Voltage Transfer Ratio Improvement of an Indirect Matrix Converter by Single
Pulse Modulation
Goh Teck Chiang

Jun-ichi ItohStudent Member, IEEE
Nagaoka University of Technology
1603-1 Kamitomioka,
Nagaoka Niigata, 940-2188, Japantcgoh@stn.nagaokaut.ac.jp

Member, IEEE
Nagaoka University of Technology
1603-1 Kamitomioka,
Nagaoka Niigata, 940-2188, Japan
itoh@vos.nagaokaut.ac.jp

Abstract –This paper proposes two over modulation strategies
for the Indirect Matrix Converter (IMC). These strategies aim
to improve the output-input voltage transfer ratio of theconverter and also maintain high efficiency. This paper will
discuss the control method of the two modulations and also
compare the total losses of the converter. The control method
uses a triangular carrier comparison method which is a simple
structure based on the concept of a non-linear amplitude control
of a voltage source inverter (VSI) output voltage. The validity ofthe proposed method will be demonstrated with the simulation
results and the experimental results. Loss analyses are includedin the paper to evaluate the efficiency of the two proposed
methods. Furthermore, a 1 kW prototype was tested andefficiency of 93.5% is obtained.
Index Terms— Indirect Matrix Converter, PWM, AC/AC
converter, Over modulation, Square wave, Trapezoidal wave

I.

INTRODUCTION

The developments of energy saving converters are studied
and researched intensively due to the global warming issue.
Especially in the field of transportation, three phaseconverters are heavily used in motor drive applications, suchas Hybrid Electric Vehicles (HEVs) or electric trains.
The Back to back converter which is composed by a
voltage source rectifier and a voltage source inverter with anenergy storage component at the DC link, is commonly
applied in the industrial. However, the electrolytic capacitors
are known with problems such as size and costing.
Consequently, the direct type of AC/DC converters without
the need of energy storage devices are actively studied, which
can be classified into; conventional matrix converter (CMC)[1]-[4] and indirect matrix converter (IMC) [5]-[8]. Thesematrix converters deliver advantages in term of size and cost
due to no energy storage components and also provide
benefits such as high efficiency, unity power factor andenergy regenerative.
However, the matrix converter faces a limitation in the
output voltage transfer ratio at output voltage < 0.866 input
voltage because of the output voltage is directly from the
input voltage by merely controlling the switching devices
with the applied modulation. When matrix converters areused in motor application, the motor capability will bedegraded by approximately 15%. Further, under the same

output power condition with a back to back converter, theoutput current of the matrix converter will be higher than theback to back converters which will results the motor loss
increased. Many researches have shown interests in term of
improving the output voltage transfer ratio [9]-[11]. Similarly,
IMC is having a same problem with the CMC, the limitationon the output voltage restricts the application of thisconverter. This paper will be discussing and analysis about
the improvement on the voltage transfer ratio of an IMC.
This paper proposes two over modulation control methods
aiming to improve the output voltage ratio of an indirect
matrix converter. The proposed method does not need extra
reactive components or switches to improve the output
voltage transfer ratio. Since the indirect matrix converter canbe divided into two stages; the secondary side which issimilar to the voltage source inverter can be applied easily
with a single pulse modulation (square-wave inverter). The
modulation will transform the output voltage into a squarewave from sinusoidal waveform (PWM) and improve theamplitude of the output voltage. The second proposed control
is to transform the output voltage into a trapezoidal shape andso to increase the amplitude of the output voltage too [12].
Simulation results and experimental results will bedemonstrated in the paper to show the validity of the
proposed method. Furthermore, loss comparison between thesimulation and experimental will be discussed in the later
chapter as well.
II.

CIRCUIT TOPOLOGY

Fig. 1 shows the circuit configuration of an indirect matrix
converter. The indirect matrix converter can be divided into
primary stage and secondary stage. The primary stage for the
3-phase input power source consists of six units of reverse
blocking IGBT (RB-IGBT) also known as a current source
rectifier. A LC filter is used at the primary side to smooth the
input current. The secondary stage consists of six IGBTs issimilar to a standard voltage source inverter that is connected
to a load or motor. A snubber circuit is included at the DC
link part of the converter for protection purpose. This snubber
circuit will absorb overshoot voltage from the reactive
elements in the circuit therefore only a small capacitancevalue is needed.

Among the many control modulation methods, two
methods are well known for achieving high efficiency; thefirst is the zero current switching (ZCS) applying at the
primary side [7]-[8]. The switches in the primary side canswitch at zero switching loss when the secondary side is inzero vectors. During the zero vectors, the load current will becirculating inside the secondary side and the DC link current
will be dropped to zero.
The second is known as the zero voltage switching (ZVS)
that is applying at the secondary side [13]. For this control,
two of the switches in the primary 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 loss
can be reduced while switching.
However, in the over modulation methods, the secondaryside will be driven with square wave or trapezoidal wave andzero vector periods are not occurring on both the primary side
neither the secondary side. Therefore, efficiency is one of theconcern factors which will be discussed in the later chapter.

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

DC linkripple cal

Primary
controller

10 kHzCarrierir*
Singleleg
mod.

Input current is*commands
it*

Carrier
generator

V/f conversion

III. OVER MODULATION CONTROL BLOCK DIAGRAM
Equation 1 shows that in the view of the secondary side,
the input voltage could be considered as the DC link voltage(Edc), and the DC link voltage is formed based on the 3-phase
input voltage with the control in primary side as shown in (2),where sxy stands for the switching units. When Sxy is turnedon, sxy =1 and when Sxy is turned off, sxy =0. t[vu vv vw ] is theoutput voltage, t[Edcp Edcn ] is the DC link voltage and t[vr vsvt] is the input voltage.
⎡ s ups un ⎤⎡ vu ⎤⎤⎥⎡E⎢v ⎥ = ⎢ss vn ⎥ ⎢ dcp ⎥ .
(1)
⎢ vp
⎢ v⎥
E
⎣ dcn ⎦⎥
⎢ s wp⎢⎣ v w ⎥⎦
s
wn ⎦
⎣

⎡vr ⎤
s tp ⎤ ⎢ ⎥v .
(2)s tn ⎥⎦ ⎢ s ⎥⎢⎣ v t ⎥⎦Fig. 2 shows the proposed control block diagram originallyfrom ref. [14]. The primary side controller is designed with acurrent type PWM rectifier command. The DC link voltage isformed from the maximum input phase voltage and the
medium input phase voltage through the switching patterns of
one phase modulation. Then, it uses a simple logic selector toconvert the pulse pattern from the voltage source into acurrent source. The DC link voltage will contain a ripple with
6 times of the input frequency, where a 3-phase 200 V input
voltage can deliver a sufficient DC link voltage at 270V.
The voltage source inverter is applied with a leancontrolled carrier modulation to distribute the zero period of
the DC link current. The lean carrier is controlled by therectifier command (Rec_duty in primary side). Then, the zerocurrent periods are allocated on the switching timing of the⎡ E dcp ⎤⎡ s rp⎢E⎥ = ⎢s⎣ dcn ⎦
⎣ rn

s sp
s sn

vq*
vd*

Square/Trapezoidal
1/s

Secondarycontroller

1/X

Transition
control

Lim.

Pulse
patternconversion
Rec_duty+-

dq-uvw
conversion

X

+
-

vv*

X

+
-

X

+ Swp
-

vw *
θ*

Sup

vu*

Svp

Fig.2. Proposed control block diagram.

primary switches. Therefore, the zero current switching(ZCS) is achieved on the primary side based on the rectifiercommand and the new carrier.
In the proposed method, no extra optimize control isrequired in the primary side control. On the other hand, thesecondary side is added with a V/f conversion and transition
control for the adjustable speed drive application in an
induction motor. Practically, under the V/f constant condition,
the maximum output voltage of the IMC is 173 V at output
frequency 43 Hz due to the 0.866 limitation with a two phasemodulation in the secondary side. In the proposed methods,
the transition control is designed to start the transformationon the output voltage at 40 Hz and finished at 50 Hz. A
sinusoidal waveform will rapidly 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 amplitude of the output voltage [15], which is a
proportional compensation to the amplitude of output voltage
command. The amplitude of the Vq* will be expended in theover modulation range according to the frequency. Then, theoutput voltage command in three-phase will be calculated

Fig. 3. Square wave modulation with transition control.

1

vout*

Trapezoidal wave
50Hz

PWM Transition
40Hz

0
-1
Pulse pattern
1

U-phase0
Fig. 4. Trapezoidal wave modulation with transition control.

from the dq conversion. A limiter is included before the dq
conversion to switch between the two proposed control
methods; which is the square wave and the trapezoidal.
A.

Square wave modulation (Single pulse modulation)
Fig. 3 explains the operation of the Square wave
modulation. The transition start from 40 Hz and theamplitude of the output voltage command is increasing
according to the frequency. When the voltage command
comes closed to the 50 Hz, the amplitude of the output
voltage command is approximately 200 times larger than thePWM voltage command. Since the voltage command isalways limited by the peak-peak of the carrier, therefore anearly square wave will be formed. At the bottom of the Fig.
3 shows the pulse pattern in the secondary side. (The gate
pulse will be active if the carrier is larger than the voltage
command.) Once the transition is completed, each of thephases is switched at 120 degree phase angle, and zero
vectors are not occurring. Furthermore, in the square wave
modulation, the switching frequency is a lot lower than the
PWM, and therefore the switching loss in the secondary stage
is greatly been reduced.

B.

Trapezoidal wave modulation
Trapezoidal wave modulation is another method that havebeen discussed and shown a possibility to increase theamplitude of the output voltage in the matrix converter [12].
The second control method is to propose using a trapezoidal
wave modulation in the secondary side of the indirect matrix
converter. Fig. 4 illustrates the transition control of the
trapezoidal waveform. The control is basically the same as
the square wave control. The transition control will start at 40
Hz and completed by 50 Hz. However, the extension of theVq* is being limited in the transition period in order toachieve a trapezoidal waveform with a rising angle of 40
degree. Although trapezoidal wave has more switching times
than the square wave in one period cycle, the zero vectors are
not occurring either.
The comparison and discussion between these two control
methods will be discussed together with the simulation resultsin the next chapter.
IV. SIMULATION RESULTS
Since the zero vector periods are not occurring in the bothcontrol methods, the switching devices in the primary side
requires a dead-time while switching. However, by applying

dead-time into the primary side, the dead-time period willcause a voltage distortion area in the DC link voltage. The
dead-time period is considered as an open circuit in the
primary side, and the DC link voltage will drop to zero. This
is indirectly affecting the output voltage by referring to (1).
On the other hand, the hard switching in the primary side
does not require a commutation with the secondary side. Thisis because of the switching pattern of the secondary side is at
120 degrees, therefore while the primary side is switching thesecondary side will be in free wheeling mode as shown in Fig.
5. The output current will be circulating among the IGBTs
and diodes even the primary side is at open circuit. In Fig. 5Sup, Svn and Swp are remaining at ON while the switchingunits in the primary side are turning On/Off.
Table 1 shows the simulation parameters for both thecontrol methods. All simulation results are simulated bycircuit simulator (PSIM, Powersim Technologies Inc.).
Square wave modulation
Fig. 6 shows the simulation result by applying the squarewave modulation with a transition control. The transition
control is programmed to start at output frequency 40 Hz andcompleted by 50 Hz, which is referring to the Fig. 6, the overmodulation starts at 0.8s and stop at approximately 1s.
During the transition process, there is no surge voltage foundin either the input side or the output side. The input current Ir
is keeping a nearly sinusoidal waveform through out theprocess, and the output current Iu can keep a sinusoidal
waveform and then transformed into a six-step waveformwhen the output voltage command becomes a square wave.
Before the transition control begins (PWM), at 40 Hz, theinput current Ir is 3.25 A, the output current Iu is 3.78 A andthe output line-line voltage Vuv is about 170 V (RMS). Aftercompleting the transition, at 50Hz, the input current Ir is
about 4.34 A, the output current Iu is 4.38 A that is nearly
equal to the input current and the output line-line voltage Vuv
is 198 V(RMS). Note that this is an ideal condition, dead timeeffect is not being considered.

Fig. 7 shows another simulation result with the squarewave modulation. This result included the dead time in theswitching units and the output frequency is 120 Hz. As
previous discussed, the DC link voltage Edc is found dropping
to zero frequently during the dead time period. The output
line-line voltage Vuv is 189 V(RMS), and the output voltage
transfer ratio is 0.94.
Other than that, the input current cannot keep a sinusoidal
waveform due to the six-step waveform in the output current.
The input current is found distorted and the harmoniccomponents are increased.
B.

Trapezoidal wave modulation

A.

Fig. 5. Circulation of output current while primary side is open circuit.

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

TABLE ISIMULATION PARAMETERS
Square wave
Trapezoidal wave
modulation
modulation
50 Hz
50 Hz
50 Hz (Figs. 5, 13)
50 Hz (Figs. 9, 15)
120 Hz (Fig. 7)
50 Hz (Fig. 8)1500 W
1500 W
10 kHz
10 kHz
200 V
200 V
98%
99%
R= 25Ω, L= 1 mH
R= 25Ω, L= 5 mH

Fig.5 Simulation results (From PWM to square wave modulation)

Fig. 9 demonstrates the simulation results by applying thetrapezoidal wave modulation with the transition control. Notethat this is an ideal condition, dead time effect is notincluded. The simulation conditions are the same as the Table
1. The transition starts at 40 Hz (0.8s in Fig.8) ends by 50 Hz(1s in Fig. 8). The simulation results show a smoothtransformation process on the transition period. Both the
input current and output current are in sinusoidal waveforms.
At 40 Hz, the input current Ir is approximately 3.20 A, theoutput current Iu is 3.80 A and the output line-line voltage Vuv
is approximately 168 V (RMS). After 50Hz, the input current
Ir is 4.15 A, the output current Iu is 4.27 A and the output
line-line voltage Vuv is 185 V(RMS).
Fig. 8 shows the simulation result with trapezoidal wave
modulation that included the dead-time. Zero vector periods
are not occurring in the secondary side and the DC link
voltage Edc will distorted due to the dead-time, same like thesquare wave modulation. The output line-line voltage Vuv is
178 V(RMS), and the output voltage transfer ratio is 0.89.
However, the input current is found less distorted with thetrapezoidal wave modulation. Further, the output current is ina sinusoidal waveform which means in the application of
motor, the motor loss is lesser because the six-step waveform
contains high harmonic components.
Comparison between the two proposed methods
Comparing between the square wave modulation and thetrapezoidal modulation; in term of the voltage transfer ratio
the square wave can achieve a better result. Furthermore,since the switching period for the secondary side is at 120
degrees, the switching loss is low and nearly to zero.
However, the input current and the output current arecontaining high harmonic components.
The trapezoidal wave modulation is achieving a better
result in term of harmonic components in the input current
and the output current. However, the voltage transfer ratio is
expected to be lower than the square wave modulation.

Fig.7 Square wave operation simulation results.
Input voltage vr [V]

200
0
-200
Input current ir [A] (LPF)
60-6
Output voltage vuv [V] (LPF)
300
0
-300
Output current iu [A]100-10
DC Link Voltage Edc [V]
500
0
0.02

0.04
Time (s)

0.06

0.08

0.10

Fig.8 Trapezoidal wave operation simulation results.

C.

V. EXPERIMENTAL RESULTS
Both the proposed methods were tested in a 1-kVA
prototype and Table 2 shows the experimental parameters.
Fig. 10 shows the experimental results of the square wave
operation. The input current Ir is 4.04 A, the output current Iu
is 4.08 and the output line-line voltage Vuv is 183V. As
discussed in the simulation section, the input current contains
of distortion due to the six-step waveform in the output
current. The voltage transfer ratio is improved from 0.866 to
0.92.
Fig. 11 shows experimental results of the trapezoidal wave
operation. In this case, the input current Ir is 3.70 A, theFig. 9. Simulation results (From PWM to trapezoidal wave modulation)

output current Iu is 3.91 A and the output line-line voltage Vuv
is 175 V. The distortion in the input current is lesser and theoutput current is nearly to a sinusoidal waveform. The
voltage transfer ratio is improved from 0.866 to 0.881.
Figs. 12(a) and 12(b) show the input current harmonic
analysis between the square wave and the trapezoidal wave
respectively. The input current THD of the square wave is
12.4 % and the input current THD of the trapezoidal wave is
9.7 %. Comparing between the Figs. 12(a) and 12(b), theinput current of the trapezoidal waveform contains lesser highharmonic components than the square wave modulation.
These results confirmed that the trapezoidal wave modulation
can deliver a better THD input current and output current.

TABLE II
EXPERIMENTAL PARAMETERS
Square wave
Trapezoidal wave
Modulation
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
Output voltage
183 V
175 V

VI. LOSS ANALYSIS & EFFICIENCYThis chapter will be discussing the losses between the two
proposed methods and then comparing the efficiency of these
two methods between the simulation results and theexperimental results. In other than that, the loss about thesquare wave modulation will additionally compare withanother square wave modulation that comes with a zerocurrent switching. The purpose of this comparison is to provethat under the single pulse modulation, even without the zerocurrent switching, the converter still can remain highefficiency. Note that the switching devices in the primary side
are assumed to be RB-IGBTs in the simulation analysis. The
simulation condition does not consider about the dead time,

Fig. 12(a). Square wave modulation

Fig. 12(b). Trapezoidal wave modulation
Fig. 12. Harmonic analysis of the input current.

LC filter loss and snubber loss. The simulation parameters aresame as the Table 1 and the analysis method is from ref. [14].
Fig.10. Square wave operation experimental results.
Input voltage vrs [V] 250 [V/div]

Output voltage vuv [V] 250 [V/div]

Input current ir [A] 5 [A/div]

Output current iu [A] 5 [A/div]

Fig. 11. Trapezoidal wave operation experimental results.

A.

Loss analysis – PWM and Square wave modulation
The proposed method can transform between the PWM
and square wave easily and therefore an efficiency analysis
between these two modulations is needed. Fig. 13 shows theloss comparison between PWM and square wave modulation.
For the PWM, zero current switching can be applied in the
primary side, and therefore the switching loss is zero.
However, the PWM uses a 10 kHz carrier which results theswitching loss is high in the secondary side. On the other
hand, for the square wave modulation, the switching loss is
moved from secondary side into the primary side. This isbecause the switching in the secondary side only happens at
120 degrees for each phase following the square wave
operation, since the switching frequency is very low, theswitching loss could be reduced nearly to zero. Further, thefrequency of the carrier is not affecting the switching loss ofthe secondary side. Also, the zero current switching cannot beapplied and results that the RB-IGBT is containing switchingloss.
In PWM, the loss for primary side is approximately 1.3 %and for secondary side is approximately 1.8 %. As for thesquare wave modulation, the loss in primary side is
proximately 1.9 % and the secondary side is 1.1 %. From theresults, we can understand the losses between the PWM andsquare wave are about the same.
B. Loss analysis –Square wave modulation (With & without
zero current switching (ZCS))
This section will be discussed on applying a zero current
switching (ZCS) into the square wave modulation. A limiteris included to the peak value of the square wave voltage
reference, and force the peak value decrease from 1.0 (peak)
to 0.95. Fig. 14 shows the diagram explanation of the spoken
method. By this control, zero vector periods are occurring
mostly at the peak of the carrier. The primary side can utilize
these periods to achieve the zero current switching. However,this method will be affecting the amplitude of the output
voltage where the voltage transfer ratio will be getting lower.
The purpose of this comparison is to prove that the losses ofthese two modulations are about the same, even the zerocurrent switching cannot be applied in the primary side.
Fig. 15 shows the loss comparison between the squarewave modulations with and without the ZCS. For the squarewave with ZCS, the loss in the primary side is approximately
1.9%, and the secondary side is eminently 1.1%, where thetotal losses are nearly the same to the square wave without
ZCS; 28 W for a 1 kW system. From this analysis, we canunderstand that the proposed method can achieve highefficiency because of the square wave in secondary sidewhich produce a low switching loss can replace the applyingof ZCS in the primary side.

Fig. 14. Explanation of square wave modulation with zero vectors.

Loss [%]

C. Loss analysis –Square wave modulation and trapezoidal
modulation
The loss comparison between the square wave andtrapezoidal is shown in Fig. 16. Note that the voltage andcurrent of each modulation are different from each otheralthough the power is same. For the square wave modulation,
the input current Ir is 3.14 A, the output current Iu is 3.00 A
and the output phase voltage Vu is 120 V. And for the
trapezoidal, the input current Ir is 2.95 A, the output current Iu
is 3.00 A and the output phase voltage Vu is 114 V.
The total loss for square wave is 28.65 W and thetrapezoidal is 28.58W. The analysis shows that these twomodulations have a similar loss under a same output power.
Therefore, both the modulations are capable to achieve highefficiency at around 97%. Note that if all switching units inthe primary side are formed by the series connected of two
IGBTs, the efficiency is approximately decreased by 2% dueto the existing of diode conduction loss (FWD).

Fig. 13. Loss comparison between PWM and square wave.

Fig. 15. Loss comparison between square wave with ZCS and without ZCS

D.

Experimental Efficiency
The last chapter will be covering the efficiency of the two
proposed methods. The parameters are the same as theexperimental section in chapter V. Note that the switchingunits in the primary side is a series connection of two IGBTs
in one unit. First the efficiency for the square wave
modulation that includes the transition from PWM to squarewave is demonstrated in Fig. 17. The output frequency ratio
is shown at the bottom where 1= 50 Hz and so on. In thegraph, below than 0.8 is the PWM operation and the squarewave starts at 1.0. It can be known that the efficiency isVII. CONCLUSION
This paper proposed two over modulation methods that
aim to improve the output-input voltage transfer ratio of an
indirect matrix converter. The two proposed methods aredemonstrated in simulation and experimental results. These
results and analysis have proven the validity of the proposed
methods. The voltage transfer ratio is 0.92 for the squarewave modulation and 0.88 for the trapezoidal wave
modulation. Further, both modulations can achieve efficiency
up to 93.5 % averagely by using series connected IGBTs in
the primary side.

Loss [%]

keeping constantly at around 93.5 % even the transition is
involved under various power.
Fig. 18 shows the efficiency comparison among the squarewave modulation, trapezoidal modulation and simulation
analysis of square wave modulation. The assumed filter
losses are including the LC filter in the primary side and thesnubber circuit at the DC link part. Experimental efficiency
shows 93.5 % for the two proposed methods and simulation
analysis shows 94 % for square wave modulation.

Fig. 16. Loss comparison between square wave and trapezoidal wave.

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