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.

1

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.

2

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.

3

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).

4

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.

5

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

6

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.

7

[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

8

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)

9

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

13

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

14

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.

15

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.

17

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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