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CHAPTER 1
INTRODUCTION
In today’s world many commercial and industrial application use various
types of power converters like AC- DC converter, AC-AC converter, DC-DC
converter, DC-AC converter due to their cost effectiveness, small sizes and their
efficiency. Even though it offered many advantages many industries found that
one power converter cannot be used for other that is a DC-DC converter cannot be
used as an AC-AC converter. Due to this disadvantage many research has been
conducted to produce a universal converter which can be used as a particular
converter depending on the application needed. That is a converter which can be
used as DC-DC converter can also be used as AC-AC converter, AC-DC
converter, DC-AC converter with same hardware. This research yielded to
creation of ‘MATRIX CONVERTER’ which can be called as universal converter.
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CHAPTER 2
MATRIX CONVERTER
2.1 What is matrix converter?
To put it simple words a Matrix Converter is a converter having m x n
bidirectional switches where m is the number of phases of voltage source and n is
the number of phase of load which can act as a four in one converter or in other
words a universal converter.
2.2 History
The concept of the matrix converter was started in late 1950’s but first publication
was in the year 1976.The first official publication of this converter topology was
in the year 1980, and the scientist behind this were Venturini and Alesina. They
were the first who introduced the name “Matrix Converter”. In the beginning
1980s, people were so enthusiast that developed several control and modulation
methods but this enthusiasm soured up at the end of the 1980s citing the following
as the reason
1. The commutation problem occurred while turning on and off switches
2. Over voltages can be attributed to the breaking of inductive paths while
switching.
3. Over currents can be attributed to the shorting of voltage sources while
switching.
4. The high count of semiconductors switches.
During the 1990s, scientist discovered several intelligent commutation techniques,
powerful processors thereby avoiding any danger to the semiconductor switches.
This technology advancement gave rebirth to matrix converter and from that time
onwards there was no looking back.
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CHAPTER 3
OPERATION OF MATRIX CONVERTER
3.1 Operation of a matrix converter
Operation of a matrix converter is based on opening and closing of m x n
bidirectional switches. As 3X3 matrix converter is common we will discuss the
operation of 3X3 matrix converter.
Figure 3.1 shows a typical 3X3 matrix converter. Since we are using 3X3
matrix converter there will be 9 bidirectional switches. Each switch can either be
turned ON or OFF that is two possible state for each switch. This gives 512
possible states (2 raised to the power 9). Out of these 512 possible states only 27
states can be used by observing the following two conditions.
1. As a matrix converter is fed by a voltage source no two switches in same
column must be closed at the same time. In simple words no two or more
phases must be shorted at the same time because it produces large current.
2. And as load typically being an inductive nature there should not be open
circuit that is inductive path should not be broken at any point of time
because breaking of inductive path produces large voltage which can cause
serious damage.
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Fig 3.1: Typical 3X3 matrix converter
These 27 states can be grouped into three namely Group I, Group II, and
Group III.
3.1.1 Group I
Group I consists of six combinations when each output (load) phase is
connected to a different input phase. Table 3.1 shows how the switches are
operated. Smn=1 implies that switch connecting m phase voltage source and n
phase load is turned on.
SAa SAb SAc SBa SBb SBc SCa SCb SCc Vab Vbc Vca
1 0 0 0 1 0 0 0 1 VAB VBC VCA
1 0 0 0 0 1 0 1 0 VAC VCB VBA
0 1 0 1 0 0 0 0 1 VBA VAC VCB
0 0 1 1 0 0 0 1 0 VBC VCA VAB
0 0 1 0 1 0 1 0 0 VCB VBA VAC
0 1 0 0 0 1 1 0 0 VCA VAB VBC
Table 3.1: Three-phase/three-phase matrix converter switching combinations for GROUP I
3.1.2 Group II
In Group II, there a total of 18 combinations which are divided into three
subgroups, each having six combinations with two output (load) phases short-
circuited (connected to the same input phase).
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GROUP SAa SAb SAc SBa SBb SBc SCa SCb SCc Vab Vbc Vca
II a
1 0 0 0 1 1 0 0 0 VAB 0 VBA
1 0 0 0 0 0 0 1 1 VAC 0 VCA
0 1 1 1 0 0 0 0 1 VBA 0 VAB
0 0 0 1 0 0 0 1 1 VBC 0 VCB
0 0 0 0 1 1 1 0 0 VCB 0 VBC
0 1 1 0 0 0 1 0 0 VCA 0 VAC
II b
1 0 1 0 1 0 0 0 0 VAB VBA 0
1 0 1 0 0 0 0 1 0 VAC VCA 0
0 1 0 1 0 1 0 0 0 VBA VAB 0
0 0 0 1 0 1 0 1 0 VBC VCB 0
0 0 0 0 1 0 1 0 1 VCB VBC 0
0 1 0 0 0 0 1 0 1 VCA VAC 0
II c
1 1 0 0 0 0 0 0 1 0 VAC VCA
1 1 0 0 0 1 0 0 0 0 VAB VBA
0 0 0 1 1 0 0 0 1 0 VBC VCB
0 0 1 1 1 0 0 0 0 0 VBA VAB
0 0 1 0 0 0 1 1 0 0 VCA VAC
0 0 0 0 0 1 1 1 0 0 VBC VBC
Table 3.2: Three-phase/three-phase matrix converter switching combinations for GROUP II
3.1.3 Group III
Group III includes three combinations with all output (load) phases short-
circuited.
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SAa SAb SAc SBa SBb SBc SCa SCb SCc Vab Vbc Vca
1 1 1 0 0 0 0 0 0 0 0 0
0 0 0 1 1 1 0 0 0 0 0 0
0 0 0 0 0 0 1 1 1 0 0 0
Table 3.3: Three-phase/three-phase matrix converter switching combinations for GROUP III
These 27 states can also be represented in the form of a diagram shown in
Figure 3.2.
Fig 3.2: Switching matrix- Diagram representation
CHAPTER 4
CONTROLLING
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4.1 Basics
Before moving into controlling some terms, notation and theory which are
particularly useful for understanding will be discussed in the following sections
4.1.1 Terms
Input Displacement Angle (IDA)
It is the Angular displacement between the fundamental component of the AC line
current and associated line to neutral voltage
Input Displacement Factor (IDF)
It is the Cosine of IDA
IDF = Cos(IDA) (4.1)
❖ Input Power Factor (IPF)
It the ratio of product of Rms value of fundamental component of AC line current
and IDF to Rms value of source current.
IPF=Rms value of the fundamental component of the AC line current * IDFRms value of the source current
(4.2)
4.1.2 Notations and theory
The matrix converter is used in such a way that with a given set of input
three-phase voltages, any desired set of three-phase output voltages can be
synthesized (Practical limitations apply) by adopting a suitable switching strategy.
The converter connects any input phase (A, B,and C) to any output phase
(a, b, and c) at any instant. When connected, the voltages Van, Vbn, Vcn at the
output terminals are related to the input voltages VAo, VBo, VCo.
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[V an
V bn
V cn]=[S Aa SBa SCa
S Ab SBb SCb
S Ac SBc SCc] [V Ao
V Bo
V Co] (4.3)
For a balanced linear star-connected load at the output terminals, the input phase
currents are related to the output phase currents by
[ iA
iB
iC]=[S Aa SBa SCa
S Ab SBb SCb
S Ac SBc SCc] [ia
ib
ic] (4.4)
4.2 Need for controlling
The matrix converter should be controlled using a specific and appropriately
timed sequence of the values of the switching variables, which will result in
balanced output voltages having the desired frequency and amplitude, even while
the input currents are balanced and in phase (for unity IDF) or at an arbitrary
angle (for controllable IDF) with respect to the input voltages.
4.3 Control strategies
The control methods employed are quite complex in the case of matrix converter.
Of the many methods proposed for independent control of the output voltages and
input currents, two methods are of widely in use are:
❖ The Venturini method which is a mathematical approach of transfer
function analysis
❖ The Space Vector Modulation (SVM) approach
4.3.1 The Venturini method
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The venturini method [2] can be explained as given a set of three-phase input
voltages with constant amplitude Vi and frequency fi=Ѡi/2*∏ , calculate a
switching function involving the duty cycles of each of the nine bidirectional
switches such that it generates the three-phase output voltages by sequential
piecewise sampling of the input waveforms which satisfy the following
conditions: Output voltages must follow a predetermined set of reference or target
voltage waveforms. With a three-phase load connected, a set of input currents I i ,
and angular frequency Ѡi should be in phase for unity IDF or at a specific angle
for controlled IDF.A transfer function approach is employed to achieve the above
mentioned features by relating the input and output voltages and the output and
input currents shown in equation (4.5) and (4.6) .Where the elements of the
modulation matrix mij(t) ( i,j=1, 2, 3) represent the duty cycles of a switch
connecting output phase i to input phase j within a sample switching interval.
[V o 1(t)V o 2(t)V o 3(t)]=[m11(t) m12(t) m13( t)
m21(t ) m22(t) m23( t)m31(t ) ¿ ¿m33(t)] [
V i 1(t)V i 2(t)V i 3(t)] (4.5)
[ ii 1(t )ii 2(t )ii 3(t )]=[m11(t ) m21(t) m31( t)
m12(t ) m22(t) m32( t)m13( t) ¿ ¿m33(t)] [
io1(t )io2(t )io3(t )] (4.6)
The elements of mij(t) are limited by the constraints shown in equation
(4.7)
0 ≤ mij(t) ≤ 1 and mi1(t) + mi2(t) + mi3(t) =1 (i=1,2,3) (4.7)
Skipping the derivation [2] and simplified expression for mij(t) IDF of
unity with Vom ≤0.866 *Vim [4] is given by equation (4.9):
q=V omV im
(4.8)
mij=13¿ (4.9)
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Where i,j=1,2,3
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CHAPTER 5
ADVANTAGES AND DISADVANTAGES
5.1 Advantages
Since there is no DC link as in common converters, the matrix converter
can be built as a full-silicon structure. However, a mains filter is necessary to
smooth the pulsed currents on the input side of the matrix converter. Using a
sufficiently high pulse frequency, the output voltage and input current both are
shaped sinusoidal. The matrix converter is an alternative to an inverter drive for
three-phase frequency control.
The matrix converter has several advantages over traditional rectifier-
inverter type power frequency converters. It provides sinusoidal input and output
waveforms, with minimal higher order harmonics and no sub harmonics; it has
inherent bidirectional energy flow capability; the input power factor can be fully
controlled.
Last but not least, it has minimal energy storage requirements, which
allows to get rid of bulky and lifetime- limited energy-storing capacitors.
5.2 Disadvantages
The matrix converter has also some disadvantages. First of all it has a
maximum input output voltage transfer ratio limited to ≈ 87 % for sinusoidal input
and output waveforms. It requires more semiconductor devices than a
conventional AC-AC indirect power frequency converter, since no monolithic bi-
directional switches exist and consequently discrete unidirectional devices,
variously arranged, have to be used for each bi-directional switch.
In addition to above this control strategy involved is quite complex when
compared to other converters and at high frequency the non-availability of a fully
controlled bidirectional high-frequency switch integrated in a silicon chip. Finally,
it is particularly sensitive to the disturbances of the input voltage system.
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CHAPTER 6
APPLICATIONS AND PRODUCTS
6.1 Application
The low voltage transfer ratio is often seen as the biggest
disadvantage of a matrix converter if a like-for-like replacement
for an industrial drive is required. Some attempts to address the
problem on an over modulation basis have been performed, but
inevitably, input power quality is sacrificed in favour of output
drive capability. Work based on minor topology changes,
particularly using the indirect matrix converter, has been
proposed at the cost of increased complexity and size.
In applications where the load motor in the drive system
can be specified and appropriately selected, the voltage transfer
ratio limitation is not an issue.In motor drive where the converter
is integrated with or sold with the motor, clearly, the matrix
converter should have a size and a weight advantage over
competing VSI technologies.
The potential size and weight advantages of the matrix
converter and the elevated temperature capability due to the
lack of dc-link components lend themselves to aircraft
applications. Several prototype aircraft actuator projects have
been reported in the literature. Collaboration with Smiths
Aerospace led to the creation of a 7-kW matrix converter used to
drive a 10 000-r/min PMSM integrated into an electro hydrostatic
actuator. The matrix converter was chosen in this application
because of the ability to be driven from a frequency wild supply.
This prototype was based on the Infineon Economac matrix
converter module. Collaboration with Smiths Aerospace, which
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later became GE Aviation, resulted in the development of both a
20-kW integrated matrix converter and a 20-kW 10 000-r/min
PMSM to create a fully integrated rudder actuator.
An indirect matrix converter drive was developed in
collaboration with MOOG for an EMA application .The same
requirements for a variable frequency supply with aircraft power
quality specifications were desired as per the previous two
examples. The main difference in this project was the
requirement to prevent the regeneration of energy back to the
supply. This process can be more easily achieved using an
indirect matrix converter using a suitable dissipation circuit
connected to the standard protective clamp circuit.
A deep sea remotely operated vehicle (ROV) matrix
converter drive application was the subject of research for some
time. The extreme pressure experienced by ROVs and the lack of
large and fragile DC-link components were the reason that the
matrix converter was chosen as a potential topology for the
application. Research into the effects of high atmospheric
pressure on the constituent parts of typical drive systems was
carried out at 300 bar. The paper also investigates the use of
observer-based sensor less control of a PMSM using the matrix
converter.
The matrix converter has also been applied to drive the
rotor circuit of a doubly fed induction generator for wind turbine
applications using direct and indirect matrix converters.
This technique has the advantage that a relatively low
power four-quadrant power converter can be used to control a
high-power generator system. Research into the stability of such
systems and the effects of rotor-side harmonics in a similar
system
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A reduced matrix converter (three phase to two phase) was
used to control a wind turbine generator and drive a single phase
transformer which was then connected through an AC rectifier to
a dc transmission line.
Further work into a novel matrix converter topology to
allow the coupling of energy generation resources and the grid
was recently presented research topic.
Matrix converters are finding application in the power supply
generation area. Instead of the typical motor drive application,
an output filter is used in order to provide a voltage source of the
desired amplitude and frequency. This concept allows fixed
voltage and frequency power supplies to be implemented and
driven from variable frequency diesel generators. The operation
of the generator at the optimum speed, particularly under lightly
loaded conditions, can offer increased fuel efficiency.
The application of the matrix converter transforms not only
the input frequency and voltage but also the number of phases.
Since the matrix converter circuit is modular, any number of
input and output phases can be implemented.
An interesting use of a matrix converter using only nine
unidirectional switches was used to drive an induction machine. A
dc offset was demanded for each of the output phases to enable
a sinusoidal component to be present at the output of the
converter. Two methods to then remove the effect of the
converter output dc component were suggested in order to
maintain the performance of the induction machine.
The main advantage of this technique was that the number
of IGBTs and diodes is reduced to 50% of those required by a
conventional three-phase to three-phase matrix converter and
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that, since the current can only flow in one direction, the current
commutation process becomes inherently safe.
Another application of a unidirectional matrix converter was to
drive a five-phase fault-tolerant brushless dc (BLDC) motor for
the pump in an electro hydrostatic actuator.
A unidirectional matrix converter was also used to drive a
switched reluctance motor (SRM). The power circuit consists of
six output phases. Each winding on the SRM is galvanically
isolated from the others and is driven by two of the output
phases of the converter. In one of these output phases, the
devices are arranged such that current can only flow in one
direction from the supply to the motor, and in the other phase,
current can flow from the motor winding to the supply. The
switching of the converter is then modulated to deliver the
desired output voltage and therefore control the current in the
motor.
6.2 Products in the market
To date, the only drive manufacturers to offer matrix
converter products are Yaskawa and Fuji Electric Systems. Both
series are aimed at the general drives market with emphasis on
the energy saving potential with the inherent regeneration
capability.
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Fuji Electric Systems has developed the FRENIC-MC series
of matrix converters which are available in 15- and 30-kW
versions with a 230-V input and 15-, 30-, and 45-kW versions
using a 480-V input.
Yaskawa currently advertises two ranges of converters for
use on low voltage power systems of either 230- or 480-V input.
The AC7 converter is available in four power levels ranging from
7.5 to 60 HP for a 230-V input and in five power levels ranging
from 10 to 125 HP for the 480-V option. The AC7 offers all of the
typical features that one would expect from a programmable
industrial vector drive with some additional benefits. It is a fully
regenerative drive with a 150% overload capability in either
direction for 1 min and with a maximum input current total
harmonic distortion of 7%. Since it is fully regenerative, it is
advertised as an energy-reducing technology for applications
such as lifts, hoists, conveyors, and escalators. All external add-
on units such as external breaking resistors are eliminated in the
AC7.
Yaskawa also offers a range of medium-voltage matrix
converter drives. The FSDrive-MX1S is aimed at two voltage
systems, 3 and 6 kV. A major selling point is again the potential
efficiency savings in using an inherently regenerative drive. The
power level of the different models in the MX1S series range from
200 kW to 3 MW for a 3-kV system and from 400 kW to 6 MW for
the 6-kV version. The power factor is always maintained to be
greater than 0.95 with an efficiency of 98%. These products can
be seen as the start of a growing range of industrial products
from other companies. As more companies invest in matrix
converter technology, it will encourage other drives
manufacturers to follow.
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CHAPTER 7
FUTURE AND CONCLUSION
7.1 Future of matrix converter
Although there is much reduced usage of matrix converter however, with
the advances in device technology, it is hoped that the problems associated with
the matrix converter will be solved eventually and the matrix converter will not
only replace the Natural Commutated Cycloconverters in all the applications but
will also take over from the PWM rectifier inverters as well. It has been shown
that with space vector PWM control using over modulation, the voltage transfer
ratio may be increased to 1.05 at the expense of more harmonics and large filter
capacitors.
7.2 Conclusion
In today’s world many commercial and industrial application rely on the
use of various power converters. Matrix converter is single converter which can
be used as various power converters by varying the switching conditions.
Although matrix converter offer many advantages and had been a subject
of research for quite long time its complex control strategies and disadvantages
makes it application limited.
However with the advancement of time it is hoped that the matrix
converter will be replacing all the existing power converters in the market.
In this report a brief overview of matrix converter, its working, control
strategies, advantages, disadvantages, application and futuristic point view was
discussed.
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CHAPTER 8
REFERENCES
8.1 References
[1] POWER ELECTRONICS HANDBOOK by M H Rashid
[2] Patrick Wheeler, Jon Clare,Lee Empringham, Maurice Apap and Michael
Bland “Matrix converters”POWER ENGINEERING JOURNAL
DECEMBER 2002
[3] José Rodríguez “Guest Editorial”IEEE TRANSACTIONS ON
INDUSTRIAL ELECTRONICS, VOL. 49, NO. 2, APRIL 2002
[4] A. Alesina and M. Venturini, ‘‘Analysis and design of optimum amplitude
nine-switch direct ac-ac converters.’’ IEEE Trans. Power Electron. 4:(1),
101–112, Jan. 1989.
[5] Power electronics by SINGH-KHANCHANDANI
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