IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 2, APRIL 2007
797
Control of Single-Phase-to-Three-Phase AC/DC/AC
PWM Converters for Induction Motor Drives
Dong-Choon Lee, Member, IEEE, and Young-Sin Kim
Abstract—This paper proposes a novel control scheme of singlephase-to-three-phase pulsewidth-modulation (PWM) converters
for low-power three-phase induction motor drives, where a single-phase half-bridge PWM rectifier and a two-leg inverter are
used. With this converter topology, the number of switching devices is reduced to six from ten in the case of full-bridge rectifier
and three-leg inverter systems. In addition, the source voltage sensor is eliminated with a state observer, which controls the deviation
between the model current and the system current to be zero.
A simple scalar voltage modulation method is used for a two-leg
inverter, and a new technique to eliminate the effect of the dc-link
voltage ripple on the inverter output current is proposed. Although
the converter topology itself is of lower cost than the conventional
one, it retains the same functions such as sinusoidal input current,
unity power factor, dc-link voltage control, bidirectional power
flow, and variable-voltage and variable-frequency output voltage.
The experimental results for the V /f control of 3-hp induction
motor drives controlled by a digital signal processor TMS320C31
chip have verified the effectiveness of the proposed scheme.
Index Terms—AC/DC/AC pulsewidth-modulation (PWM) converter, dc-link voltage ripple, induction motor, source voltage
estimation, two-leg inverter.
I. I NTRODUCTION
I
N VIEW of the machine efficiency, power factor, and torque
ripples, a three-phase induction motor is preferable to a
single-phase induction motor. Therefore, it is desirable to replace the single-phase induction motor drives by the threephase induction motor drives in residential appliances, farming,
and low-power industrial applications [1].
However, where only a single-phase utility is available, a
single-phase-to-three-phase power converter system is required
to feed the three-phase induction motor drives. Conventionally, a full-bridge diode rectifier plus three-leg pulsewidthmodulation (PWM) inverter has been used. However, the diode
rectifier produces harmonic currents to flow into the supply and
has no capability of regenerative operation.
A few recent papers dealt with the half-bridge PWM rectifier
and the two-leg three-phase PWM inverter. However, most of
Manuscript received January 25, 2006; revised October 27, 2006. Abstract
published on the Internet January 14, 2007. This work was supported by
the Korea Electrical Engineering and Science Research Institute under Grant
R2005-B-109, which is funded by the Ministry of Commerce, Industry and
Energy, Korea. This paper was presented in part at the International Conference
on Power Electronics and Intelligent Control for Energy Conservation, Warsaw,
Poland, October 16–19, 2005.
D.-C. Lee is with the Department of Electrical Engineering, Yeungnam
University, Gyeongsan 712-749, Korea (e-mail: dclee@yu.ac.kr).
Y.-S. Kim is with LG Philips LCD Company, Kumi 730-726, Korea (e-mail:
antonio41@hanmail.net).
Digital Object Identifier 10.1109/TIE.2007.891780
Fig. 1. Single-phase-to-three-phase ac/dc/ac converter with a dc boost
chopper.
them investigated its modulation schemes and output performance [2]–[8], and its control scheme has not been very much
studied [9]–[11]. Moreover, the sensor elimination technique
for this kind of converter is very rare since it usually requires a
high-performance digital signal processor (DSP) [12]–[14].
In this paper, a low-cost power converter combined with a
half-bridge PWM rectifier and a two-leg PWM inverter for
the three-phase induction motor drives are studied, and an
algorithm of the source voltage sensor elimination technique
is presented, which makes the system cheaper and robust to
measurement noises. Also, a new compensation scheme of the
dc-link voltage ripple effect on the inverter output voltage is
proposed. In addition, a balancing control of the neutral voltage
in the dc link is applied for the symmetrical output voltage
of the inverter. The proposed algorithm has been implemented
for the V /f control of the three-phase induction motor drives
controlled by a DSP TMS320C31.
II. C ONVENTIONAL S INGLE -P HASE - TO -T HREE -P HASE
AC/DC/AC C ONVERTERS
The simplest circuit of an ac/dc/ac converter topology
converting from a single-phase supply to a three-phase
variable-voltage and variable-frequency (VVVF) system is a
single-phase full-bridge diode rectifier and a three-leg PWM
inverter system. This circuit is simple and relatively of low
cost. However, it has significant disadvantages such as nonreversible power flow and source current distortion with poor
power factor [1].
Fig. 1 shows the power circuit structure with a dc boost
chopper intervening between the diode rectifier and the threeleg PWM inverter. With the dc chopper, the source current
can be controlled to be sinusoidal, with unity power factor.
However, the power flow is still unidirectional, not reversible [2].
0278-0046/$25.00 © 2007 IEEE
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 2, APRIL 2007
When is > 0, for the upper part of the rectifier, the current
and voltage are given by
ic1 = idc1 − il
Fig. 2. Single-phase-to-three-phase ac/dc/ac PWM converter.
idc1 = Sa ∗ is
1
vdc1 =
ic1 dt
C
1
=
(idc1 − il )dt
C
(1)
(2)
(3)
where Sa is a switching state, i.e., 1 or 0. For the lower part, the
similar equations are obtained as follows:
ic2 = − idc2 − il
(4)
idc2 = Sb ∗ is = (1 − Sa ) ∗ is
1
1
vdc2 =
ic2 dt =
(−idc2 − il )dt.
C
C
Fig. 3. Single-phase half-bridge plus two-leg three-phase ac/dc/ac PWM
converter topology.
Fig. 2 shows a single-phase full-bridge PWM rectifier
with a three-phase full-bridge PWM inverter system. This
converter gives excellent performance such as sinusoidal control of source current, unity power-factor control of the source
side, constant dc voltage control, and bidirectional power flow.
However, it requires ten active switching devices, so that it is
more expensive than other circuits [2].
III. S INGLE -P HASE H ALF -B RIDGE PWM R ECTIFIERS
Fig. 3 shows a single-phase half-bridge PWM rectifier and a
two-leg three-phase PWM inverter. Compared with the circuit
of Fig. 2, the number of the switching devices is reduced to
six from ten, whereas it retains the function of the topology in
Fig. 2. However, it also has some disadvantages such as higher
output current distortion and doubly high dc-link voltage requirement [3]. The circuit topology shown in Fig. 3 is not new.
However, it has usually been applied to two-phase induction
motor drives, where one output is fed to the main winding and
the other output is for the auxiliary winding [15].
In this paper, the application of this converter to the V /f
control of the three-phase induction motor drives is studied. In
addition, the source voltage elimination technique is proposed
to reduce the system cost and for better reliability to the sensing
noise.
A. Half-Bridge PWM Rectifier
There are two operating modes in half-bridge PWM rectifiers, namely: 1) charging mode and 2) discharging mode, as
shown in Fig. 4 [7], where vs and is are the source voltage and
current, respectively; vdc1 and vdc2 are the capacitor voltages in
the dc side; and vr is the rectifier input voltage.
(5)
(6)
For is < 0, the same equations can be applied to the relation of
current and voltage.
Combining (1)–(6), the input voltage of the rectifier and the
dc-link voltage are expressed as
vr = Sa ∗ vdc1 − Sb ∗ vdc2
vdc = vdc1 + vdc2 .
(7)
(8)
B. Source Voltage Estimation
In order to control the source current at unity power factor,
a source voltage sensor is normally required. Unlike the input
current sensor necessary for system protection, the voltage
sensor may be eliminated without loss of safety. By controlling
the deviation between the measured current and the model
current to be zero, the source voltage can be estimated, and
then, the source voltage sensor may be eliminated. A block
diagram of the source voltage estimation is shown in Fig. 5
[12]–[14].
The voltage equation at the source can be expressed as
follows:
vs = Rs is + Ls
d
is + vr .
dt
(9)
Expressing (9) in a discrete domain
vs (n−1) = Rs is (n−1)+
Ls
{is (n)−is (n−1)}+vr (n−1).
Ts
(10)
The source voltage in (10) is expressed as
vs (n − 1) = V cos θ
(11)
where V and θ are the magnitude and phase angle of the source
voltage, respectively. The phase angle at the nth sampling
instant is given by
θ(n) = (n − 1)ωTs + θ0
(12)
LEE AND KIM: CONTROL OF SINGLE-PHASE-TO-THREE-PHASE AC/DC/AC PWM CONVERTERS
Fig. 4.
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Operating modes of the circuit. (a) and (b) Charging. (c) and (d) Discharging.
Similarly to (13), the model current is given by
iM (n) = is (n − 1) +
Ts
{VM cos θM − RM is (n − 1)
LM
− vr (n − 1)}
(15)
where LM and RM are the model parameters.
It is assumed that the inductance and resistance in both
the real system and the model are the same, which is usually
reasonable in the rectifier system. Then, subtracting (15) from
(13) gives
Fig. 5.
∆is (n) = is (n) − iM (n)
Block diagram for source voltage estimation.
where θ0 is an initial angle at the (n − 1)th sampling. From
(10), the source current in a discrete domain can be written as
is (n) = is (n−1)+
Ts
{vs (n−1)−Rs is (n−1)−vr (n−1)} .
Ls
(13)
On the other hand, the estimated source voltage in the
rectifier model from (11) can be expressed as
vM (n − 1) = VM cos θM
(14)
where VM and θM are the magnitude and phase angle of the
source voltage at the (n − 1)th sampling point, and the subscript M means the variable or parameter in the rectifier model.
Ts
∼
{∆V cos θM − ∆θ · V sin θM }.
=
Ls
(16)
It should be noted that the deviation of ∆is is caused by the
estimation error of the source voltage, i.e., the magnitude error
and the phase angle error. Applying Fourier series to (16)
Ls 1
∆V =
Ts π
2π
∆is cos θM dθM
(17)
0
Ls 1
∆θ = −
Ts V π
2π
∆is sin θM dθM .
0
(18)
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 2, APRIL 2007
Fig. 6. Control block diagram for half-bridge PWM rectifier.
Fig. 8.
Voltage modulation in triangular comparison method.
TABLE I
SWITCHING STATES AND OUTPUT VOLTAGES
Fig. 7. Two-leg three-phase PWM inverter.
From (17) and (18), VM and θM are estimated as
VM (n) = VM (n − 1) + KE ∆is (n) cos θM (n − 1) (19)
θM (n) = θM (n − 1) + ωTs
− Kθ ∆is (n) sin θM (n − 1)
(20)
where KE (= 2.36) and Kθ (= 0.02) are gains.
C. Control of the System
Fig. 6 shows the control block diagram for a half-bridge
PWM rectifier. For controlling the source current and the dclink voltage, the proportional–integral regulators are employed.
For a balancing control of the neutral voltage of the dc link, the
difference of vdc1 and vdc2 is fed back to the current controller
through the proportional gain of Kff (= 0.5) [7]. For the dclink voltage feedback, a cutoff frequency of the low-pass filter
has been chosen as 50 Hz, and for the balanced control loop,
it has been chosen as 0.01 Hz. Also, to avoid using the source
voltage sensor, the source voltage is estimated, as discussed in
Section III-B.
IV. PWM IN T WO -L EG I NVERTERS
Fig. 7 shows a two-leg inverter, which gives a three-phase
VVVF output voltage. For the induction motor drive, the threephase voltage references are given in a balanced set as
∗
vas
= Vm cos ωt
2π
∗
vbs = Vm cos ωt −
3
2π
∗
= Vm cos ωt +
.
vcs
3
(21)
(22)
(23)
Fig. 9.
Switching states of two legs.
There are two kinds of voltage modulation schemes for the
two-leg three-phase PWM inverter [4], [11]. One is named
a vector modulation using a space voltage vector concept.
The other is called a scalar modulation, which uses the phase
voltages in calculating the switching time. Here, the scalar modulation scheme is adopted since it is simple and straightforward.
Since the two phases of the induction motor are connected
to the inverter legs and the third phase is connected to the
neutral point of the dc link, the line-to-line voltage can be used
for the PWM instead of the phase voltage. Let the c-phase be
connected to the neutral point. Then, from (21)–(23), the two
line-to-line voltage references are given by
√
π
3Vm cos ωt −
6
√
π
.
= 3Vm cos ωt −
2
∗
∗
∗
= vas
− vcs
=
vac
(24)
∗
∗
∗
vbc
= vbs
− vcs
(25)
√
The magnitude of these two voltages is 3 times that of the
phase voltage and displaced by π/3 relative to each other. By
LEE AND KIM: CONTROL OF SINGLE-PHASE-TO-THREE-PHASE AC/DC/AC PWM CONVERTERS
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Fig. 10. Configuration of experimental system.
Fig. 11. Source voltage estimation.
using the proportionality of the triangle, as shown in Fig. 8, the
switching time can be calculated as
v∗
Ts
+ ac Ts
T1 =
2
vdc
v∗
Ts
+ bc Ts .
T2 =
2
vdc
(26)
(27)
When vdc1 and vdc2 are exactly equal to each other, the time
duration of T1 and T2 in (26) and (27) gives precise modulated
voltages. However, due to the dc-link voltage ripples and the
deadtime effect, the output currents as well as the output voltages are unbalanced and distorted. The deterioration of these
waveforms can be eliminated by compensating for the dc-link
voltage ripples and the dead-time effect.
From (26) and (27), the average voltages over one switching
period are calculated as
vdc v̄ac = T1 vdc − Ts
(28)
/Ts
2
vdc /Ts .
v̄bc = T2 vdc − Ts
(29)
2
Fig. 12. Unity power-factor control of source side. (a) Positive power flow.
(b) Negative power flow.
Although the average value of vdc1 is the same as that of vdc2 ,
their instantaneous values are not the same due to the ac ripple
components. These ac ripple components cause the voltage
modulation error in (26) and (27). Thus, the instantaneous
difference of the two dc voltages should be compensated.
According to the switching state, the output voltages of the
inverter are given in Table I. For example, when the switching
state is given, as shown in Fig. 9, the output voltages in case of
the unequal vdc1 and vdc2 are modified from (28) and (29) as
v̄ac
= {(Ts − T1 )(−vdc2 ) + (T1 − T2 )vdc1 + T2 vdc1 } /Ts
= {T1 (vdc1 + vdc2 ) − Ts vdc2 } /Ts
= (T1 vdc − Ts vdc2 )/Ts
(30)
v̄bc = {(Ts − T1 )(−vdc2 ) + (T1 − T2 )(−vdc2 ) + T2 vdc1 } /Ts
= {T2 (vdc1 + vdc2 ) − Ts vdc2 } /Ts
= (T2 vdc − Ts vdc2 )/Ts .
(31)
For precise modulation, a voltage component to be compensated can be derived from the difference between the real
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 2, APRIL 2007
Fig. 13. DC-link voltage control. (a) vdc . (b) vdc1 and vdc2 .
Fig. 15. Induction motor currents at half-load condition (60 Hz) with compensation for (a) none, (b) dc-link ripple voltage, (c) dead-time effect, and
(d) both dc-link ripple voltage and dead-time effect.
On the other hand, the deadtime is required to prevent the
shoot-through of the inverter switching leg. This dead time
should be compensated for eliminating the voltage distortion.
The dead-time effect will be considered in Section V.
V. E XPERIMENTAL R ESULTS
Fig. 14. Induction motor currents at half-load condition (10 Hz) with compensation for (a) none, (b) dc-link ripple voltage, (c) dead-time effect, and
(d) both dc-link ripple voltage and dead-time effect.
output voltage and its reference as
− v̄ac
vcomp = v̄ac
= v̄bc − v̄bc
vdc1 − vdc2
.
=
2
(32)
Including this term in the calculation of the switching time
T1 =
v ∗ − vcomp
Ts
+ ac
Ts
2
vdc
(33)
T2 =
v ∗ − vcomp
Ts
+ bc
Ts .
2
vdc
(34)
Fig. 10 shows the configuration of the experimental setup. It
is a single-phase, 110-V, 60-Hz source voltage, and the boost inductance and its resistance are 2 mH and 0.06 Ω, respectively. In
addition, the capacitance of each dc-link capacitor is 3300 µF,
which is connected in series across the dc bus bar. The switching frequency of the insulated gate bipolar transistor devices is
5 kHz, the sampling period of the current control loop is 100 µs,
and the dc-link voltage is controlled to be 540 V for the ease of
experiment. The deadtime of the inverter is 2.7 µs, where it is
compensated by using the method [16]. The three-phase, 220-V,
four-pole, 3-hp induction motor is operated by V /f constant
control mode. For applying the load to the induction motor,
the separately excited dc motor coupled is operated in torque
control mode. The main controller is a DSP TMS320C31.
Fig. 11 shows the estimated source voltage waveform. With
the proposed estimation strategy, the source voltage is well
performed, so that the source voltage sensor can be eliminated.
Fig. 12 shows the source voltage and current waveforms in
steady state. The source current is controlled to be sinusoidal,
with unity power factor kept for bidirectional power flow operation. Fig. 13 shows the dc-link voltages of vdc , vdc1 , and vdc2 .
LEE AND KIM: CONTROL OF SINGLE-PHASE-TO-THREE-PHASE AC/DC/AC PWM CONVERTERS
803
It should be noted that the current sensors are required for
the deadtime effect compensation. However, the current sensors
are not usually used for the V /f control of the induction motor
drives, whereas they are used for the high-performance vector
control. Thus, it is up to the users whether the current sensors
are employed or not for the deadtime effect compensation.
VI. C ONCLUSION
In this paper, an integrative control algorithm for a singlephase half-bridge PWM rectifier and a two-leg PWM inverter
for three-phase induction motor drives has been studied. Here,
adverse influences of a dc-link voltage ripple and the deadtime
of the inverter switching legs on the inverter output current
have been investigated, and a solution was proposed, which
resulted in a balanced set of a three-phase output current.
Also, an algorithm to eliminate the source voltage sensor in
the half-bridge PWM rectifier was studied, which proved that
the estimated source voltage coincides well with the measured
voltage. In addition, a balancing control of the neutral voltage
in the dc link was applied for the symmetrical output voltage
of the inverter. The validity of the proposed algorithm has
been verified by experimental results. The proposed digital
control algorithm for the given circuit topology can be applied
to the residential appliance, farming, and low-power industrial
applications with a low-cost DSP chip such as TMS320LF2407.
R EFERENCES
Fig. 16. Transient response of induction motor currents for load variation.
(a) Load torque. (b) Induction motor currents. (c) DC-link voltage. (d) Source
current.
vdc coincides with its reference value of 540 V with low ripple
components. With the balancing control, vdc1 and vdc2 are well
balanced.
Fig. 14 shows the induction motor currents at half load and
at 10-Hz operation. Without any compensation in Fig. 14(a),
the motor current is much distorted. In Fig. 14(b) and (c),
with the compensation of either the dc-link ripple component
or the dead-time effect, it is shown that the distortion of the
waveforms still exists. With the compensation for these two
effects in Fig. 14(d), the waveform becomes a balanced set of
sinusoidal currents. Fig. 15 shows the same results as in Fig. 14
except in operating at 60 Hz. Since the output voltage at high
speeds is larger than that at low speeds, the degree of distortion
without proper compensation is less than that at low speeds.
However, there still exist some distortion and unbalance. With
compensation, the set of the three-phase current has been made
sinusoidal and balanced.
Fig. 16 shows the transient response of the three-phase motor
currents [Fig. 16(b)], dc-link voltage [Fig. 16(c)], and source
current [Fig. 16(d)] at impact loading of 12 N · m [Fig. 16(a)],
which is applied by the torque control of the dc motor coupled.
Due to the compensation, the motor currents are well balanced
and sinusoidal in transient state, and the source current is
controlled well, too.
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Dong-Choon Lee (S’90–M’95) received the B.S.,
M.S., and Ph.D. degrees in electrical engineering
from Seoul National University, Seoul, Korea, in
1985, 1987, and 1993, respectively.
He was a Research Engineer at Daewoo Heavy
Industry from 1987 to 1988. He was also with the
Research Institute of Science Engineering, Seoul
National University, under a Postdoctoral Fellowship
for one year. Since 1994, he has been a Faculty
Member in the Department of Electrical Engineering, Yeungnam University, Gyeongsan, Korea, where
he is currently a Professor. As a Visiting Scholar, he was with the Power Quality
Laboratory, Texas A&M University, College Station, in 1998, the Electrical
Drive Center, University of Nottingham, Nottingham, U.K., in 2001, and the
Wisconsin Electric Machines and Power Electronics Consortium, University of
Wisconsin, Madison, in 2004. His research interests include ac machine drives,
control of power converters, wind power generation systems, and power quality.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 2, APRIL 2007
Young-Sin Kim was born in Korea in 1978. He
received the B.S. and M.S. degrees in electrical
engineering from Yeungnam University, Gyeongsan,
Korea, in 2004 and 2006, respectively.
He is currently a Research Engineer at LG Philips
LCD Company, Kumi, Korea. His research areas are
high-voltage power supplies and control of power
electronics circuits.