DC Ripple Component Cancelation Method of
Isolated AC-DC Converter with Matrix Converter
for Input Current Harmonics Reduction
Shunsuke Takuma
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
takuma_s@stn.nagaokaut.ac.jp

Keisuke Kusaka
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
kusaka@vos.nagaokaut.ac.jp

Abstract— This paper proposes a current ripple
cancelation method in DC side for an isolated AC-DC
converter with a matrix converter. In this system, input
currents are distorted by an error between a reference andactual input current caused by a ripple component at a dc
current in the output side when the smoothing inductor in the
output side is minimized. The proposed ripple cancellation
method combines current slopes during positive with negative
cycles of a high-frequency current. In addition, dead-timeinduced voltage error is also reduced by the extension of aminimum pulse width of each switch in the matrix converterwith the proposed method. It is demonstrated that the input
current total harmonic distortion (THD) is improved byeliminating the ripple components regardless of the amplitudeof the ripple component. From the experimental results withthe 10-kW prototype, the input current THD is reduced from
8.2% to 5.3% at the 0.2 p.u..
Keywords—matrix converter, space vector control, threephase AC to DC converter, current ripple cancellation

I. INTRODUCTION
Recently, electric vehicles and hybrid vehicles have been
actively developed to reduce an environmental load
substance such as CO2. A rapid charger is required to
improve usability for consumers. A battery charger with alow power system is used as a DC-DC converter without thegalvanic isolation or a single-phase AC to DC converter [1][3]. Generally, a rapid charger with a large power capacity
consists of a three-phase PWM rectifier and an isolated DCDC converter. However, three boost inductors at the grid sideand the DC-link capacitor are required [4]-[6]. Therefore, anisolated AC-DC converter with a buck-type matrix converter
has been researched to reduce such passive components [7][14]. Both the DC link capacitor and boost inductors are
removed by the direct conversion from grid-frequency AC tohigh-frequency AC with a matrix converter.
The current ripple of a dc current in the output side
becomes large when the inductance of a smoothing inductor
decreases to achieve the high-power density. The iron loss
and switching loss increases due to the high switchingfrequency to reduce the volume of the smoothing inductor.
However, the input current also is conposed by an output
current ripple due to the use of a minimized smoothing
inductor in the dc side because the output current is assumed
to be constant in the conventional control methods in order tosimplify the control strategy. Furthermore, the volume of the
input filter also becomes large to achieve the low input

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

current distortion because low-order harmonics of the output
current ripple affects the input currents.
In order to solve this problem, the optimized switchingpattern has been proposed to achieve the minimum current
ripple at the dc side [13]. However, the input currents still
distort by the incomplete cancelation of the current ripple. In
addition, the input current ripple is increased compared withthat of the conventional control scheme. In [14], theimprovement of the eight-segment control method has been
proposed to cancel the control error due to the current ripple.
However, this duty calculation requires the smoothing
inductor value. Therefore, the input currents may still distortby the error between the actual inductor value and nominal
inductor value. In addition, the output voltage is not
linearized by the dead-time for the commutation of thematrix converter in the low modulation index. The authors
confirmed the verification by simulation results only.
In this paper, the cancelation of the output current ripple
is proposed in order to reduce the harmonics components in
the input current. The original idea of this paper is that thecancelation of the output current ripple is independent of thesmoothing inductor value and linearization of therelationship between the reference and actual voltage. The
effect of the output current ripple is eliminated by changing
the switching pattern. The fundamental operation is obtainedby the experiment with a 10 kW proto-type. The input
current distortion is reduced by the proposed method
regardless of the output current ripple.
II. PROPOSED DC CURRENT RIPPLE CANCELATION METHOD
Figure 1 shows the circuit configuration of the isolated
AC-DC converter with the buck-type matrix converter. The
input currents and output DC voltage are controlled by the
buck-type matrix converter with the space vector control(SVM). The smoothing capacitor and initial charger circuit
are not required by applying the matrix converter at the
primary side of the transformer.
Figure 2 shows the control diagram using traditional
SVM. The traditional SVM is based on the constant output
current during one switching periods. Vz is defined as zero
vectors V7, V8, and V9. The output voltage vectors V1, V2, andVz are selected during the first half switching periods togenerate a positive voltage. On the other hands, the output
voltage vectors V4, V5, and Vz are selected during the otherhalf periods to generate the negative voltage. These dutyreference T1, T2, and Tz are calculated by

T1 

1 va
| A | vb

V2a
V2 b

Srp



Ssp

Idc

Stp

Ldc

T2 

1 V1a
| A | V1b

va
vb




V1a
Tz  1  (T1  T2 )  | A |

V1b


V2a 

V2 b 



Vz

V4

V5

vr-vt

V1

N1 : N2

V4 001
100

Sector V
V5

001
010

Fig. 2. Space vector control.

current ripple during one switching periods is proposed tosuppress the input current distortion.
V2

Vz

V4

V5

vt-vs
vt-vr

vt-vs
vt-vr

idc

idc_ideal

idc_ideal
0

0

isref

Periodic by T

iac 0

is

Vz

V5

V4

ir

is
A’
Cancellatin

ir

is

imc 0
is

idc
|B|=|B’|
idc_ideal|A|=|A’|
Error

Avg. is > isref
isref

B’

0

Error isref

iac 0(a) Ideal

V2

B
A

ir

idc

V1

vr-vt

vt-vs
vt-vr

is

va
Zero vectors
100
V7
100
010
V8
010
001
V9
001

※ The number of ”1”means switch is Turn on
100 Srp=ON, Ssp=OFF, Stp=OFF
Example001 Srn=OFF, Ssn=OFF, Stn=ON

vmc 0

ir

100
010

V6

vmc 0

ir

Sector VI

Sector IV

vmc 0

imc 0

100
V1 001

i*

Vz

vs-vt

is

010
001

Sector I
Sector III

vs-vt

ir

V2

Sector II

vs-vt

imc 0

Diode rectifiervb

V3 010100

Figure 3(b) shows the operation waveforms of thevoltage and current at the primary side of the transformer, thenon-ideal dc current with the current ripple, and the input
current when the conventional control method is applied. In
this case, the actual input current at S-phase has the error
which is the shaded area due to the DC current ripple. In
particular, R-phase and S-phase current are lower and higher
than the input current reference, respectively, leading to the
distortion of the input current. The duty compensation for theerror caused by the output current ripple is difficult because
the relationship between the duty and the input current isnonlinear. Therefore, the cancellation method of the DC
V2

Vdc

Fig. 1. Circuit configuration of isolated AC-DC converter using bucktype matrix converter. The isolated AC-DC converter consists of thethree-phase to single phase matrix converter, the high-frequency
transformer, the diode rectifier, and the smooting inductor.

Figure 3(a) shows the operation waveforms of the voltage
and current at the primary side of the transformer, the ideal
dc current without the current ripple, and the input current. It
is assumed that the transformer is the ideal condition without
the leakage inductance and magnetic inductance. The
conventional control method assuming the ideal dc current
simply regulates the input current to the reference.

V1

Vrec

vmc

Srn Ssn
Stn
3f -1f Matrix converter

where va and vb are ab components of the input current
reference, v1a, v1b, v2a, and v2b are also ab components of thevectors V1 and V2 which are selected based on the area
located in the input current reference.

vr-vt

Input filter

imc

vr
vs
vt

Avg. is = isref

iac 0(b) Conventional method(c) Proposed method

Fig. 3. Effect of dc current ripple against input current. The error between the reference and actual current of the input current is caused by the dc
current ripple with the conventional control method. In the proposed control method, the ripple component of the phase-current during one switching
periods is cancelled to by changing the order of the selected voltage vectors.

Figure 3(c) shows the operation waveforms of the voltage
and current at the primary side of the transformer, the nonideal dc current with the current ripple, and the input current
when the proposed control method is applied. The effect ofthe dc current ripple is eliminated by changing the switchingpattern during half cycle. The order of the output voltage
vector V4 and V5 is alternated compared to the conventional
control method. The advantages of the changing waveforms
are as follow: 1) Cancellation of the ripple current 2)
Extension of the pulse width. The detail of the twoadvantages is explained in the next chapter.
A. Principle of current ripple cancellation
Figure 4 depicts the ripple cancellation principle for the
input current during one switching period. Two amplitudes atpoint A and B are equal to those at point A’ and B’,
respectively. The solid line and dotted line depict the
instantaneous currents from point A to B and A’ to B’ during
the transition of the output vectors V1, V2 and V4, V5,
respectively. The average currents Iave1, Iave2 during durations
T1, T2 are expressed as

V,V4

VV5
B

B’

i2
Iave

A’

i0

A

0

T

T2

Fig. 4. Principle of current ripple cancellation.

Vdc

Vdc

0

0

Ip-p1

Ip-p2

Vrec

Idc
0

0

i i
I ave  I ave1  I ave 2  0 22(a) Nv1 > Vdc > Nv2

4

B. Analytical results of DC current ripple
In this chapter, the DC current ripple with the proposed
method is clarified to design the inductor at the DC side.
Figure 5 shows the rectified voltage Vrec, DC voltage Vdc,
and the instantaneous current of the inductor at the DC side
during one switching cycle. The output voltage of the matrix
converter is controlled to cancel the DC current ripple. The
amplitudes of the current ripple Ip-p1 and Ip-p2 with theconventional and proposed method are expressed as

Vrec

Vdc

Vdc

0

0

Ip-p1

Ip-p2

0

0

Idc

(b) Nv1 > Nv2 > Vdc
Fig. 5. DC current ripple waveforms. The DC current ripple is decided by
the grid voltage, DC voltage, and turn ration of the transformer.
Peak to peak DC current ripple[A]where, i0 is the initial current at V1, and i2 is the final state at
V2. Therefore, the input current is controlled by the proposedcancellation method regardless of the amplitude of the ripple
components. Therefore, the duty for the proposed control
method is calculated by Eq. (1)-(3) without the inductor
parameter. By applying the proposed method, the periodic
output current of the matrix converter is controlled to theconstant current which is necessary to use the traditional
SVM.

5.0
4.0
Prop. method

3.0
2.0

Conv. method

1.0

0.0
0

0.2

0.4

0.6

0.8

1

Step-down ratio ( Nv1  Vdc )T1  ( Nv2  Vdc )T2
LdcI p p2  
 ( Nv1  Vdc )T1  ( Nv2  Vdc )T2Ldc(a) Amplitude of ripple current

Nv1  Vdc  Nv2

Design point18

5
Nv1  Nv2  Vdc

Nv1  Vdc  Nv2

Nv1  Nv2  Vdc

where N is the turn ratio of the transformer, Ldc is theinductance of the inductor at the DC side, and v1 and v2 are
the maximum and medium line to line voltage.

16

DC current ripple ratio[-] ( Nv1  Vdc )T1LdcI p  p1  
 ( Nv1  Vdc )T1  ( Nv2  Vdc )T2

Ldc

14
Prop. method

1210Conv. method

8
6
4
2
0
0

0.2

0.4

0.6

0.8

1

Step-down ratio(b) Ripple current ratio
Fig. 6. Relationship between step-down ratio and DC current

Figure 6(a) shows the relationship between the step-down
ratio and current ripple ratio. It is confirmed that the current

ripple amplitude of the proposed method is larger than themof the conventional method over the 0.8 of the step-down
ratio. However, the amplitude of the current ripple is thesame under the 0.8 of the step-down ratio. The amplitude of
the current ripple is depending on the relationship between
the grid voltage, DC voltage, and turn ratio.

V2

V1

V1

0

0

V4

V4

V5

Figure 6(b) shows the relationship between the DC
current ripple ratio and step-down ratio with the conventional
and proposed method. It is assumed that the transition power
is constant when the step-down ratio is changed by thematrix converter. Generally, the inductor at the DC side isdesigned by the requirement of the current ripple ratio. In a
comparison of both the conventional and proposed topology
design point, the step-down ratio is 0.77 because the worst
current ripple ratio is the same. Therefore, the proposed
method is not affected to design the inductor at the inductor.

V5
Min. pulse wide

Srp

Ssp
T2

Stp

Srn

Ssn

Ssn

Stn

Stn
Tz

T2

Tz

T1

T2

Tz

T1

T2

Tz

T2

T1

(b)Proposed method

Fig. 7. Comparison among minimum pulse width. The minimum pulse
width is extended by the proposed method.
Modulation index : 0.85

0.5With proposed method
0.4
0.3
0.2
0.1

With conventional methodEx.) Dead-time 5% ofswitching cycle

Error

0

0.5 ms/div

Time

Fig.8. Minimum duty during one switching cycle.
TABLE I. SIMULATION AND EXPERIMENTAL CONDITIONS.

Element

SymbolValue

Rated output power

Pout

10 kW

Grid voltage

vac

200 V

DC voltage

Vdc

400 V

DC inductor
Current ripple

Ldc
Ip-p

1.6 mH
2.5 A(10%※1)

Lf (%Z)
Cf (%Y)Td

350 mH(2.3%)
11 mF(4.7%)
1.0 µsCarrier frequency

fc

20 kHzTurn ratio

N=N2/N1

2.4

Input filter
Commutation time

※1 Current ripple is designed at rated output power.

1.0

1.0

Input current [p.u.]

Table I shows the simulation and experimental conditions.
The switching devices at the three-phase to single-phasematrix converter are IGBTs (MITSUBISHI ELECTRIC:
CM400C1Y-24S). Note that the four-step voltage
commutation [7] is applied to prevent the commutation
failure such as the short-circuit of the grid voltage, whereas
one step period of the four-step commutation is set to 1.0 ms.
The inductor at the DC side is designed by the current ripple
ratio which is lower than 10 % at the rated power.

T1(a) Conventional method

Input current [p.u.]

III. EXPERIMENTAL VERIFICATION

T2 + Tz

Stp

Srn

D. Extension of minimum pulse width
Figure 7(a) and 7(b) show the switching pattern during
on switching period. It is assumed that two switches of thebi-directional switch turn-on and turn-off at the same time
without the commutation. The relationship between each
duration is T1 > T2 > Tz. The minimum pulse width is definedas the pulse width which is shorter than another pulse widthin six bi-directional switches during one switching period. In
the conventional method, the minimum pulse width is T2 at
the switches Ssp and Ssn. On the other hand, in the proposed
method, the minimum pulse width is the width of the sum of
T2 and Tz at the switches Ssp and Ssn. Hence, the proposed
method extends the minimum pulse width, leading to the
reduction of the dead time effect.
Figure 8 shows the minimum duty in the conventional
method and the proposed method. In the conventional
method, the dead-time-induced output voltage error occurs
when the minimum duty is lower than 5%. Therefore, theinput current distortion becomes more severe due to thedead-time. Meanwhile, the minimum duty with the proposed
method is always higher than that of the conventional
method.

Min. pulse wide

Srp

Ssp

Minimum duty
during one switching cycle

C. Limitation of proposed cancellation method
The proposed cancellation method has the limitation to
apply the matrix converter. The limitation is decided by thecurrent ripple because the proposed method is based on acontinuous current mode. If the matrix converter is operated
by a discontinuous current mode under the voltage conditionof Fig 5(a), the output current at the negative half cycle iszero because the DC voltage is larger than the output voltageof the matrix converter. However, the limitation to apply the
proposed method is nothing when the DC voltage.

V2

0

0

-1.0

-1.0
Error THD : 11.8% 5 ms/div

THD : 0.8%(a) Conventional method(b) Proposed method
Fig. 9. Comparison among minimum duty.

5 ms/div

Figure 9(a) and (b) shows the input current waveforms
and the harmonic analysis with the conventional andproposed control method. The same inductor value is used
for the evaluation of each control method. The commutation
operation and the input filter are not applied to evaluate only

the effect of the dc current ripple. The input currents are
distorted by the error caused by the dc current ripple with theconventional method, resulting in the high values of the 5th
and 7th order harmonic components. In the proposed current
ripple cancelation method, the input current THD is
improved by 90% at a load of 0.2 p.u..

0

-0.3

Figure 10(a) and (b) depicts the input current waveforms
with dead-time of 5% against the switching cycle in theconventional method and the proposed method. In theconventional method, the minimum duty which is lower thandead-time is eliminated to avoid short-circuit. The input
current distortion due to dead-time is dominant at the lightload. Therefore, the input current THD is too large. On theother hands, the input current distortion is significantly
reduced because the error due to the dead-time is suppressedby the proposed method.

0

-0.3

THD : 4.9% 5 ms/div

THD : 0.5% 5 ms/div(a) Conventional method(b) Proposed method

Harmonic component [p.u.]

1

Figure 11 shows the THD characteristics with theconventional and proposed control method when the dc thesmoothing inductor is changed to adjust the DC current
ripple. In the conventional method, the input current
distortion due to the error is improved to decrease the ripple
ratio of the dc current. However, the input current is still
distorted due to DC current ripple because the output current
is not constant such as an ideal current source. On the other
hand, the input current THD is greatly improved by applying
the proposed method regardless of the ripple ratio of the dc
current. In other words, the error between the reference andactual current at the grid side is completely eliminated by the
proposed method.

1p.u. = Fundamental component

0.1

Reduced by 95%

With conventional method
With proposed method

0.01

0.001

0.0001

1

3

5

7

9

11

13

Number of harmonics

15

17

19

(c) Harmonic analysis
Fig. 10. Harmonic comparison at load of 0.2p.u..
Ripple ratio at rated power

16

1p.u. = 10 kW

30%
14Input current THD[%]

12

Figure 12(a) and (b) show the waveforms of the rectified
voltage, DC voltage, and DC current with the conventional
and proposed method at 0.2p.u.. The inductor is designed by
the current ripple which is the maximum current ripple of
10%. The amplitudes of the current ripple with theconventional and proposed method are the same because thestep-down ratio is 0.75.

20%
10
8

With conventional method
10%6With proposed method

Fig. 6(a)

4
30%
2

20%

Fig. 6(b)10%0Figure 13 (a) and (b) show the experimental waveforms
with the conventional method at the high modulation index.
Hence, the error between the reference and actual input
current occurs due to the dc current ripple which is not
eliminated in the conventional method. As a result, the input
current THD is high at 4.1%. Meanwhile, Figure 13 (c) and(d) show the experimental waveforms with the proposed
method at the high modulation index. Consequently, the

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Input power [p.u.]

Fig. 11. Characteristic of input current THD against input power. The
input current distortion due to the DC current ripple is suppressed by the
proposed method every current ripple ratio.

input current THD is reduced from 4.1% to 3.3% at rated
load compared to that of the conventional method.

Vrec 500[V/div]

Vrec 500[V/div]00

Vdc 500[V/div]

Vdc 500[V/div]

0

0

0

0.3

Input current [p.u.]

Input current [p.u.]

0.3

Idc 2[A/div]

10[ms/div]0

Idc 2[A/div](a) Conventional method(b) Proposed method
Fig. 12. Voltage and current waveforms at DC side at 0.2p.u..

10[ms/div]

00

vu 250[V/div]0

vu 250[V/div]0

iu 50[A/div]

iu 50[A/div]

vmc 500[V/div]

vmc 500[V/div]

0

0

0

0
4[ms/div]

imc 50[A/div](b) Extended Fig. 13(a)00vu 250[V/div]

vu 250[V/div]00

iu 50[A/div]

iu 50[A/div]
THD 3.3 %vmc 500[V/div]

vmc 500[V/div]

0

0

0

0
4[ms/div]

imc 50[A/div]

20[ms/div]

imc 50[A/div](a) Conventional method

20[ms/div]

imc 50[A/div](c) Proposed method(d) Extended Fig. 13(c)Fig. 13. Input and output waveforms of matrix converter at rated power of 10 kW. The DC voltage is 400 V.
vu 250[V/div]
0

0

0

0

iu 50[A/div]
vmc 500[V/div]

vu 250[V/div]
iu 50[A/div]
vmc 500[V/div]

0

0

0

0

10[ms/div]

imc 100[A/div](b) Extended Fig. 14(a)vu 250[V/div]

vu 250[V/div]
0

0

0

0
iu 50[A/div]
vmc 500[V/div]

0

0

0

10[ms/div]

iu 50[A/div]
vmc 500[V/div]

THD 2.8 %0

imc 50[A/div]

10[ms/div]

imc 100[A/div](a) Conventional method

imc 100[A/div]

10[ms/div](c) Proposed method(d) Extended Fig. 14(c)Fig. 14. Input and output waveforms of matrix converter at rated power of 0.6p.u.. The DC voltage is 200 V.

Figure 14 (a) and (b) show the experimental waveforms
with the conventional method at the low modulation index.
The dead-time-induced output voltage error occurs because

the duty is shorter than the dead-time. As a result, the input
current THD becomes high at 8.1%. Meanwhile, Figure 14(c) and (d) show the experimental waveforms with thevu 250[V/div]

vu 250[V/div]00

iu 20[A/div]

iu 20[A/div]00vmc 500[V/div]

vmc 500[V/div]
0

0

0

0
10[ms/div]

imc 50[A/div]

10[ms/div]

imc 50[A/div]

10

10

8

8
Conv. method

64Input current THD[%]

Input current THD[%](a) Conventional method(b) Proposed method
Fig. 15. Input and output waveforms of matrix converter at 0.2p.u. of the rated power. The DC voltage is 400 V. The input current THD is greatly
reduced from 8.2% to 5.3% by the proposed cancellation method.

Prop. method
Improved
by 28%

2
1p.u. =10 kW

0
0.0

0.2

0.4

0.6

0.8

1.0

Power[p.u.]

Conv. method

6Prop. method
Improved
by 35%

4

2
1p.u. =10 kW

0
0.0

0.2

0.4

0.6

0.8

1.0

Power[p.u.](a) Ripple current ratio is 10%(b) Ripple current ratio is 20%
Fig. 16. Relationship between input current THD and input power. The input current THD is improved by the proposed method regardless of the current
ripple ratio.

proposed method at the low modulation index. The output
voltage error does not occur thanks to the extension of theminimum duty. The low input current THD of 2.8% isachieved even with a low modulation index and low powerof 0.6p.u..
Figure 15(a) and (b) show the input and output
waveforms of matrix converter at 0.2p.u. of the rated power.
The input current distortion is high at 8.2% with theconventional method due to the DC current ripple. The input
current distortion is suppressed by the cancellation of the DC
current ripple to apply the proposed method. As a result, theinput current THD is improved by 35% compared with theconventional method.
Figure 16(a) and (b) show the input current THD
characteristics with the current ripple ratio of 10% and 20%
respectively. In the conventional method, the current ripple
at the DC side is not ignored at the light load. Therefore, theinput current is distorted due to the DC current ripple
component with the traditional SVM. The input current
distortion with the proposed method is improved from 8.2%
to 5.3% by 35% compared with the conventional one.
Figure 17 shows the efficiency characteristics of theconventional and proposed method. The maximum
efficiency is 91.7% with the proposed method. The

efficiencies with the conventional and proposed method arealmost the same. By applying the proposed method, the input
current distortion is suppressed by the DC ripple cancellation
to keep the high efficiency.
IV. CONCLUSION
In this paper, the dc current ripple cancelation was
proposed to improve the input current THD. The proposed
method eliminated the ripple component by the combinationof the current slope during the positive and negative cyclesof the high-frequency current. The amplitude of the DC
current ripple was clarified to design the inductor at dc sidewith the proposed method. The 5th and 7th order harmoniccomponents were decreased by over 95% with the proposed
method in the simulation. As experimental results, thefundamental operations with the conventional method andproposed method were obtained. The input current THD is
improved by 35% to cancel the DC current ripple at the lightload.
In the future works, the improvement of the input current
THD with a discontinuous current mode will be conducted.

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Prop. method
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94

[1]

90

88
86
84
1p.u. =10 kW

82
0

0.2

0.4

0.6

0.8

1

Power[p.u.]

Fig. 17. Efficiency characteristics with conventional and proposed
method.