IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO.

1, JANUARY 2012

93

A Research on Space Vector Modulation Strategy

for Matrix Converter Under Abnormal
Input-Voltage Conditions
Xingwei Wang, Hua Lin, Member, IEEE, Hongwu She, Student Member, IEEE, and Bo Feng

AbstractThe matrix converter is a single-stage acac power

conversion device without dc-link energy storage elements. Any
disturbance in the input voltages will be immediately reflected to
the output voltages. In this paper, a modified space vector modulation strategy for matrix converter has been presented under
the abnormal input-voltage conditions, in terms of unbalance,
nonsinusoid, and surge (sudden rising or sudden dropping). By
using the instantaneous magnitude and phase of input-voltage
vector to calculate the voltage modulation index and input-current
phase angle, this modified modulation strategy can eliminate the
influence of the abnormal input voltages on output side without an
additional control circuit, and three-phase sinusoidal symmetrical
voltages or currents can be obtained under normal and abnormal
input-voltage conditions. The performance of the input currents
is analyzed when the matrix converter uses different modulation
strategies. Some numerical simulations are presented to confirm
the analytical results. Tests are carried out on a 5.5-kW matrix
converter prototype. Experimental results verify the validity of the
proposed strategy.
Index TermsAbnormal input, matrix converter, modulation
index, modulation strategy, space vector modulation (SVM).

I. I NTRODUCTION

ATRIX converter offers a number of advantages, including simple and compact power circuit, generation of
load voltage with arbitrary amplitude and frequency, sinusoidal
input and output currents, and operation with unity power factor
for any load [1][3]. It has found more and more applications
in motor drive, power supply, wind generation, dynamic voltage
restorer, etc. [4][7].
Three approaches are widely used when developing modulation strategies for matrix converters. The first one is the
AlesinaVenturini modulation strategy based on transfer function analysis and has been proposed in [8] and [9]. The second
one is the space vector modulation (SVM) strategy, including

Manuscript received December 6, 2010; revised March 28, 2011; accepted

April 28, 2011. Date of publication May 23, 2011; date of current version
October 4, 2011. This work was supported in part by the Natural Science
Foundation of Hubei Province, China, under Grant 2009CDB413 and in part
by the National Basic Research Program of China (973 Program) under Grant
2010CB227206.
The authors are with the College of Electrical and Electronic Engineering,
Huazhong University of Science and Technology, Wuhan 430074, China
(e-mail: wxw@mail.hust.edu.cn; lhua@mail.hust.edu.cn; hongwu.she@
ieee.org; fengbohust@163.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2011.2157288

indirect SVM and direct SVM proposed in [10] and [11],

respectively. The SVM modulation strategy is often used in
matrix converter for it has some advantages, such as immediate
comprehension of the required commutation processes, a simplified control algorithm, and maximum voltage transfer ratio
without adding third harmonic components [1]. The third one
is based on the double input line-to-line voltages and has been
proposed in [12].
However, these conventional modulation strategies are derived under the assumption that the input voltages are well
balanced and sinusoidal. In practice, the matrix converter may
operate under abnormal input-voltage conditions, in terms of
unbalance, nonsinusoid, and surge (sudden rising or sudden
dropping). Due to lack of dc-link capacitors for energy storage,
the matrix converter is highly sensitive to disturbances in the
input voltages. For most of the modulation strategies, the unbalanced and nonsinusoidal input voltages can result in unwanted
output harmonic voltages. The short-time input-voltage surge
could bring the voltage surge on the load side instantly [13],
[14]. Several techniques that reduce this influence of the abnormal input voltages for these conventional modulation strategies
have been reported.
For the AlesinaVenturini modulation strategy, by incorporating the characteristics of the supply voltage into the computation and adjusting the calculated duty cycles accordingly
[15][17], the modified strategy can synthesize the desired
output voltages when the supply voltages are either unbalanced
or distorted. Another strategy using a single output-voltage
control loop employing a repetitive controller has been implemented [18]. This controller can attenuate the intermodulation
harmonic components generated at the output of a matrix
converter.
In [19], an improved double input line-to-line voltage
synthesis strategy is developed to improve the input and
output performances of matrix converter when the input voltages are unbalanced, and it has been applied to industries by
YASKAWA [20].
An effective modified SVM is proposed in [21] for the
indirect SVM. The output-voltage waveforms are improved obviously by adding negative sequence components into the modulation vector of fictitious rectifier. This method can improve
the output-voltage performance, but it is too complex and only
used under the unbalanced input voltages. Two compensation
techniques are proposed to improve the output performance of
the matrix converter. The first one is a feedback compensation

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012

Fig. 2.

Emulation of the (a) VSR and (b) VSI conversions.

Fig. 1. Schematic diagram of a three-phase/three-phase matrix converter.

method using closed-loop control of output currents [22], [23].

The other technique is a feedforward compensation method
[22][25], which is based on the instantaneous values of the
three-phase input voltages. In [22] and [24], the inverter stage
modulation index is adjusted adaptively according to the variation of the virtual dc-link voltage, and this method can be only
used with indirect SVM, whereas the modulation index with the
whole matrix converter is calculated using actual input voltages
to compensate the distortion presented in [23] and [25]. The
feedforward compensation method can reduce the load current
distortion considerably but not totally if the supply voltages are
distorted [23]. To achieve sufficient compensation, a combination of feedback and feedforward compensation methods is
proposed in [23].
A simple modified strategy is proposed in [26] for the spacevector-modulated matrix converter, including indirect SVM and
direct SVM. In this method, not only the modulation index
is calculated using instantaneous vector magnitude of output
voltages and input voltages but also the input-current vector
angle is calculated using the actual input-voltage vector angle.
In this paper, the derivation process of the proposed SVM
strategy is presented in detail based on [26], and the modified
calculation of the sector angle of the input-current vector is
analyzed further compared with various input-voltage conditions. First, a review of the conventional SVM theory for matrix
converters is presented in Section II. Then, in Section III,
the modified strategy is derived from the conventional SVM.
The numerical simulations compared with different modulation
methods have been carried out in Section IV. Moreover, the
performance of the input currents is analyzed when the matrix
converter uses different modulation strategies in Section V.
Finally, a prototype has been built to testify the validity of
the modified method. The validity of the theoretical analysis
and the performance of the modulation strategy have been
confirmed.
II. R EVIEW OF SVM FOR A M ATRIX C ONVERTER
In a three-phase/three-phase matrix converter, the nine bidirectional switches allow any output phase to be connected to
any input phase, as schematically shown in Fig. 1.

When the input voltages are purely symmetric and sinusoidal, the input phase voltages can be expressed as

cos(i t)
ua
(1)
ui = ub = Uim cos(i t 2/3)
cos(i t + 2/3)
uc
where i is the input angular frequency and Uim is the amplitude of input phase voltages.
If it is desired that the local-averaged output line voltages be
sinusoidal, i.e.,

cos (o to +/6)
uAB

uol = uBC = 3Uom cos (o to +/62/3) (2)

uCA
cos (o to +/6+2/3)
where Uom is the amplitude of output phase voltages, o is
the output angular frequency, and o is the load displacement
angle.
It has been proved that the indirect and direct SVM approaches, although seems apparent, can be regarded as a unique
modulation approach [27]. Indirect SVM approach is adopted
in this paper for it is simplicity in realization. The emulation
of virtual voltage source rectifier (VSR) and voltage source
inverter (VSI) converters of three-phase/three-phase matrix
converter is shown in Fig. 2(a) and (b), respectively.
Consider the virtual VSI in Fig. 2(b) as a stand-alone inverter
supplied by a dc voltage source udc . In order to avoid open
circuit of the load, there exist six active switching configurations which yield nonzero output voltages and two switching
configurations which yield zero voltages.
In virtual VSI modulation, switching configuration 1, 0, 0
represents that the output phase A is connected to the anode
of the dc power supply and the output phases B and C are
connected to the cathode of the dc power supply, which are the
same to other switching configurations. The six active switching configurations and their corresponding output-voltage vectors are shown in Fig. 3(a).
The complex plane is divided into six sectors by six active
voltage vectors. In each output-voltage sector, the reference
output-voltage vector can be synthesized by two adjacent active
voltage vectors. If the reference output-voltage vector is lying
in Sector 1 and the duty cycles of the two active voltage vectors

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS

95

subscripts , , and i, respectively. The VSR hexagon is shown

in Fig. 3(b), and the duty cycles are

d = mc sin(/3 i )
(7)
d = mc sin(i )
where mc is the VSI modulation index
mc = |ii |/idc ,

0 mc 1.

(8)

Moreover, i is the input-current vector angle within the corresponding sector. In addition, for Sector 1
0 i /3,

i = i i + /6

(9)

where i is the input-voltage vector angle and i is the inputcurrent displacement angle.
The input active power of VSR is equal to the output active
power
udc idc =

31
(u ii + ui ii )
22 i

(10)

where the symbol denotes the complex conjugate.

Then, the output dc voltage of the VSR can be obtained
from (10)
udc =

3
|ui |mc cos i .
2

(11)

The combination of two switching configurations in the

virtual VSR and two switching configurations in the virtual
VSI results in four matrix converter switching configurations.
The final duty cycles of the four active and one zero switching
configurations can be obtained from (4), (5), (7), and (11)
Fig. 3. Synthesis of the output-voltage vector and the input-current vector.
(a) VSI hexagon and (b) VSR hexagon.

are d and d in counterclockwise, the relationship of reference

output-voltage vector and the duty cycles is
|uo |ej(o /6) = d (2udc /3)ej/6 + d (2udc /3)ej/6 (3)
where d + d 1,
0 d 1; 0 d 1.
Using the law of sine, the duty cycles are

d = mv sin(/3 o )
d = mv sin(o )

(4)

where mv is the VSI modulation index

mv =

|uo |
,
udc / 3

0 mv 1.

(5)

Moreover, o is the output-voltage vector angle within the

corresponding sector. At any sampling instant, o is known as
reference quantities. Furthermore, for Sector 1
0 o /3,

o = o t o + /6 + /6.

(6)

Then, consider the virtual VSR in Fig. 2(a) as a stand-alone

VSR loaded by a dc current generator idc . The VSR inputcurrent SVM is completely analogous to the VSI output-voltage
SVM. The VSI subscripts , , and o are replaced with the VSR

|uo |
2
sin(/3 o ) sin(/3 i )
d = d d =
3 cos i |ui |
|uo |
2
sin(/3 o ) sin(i )
d = d d =
3 cos i |ui |
|uo |
2
sin(o ) sin(/3 i )
d = d d =
3 cos i |ui |
|uo |
2
sin(o ) sin(i )
d = d d =
3 cos i |ui |
d0 = 1 d d d d .
(12)
The zero voltage vectors are applied to complete the switching cycle period. Moreover, it can be verified that (12) has a
general validity.
In general, the conventional modulation strategy is derived
under the assumption that input voltages are sinusoidal and
balanced. Thus, i can be achieved by detecting the zero
crossing of one input phase voltage and by using a softwareimplemented phase-lock loop (PLL) [23]. It is calculated as
i = mod(i t i + /6, /3)

(13)

where the mod(x, y) function returns the remainder when x is

divided by y.
Moreover, the modulation index m is usually defined as
m=

Uom
Uim

(14)

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012

where Uim and Uom represent the constant values of the input
and output phase voltage amplitudes.
The modulation index m can be calculated according to the
amplitude of the desired three-phase output line voltages. If the
amplitude of the output voltages remains as a constant value,
then the voltage modulation index m is fixed. The desired
output voltages of matrix converter can be acquired based
on (12).
Unfortunately, when abnormal input-voltage conditions are
presented, the influences of input-voltage disturbances on the
output behavior of matrix converter are significant and undesirable. From (11), the virtual dc-link voltage udc includes
the harmonic content. Thus, the strategy cannot synthesize
the desired reference output voltages and generates low-order
harmonics.
For example, in the case of unbalanced supply voltages,
(2i + o ) and (2i o ) frequency components are concluded in the output voltage of the synchronous reference frame
when the fixed modulation index m is used to calculate the
duty cycles [13]. Similar to the unbalanced condition, it can
be derived for this case also that, if the input power-supply
voltages contain the harmonics on the order of k, the harmonic
components with the frequency of (k 1)i o and (k +
1)i o will be introduced in output voltages [13].
III. M ODIFIED SVM S TRATEGY
Several strategies mentioned in Section I reduce the influence
of the abnormal input voltage by measuring the instantaneous
value of the input voltages or load currents. However, the
output-voltage waveforms are only improved at a certain extent
by these strategies. This paper modifies the conventional SVM
also by incorporating the characteristics of the input voltage
into the computation and adjusting the calculated duty cycles
accordingly. It is carried out by adjusting both the voltage
modulation index m and the input-current vector angle i
according to the input voltages.
It is found that, when the SVM is employed in the matrix
converter, the voltage modulation index m should be calculated
using the instantaneous values of the output- and input-voltage
vector magnitudes according to the voltage space vector synthesis principle. That is
m=

|uo |
.
|ui |

If using the following Clarkes transformation:



1 12 12
abc

C
=
3
0
23
2
so

|uo | = u2o + u2o = 3 Uom

2

|ui | = u2 + u2 , ui = C abc ui .
i

(15)

(16)

(17)

With the normal supply voltage, |ui | can be expressed by

|ui | =

3
Uim .
2

(18)

TABLE I
L OCAL -AVERAGED O UTPUT VOLTAGES

In particular, the amplitude ratio of the voltage vector equals

to the amplitude ratio of the phase (or line) voltage, and the
voltage modulation index is fixed.
Whereas for unbalanced nonsinusoidal power supply, the
voltage modulation index m is not constant and can be adjusted
according to the input voltages. This make the modulation
process adaptive to the characteristics of the input voltages,
hence enabling the output voltages to track closely their reference counterpart when the supply voltages are abnormal.
As under abnormal conditions, the synchronization of the
current reference vector defined with PLL is no longer applicable, and the input-current vector angle i should also be
calculated as
i = mod(i i + /6, /3)

(19)

where

ui
arctan ui
,

ui
arctan ui + ,
i =

2,
3
2 ,

when ui
when ui
when ui
when ui

>0
<0
= 0, ui > 0
= 0, ui < 0.

By using the instantaneous vector magnitude of input voltage

to calculate the modulation index m and introducing (19) in
(12) lead to modified SVM strategy.
In order to explain the modulation strategy, the outputvoltage vector uo and input-current vector ii are assumed to
be both lying in Sector 1, without missing the generality of the
analysis.
With the VSI output-voltage SVM, the local-averaged output
voltages are [10]

d + d
uAB
uBC = d udc .
(20)
uCA
d
Moreover, the local-averaged output voltage in other outputvoltage sectors is summarized in Table I.
With the VSR input-current SVM, the local-averaged input
currents are [10]

ia
d + d
ib = d idc .
(21)
ic
d
Moreover, the local-averaged input current in other inputcurrent sectors is summarized in Table II.

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS

Substituting sin i = (ui /|ui |), cos i = (ui /|ui |), and
(15) in (25), the output line voltages of this converter could be
expressed by

cos(o t o + /6)
uAB

uBC = 3Uom cos(o t o + /6 2/3) . (26)

uCA
cos(o t o + /6 + 2/3)

TABLE II
L OCAL -AVERAGED I NPUT C URRENTS

Thus, the local-averaged output voltages with the input voltage can be obtained from (20) and (21)

d + d d + d
ua
uAB
uBC = d d ub
uCA
d
d
uc

1d0
d d d d ua
ub .
= d d
d
d
d d
d
d
uc
(22)
Using the same procedure, the local-averaged output voltages
in other output-voltage sectors and input-current sectors can be
derived.
If the input three-phase voltages are unbalanced and nonsinusoidal, they can be written in Fourier series as


Uak cos(ki t)

k=1
ua 

U cos(k t k 2/3)

(23)
ui = u b
.
bk
i

uc k=1


Uck cos(ki t + k 2/3)
k=1
abc 1
Substituting ui = [C
] ui in (22) becomes

(1d0 )ui + 33 (d d +d +d )ui

uAB

uBC =
.

(d +d )ui + 33 (d d )ui

3
uCA
(d +d )ui + 3 (d d )ui
(24)

With the input-current and output-voltage vectors laid in

Sector 1, with o = o t o + /3 and i = i i + /6,
and substituting (12) in (24), we can deduce

uAB
uBC = 2m
3 cos i
u
CA

[ui (cos i cos i + sin i sin i )

+ ui (sin i cos i cos i sin i )]

cos(o t o + /6)
cos(o t o + /6 2/3) .
(25)
cos(o t o + /6 + 2/3)

97

It is clear from the aforementioned equation that the modified

method can restrain the disturbance of the input voltages. Thus,
the output line voltages keep with the reference voltages under
the abnormal input voltages.
Although the analysis presented is based on the indirect
SVM, the proposed method is valid for both indirect SVM and
direct SVM.
IV. S IMULATION A NALYSIS U NDER THE A BNORMAL
I NPUT-VOLTAGE C ONDITIONS
In order to verify the effectiveness of the modified method,
numerical simulations have been carried out on the matrix
converter by using MATLAB. In the simulations, Y-connected
RL loads are with resistors of 10 and inductors of 10 mH.
The fundamental amplitude of input-voltage sources Uim is
311 V, and the input frequency fin is 50 Hz. The output-voltage
amplitude and frequency are set at 100 V and 30 Hz.
The simulations have been carried out assuming a sampling
period of 200 s and ideal switching devices.
A. Simulation of the Modified Modulation Under Abnormal
and Sudden-Dropping Input Voltages
The simulated tests under unbalanced and nonsinusoidal
input voltages are carried out with the modified SVM strategy.
Supposed that the steady input voltage ui is unbalanced and
contains harmonic components, expressed as

Uim cos(i t)
ua
ui = ub = 1.4Uim cos(i t 2/3)
uc
0.6Uim cos(i t + 2/3)

0.5Uim cos (3(i t + /20))

+ 0.4Uim cos (3(i t 2/3 + /20))
0.4Uim cos (3(i t + 2/3 + /20))

0.3Uim cos (5(i t + /15))

+ 0.2Uim cos (5(i t 2/3 + /15)) . (27)
0.2Uim cos (5(i t + 2/3 + /15))
The input voltages, the input-current vector angle, the voltage
modulation index, R-load voltages, and spectrum of A-phase
R-load voltage under unbalanced and nonsinusoidal input voltages are shown in Fig. 4(a)(e), respectively.
Under the abnormal input-voltage conditions, owing to the
modified method, the duty cycles of the power switches are
not constant anymore and are variable according to the disturbance in the input voltages. Thus, the output voltages can be
kept balanced and sinusoidal even in abnormal input-voltage
conditions.

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Fig. 4. Simulation waveforms under unbalanced and nonsinusoidal input voltages. (a) Input voltages. (b) Input-current displacement angle. (c) Voltage modulation index. (d) R-load voltages. (e) Spectrum of A-phase R-load voltage.

Similar to the simulations under unbalanced and nonsinusoidal input voltages, the simulated tests under suddendropping input voltages are also carried out with the modified
SVM strategy.
When 0 time < 0.03 s, the input voltages are balanced and
sinusoidal in 311 V/50 Hz, and when 0.03 s time < 0.06 s,
the amplitude of the input voltages Uim decreases to 80% of the
rated value. The input voltages, the input-current displacement
angle, the voltage modulation index, R-load voltages, and
spectrum of A-phase R-load voltage under sudden-dropping
input voltages are shown in Fig. 5(a)(e), respectively.
The simulation results show that the voltage modulation
index can be adjusted quickly according to the variation of

Fig. 5. Simulation waveforms under sudden-dropping input voltages.

(a) Input voltages. (b) Input-current displacement angle. (c) Voltage modulation
index. (d) R-load voltages. (e) Spectrum of A-phase R-load voltage.

input voltages, and the output voltages remain the same when
the input voltages decrease. The proposed method improves the
performance of the matrix converter effectively.
B. Comparison of Simulation in Terms of Three Conditions
The simulated tests under unbalanced and nonsinusoidal
voltages are carried out in terms of three conditions: Method 1
with the conventional SVM, Method 2 with the modified voltage modulation index, and Method 3 with the modified voltage
modulation index and input-current vector angle.
Fig. 6 shows the R-load voltages of the matrix converter in
the condition that the amplitude values of ua , ub , and uc are
311, 373, and 249 V, respectively.

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS

Fig. 6.

Simulation waveforms of R-load voltages under unbalanced input voltages. (a) With Method 1. (b) With Method 2. (c) With Method 3.

Fig. 7.

Simulation waveforms of R-load voltages under nonsinusoidal input voltages. (a) With Method 1. (b) With Method 2. (c) With Method 3.

The simulation results show that the low-order harmonic

components in output voltages are reduced obviously by the
use of the modified method. Furthermore, the control effect
of the modified method with the voltage modulation index

99

and input-current vector angle is better than that of the simple

synchronization method.
Fig. 7 shows the R-load voltages of the matrix converter
in the condition that each of the three-phase input voltages

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Fig. 8. Simulation waveforms of input currents under unbalanced input voltages. (a) With Method 1. (b) With Method 2. (c) With Method 3.

contains 30% fifth-order harmonic component with the initial

phase angle of 15 .
The main low-order harmonics in output voltages resulted
from fifth-order input voltages are the harmonic components
with frequencies of 330 and 270 Hz. From the simulation
results, it can be seen that, when the input voltages contain
fifth-order harmonics, the distortion occurs in the output voltages with the conventional SVM. However, using the modified
technique, the output waveforms could be improved effectively.
V. P ERFORMANCE OF I NPUT C URRENTS U NDER THE
U NBALANCED I NPUT-VOLTAGE C ONDITIONS
There is, however, an important issue to be noted. Although
the aforementioned modified strategy results in sinusoidal output voltages under abnormal supply, it will generate distorted
input currents.
In the case of unbalanced supply voltages, also with 20%
unbalance with the input peakpeak voltages in phases a, b,
and c being 311, 373, and 249 V , respectively, the fundamental
negative sequence component which appears causes variations
in both magnitude and angular velocity of the input-voltage
vector: The input-voltage vector trajectory changes from circular to elliptical.
The simulation of the input currents under unbalanced voltages is also carried out in terms of three conditions: Method 1
with the conventional SVM, Method 2 with the modified voltage modulation index, and Method 3 with the modified voltage
modulation index and input-current vector angle.

Fig. 8 shows the results with unity input power factor. As

can be seen, the input currents have the harmonic content under
unbalanced voltages in terms of three conditions. Fig. 8 also
shows the harmonic spectrum of the input a-phase current. As
the spectrum indicates, the third-order harmonic component
is very large with the modified voltage modulation index and
input-current vector angle method.
In order to reduce or eliminate the harmonic content of the
input currents under unbalanced conditions, a strategy proposed
in [28] and [29] is used.
As in the previous modulation strategy, the input-current
vector is kept in phase with the input-voltage vector. Thus,
the input-current vector displacement angle i is constant and
equal to a reference value. In addition, the input-voltage vector
angle is quite easily determined by synchronizing a timer to
the zero crossing of the voltage or measuring the instantaneous
values of the input voltages.
However, in [28] and [29], the strategy is defined with the
purpose of reducing the harmonic content of the input currents
under unbalanced supply voltage conditions. Moreover, the
input-current displacement angle i is dynamically modulated
as a function of positive and negative sequence components
of the input voltages. Thus, this strategy does not lead to an
instantaneous unity input power factor under unbalanced supply
voltage conditions.
The simulations in Fig. 9 show the input-current control
performance and the output voltages of the matrix converter
under unbalanced grid voltages with the proposed strategy in
[28] and [29].

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Fig. 9.

101

Simulation waveforms with the method of reducing the harmonic content of the input currents. (a) Input currents. (b) R-load voltages.

Fig. 11. Hardware structure of the matrix converter prototype.

Fig. 10. Top view of the matrix converter prototype.

The waveforms show that, using this unbalanced compensation technique, there are no significant harmonic components
apart from the fundamental. However, the input currents are
also unbalanced, and the total harmonic distortion of the output
voltages is larger than that of the modified strategy. Therefore,
it can be concluded that the harmonic components in the output
voltages and the input-current spectrum cannot be eliminated at
the same time under the abnormal input conditions.
VI. E XPERIMENTAL R ESULTS
In order to verify the modified SVM modulation strategy
under the abnormal input conditions, a 5.5-kW experimental
prototype of matrix converter, as shown in Fig. 10, has been implemented to feed a three-phase RL load and a three-phase induction motor. The hardware configuration for matrix converter
is shown in Fig. 11. The instantaneous input voltages of the
matrix converter are sampled by three high-precision voltage
transducers and a high-speed 16-b A/D converter (ADS8361
from Texas Instruments Incorporated), which is controlled by
a field-programmable gate array (FPGA) (EP2C8 from Altera).

The input-voltage signals are also transferred to a microcontroller (TMS320LF2407A from Texas Instruments Incorporated) for modulation algorithm; the data of switching states
and their duty cycles are then transferred back to the FPGA for
pulsewidth modulation pulse generation. The input filter is a
three-phase LC filter with a damping resistor, and the parameters are Lf = 1 mH, Cf = 10 F, and Rf = 51 , respectively.
A. RL Load
A three-phase RL load (R = 37 , L = 50 mH) with star
connection is used to verify the modified modulation strategy.
Moreover, the output voltage is set at 88 V, and the frequency
is 30 Hz.
For the purpose of generating various power-supply voltages,
a three-phase variac is used in the experiments. The three-phase
variac outputs are connected to the three-phase symmetrical
380 VAC/50 Hz while the inputs are open circuited. The variac
contactors are moved when the core is saturation, and then, the
third-order harmonic component can be obtained at the variac
neutral point. It is added into the input c-phase voltage. The
input line voltages are shown in Fig. 12(a). The output phase
voltage waveform using the conventional SVM method and that
using the modified method are shown in Fig. 12(b) and (d),
respectively.

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Fig. 12. Experimental waveforms under abnormal input-voltage conditions.

(a) Input line voltage. (b) Output voltage with the conventional strategy.
(c) Modulation index with the modified strategy. (d) Output voltage with the
modified strategy.

Fig. 13. Experimental waveforms under sudden-dropping input-voltage conditions. (a) Input line voltage. (b) Output voltage with the conventional strategy.
(c) Modulation index with the modified strategy. (d) Output voltage with the
modified strategy.

Fig. 12 shows the steady-state performance of the threephase output voltage using the conventional SVM and the
modified method proposed in this paper. Within the distorted
input voltages, Fig. 12(b) shows that distortion occurs in the
output voltages, measured across R of the Y-connected RL
loads, whereas Fig. 12(d) shows that the output voltages are

unaffected from the abnormal input voltages with the instantaneous voltage modulation index.
The magnitude of the input voltages decreases to 55% of the
rated value by adjusting the variac. Fig. 13 shows the output
voltages using the two methods.

WANG et al.: RESEARCH ON SVM STRATEGY FOR MATRIX CONVERTER UNDER ABNORMAL CONDITIONS

TABLE III
PARAMETERS OF I NDUCTIVE M OTOR

103

VII. C ONCLUSION
This paper has proposed a modified SVM strategy for a
matrix converter under abnormal conditions. In this strategy,
the instantaneous vector magnitude of output voltages and input
voltages is used to calculate the voltage modulation index and
input-current phase angle. Thus, the duty cycles of the switch
states can be adjusted according to the distortion of the input
voltages in time. By using this strategy, the output voltages can
keep with the reference voltages under normal and abnormal
input-voltage conditions. The validity of the theoretical analysis
and the performance of the modulation strategy have been
confirmed by simulations and experimental results.

R EFERENCES

Fig. 14. Experimental waveforms of induction motor drive system at

600 r/min. (a) With the conventional strategy and (b) with the modified strategy.
Waveforms from top to bottom: rotor speed n and stator current is .

In Fig. 13(b), when the input voltages are sudden dropping,

the amplitude of output voltages has also notable variety with
the conventional SVM method. In Fig. 13(d), the amplitude of
output voltages is steady with the proposed method.
B. Induction Motor Drive Application
The modified modulation strategy is then applied to a
1.1-kW induction motor drive system. The parameters of
inductive motor are given in Table III.
The control experiments in the two cases (same as RL
load experiments) are implemented: 1) with the conventional
strategy and 2) with the modified strategy.
Fig. 14(a) and (b) shows the experimental results of the
steady-state performance of the induction motor at 600 r/min.
It can be seen from this result that there are some ripples on
the rotor speed and stator current waveforms in case 1), and
the stator current is more distorted. This will result in poor
performance of the drive system. Moreover, in case 2), the
stator current waveform quality is significantly modified, and
the ripples on rotor speed are significantly eliminated. It can
be said that the motor performance is improved by using the
modified modulation strategy.

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Xingwei Wang was born in Hubei, China, in 1980.

He received the B.S. and M.S. degrees in electrical
engineering from Huazhong University of Science
and Technology (HUST), Wuhan, China, in 2002
and 2005, respectively, where he is currently working
toward the Ph.D. degree.
From 2005 to 2007, he was with the Mindray
Medical International Limited, Shenzhen, China, as
a Research and Development Engineer. Since 2007,
he has been with the College of Electrical and Electronic Engineering, HUST, where he is currently a
Faculty Member. His research interests include matrix converter and ac motor
drive.

Hua Lin (M10) was born in Wuhan, Hubei, China,

in 1963. She received the B.S. degree in industrial
automation from the Wuhan University of Technology, Wuhan, in 1984, the M.S. degree in electrical
engineering from the Naval University of Engineering, Wuhan, in 1987, and the Ph.D. degree in
electrical engineering from Huazhong University of
Science and Technology (HUST), Wuhan, in 2005.
From 1987 to 1999, she was with the Department
of Electrical Engineering, Naval University of Engineering, as a Lecturer and Associate Professor. Since
1999, she has been with the College of Electrical and Electronic Engineering,
HUST, where she became a Full Professor in 2005. In October 2010, she was
a Visiting Scholar at the Center for Advanced Power Systems, The Florida
State University, Tallahassee. She has been engaged in research and teaching in
the field of power electronics and electric drive. Her research interests include
high-power high-performance ac motor drives and novel power converters and
their control. She has authored or coauthored more than 50 technical papers in
journals and conferences.
Dr. Lin was a recipient of the Second-Grade National Scientific and Technological Advance Prize of China in 1996 and 2003.

Hongwu She (S09) was born in Hubei, China, in

1982. He received the B.S. degree in electrical engineering from the Naval University of Engineering,
Wuhan, China, in 2004, the M.S. degree in electrical
engineering from Huazhong University of Science
and Technology (HUST), Wuhan, in 2007, where he
is currently working toward the Ph.D. degree.
His research interests include matrix converter and
induction motor drive.

Bo Feng was born in Hubei, China, in 1987. He

received the B.S. degree in electrical engineering
from Huazhong University of Science and Technology (HUST), Wuhan, China, in 2009, where he is
currently working toward the Ph.D. degree.
His research interests include matrix converter and
direct torque control.