase shift control is used but again it is not sufficient to keep soft switching in full range. An improved modulation technique for DHB converter can be found in [8]. In DHB the bus current at low voltage side is much smoother than a voltage fed bridge. Due to the half bridge structure this converter is not suitable for high power unless multiple converters are used together.

To address the problems mentioned for conventional DAB converters the modified DAB (Fig. 2) along with a new modulation technique is presented in this paper. Other advantages are also achieved that will be discussed later.

978-1-4577-1216-6/12/$26.00 ©2012 IEEE 1348

II. MODIFIED DUAL ACTIVE BRIDE

A. Modified DAB Topology

Unlike traditional current fed converters, in the modified DAB converter inductors are connected to the center pole of the bridge legs instead of dc bus (Fig. 2). With this arrangement no extra components for soft switching are necessary and the inductors not only smooth the dc bus current but also help soft switching of the converter. Similar idea can be implemented for bridges with other number of legs, like 3 phase dc bridges. In this topology the A-side converter has a current-fed operation with a much smaller ripple because the currents in the two dc inductors (Ldc1=Ldc2) are in opposite phase and ripples cancel out each other. Besides, the boosting operation of dc inductors along with their associated switching legs increases the voltage level on the primary side of transformer and the turn ratio and primary current are reduced (almost halved) compared to a regular DAB converter. The cost of these advantages is an imbalance in current stress on top and bottom switches of each leg. The bottom switch should have higher current ratings. This will not be a major problem when MOSFETs are used because low voltage switches have very small on-resistances and it can be decreased even more by putting them in parallel if higher current rating is desired.

B. Modified DAB converter operation

The basic principles of energy transfer for a modified DAB converter is similar to the conventional one that is discussed in [1-4]. In a few words, the energy transfer principle is based on phase shift and can be explained as follows: in each switching cycle the energy is first stored by the source side bridge in the magnetic field of inductance L comprised of transformer leakage inductance plus any other series inductance, then in the rest of the switching cycle this energy is released to the load side through the other bridge. In the modified topology, LV side switches have two roles in both power flow directions. Their first role in the forward (AB) power flow direction is boosting LV side voltage source VA to higher auxiliary bus voltage (VM) and the second role is to invert dc voltage VM onto transformer primary (vP). This voltage will be amplified by transformer and rectified by the other bridge to the B side dc bus as VB. In the reverse power flow direction (BA) the dc voltage VB is inverted to ac voltage vS and appears as vP in transformer primary. The first role of the A side bridge is rectifying ac voltage vp from transformer to dc voltage VM and second role is to act as a buck converter and reduce dc voltage VM to output voltage VA. The two legs of LV bridge operate in opposite phase, so by interleaving, the total A-side current (iA) has much less

ripple compared to individual dc inductors (iA1 and iA2). Three parameters are controlled. The first controlled parameter is phase shift (θ) that is defined as the phase angle between centers of positive voltage pulses applied to the series inductance. The two other control parameters are duty cycles in LV and HV bridges. Phase shift is usually the main control parameter that controls the amount of power and its direction. For example when duty cycles are equal, sign of phase shift determines the direction of power flow [1, 7]. The duty cycles also affect the amount of power but they are mainly employed to adjust the currents such that soft switching can be maintained. The three parameters are coupled and have interactions so a detailed analysis is necessary to understand the detailed operation of the converter in general case.

III. STEADY STATE ANALYSIS

A simplified and lossless model of the converter is used to analyze steady state operation of the converter (Fig. 3). The more realistic model that includes parasitic resistances is later considered in finding the soft switching zones of the converter and in efficiency optimization. To simplify the converter operation analysis, a number of cases based on the relative position of the voltage pulses (vP, vS), applied to the two sides of series inductance L should be considered. Only four main modes of operation are considered and analyzed here. Other modes that are not reasonable for dc-dc application are ignored. They are the modes in which one voltage pulse is completely inside another or the ones with too large phase shifts. In these cases circulating currents are large and reactive power through the transformer is very high compared to active power, resulting in excessive losses and low efficiency. The transformer and dc inductor waveforms are shown in Fig 4. The controlled parameters are θ, d1 and d2 . Duty cycles of the switches (Q1 and Q3 : d1 ; Q2 and Q4 : 1-d1, Q5 and Q7 : d2 ; Q6

and Q8 : 1-d2) are used to shape transformer voltages. The duty cycles of voltages applied to the series inductance are dA=min(d1,1-d1) for vP and dB =min(d2,1-d2) for vS. The theoretical range of three control parameters are (-π<θ<π; 0 < d1 <1; 0 < d2 <1) and (0<dA<0.5 and 0<dB<0.5). But in practice smaller ranges have to be considered. For example a reasonable duty cycle range can be from 0.2 to 0.8 depending on acceptable stress on the switches. For θ, usually zero power is achieved at zero phase shifts and peak power is achieved at π/2 in phase shift converters and so the range is limited to (-π/2<θ<π/2) [1,7]. These are not necessarily valid here because net phase shift between main harmonic components of square wave voltages depends also on the duty cycles. To simplify the analysis and make the controller parameters lucid a new auxiliary parameter is defined as

VB

L

Q1

Q6Q2

i

iB

vpVA

Side ‘A’ Side ‘B’

vs

Q3

Q4

Q5

Q8

Q7

CA

1:n

CB

iA

Figure 1: Conventional Dual Active Bridge (DAB) Converter

VB

(HV)

L

Q1

Q6Q2

i

iB

Ldc1

vp

VM

iA1

VA

(LV)

Side ‘A’ Side ‘B’

vs

Q3

Q4

Ldc2iA2

Q5

Q8

Q7

CM

1:n

CBiA

CA

Figure 2: Modified Dual Active Bridge Converter

1349

dθ =θ/π. Also note that VM=VA/d1. Here the analysis is given only for positive phase shift values. The process is the same for negative phase shifts.

In all cases average active power transferred through transformer (Pav) is calculated from:

𝑃𝑎𝑣 =1

2𝜋 (𝑣𝑝

2𝜋

0∙ 𝑖)𝑑 𝜔𝑡 . (1)

where ω is the angular switching frequency.

For dc inductors in side A we also have:

𝑖𝐴1𝑎𝑣𝑔 ≈𝑃𝑎𝑣

2𝑉𝐴 ; 𝑖𝐴1𝑚𝑖𝑛 = 𝑖𝐴1𝑎𝑣𝑔 −

∆𝑖𝐴1

2 ;

𝑖𝐴1𝑚𝑎𝑥 = 𝑖𝐴1𝑎𝑣𝑔 +∆𝑖𝐴1

2 ;

∆𝑖𝐴1 =1

𝐿𝑑𝑐1𝜔𝜋 1 − 𝑑1 𝑉𝐴 . (2)

where iA1 and ΔiA1 are Ldc1 inductor current and its the peak to peak value respectively. The calculation of power is based on the transformer corner currents. The resulting equations for average power are as follows:

Case 1

This case happens when:

𝑑𝐴 − 𝑑𝐵 < 𝑑𝜃 < min(𝑑𝐴 + 𝑑𝐵 , 1 − 𝑑𝐴 − 𝑑𝐵). (3)

As shown in Fig. 4, in this case transformer current can be described by 3 independent corner values. Using circuit analysis the values of these currents in terms of control variables are given by:

𝑖0 =𝜋

𝐿𝜔 −𝑑𝐴𝑉𝑀 + 𝑑𝐵

𝑉𝐵

𝑛 ;

𝑖1 =𝜋

𝐿𝜔 (𝑑𝜃 − 𝑑𝐵)𝑉𝑀 + 𝑑𝐵

𝑉𝐵

𝑛 ;

𝑖2 =𝜋

𝐿𝜔 𝑑𝐴𝑉𝑀 + 𝑑𝜃 − 𝑑𝐴

𝑉𝐵

𝑛

. (4)

and the power is given by:

𝑃𝑎𝑣 =𝜋𝑉𝑀𝑉𝐵

𝑛𝐿𝜔 𝑑𝐴𝑑𝐵 + 𝑑𝐴𝑑𝜃 + 𝑑𝐵𝑑𝜃 −

1

2 𝑑𝐴

2 +

𝑑𝐵2 + 𝑑𝜃

2 . (5)

Case 2

The condition is given by (6). In this case the transformer

current is determined by four corner values.

Power is given by:

𝑃𝑎𝑣 =𝜋𝑉𝑀𝑉𝐵

𝑛𝐿𝜔 𝑑𝐴 + 𝑑𝐵 + 𝑑𝜃 −

1

2− 𝑑𝐴

2 + 𝑑𝐵2 +

𝑑𝜃2 . (7)

Case 3

In this case there is no overlap between non zero values of voltage pulses. The condition is:

𝑑𝐴 + 𝑑𝐵 ≤ 𝑑𝜃 ≤ 1 − 𝑑𝐴 − 𝑑𝐵 . (8)

And transformer current is determined by only two corner values.

In case 3, average power is given by:

𝑃𝑎𝑣 =𝜋𝑉𝑀𝑉𝐵

𝑛𝐿𝜔 2𝑑𝐴𝑑𝐵 . (9)

Note that the power is independent of θ that is expected, because phase shift changes only circulating currents in this case.

Case 4

The condition is:

𝑀𝑎𝑥(𝑑𝐴 + 𝑑𝐵 , 1 − 𝑑𝐴 − 𝑑𝐵) ≤ 𝑑𝜃 ≤ 1 + 𝑑𝐴 − 𝑑𝐵 . (10)

And transformer current is determined by three corner values.

Power is given by:

𝑃𝑎𝑣

=𝜋𝑉𝑀𝑉𝐵

𝑛𝐿𝜔(𝑑𝐴𝑑𝐵 − 𝑑𝐴𝑑𝜃 − 𝑑𝐵𝑑𝜃 + 𝑑𝐴 + 𝑑𝐵 + 𝑑𝜃 −

1

2 (𝑑𝐴

2

+ 𝑑𝐵2 + 𝑑𝜃

2 + 1)). (11)

This is the only case where there is an asymmetry between dθ and dA or dB.

Note that equations for power and transformer currents can be directly used for a conventional DAB converter too.

IV. SOFT SWITCHING OPERATION

A. Soft switching conditions

The converter is capable to operate with zero voltage

switching (ZVS) to remove switching losses. For turn on zero

voltage switching each MOSFET should have a negative

current just before turning on, such that the body diode is on

1 − 𝑑𝐴 − 𝑑𝐵 ≤ 𝑑𝜃 < 𝑑𝐴 + 𝑑𝐵 . (6)

Figure 3: Simplified model of converter

VB/n

LQ1

Q6Q2

in.iB

Ldc1

vp

VM

iA1

VA

Side ‘A’ Side ‘B’

vs

Simplified ModelQ3

Q4

Ldc2iA2

Q5

Q8

Q7

CM

i L

vP vS

1350

and the voltage across the switch is almost zero. Turn off

ZVS, is achieved using a snubber capacitor (CS) across the

switch. When the switch is turned off the voltage across CS is

still almost zero and the current passing through the switch

will transfer to the snubber capacitor. The voltage will

increase a little bit during the turn off process of the

MOSFET, so the voltage is almost zero during turn off. When

two switches are arranged as a leg on a dc bus, like Q1 and Q2

or Q3 and Q4, the ZVS condition for both switches on each

leg is that the net current leaving the leg pole (center of the

leg) lags the voltage of the pole. The net leg output current

should not change direction during dead time until opposite

Figure 4: Four main operation cases of modified DAB converter

iA1(d1<0.5):iA2(d1<0.5):

iA1(d1>0.5):

VM

V’B

0

0

0

2πdA

θ

ωt

ωt

ωt0 ωt1 ωt2 ωt3 ωt8

i0

i1

i2

VM-V’B

vp:

v’s:

(vp- v’s)

-VM

-V’B

π

VM

-V’B -VM

-VM+V’B

V’B

θ-d

Bπ

π-π

dA

vL

ωt4 ωt5 ωt6 ωt7

0

2πdA

2πdB

2πdBπ

dA

θ+

dBπ

i4=-i0

i7=-i3

i5=-i1

i8=i0i3

i6=-i2

0-πd

A

CASE 1

i:

VM

V’B

0

0

0

θ

i:

ωt0 ωt1 ωt2 ωt3 ωt8

i0

i1

i2

VM-V’B

iA1(d1<0.5):

vp:

v’s:

(vp- v’s)

-VM

-V’B

VM+V’B

-V’B

-VM-V’B

-VM

V’B

θ-(

1-d

B)π

0 π(1

-dA)

vL

ωt4 ωt5 ωt6 ωt7

2πdA

2πdB

2πdB

πd

A

i5=-i1

i8=i0i6=-i2

i7=-i3

2πdA

VM-V’B

-VM+V’B

2πdB2πdB

iA1(d1>0.5):

θ

i3

i4= -i0

-πd

A

θ-π

dB

θ+

πd

B

θ+

(1-d

B)π

π(1

+d

A)

π(2

-dA)

iA2(d1<0.5):

CASE 2

VM

V’B

0

0

0

θ

i:

ωt0 ωt1ωt2 ωt3 ωt8

i0

i1 i2

0

iA1(d1<0.5):

vp:

v’s:

(vp- v’s)

-VM

-V’B

-V’B

0

-VM

V’B

θ-(

1-d

B)π

0 π(1

-dA)

vL

ωt4 ωt5 ωt6 ωt7

2πdA

2πdB

2πdB

πd

A

i 5=

-i1

i 8=

i 0

i 6=

-i2

i 7=

-i3

2πdA

VM-V’B

0

iA1(d1>0.5):

θ

i3

i4 = -i0

-πd

A

θ-π

dB

θ+

πd

B

θ+

(1-d

B)π

π(1

+d

A)

π(2

-dA)

iA2(d1<0.5):

CASE 3VM

V’B

0

0

0

θ

i:

ωt0 ωt1 ωt2ωt3 ωt8

i0

i1

i2

0

iA1(d1<0.5):

vp:

v’s:

(vp- v’s)

-VM

-V’B

VM+V’B

-V’B

-VM-V’B

-VM

V’B

θ-(

1-d

B)π

0 π(1

-dA)

vL

ωt4 ωt5 ωt6 ωt7

2πdA

2πdB

2πdB

πd

A

i5=-i1 i8=i0

i6=-i2

2πdA

VMV’B

0

iA1(d1>0.5):

i4= -i0

-πd

A

θ+

πd

B

θ+

(1-d

B)π

π(1

+d

A)

π(2

-dA)

iA2(d1<0.5): i3=i2

i7=i6

θ

θ-π

dB

CASE 4

1351

switch is turned on. During dead time this current charges one

and discharges the other snubber capacitor on the leg,

resulting in a soft dv/dt. Dead times should not be too short to

allow a complete charge/discharge of snubber capacitors. On

the other hand they should not be too long such that the

current will changes direction and snubber capacitor begin to

reverse their charge discharge process. So compared to hard

switching not only ZVS is achieved for both switches, the

dv/dt during switching instances is highly reduced. These

charge and discharge is basically a resonant between snubber

capacitors and the inductance seen by the pole. All eight switches of the converter have snubber capacitors

to operate with (ZVS), by symmetry, the conditions can be checked only for one leg on each bridge that is, if Q1, Q2 and Q5, Q6 have ZVS the other four switches will also operate with ZVS because their current and voltage waveforms are similar to their counterparts with 180 degrees phase delay. The total current going out from the center of each leg should be positive when the top switch turns off and negative when the bottom switch turns off. In practice a turn off ZVS of one switch on each leg will be followed by a turn on ZVS for the opposite switch if dead time conditions as mentioned earlier apply. Available ZVS currents, Iz1, Iz2, Iz5 and Iz6 can be defined at turn off switching instances for Q1, Q2, Q5 and Q6 respectively. For each switch the ZVS condition is that its ZVS current should be positive. These conditions can be summarized and formulated as below:

𝐼𝑧1 = 𝑖𝐴1,(𝑄1,𝑡𝑢𝑟𝑛 𝑜𝑓𝑓 ) − 𝑖(𝑄1,𝑡𝑢𝑟𝑛 𝑜𝑓𝑓 ) > 0;

𝐼𝑧2 = 𝑖(𝑄2,𝑡𝑢𝑟𝑛 𝑜𝑓𝑓 ) − 𝑖𝐴1,(𝑄2,𝑡𝑢𝑟𝑛 𝑜𝑓𝑓 ) > 0;

𝐼𝑧5 = −𝑖(𝑄5,𝑡𝑢𝑟𝑛 𝑜𝑓𝑓 ) > 0;

𝐼𝑧6 = 𝑖(𝑄6,𝑡𝑢𝑟𝑛 𝑜𝑓𝑓 ) > 0. (12)

The turn-off instances are different for each case of operation so they should be evaluated separately. In practice the ZVS currents should be larger than a small positive threshold to compensate for ignoring dead times and snubber capacitor sizes as well as circuit tolerances and parasitics. The thresholds can be a few percent of peak values of these current when converter operates with nominal power at maximum voltages. At maximum bus voltages the snubber capacitors need maximum energy for full charge/discharge.

B. Soft switching zones

To find the soft switching zones of the converter in the 3D control space (d1, d2, dθ) the conditions should be evaluated in different values of bus voltages (VA, VB). Due to continuity, if converter has ZVS at minimum and maximum range of bus voltage values, it is expected that it will operate with ZVS inside the voltage range too. So ZVS will be checked only at extreme voltage values. To evaluate the method the parameters of a bidirectional converter designed for an aircraft power network are used. This bidirectional dc-dc converter is

needed to connect a low voltage (LV) dc bus (18 to 32V, nominal 28V) and an isolated high voltage (HV) dc bus (240V to 290V, nominal 270V). The LV side is mainly fed by a 28V battery while the HV bus is primarily supplied by ac sources coupled to engine. HV bus needs power from the LV side during startup, burst power demands and in emergency conditions. Power flow is reversed from HV side to LV side to charge the battery or just to restore regenerated power from HV side. The zones should be checked for all cases of converter operation. The results of the above analysis for the described bidirectional dc-dc converter are shown in Fig. 5. In this analysis resistive parasitics of the elements are considered. Recursive algorithms are used to include parasitics in ideal model. Converter was designed for 250 KHz operating frequency with Ldc1= Ldc2=0.8 µH, L=800 nH and n=3. The figure shows the zones in the (d2-d1) planes for different values of θ over which all four switches operate with ZVS. The contours inside boundaries of the ZVS zones correspond to equal power levels. It is clear that in all cases, there is a range of duty cycles, even at θ=0 that ZVS for all switches can be achieved. So full soft switching in the full range is achievable. Note that zero phase-shift corresponds to zero or very small power levels. As expected from equations there is symmetry over d2 in the figures. Another important conclusion is that if a fixed duty cycle (i.e. d1=d2=50%) is used, soft switching is limited to relatively higher powers and its range is very limited especially when voltage ratio (r=VB/2nVA) is far from 1. The results are then examined by a precise simulation of the converter that includes parasitics of practical circuit and other non ideal features of the converter like dead time and snubber capacitors. Simulation results confirmed the validity of full soft switching ranges found by the analysis on different cases of bus voltages and circuit parameters.

V. OPTIMAL EFFICIENCY

The analysis results for converter soft switching regions

show that a range of (d1,d2,θ) triples in ZVS zones are

available to transfer a specific power through the converter.

This implies that for each power level and for each pair of bus

voltages (VA,VB) an optimal point (θopt, d1opt, d2opt) can be

chosen to have the minimum conduction losses to maximize

efficiency. Based on the soft switching analysis the trajectories

of the optimal control parameters for minimum loss when

output power is varied are found using a search algorithm. The

magnetic losses on dc inductor and the transformer are not

considered in optimization analysis because they are mainly a

function of bus voltages that are basically independent of

control parameters. With a proper magnetic design these

losses are usually much less than total conduction losses of a

soft switched converter. The switching losses are assumed to

be zero in this analysis because of soft switching.

A peak efficiency of 98.5% was measured by inserting the

results in a precise simulation model and using the optimal

trajectories to control the converter. The peak measured

efficiency with the implemented converter was almost 97%.

1352

d2/d

1

VA=18V VB=240V VA=18V VB=290V VA=32V VB=240V VA=32V VB=290V

θ

0 d

egre

es

θ

0

deg

rees

θ

0

deg

rees

θ

0

deg

rees

Figure 5: ZVS zones of modified DAB converter designed for the aerospace application in different bus voltage values. Contours show power levels.

Vertical and horizontal axes are d2 and d1 respectively .

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

40

40.2

40.4

40.6

40.8

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

48

48.2

48.4

48.6

48.8

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

71

71.5

72

72.5

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

86

86.5

87

87.5

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

340

360

380

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

380

400

420

440

460

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

640

660

680

700

0.2 0.4 0.6 0.8

0.2

0.4

0.6

0.8

750

800

850

0.2 0.4 0.6 0.8

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VI. CONTROLLER IMPLEMENTATION

The bidirectional dc-dc converter may operate on different operation modes depending on application, like regulating HV side bus voltage or regulating current in battery charging mode. In any case the controller shall keep the controlling variables on the optimal trajectories to minimize the losses. A digital controller with lookup tables containing optimal trajectory information will be necessary. For each pair of (VA, VB) three look up tables for θ, d1 and d2 are stored in memory. Considering the continuity and smooth changes of the optimal trajectories when bus voltages are slightly varied, the number of voltage levels (tables) for different values of VA and VB can be reduced to a reasonable size that can fit in controller memory. The bus voltage ranges can be divided into a limited number of narrow voltage ranges each represented by its central value. Tables are calculated offline and stored in controller memory for each pair of VA and VB central values. The controller finds the optimal control parameters in real time by interpolating (e.g. weighted averaging) results from 9 stored tables that their center points are close to current VA and VB values.

A modification to traditional phase shift modulators is also necessary in final stage of the controller because the values of the control parameters depend on power and bus voltages. To explain the implementation, the final stage of a current mode controller that uses dc inductor current as controlled parameter is shown in Fig 6. Because the rate of bus voltage changes are very slow compared to converter dynamics, the digital controller simply monitors the bus voltages to choose the appropriate tables. Power is also calculated and used as an index for the lookup tables. The outputs of tables are directly applied to the converter using phase shifted PWM modulators.

VII. RESULTS

A 2KW hardware prototype was designed and implemented to verify the results and evaluate the converter performance using three control parameters. One set of typical operating waveforms of the implemented hardware is shown in Fig 7. In preliminary open loop tests, efficiencies as high as 97% are measured. Further results along with the detailed design procedure will be presented in another paper. Practical and simulated results were very close and agree with analysis results. Some ringing in practical circuit is present that is due to the differences in size of practical parasitic capacitors and inductances of the real MOSFET switches and the models used in simulation.

VIII. CONCLUSION

The modified DAB dc-dc converter along with a three parameter modulation technique is presented as a superior alternative to conventional DAB converter especially for applications with one low voltage dc bus. The converter is mathematically analyzed and closed form operating equations of the converter when control parameters are varied in their

reasonable range are extracted. Soft switching regions are also analyzed and it is shown that with proper design, wide soft switching range is achievable in spite of large bus voltage and load variations. The efficiency of the converter was then optimized using the advantage of more degrees of freedom. An implementation technique is also proposed for optimized controller. The results from simulation and implemented hardware confirmed the validity of the method. The mathematical analysis proposed in this paper is general and can be used for conventional DAB converter as well as other similar topologies.

REFERENCES

[1] R. W. A. A. De Doncker, D. M. Divan and M. H. Kheraluwala, "A three-phase soft-switched high-power-density DC/DC converter for high-power applications," Industry Applications, IEEE Transactions on, vol. 27, pp. 63-73, 1991.

[2] M. N. Kheraluwala, R. W. Gascoigne, D. M. Divan and E. D. Baumann, "Performance characterization of a high-power dual active bridge DC-to-DC converter," Industry Applications, IEEE Transactions on, vol. 28, pp. 1294-1301, 1992.

[3] G. G. Oggier, G. O. Garcia and A. R. Oliva, "Switching Control Strategy to Minimize Dual Active Bridge Converter Losses," Power Electronics, IEEE Transactions on, vol. 24, pp. 1826-1838, 2009.

[4] F. Krismer and J. Kolar, "Efficiency-Optimized High Current Dual Active Bridge Converter for Automotive Applications," Industrial Electronics, IEEE Transactions on, vol. PP, pp. 1-1, 2011.

[5] K. Wang, C. Y. Lin, L. Zhu, D. Qu, F. C. Lee and J. S. Lai, "Bidirectional DC to DC converters for fuel cell systems," Power Electronics in Transportation, 1998, pp. 47-51, 1998.

[6] R. Watson and F. C. Lee, "A soft-switched, full-bridge boost converter employing an active-clamp circuit," in Power Electronics Specialists Conference, 1996. PESC '96 Record., 27th Annual IEEE, 1996, pp. 1948-1954 vol.2.

[7] G F. Z. Peng, Hui Li, Gui-Jia Su and J. S. Lawler, "A new ZVS bidirectional DC-DC converter for fuel cell and battery application," IEEE Transactions on Power Electronics, vol. 19, pp. 54-65, 2004.

[8] H. Daneshpajooh, A. Bakhshai and P. Jain, "Optimizing dual half bridge converter for full range soft switching and high efficiency," in Energy Conversion Congress and Exposition (ECCE), 2011 IEEE, 2011, pp. 1296-1301.

Figure 7: An screen shot of converter waveforms. Blue traces are dc

inductor currents. Green is transformer secondary voltage and the two

other traces are voltages of the bottom switches at LV side.

Figure 6: Controller to operate converter with optimal efficiency

d 1

lo o k u p tab le fo r (V A , V B)

?lo o k u p

tab le fo r(V A ,V B)

d c-d cC o n verter

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IA 1 ,d

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cu rren t con troller

M u ltip lier

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volta g e

P A ,d

D esired

P ow er

d 1

?

d 2

lo o k u p tab le fo r (V A , V B)

d 2

M easu re

V AV BIA 1IA 2IB

Set P o in tsvo ltage an d

cu rren t co n tro llers

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