2440

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 9, SEPTEMBER 2010

Output Voltage Correction for a Voltage Source Type
Inverter of an Induction Motor Drive
Tetsuma Hoshino, Member, IEEE, and Jun-ichi Itoh, Member, IEEE

Abstract—A proposed voltage error correction method that uses
a disturbance observer for various types of induction motor control was evaluated. The features of the proposed control method
are: 1) control parameters are easily determined according to themotor model and the parameter sensitivity is robust, and 2) the
proposed method can be applied for field-oriented vector control,
speed sensor-less vector control, and V/f control of the induction
motor by modification of a back electromotive force compensation
term in the observer. The disturbance observer is designed to havefast response that is ten times faster than the current controller forvector control. The voltage error is efficiently corrected using the
proposed method, and the current distortion can be reduced byapproximately 1/3. The proposed method is validated on the basisof experimental results.
Index Terms—DC–AC power conversion, induction motor drive,
observers.

NOMENCLATURE
p
fs
iu
i1
GACR (s)GLPF (s)GM otor (s)
KACR
KF F
Lm
Lσ
R1
R2
Td
T f , Ts
Vdc
VON
V1
V1∗
V1∗∗
∆V

Differential operator d/dt.
Switching frequency.
Output current of the leg.
Motor current of primary side.
Transfer function of automatic current regulator (ACR).
Transfer function of low-pass filter in the disturbance observer.
Transfer function of motor.
ACR proportional gain.
Compensation gain.
Magnetizing inductance.
Equivalent leakage inductance.
Primary resistance.
Secondary resistance.
Dead-time period.
Time constant of the observer.
DC-link voltage.
Saturation voltage of the switching device.
Motor voltage of primary side.
Command voltage for disturbance observer.
Command voltage for inverter.
Disturbance voltage.

Manuscript received December 9, 2009; revised February 5, 2010 and April
3, 2010; accepted April 9, 2010. Date of current version September 17, 2010.
Recommended for publication by Associate Editor J. O. Ojo. This paper waspresented at the IEEE Sixth International Power Electronics and Motion Control
Conference, Wuhan, China, May 2009.
The authors are with Nagaoka University of Technology, Nagaoka 940-2188,
Japan (e-mail: tetsuma@stn.nagaokaut.ac.jp; itoh@vos.nagaokaut.ac.jp).
Digital Object Identifier 10.1109/TPEL.2010.2049031∆V∆V̂
V̂EM Fφ2
ωm
ω1
Subscripts
Cd, qAverage disturbance voltage.
Estimated error correction voltage.
Estimated speed electromotive force (EMF).
Motor flux of secondary side.
Motor speed in electric angular frequency.
Primary-side angular frequency.
Controller quantity.
d-and q-axes quantity.
I. INTRODUCTION

HE output voltage of a power converter requires high accuracy to achieve high-performance operation of a motor
drive, especially around the low-speed region. However, output voltage errors can be generated for two reasons. The firstis the influence of a dead-time period. All voltage source typeinverters require a dead time to prevent a short-circuit current in
power devices. However, the dead time results in output voltage
errors and significant distortion of the current waveform aroundthe zero crossing point of the current. The second reason is
the saturation voltage of a power device. The saturation voltage
depends on the temperature and collector current of the powerdevices; therefore, the saturation voltage is varied.
In order to perform high-starting torque, low-speed ripple,
low-torque ripple, and high-accuracy torque, correction of theoutput voltage error is a very important issue. In particular, when
an induction motor drive operates without a speed sensor suchas V/f control and sensor-less vector control, the output voltage
error cannot be neglected in the low-voltage output range, suchas at low speed.
Various voltage compensation methods have been previously
proposed [1]–[10]. The most common method to compensate
the dead time is the addition of the correction voltage to the
output voltage command, according to the polarity of the current. If delay of the polarity detection or mismatching of thecorrection voltage occurs during the correction process, thena large distortion of the current waveform and a large torqueripple are generated. Polarity detection of the load current isparticularly difficult in the low-speed region, because the transition of the polarity is very slow. In any case, it is difficult tocompensate the voltage error using the saturation voltage of thepower device, due to its nonlinear characteristics. It should be
noted that the saturation voltage of the device is also a cause of
the voltage error. Therefore, the dead-time elimination method
is not sufficient for elimination of the voltage error [11]–[16].
On the other hand, a voltage error correction method thatuses a disturbance observer has been proposed for vectorcontrolled systems [1], [9]. Compensation by a disturbanceT

0885-8993/$26.00 © 2010 IEEEHOSHINO AND ITOH: OUTPUT VOLTAGE CORRECTION FOR A VOLTAGE SOURCE TYPE INVERTER OF AN INDUCTION MOTOR DRIVE

observer is useful, because the disturbance observer can estimate the amount of voltage error, consisting of the saturation
voltage of switching devices and the dead-time voltage error. In
the method reported in [1], the disturbance observers decide only
the compensation value. The output voltage correction is thenimplemented by adding the compensation value to the output
voltage command according to the polarity of the load current, aswith the conventional method. Therefore, it is difficult to solve
the mismatch problem of the current polarity detection in the
low-speed region using this method. For industrial products suchas general purpose inverters, in order to compensate the voltage
error by current polarity detection, the compensation value isadjusted at around the zero crossing point. This adjustment isvery complex, because the voltage error characteristics are nonlinear. There have been some discussions regarding the voltage
error correction without current polarity detection for induction
motor drive applications. For example, support vector regression (SVR) algorithm has been proposed to correct the voltage
error [12]. However SVR algorithm requires many memories
for on-line voltage error estimation. On the other hand, the direct estimation of the voltage error using a disturbance observer
was proposed for a permanent magnetic synchronous motor(PMSM) drive [9]. However, induction motors are widely usedfor various applications in comparison with the PM motor drive
systems. The voltage error correction for an induction motor isstill more important. There is a paper using a disturbance observer to correct voltage error for field-oriented vector control
of an induction motor drive [17]. However, there has been noreport of using a disturbance observer to correct voltage error
for V/f control method, which is the most common method for
adjustable speed drive.
We propose a voltage error correction method that uses a
disturbance observer without current polarity detection. There
are two main advantages of the proposed method. The first isthat the control parameters can be easily determined according to the motor model, and the parameter sensitivity is robust.
Even if the dead-time values changed, the proposed method canestimate the voltage error at on-line without parameter tuning.
That is, the proposed method does not require parameter adjustment according to the load current, temperature, and deadtime. The second advantage is that the proposed method canbe applied to various control methods on the induction motor
by only modification of a back EMF compensation term in theobserver. The fundamental principle of the proposed compensation method is first described. Variation of the proposed method
applied to sensor-less vector control and V/f control is then described. Lastly, experimental verifications are implemented oneach control.
II. PRINCIPLES OF THE DISTURBANCE OBSERVER FOR
VOLTAGE ERROR CORRECTION
A. Problems With Conventional Compensation
Fig. 1(a) shows a circuit diagram of a voltage-source inverter,and Fig. 1(b) shows the voltage error behavior during a deadtime period. The voltage error is mainly caused by the dead-time
period. The dead-time period Td , when both switches are off, is2441

Fig. 1. Inverter leg circuit diagram and the relationship between the reference
pulse and voltage error. (a) Inverter leg. (b) Relationship between the reference
pulse and voltage error.

added at the transition of gate pulses up and un in order to avoid
the short circuit between the upper and lower arms. An ideal inverter can set the dead time to zero; however, a real inverter mustassign some dead-time period, because the actual switching device has a delay and dispersion of the switching characteristics.
The voltage error is then caused from the conduction of thefree-wheeling diode (FWD) during the dead-time period.
The voltage error during the dead-time period depends on the
direction of the flowing current. When the direction of the output
current from the leg to load is positive, the current in the leg flows
through the FWD of the lower arm during the dead-time period.
Thus, the output voltage is decreased by the dead-time period.
On the other hand, when the output current direction is negative,
the current in the leg flows through the FWD of the upper arm,and the output voltage is increased. The value of the voltage
error depends on the dead-time period and the dc-link voltage,
as shown in Fig. 1. The voltage error is calculated using (1).
∆V = −fs Td Vdc sign(iu )(1)where sign(x) is a sign function. If x > 0 then sign(x) = 1, if x
< 0 then sign(x) = −1, and if x = 0 then sign(x) = 0.
It should be noted that the magnitude of the voltage error
is not dependent on the amplitude of the output voltage andthe output current. Therefore, when the output voltage is small,such as during low-speed operation, the effect of the dead timeis strong, because the ratio of the voltage error to output voltage
becomes larger.
The voltage error is also derived from the saturation voltage
VON of the switching device. When the output current direction of
the leg is positive, the current in the leg does not flow through theswitching device of the upper arm during the dead-time period.
Thus, the output voltage is decreased by the saturation voltage ofthe device. On the other hand, when the output current direction
is negative, the current in the leg flows through the device ofthe lower arm, and thus the output voltage is increased. The
voltage error, which is dependent on the saturation voltage ofthe switching device, is calculated using (2).
∆V = − (1 − fs Td ) VON sign(iu ).

(2)

2442

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 9, SEPTEMBER 2010

Fig. 2. Conventional voltage error correction method corresponding to thedirection of the motor current.

Fig. 2 shows a control block diagram of practical voltage
error correction according to the current polarity. The error correction voltage is calculated from KF F iu limited to −1 and
1, where KF F compensates the gain to maintain linearity at
the zero-crossing point and prevent hunting. In order to achieveprecise correction, the conventional method requires tuning of
the gain KF F for each converter. A practical inverter determines
the voltage error differently from (1), because the output voltage
is changed slowly by the junction capacitance of the switching
device when the load current is around the zero-crossing point.
In order to correct the voltage error precisely, an edge of thecorrection voltage is dulled by the gain KF F at around the zerocrossing of the current waveform. The optimum value of the gain
KF F depends on the characteristics of each switching device;
therefore, the tuning operation for each converter is a significant problem due to the long work time of practical inverters
such as general-purpose inverters. In addition, the compensation
value fs Td Vdc must also be adjusted according to the voltage
saturation and switching characteristics of the power device.

B. Dead-Time Correction Method Using
Disturbance Observers
A dead-time compensation method is proposed using a disturbance observer. The voltage error estimation uses the relationship between the motor voltage v1 and current i1 on a rotationalframe, which is obtained using (3). Consequently, the tuning
used for the conventional method will not be discussed here.
R1 + pLσv1d ω1 Lσ v1q  
 =  −R2

0


0
0







i1d
i 
×  1d  .
φ2dφ2q−ω1 LσR1 + pLσ

p
ω1

0

R2
+p
Lm

−R2

ω1 − ωm

−ω1
p






−ω1 + ωm 


R2
+p
Lm
(3)

Fig. 3 shows the equivalent circuit of an induction motor
on a d–q rotating frame. The secondary leakage inductance isconverted into that of the primary side. The dead-time voltage error is estimated from the output current. From (3), when
the d-axis corresponds to the vector of the secondary flux φ2 ,the primary-side voltage v1 is calculated using (4), because

Fig. 3.

Equivalent circuit of an induction motor.

Fig. 4. Block diagram of the voltage error correction method using a disturbance observer.

the q-axis component φ2q is equal to zero.
v1d = (R1 + R2 + pLσ ) i1d − ω1 Lσ i1q −



R2
Lm


φ2d

(4)

v1q = (R1 + R2 + pLσ ) i1q + ω1 Lσ i1d + ωm φ2d .
Fig. 4 shows a block diagram for the vector control method,using the proposed voltage error correction method. The disturbance observers calculate the difference between the command
voltage V1∗∗ and the actual output voltage V1 of the inverter,and estimates the disturbance voltage ∆V. The voltage error of
the inverter becomes the disturbance of the voltage controller.
The estimated voltage error is added to the voltage command as
the error correction voltage ∆V̂ , which is calculated using (5)derived from (4).
∆v̂d =

1
1 + sTf(R1C + R2C + pLσ C ) i1d − ω1 Lσ i1q
−∆v̂q =

R2
Lm



∗∗
φ2d − v1d

1{(R1C + R2C + pLσ C ) i1q + ω1 Lσ i1d
1 + sTf∗∗.
+ ωm φ2d − v1q(5)

Bandwidth of the disturbance observer is determined by thetime constant of the observer Tf . So Tf should be set as fast as
possible, with consideration of the time delay of the feedback
loop in order to neglect discretization effect such as phase lag.
The method proposed in Fig. 4 corrects only the first termon the right side of (5), which is the back EMF of the RL. The
second and third terms in (5) are in proportion to the angularfrequency of the primary and secondary sides, respectively. The
second and third terms are referred to as the cross term andHOSHINO AND ITOH: OUTPUT VOLTAGE CORRECTION FOR A VOLTAGE SOURCE TYPE INVERTER OF AN INDUCTION MOTOR DRIVE

2443

speed EMF term, respectively. In the low-speed region, theseterms can be neglected, because they are much smaller than
the first term. The proposed method has good compensation
performance in the low-speed region for each control methodof the induction motor drive operation. However, the cross term
and the speed EMF term interfere with the control performancein the middle- and high-speed regions. Therefore, the key pointof applying the proposed method to various control methods isthe implementation of these terms for correction according to
the features of the control methods. In particular, calculationof the speed EMF term is important for the proposed method.
When the disturbance observer is combined with the ACR for
voltage error correction, the transfer function of the proposed
method from disturbance voltage ∆V to motor voltage V1 isderived as−(1 − GLPF (s))
V1
=
.
∆V
1 + GACR (s)GM otor (s)(6)

On the other hand, the transfer function of ACR from thedisturbance voltage ∆V to the motor voltage V1 is
−1
V1
=
.
∆V
1 + GACR (s)GM otor (s)(7)

That is, the transfer function from the disturbance voltage ∆V
to the motor voltage V1 does not equal regardless of the parameters in ACR. Then the slope of the magnitude characteristic
in bode diagram at low frequency of the proposed method isdifferent from that of ACR. The slope of the proposed method
is −40 dB/dec, which is larger than −20 dB/dec of ACR.
Nonlinear voltage error is corrected by the disturbance observers in the proposed method. However, the voltage error
correction in the overmodulation region cannot be corrected,
because there is no margin to correct output voltage. The correction in the overmodulation region will be considered in future
works.
An internal model control (IMC) method can estimate the output signal of plant, using an inverse model of the plant such as an
induction motor. However, the IMC only estimates disturbanceon the output side of the plant [18]. In this paper, the output
signal of the plant is the input current of the motor. Therefore,
the IMC is not suitable to use voltage error correction, because
IMC does not estimate disturbance voltage of the input side.
III. COMPENSATION TERMS FOR EACH CONTROL METHODS
A. Compensation Term for Field-Oriented Vector
Control Method
Fig. 5 shows a block diagram of the proposed method applied to the field-oriented vector control method. In this control
method, the cross term and speed EMF term in (5) are compensated by the feedforward control, because all parameters in thiscontrol method are known and the secondary angular frequency
is known from the speed sensor. The disturbance observer is
attached to the d-and q-axes.
The proposed method can also be applied to a sensor-lessfield-oriented vector control method. However, the speed sensorless control method should use an estimated motor speed instead

Fig. 5. Block diagrams of the voltage error correction method, using fieldoriented vector control. (a) d-axis. (b) q-axis.

of an actual value ωm for the speed EMF compensation. Itshould be noted that the voltage sensor for sensor-less vector
control is not used for voltage error correction. Sometimes, avoltage sensor is used to achieve high performance in sensorless vector control; however, a voltage sensor for voltage error
correction requires a higher response than that of the sensor-lessdrive voltage sensor. Therefore, there is a difficulty to detect the
average value of the pulsewidth modulation waveform without
delay.
The stability of the field-oriented vector control system ismaintained by the disturbance observer, because the pole positions of the proposed system are combined with the conventional field-oriented vector control system and the disturbanceobserver. When the stability of both the disturbance observer
and the field-oriented vector control are ensured, the system isstable.
B. Compensation Term for V/f Control Method
The V/f control is very useful in practical applications. A
sensor-less drive system requires a higher cost controller and issensitive to the motor parameters, especially in the low-speed
region. In addition, V/f control has robust characteristics for the
motor parameters. It should be noted that practical V/f control
systems have current sensors for protection and compensationof the voltage error.
Fig. 6 shows a block diagram of the proposed method applied
to V/f control. With this control method, the d-axis no longer

2444IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 9, SEPTEMBER 2010

TABLE IANALYSIS CONDITIONS

Fig. 6.

Block diagram of voltage error correction method, using V/f control.

corresponds to the direction of the secondary flux vector. Therefore, the proposed disturbance observer is attached only to theq-axis, because the voltage error mainly appears in the q-axis
with V/f control. On the other hand, an ACR is applied to thed-axis in order to maintain the excitation current. The ACR on
the d-axis also improves the stability of the controller. In orderto stabilize the system, KACR should be set as high as possible;
however, the maximum value of KACR is limited by the delay
time of the feedback loop in a practical system.
The cross term is calculated from the leakage inductance,d-axis current, and primary angular frequency. It should be notedthat the cross term compensation is disabled in the low-speed
region, because the rotation frame of the controller mismatches
that of the motor.
The speed EMF term V̂EM F is also difficult to correct using
the speed ωm , because the V/f control does not have the motor
speed information. The motor speed variation depends on amechanical time constant, and the mechanical time constantof the motor is generally much longer than the electric time
constant of the motor. The current distortion due to the voltage
error is changed by the electric time constant, and the speed
EMF has different frequency components to the voltage error.
Therefore, a slow-response observer is designed to detect the
speed EMF, and a fast-response observer is designed to detect
the voltage error.
It is important to analyze a stability of the disturbance observer; however, the V/f control method is difficult to separate
the d- and q-axis components in actual axes. Therefore, the stability of the proposed system was analyzed using a bode diagram
and a root locus in the complex plane. The analyses conditions
used the parameters of a general purpose 750-W induction motor
under constant speed, in addition to those given in Table I.
Fig. 7(a) shows the bode diagram of the transfer function
from the voltage error ∆Vq to the motor voltage V1q . The bode
diagram of the transfer function represents as a band eliminate filter. The gain indicates a negative value in the operation
frequency from 1 to 50 Hz, which means that the voltage er-ror does not appear in the motor terminal voltage because thegain of the transfer function becomes smaller though the phase
property varies widely. On the other hand, the gain and phase
are almost zero when located at outside of the operation range.
When the controller parameters varied to half or double of the
motor parameter, detail of the frequency response is slightly
varied. However, the overall property of the frequency response
is not changed; therefore, the affection of the motor parametervariation is negligible.
Fig. 7(b) shows the bode diagram of the transfer function
from the command voltage V1q∗ to the motor voltage V1q . Whenthe controller parameters are same to the motor parameters, thegain and the phase is zero in all frequency range. The variationof motor resistance R makes phase shift in the operation frequency. On the other hand, the variation of motor inductanceLσ makes phase shift in the higher frequency range of the operation frequency.
Fig. 8(a) shows the root loci under the condition that Tf =1 ms, Ts = 100 ms, KACR = 0.5, and ω1 = ωm = 0.65 p.u.
State equation (8), which is shown at the bottom of the next
page, gives the root loci of proposed system. This system has six
roots, because it is a sixth-order system. The positions of roots
No. 1–4 in Fig. 8(a) indicate sufficient stability, because they
are dispersed on the real axis in an area that is negatively distantfrom the imaginary axis. However, the remaining roots, Nos. 5
and 6, are located nearest to the imaginary axis. Therefore, thestability of the proposed system can be discussed based on root
No. 5.
Fig. 8(b) shows the root No. 5 loci with variations in
KACR , Tf , and Ts . Each of the parameters is varied ±20%from each of the given values. In order to stabilize the system,
the roots should be located in the area negatively distant fromthe imaginary axis, in addition to minimizing the imaginary part.
Thus, Tf and Ts are set to slower values, and KACR is set to ahigher value in order to stabilize the system. It should be notedthat a slow Tf avoids voltage error correction, and a slow Ts
deteriorates the acceleration performance due to the back EMF.
In contrast, KACR should be set as high as possible for stabilization, with consideration of the time delay of the feedback
loop. As a result, the parameters should be designed according
to the following terms.
1) Tf is set as fast as possible for the controller.
2) Ts is set to faster than the mechanical time constant.
3) KACR is then adjusted for the stability of the system.

HOSHINO AND ITOH: OUTPUT VOLTAGE CORRECTION FOR A VOLTAGE SOURCE TYPE INVERTER OF AN INDUCTION MOTOR DRIVE

2445

Fig. 7. Bode diagram of the proposed V/f control system. (a) Bode diagram of the transfer function from ∆Vq to V 1 q . (b) Bode diagram of the transfer function
from V 1∗q to V 1 q .

IV. EXPERIMENTAL RESULT
A. Evaluation of the Proposed Voltage Error Compensation
Method for Each Motor Control
Fig. 9 shows control block diagrams for the various control
methods of the experimental system. Fig. 9(a) shows a block diagram for a 2.2 kW motor controlled using field-oriented vector
control to maintain constant speed. Where Td : dead-time period
is 3 µs, fs : switching frequency is 10 kHz, Vdc : dc-link voltage
is 300 V, sampling frequency is 10 kHz, ACR gain is 1 p.u., ACR
time constant is 1 ms. Fig. 9(b) is based on reference [10], and it
shows an experimental system composed of a general purpose
induction motor and an inverter, where the motor is controlledusing sensor-less vector control to maintain constant speed.
Where Td : dead-time period is 3 µs, fs : switching frequency
is 20 kHz, Vdc : dc-link voltage is 300 V, sampling frequency
 KA C R R1 + R2
−
−
Lσ
Lσ


−ω 1

 

id

 iq   R2
 φ2 d  s φ2 q  =  0 V̂d ist  Lσ C ω1V̂ e m f

Tf



i



0

V̂ e m f

0

R2
Lm Lσ

ωr e
Lσ

0

−

ωr e
Lσ

R2
Lm Lσ

1
Lσ

0

−

R2
Lm

(ω 1 − ω r e )

0

0

R2

− (ω 1 − ω r e )00

Lσ C R1 + R2
R1 C + R2 C
−
Lσ
Tf
Tf

Lσ C ωr e
Lσ Tf

R2
Lm
Lσ C R2−
Lσ Tf Lm

R1 C + R2 C
Lσ C R1 + R2
−
Lσ
Ts
Ts

Lσ C ωr e
Lσ Ts










 I∗ +  1d 


 1

 Tf




1
Ts

0
1
Lσ
0
0
Lσ C
1−
Lσ
Lσ C
1−
Lσ





0
1
−
Lσ
0

−

−



Lσ C R2
Lσ Ts Lm













 ∗ 
 Vq +  0  ∆V Lσ C 1  Lσ Tf 




L
1
σC

Lσ Ts

−
1
Ts



0

R1 + R2Lσ− KA C R dLσ iq  0  φ2 d  

0


×
 φ2 q  + 0  V̂d ist  Fig. 10 shows waveforms of the d-axis, q-axis, and u-phasecurrent under conditions where the motor speed is 750 r/min
with the rated load torque (1.0 p.u.) using field-oriented vector

ω1

Lσ C ω1Ts

is 10 kHz, ACR gain is 1 p.u., ACR time constant is 3 ms.
This method estimates the motor speed from the speed EMF,
which is calculated using voltage–current differential equationof the motor. The rotating frame of the controller correspondswith that of the motor by controlling the d-axis induced voltage.
Fig. 9(c) shows a block diagram for the experimental system ofa 750 W motor controlled using V/f control to maintain a constant primary frequency. Where Td : dead-time period is 3 µs,
fs : switching frequency is 20 kHz, Vdc : dc-link voltage is 300 V,
sampling frequency is 10 kHz, KACR : ACR gain is 2 p.u. In
Fig. 9(c), the boost voltage is calculated using (9).
ω∗vb o ost = R1 i1q 1 − 1 .
(9)
ωn

−

1
Lσ

Lσ C 1
Lσ Tf

−

1
Tf

1−

Lσ C
Lσ

Lσ C
Lσ

−

1
Ts

2−

Lσ C
Lσ

1−




















(8)

2446

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 9, SEPTEMBER 2010

Fig. 8. Placement and loci of roots. O indicates no parameter variations, ∆ indicates +20%, and ∇ indicates −20%. The solid, dashed dot, and dashed lines
represent the K A C R current regulator gain and the T f and T s observer time-constant variations, respectively. (a) Placement of six roots. (b) Loci for the mostvibratile root (No. 5).

control. The current distortion at the zero-crossing point of theu-phase current is also suppressed when using the voltage error
correction method based on the disturbance observer. In orderto evaluate performance of the proposed method, total harmonic
distortion (THD) k is calculated as√
I2 + I3 + · · · + In
(10)
k=
I1
where
I1 :

Fig. 9. Experimental systems for evaluation of correction performance.
(a) Field-oriented vector control. (b) Sensor-less vector control. (c) V/f
control.

RMS value of fundamental frequency of output current,
I2 , I3 , . . . In : RMS value of nth-order harmonic of output
current.
The THD of the current, as shown in Fig. 10(b), is 0.35%,
which is a 1/3 reduction of that in Fig. 10(a). It is noted that thefundamental frequency component in the output current without
the correction is reduced by the voltage error.
Fig. 10(c) shows the THD variation according to the motor
speed. At middle- and high-speed region, frequency of the voltage error increases by increasing the frequency of the output
voltage and current. Then THD will increases because the error
correction performance of the PI controller is degraded when
the frequency of the error voltage is increased. THD of the result using the conventional method is still high as the result of
the PI controller because conventional method has errors in correction quantity and timing. However, THD of the result using
proposed method is reduced below 1.0%. It should be notedthat the voltage error correction using the disturbance observer
can avoids problems, such as torque ripple or control precision,and improves the response of the acceleration, deceleration, andload variation.
Fig. 11 shows the waveforms of the motor speed, d-axis,
q-axis, and u-phase current under conditions where the motor
speed is 300 r/min with the rated load torque (1.0 p.u.) using
sensor-less vector control. The experimental result shownin Fig. 11(a) is without voltage error correction and that inFig. 11(b) is using the disturbance observer based on thevoltage error correction method. In Fig. 11(a), the current
distortion occurs at the zero crossing point of the u-phasecurrent, because the voltage error is changing significantly atthis point. In contrast, the distortion is almost corrected using
the fast-response disturbance observer, as shown in Fig. 11(b).

HOSHINO AND ITOH: OUTPUT VOLTAGE CORRECTION FOR A VOLTAGE SOURCE TYPE INVERTER OF AN INDUCTION MOTOR DRIVE

2447

Fig. 10. Comparison of correction performance for a disturbance observer, using the field-oriented vector control method. (a) No correction method.
(b) Correction method based on disturbance observer. (c) THD variation about motor speed.

Fig. 11. Comparison of correction performance for a disturbance observer, using the sensor-less vector control method. (a) No correction method. (b) Correction
method based on disturbance observer.

In addition, the THD of the current shown in Fig. 11(b) is
1.20%, which is a 1/3 reduction of that in Fig. 11(a).
Fig. 12 shows waveforms of the d-axis, q-axis, and u-phasecurrent under conditions, where the primary side angular frequency is 1 Hz with no load torque using V/f control. The current
distortion at the zero-crossing point of the u-phase current isalso suppressed when using the voltage error correction method
based on the disturbance observer. Accordingly, the THD of
the current, as shown in Fig. 12(b), is 0.98%, which is a 1/9
reduction of that in Fig. 12(a).
It should be noted that the proposed method obtains the sinusoidal output voltage, which has no low order harmonics
components because the output current is sinusoidal.

Fig. 12. Comparison of correction performance for a disturbance observer,using the V/f control method. (a) No correction method. (b) Correction method
based on disturbance observer.

B. Sensitivity for Motor Parameter Variations
Fig. 13 shows the effect of RC or Lσ C parameter mismatchesof on the THD, using the field-oriented vector control method.

When RC or Lσ C was varied to R or Lσ multiplied or divided bytwo, the increase in the THD was less than 0.03 point. Therefore,

2448

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 9, SEPTEMBER 2010

Fig. 13. Influence of parameter variations on vector control with the proposed compensation. (a) No parameter variations. (b) R c = 0.5R, L σ c = 0.5L σ ,(c) R c = 2R, L σ c = 2L σ .
TABLE IISUMMARY OF THE CURRENT THD FOR EACH CONTROL METHOD IN LOW-SPEED REGION

C. Comparisons of Each Result

Fig. 14.

THD variations for parameter mismatching with V/f control.

Table II shows a summary of the current THD for each control method in low-speed region less than 5 Hz. The correction
method using the disturbance observer reduces the distortion of
the current for all the control methods. In particular, THD of thecurrent with V/f control was drastically reduced to 1/9, because
the original V/f control method has no current regulators. As aresult, the THD of the current with field-oriented vector control
is decreased to 1/2, and the THD of the current with sensor-lessmethod is decreased to 1/3. Therefore, the proposed voltage error correction method is effective for any of the control methods
examined.
V. CONCLUSION

the proposed system has stable operation, even when there areparameter mismatches of RC or Lσ C . It should be noted thatthe influence of the parameter variation on the sensor-less vector
control is almost the same as that of the field-oriented control,
because the sensor-less control has a flux estimator based on thefield-oriented control.
Fig. 14 shows the effect of RC or Lσ C parameter mismatcheson the THD, using the V/f control method. When RC is smaller
than R, the THD is increased. Similarly, when RC is bigger
than R, the THD is decreased. On the other hand, when the Lσ C
parameter is different to the actual Lσ , the THD is increased.
It is noted that the proposed method uses the current sensor
to correct voltage error. Therefore, the gain and offset of thecurrent sensor should be adjusted for each phase to achieve highperformance in the adjustable speed drive system. The gain
mismatching is the same as the parameter error of resistance
RC , because the gain of the transfer function from the actual
current to the output voltage mentions resistance dimension. On
the other hand, the offset and gain unbalance for each phase in
the current sensor causes voltage commands and current ripple
as same as other control methods.

A disturbance observer was proposed for dead-time voltage
error correction. Application of the proposed method was shownfor field-oriented vector control and V/f control method. The
proposed method is able to decrease the current distortion by
1/3 when using the field-oriented vector control method. Whenusing the V/f control method, the proposed method is able todecrease the current distortion by 1/9. The proposed method is
not dependent on the circuit topology; therefore, the proposed
method can be used for voltage error correction with different
circuit topologies, such as a matrix converter.
REFERENCES[1] N. Urasaki, T. Senjyu, K. Uezato, and T. Funabashi, “An adaptive deadtime compensation strategy for voltage source inverter fed motor drives,”
IEEE Trans. Power Electron., vol. 20, no. 5, pp. 1150–1160, Sep. 2005.
[2] T. Sukegawa, K. Kamiyama, K. Mizuno, T. Matsui, and T. Okuyama,“Fully digital, vector-controlled PWM VSI-fed AC drives with an inverter
dead-time compensation strategy,” IEEE Trans. Ind. Appl., vol. 27, no. 3,
pp. 552–559, May/Jun. 1991.
[3] J. W. Choi and S. K. Sul, “Inverter output voltage synthesis using novel
dead time compensation,” IEEE Trans. Power Electron., vol. 11, no. 2,
pp. 221–227, Mar. 1996.

HOSHINO AND ITOH: OUTPUT VOLTAGE CORRECTION FOR A VOLTAGE SOURCE TYPE INVERTER OF AN INDUCTION MOTOR DRIVE[4] A. R. Munoz and T. A. Lipo, “On-line dead-time compensation techniquefor open-loop PWM-VSI drives,” IEEE Trans. Power Electron., vol. 14,
no. 4, pp. 683–689, Jul. 1999.
[5] S.-G. Jeong and M.-H. Park, “The analysis and compensation of deadtime effects in PWM inverters,” IEEE Trans. Ind. Electron., vol. 38,
no. 2, pp. 108–114, Apr. 1991.
[6] A. Cichowski and J. Nieznanski, “Self-tuning dead-time compensation
method for voltage-source inverters,” IEEE Power Electron. Lett., vol. 3,
no. 2, pp. 72–75, Jun. 2005.
[7] H. Zhao, Q. M. J. Wu, and A. Kawamura, “An accurate approach ofnonlinearity compensation for VSI inverter output voltage,” IEEE Trans.
Power Electron., vol. 19, no. 4, pp. 1029–1035, Jul. 2004.
[8] S. Kakizaki, M. Ito, T. Fukumoto, H. Hamane, and Y. Hayashi, “Measurement of parameters and the automatic measurement of an error voltage
by dead time of an induction motor,” in IEEJ Annu. Meeting, Mar. 2007,
pp. 4–143.
[9] H. S. Kim, H. T. Moon, and M. J. Youn, “On-line dead-time compensation method using disturbance observer,” IEEE Trans. Power Electron.,
vol. 18, no. 6, pp. 1336–1345, Nov. 2003.
[10] H. Tajima, Y. Matsumoto, and H. Umida, “Speed sensorless vector control
method for an industrial drive system,” Trans. IEEJ, vol. 116-D, no. 11,
pp. 1103–1109, Nov. 1996.
[11] L. Chen and F. Z. Peng, “Dead-time elimination for voltage source inverters,” IEEE Trans. Power Electron., vol. 23, no. 2, pp. 574–580, Mar.
2008.
[12] C. H. Choi, K. R. Cho, and J. K. Seok, “Inverter nonlinearity compensation in the presence of current measurement errors and switching device
parameter uncertainties,” IEEE Trans. Power Electron., vol. 22, no. 2,
pp. 576–583, Mar. 2007.
[13] V. Yousefzadeh and D. Maksimovic, “Sensorless optimization of deadtimes in DC–DC converters with synchronous rectifiers,” IEEE Trans.
Power Electron., vol. 21, no. 4, pp. 994–1002, Jul. 2006.
[14] C. Attaianese, V. Nardi, and G. Tomasso, “A novel SVM strategy for
VSI dead-time-effect reduction,” IEEE Trans. Ind. Appl., vol. 41, no. 6,
pp. 1667–1674, Nov./Dec. 2005.
[15] J. A. Abu-Qahouq, H. Mao, H. J. Al-Atrash, and I. Batarseh, “Maximum
efficiency point tracking (MEPT) method and digital dead time control
implementation,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1273–
1281, Sep. 2006.
[16] W. Song and B. Lehman, “Dual-bridge DC–DC converter: A new topology
characterized with no deadtime operation,” IEEE Trans. Power Electron.,
vol. 19, no. 1, pp. 94–103, Jan. 2004.

2449[17] X. Yuan, I. P. Brown, R. D. Lorenz, and A. Qui, “Observer based inverter
disturbance compensation,” presented at the IEEE Energy Conversion
Congress and Exposition (ECCE 2009), San Jose, CA, Sep. pp. 20–24.
[18] Y. A.-R. I. Mohamed and E. F. El-Saadany, “Robust high bandwidth
discrete-time predictive current control with predictive internal model:
A unified approach for voltage-source PWM converters,” IEEE Trans.
Power Electron., vol. 23, no. 1, pp. 126–136, Jan. 2008.

Tetsuma Hoshino (S’07) was born in Niigata, Japan,
in 1983. He received the B.S. and M.S. degrees inelectrical, electronics, and information engineering,in 2006 and 2008, respectively, from Nagaoka University of Technology, Nagaoka, Japan, where he has
been working toward the Doctoral degree since 2008.
His current research interests include adjustablespeed driving method and power converters.
Mr. Hoshino is a member of the Institute of Electrical Engineers of Japan.

Jun-Ichi Itoh (M’01) was born in Tokyo, Japan, in
1972. He received the M.S. and Ph.D. degrees inelectrical and 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,
Japan. Since 2004, he has been with Nagaoka University of Technology, as an Associate Professor. His
current research interests include 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 TechnicalDevelopment Award) in 2007.