1
Instantaneous Reactive Power Minimization and
Current Control for an Indirect Matrix Converter
under a Distorted AC-Supply
Marco Rivera, Member, IEEE, Jose Rodriguez, Fellow Member, IEEE, Jose R. Espinoza, Member, IEEE,
and Haitham Abu-Rub, Senior Member, IEEE
Abstract—This paper presents a current control scheme
with instantaneous reactive power minimization for an
indirect matrix converter. The strategy uses the commutation
state of the converter in the subsequent sampling time
according to an optimization algorithm given by a simple
cost function and the discrete system model. Using this
strategy, harmonics in the input current generated by the
resonance of the input filter are strongly reduced. Simulation
and experimental results with a laboratory prototype are
provided in order to validate the control scheme, and the
effects of a distorted source voltage and filter resonance are
analyzed.
Index Terms—AC-AC power conversion, Current control,
Matrix converter, Predictive control.
N OMENCLATURE
is
vs
ii
vi
io
vo
i∗o
vdc
idc
Cf
Lf
Rf
RL
LL
(α, β)
Source current
Source voltage
Input current
Input voltage
Load current
Load voltage
Output current reference
dc-link voltage
dc-link current
Filter capacitor
Filter inductor
Filter resistor
Load resistance
Load inductance
Stationary coordinates
[isA isB isC ]T
[vsA vsB vsC ]T
[iA iB iC ]T
[vA vB vC ]T
[ia ib ic ]T
[van vbn vcn ]T
[i∗a i∗b i∗c ]T
Copyright (c) 2012 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes
must be obtained from the IEEE by sending a request to pubspermissions@ieee.org.
This work was supported by the Centro Cientı́fico-Tecnológico de
Valparaı́so (CCTVal) N◦ FB0821, the Universidad Técnica Federico
Santa Marı́a, FONDECYT Project 1110794 and NPRP grant 4-0772-028 from the Qatar National Research Fund (a member of Qatar
Foundation). The statements made herein are solely the responsibility
of the authors.
M. Rivera and J. Rodriguez are with the Electronics Engineering Department, Universidad Técnica Federico Santa Marı́a, Av. España 1680,
Valparaı́so, 2390123 Chile, (e-mail: marco.rivera@usm.cl; jrp@usm.cl).
J. R. Espinoza is with the Department of Electrical Engineering, Universidad de Concepción, Concepción, (e-mail: jose.espinoza@udec.cl).
H. Abu-Rub is with Texas A&M University at Qatar, Doha, Qatar,
(e-mail: haitham.abu-rub@qatar.tamu.edu) .
I. I NTRODUCTION
Within the family of ac-ac converters it is possible to
distinguish two main groups: the converters with energy
storage or dc-link and those without. In the first group are
the current and voltage source topologies, with which it
is possible to obtain ac-ac conversion taking into consideration the presence of a capacitive or inductive dc-link,
respectively. These structures have been widely studied
and they are the converters used in the industry today.
In the group of ac-ac circuits without dc-link, different
topologies have been reported in the literature and are
classified into three main groups: the cycloconverter in a
wide power variety, the direct matrix converter (DMC)
and the indirect matrix converter (IMC), both in low
power range [1]. The cycloconverter is very common in
high power applications such as ball mills in mineral
processing and cement kilns. However, it is severely
limited in terms of output frequency with respect to the
input, because of the presence of a high harmonic content
caused by the commutations, which cannot be filtered by
the load inductance. The IMC [2], has been subject of
investigation for some time. One of the favorable features
of an IMC is the absence of a dc-link capacitor, which
allows for the construction of compact converters capable
of operating under adverse atmospheric conditions such as
extreme temperatures and pressures. These features have
been explored and are the main reasons why the matrix
converter family has been investigated for decades [3].
Compared to a DMC [1], the IMC features an easierto-implement and more secure commutation technique:
the dc-link zero current commutation [4]. Moreover, the
conventional IMC has bidirectional power flow capabilities and can be designed to have small sized reactive
elements in its input filter. These characteristics make the
IMC a suitable technology for high efficiency converters
for specific applications such as military, aerospace, wind
turbine generator systems, external elevators for building
construction and skin pass mills, as reported in [5]–[7].
Therefore, these advantages make up for the additional
cost of an IMC compared to conventional converters.
IMC uses complex pulse width modulation (PWM) and
space vector modulation (SVM) schemes to achieve the
goal of unity power factor and sinusoidal output current
[3], [8]–[21]. The subject of harmonics control in current
waveforms of three-phase converters is a very important
2
idc
Si1
vs
isA
N
Sr1
Rf
Lf
vi
Si5
A
Cf
ia
iB
B
iC
C
Sr4
RL LL
a
vdc > 0
ib
b
n
ic
c
Sr6
Sr2
Si4
Fig. 1.
Si3
Sr5
iA
isB
isC
Sr3
Si6
Si2
General topology of the indirect matrix converter.
and timely topic. In effect, in [22], the reduction of current
harmonics is achieved using the theory of instantaneous
active and reactive power. Since power converters have
a discrete nature, the application of predictive control
constitutes a promising and better-suited approach, as
compared to standard schemes that use mean values of the
variables. Model-based predictive strategy is a powerful
kind of control due to the simplicity and effectiveness
of its control algorithm [23]. Using an accurate model
of the system to be controlled, expressed in terms of
space state equations, an optimal switching state from a
power electronics converter can be determined to achieve
the best response relative to a control variable reference
input [24]–[29]. As the IMC is a finite commutation states
machine, the predictive control algorithm is simplified
to the prediction of every possible switching state and
the application of the best suited one to follow certain
references. Until today, most of predictive techniques
applied to matrix converters have been validated by considering a programmable ac-supply [4], [30], [31], but
in the following pages, a more realistic behavior will
be presented by considering an ac-supply with low-order
harmonics that introduce distortion in both source voltage
and currents.
II. I NDIRECT M ATRIX C ONVERTER M ODEL
A conventional IMC is shown in Fig. 1. For the rectifier
side, the dc-link voltage vdc is obtained as a function of
the rectifier switches and the input voltages vi as,
vdc = Sr1 − Sr4 Sr3 − Sr6 Sr5 − Sr2 vi , (1)
and input currents ii are defined as a function of the
rectifier switches and the dc-link current idc as,


Sr1 − Sr4
ii =  Sr3 − Sr6  idc .
(2)
Sr5 − Sr2
For the inverter side, dc-link current idc is determined
as a function of the inverter switches and the output
currents io as,
idc = Si1 Si3 Si5 io ,
(3)
and finally, output voltages are synthesized as a function
of the inverter switches and the dc-link voltage vdc as,


Si1 − Si4
vo =  Si3 − Si6  vdc .
(4)
Si5 − Si2
These equations correspond to the nine and eight valid
switching states for the rectifier and the inverter stages of
a conventional IMC, respectively, as reported in [4]. To
comply with the restrictions, the equations have no short
circuits in the input and no open lines in the output. Also
mandatory for a conventional IMC is to always have a
positive dc-link voltage; consequently, the nine rectifier
states reduce to only three valid states in every sampling
time Ts . In addition, the rectifier includes an Lf Cf filter
on the input side which is needed to prevent over-voltages
and to provide filtering of the high frequency components
of the input currents produced by the commutations and
the inductive nature of the load. The filter consists of a
second order system described by the following,
1
Rf
dis
=
(vs − vi ) −
is ,
dt
Lf
Lf
(5)
1
dvi
=
(is − ii ).
dt
Cf
(6)
The load model is obtained similarly. Assuming an
inductive-resistive load, as shown in Fig. 1, the following
equation describes the behavior of the load,
dio
1
RL
=
vo −
io .
dt
LL
LL
III. C ONTROL S CHEME
FOR THE
(7)
IMC
The control scheme for the IMC is represented in Fig.
2. The approach pursues the selection of the switching
state of the converter that leads the output currents closest
to their respective references at the end of the sampling
period. In addition, the instantaneous reactive power on
the line side of the rectifier must be minimized. And
finally, the dc-link voltage must always be positive [32].
First, the control objectives are determined and the
variables necessary to obtain the prediction model are
measured and calculated. The model of the system and
the measurements are used to predict the behavior of
the variables that will be controlled in the subsequent
3
IMC
vs
is
Rf
Lf
3
io
ii
3
vi
input filter
3
3
Cf
reactive
power
prediction
qsp
3
cost
function
optimization
3 3
vs is vi
qs∗
LL
load
io p
8
output
current
prediction
3
1
3
Fig. 2.
gate
signals
12
RL
3
vi
i∗o
3
io
Predictive current control scheme.
to produce the lowest error between the desired load
current io ∗ and the predicted load current response io
in k + 1 sampling time. Hence, if the dynamic model is
accurate, the control algorithm will always give the best
performance. This very simple and intuitive technique is
also highly precise in achieving its goal. A cost function
is then defined in order to be able to measure the error
between the reference and the predicted load current
response. Then, every sample period, this cost function
is computed for each possible commutation state on the
converter. The one with the smallest error is selected and
applied at the beginning of the next sample period. The
cost function can be as simple as,
△io = (i∗oα − ioα ) + (i∗oβ − ioβ ),
sampling time, for each of the valid switching states. The
predicted values are then used to evaluate a cost function
which deals with the control objectives. After that, the
valid switching state that produces the lowest value of
the cost function is selected for the next sampling period.
In order to compute the differential equations shown in
eq. (1)-(7), the general forward-difference Euler formula
is used as the derivative approximation to estimate the
value of each function one sample time in the future (the
variable’s predicted value).
A. Input Filter and Load Discrete Equations
Below are the predicted values of the input and output
side:
vi (k + 1)
vi (k)
vs (k)
=Φ
+Γ
, (8)
is (k + 1)
is (k)
ii (k)
where,
Φ∼
= eATs ,
Γ∼
=A
−1
(9)
(Φ − I2x2 )B.
(10)
Matrices A and B are given as follows:
0
1/Cf
A=
,
−1/Lf −Rf /Lf
(11)
B=
0
1/Lf
−1/Cf
0
.
The load current prediction can be obtained using a
forward Euler approximation in eq. (7) such as,
io (k + 1) = d1 vo (k) + d2 io (k),
(12)
where, d1 = Ts /LL and d2 = (1 − RL Ts /LL ) are
constants dependent on load parameters and Ts [30]. Note
that the currents is (k + 1) and io (k + 1) depend on the
switching state through eq. (2) and eq. (4), respectively.
B. Cost Function Definition
With the discretized system model, including the load,
the input filter and the IMC, the implementation of the
predictive algorithm is very straight forward. The goal of
this method is to always apply the IMC switching state
that gives the right voltage space vector vo , in order
(13)
where ioα and ioβ denote the load current in αβ coordinates for k + 1 sample time, and i∗oα and i∗oβ are their
respective references. An extra term can be added to this
cost function to minimize other parameters which should
be subject to control, such as the instantaneous reactive
power consumed by the IMC input along with the filter,
the common-mode voltage, the commutation losses, the
positive voltage in the dc-link, and so forth. The cost
function used to validate the control scheme in this paper
is below:
g = △i2o + λq △qs2 ,
(14)
which allows for control of the load current and the minimization of the instantaneous reactive power on the input
side. In eq. (14), λq is a weighting factor and △qs denotes
the error between the reference and predicted value of
the instantaneous reactive power in k + 1 sampling time,
expressed as follows:
△qs = qs∗ − (vsα isβ − vsβ isα ),
(15)
with vsα , vsβ , isα and isβ being the source voltages and
currents in αβ coordinates, respectively. The instantaneous reactive power reference is established as qs∗ = 0,
in order to have a unity power factor on the input side.
Noting that g = 0 (for an arbitrary λq ) gives perfect
tracking of the load current and unity power factor on
the source side, then by minimizing g, the optimum value
for commutation state is guaranteed. In practice, by the
appropriate selection of the weighting factor λq , a given
THD of the input and output currents is obtained. The
principal method for selecting the weighting factors has
been presented in [33].
C. Discrete Time Delay Error Compensation
Several measured and calculated variables are needed,
as well as the knowledge of the nine rectifier-side and the
eight inverter-side valid switching states, to compute the
control scheme algorithm. With these IMC rectifier and
inverter side valid states there are 72 possible switching
combinations that must be calculated to select the one
resulting in the least error in the cost function. If the
three valid rectifier-side switching states giving positive
dc-link voltage are calculated before the cost function
4
10
calculation routine, then only 24 switching combinations
must be computed. This results in saved computation
time, but the microelectronic controller still carries a
large numerical burden, causing an unwanted delay. The
variables measured are vs (k), is (k), vi (k), and io (k),
leaving the IMC input current and the IMC output voltage
as functions of the k th selected switching state, ii (k) and
vo (k) respectively, to be calculated. In order to counter
the delay error due to the discrete time computation, an
effective and simple method is implemented: the cost
function calculation for k + 2. First, the variables in k + 1
are predicted using the already applied switching state
S(k); then the variables to be controlled are predicted for
k+2 using the best switching state S(k+1) to get g(k+2)
to a minimum. The sample time should be sufficient to
begin the data acquisition at time t(k). The variables are
then computed for k + 1 using S(k), and the g(k + 2) is
calculated to select the optimum S(k + 1); this is all done
in the same time interval so the latter can be applied in
t(k + 1). vs (k + 1) is considered equal to vs (k) due to
its very small change in one sample time [4], [34].
a)
vsA
-10
0.4
0.41
5
b)
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.44
0.45
0.46
0.47
0.48
0.49
0.5
io
i∗o
0
-5
0.4
0.41
0.42
1000
c)
isA
0
0.43
qs
500
0
0.4
0.41
0.42
0.43
Time [s]
Fig. 3. Simulation results of current control without instantaneous
reactive power minimization. a) source voltage vsA [V/10] and current
isA [A]; b) output current ia and reference i∗a [A]; c) instantaneous
reactive power qs [VAR].
vsA
1
a)
0.5
0
0
IV. S IMULATION R ESULTS
Two different simulations were carried out to feasibility
probe the control method. Simulations with and without
instantaneous reactive power minimization were done in
order to evaluate the effect of introducing the instantaneous reactive power minimization in the control scheme.
The simulation parameters are established according to
the experimental setup available in our laboratory (they
are indicated in Appendix - Table I), and the sampling
period of the control algorithm was set at Ts = 20µs.
The outputs of the controller are used to deliver the gate
driver signals for the IGBTs. These outputs are directly
set by the control algorithm and no modulator is needed.
A. Simulation Results without Instantaneous Reactive
Power Minimization
First, the control scheme is simulated without including
the term that minimizes the instantaneous reactive power
on the input side of the system, so λq = 0 in eq. (14).
Results show that the input current in Fig. 3(a) has a
strong distortion. This is also clearly indicated in the
frequency spectrum of Fig. 4(b), where it is shown that the
resonance of the input filter is situated in fres = 650Hz,
according to the filter parameters, and with this it is
possible to observe 1.1%, 87.2% and 91.3% of the 3rd ,
5th and 7th harmonics, respectively. On the other hand,
the output currents follow the reference accurately as
indicated in Fig. 3(b). Fig. 4(c) shows the spectrum of the
load current ia . Fig. 3(c) shows the instantaneous reactive
power on the input side. Due to the strong distortion of the
source current, an unwanted high reactive power is present
on the input side. In this case, the ac-supply vsA is clean
with a sinusoidal waveform and no harmonic distortion
(Fig. 4(a)).
1
b)
100
200
isA
300
400
th
th
5
7
500
600
700
800
900
1000
fres
0.5
0
0
1
c)
100
200
300
200
300
400
500
600
700
800
900
1000
400
500
600
700
800
900
1000
ia
0.5
0
0
100
Frequency [Hz]
Fig. 4. Simulation results of current control without instantaneous
reactive power minimization. a) spectrum of source voltage [pu]; b)
spectrum of source current [pu]. c) spectrum of output current [pu].
B. Simulation Results with Instantaneous Reactive Power
Minimization
In the second case, the control strategy is evaluated
considering λq = 0.003 in eq. (14). Fig. 5(a) shows
an improved input behavior, with sinusoidal current in
correct phase with the input phase voltage, fulfilling
the condition of unitary power factor, with a reduced
harmonic distortion as indicated in Fig. 6(b). In this case,
it is possible to observe 0.3%, 2.7% and 1.2% of the 3rd ,
5th and 7th harmonics, respectively. On the output side,
the load current presents a good tracking with respect its
reference, Fig. 5(b). Fig. 5(c) shows the improvement in
the instantaneous reactive input power minimization, and
thus, the goal of the proposed predictive current control is
clearly achieved. It must be acknowledged that the main
advantage of the proposed control method is the simplicity
of implementation, since the controller does not need a
complex modulation unit. This can reduce the overall cost
of the entire system.
5
10
a)
vsA
-10
0.4
0.41
5
b)
isA
0
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.44
0.45
0.46
0.47
0.48
0.49
0.5
io
i∗o
0
-5
0.4
0.41
0.42
0.43
1000
c)
500
0
0.4
qs
0.41
0.42
0.43
Time [s]
Fig. 5. Simulation results of current control including instantaneous
reactive power minimization. a) source voltage vsA [V/10] and current
isA [A]; b) output current ia and reference i∗a [A]; c) instantaneous
reactive power qs [VAR].
vsA
1
a)
0.5
0
0
1
b)
100
200
300
400
500
600
700
800
900
1000
isA
0.5
fres
5th 7th
0
0
1
c)
a high harmonic distortion, as indicated in Fig. 8(b).
There, it is evident that according to the filter parameters,
the input filter resonance is situated at approximately
fres = 650Hz. As mentioned before, an input filter must
be added to assist the commutation of switching devices
and to mitigate against line-current harmonics. However,
the filter configuration which is shown in Fig. 1 presents
a resonance frequency, and it can be excited by the utility
due to the potential 5th and 7th harmonics in the ac-source
and also by the converter itself. Due to the available
ac-source in our laboratory, the input filter resonance is
reflected in the source voltage as seen in Fig. 7(a) and Fig.
8(a). Finally, as reported in [35]–[37], when a distortion
is present in the source voltage, the source current is
not sinusoidal. For all the aforementioned reasons, it is
necessary to include a term in the cost function that can
help overcome this problem. A summary of the total
harmonic distortion (THD) is presented in Appendix Table II.
100
200
300
200
300
400
500
600
700
800
900
1000
400
500
600
700
800
900
1000
ia
0.5
0
0
100
Frequency [Hz]
Fig. 6. Simulation results of current control with instantaneous reactive
power minimization. a) spectrum of source voltage [pu]; b) spectrum of
source current [pu]. c) spectrum of output current [pu].
V. E XPERIMENTAL R ESULTS
An IMC laboratory prototype designed and built by
Universidad Técnica Federico Santa Marı́a, thanks to the
support of the Power Electronics Systems Laboratory of
ETH in Zurich, was used for the experimental evaluation.
The converter features IGBTs of type IXRH40N120 for
the bidirectional switch, standard IGBTs with anti-parallel
diodes IRG4PC30UD for the inverter stage. The control
scheme was implemented in a dSPACE 1103, which is
connected to additional boards that include the FPGA for
the commutation sequence generation and the signal conditioning for the measurement of voltages and currents.
The parameters used in the experimental tests are given
in Appendix - Table I. The sampling period of the control
algorithm was set in Ts = 20µs.
A. Experimental Results without Instantaneous Reactive
Power Minimization
First, the control strategy is evaluated considering
λq = 0 in eq. (14). Fig. 7 shows the input current with
B. Experimental Results with Instantaneous Reactive
Power Minimization
It is known that most industrial applications require
unity power factor in the grid side. For this reason,
through the instantaneous reactive power minimization,
the system is forced to work with a unity power factor
on the input side. Fig. 9(a) shows the measured source
current and voltage of phase A, and Fig 9(b) shows the
reference and measured output current of phase a. As
expected, the source current fulfills the condition of unitary power factor showing an almost sinusoidal waveform
and, as a consequence, the instantaneous reactive power
is minimized. This is achieved by increasing the value of
the weighting factor from λq = 0 to λq = 0.003 which
has been empirically adjusted as explained in [33]. There,
first it is established as a value equal to zero in order
to prioritize the control of the output current; later it is
slowly increased with the aim to obtain unity power factor
in the input currents while maintaining a good behavior
on the output side. In Fig. 9(b) a very good tracking of
the load current ia with respect to its reference i∗a can be
seen. The improvement in the quality of the source current
is remarkable, because due to the mitigation of the input
filter resonance, a significant reduction of distortion is
apparent in Fig. 10(b) compared to Fig. 8(b). The same
effect is observed in the source voltage, Fig. 10(a). As
evident in Fig. 9(a), the source currents show a ripple
corresponding to the resonance frequency of the input
filter and the harmonic distortion of the ac-supply, as
observed in the spectrum of Fig. 10(a). The THD of
the source voltage and current and the output current are
indicated in Appendix - Table III.
C. The Problem with a Weak AC-supply
In Fig. 8(a) and 10(a), the spectrum of the source voltage vsA is shown in both cases, when λq = 0, Fig. 8(a),
and λq = 0.003, Fig. 10(a).
6
vsA
vsA
isA
isA
a)
a)
b)
b)
i∗a
i∗a
ia
ia
Fig. 7. Experimental results of current control without instantaneous
reactive power minimization. a) source voltage vsA [V] and current isA
[A]; b) output current ia [A].
1
Fig. 9. Experimental results current control including instantaneous
reactive power minimization. a) source voltage vsA [V] and current
isA [A]; b) output current ia [A].
vsA
1
vsA
a) 0.5
a) 0.5
fres
fres
0
0
0
1
200
400
600
800
0
1000
1
isA
b) 0.5
5th 7th
200
b) 0.5
fres
5th 7th
0
0
0
200
400
600
800
0
1000
1
1
400
600
800
1000
isA
200
fres
400
600
800
1000
400
600
800
1000
ia
ia
c) 0.5
c) 0.5
0
0
0
200
400
600
800
1000
Frequency [Hz]
0
200
Frequency [Hz]
Fig. 8. Experimental results of current control without instantaneous
reactive power minimization. a) spectrum of source voltage [pu]; b)
spectrum of source current [pu]; c) spectrum of output current [pu].
Fig. 10. Experimental results of current control including instantaneous
reactive power minimization. a) spectrum of source voltage [pu]; b)
spectrum of source current [pu]; c) spectrum of output current [pu].
In the first case, the ac-source was highly distorted
due to the high input current distortion and the low-order
harmonics of the grid. This phenomenon occurs because
a three-phase variac as the ac-supply is used. The variac
behaves like a weak ac-source for the system, due to the
associated inductance with the autotransformer connection. Thanks to the minimization of the instantaneous
reactive power, the harmonic distortion of the source
voltage is decreased from a THD of 36.48% to 14.82%.
In Fig. 7(a) a distorted source current with a THD of
66.07% was observed, but when the instantaneous reactive
power is minimized, a THD of 21.03% is obtained. The
load current THD was 8.80% in the first case, but when
the weighting factor λq is considered as λq = 0.003, an
output current with a THD of 8.54% is observed.
The resonance of the input filter is still a major concern
that directly affects the selection of the design parameters
and the modulation method. In Fig. 11, the predictive
controller is enhanced by including an active damping
scheme in order to mitigate the potential resonances in the
input filter. The method is based on a virtual resistor that
damps the Lf Cf resonance, improving the performance
of the system as indicated in [38]–[40]. By considering
this method, the source voltage and current THD are
13.67% and 22.81%, respectively, with a THD of 7.49%
in the load current.
VI. C ONCLUSION
A current control with instantaneous reactive power
minimization for an indirect matrix converter has been
presented in this paper. The control scheme uses the
predicted values of the input and output currents to
evaluate the best-suited converter state considering the
output current error and the input power factor.
Our experimental results indicate that the presented
strategy provides good tracking of the output current to
its reference and at the same time minimizes the instantaneous reactive power on the input side. In addition,
the strategy presented in this paper produces a drastic
reduction in the input current harmonics generated by
the resonance of the input filter, which is usually a
major problem in matrix converters. The method also
presents drawbacks, as the cost function is explicitly
solved for each switching state. This can be a problem
7
R EFERENCES
vsA
isA
a)
b)
i∗a
ia
Fig. 11. Experimental results with active damping implementation. a)
source voltage vsA [V] and current isA [A]; b) output current ia [A].
if a slow controller is used, as a higher sampling time
could increase the harmonic distortion in the currents.
The ac-supply and the filter resonance have an important
influence on the behavior of the source current and better
results can be expected by optimizing the input filter, by
adding active damping but also with a clean ac-supply.
A PPENDIX
The parameters of the simulation and experimental
setup are indicated in Table I and the THD information
is detailed in Table II and Table III.
TABLE I
E XPERIMENTAL SETUP PARAMETERS
Variables
Ts
Vs
fs
Lf
Cf
Rf
RL
LL
fo
λq
Description
Sampling time
Supply phase voltage
Supply frequency
Input filter inductance
Input filter capacitance
Input filter resistance
Load resistance
Load inductance
Output frequency
Weighting factor
Value
20 [µs]
90 [V]
50 [Hz]
5.9 [mH]
10 [µF]
0.5 [Ω]
10 [Ω]
15 [mH]
50 [Hz]
0; 0.003
TABLE II
E XPERIMENTAL THD RESULTS WITH λq = 0
Harmonic
THD
3th
5th
7th
vsA
36.48%
2.22%
3.11%
2.82%
isA
66.07%
12.25%
6.40%
8.55%
ia
8.80%
0.20%
0.23%
0.31%
TABLE III
E XPERIMENTAL THD RESULTS WITH λq = 0.003
Harmonic
THD
3th
5th
7th
vsA
14.82%
1.57%
4.90%
2.21%
isA
21.03%
10.68%
2.25%
5.21%
ia
8.54%
0.97%
1.41%
1.15%
[1] P. Wheeler, J. Rodriguez, J. Clare, L. Empringham, and
A. Weinstein, “Matrix converters: a technology review,” Industrial
Electronics, IEEE Transactions on, 2002.
[2] T. Wijekoon, C. Klumpner, P. Zanchetta, and P. Wheeler, “Implementation of a hybrid ac-ac direct power converter with unity
voltage transfer,” Power Electronics, IEEE Transactions on, 2008.
[3] J. Kolar, T. Friedli, F. Krismer, and S. Round, “The essence
of three-phase ac-ac converter systems,” Power Electronics and
Motion Control Conference (EPE-PEMC), Poznan, Poland, 2008.
[4] P. Correa, J. Rodriguez, M. Rivera, J. Espinoza, and J. Kolar,
“Predictive control of an indirect matrix converter,” Industrial
Electronics, IEEE Transactions on, 2009.
[5] P. Zanchetta, P. Wheeler, J. Clare, M. Bland, L. Empringham, and
D. Katsis, “Control design of a three-phase matrix-converter-based
ac-ac mobile utility power supply,” Industrial Electronics, IEEE
Transactions on, 2008.
[6] S. Lopez Arevalo, P. Zanchetta, P. Wheeler, A. Trentin, and
L. Empringham, “Control and implementation of a matrixconverter-based ac ground power-supply unit for aircraft servicing,” Industrial Electronics, IEEE Transactions on, 2010.
[7] E. Yamamoto, T. Kume, H. Hara, T. Uchino, J. Kang, and H. Krug,
“Development of matrix converter ans its applications in industry,”
Annual Conference of the IEEE Industrial Electronics Society
(IECON), Porto, Portugal, 2009.
[8] J. Rodriguez, M. Rivera, J. Kolar, and P. Wheeler, “A review of
control and modulation methods for matrix converters,” Industrial
Electronics, IEEE Transactions on, vol. 59, no. 1, pp. 58 –70, jan.
2012.
[9] X. Lu, K. Sun, G. Li, and L. Huang, “Analysis and control of input
power factor in indirect matrix converter,” Annual Conference of
the IEEE Industrial Electronics Society (IECON), Porto, Portugal,
2009.
[10] S. Ahmed, A. Iqbal, H. Abu-Rub, J. Rodriguez, C. Rojas, and
M. Saleh, “Simple carrier-based pwm technique for a three-tonine-phase direct ac-ac converter,” Industrial Electronics, IEEE
Transactions on, vol. 58, no. 11, pp. 5014 –5023, nov. 2011.
[11] P. Kiatsookkanatorn and S. Sangwongwanich, “A unified pwm
method for matrix converters and its carrier-based realization
using dipolar modulation technique,” Industrial Electronics, IEEE
Transactions on, vol. 59, no. 1, pp. 80 –92, jan. 2012.
[12] Z. Yan, M. Jia, C. Zhang, and W. Wu, “An integration spwm
strategy for high-frequency link matrix converter with adaptive
commutation in one step based on de-re-coupling idea,” Industrial
Electronics, IEEE Transactions on, vol. 59, no. 1, pp. 116 –128,
jan. 2012.
[13] M. Jussila and H. Tuusa, “Comparison of simple control strategies
of space-vector modulated indirect matrix converter under distorted
supply voltage,” Power Electronics, IEEE Transactions on, 2007.
[14] R. Pena, R. Cardenas, E. Reyes, J. Clare, and P. Wheeler, “A
topology for multiple generation system with doubly fed induction
machines and indirect matrix converter,” Industrial Electronics,
IEEE Transactions on, 2009.
[15] M. Y. Lee, P. Wheeler, and C. Klumpner, “Space-vector modulated
multilevel matrix converter,” Industrial Electronics, IEEE Transactions on, 2010.
[16] R. Cardenas-Dobson, R. Pena, P. Wheeler, and J. Clare, “Experimental validation of a space vector modulation algorithm for fourleg matrix converters,” Industrial Electronics, IEEE Transactions
on, vol. PP, no. 99, pp. 1 –1, 2010.
[17] T. Friedli and J. Kolar, “Comprehensive comparison of threephase ac-ac matrix converter and voltage dc-link back-to-back
converter systems,” International Power Electronics Conference
(IPEC), Sapporo, Japan, 2010.
[18] J. Kolar, F. Schafmeister, S. Round, and H. Ertl, “Novel threephase ac-ac sparse matrix converters,” Power Electronics, IEEE
Transactions on, 2007.
[19] X. Wang, H. Lin, H. She, and B. Feng, “A research on space vector
modulation strategy for matrix converter under abnormal inputvoltage conditions,” Industrial Electronics, IEEE Transactions on,
vol. 59, no. 1, pp. 93 –104, jan. 2012.
[20] X. Lie, J. Clare, P. Wheeler, L. Empringham, and L. Yongdong,
“Capacitor clamped multilevel matrix converter space vector modulation,” Industrial Electronics, IEEE Transactions on, vol. 59,
no. 1, pp. 105 –115, jan. 2012.
8
[21] H. She, H. Lin, B. He, X. Wang, L. Yue, and X. An, “Implementation of voltage-based commutation in space-vector-modulated
matrix converter,” Industrial Electronics, IEEE Transactions on,
vol. 59, no. 1, pp. 154 –166, jan. 2012.
[22] S. Mikkili and A. Panda, “Instantaneous active and reactive power
and current strategies for current harmonics cancellation in 3-ph
4wire shaf with both pi and fuzzy controllers,” Energy and Power
Engineering, 2011.
[23] S. Kouro, P. Cortes, R. Vargas, U. Ammann, and J. Rodriguez,
“Model predictive control, a simple and powerful method to control power converters,” Industrial Electronics, IEEE Transactions
on, 2009.
[24] P. Correa, J. Rodriguez, I. Lizama, and D. Andler, “A predictive control scheme for current-source rectifiers,” Industrial
Electronics, IEEE Transactions on, 2009.
[25] P. Cortes, G. Ortiz, J. Yuz, J. Rodriguez, S. Vazquez, and L. Franquelo, “Model predictive control of an inverter with output lc filter
for ups applications,” Industrial Electronics, IEEE Transactions
on, 2009.
[26] H. Miranda, P. Cortes, J. Yuz, and J. Rodriguez, “Predictive
torque control of induction machines based on state-space models,”
Industrial Electronics, IEEE Transactions on, 2009.
[27] M. Preindl, E. Schaltz, and P. Thφgersen, “Switching frequency
reduction using model predictive direct current control for high
power voltage source inverters,” Industrial Electronics, IEEE
Transactions on, vol. PP, no. 99, pp. 1 –1, 2010.
[28] J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, and C. Rojas,
“Predictive torque and flux control of an induction machine fed
by an indirect matrix converter with reactive power minimization,”
International Symposium on Industrial Electronics (ISIE), Bari,
Italy, 2010.
[29] M. Rivera, J. Rodriguez, P. Wheeler, C. Rojas, A. Wilson, and
J. Espinoza, “Control of a matrix converter with imposed sinusoidal source currents,” Industrial Electronics, IEEE Transactions
on, vol. 59, no. 4, pp. 1939 –1949, april 2012.
[30] S. Muller, U. Ammann, and S. Rees, “New time-discrete modulation scheme for matrix converters,” Industrial Electronics, IEEE
Transactions on, 2005.
[31] R. Vargas, J. Rodriguez, U. Ammann, and P. Wheeler, “Predictive
current control of an induction machine fed by a matrix converter
with reactive power control,” Industrial Electronics, IEEE Transactions on, 2008.
[32] J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, and C. Rojas,
“Predictive current control with reactive power minimization in an
indirect matrix converter,” International Conference on Industrial
Technology (ICIT), Viña del Mar, Chile, 2010.
[33] P. Cortes, S. Kouro, B. La Rocca, R. Vargas, J. Rodriguez,
J. Leon, S. Vazquez, and L. Franquelo, “Guidelines for weighting
factors design in model predictive control of power converters and
drives,” International Conference on Industrial Technology (ICIT),
Gippsland, Australia, 2009.
[34] P. Cortes, J. Rodriguez, C. Silva, and A. Flores, “Delay compensation in model predictive current control of a three-phase inverter,”
Industrial Electronics, IEEE Transactions on, vol. 59, no. 2, pp.
1323 –1325, feb. 2012.
[35] D. Casadei, G. Serra, and A. Tani, “A general approach for the
analysis of the input power quality in matrix converters,” Power
Electronics, IEEE Transactions on, vol. 13, no. 5, pp. 882 –891,
1998.
[36] F. Blaabjerg, D. Casadei, C. Klumpner, and M. Matteini, “Comparison of two current modulation strategies for matrix converters
under unbalanced input voltage conditions,” Industrial Electronics,
IEEE Transactions on, vol. 49, no. 2, pp. 289 –296, 2002.
[37] A. Timbus, P. Rodriguez, R. Teodorescu, M. Liserre, and F. Blaabjerg, “Control strategies for distributed power generation systems
operating on faulty grid,” International Symposium on Industrial
Electronics (ISIE), Montreal, Canada, 2006.
[38] M. Rivera, P. Correa, J. Rodriguez, I. Lizama, and J. Espinoza,
“Predictive control of the indirect matrix converter with active
damping,” International Power Electronics and Motion Control
Conference (IPEMC), Wuhan, China, 2009.
[39] M. Rivera, C. Rojas, J. Rodriguez, P. Wheeler, B. Wu, and
J. Espinoza, “Predictive current control with input filter resonance
mitigation for a direct matrix converter,” Power Electronics, IEEE
Transactions on, vol. 26, no. 10, pp. 2794 –2803, 2011.
[40] M. Rivera, J. Rodriguez, B. Wu, J. Espinoza, and C. Rojas, “Current control for an indirect matrix converter with filter resonance
mitigation,” Industrial Electronics, IEEE Transactions on, vol. 59,
no. 1, pp. 71 –79, 2012.
Marco Rivera (S’09 M’10) received his B.Sc.
in Electronics Engineering and M.Sc. in Electrical Engineering from the Universidad de
Concepción, Chile in 2007 and 2008, respectively. In 2011, he received his PhD degree
at the Department of Electronics Engineering,
Universidad Técnica Federico Santa Marı́a, in
Valparaı́so, Chile.
His research interests include direct and
indirect matrix converters, predictive and digital controls for high-power drives, four-leg
converters and development of high performance control platforms
based on Field-Programmable Gate Arrays. Dr. Rivera was awarded
a scholarship from the Marie Curie Host Fellowships for Early Stage
Research Training in Electrical Energy Conversion and Conditioning
Technology at University College Cork, Ireland in 2008. During January
and February of 2010 he was a visiting PhD student of the Electrical
and Computer Engineering Department at Ryerson University, Canada,
where he worked on predictive control applied on four-leg inverters.
He was also a visiting PhD student at the Departamento de Ingenierı́a
Eléctrica y Computacional of ITESM, Monterrey, Mexico, where he
worked on experimental aspects of a Double Fed Induction Generator Indirect Matrix Converter System. Between September and November
of 2011 he was a visiting researcher in the Laboratoire PLAsma
et Conversion d’Energie (LAPLACE) at the Université de Toulouse
in France. Currently he is working in a Post Doctoral position at
Universidad Técnica Federico Santa Marı́a, Chile.
Jose Rodriguez (M’81-SM’94-F’10) Received
the Engineer degree in electrical engineering
from the Universidad Técnica Federico Santa
Marı́a (UTFSM), Valparaı́so, Chile, in 1977
and the Dr.-Ing. degree in electrical engineering from the University of Erlangen, Erlangen,
Germany, in 1985. He has been with the Department of Electronics Engineering, Universidad Técnica Federico Santa Marı́a since 1977,
where he is currently full Professor and Rector.
He has co-authored more than 300 journal
and conference papers. His main research interests include multilevel
inverters, new converter topologies, control of power converters, and
adjustable-speed drives.
Prof. Rodriguez is Associate Editor of the IEEE T RANSACTIONS
ON P OWER E LECTRONICS and IEEE T RANSACTIONS ON I NDUSTRY
E LECTRONICS since 2002. He received the Best Paper Award from the
IEEE T RANSACTIONS ON I NDUSTRY E LECTRONICS in 2007, the Best
Paper Award from the IEEE I NDUSTRIAL E LECTRONICS M AGAZINE
in 2008 and Best Paper Award from the IEEE T RANSACTIONS ON
P OWER E LECTRONICS in 2010. Dr. Rodrguez is member of the Chilean
Academy of Engineering and Fellow of the IEEE
9
Jose R. Espinoza (S’92-M’97) received the
Eng. degree in electronic engineering and the
M.Sc. degree in electrical engineering from
the University of Concepción, Concepción,
Chile, in 1989 and 1992, respectively, and the
Ph.D. degree in electrical engineering from
Concordia University, Montreal, QC, Canada,
in 1997.
Since 2006, he has been a Professor in the
Department of Electrical Engineering, Universidad de Concepción, where he is engaged in
teaching and research in the areas of automatic control and power
electronics. He has authored and coauthored more than 100 refereed
journal and conference papers.
Prof. Espinoza is currently an Associate Editor of the IEEE T RANS ACTIONS ON I NDUSTRY E LECTRONICS and IEEE T RANSACTIONS ON
P OWER E LECTRONICS .
Haitham Abu-Rub (M99SM07) received the
M.Sc. degree in electrical engineering from the
Gdynia Maritime University, Poland, in 1990
and the Ph.D. degree from Gdansk University
of Technology, Poland, in 1995, in which he
was later on hired as assistant professor. For
eight years, he has been hired as an Assistant
Professor and as an Associate Professor at
Birzeit University, Palestine. For four years, he
has been appointed the Chairman of Electrical
Engineering Department at the same university
for four years. He is currently an Associate Professor with Texas
A&M University at Qatar. His main research interests include electric drives and power electronics. Dr. Abu-Rub is the recipient of
many prestigious international awards, such as the American Fulbright
Scholarship (at Texas A&M University), the German Alexander von
Humboldt Fellowship (at the University of Wuppertal), the German
DAAD Scholarship (at Bochum University), the British Royal Society
Scholarship (at Southampton University), and others. Dr. Abu-Rub
has published/accepted more than one hundred and forty journal and
conference papers.