Control Strategy for a Three-Phase to Single-Phase
Power Converter Using an Active Buffer with a Small
Capacitor
Yoshiya Ohnuma1 and Jun-ichi Itoh1
1 Nagaoka University of Technology/Department of Electrical Electronics and Information Engineering, Nagaoka-city Niigata, 940-2188, Japan

Abstract- A novel three-to-single-phase power converter thatallows for smaller smoothing capacitors in the DC link is proposed.
Large smoothing capacitors are conventionally required in such
converters to absorb power ripple at twice the frequency of the single
phase AC. The proposed topology consists of an indirect matrix
converter and an active snubber to absorb the power ripple, and does
not require a reactor or large smoothing capacitors. In this paper, thefundamental operation of the proposed converter is confirmed
through simulations and experiments. The experimental results
indicate that for a 1kW-class prototype circuit, the power ripple attwice the frequency of the power supply can be adequately suppressedusing a buffer capacitor of only 50µF. Moreover, the single-phasepower factor of over 99% and good waveforms for input and output
current.

I.

INTRODUCTION

Recently, distributed power systems have been studied
intensely. In particular, generators such as gasoline or diesel
engine generator, micro gas turbine, wind turbine, these areimportant to supply power in case of massive blackout or
disaster in addition to supporting regular power demand.
Generally, home appliances require a small single-phase
generator system. However, a system requires a three-phase AC
generator to reduce sizing and achieve high efficiency.
Therefore, a three-phase to single-phase converter is consideredto supply the desires power. In a conventional converter,
electrolytic capacitors with large capacitance have beenconnected on the DC link part in order to absorb the power
ripple of twice of the frequency caused by single-phase AC.
On the other hand AC/AC direct converters, such as matrix
converters, have also been studied to attain the following
advantages; smaller in size, lower in cost, and longer lifetimes,
since the large energy buffer is not required in the converters. A
number of matrix converter schemes have been proposed forthree-to-single-phase conversion. In one example, power ripple
is absorbed by the inertial moment of a motor or generator [1].
This method does not require additional components over theconventional converter, yet this approach increases power loss
due to distortion current flows into the generator. In anotherapproach, the single-phase power supply and energy capacitor

Fig. 1. Block diagram of proposed system.

are connected to the input side of the three-phase matrix
converter [2]. However, this method requires 18 switching
devices, detracting from the advantages of three-phase design.
In this paper, a novel three-to-single-phase power converter
involving smaller energy buffer capacitors is proposed. The
proposed converter is constructed based on an indirect matrix
converter coupled with an active snubber circuit without areactor or large electrolytic capacitor [3]. The active snubber
circuit is used as an active buffer to absorb power ripple. The
values of the capacitor can be reduced by controlling thecapacitor voltage variation, allowing for the use of small buffer
capacitors such as film capacitors. The fundamental operationsand validity of the proposed converter are confirmed bysimulation and experimental results, which demonstrate good
waveforms of the input and output current and output voltage.
II.

CIRCUIT TOPOLOGY

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 a voltage source rectifier, andthe inverter stage is operated as a current source inverter. A
buffer circuit consisting of a small capacitor and a switch Sbuf isinserted into the DC link to absorb the power ripple, which has
twice of the frequency of the power supply. Note that the buffer
circuit is also used as a snubber circuit for circuit protection.

Figure 2 shows the specific circuit topology of the proposed
converter. Zero-current switching operations of both the buffer
switch and the inverter switch are achieved by matching theswitch timing to the zero-voltage vector output of the rectifier.
In this method, there is no switching loss at the buffer switch andinverter switch.
III.

CONTROL STRATEGY

A. Principle of the power ripple compensation
Figure 3 shows the compensation principle of power ripple.
When both the output voltage and current waveform issinusoidal, the instantaneous output power, Pout is expressed as,
p out = Vm I m sin 2 (ωt )11= Vm I m − Vm I m cos(2ωt )(1)2
2
where, Vm is peak single-phase voltage, Im is peaksingle-phase current, ω is angular frequency of single-phase.
From (1), the power ripple with twice the frequency appearson the DC bus link part.
In order to absorb the power ripple, the buffer circuit
instantaneous power, Pbuf, is required by (2). Note that the mean
power of the buffer circuit is zero because the buffer circuit
absorb only ripple. Therefore, the a small capacitor can be usedin the buffer circuit.
1
pbuf = Vm I m cos(2ωt )(2)
2Consequently the instantaneous input three-phase power, Pin
can be constant (3).
1pin = Vm I m(3)
2
B. Control approach
Figure 4 shows the equivalent circuit of the proposed
converter. The output current of the rectifier Idc is divided by Sbuf
into the capacitor current ic and inverter current iinv. Note that thezero-period current iz is a circulation current, as given by therectifier output zero-voltage vectors. The equivalent circuit thenconsists of three switches; SINV, SC, SZ, which are related asfollows.
iinv  d INV i  =  d ⋅I(4) c   C  dc
 iz   d Z 
Here, dINV, dC, and dZ are the duty ratios of SINV, SC, and SZ,
respectively, Note that the duty ratios are constrained bycontinuous current (Idc) as follows.

d INV + d C + d Z = 1(5)
The term dINV is controlled so as to obtain a sinusoidal
waveform for the single-phase current iinv, as described in(6) and (7).
iinv = I m sin (ωt )(6)Fig. 2. Proposed circuit with single switch in buffer.

Fig. 3. Compensation principle of power ripple.

Fig. 4. Equivalent circuit of proposed system.

Imsin (ωt )(7)
I dc
The ic is controlled to absorb the power ripple of the power
supply through the charge or discharge of a capacitor dependingon the direction of capacitor current.
V I
ic = m m cos(2ωt )(8)
2VC
Here, VC is the capacitor voltage, and Vm is the peaksingle-phase voltage.
Since negative capacitor current (discharge current) is notpossible when the direction of Idc is positive, Idc is to becontrolled as negative by the rectifier when the discharge current
mode is selected. Therefore the duty ratio dc can thus beobtained as follows.
d inv =

DC link voltage ( p.u. )Vm I m(9)cos(2ωt )2VC I dc
d Z = 1 − d C − d INV(10)Meanwhile, the ratio of Im divided by Idc can be obtained asfollows from the maximum voltage transfer ratio;
Im
2VC
(11).
=
I dc 2VC + Vm
Finally dinv and dc can be obtained as (12) from (7), (9) and
(11).
2VC

d INV = 2V + V sin (ωt )

C
m
(12)

V
m
d =
cos(2ωt ) C 2VC + Vm
dC =Fig. 5. Relation between capacitor voltage and direct voltage.

C. Maximum input voltage for the three-phase side
When compensation of the power ripple at the maximum
output voltage, the theoretical DC link voltage Vdc can be
expressed as
1
I dcVdc = Vm I m
2
(13)
VC
Vdc =
Vm
2VC + Vm
Figure 5 shows the relation between the capacitor voltage andthe DC link voltage requested by (13) when normalization ofpeak single phase voltage Vm. Therefore even then Vc is infinity,
The maximum Dc link voltage is limited to Vm/2. That is, themaximum input voltage is less than half of Vm.

Inverted commands

Vr*

Vt*

Vs*
Vs*

Vt*

D. Pulse generation method
Figure 6 shows the PWM pattern generation using a carriercomparison strategy. To obtain a PWM pulse according to (10)and (12), the command dINV+dZ is compared with a triangularcarrier. The pulse patterns are then obtained by

s C = s INVZ
(14)s Z = s INV ⋅ s INVZ
where sC is the gate pattern for SC, sZ is the gate pattern for SZ,
sINVZ is the gate pattern obtained by dINV +dZ, and sINV is the gate
pattern obtained by dINV.
A special trapezoidal carrier is used to generate the PWM
pattern of the rectifier. To generate the zero-voltage vectors
according to sZ, the rectifier side carrier is set to 1 or 0 when sZ isin the on state. The slope of the rectifier side carrier is controlled
by the voltage ratio between vINV and vc. As a result, the same
voltage is obtained in one carrier cycle, while the different
voltage of vc and vINV is provided to the rectifier.
The voltage command of the rectifier is obtained using a
trapezoidal carrier. It should be noted that the rectifiercommands must be inverted when Sc is in the on state, whichcorresponding to the capacitor discharge mode.
The gate pattern sbuf of the capacitor switch is obtained byconversion from gate pattern sC. The capacitor voltage is always

Inverted commands

Vr*
Zero voltage
area

Zero voltage
areaFig. 6. Relationship of duty commands andinverter side carrier and inverter commands.

∫

Fig. 7. Control block diagrams.

higher than the output voltage. Since sC is not active when sZ isactive, the relationship between sbuf and sINV can be expressed assbuf = s INV(15)
Figure 7 shows the control block diagram of the proposed
circuit. From (10) and (12), the duty ratio commands arecalculated from the single-phase angular frequency, the peaksingle-phase voltage, and the capacitor voltage. The gate pulses
are given in order to compare the duty command with thetrapezoidal carrier, and the gate pattern is converted to sbuf by(15). The current of a three-phase generator is controlled by the
PI regulator. The current of the generator is separated d-q axis
components which correspond to the rotor position of thegenerator. The rotor position is detected by position sensor suchas a encoder or resolver. The d-axis current command is set tozero to perform the minimum loss of the generator. On the otherhands, the q-axis current command depends on the powercommand from the generator to the power grid.
The inverted commands controller is used in order to thecapacitor current ic is negative direction. When the ic requires
the negative direction, the switching patterns are reversed.
D. Consideration of the capacitor value
The minimum capacitance in the buffer circuit to compensate
the power ripple can be determined by electric energy and thefluctuation capacitor voltage. The minimum capacitance tocompensate for the power ripple, Wc, is obtained by (16) because
Wc is equal to the electric power of the single phase side for halfcycle.
1
4f
1
WC = Vm I m ∫ sin (2ωt )dt
2
0(16)
Vm I m Pout==2ωω
Moreover, the electric storage energy in the capacitor isrequested from the relation between the electric power and thevoltage of the capacitor by (17).
1122WC = CVC max − CVC min(17)22
where WCmax is the maximum voltage, WCminis the minimum
voltage of the buffer capacitor.
Therefore, the minimum capacitance in the buffer circuit isobtained by (18) from (16) and (17).
2WC
(18)
C=
2
2
VC max − VC min

Figure 8 shows the relationship between necessary capacitor
and output voltage. The conditions of the calculation are used
where VCmax is 400 V, VCmin is 150 V.
From the minimum capacitance of 1 kW rated power is 46.3
µF. Therefore, a film capacitor of small capacity can be usedinstead of an electrolytic capacitor. Note that the maximum
value of the current of the capacitor reaches the peak value of thethree-phase current.

Fig. 8. Relationship between necessary capacitor and output voltage. When
Vcmax=400 V and Vcmin=150 V.
Table 1. Simulation parameters.
Generator frequency

30 Hz

Output voltage

100 V

Output frequency

50 Hz

Output power

1000 W

Buffer capacitor

50 µF

Leakage inductance

0.51 mH

Speed electromotive force

16.7 V

Next, the maximum voltage of the capacitor voltage isdiscussed. The electric power of the capacitor, Wcom, is obtainedby integration of (2) and (3).
P
Wcom = W pri − out sin (2ωt )(19)
2ω
where Wpri is the initial electric energy in the buffer capacitor.
On the other hands, Vbuf0 is assumed as the average voltage ofthe capacitor, Wpri can be expressed by (20)1
2
W pri = CVbuf0(20)
2
Therefore, capacitor voltage Vbuf is given by (21)
P
1
1
2
2
Cvbuf = CVbuf0 − out sin (2ωt )
2
2
2ω
p
2
vbuf = Vbuf0 − out sin (2ωt )(21)
ωC
The rated voltage of the buffer capacitor increased when in caseof low capacitance, low output frequency for the single phase.
IV.

SIMULATION RESULTS

The operation of the proposed circuit is demonstrated here by
simulations, given the conditions listed in Table 1. In thesimulation, the capacitor of 50 µF is used for the output power of1000 W. In this case the capacitor voltage fluctuates from 150 V
to 400 V. In addition, a generator simulates the power supplies,
which mean speed electromotive force, and leakage inductances.
It is note that this simulation does not consider the commutation
time for the single –phase converter and the input side inverter.

Figure 9 shows the simulation results for the proposed control
method. After 50 ms, the operation mode changed frommotoring mood to generator mode. The generator terminal
voltage vrs(LPF) and the output single-phase current ia(LPF) wereobserved using a low-pass filter (LPF) with a cut-off frequencyof 1 kHz in order to confirm the low frequency distortion on the
waveforms. In each case, good sinusoidal waveforms without
distortion are obtained for the generator terminal voltage vrs(LPF)of the rectifier, the output current for the single-phase power
grid.
Figure 10 shows the simulation results for the step response of
the input current command. At the first change point, the input
current command increased from 0.5 p.u. to 1 p.u. and thesecond change point, decreased 1 p.u. to 0.5 p.u. Goodsinusoidal waveforms are also obtained in this condition.
Figure 11 shows the harmonic analysis of the total harmonic
distortion (THD) of the input and output currents. As a result,
THD of the generator terminal voltage vrs is less than 3 % andoutput current ia of the shingle-phase is also less than 1 %.

50
0
-50
400
300
200
100
0
-100
10
0
-10

VI.

40

0

Fig. 9.Simulation results for motoring mode and generation mode.
Input current
command 50 (% )Input current
command 100 (% )Input current
command 50 (% )

30
0
-30
50
0
-50
400
300
200
100
0
-100
10
0
-10
0

40

80

160

120

Time [ms]Fig. 10. Simulation results when input current command changes.
Table 2. Experimental parameters.
Single-phase voltage

100 V

Single-phase frequency

50 Hz

Three-phase frequency

30 Hz

Three-phase R-load

1Ω
1 mH

Output power

1000 W

Buffer capacitor

50 µF

FFT of vrs

Three-phase L-load

CONCLUSION

A novel control method for a three-to-single-phase power
converter was proposed. The validity of the method is confirmedby simulations and experiments. The experimental results
indicate that for a 1kW-class prototype circuit, the power ripple
at twice the frequency of the power supply can be adequately

120

80

Time [ms]EXPERIMENTAL RESULTS

To demonstrate the proposed system, the prototype circuit istested. However, since the load machine is not enough, theregenerating mode operation, which the power flows from thesingle-phase grid to three-phase side, was tested, given theconditions listed in Table 2. In this experiment, Three-phase
R-L load is used instead of the generator.
Figure 12(a) shows the operation waveforms without active
buffer. The three-phase current contains large distortion of twice
the frequency of the power grid. The distortion current of thegenerator causes the increasing loss of that.
Figure 12(b) shows the operation waveforms of the proposed
circuit. Good sinusoidal waveforms are obtained for the
single-phase current and three-phase current, with asingle-phase power factor of over 99%. The proposed system
can achieve the high efficiency because the current distortion of
the generator is very low.
Figure 12(c) is single-phase waveforms and capacitor voltage
waveforms. The capacitor voltage is controlled according to the
proposed strategy by 400 V to 150 V. It should be noted that theregeneration operation is required to improve efficiency forwind turbine system or to start the engine. In addition, thefundamental control strategy in the regeneration mode is thesame as the generation mode. These experimental results
demonstrate the validity of the proposed circuit and control
strategy.

Generation mode

FFT of ia

V.

Motoring mode
50
0
-50
-100

Fig. 11. Harmonic analysis results.

suppressed using a buffer capacitor of only 50µF. Future workon this design will be focused on generating mode operation.
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Single-phase voltage [250V/div]0Single-phase current [10A/div]0300
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Fig. 12. Experiment results.
(The power flows from the single-phase grid to three-phase side)