IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011

805

Square-Wave Operation for a Single-Phase-PFC
Three-Phase Motor Drive System Without a Reactor
Jun-ichi Itoh and Nobuhiro Ohtani

Abstract—This paper proposes a square-wave control strategy
for a single-phase power factor correction with a new boost-up
converter which uses the leakage inductance of a motor insteadof a boost-up reactor. Since the power supply is connected to theneutral point of the motor, the current distortion in the power
supply occurs when the inverter outputs square waveforms. First,
this paper describes the characteristic of the proposed circuit andthe problems in the square-wave operation. Next, a current control
method for the square waveform is proposed to suppress thecurrent distortion. Finally, the validity of the proposed converter
and its control strategy are demonstrated by experimental results.
Index Terms—Boost-up converter, leakage inductance, neutral
point, square-wave operation.

I. I NTRODUCTIONR

ECENTLY, single-phase motors have often been usedin consumer electronics. However, in terms of size andweight, it is better to use a three-phase motor instead of a singlephase motor [1]. Single-phase input consumer electronics needa single- to three-phase converter to drive a three-phase motor.
The converter needs to achieve high efficiency and small size.
Furthermore, an input current is required to meet the harmonicstandard [2].
Fig. 1 shows a full-bridge pulsewidth modulation (PWM)
rectifier that is commonly applied in a single- to three-phaseconverter [1], [3], [4]. A PWM rectifier has high efficiency anda good solution for power factor correction (PFC); however, all
PFC circuits require a large boost-up reactor in the rectifier,and therefore, the cost is high. Another low-cost structure
single- to three-phase converter is composed by a diode-bridge
rectifier, a boost chopper circuit, and a three-phase inverter.
Although a diode rectifier has low cost, it cannot meet the input
current harmonic standard since the input current contains large
distortion [5]–[7]. In order to reduce the harmonic, a dc reactor
with a diode rectifier is used; however, the dc reactor cannot
suppress the harmonic current under a large output power. The
boost chopper works as a PFC converter [8], [9].

Manuscript received April 14, 2010; revised July 13, 2010 and August 30,
2010. Date of publication December 30, 2010; date of current version
March 18, 2011. Paper 2010-IDC-117, presented at the 2009 International
Conference on Electrical Machines and Systems, Tokyo, Japan, November
15–18 and approved for publication in the IEEE T RANSACTIONS ON I NDUS TRY A PPLICATIONS by the Industrial Drives Committee of the IEEE Industry
Applications Society.
J. Itoh is with Nagaoka University of Technology, Nagaoka 940-2188, Japan(e-mail: itoh@vos.nagaokaut.ac.jp).
N. Ohtani was with Nagaoka University of Technology, Nagaoka 940-2188,
Japan. He is now with TDK-Lambda Corporation, Ltd., Tokyo 103-8272, Japan(e-mail: ohtani@stn.nagaokaut.ac.jp).
Digital Object Identifier 10.1109/TIA.2010.2102736

Fig. 1. Conventional full-bridge circuit.

The authors have proposed a method that a leakage inductance of the motor is used instead of a boost-up reactor [9],[10]. Since it consists of a simpler circuit structure than theconventional circuit, the proposed circuit can achieve a smaller
size and lower cost application. The motor is controlled by the
proposed converter using PWM.
On the other hand, a square-wave operation is popularly usedin many applications such as high-speed motor drive, electricvehicle, and rail way system. The square-wave operation of theinverter can increase the voltage utilization and can achieve
higher efficiency than a PWM operation since the switchingfrequency of a square-wave operation is lower than the PWM
drive [11]. In the proposed circuit, when the square-wave operation is applied to the inverter control, the voltage of the neutral
point of the motor has fluctuation that contains three times ofthe output frequency. Since the power supply is connected to
the neutral point of the motor in the proposed circuit, the input
current contains distortion that results from the fluctuation of
the neutral point of the motor.
This paper proposes a square-wave operation strategy for the
proposed circuit, which uses the neutral point of a motor. The
objective of this paper is to suppress the input current distortion
under a square-wave operation. The input current distortion issuppressed by an automatic current regulation (ACR) and afeedforward compensation. First, this paper describes the characteristic of the proposed circuit and the principle operation.
Thus, when the output frequency is high, it is presented thatthe dc-link voltage is two times higher than the peak input
voltage. Next, this paper discusses the problem of the input
current distortion which is caused by the fluctuation of theneutral point of the motor under the square-wave operation. In
addition, a high power factor control for suppressing the input
current distortion with a square-wave operation is proposed.
Finally, the validity of the proposed circuit will be demonstrated
by experimental results.

0093-9994/$26.00 © 2010 IEEE

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011

Fig. 2. Proposed circuit using the neutral point motor.

Fig. 4. Equivalent circuit of the zero phase in the proposed circuit using theneutral point voltage.

the zero-phase current in the motor does not generate torquebecause the zero-phase flux denies each other. The control
for the input current of the proposed circuit is achieved by azero-phase component of the output voltage, and the control
for motor current is achieved by a positive phase at the sametime. The conduction loss in the rectifier side can be greatly
reduced because of using two IGBTs. However, note that the
motor loss will be increased subsequently since the output
current contains of the rectifier current during the zero-phasesequence.
Fig. 3. Equivalent circuit of the positive phase in the proposed circuit using
the neutral point of the motor.

II. R EACTOR -F REE PFC C ONVERTER
A. Circuit Configuration
Fig. 2 shows the proposed circuit that connects to the neutral
point of the motor. The proposed circuit consists of a threephase inverter, an electrolytic capacitor, and a switching leg using a series insulated-gate bipolar transistor (IGBT). The input
power supply is connected between the center of the leg andthe neutral point of the motor. The input reactor of the proposed
circuit is replaced with the zero-phase inductance, which is also
known as the leakage inductance of the motor [9], [10]. The
required leakage inductance for the control is varied according
to the type of the motors. In an induction motor, a minimumof 3% of the inductance is enough for the proposed control
method. On the other hand, in the case of a permanent-magnet
motor, a minimum of 10% of the synchronous reactance issufficient for the proposed control method. Therefore, the input
reactor is unnecessary in the proposed circuit. In addition, thenumber of switching elements can be decreased in comparison
to a conventional single-phase full-bridge PWM rectifier andinverter system because the inverter parts in the proposed circuit
can substitute as another leg in the rectifier. As a result, the gate
drive circuits or peripheral control units in the rectifier can be
reduced.
Fig. 3 shows the equivalent circuit of the positive phasesequence in the proposed circuit. In this case, the power supply
and the rectifier leg do not appear in the equivalent circuit
since it is in zero-phase components. This figure also showsthe equivalent circuit of the motor current control which issimilar to a conventional three-phase inverter. It is noted that

B. Series–Parallel CompensationPWM Operation: The proposed circuit is initially controlledwith a PWM drive and delivers sinusoidal output waveforms.
Then, a transition control is added to the controller to transformthe output voltage from sinusoidal wave to square wave while
operating at high output frequency. In PWM drive, the zerophase sequence occurs at the zero vector periods of the inverter
side. Fig. 4 shows the zero-phase sequence equivalent circuit.
The motor is equaled to a leakage inductance, and the inverter
can be considered as a single-leg topology, where this equivalent circuit is similar to a conventional single-phase full-bridge
circuit topology. The back electromotive force (EMF) does notappear in the zero-phase equivalent circuit but only the leakage
inductance occurs. It is noted that the EMF includes multiple
third-order harmonics; those harmonic components appear in
the zero-phase equivalent circuit.
The inverter output voltages vu , vv , and vw are expressed in
the following:⎧E⎨ vu = a 2dc sin ωt + vo
Edc
v = a 2 sin(ωt − 2π
(1)3 ) + vo⎩ v
vw = a E2dc sin(ωt − 4π
)
+
v
o
3
where a is the modulation index of the inverter phase voltage,
0 < a < 1, vo is the neutral point voltage, and ω is the inverter
output angler frequency.
Square-Wave Operation and DC-Link Voltage Analysis: A
square-wave operation for the three-phase inverter is applied
to reduce the switching loss of the inverter in comparison
to a PWM. During the square-wave operation, the switchingfrequency agrees with the output frequency. The output line

ITOH AND OHTANI: SQUARE-WAVE OPERATION FOR A PFC MOTOR DRIVE SYSTEM WITHOUT A REACTOR

807

Fig. 6. Control block diagrams of the current control.

Fig. 5.

Relations between each of the phase voltage and the load neutral point.

voltage becomes a 120◦ square waveform, and then, the fundamental voltage of the output is given by√
6
Edc
Vout =(2)π
where Vout is the output line voltage and Edc is the dc-link
voltage.
Fig. 5 shows the relations of the phase voltage and theneutral point voltage during the square-wave operation. Whenthe inverter is operated at the square wave, the neutral point of
the motor has a fluctuation that is plus or minus one-sixth of the
dc-link voltage. As a result, each of the phase voltage becomes
the square wave of ± one-sixth of the dc-link voltage.
In the proposed circuit, the neutral point of the motor isconnected to the power supply. That is, the voltage fluctuationof the neutral point disturbs the current control of the power
supply. Subsequently, the input current contains distortion thatis three times of the output frequency. When the output voltageof the inverter leg fluctuates with ± one-sixth of the dc-link
voltage, the rectifier leg has to output the sum of ± one-sixthof the dc-link voltage and peak voltage of the input power
supply. Therefore, in order to compensate the disturbance by
the square-wave operation, the dc-link voltage is constrained by√
1
Edc≥ Edc + 2Vin
2
6√
Edc ≥ 3 2Vin
(3)where Edc is the dc-link voltage and Vin is the power supply
voltage.
On the other hand, if the frequency of the fluctuation in theneutral point of the motor is higher than the input current control response, the voltage fluctuation can be neglected. Then,the dc-link voltage requires only two times of the power supply
voltage because the control of the rectifier is the same as thehalf-bridge PWM rectifier.
Fig. 6 shows a control block diagram of the current control
in order to discuss the condition of the required dc-link voltage.
A proportional–integral (PI) controller is used as a current
regulator, and the neutral point of the motor is considered as

Fig. 7. Relations between the input current THD and inverter output
frequency.

Fig. 8. Block diagram of the proposed circuit.

a voltage disturbance. When the influence of the disturbancevoltage can be disregarded for the input current, the dc-link
voltage may be twice of the peak voltage of the input voltage.
The transfer function from a disturbance voltage to the input
current is obtained by

3
Ti
1
Iin
(4)
=s
× 2 LTi×
Vdis
Kp2
s K + sTi + 1
pwhere Kp is the proportional gain, Ti is the integration time
constant of the PI regulator, L is the leakage inductance, and s
is the Laplace operator.
Fig. 7 shows the relations between the input current total harmonic distortion (THD) and the inverter output frequency. The
natural angular√frequency ωn is 4000 rad/s, and the damping
factor ζ is 1/ 2. It is noted that the disturbance frequency

808IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011

Fig. 9. Simulation result without the proposed control. (a) Simulation waveform. (b) Harmonic analysis results of the input current.

is three times of the inverter output frequency and the dclink voltage is set to twice of the peak voltage of the input
voltage. The symbol “” shows the theoretical curve calculatedby (4), and the symbol “” shows the current THD calculated
by a circuit simulator. When the inverter frequency is low,
THD increases in the simulation results because the disturbancevoltage cannot be neglected in the current controller. That is, thedc-link voltage is not enough to control the current. In order toovercome the problem, the dc-link voltage is required to haveat least two times or more than the input peak voltage. In thiscondition, the limit of the inverter output frequency is set to330 Hz. That is, before 330 Hz, the required dc-link voltage isthree times of the input peak voltage, and after that, the dclink voltage has to increase according to the inverter output
frequency. In this paper, the dc-link voltage is set to three times
higher than the input peak voltage with an output frequency at
70 Hz in the simulation and also tested experimentally with an
output frequency of 44 Hz.

that the control can distinguish between the PWM and squarewave modulation from the control of the “Over modulation
det.” The feedforward control sends zero signal to the rectifiercontrol while PWM is operating.
For the inverter side, the PWM control is slowly changed into
a square-wave control via the trapezoidal pulse modulation. The
transition control block shown in Fig. 8 is the control of Vq∗ axis
with regard to the output frequency. The Vq∗ axis will be linearlyextended into the overmodulation region where the amplitude
of output voltage reference is nonlinearly increasing, following
the modulation index. As a result, the sinusoidal wave of theoutput voltage will be turned into a square wave completely
when the Vq∗ axis has finished extending in the overmodulation
area.
The PI controller is designed according to (4). That is, thenatural angular frequency ω√n is set to 4000 rad/s, and thedamping factor ζ is set to 1/ 2.
IV. S IMULATION R ESULTS

III. P ROPOSED C ONTROL S TRATEGY
Fig. 8 shows the block diagram of the proposed circuit. Vd∗
and Vq∗ are the d−q-axes in the three-phase transformation,
respectively. Vu∗ , Vv∗ , and Vw∗ are the pulse patterns for inverter
side, and Vr∗ is the pulse pattern for the rectifier. The current
control of the power supply is the same as the conventional
PWM rectifier. It is noted that the leakage inductance is usedinstead of the boost reactor; however, the volume of the inductance decreases to one-third because the leakage inductance ofthe motor is connected in parallel in the zero-phase equivalentcircuit.
As discussed in the previous chapter, the neutral point voltage of the motor has a fluctuation of ±1/6Edc with three timesof the inverter output frequency in the square-wave operation.
In order to compensate for the voltage fluctuation, a feedforward control is applied to the ACR. The feedforward signal
is obtained from the sum of the inverter pulse patterns andadjusted in a reverse polarity of the actual fluctuation waveformat the neutral point of the motor. This reverse signal is thenadded with the estimated dc-link voltage and sent into therectifier control to cancel off the fluctuation waveform. NoteFig. 9 shows the simulation results during a square-wave
operation. The motor model is expressed in the EMF, theleakage inductance, and the armature resistance. The input
voltage is 50 V, the input frequency is 50 Hz, and the output
frequency is 70 Hz. From Fig. 9, it is confirmed that the input
current contains the third-harmonic components of the output
frequency. The THD of the input current is 56.5% in Fig. 9.
Fig. 10 shows that the distortion of the input current issuppressed by the proposed control. The THD of the input
current THD is 1.3%. In contrast to Fig. 10, the distortion of
the input current is suppressed drastically by the feedforward
compensation.
V. E XPERIMENTAL R ESULTS
Fig. 11 shows the experimental results where the inverter
uses the PWM operation mode. The input voltage, input current, line current, and u − v line-to-line voltage were examined.
The parameters of the induction motor used in the experimentare shown in Table I. The input voltage is 50 V and 50 Hz. In
Fig. 11, the output frequency of the positive phase is 44 Hz.
A sinusoidal input current waveform is obtained because theITOH AND OHTANI: SQUARE-WAVE OPERATION FOR A PFC MOTOR DRIVE SYSTEM WITHOUT A REACTOR

809

Fig. 10. Simulation result with the proposed control. (a) Simulation waveform. (b) Harmonic analysis results of the input current.

Fig. 11. Experimental results using the inverter in the PWM operation mode. (a) Operation waveform. (b) Harmonic analysis results of the input current.
TABLE IM OTOR PARAMETERS (FUJI: MLH6085M)

neutral point of the motor voltage is constant during the PWM
operation. The THD of the input current is 3.9%. The amplitudeof the line current is changed because the line current consistsof an input current of 50 Hz and a positive current of the motorof 44 Hz.
Fig. 12 shows the acceleration characteristics from the PWM
operation to square-wave operation. The PWM waveform is
gradually changed into a square-wave control that can be
confirmed by the u − v line voltage. The pulse mode moves
from PWM to the square mode without rush current. It is notedthat the fluctuation of the line current is generated due to thedifference between the input and output frequencies.
Fig. 13 shows the experimental results during a square-wave
operation. In Fig. 13, the harmonic distortion of the input
current is suppressed, and the dc-link voltage is kept constantthat can be confirmed by the u − v line voltage. In addition,
the input current is confirmed to contain the third-harmoniccomponents of the output frequency. The THD of the input
current is 29.1%. It is noted that the output current includes
ripple due to the square-wave operation.
Fig. 14 shows that the distortion of the input current issuppressed by the proposed control. The THD of the input
current THD is 6.1%. In comparison with Fig. 13, the distortionof the input current is suppressed to less than 1/20 times. In
addition, the THD of the input current is 23% reduced. The
input current harmonics of the proposed control method meetthe standard of IEC61000-3-2.
Overall, the experimental results confirmed the validity of the
proposed feedforward compensation control method.
VI. C ONCLUSION
A control strategy for a reactor-free converter has been proposed to apply in a square-wave operation with an adjustablespeed drive motor. The known problem is where the current
distortion in the power supply occurs when the inverter outputs
square waveforms. In order to overcome the problem, a feedforward control has been proposed to suppress the input current
distortion with a square-wave operation. The proposed control
method successfully suppresses the input current distortion to810

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011

Fig. 12. Acceleration characteristics. (a) Operation waveform from PWM transition span. (b) Operation waveform from span to transition span to squarewave span.

Fig. 13. Experimental results without the proposed control. (a) Operation waveform. (b) Harmonic analysis results of the input current.

Fig. 14. Experimental results with the proposed control. (a) Operation waveform. (b) Harmonic analysis results of the input current.

ITOH AND OHTANI: SQUARE-WAVE OPERATION FOR A PFC MOTOR DRIVE SYSTEM WITHOUT A REACTOR

1/20 than the ordinary control. In addition, the THD of the input
current is reduced by 23%.
In future works, the proposed converter and controller will
be applied and examined in a high-speed permanent-magnet
motor.

811[10] J. Itoh and S. Ishii, “Novel single-phase high power factor converterwith load neutral point applied to PM motor drive,” Trans. Inst. Elect.
Eng. Jpn., vol. 121-D, no. 2, pp. 219–224, 2001.
[11] K. Moriya, H. Nakai, Y. Inaguma, and S. Sasaki, “A DC/DC converter
using motor neutral point and its control method,” in Proc. Annu. Meeting
IEEJ, vol. 4, pp. 119–120, 2004. [in Japanese].

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Jun-ichi Itoh was born in Tokyo, Japan, in 1972.
He received the M.S. and Ph.D. degrees in electricaland electronic systems engineering from Nagaoka
University of Technology, Nagaoka, Japan, in 1996
and 2000, respectively.
From 1996 to 2004, he was with Fuji Electric
Corporate Research and Development Ltd., Tokyo.
Since 2004, he has been with Nagaoka Universityof Technology as an Associate Professor. His research interests are matrix converters, dc/dc converters, power factor correction techniques, and motor
drives.
Dr. Itoh is a member of the Institute of Electrical Engineers of Japan (IEEJ).
He was the recipient of the IEEJ Academic Promotion Award (IEEJ Technical Development Award) in 2007 and the Isao Takahashi Power Electronics
Award at the 2010 International Power Electronics Conference, Sapporo, fromthe IEEJ.

Nobuhiro Ohtani was born in Tokyo, Japan, in
1983. He received the B.S. and M.S. degrees inelectrical, electronics, and information engineeringfrom Nagaoka University of Technology, Nagaoka,
Japan, in 2008 and 2010, respectively.
Since 2010, he has been with TDK-Lambda Corporation, Ltd., Tokyo. His main research interests
include motor drives and new converter topologies.
Mr. Ohtani is a member of the Institute of Electrical Engineers of Japan.