Dynamic-Circulating-Current-Minimization
Control for Isolated Three-phase AC-DC Converterwith Matrix Converter
Hiroki Watanabe
Dept. of Electrical Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Japanhwatanabe@vos.nagaokaut.ac.jp

Abstract—This paper proposes a circulating current
minimization control for an isolated AC-DC converter which
combines a Dual Active Bridge (DAB) converter and a threephase to single-phase matrix converter. The isolated AC-DC
converter achieves Zero-Voltage-Switching (ZVS) to reduce
switching losses. However, the circulating current occurs
depending on the matrix converter`s transformer voltage andswitching patterns. This paper proposes the DynamicCirculating-Current-Minimization (DCCM) control based on
online calculation. The proposed control reduces the inductor
RMS current with the wide operating region for the isolated
three-phase AC-DC converter with the matrix converter. The
experiment confirms the validity of the proposed control. The
experimental results demonstrate that the transformer RMS
current is reduced by 47% with the proposed DCCM control.
Keywords—DAB converter, Matrix converter, Isolated AC/DC
converter

I. INTRODUCTION
Electric Vehicles (EVs) are one of the major trends for
future automotive applications owing to their non-carbon
dioxide emission. Recently, EV chargers have been widely
placed at fast-charging stations, parking lots, and housings tooffer battery charging for EVs. The EV charger require some
capability, e.g., (1) wide DC voltage control for battery
charging, (2) galvanic isolation for human safety, and (3) highpower density and a long lifetime to realize the highconvenience for consumers [1]-[10].
The EV charger typically consists of a three-phase PWM
rectifier and a bidirectional isolated DC-DC converter. Thisconfiguration assures the stable operation of the isolated threephase AC-DC converter owing to the simple structure.
Furthermore, the bidirectional isolated DC-DC converter hascapable of galvanic isolation with the high-frequency
transformer. Hence, the size of the isolation transformer isreduced compared to the low-frequency transformer.
However, this circuit configuration requires some bulky
passive components, such as the grid-tied inductor and theelectrolytic capacitor. These components may become thecause of the increase in the circuit volume. Significantly, theelectrolytic capacitor may decay the reliability of the EV
charges due to its temperature dependence of the lifetime.
The isolated three-phase AC-DC converters applying amatrix converter have been actively researched [11]-[20]. The
matrix converter directly converts the three-phase AC voltage

Jun-ichi Itoh
Dept. of Electrical Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

to the high-frequency square voltage with several kilo Hz
instead of the three-phase PWM rectifier. The attractive
advantages of this converter are that the bulky grid-tied
inductor and the electrolytic capacitor are not necessary.
Moreover, the matrix converter combines with the DAB
converter as the square waveform inverter to reduce thenumber of the conversion stage compared to the conventional
two-stage configuration. The bidirectional power control
realizes by the phase-shift modulation like the typical DAB
converter. Furthermore, Zero-Voltage-Switching (ZVS) is
achieved to reduce switching losses. According to thesefeatures, high power density and high conversion efficiency
are expected by the isolated three-phase AC-DC converterwith the matrix converter. The reduction of circulating current
in the isolated three-phase AC-DC converter is important toimprove conversion efficiency. The circulating current occurs
depending on the condition of the transformer voltage and theswitching patterns of the matrix converter. However, it isdifficult to find the minimum condition of the circulating
current because the matrix converter has complicatedswitching patterns.
This paper proposes the Dynamic-Circulating-Current
Minimization (DCCM) control for the isolated three-phase
AC-DC converter with the matrix converter. The newcontribution of the proposed method is that the duty ratio isadjusted to minimize the circulating current according to theenvelope of the input three-phase voltage. Besides, it isautomatically optimized by online calculation in order to keep
the minimum circulating current condition. According to theexperimental result, the inductor current was reduced by 47%
by the proposed control compared with the conventional
method.
II. CIRCUIT CONFIGURATION AND OPERATION PRINCIPLE
Fig.1 shows the circuit configuration of the isolated threephase AC-DC converter applying the matrix converter. The
matrix converter converts the three-phase AC voltage to thehigh-frequency square voltage of more than several kilo Hz.
The high-frequency transformer is placed between the matrix
converter and the H-bridge converter for galvanic isolation.
The phase shift modulation realizes the bidirectional power
control to make the phase difference between the primary andsecondary transformer voltage.
Fig. 2 shows the transformer voltage waveforms and thetransformer current in the isolated three-phase AC-DC

converter. The peak value of the transformer primary voltage
vp is determined by the line voltage of the three-phase grid.
The phase difference δ is given to decide the transmission
power, the same as the DAB converter.
The transformer voltage conditions of vp and vs give thetransformer current. The transformer current at each voltage
condition is expressed asvT
i1 = 1 sw Da
2L
D1

(2)

sw

D2

(3)

( v − NV ) T
2

dc

2L

i4 = i3 −N

Matrix converter

NVdcTsw
Db
2L(4)

where N is the turn ratio of the high-frequency transformer,
Vdc is the DC voltage, L is the inductance, Da, D1, D2, and Db
are the duty of each voltage condition, respectively.
Fig.3 shows the space vector diagram of the matrix
converter [21]. The current command vector Iin* is obtainedby the current vector of Imid and Imin. The relationship between
each current vector is expressed as(5)*

I in = I mid + I min

Matrix converter voltage vmc
Inverter volta ge Nv inv

i3 = i2 −Vdc

H-bridge converter

Fig.1. Isolated three-phase AC-DC converter with matrix converter.

sw

2L

+
vs
-

+
vp
-

Np : Ns
N=Np / Ns

NVdc
0

-NVdc

Transformer current itr

i2 = i1 +

dc

L

ir
vr →
vs is LC→vt it filter→(1)( v − NV ) T
1P

T0 Ta T1 T2
i2

i1

Tb

T0

Ta T1 T2

Tb

T0

i3

i0

0

-i0
-i1

-i3

-i2

Tsw

Fig.2. Each transformer voltage waveforms and transformer current in ahigh-frequency transformer.
iβ

i
i +i
I mid = 1 Da + 1 2 D1
2
2

(6)

P (1 + vratio _ a ( a + 1) + vratio _ b K )NVdc imid vratio _ a
2

2

(8)

( a +1) − v

ratio _ avratio _ b − vratio _ a2i  ( a + 1) − vratio _ a 
k 2 = min 
imi d  vratio _ b − vratio _ a 

Sector Iiα
Iin*

Sector V

Sector VI

I1

001 I5010

Iz : Zerovectors
100
I7
100

imin

imid

100
001

I8

010
010

I9

001
001

100
I6
010
I1 100 S rp,Spr = ON, S sp,Sps = OF F, S tp,Spt = OFF
001 S rn,Snr = OFF , S sn,Sns = OFF , S tn,Snt = ON
※The number of ”1” mea ns switch is turn on.

Fig.3. Space vector diagram of matrix converter.

(9)

db =

(a + 1 − vratio _ a )d1 + ( vratio _ b − vratio _ a ) d2
vratio _ ad0 =K = −k1 ± k12 + 4k2

Iz

Sector II

010
001

Sector IV
imin'

(10)

d 2 = Kd1

k1 =

imid'

Ex.)

NVdc imid vratio _ a

P (1 + vratio _ a ( a + 1) + vratio _ b K )Sector III(7).

According to these equations, the duty conditions are
obtained as

d1 =

I2

001
I
100 4

i +i
I min = 2 3 D2
2

da = a

010
I
100 3

1 − ( ( a + 1) d1 + d 2 + d b )
2

(14)

(15)

(11)
iratio =

imin
imid

(16)

vratio _ a =

NVdc
vmax

(17)

(12)

(13)

vmid
vmax

DCM-CCM boundary line
Transmission power limit line

1.6

where a is the ratio of da and d1, and it is expressed as
d
a= a
d1

1.8

(18)

(19).

NVdc/Vin_peak [-]vratio _ b =1.4

Region B
(DCM)

1.2
1.0

Region D(CCM)

0.8
Region C
(DCM)

0.6
0.4

Note that a is the arbitrary constant. However, thisparameter is very important in deciding the performance of
the isolated three-phase AC-DC converter because thecirculating current and the transmission power depending on
the parameter of a. In the next chapter, the detail of the
proposed control is introduced.

Region A(inoperable)

0.2
0.0

0

0.1

0.2

0.3

0.4

A. Minimum circulating current condition in region B
Fig. 6 (a) shows the transformer voltage and transformer
current waveforms in region B. The transformer current
increases during da. On the other hand, the transformer
current decreases during d1 and d2 due to the transformer
voltage condition. Therefore, the proposed DCCM control
adjusts the parameter of a to remove the period db. The
parameter a in region B is derived from (8) to (15) when db
equals zero, and it is expressed as−r ± r 2 − 4 s
a = −1 +2

Qr = −(20)

2vratio _ a
1 + iratio ( vratio _ b − vratio _ a )Q s = vratio _ a(1 + iratio )vratio _ a − iratio vratio _ b
1 + iratio ( vratio _ b − vratio _ a )B. Minimum circulating current condition in region C
Fig. 6 (b) shows the transformer voltage and transformer
current waveforms in region C. In this region, da is set to zero
because the transformer current increases during d1 and d2.
Therefore, the proposed DCCM control adjusts the parameterof a to remove the period of da.

0.6

0.7

0.8

0.9

1.0

Fig.4. Relationship between the operating region and current mode inisolated three-phase AC-DC converter.

III. DYNAMIC-CIRCULATING-CURRENT-MINIMIZATION(DCCM) CONTROL
Fig.4 shows the relationship between the operation region
and current mode in the isolated three-phase AC-DC
converter. The operation region is separated by the current
mode of the Continuous Current Mode (CCM) and the
Discontinuous Current Mode (DCM). The green line means
the boundary condition of each current mode. According to
Fig.5, the circulating current occurs during the zero-voltage
period of da and db because the current path to the powersource does not make during this period. From (19), dadepends on the ratio a. Hence, the parameter a influences thecirculating current. The proposed DCCM control adjusts theparameter a to reduce the circulating current.
Fig.5 shows the flow chart of the calculation of a tominimize the circulating current. The parameter of a iscalculated for each operating region of regions B, C, and D.
The detail of the calculation is following.

0.5

Transmission power [p.u.] 1 p.u. =4.8[kW]Sam ple: NV dc, P*

Buck mode

Yes

No

Boost mode

vmax > NV dc
Calcula tion of
maximum , middle
and minimum
Rario aEq. (24) ,(25)Calculation of
maximum power
P in Eq. (22)assuming da = 0

Calcula tion of K
and First-orde r
linearization of K
Eq. (11)Yes

P* > PNo

Calcula tion of
maximum power
P in Eq. (22)assuming db=0

Yes

P* > PNo

Calcula tion of
Z ,CRatio a = 0

Ratio a= Eq. (14)Yes

Ratio a1> Ratio a2
No

a= Ratio a2

a= Ratio a1

end

Fig.5. Flowchart of proposed DCCM control.

C. Minimum circulating current condition in region D
Fig. 6 (c) shows the transformer voltage and transformer
current in region D. In this region, d0 becomes zero because
the transformer current is CCM without a zero-current period.
In this region, it is necessary to calculate the non-linear
equation to derive a. In order to derive the parameter a, thefunction K approximates the first-order equation as

K = Za + C(21)

where Z is the coefficient of the first-order equation, and C is
the intercept of the first-order equation. Note that K has two
different slopes by the parameter a. Therefore, theapproximated K is calculated by the polygonal approximation.
Firstly, the transmission power in region D is expressed as

2( a + 1) − vratio _ a
NVdc 2
2
4 Lf sw a (1 + v+ Kvratio _ bratio _ a )

(22)

NVdc
vmax
vmin

where P is the transmission power, and fsw is the switchingfrequency. The parameter a in region D is derived from (21)and (22), and it is expressed as

-vmin
-vmax
-NVdc

P=

(

)

0

2
1

a = −b1 + b − c10

ratio _ a

+ vratio _ b Z )(1 + vratio _ b C ) −Q b1 =(1 + v(1 + v
Q c1 =

2

ratio _ a

+ vratio _ b Z ) −2

ratio _ b C ) −2

NVdc
4 Lf sw P

NVdc
4 Lf sw P

0(b)

Matrix converter voltage vmc Rectifier voltage
vrec

d1

d2 db
Tsw/2

d0

Transformer voltage and current waveform in region C under
DCM.

vmax
vmin
NVdc
0

Matrix converter voltage vmc
Rectifier voltage
vrec

-NVdc
-vmin
-vmax

Transformer current itr

2vratio _ a + 2{1 + vratio _ a3 }(24).

1 + vratio _ a {1 − vratio _ a }

0

da d1

x1 + x 2 + x 3 x 4 − { x 4 + x 5 }

(25).

x4

Q x2 = iratio {vratio _ a 3 − vratio _ a 2 + vratio _ a vratio _ b − vratio _ a 2 vratio _ b }2

Q x3 = {iratio vratio _ a (1 + iratio (vratio _ b − vratio _ a ) − vratio _ a )} 3
Q x4 = 1 + iratio (vratio _ b − vratio _ a )Transformer voltage and current waveform in region D under
CCM.
Fig.6. Transformer voltage and transformer current waveforms withdifferent current mode.

p−0

 K − K 0, C p−0} =  p, K0 
ap



(27)

Fig.7 shows the control block diagram of the proposed
DCCM control. the proposed control consists of a duty
calculation, calculation of parameter a for minimization of
the circulating current, and the switching pulse generator. The
phase information is provided by the Phase Looked Loop
(PLL). The switching duty is calculated by the phase current
command, line voltage, DC voltage, and parameter a.
IV. EXPERIMENTAL RESULT

Q x5 = vratio _ a
According to (11) and (25), the function of Kb at the
breaking point is obtained.
Finally, the minimum value of Kzero is obtained when theparameter a is zero. The approximated line for the functionof Kzero is obtained from the above three points of Kmax, Kb,
and Kzero. The parameter Z and C in (21) are obtained fromthe following equation
 K− K p K p a max − K max a p 
, C m ax − p } =  m ax,
aa m ax − a p m ax − a p


d2 db
Tsw/2

(c)

{Z

Q x1 = iratio 2 {vratio _ a 3 + vratio _ a 2 vratio _ b − 2vratio _ a 2 vratio _ b }m ax − pd0Transformer current itr

NVdc 2 + vratio _ a NVdc 2

According to (11) and (18), the function of Kmax with the
maximum transmission power in region D is obtained.
Next, the breaking point of the function Kb is calculated.
The parameter a at the breaking point is calculated by thetwice-derivation of (11), and it is expressed as

{Z

d1
d2
Tsw/2

-NVdc
-vmin
-vmax

According to (22), the transmission power in region D
depends on the parameter a. The parameter a with the
maximum transmission power is obtained by the derivationof (22), and it is expressed as

ap =

da

Transformer voltage and current waveform in region B under
DCM.

vmax
vmin
NVdc
0

2

4 Lf sw P
22dc(1 + vratio _ a + vratio _ b Z ) − 4NV
Lf sw P

amax = vratio _ aTransformer current itr

(23)
(a)

(1 + vMatrix converter voltage vmc
Rectifier voltage
vrec

(26)

The validity of the proposed DCCM control isdemonstrated by the experiment. Table I shows theexperimental parameters. The grid voltage is 200 Vrms, theswitching frequency is 50 kHz, and the rated power of the
proto type circuit is 3.7kW. The DC voltage is set from 26V
to 62V for buck and boost mode operation.
Fig.8 shows the U-phase current and the transformer
current. According to Fig.8, the sinusoidal waveform of the
U-phase current is obtained by the proposed DCCM control.
The proposed DCCM control adjusts the control parameter of
a in each operating region. The proposed DCCM control kept
the low harmonic distortion for the grid current when theoperation region was changed, as shown in Fig.8.

*

I peak
vuv
vvw
vuw

θ
PLL

1
iu = I peak sin(θ − π )65iv = I peak sin(θ − π )61iw = I peak sin(θ + π )
2

iu
iv
iw

iα

3ϕ / 2ϕiβ

imid
Cramer's
rule

imin
da

v1a,v1b,v2b,v2b
Duty Cal.
Eq.
(1)
(6)

Area
Area
identification

Switing
table based
space vector

Cal.ofratio a

a

d1
d2
db

Pulse
Gen.

d0
Maximum line voltage
vmax
Voltagemax,mid,min Middle line voltage
vmid
identification
DC voltage
Vdc
detection
Inductance L, Transformer turn ratio N,
Switching frequency fsw

Sup
Svp
Swp
Sun
Svn
Swn
Sap
San
Sbp
Sbn

CarrierFig.7. Control block diagram of proposed DCCM control.

Fig. 9 shows the transformer voltage and the transformer
current when the operating condition is DCM and boost mode.
According to Fig.9, the peak current of the transformer
current is 36.0 A, and the transformer RMS current is
15.2Arms. On the other hand, the proposed DCCM control
reduces the transformer RMS current to 12.1Arms from
15.2Arms in the conventional control. In this condition, thetransformer RMS current is reduced by 22.2%.
Fig. 10 shows the transformer voltage and the transformer
current when the operating condition is DCM and buck mode.
According to Fig. 10, the peak current of the transformer
current is reduced when the proposed DCCM control isapplied. In this condition, the transformer RMS current in the
proposed DCCM control is reduced by 17.2% compared tothat the conventional control.
Fig. 11 shows the transformer voltage and the transformer
current when the operating condition is CCM and buck mode.
According to Fig. 11, the peak current of the transformer
current is reduced by 30.7% compared to the conventional
method.
According to these experimental results, it was confirmedthat the transformer rms current is reduced wide operating
region by the proposed DCCM control. In the conventional
control, the high transformer RMS current occurs due to thelarge circulating current. On the other hand, the proposed
DCCM control reduces the circulating current in thetransformer current. Therefore, the proposed control reduces
the conduction losses and the copper loss in the isolated threephase AC-DC converter.
Fig. 12 shows the transient test result when thetransmission power is changed from 0.2 p.u. to 0.8 p.u.. In
this condition, the operation mode is changed to CCM from
DCM. Moreover, Fig. 12 (a) shows the test result when theoperating region is changed to region D from region B. On
the other hand, the Fig.12 (b) shows the transient test result
when the operating region is changed to region D from region
B. According to Fig.12, the operation mode is smoothly
changed without current overshoots in Fig. 12 (a) and Fig. 12(b).
Fig.13 shows the transformer current comparison with theconventional control and the proposed DCCM control. Notethat the transformer current is compared at each operating
region, as shown in Fig.4. According to Fig.13, it was

Table 1. Experimental parameter.
Quantity
Rated power
Three-phase AC voltage
DC voltage
Input frequency
Carrier frequency
Leakage inductanceTurn ratio of transformer
Input filter
Dead-time

Symbol
P
vac
Vdc
f
fsw
L
N1:N2
Lf
Cf
Td

Value
3.7 kW
200 V
26~62V
50 Hz
50 kHz21.5 µH(%Z = 0.01 %)5.5:1
0.19 µH (%Z = 1.0 %)10 µF (%Y = 5.0 %)250 nsconfirmed that the transformer RMS current was reduced at
all transmission power condition. Especially, the transformer
current is reduced in all operating regions.
V. CONCLUSIONSThis paper proposes the Dynamic-Circulating-Current
Minimization (DCCM) control for the isolated three-phase
AC-DC converter with the matrix converter. The newcontribution of the proposed method is that the duty ratio isadjusted to minimize the circulating current according to theenvelope of the input three-phase voltage. Besides, it isautomatically optimized by the online calculation in order tokeep the minimum circulating current condition. According to
the experimental result, the inductor current in the proposed
DCCM control was reduced by 47% compared with that of theconventional method.
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[2]

[3]

[4]

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Region C
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W/O Pro. cont.

Region D

Matrix converter voltage 500[V/div]000

Rectifier voltage 100[V/div]Pri. trans. Voltage 500V/div
0

With Proposed control

0Sec. trans. Voltage 500V/div

00

Transformer current 20A/div

10.0[ms/div]

Transformer current 50[A/div]

Fig.8. Experimental result of steady-state operation.
W/O Pro. cont.

10.0[us/div]

Fig.9. Transformer voltage and current in region B.

With Proposed control

W/O Pro. cont.

Matrix converter voltage 500[V/div]

With Proposed control

Matrix converter voltage 500[V/div]0

0

Rectifier voltage 100[V/div]

Rectifier voltage 100[V/div]
0

0

0

0

Transformer current 20[A/div]

10.0[us/div]

Transformer current 50[A/div]

Fig.10. Transformer voltage and current in region.
P: 0.2 p.u.

8.0[us/div]

Fig.11. Transformer voltage and current in region D.
P: 0.2 p.u.

P: 0.8 p.u.

P: 0.8 p.u.

Matrix converter voltage 500[V/div]

Matrix converter voltage 500[V/div]0

0

Rectifier voltage 100[V/div]

Rectifier voltage 100[V/div]
0

0

0

0

Transformer current 20[A/div](a)40[us/div]

Transformer current 20[A/div]

40[us/div]

Transient response from region B to region D.
(b) Transient response from region C to region D.
Fig.12. Transient test result with proposed DCCM control.

Transformer current RMS [Arm s]

25

Boost ratio 1.2(Region B)

20

20% reduced
Conventional method(a=2.8)15

Proposal method

105

1 [p.u.] =3.7 [kW]
0
0.0

0.2

0.4
0.6
Transmission power [p.u.]

Transformer current RMS [Arm s]

(a)

0.8

1.0

Operation region B

20

Boost ratio 0.5(Region C)

15

Conventional method(a=1.3)18% reduced

10

Proposal method

5
1 [p.u.] =3.7 [kW]
0
0

0.1

0.2
0.3
0.4
Transmission power [p.u.](b)
25
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0.5

0.6

Operation region C

Boost ratio 0.9(Region D)

20
Conventional method(a=3.9)15

47% reduced
10
Proposal method
5
1 [p.u.] =3.7 [kW]
0
0.0

0.2

0.4
0.6
Transmission power [p.u.]

0.8(c) Operation region D
Fig. 13. Transformer RMS current comparison results.

1.0