Comparison of Two Overmodulation Strategies in an Indirect Matrix Converter
Goh Teck Chiang, Student Member, IEEE, Jun-ichi Itoh, Member, IEEE
Abstract –This paper discusses two overmodulation controls,
namely, square wave and trapezoidal, in the indirect matrix
converter (IMC) for motor drives application. The differences
between these two modulations are analyzed based on the
output-input voltage transfer ratio, the efficiency, and thecurrent THD under two load conditions. Moreover, theperformance is then improved by implementing four-step
commutation methods in the primary side of the IMC. The
validity of the proposed methods will be demonstrated throughsimulation and experimentally. The experimental results showthat the voltage transfer ratio can be improved from 0.866 to
0.97 in the square wave modulation and 0.92 for the trapezoidal
wave modulation in an induction motor drive system.
Index Terms— Indirect Matrix Converter, PWM, AC/AC
converter, Overmodulation, Square wave, Trapezoidal wave

I.

INTRODUCTION

Energy savings and energy efficiency have been
investigated extensively. In particular, in the field of motor
drives, high-efficiency converters are essential.
The back-to-back converter, which is composed of a
voltage source rectifier, and a voltage source inverter with anenergy storage component at the DC link is commonly
applied in industrial applications [1]-[2]. However, the use ofelectrolytic capacitors at the DC link part is known to cause
sizing and costing problems. Consequently, direct type
AC/AC converters, which do not require energy storage
devices, are actively investigated, and can be classified aseither conventional matrix converters (CMCs) [3]-[7] orindirect matrix converters (IMCs) [8]-[12]. These matrix
converters deliver advantages in term of size and cost due tothe lack of energy storage components and provide benefits
such as high efficiency, unity input power factor, and energy
regenerative.
However, the matrix converter faces a limitation in thevoltage transfer ratio (VTR) at 0.866, which is defined as theoutput voltage/input voltage, because the output voltage isdirectly converted from the input voltage by merely
controlling the switching devices with the applied modulation.
When matrix converters are used in motor applications, themotor voltage capability will be degraded by approximately
15%. Furthermore, under the same output power condition asthat for a back-to-back converter, the output current of theManuscript received November 3, 2011. Accepted for publication
December 21, 2011. Copyright © 2009 IEEE. Personal use of this material
is permitted. However, permission to use this material for any otherpurposes must be obtained from the IEEE by sending a request to pubspermissions@ieee.org.
T.C. Goh is with the Nagaoka University of Technology, Niigata 9402188, Japan (email: tcgoh@stn.nagaokaut.ac.jp).
Itoh J-i is with the Nagaoka University of Technology, Niigata 940-2188,
Japan (email:itoh@vos.nagaokaut.ac.jp).

matrix converter will be higher than the back-to-backconverters, which will result in increased motor loss.
Several studies that focus on improving the voltage
transfer ratio of the CMC have been proposed [13]-[14].
These circuits added extra switches in the input side of the
CMC and control the CMC into several modes, such as boost
and buck-boost. This circuit topology improves the voltage
transfer ratio greater than 1.0 but in return higher losses are
generated due to the required of additional switches.
Another type of direct AC/AC converter, known as anindirect matrix converter (IMC), has a problem similar to thatof the CMC with respect to the VTR, which restricts theapplication of this converter. In order to address this problem,
a number of studies have used the available DC link partconnected to a boost converter, thereby increasing the DC
link voltage to improve the VTR [15]-[16]. This method can
improve the VTR beyond 0.866 and can deliver a clean
sinusoidal output waveform with low THD. However, in
return, the additional IGBTs and passive components used toform the boost converter, will decrease the overall efficiencyof the circuit. In particular, when the boost converter operates
at more than 50% of the duty ratio in order to provide ahigher DC link voltage, the loss in the boost converter isremarkably high.
Overmodulation is an alternate method that can improve
the VTR without the need for extra reactive components orswitches. A number of studies have investigated improving
the VTR of the matrix converter using overmodulation.
Simultaneously, the overmodulation is applied in either the
input side or the output side of the matrix converter toimprove the VTR [17]-[19].
In the IMC, zero vector periods will normally be created ineither the primary side or the secondary side, and zero current
switching (ZCS) or zero voltage switching (ZVS) can beapplied in order to reduce the switching loss during pulse
width modulation (PWM). However, the overmodulation willtransform the output voltage from a sinusoidal waveform to asquare wave in order to improve the amplitude of the output
voltage. The switching frequency in the secondary side will
be greatly reduced because the frequency switches only at
120-degree phase angle per phase cycle. As a result, zero
vector periods cannot be created in the secondary side, whichmeans that the ZCS cannot be applied in the overmodulation.
In an attempt to improve the output voltage ratio of an
indirect matrix converter, the authors have proposed two
overmodulation control methods [20]. In this present paper,
we discuss to improve the VTR and performance of theconverter by implementing commutation control between the
primary side and the secondary side. The primary side applies

DC link
ripple cal

Primary
controller
v r*
vs* ABC-αβvt* trans.
θ*

ir*
is*

a four-step commutation pattern to improve the DC link
voltage and thereby improve the voltage transfer ratio.
The first control applies a square wave modulation in thesecondary side of the IMC, and the second control transforms
the output voltage into a trapezoidal shape, thereby
increasing the amplitude of the output voltage [21].
Simulation results and experimental results are presented inorder to demonstrate the validity of the proposed methods.
Finally, the loss obtained through simulation is compared tothat obtained experimentally.
II.

CIRCUIT TOPOLOGY

Figure 1 shows the circuit configuration of an indirect
matrix converter. The indirect matrix converter can bedivided into the primary stage and the secondary stage. The
primary stage for the three-phase input power source consistsof twelve insulated gate bipolar transistor (IGBT) units and is
known as a current source rectifier. An LC filter is used at the
primary side to smooth the input current. The secondary stage
consists of six IGBTs and is similar to a standard voltage
source inverter connected to a load or motor. A snubber
circuit is included at the DC link part of the converter toprotect the circuit. Since this snubber circuit can absorb
overshoot voltage from the reactive elements in the circuit,only a small capacitance value is needed.
Two control modulation methods are well known forachieving high efficiency in PWM. The first is zero current
switching (ZCS) applied at the primary side [9]-[10]. The
switches in the primary side can switch with zero switchingloss when the secondary side is in zero vectors. During thezero vectors, the load current will be circulating inside thesecondary side and the DC link current will drop to zero.
The second is zero voltage switching (ZVS), which isapplied at the secondary side [22]-[23]. For this control, twoof the switches in the primary side will turn on together tocreate a zero vector period and hence allow the IGBTs in thesecondary side to switch without switching loss. During thezero vectors, the DC link voltage will drop to zero and thevoltage is not formed in the secondary side and therefore theloss can be reduced.
However, in overmodulation methods, the secondary sideis driven with a square wave or a trapezoidal wave, and zero

Transition
controlvq*
Lim.

Rec_duty

Max-mid-min
phase
detection

Carrier
generator

V/fconversion

Fig.1. Circuit topology of an Indirect Matrix Converter (IMC).

Pulse
patternconversion+-

Single leg
mod.

i t*

Input
current
commands

10 kHzCarrier

0/1Mod.
reader4-stepcom

Secondarycontroller

1/X
Sup

vu*

X

+
-

dq-uvw vv*
vd* conversion

X

vw*

X

+ Svp
+ Swp
-

Square/Trapezoidal

θ*

1/s

Srp
Ssp
Stp
Srn
Ssn
Stn

Fig.2. Proposed control block diagram.

vector periods do not occur in the secondary side. Therefore,
the efficiency will be considered later herein.
III. CONTROL STRATEGIES
Equation 1 shows that, with respect to the secondary side,
the input voltage can be considered as the DC link voltage(Edc), and the DC link voltage is formed based on the threephase input voltage with the control in primary side, as
shown in (2), where sxy stands for the switching units. When
Sxy is turned on, sxy = 1, and when Sxy is turned off, sxy = 0.
t[vu vv vw ] is the output voltage, t[Edcp Edcn] is the DC link
voltage, and t [vr vs vt] is the input voltage.
⎡ s ups un ⎤⎡vu ⎤⎤⎥⎡E⎢v ⎥ = ⎢ ss vn ⎥ ⎢ dcp ⎥ .
(1)
⎢ vp
⎢ v⎥
⎣ E dcn ⎦⎢ s wp⎥⎢⎣ v w ⎥⎦s
wn ⎦⎣⎡ E dcp ⎤⎡ s rp⎢⎥ = ⎢⎣ E dcn ⎦⎣ s rn
A.

s sp
s sn

⎡vr ⎤
s tp ⎤ ⎢ ⎥⎥ vs .
s tn ⎦ ⎢ ⎥⎢⎣ v t ⎥⎦(2)

Sinusoidal wave modulation (PWM)
Figure 2 shows the proposed control block diagram(originally from Ref. [24]). The primary side controller isdesigned with a single leg modulation. Fundamentally, theinput voltage that contains the maximum absolute phasevoltage is always selected and corresponding switch isalways turned on. Then, the other two switches that
containing the medium absolute phase voltage and minimum
absolute phase voltage are in the switching state. The input
current commands are derived from the input voltages which
are transformed from a three-phase signal into a twodimensional vector in the stationary reference frame. Current
angles are calculated based on values from the transformationin order to keep a unity input power factor. The primary sidecontroller then uses a simple logic selector to convert thepulse pattern from the voltage source into a current source.
The DC link voltage will contain a ripple with six times the
input frequency, where a three-phase 200 V input voltage candeliver a sufficient DC link voltage at 270 V.
According to Eq. (1), this DC link voltage is then used forthe voltage source inverter (secondary controller). The
voltage source inverter is applied with a lean controlled
carrier modulation to distribute the zero period of the DC linkcurrent. The lean carrier is controlled by the rectifiercommand (Rec_duty). The zero current periods are then put
on the switching timing of the primary switches. Therefore,
zero current switching (ZCS) is achieved on the primary side
based on the rectifier command and the carrier. That is, azero vector period is formed in the secondary side so that theoutput current is circulating within the secondary switches.
As a result of that, the switching stage in the primary side is
generating conduction loss only.
B.

Overmodulation
The secondary side is added with a V/f conversion andtransition control for the adjustable-speed drive application in
an induction motor. In this paper, the motor uses Volt/Hertz
control, which takes only the speed reference command tovary the voltage and frequency applied to the induction motor.
Then, overmodulation control is involved before thecoordination transformation. The output voltage is controlled
proportional to the output frequency under a constant V/fcondition. That is, from the specification of the induction
motor (shown in Table 3), by following the rated values, thefrequency needs to be 50 Hz and the output voltage is 200 V.
Practically, due to the 0.866 limitation of the IMC, themaximum output voltage of the IMC is only 173 V at a
proportional frequency of 43 Hz. Therefore, in the proposed
methods, the transition control is designed to start thetransformation in the output voltage at 40 Hz and to finish at
50 Hz. Below then 40 Hz is the PWM modulation. A
sinusoidal waveform will slowly change over to a squarewave or a trapezoidal wave within the transition period.
The transition control is based on the non-linear control of
the fundamental frequency amplitude of the output voltage[25], which proportionally compensates the amplitude of theoutput voltage command. The dqo-uvw transformation isapplied in the secondary side with the transition control asshown in Fig. 2, where vq is the q-axis voltage control
command and vd is the d-axis voltage control command. The
amplitude of vq will be extended in the overmodulation range
according to the frequency. Then, the three-phase output
voltage commands are calculated based on the dq conversion
from the following equations.

vu = vd cos ωt + vq sin ωt
2π
2π).
) + vq sin(ωt −
(3)
3
3
2π
2π
v w = vd cos(ωt +)) + vq sin(ωt +33where, vu, vv, vw are the output voltage commands and ω isthe frequency.
A gain controller (indicated as Lim. in Fig 2) is included
before the dq conversion to regulate the value of vq. As the vq
is regulating and extending by the gain during the transition
period, the voltage command becomes a square wave or
trapezoidal wave, where the voltage command is proportional
to the fundamental frequency. Since the peak value is always
limited by “1” in the carrier comparison, the gain value isused to determine the shape of transformation between the
trapezoidal wave and the square wave.
In the proposed method, the primary side is optimized byadding a four-step commutation pattern. Four-step
commutation is used in order to avoid the occurrence of open
circuits in the primary side during overmodulation. The
details of the four-step commutation are explained in Section
E. The activation of the four-step commutation is decided by
the signal from the “Mod reader”, which is used to
distinguish between PWM and overmodulation based on the
output frequency of the secondary controller, where “0” =PWM and “1” = overmodulation. Four-step commutation iscompletely turned off when the “Mod reader” outputs “0”,which indicates the PWM operation.
The Max-mid-min phase detection in Fig. 2 is used to
distinguish the input phase voltage into three forms;
maximum, medium and minimum. Note that the input
voltages are calculated in absolute value. These signals arethen send to the block 4-step com, so that the related
switching devices that including the phase voltage will
perform the four-step switching pattern. For example, R is
the medium phase input voltage, S is the minimum phase
input voltage and T is the maximum phase input voltage.
Then, these signals are send to block 4-step com, SRP and
SSP will enable the four-step switching pattern.
vv = vd cos(ωt −C.

Square wave modulation (single pulse modulation)
Figure 3 explains the operation of the square wave
modulation. The transition start from 40 Hz and theamplitude of the output voltage command increases
according to the frequency. Equation 3 shows that the output
voltage command is proportional to the vq axis command. As
the vq axis command increases accordingly to the frequency,
the amplitude of the output voltage command becomessignificantly large. Since the voltage command is always
limited by the peak-to-peak offset of the carrier, a nearlysquare wave will be formed. The pulse pattern in thesecondary side is shown at the bottom of Fig. 3. (The gate
pulse will be active if the carrier is larger than the voltage
command.) Once the transition is complete, each of thephases is switched at a 120-degree phase angle, and zero
vectors do not occur. Furthermore, in the square wave
modulation, the switching frequency is much lower than the
PWM, and therefore the switching loss in the secondary stage
is greatly reduced.
D.

Trapezoidal wave modulation
Trapezoidal wave modulation is another method that may
increase the amplitude of the output voltage in the matrix
converter as previously discussed in Ref. [18]. The second
control method uses a trapezoidal wave modulation in thesecondary side of the indirect matrix converter. Figure 4
illustrates the transition control of the trapezoidal waveform.
The control is basically the same as that of the square wave
control. The transition control starts at 40 Hz and iscompleted by 50 Hz. The extension of vq is limited in thetransition period in order to achieve a trapezoidal waveform.
The vq controls the amplitude of the output voltage command(Vout*) and then the vq restricts the extension once theoutput voltage command becomes a trapezoidal wave before
the output voltage becomes a complete square wave.
Each of the phases is controlled to switch at a 120-degree
phase angle similar to the square wave modulation. Although
the switching pattern of the trapezoidal wave has a greaternumber of switching per cycle than the square wave, the zero
vectors do not occur either. The bottom of the Fig. 4
illustrates the switching pattern of the trapezoidal wave
modulation. The switching pattern shows the three output
phases (U,V,W) are in a sequence that; one phase is always
turn on, one is always turn off and the other phase isswitching. Therefore, zero vector periods are eliminated inthis modulation.
Note that, the control is dynamic responsive and therefore
transforming back from overmodulations to PWM is thesimilar process which has explained in Fig. 3 and Fig. 4 but
in a reverse order. In the next section, these two control
methods will be discussed and simulation results will becompared.

Fig. 3. Square wave modulation with transition control.

Fig. 4. Trapezoidal wave modulation. The Vout* is controlled by the vq to an extension that the Vout* becomes a
trapezoidal waveform on 50 Hz onwards.

Fig. 5. Primary side switching patterns.

Fig. 6. Relations between the Rec_duty and 4-step commutation pattern.

(a) Motoring mode (ΔV > 0).

(b) Regenerating mode (ΔV > 0).
Fig. 7. Current flow pathway and four-step commutation switching pattern
among the four IGBTs in the primary sideE.

Optimization of the switching pattern in the rectifier
Since zero vector periods do not occur in both control
methods, as discussed previously, the dead-time period in theswitching devices of the primary side will cause voltage
distortion in the DC link voltage. The dead-time period leads
to an open circuit in the primary side, and the DC link
voltage drops to zero. This indirectly affects the output
voltage by referring to (1). This phenomenon is shown in Fig.
5, where (a) shows the output current flowing pathway
during the dead-time period with the square wave modulation,(b) shows the dead-time switching operation, and (c) shows
the four-step switching operation. As seen in (b), while theprimary side is switching, dead-time period is happened to be
an open circuit condition. By the open circuit condition on
the primary side, the DC link current is forced through the
low and high side of the free-wheeling diode in the inverter(Sun, Sup) and as a result the DC link voltage drops down to
zero. In (b), the current flows via the diode of Sun is shownwith a positive value during the dead-time period because of
the diode of Sun becomes a returning path of the output
current.
Figure 5(c) shows better results than Fig. 5(b), where theincorporation of four-step commutation patterns in the
primary side is proved to avoid the distortion in the DC link
voltage.
Figure 6 illustrates the switching pattern of the four-step
commutation between the two legs in the primary side. These
two legs always contain either the medium-phase input
voltage or the min-phase input voltage, which are determinedby the max-med-min phase detection. In Fig. 6, RP is the gate
pulse reference representing the medium-phase input voltage,and SP is the gate pulse reference representing the min-phase
input voltage. Note that the max-phase voltage is always ON.
All the phase voltages are referred to absolute values. The
input current flows to the load via Srp and Ssp, and the load
current is returning to the source via Stn.
Each upper and lower arm of the leg is composed of two
IGBTs that are connected in series. In addition, SRP, SPR,
SSP, and SPS are the gate signals among the four IGBTs in
Fig. 5. The switching pattern is basically divided into two
sections, in which Rec_duty < Carrier or Rec_duty > Carrier.
Then, each of the gate signals will be calculated by anindividual counter to operate a four-step switching sequence,as shown in Fig. 6. The period of the counter Δt isapproximately 2.5 μs.
Figure 7(a) shows the switching sequence among the four
IGBTs and the current flow pathway for motoring mode. For
the case in which Rec_duty > Carrier, Srp is first turned off(step 1), but the current can still flow via the freewheeling
diode of Srp and goes to the DC link part via Spr. In Step 2,
the Sps is turned on and follow up in Step 3 Spr is turned off,
then the input current flows from the diode in Ssp to Sps
towards to the DC link part. Finally, the switching will becompleted by turning on the Ssp. For the case in which
Rec_duty < Carrier, the switching sequences of the medphase leg and the min-phase leg are in opposite order. These
switching patterns will prevent the occurrence of an open

Fig. 8. Simulation results (From PWM to square wave modulation)

circuit in the primary side and hence the VTR will be
improved. The behavior of the Edc can be seen from Fig. 5(c).
The proposed four-step commutation is less complicatedthan the classical four-step commutation (in CMC), because
it only needs to handle two switching intervals at per
switching time comparing to the classical, which is threeswitching intervals. Furthermore, the proposed four-step
commutation which can be known as current-dependentcommutation shows better result than the voltage-dependentcommutation in the IMC circuit structure. This is because in
the voltage-dependent commutation that based on themeasured value of three input phase voltage, switching errorof closed circuit will happen when two phase voltages arecrossed over. On the other hand, the current-dependentcommutation will prevent the closed circuit and shows abetter solution in the IMC.
However, in order for the proposed four-step commutation
to work in the regeneration, the inverter first needs todistinguish between the motoring and regenerating, then only
the correct pattern will be chosen. Figure 7(b) shows thefour-step commutation for the regeneration mode. Note that,the switching sequence is similar to the motoring mode (Fig.
7(a)). The difference is where the switches are supposedly
turned on (or off) during the motoring is needed to turn off(or on) in the regenerating mode. These minor changes canbe modified in the FPGA once the inverter can distinguishbetween the operating modes. Furthermore, the four-step
commutation shows a better performance in the case ofregenerating mode. This is because for the dead-time,
rectifier has no current pathway and all energy goes into theDC-link snubber which result the performance gets poor
during the intervals. Moreover, this snubber has to be large
enough due to the comparably large amount of energy thesnubber has to take in the regenerating mode, which will be
explicitly designed for the dead-time intervals.

Modulation
Input frequency
Output frequency
Output power
Carrier frequency
Input voltage
Input power factor
Load condition

TABLE 1SIMULATION PARAMETERS
Square wave
Trapezoidal wave
modulation
modulation
50 Hz
50 Hz
50 Hz (Fig. 8)
50 Hz (Fig. 9)1500 W
1500 W
10 kHz
10 kHz
200 V
200 V
99%
99%
R= 25Ω, L= 2 mH
R= 25Ω, L= 5 mH

Input voltage vr [V]
200
0
-200
Input current ir [A] (LPF)
100-10
Output voltage vuv [V] (LPF)
300
0
-300
Output current iu [A]100-10
DC Link Voltage Edc [V]
300
0

0.02

0.04 Time (s)

0.02

0.04

(a) Dead-time pattern(b) Four-step commutation pattern.
Fig. 9. Square wave operation simulation results.

(a) Dead-time pattern(b) Four-step commutation pattern.
Fig. 10. Trapezoidal wave operation simulation results.

IV. SIMULATION RESULTSTABLE 2
EXPERIMENTAL PARAMETERS
Modulation
Square wave
Trapezoidal wave
modulation
modulation
Input frequency
50 Hz
50 Hz
Output frequency
50 Hz
50 Hz
Output power
1500 W
1500 W
Input voltage
200 V
200 V
VTR
0.97
0.92
(VoutRMS / VinRMS)
TABLE 3
MOTOR PARAMETERS
Induction motor (Fuji: MLH6085M)

Table 1 shows the simulation parameters for both control
methods. All simulation results are simulated by the PSIM
circuit simulator (Powers Technologies Inc.).
A.

Square wave modulation
Figure 8 shows the simulation results obtained by applying
the square wave modulation with a transition control. The
transition control is programmed to start at an output
frequency of 40 Hz and to be completed by 50 Hz, as
indicated in Fig. 8, the overmodulation starts at 0.8 s andends at approximately 1 s. During the transition process,there is no surge voltage in either the input side or the output
side. The input current Ir exhibits a nearly sinusoidal
waveform throughout the process, and the output current Iu
exhibits a sinusoidal waveform and is then transformed into a
six-step waveform when the output voltage command
becomes a square wave. Before the transition control begins
at 40 Hz, the input current Ir is 3.25 A (RMS), the output
current Iu is 3.78 A (RMS), and the output line-line voltage
Vuv is approximately 170 V (RMS). After completing thetransition, at 50 Hz, the input current Ir is 4.34 A (RMS), theoutput current Iu is 4.38 A (RMS), which is nearly equal tothe input current, and the output line-line voltage Vuv is 198 V(RMS). The four-step commutation will be activatedautomatically as the overmodulation starts.
Figure 9(a) shows the simulation results, where the squarewave modulation is applied with the dead-time switchingpattern. As discussed previously, the DC link voltage Edc
frequently drops to zero during the dead-time period. Figure9(b) shows the simulation results, where the square wave
modulation is applied with the four-step commutation pattern.
Note that Edc is greatly improved, confirming that no open
circuits occurred in the primary side. The input current isfound to be distorted due to the direct effect of the six-step
waveform in the output current, because IMC is a direct type

Motor Power

750 W

Rated Voltage

200 V

Rated Current
Resistor

Poles

Rated RPM
Leakage
3.6 A
inductanceResistance-inductance Load
35 Ω

Inductor

PWM
50 Hz
35 Hz
1250 W
200 V
0.75

4/ 50 Hz1420
4.42 mH
5 mH

converter. As a result, the harmonic component in the input
current is increased slightly. However, the output line-line
voltage Vuv can deliver 202 V (RMS), and the output voltage
transfer ratio becomes 1.01.
B.

Trapezoidal wave modulation
Figures 10 (a) and (b) show the comparison between thedead-time pattern and the four-step commutation pattern inthe trapezoidal wave modulation. The output current is anearly sinusoidal waveform, which means that the motor loss
is reduced because the harmonic components are low. In
addition, the THD of the input current is lower than that of
the square wave due to the nearly sinusoidal output current.
Figure 11 shows the simulation results obtained byapplying the trapezoidal wave modulation with the transition
control. The simulation conditions are as listed in Table 1.
The transition starts at 40 Hz (0.8 s in Fig. 10) and ends by
50 Hz (1 s in Fig. 10). This simulation result reveals a

Fig. 11. Simulation results (From PWM to trapezoidal wave modulation)

smooth transformation process on the transition period. The
four-step commutation is applied automatically after 40 Hz.
The input current is quasi sinusoidal waveform and theoutput current is sinusoidal waveform. At 40 Hz, the input
current Ir is approximately 3.20 A (RMS), the output current
Iu is 3.80 A (RMS), and the output line-line voltage Vuv isapproximately 168 V (RMS). After 50 Hz, the input current Ir
is 4.15 A (RMS), the output current Iu is 4.27 A (RMS), andthe output line-line voltage Vuv is 185 V(RMS).
V.

EXPERIMENTAL RESULTS

Both of the proposed methods were tested in a 1.5-kVA
prototype using two load conditions, namely, a resistanceinductance load and a 750-W induction motor. The
experimental and motor parameters are shown in Tables 2
and 3, respectively.
Resistance-inductance load
Figure 12 shows the experimental results of the squarewave operation. The input current Ir is 4.6 A (RMS), theoutput current Iu is 4.4 A (RMS), and the output line-line
voltage Vuv is 194 V (RMS). With the application of four-step
commutation, the voltage transfer ratio is improved from
0.866 to 0.97 (VoutRMS / VinRMS =194 V/ 200 V = 0.97). As
discussed in Section IV, the input current contains distortiondue to the six-step waveform in the output current. When the
output current is outputting a step waveform, the input
current will be affected and distorted due to the sudden step
wave. Note that the input voltage can maintain a clean
sinusoidal waveform and are not affected by the input current.
Figure 13 shows the experimental results of the trapezoidal
wave operation. The DC link voltage supplies a stable
voltage with no zero voltage drops, and the output line-line
voltage Vuv is 184 V (RMS). The voltage transfer ratio is
improved from 0.866 to 0.92 (184 V/ 200 V = 0.92).
Fig. 14 shows the experimental results of the PWM in a
RL load, where it is transformed back into PWM from squarewave modulation. The result shows that the output current isrelatively higher than the input current due to the limitationon the output voltage.
The distortion in the input current is less than the squarewave modulation because the output current is similar to asinusoidal waveform.

Fig. 12. Square wave modulation experimental results in R-L load.

A.

Induction motor drive
The input current THD and the output current THD of thetwo proposed methods are analyzed for a motor drive
application, as shown in Fig. 15. This figure shows the THD
characteristics of the two proposed methods for various
motor torques. At motor torque of 120 %, the input current
THD is approximately 10 %, and the output current THD isslightly higher at around 13 %. However, the trapezoidal
wave modulation shows better values in terms of harmoniccomponents. The input current THD is approximately 7 %,Fig. 13. Trapezoidal wave modulation experimental results in R-L load.

Fig. 14. Sinusoidal wave (PWM) experimental results in a R-L load.

B.

and an output current THD of approximately 5 % can beachieved due to the clean sinusoidal waveform.
Figure 16 shows the relationships between the motor speed
and motor torque. The frequency shown on the left of thegraph represents the output frequency. At 40 Hz, which is the
PWM, both the square wave and trapezoidal wave
modulations provide equivalent speed data. Moreover, at 45
Hz, where the modulation is transforming, both of themodulations provide approximately the same speed data.
However, at 50 Hz, since the square wave can achieve ahigher output voltage, the square wave enables a higher
motor speed than the trapezoidal wave modulation under thesame output power.
Furthermore, the slip in the induction motor is reduced byapplying the square wave modulation. The motor efficiency
could be improved because the copper loss in the secondary
winding is reduced due to the lower slip.
C.

Comparison of the proposed methods
Figures 17(a) and 17(b) show the input current harmonic
analysis for the square wave and the trapezoidal wave,
respectively. Comparing these two figures, the input currentof the trapezoidal waveform contains fewer high harmoniccomponents than the square wave modulation. These results
confirmed that the trapezoidal wave modulation can deliver abetter THD input current and output current, as shown in Fig.
15.
Comparing the square wave modulation and thetrapezoidal modulation in terms of the voltage transfer ratio,
the square wave provides better results. From Fig. 16, at 50
Hz, the square wave modulation can deliver a 4 % higher
speed than the trapezoidal wave modulation under the sameload torque. In addition, with respect to the motor, although
the harmonic component of the output current of the squarewave modulation is higher than that of the trapezoidal wave
modulation, the RMS value of the motor current in thesecondary winding is smaller than the trapezoidal wave
modulation. Therefore, the motor losses of these twomodulations are estimated to be approximately the same.
The trapezoidal wave modulation provides better results interms of the harmonic components in the input current andthe output current. However, the voltage transfer ratio is 6 %lower than for the square wave modulation. A trade-off
relationship is shown between these two modulations.

Fig. 15. Current THD characteristics under a motor condition.

Fig. 16. Modulation comparison in term of speed and torque.

VI. LOSS ANALYSIS AND EFFICIENCYThis section discusses the losses of the proposed methods
and compares the simulation results and the experimental
results for the efficiency of these two methods. The purposeof this comparison is to prove that under the overmodulation,even without the zero current switching (ZCS), the converter
maintains high efficiency. Note that the switching devices in
the primary side are assumed to be two series-connected
IGBTs in the simulation analysis. The simulation condition
does not consider the dead time. However, the primary side isapplied with four-step commutation. The assumed filter loss
is approximately 1% of the total power, which includes the
LC filter in the primary side and the snubber circuit in the DC
link part [26]. The simulation conditions for part A and part
B are output power 1-kW, and part C is identical to theexperimental condition.
A.

Loss analysis – PWM and square wave modulation
The proposed method can switch between the PWM andsquare wave easily, and therefore an efficiency analysis ofFig. 17(a). Square wave modulation(Output power = 750 W, motor torque = 95 % )Fig. 17(b). Trapezoidal wave modulation(Output power =750 W, motor torque = 95% )Fig. 17. Harmonic analysis in the input current.

B. Loss analysis – square wave modulation and trapezoidal
trapezoidal modulation
The loss comparison between the square wave modulationand trapezoidal modulation is shown in Fig. 19. Note that thevoltage and current of each modulation differ from each other,although the power is same for each modulation. For thesquare wave modulation, the input current Ir is 3.10 A (RMS),
the output current Iu is 2.98 A (RMS), and the output phasevoltage Vu is 120 V (RMS). For the trapezoidal modulation,
the input current Ir is 3.00 A (RMS), the output current Iu is
3.05 A (RMS), and the output phase voltage Vu is 115 V(RMS).
The total loss for the square wave modulation is 45.30 W
and that for the trapezoidal modulation is 45.18 W. The
analysis reveals that these two modulations have similar
losses under the same output power. Therefore, both
modulations enable high efficiency.
Experimental efficiency
This section describes the experimental efficiency of thetwo proposed methods. The measurements are based on RL
load condition and the parameters are the same as in Section
V. First, the efficiency for the square wave modulation that
includes the transition from PWM to the square wave isshown in Fig. 20. The output frequency ratio is shown at thebottom, where 1.0 = fa/ fo = 50 Hz/ 50 Hz (fa=actual output
frequency, fo= design output frequency). In the graph, thearea below 0.8 is for the PWM operation and the area for thesquare wave starts at 1.0. The efficiency remains constant at
approximately 93.5%, even when the transition involves
various power supplies.
Figure 21 shows the efficiencies for the square wave
modulation and the trapezoidal modulation, as well as thesimulation results for the square wave modulation.

5

Loss [%]

these two modulations is needed. Figure 18 shows the loss
comparison between the PWM and the square wave
modulation. For the PWM, zero current switching can beapplied in the primary side, and therefore the switching loss
is zero. However, the PWM uses a 10-kHz carrier, whichcauses the high switching loss in the secondary side. On theother hand, for the square wave modulation, the switchingloss is moved from the secondary side to the primary side
because the switching in the secondary side only occurs at
120 degrees for each phase, following the square wave
operation. Since the switching frequency is very low, theswitching loss could be reduced to nearly zero. Furthermore,
the frequency of the carrier does not affect the switching lossof the secondary side. However, the zero current switching
cannot be applied, and so the IGBTs contain switching loss.
In PWM, the loss for the primary side is approximately
2.9% and that for secondary side is approximately 1.8%. As
for the square wave modulation, the loss in the primary side
is approximately 3.5%, and that in the secondary side is 1.1%.
Based on these results, the losses between the PWM andsquare wave are found to be approximately the same.

Pout = 1000W

4

Recovery loss

3

Switching loss
(Turn-on)
Conduction loss

Switching loss
(Turn-off)2
10

Primary side

Secondary side

Primary side

Secondary side

Square wave
PWM
Fig. 18. Loss comparison between PWM and square wave modulation.

Fig. 19. Loss comparison between square wave and trapezoidal wave.

C.

Fig. 20. Experimental efficiency of square wave with transition control.

Fig. 21. Comparison of efficiency. (Output frequency = 50Hz)

Simulation results A are for the theoretical calculation thatshows only the switching device losses, and Simulation
results B include the LC filter loss and the no-load test resultswith the switching devices losses. The no-load test results
obtained from the prototype, including the possible losses
occurring in the parasitic capacitor and the leakage current,
are approximately 10 W. Both the experimental andsimulation results reveal that the efficiency is approximately
93.5%.
VII.

CONCLUSION

Two overmodulation methods were proposed in an attempt
to improve the output-input voltage transfer ratio of an
indirect matrix converter. The proposed methods aredemonstrated through simulation and experimentally. The
results of the present study confirm the validity of the
proposed methods. The voltage transfer ratio is 0.97 for thesquare wave modulation and 0.92 for the trapezoidal wave
modulation. Furthermore, both modulations can achieve
efficiencies of up to 93.5% on average by using seriesconnected IGBTs in the primary side. In respect to the
distortion in the input current, the LC filter needs to beredesigned to improve the THD in the future.
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Goh Teck Chiang (M’09) was born in Seremban,
Malaysia, in 1981. He received the B.S. degree inelectricalandelectronicengineering

fromQueensland University of Technology, Brisbane,
Australia in 2004 and the M.S. degree in electricalandelectronicengineeringfrom

Nagaoka

University of Technology, Japan in 2009, where
currently, he is working towards to the Ph.D. degree
in electrical and electronic engineering. His
research interests include indirect matrix converter, PWM and motor drives.

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, Niigata, Japan,
in 1996, 2000, respectively. From 1996 to 2004, he
was with Fuji Electric Corporate Research andDevelopment, Ltd., Tokyo, Japan. Since 2004, hehas been with Nagaoka University of Technology,
Niigata, Japan as Associate Professor. His research interests are matrix
converters, dc/dc converters, power factor correction techniques and motor
drives. Dr. Itoh received the IEEJ Academic Promotion Award (IEEJ
Technical Development Award) in 2007.