A Control Method for a Single-to-three-phase Power Converterwith an Active Buffer and a Charge Circuit

Yoshiya Ohnuma

Jun-ichi ItohStudent Member, IEEE
Nagaoka University of Technology
1603-1 Kamitomioka-machi Nagaoka City
Niigata, Japanohnuma@stn.nagaokaut.ac.jp

Member, IEEE
Nagaoka University of Technology
1603-1 Kamitomioka-machi Nagaoka City
Niigata, Japan
itoh@vos.nagaokaut.ac.jp

Abstract -- This paper proposes a new circuit configuration
and a control method for a single-phase to three-phase power
converter with power decoupling function. The proposed
converter does not require a large reactor and large smoothing
capacitors in the DC link part. Large smoothing capacitors areconventionally required in such converters to absorb the power
ripple with a frequency that is twice of the power supply. The
proposed topology is constructed based on an indirect matrix
converter with an active buffer to decouple the power ripple.
The buffering energy is kept by the voltage variation of thecapacitor instead of its capacitance. In addition, the transfer
ratio between the input and output voltage is obtained to 0.707
due to the connected charge circuit. In this paper, thefundamental operations of the proposed converter are
confirmed by simulation and experiment results. As theexperimental results, the input current THD and the output
current THD are 3.17% and 3.64 %, respectively. The input
power factor (P.F.) of over 99 % is obtained. In addition, themaximum efficiency of over 90.2% (input voltage = 100V) or
94.6 % (input voltage = 200V) is obtained by prototype.

ripple at the DC link part, some strategies have been
proposed, such as DC active filters, power decoupling
methods [5]-[8]. Certainly, these topologies can reduce thecapacitance value of the DC link capacitor by storing thepower ripple in a sub-capacitance with using an additional
circuit. However this additional circuit requires more
switches and a large reactor. Consequently, the additional
circuit increases the total power consumption.
AC-AC direct converters, such as matrix converters,
have also been studied. AC-AC direct converters are smaller
in size, lower in cost, and have longer lifetimes, since thelarge energy buffer is not required. A number of matrix
converters have been proposed for single-to-three-phaseconversion. For example, the power ripple is absorbed by theinertial moment of a motor [9]. This method does not require
additional components over the conventional converter;
however this approach limits the applications because thelarge torque ripple will occur in the motor. In anotherapproach, the single-phase power supply and energy
capacitor are connected to the input side of the three-phasematrix converter [10]. However, this method increased theswitching devices to 18 units.
A single-to-three-phase power converter using an active
buffer has been proposed in [11]. This converter is based on
the concept of an indirect matrix converter that coupled withan active buffer to absorb the power ripple. The size of theconverter can be reduced because the converter does not
require a large smoothing capacitor in the DC link part and aboost up reactor. However, the voltage transfer ratio between
the input voltage and the output voltage is less than 0.5
because a load inductance is used to charge the buffer
capacitor.
This paper proposes a new circuit configuration using anactive buffer, which has a charge circuit in the DC link part.
By using the charge circuit in the DC link part, the voltage
transfer ratio between the input and output voltage is
improved to about 0.707. In this paper, the principle of the
proposed converter is described. After that, the fundamental
operation and the validity of the proposed method are
confirmed by simulation and experimental results, which aredemonstrating good waveforms at the input/output current

Index Terms— Single-phase to three-phase power converter,
Indirect matrix converter, Power factor correction

I. INTRODUCTION
Single-phase to three-phase converters are required inorder to apply the three-phase motor to home appliances inthe terms of energy-saving. One of the most significant
problems for a single-to-three-phase converter is that thepower ripple is found with a frequency that is twice of thepower supply.
A conventional converter consists of a diode rectifier, athree-phase inverter, and a large energy buffer, such as anelectrolytic capacitor. A power factor correction (PFC)
rectifier is also required in order to suppress the input current
harmonics [1]-[4]. Many of the three-phase inverters with asingle phase PFC have been proposed. However, almost all of
the converters require a large boost-up reactor and a large
energy buffer such as electrolytic capacitor. In addition,
almost all of PFC circuits use additional switching devices ordiodes in the main circuit in series and it causes substantial
power loss.
On the other hand, in order to compensate the powerand output voltage.
II.

CONTROL STRATEGY

Figure 1 shows a block diagram of the proposed
converter. The converter is based on an indirect matrix
converter topology, where the rectifier is operated as acurrent source rectifier, and the inverter stage is operated as a
voltage source inverter. A buffer circuit that consists of adischarge circuit and a charge circuit is inserted into the DC
link to decouple the power ripple, which has a frequency thatis twice of the power supply. A discharge circuit consists of asmall capacitor and a switch. A charge circuit is a kind of aboost-up circuit. It should be note that the discharge circuit isalso used as a snubber circuit for protection in the proposed
converter.
Figure 2 shows the circuit topology of the proposed
converter. Low cost diode rectifier is used as the AC-DC
stage converter because most home appliances do not requirea regeneration mode from the output power. In this control
method, half of the input power is supplied directly to theinverter. The power ripple is compensated by the discharge
circuit and the charge circuit. Zero current switching of thedischarge switch SC is achieved because the discharge switch
is turned on or off while the inverter outputs zero-voltage
vector. In this manner, there is no switching loss at thedischarge switch or recovery loss at the diode rectifier. In
addition, the charge circuit and the discharge circuit
alternately operate at per quarter cycle of the input voltage.
Therefore, the efficiency of the proposed circuit will behigher than the conventional PFC circuits

Fig. 1. Block diagram of proposed system.

Fig. 2. Proposed circuit.

Fig. 3. Compensation principle of power ripple.

III. CONTROL STRATEGY
Principle of the power ripple compensation
Figure 3 shows the principle of the power ripplecompensation. When both the input voltage and the input
current waveform are sinusoidal, the instantaneous input
power, pin is expressed aspin = VIN I IN sin 2 (ωt )
(1) ,
1
1
= VIN I IN − VIN I IN cos(2ωt )22where, VIN is the peak single-phase voltage, IIN is the peaksingle-phase current, and ω is the single phase angularfrequency.
From (1), the power ripple that contains twice thefrequency appears at the DC bus link part. In order to absorb
the power ripple, the buffer circuit instantaneous power pbuf,
is required by1
pbuf = VIN I IN cos(2ωt )(2),2where the polarity of the pbuf is defined as positive when thebuffer circuit discharges. The mean power of the capacitor iszero because the discharge circuit and the charge circuit do
not generate active power.

SREC

A.

irec
|vin|

il
SL

SC

SZ

ic

iz

Idc

vc

Fig. 4. Equivalent circuit of proposed system.

Control approach
Figure 4 shows the equivalent circuit of the proposed
converter. Each current can be expressed by⎡irec ⎤ ⎡d rec d l ⎤⎢i ⎥=⎢d⎥ ⎡ I dc ⎤(3),
⎢ c ⎥ ⎢ c 0 ⎥⋅⎢ i ⎥l ⎦⎣⎢⎣ iz ⎥⎦ ⎢⎣ d z 0 ⎥⎦B.

where, drec, dc, dz, and dl are the duty ratios of SREC, SC, SZ,
and SL. Here, the duty ratios are constrained by continuous
current (Idc) as follows.
d rec + d c + d z = 1(4)
However, SREC does not control independently due to thediodes. That is, the rectifier current irec becomes active whenthe switch SL is turned on. During the discharge period, thecharge circuit does not work i.e. dl equals zero. In order toobtain the sinusoidal input current, the rectifier duty ratio drec
is constrained by (5). In addition, the capacitor duty ratio dc
can be obtained from (6) to compensate the power ripple.
Id rec = IN sin(ωt )(5)
I dc
VIN I INcos(2ωt )(6)
2vc I dc
On the other hand, during the charge period, thedischarge circuit does not work (dc = zero). Therefore drec
can be obtained by (7) to keep the output power constantly.
I IN(7)
d rec =
2 I dc sin(ωt )The control method of the charge circuit is based on the
discontinuous mode of reactor current. In this case, thereactor current is obtained by (8) when the input current isassumed as sinusoidal.
I IN(8)
il = I IN sin(ωt ) −2 sin(ωt )Therefore, the duty ratio dl can be expressed bydc =π
2 Lm (vc − vin )il
3π, when< 2ωt <
(9),22
vin vcT
where, Lm is inductance of the charge circuit and T isswitching period.
Meanwhile, the relations between IIN and Idc are obtained
from the maximum voltage transfer ratio as follows;
1
I IN
=
= 2
(10).
I dc sin(π 4)Finally, dREC and dC are obtained as (11) from (5), (6),(7) and (10).
dl =d rec = 2 sin(ωt ), when−π2< 2ωt <

2d rec =
2 sin(ωt ), when

π
2

dc =

2V IN
cos(2ωt )
2v c

π
2

(11)

dc = 0< 2ωt <

3π
2

Maximum output voltage for the three-phase side
When the DC link power is constant, the DC link
voltage is expressed as (12) because the instantaneous powerof the input side and DC link side is the same. Therefore, thevoltage transfer ratio of 0.707 is obtained.
1
Vdc max =VIN = 0.707VIN
(12).
2

C.

D. Estimation method of the maximum value of input
current
In order to calculate the reactor current il by (8), themaximum value of input current IIN is necessary. However IIN
is difficult to decide due to the fluctuation in the output
power.
Therefore this paper proposes a method where themaximum value of input current is estimated by using voltage
drop of the buffer capacitor voltage. The electric storage
energy required to compensate the power ripple WC is
obtained by (14) because WC equals to the electric power ofthe single phase side in half cycle time.
1

4f
1
WC = V IN I IN ∫ sin (2ωt )dt02(14)
V IN I IN=
2ω
Moreover, the WC in the capacitor is required from therelations between the electric power and the voltage of thecapacitor by (15).
1122WC = CVC max − CVC min(15)22
where, VCmax is the maximum voltage, VCmin is the minimum
voltage of the buffer capacitor. VCmax and VCmin can bedetected from sensor. Therefore, the IIN is calculated by (16)from (14), (15).
2ωWC ωC
2
2
I IN ==
VC max − VC min
(16)
V IN
V IN
From (16), this method does not need a current sensor
because of the IIN can be calculated by the capacitor voltage
from a voltage sensor.

()

E. The pulse generation method by space vector
modulation
In order to implement the inverter vector command v*,
approximate two vectors are required, and the duty ratios ofthese vectors are calculated by using the projection of thevector commands in the α axis(vα) and in the β axis(vβ) as
following.
⎧ vα = V1α T1 + V2α T2 + V0α TZ⎪(17)⎨v β = V1β T1 + V2 β T2 + V0 β TZ
⎪ 1=T + T +T
1
2
Z⎩
where, T1, T2 and Tz are the output duty ratios of V1 vector, V2
vector and zero vector, respectively.
Therefore, the duty ratios T1, T2 and Tz can be obtained
by

T1 =
T2 =

1 vα
A vβ

V2α
V2β

1 V1α
A V1β

vα
vβ

Carrier(18).

⎛
V
V 2α ⎞⎜∵ A = 1α⎟TZ = 1 − (T1 − T2 )
⎜
⎟
V
V
1
β
2
β
⎝
⎠
Finally, the output duty ratios for each switch are
obtained from (11) and (15).
T1REC = T1 ⋅ d REC T1C = T1 ⋅ d C T1Z = T1 ⋅ d Z(19)
T2 REC = T2 ⋅ d REC T2C = T2 ⋅ d C T2 Z = T2 ⋅ d Z
In order to reduce the number of the switching times, allzero vectors should be summarized to one.
T ZZ = T1Z + T2 Z + TZ
(20)
Figure 5 shows the inverter carrier, each duty andswitching pattern of the proposed method. In the charge modeas shown in Figure 5(a), duty ratio dc is zero. Therefore
switch SC does not turn on and the inverter outputs threevector; V1rec vector and V2rec vector from the input voltage
vectors and the zero vector. In order to charge the buffer
capacitor, Switch SL is operated. It should be noted that theturning on of the switch SL is zero current switching due todiscontinuous method of an inductor current. On the other
hand, in the discharge mode (Fig. 5 (b)), the voltage vector
outputs a buffer capacitor voltage vector. That is, the inverter
outputs five-vector; V1rec and V2rec from the input voltage
vectors, V1c and V2c from the capacitor voltage vectors andzero vector. The discharge switch SC is turned on or off while
the inverter outputs zero-voltage vector. Therefore, zerocurrent switching of the discharge switch Sc is achieved.
Figure 6 shows the control block diagram of the proposed
circuit. From (11), the duty ratio commands are calculated
from the input voltage vin, the input angular frequency, thecapacitor voltage vc and the maximum input current IIN. Notethat the maximum input current IIN is calculated by commandof maximum capacitor voltage VCmax* and detection value ofminimum capacitor voltage. The gate pulses are given bycomparing between the duty command and the triangle
carrier, as shown in Fig. 5.
IV. CONSIDERATION OF PARAMETERSA.

The buffer capacitor
The electric storage energy used for compensates thepower ripple WC is obtained by (14) and (15). Therefore, theminimum capacitance in the buffer circuit is obtained by (21).
2WC
C=
2
2
VC max − VC min(21)
2 Pout=ω (VC max 2 − VC min 2 )T1rec+T2rec
T1rec
dl

1

0

1

SUp 0
1

SVp 0

SWp 01
1

SL 0

1

SC 0 ZCS

ZCS(a) Charge mode
Trec=T1rec+T2rec

Carrier

Trec+Tzz+T1c
Trec+Tzz
T1rec+T2rec
T2rec

1

0

(dl=0)
1

SUp 0
1

SVp 0

1

SWp 0

1

SL 0

1

SC 0
ZCS

ZCS

(b) Discharge mode
Fig. 5. Carrier and switching pattern.

Fig. 6. Control block diagram.

Accordingly, the minimum capacitance requires in the buffer
circuit to compensate the power ripple can be determined by
the output power, Input angular frequency and the fluctuation
capacitor voltage.
Figure 7 shows the relations among the necessary
electric energy or necessary capacitor and the output power
when the input angular frequency is 50 Hz. In this condition,
the necessary electric storage energy to compensate thepower ripple WC requires for a 1kW rated output poweris 3.18 J. The minimum voltage of the buffer capacitor
VCmin is limited by peak input voltage. So, when the
input voltage is 100 V, solid lines is selected. In
addition, the maximum voltage of the buffer capacitor
VCmax and capacitance of buffer have trade-off problem.

From there, the minimum capacitance requires 46.3 μF
or 94.3 μF. Therefore, a film capacitor of small capacity canbe used instead of an electrolytic capacitor.
The inductance value
The control method of the charge circuit is based on the
discontinuous method of an inductor current. Therefore, there
is limitation on the inductance and switching duty. The
limitation of the maximum duty of switch SL is calculated by(22).
V − V INd l max = C 0
(22)
VC 0
where VC0 is the average voltage of capacitor when output
power is at maximum value.
From (9), the inductance of charge circuit has to besmaller than the calculation value in (23).
B.

2d l max V IN VC 0T(23)
I IN (VC 0 − V IN )Note that, the peak current value of the charge circuit
will increase when the inductance value is decreased.
Therefore, it needs to consider about the current capacity ofthe switching device.
Lm ≤

V.

Necessary electric energy tocompensate for power ripple [J]
200 0

1

(Input frequency = 50 Hz)

2

VCmax = 350V
VCmin = 300V

3

4

6

VCmax = 300V
VCmin = 150V

150
VCmax = 400V
VCmin = 300V

100
50

0

VCmax = 400V
VCmin = 150V

500

1000
1500
Output power [W]2000

Fig. 7. . Relationship between necessary electric energy or necessary
capacitor and output power when input frequency is 50 Hz..
Table 1. Simulation and experimental parameters.

SIMULATION RESULTS

The operation of the proposed circuit is demonstrated bysimulation results. Table 1 shows the simulation parameters.
In this simulation, the 100 μF capacitor is used for the 1 kW
output power. In this case, the capacitor voltage is controlledfrom 150 V to 300 V. It is note that this simulation is
implemented without dead time and the input filter.
Figure 8 shows the simulation results with the proposed
control method. The input current iin and the output voltage
vuv(LPF) were observed using a low-pass filter (LPF) with acut-off frequency of 1 kHz in order to confirm the low
frequency distortion on the waveforms. Output load isdecreased from 100 % to 20 % after 40 ms, and 110 ms after,
it is increased from 20 to 75 %. In each case, sinusoidal
waveforms without distortion are obtained for the output
voltage. In addition, an input current is obtained as sinusoidal
waveform in its half period. Moreover capacitor maximum
voltage is controlled under 300 V. THD of input and output
current under 1 kHz are reduced within 1%. Thus, theproposed method is confirmed by the result of powerfluctuation correction.
VI. EXPERIMENTAL RESULTS
In order to demonstrate the validity of the proposedsystem, a 1-kW class prototype circuit has been tested. The
experimental conditions are the same as the simulation, in
Table 1. Note that three-phase R-L load is used to confirm theprinciple of the proposed converter.
Figure 9(a) shows the operation input and capacitor
waveforms of the proposed method. From the result,

5Fig. 8. Simulation results.

100

Input power factor
97.5
95

92.5

Efficiency

90(a) Input and capacitor voltage waveforms.

87.5
85

0

200

400

600

800

1000

Output power [W]
Fig. 11. Efficiency and Input power factor of proposed circuit.
(Input voltage = 100V)(b) Output voltage and current waveforms.
Fig. 9. Experimental results.

16
THD of input and output current [%]14
12

Output current
THD

10
8
6
4
2
0

Fig. 12. Efficiency and Input power factor of proposed circuit.

Input current THD
0.2

0.4
0.6
0.8
Output power [W](Input voltage = 200V)

1

1.2

Fig. 10. THD of input and output current

sinusoidal waveforms without distortion are obtained at the
input current. In addition, the capacitor voltage is controlledfrom 300 V to 150 V of twice the frequency of the input
voltage according to the proposed strategy.
Figure 9(b) shows output current and voltage waveform.
The output voltage vuv(LPF) was observed using a low-passfilter (LPF) with a cut-off frequency of 1.5 kHz. As a result,
sinusoidal waveforms of the output voltage and current wereobtained. In addition, the peak voltage is obtain about 100 V
as same as calculation value by (12). That is, the voltage
transfer ratio between the input and output voltage can output
about 0.707.

Figure 10 shows the total harmonics distortion (THD) of
the input current and the output current. The minimum value
for the input current THD is 3.17% and the output current
THD is 3.64%. It should be also noted that THD is calculated
by using harmonics components less than 1 kHz. The input
current harmonics in the proposed circuit is much lower thanstandard of IEEE 61000-3-2.
Figure 11 shows the efficiency and input power factor in
respects to the output power of the proposed circuit. As aresult, the maximum efficiency of 90.0 % and almost all
efficiency of over 89 % are obtained. The input power factor(P.F.) of over 99 % is obtained even if a diode rectifier isused as input circuit.
Figure 12 shows the efficiency and the input power
factor of the proposed circuit when the input voltage is 200 V.
In this case, the capacitor voltage is controlled from 400 V to

300 V. The input power factor (P.F.) over 99% and highefficiency of 94.6% were obtained. The reason of low power
factor in the light load region is because the lead current
flows in the capacitor of the input filter initially.
VII.
CONCLUSION
This paper proposes a circuit configuration and a control
method for a single-phase to three-phase converter with anactive discharge and a charge circuit for the power
decoupling between the input and output side. The proposed
circuit can improve voltage transfer ratio to 0.707. The
validity of the proposed control strategy is confirmed bysimulation results. The power ripple at twice the frequency ofthe power supply can be adequately suppressed using a buffer
capacitor of only 100 μF at 1 kW. The input current andoutput current THD are less than 4% and unity power factor
are obtained. In addition, almost all efficiency of over 89%(input voltage = 100V) or 94 % (input voltage = 200V) is
obtained by prototype.
This study was supported by Industrial Technology
Grant Program in 2009 from New Energy and Industrial
Technology Development Organization (NEDO) of Japan.
REFERENCES[1] T.Ohnishi, M.Hojo: "DC Voltage Sensorless Single-Phase PFC
Converter" IEEE Transactions Vol.19 Issue 2, pp404410,(2004)[2] K.Taniguchi, S.Saegusa, T.Morizane, N.Kimura: "Single-Phase
Buck-boost PFC Converter for V-connected Three-phase
Inverter", PCC Nagoya, pp1540-1546,(2007)[3] Zhonghui Bing, Min Chen, S.K.T.Miller, Y.Nishida, Jian Sun :" Recent Developments in Single-Phase Power Factor
Correction", PCC Nagoya, pp1520-1526,(2007)[4] C.B.Jacobina, E.C.Dos Santos Jr., N.Rocha, E.L.L.Fabricio : "Single-Phase to Three-Phase Drive System Using Two Parallel
Single-Phase Rectifiers" IEEE Transactions Issue 99, pp1-1,
ISNN 0885-8993 (2010)[5] F.Hayashi, J.Itoh, : " Ripple Current Reduction of a Fuel Cell for aSingle-Phase Isolated Converter Using a DC Active Filter With aCenter Tap " IEEE Transactions Vol.25 Issue 3, pp550-

556,(2010)[6] F.Shinjo, K.Wada, T.Shimizu: " A Single-Phase GridConnected Inverter with a Power Decoupling Function " PESC
2007, pp.1245-1249, (2007)[7] Kuo-Hen Chao, Po-Tai Cheng : "Power decoupling methods
for single-phase three-poles AC/DC converters " ECCE 2009,
pp3742-3747,(2009)[8] Ruxi Wang, F.Wang, Rixin Lai, Puqi Ning, R.Burgos,
D.Boroyevich : " Study of Energy Storage Capacitor Reduction
for Single Phase PWM Rectifier " APEC 2009, pp11771183,(2009)[9] H.Haga, I.Takahashi, K.Ohishi: "Unity Power Factor Operation
Control Method For Single-phase to Three-phase Matrix
Converter", IEEJ Vol.124-D No.5, pp510-516,(2004)[10] M.Saito, N.Matsui:"A Single- to Three-phase Matrix Converter
for a Vector-Controlled Induction Motor" IEEE IAS2008,[11] Y.Ohnuma, J.Itoh:"Novel Control Strategy for Single-Phase toThree-Phase Power Converter Using an Active Buffer" EPE
LS7c-14 (2009)[12] D.Grahame Holmes, Thomas A.Lipo : " Pulse Width
Modulation For Power Converters Principles and Practice "IEEE Series on Power Engineering, Mohamed E. El-Hawary,
Series Editor,(2003)[13] H.W.van der Broeck, H.-C.Skudelny, G.V Stanke : "Analysis
and realization of a pulsewidth modulator based on voltage
space vectors" IEEE JOURNALS Vol.24 Issue 1, pp142150,(1988)[14] Y.Ohnuma, J.Itoh : "Space Vector Modulation for SinglePhase to Three-Phase Converter Using an Active Buffer"
IPEC-Sapporo 2010 22D1-5, (2010)