Square Wave Operation for a Single-phase PFC
Three-phase Motor Drive System without aReactorJun-ichi Itoh*, Nobuhiro Ohtani** Electrical and Electronic Engineering, Nagaoka University of technology

1603-1 Kamitomioka-cho Nagaoka city Niigata, Japan
Abstract-- This paper proposes a square wave control
strategy for a new boost-up converter which uses theleakage inductance of a motor instead of a boost up reactor.
Since the power supply is connected to the neutral 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 and the problems in the square wave
operation. Next, a current control method for the square
waveform is proposed to suppress the current distortion.
Finally, the validity of the proposed converter and its
control strategy are demonstrated by experimental results.
Index Terms-- Boost-up converter Leakage inductance,
Square wave operation, Neutral point

I. INTRODUCTION
Recently, single-phase motors are often to use in
consumer electronics. However, in order to reduce thesize and the weight, it is required to use a three-phasemotor instead of a single-phase motor [1]. For singlephase input consumer electronics, it needs a single-phaseto three-phase converter to drive a three-phase motor.
This system requires a high efficiency and small size
converter. Furthermore, the input current is required tomeet the harmonic standard [2].
Figure 1 shows a conventional circuit which iscomposed by a diode-bridge rectifier, a boost chopper
circuit and a three-phase inverter. Although a dioderectifier is low cost, it can not meet the input current
harmonic standard since the input current involves large
distortion [3-5]. A DC reactor with a diode rectifier isused so the input current can meet the harmonics
standard; however the DC reactor can not suppress the
harmonics current under a large output power. The boost
chopper works as a power factor correction (PFC)
converter [6-7]. In the view of the efficiency, a fullbridge or half bridge pulse width modulation (PWM)
rectifier is one of good solution for PFC. However, all
PFC converters require a large boost up reactor andconsequently, it needs higher cost and larger size.
The authors have been proposed that a leakage
inductance of the motor is used instead of boost-up
reactor [7-8]. Since it consists of a simple circuit structure
than the conventional circuit, the proposed circuit canachieve a smaller size and lower cost application. The
motor is controlled by the proposed converter using
PWM.
On the other hands, a square wave operation is used

Motor
u
v
w

Fig. 1. Conventional circuit with the diode-bridge rectifier and boost
chopper circuit.

for many applications such as high speed motor drive,electric vehicle, rail way system. The square wave
operation of the inverter can increase the voltage
utilization and can achieve higher efficiency than a PWM
operation since the switching frequency of a square wave
operation is lower than that of PWM drive [9]. In the
proposed circuit, when the square wave operation isapplied to the inverter control, the voltage of the neutral
point of the motor has fluctuation of three times of theoutput frequency. Since the power supply is connected to
the neutral point of the motor, the input current distortion
occurs 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 is suppressed by auto current
regulation (ACR) and feed forward compensation. First,
this paper describes the characteristic of the proposed
circuit and the principle operation. So, when the output
frequency is high, it is presented that the DC link voltage
is two times higher than the peak input voltage. Next, thispaper discusses the problem of the input current
distortion which is caused by the fluctuation of theneutral point of the motor under outputs square wave
operation. In addition, a high power factor control forsuppressing the input current distortion with a squarewave operation is proposed. Finally, the proposed circuit
control strategy is demonstrated by experimental results.

II. REACTOR FREE PFC CONVERTER
A. Circuit configuration
Figure 2 shows the proposed circuit using the neutral
point of the motor. The proposed circuit consists of athree phase inverter, a electrolytic capacitor and aswitching leg using series IGBT. The input power supply
is connected between the center of the leg and the neutral
point of the motor. The input reactor of the proposed
circuit is substituted with the zero phase inductancewhich is also known as the leakage inductance of the
motor [7-8]. Therefore the input reactor is unnecessary in
the proposed circuit. In addition, the number of theswitching elements can be decreased in comparison to aconventional single phase full-bridge PWM rectifier andinverter system because the inverter parts in the proposed
circuit is substituted for another leg in the rectifier. As aresult, the parts in gate drive circuits or peripheral control
units are reduced.
The input current control of the proposed circuit isachieved by a zero phase component of the output voltage
and the motor current control is achieved by a positive
phase at the same time.
B. Positive phase equivalent circuit
Figure 3 shows the equivalent circuit of the positive
phase sequence in the proposed circuit. In this case, thepower supply and the rectifier leg do not appear in theequivalent circuit since it is in zero phase components. So,
the equivalent circuit of motor current control is similar
to a conventional three-phase inverter. It is noted that thezero phase current in the motor does not generate torquebecause the zero phase flux denies with each other.
A square wave operation for the three-phase inverter isapplied to reduce the switching loss of the inverter incomparison to a PWM inverter. During the square wave
operation, the switching frequency agrees with the output
frequency. The output line voltage becomes a 120 degreesquare waveform, then, the fundamental voltage of theoutput is given by (1).

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

Fig. 3. Equivalent circuit of the positive phase in the proposed circuit
using the neutral point of the motor.

Leakageinductance6
Vout =E ............................................................ (1)π dc

where Vout is the output line voltage, Edc is the DC link
voltage.
C. Zero phase equivalent circuit
Figure 4 shows the equivalent circuit of the zero phasesequence in the proposed circuit. The back electromotive
force (EMF) does not appear in the zero phase equivalentcircuit but only the leakage inductance occurs. It is notedthat the EMF includes of multiple third order harmonics,
those harmonics components appear in the zero phaseequivalent circuit. On the other hands, the inverter legs
become single leg which will switch at zero-vector output
ratio.
Figure 5 shows the relations of the phase voltage andthe neutral point voltage during the square wave
operation. When the inverter is operated at the squarewave, the neutral point of the motor has a fluctuation thatis plus or minus one of sixth of the DC link voltage. As a

Fig. 4. Equivalent circuit of the zero phase in the proposed circuit using
the neutral point of the motor.

result, each of the phase voltage becomes the squarewave of ±1/6 of the DC-link voltage.
In the proposed circuit, the neutral point of the motor
is connected to the power supply. That is, the voltage
fluctuation of the neutral point disturbs the current
control of the power supply. Subsequently, the input
current has the distortion three times of the output
frequency. When the output voltage of the inverter leg
fluctuates with ±1/6 of the DC-link voltage, the rectifier
leg has to output the sum of ±1/6 of the DC-link voltage
and peak voltage of the input power supply. Therefore, inorder to compensate the disturbance by the square wave

operation, the DC link voltage is constrained by (2).
E dc 1≥ E dc + 2Vin
2
6

Edc/2

U-phasevoltage-Edc/2

Edc ≥ 3 2Vin ................................................................. (2)where Edc is the DC link voltage, Vin is the power
supply voltage.
On the other hands, if the frequency of the fluctuationin the neutral point of the motor is much higher than the
input current control response, the voltage fluctuation canbe neglected. Then, the DC link voltage requires only twotimes of the power supply voltage because the control of
the rectifier is the same as the half-bridge PWM rectifier.
Figure 6 shows a control block diagram of the current
control in order to discuss the condition of the required
DC link voltage. A proportion-integration (PI) controller
is used as a current regulator and the neutral point of the
motor is considered as a voltage disturbance. When theinfluence of the disturbance voltage can be disregard forthe input current, the DC link voltage may be twice of thepeak voltage of the input voltage. The transfer function
from a disturbance voltage to the input current is obtainedby (3).

-Edc/2Edc/2W-phasevoltage-Edc/2

Load neutral Edc/6
voltage -Edc/6
0°

Kp

Figure 8 shows a block diagram of the proposed circuit.
The current control of the power supply is the same as aconventional PWM rectifier. It is noted that the leakage
inductance is used instead of the boost reactor; however,the leakage inductance decreases to 1/3 of the leakage
inductance of the motor since the leakage inductance isconnected in parallel in the zero-phase equivalent circuit.

240°

360°

480°

1 + sTi
sTi

Fig. 6. Control block diagrams of the current control.
140
120

Circuit simulation

THD [%]

100
80
60
40

Theoritical results

20
0

1

100
1000
Inverter output frequency[Hz]

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

0

V/f
conv

ω*

Transition
control

1/s

Vq*

dq
↓
uvw

θ*

Over
Modulation det.

Edc*
Edc

+
-

Vu*

*
+ Vv
V*
+ w
Carrier
+

×

×

+
+

1/Vin

VinSinIII. PROPOSED CONTROL STRATEGY

120°

Fig. 5. Relations between each of the phase voltage and the load
neutral point voltage.

I in
T
1
3
=s i ××LT
Vdis
2 ....................... (3)K p s 2 i + sT + 1
iKp

where Kp is the proportional gain, Ti is the integration
time constant of the PI regulator, L is the leakage
inductance, and s is Laplace operator.
Figure 7 shows the relations between the input current
total harmonic distortion (THD) and the inverter output
frequency. Where the natural angular frequency ωn is
4000rad/s and the damping factor ζ is 1 2 . It is notedthat the disturbance frequency is three times of theinverter output frequency and the DC link voltage is set
to twice of the peak voltage of the input voltage. Symbol‘▲’ shows the theoretical curve calculated by (3), symbol‘■’ shows the current THD calculated by a circuit
simulator. When the inverter frequency is low, THD
increases in the simulation results because thedisturbance voltage can not be neglect in the current
controller. That is, the DC link voltage is not enough tocontrol the current. In order to overcome the problem, theDC link voltage is required to have at least two times ormore than the input peak voltage. In this condition, thelimit of the inverter output frequency is set to 330Hz.
That is, before 330Hz, the required DC link voltage istwice of the input peak voltage and after that, the DC link
voltage has to increases according to the inverter output
frequency.

Edc/2

V-phasevoltage

Iin*

+

×

AVR
－

±1/6

+
ACR +

+
－

Iin
Fig. 8. Block diagram of the proposed circuit.

Vr *(a)Simulation waveforms(a)Simulation waveforms

Fundamental frequency(50 [Hz])

fout=70[Hz]100%250Hz/div

10%
1%
0.1%
0.01%
0.001%(b)Harmonics analysis results of the input current

2000
1000
1500
Frequency[Hz](b)Harmonics analysis results of the input current

Fig. 9. Simulation result without proposed control

Fig. 10. Simulation result with proposed control

As discussed in previous chapter, the neutral point
voltage of the motor has fluctuation of ±1/6Edc with threetimes of the inverter output frequency in the square wave
operation. In order to compensate the voltage fluctuation,a feed forward control is applied to the ACR. The voltage
fluctuation is estimated by the DC link voltage and pulse
pattern of the inverter. ‘Over modulation det’ finds thesquare wave operation mode by using modulation index.
For the inverter side, the PWM control is slowly
changed into a square wave control via the trapezoidal
pulse modulation. When the inverter is in PWM
operation, the output voltage is linearly increasing.
However, the output voltage is nonlinearly increasing at
the over-modulation area. The transition control in
Figure.8 is a proportional compensation to the amplitudeof the output voltage command.
IV. SIMULATION RESULTS
Figure 9 shows the simulation results during a squarewave operation. The motor model is expressed in the
EMF, the leakage inductance and the armature resistance.
The input voltage is 50V, the input frequency is 50Hz

0500

and the the output frequency is 70Hz. From Fig. 9, it isconfirmed that the input current contains the 3rd
harmonic components of the output frequency. The total
harmonic distortion (THD) of the input current is 56.5%
in Fig. 9.
Fig. 10 shows that the distortion of the input current issuppressed by proposed control. The THD of the input
current THD is 1.3%. In contrast to the Fig. 10, thedistortion of the input current is suppressed drastically by
the feed forward compensation.
V. EXPERIMENTAL RESULTS
Figure 11 shows experimental results using theinverter in PWM operation mode. The input voltage,
input current, line current, and u-v line-to-line voltage
were examined. The parameter of the induction motorthat used in experiment is 750W, 200V and 50Hz. The
input voltage is 50V and 50Hz. In Fig.11, the output
frequency of the positive phase is 44Hz. A sinusoidal
input current waveform is obtained because the neutral
point of the motor voltage is constant during PWM
operation. The THD of the input current is 3.9%. The

amplitude of the line current is changed because the line
current consists of the input current of 50Hz and thepositive current of the motor of 44Hz.
Figure 12 shows the acceleration characteristics fromPWM 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 noted that fluctuation of theline current is generated due to the difference between the
input frequency and the output frequency.
Figure 13 shows the experimental results during asquare wave operation. In Fig. 13, the harmonic
distortion of the input current is suppressed and the DC
link voltage is kept constant that can be confirmed by the
u-v line voltage. In addition, the input current isconfirmed to contain the 3rd harmonic components of theoutput frequency. The THD of the input current is 29.1%.
It is noted that the output current includes ripple due tothe square wave operation.
Figure 14 shows that the distortion of the input current
is suppressed by proposed control. The THD of the input
current THD is 6.1%. In comparison with Fig. 13, thedistortion of 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 meets the standard of
IEC61000-3-2.
Overall, the experimental results confirmed thevalidity of the proposed feed forward compensation
control method.
VI. CONCLUSIONS

Input Voltage

0100V/div
Input current
10A/div

0Line current

0

5A/div
u-v line voltage
250V/div

0

10ms/div(a) Operation waveform

100%
250Hz/div

10dB/div

10%
1%
0.1%
Fundamental frequency(50 [Hz])

01000
Frequency[Hz]2000
fout = 44[Hz](b) Harmonics analysis results of the input current

The control strategy for the reactor free converter has
proposed to achieve a square wave operation in an Fig. 11 Experimental results using the inverter in PWM operation mode.

(a) Operation waveform from PWM span to Transition span.

(b) Operation waveform from Transition span to Square wave span.

Fig. 12 Acceleration characteristics.

Input Voltage

0100V/div
Input current
10A/div

0Line current

0

5A/div
u-v line voltage
250V/div

0

10ms/div(a)Operation waveform.

100%(a)Operation waveform.

10dB/div(3×fout [Hz])100%(3×fout×(2n+1):(n=1,2,3…)[Hz])10%10dB/div

10%

1%

1%

0.1%

0.1%
Fundamental frequency(50 [Hz])0

Fundamental frequency(50 [Hz])

250Hz/div

1000
Frequency[Hz]2000
fout = 70[Hz]0(b)Harmonics analysis results of the input current.

Fig. 14. Experiment results with proposed control.

[4]

[5]

[6]

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Induction Motor Drives” IEEE Transactions on Industrial
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2000
fout = 70[Hz](b)Harmonics analysis results of the input current.

Fig. 13 Experiment results without proposed control.

adjustable speed drive motor application. 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 feed
forward control is proposed to suppress the input current
distortion with a square wave operation. The proposed
control method successfully suppresses the input current
distortion to 1/20 times smaller than the no feed forward
control. In addition, the THD of the input current is 23%
reduced.
In future works, the proposed converter and controller
will be applied and examined in a high speed permanent
magnetic motor.

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[7]

[8]

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