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IECON 2005 Matrix Converter Tutorial November 2005

School of Electrical and Electronic Engineering, University of Nottingham, UK

Matrix Converter TechnologyMatrix Converter Technology

Dr Pat Wheeler and Prof Jon Clare

Power Electronics, Machines and Control Group

School of Electrical and Electronic Engineering

University of Nottingham, UK

Tel. +44 115 951 5591 Email. [email protected]

Presentation Outline IPresentation Outline I

Basic Matrix Converter Concepts (Jon Clare)Power Circuit Implementation (Pat Wheeler)• Bi-directional switch implementation and available

semiconductor device products• Status of Devices: SiC, Reverse Blocking IGBTs• Current Commutation strategies• Power circuit protection • Practical circuit layout issues

Modulation Algorithms (Jon Clare)• Mathematical model• Basic Modulation problem and solution• Voltage ratio limitation• Principal modulation methods:

Venturini, Space vector, Max-mid-min, Fictitious DC Link



Presentation Outline IIPresentation Outline II

Design Issues (Jon Clare)• Comparison of modulation methods• Input Filter design• Matrix Converter losses and comparisons with other

topologies

Two-Stage Matrix Converters (Pat Wheeler)• Basic Principle of Operation• Circuit topologies and device count• Comparison of Sparse Matrix Converter Topologies • Modulation Schemes

Experimental Matrix Converters and applications (Pat Wheeler)• Application Examples• Industrial Products

Potential Future Application Areas (Jon Clare and Pat Wheeler)

Jon Clare



Matrix ConceptMatrix Concept

Inputfilter

3-phasesupply

Bi-directional

switchLoad

Variable frequencyVariable voltage3-phase output

Basic IdeasBasic Ideas

Switching pattern and commutation control must avoid line to line short circuits at the input

Switching pattern and commutation control must avoid open circuits at the output

Each output phase can be connected to any input phase at any time

Switch duty cycles are modulated so that the “average” output voltage follows the desired reference (for example a sinusoidal reference)

Modulation is arranged so that the “average” input current is sinusoidal when the input voltage, output reference and output current are sinusoidal



NomenclatureNomenclature

Load

SAa

A

a

B

C

b c

Phase Labelling Convention

Example Switching PatternExample Switching Pattern

Tseq (sequence time)

SAb (on)

SBa (on) SCa (on)SAa (on)

SBb (on) SCb (on)

SAc (on) SBc (on) SCc (on)

tAa tBa tCa

tAb tBb tCb

tAc tBc tCc

Outputphase a

Outputphase b

Outputphase c

Switching frequency = 1/Tseq

Possible arrangement

Modulation strategy ensures that tAa - tCc are generated so that the average output voltage during each sequence equals the target output voltage. The sequence time is constant.

Repeats



Illustrative Output WaveformsIllustrative Output WaveformsFin > Fout

Output line to supply neutral voltage

Time (ms)

Volts

-360

-240

-120

0

120

240

360

0 20 40

Time (ms)

Volts

Output line to line voltage

-600

-400

-200

0

200

400

600

0 10 20

50Hz in - 25Hz outswitching frequency 500Hz

Low switching frequency shown for visual clarity

Time (ms)

Volts

-360

-240

-120

0

120

240

360

0 10 20

Illustrative Output WaveformsIllustrative Output WaveformsFin < Fout

Output line to supply neutral voltage

Time (ms)

Volts

-600

-400

-200

0

200

400

600

0 10 20

Output line to line voltage

50Hz in - 100Hz outswitching frequency 1kHz




Illustrative Input WaveformsIllustrative Input Waveforms

Time(ms)

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0 20 40 60 80

Time(ms)

Input current (unfiltered) 50Hz in - 100Hz out

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0 5 10 15 20

Input current (unfiltered) 50Hz in - 25Hz out


Example SpectraExample Spectra

50Hz in - 25Hz out

2kHz switching

%

%

kHz

kHz

Output voltage

Input Current

25Hz

50Hz

Sidebands around multiples

of the switching frequency

Sidebands around multiples

of the switching frequency

0

20

40

60

80

100

0 1 2 3 4 5

0

20

40

60

80

100

0 1 2 3 4 5

Exact nature of spectra depends on modulation method



Modulation ControlModulation Control

A number of modulation strategies have been proposed. All of them allow flexible control with the following features:• Continuous control of output voltage amplitude from zero up

to a maximum limit

• Continuous control of output frequency up to a maximum feasible limit of approximately 1/10 of the switching frequency

• Control of input displacement factor: unity, leading and lagging regardless of output power factor

DC-AC and AC-DC conversion is an inherent feature by setting either the input or output frequency to zero

Matrix Converter FeaturesMatrix Converter Features

Direct conversion - No DC link - “all silicon solution”

No restriction on input and output frequency within limits imposed by switching frequency

Inherent bi-directional power flow in all modes with 4 quadrant voltage-current characteristics at both ports

“Sinusoidal” input and output currents

Potential for high power density if switching frequency is high enough

Output voltage limited to 87% of input voltage (for most modulation schemes)

Higher semiconductor count than other AC-AC configurations



AlternativesAlternatives

Industry “workhorse” - made from a few kW to MW

Unidirectional power flow

Poor AC supply current waveforms

DC link capacitor is often 30% - 50% of the power circuit volume at 20kW upwards

3-PhaseSupply

3-PhaseLoad

Rectifier DC link Inverter

AlternativesAlternatives

3-Phase Load

3-Phase Supply

“Back to Back” DC link Inverter

Bi-directional power flow

PWM control of input bridge with line inductors gives sinusoidal input currents

Large DC link capacitor and line inductors

Matrix converter provides the same functionality



Perceived and Actual LimitationsPerceived and Actual Limitations

Voltage Transfer Ratio• Output voltage is limited to 86% of the input

voltage• Only a problem if standard motors are used from a

standard supply

Device Count• Normally requires 18 fully controllable switching

devices for a 3-phase to 3-phase converter• Compares to 12 switching devices and large

reactive components for a back-to back inverter circuit

Control Algorithms• Considered complex by some researchers• Have been reported as processor intensive• No longer really and issue

Device CountDevice Count

Topology Fully

Controlled Devices

Fast Diodes

Rectifier Diodes

Large Electrolytic Capacitors

Large Inductors

Matrix Converter 18 18 0 0 0

Back-to-Back

Inverter 12 12 0 1 3

Inverter with Diode

Bridge 6 6 6 1 0 or 1

Conventional rectifier DC Link inverter

• Has poor supply current waveforms

• Provides no regenerative capability• Requires a DC link capacitor

Back to back inverter• Provides regenerative

capability • Has sinusoidal supply

currents• Requires a DC link capacitor



Pat Wheeler

Presentation OutlinePresentation Outline

Power Circuit Implementation• Bi-directional switch implementation and available

semiconductor device products

• Current Commutation strategies

• Practical circuit layout issues

• Power circuit protection



Matrix ConceptMatrix Concept

Bi-directional

SwitchMotor

The Bi-directional Switch• Must be able to conduct positive and negative currents• Must be able to block positive and negative voltages

Possible Switch ConfigurationsPossible Switch Configurations

Diode Bridge • High conduction losses

» Two diodes and a switching device conducting

• Only one switching device per switch




Back to Back Switch• Two switching devices per switch• Conduction losses of only one diode and one switching device• Common Collector

» Pair of switching devices arranged with collectors connected» Diodes required for reverse blocking capability


Back to Back Switch• Common Emitter

» Pair of switching devices arranged with emitters connected» Both devices can be gated from the same isolated power supply

• Can Control Direction of Current Flow within each Switch» Useful for most current commutation strategies

• Diodes can be Si or SiC » SiC may offers lower conduction losses, depending on device

rating




Back to Back Switch• Reverse Blocking IGBTs

» Pair of reverse blocking IGBTs» Lower conduction losses» Reverse recovery can be an issue and may lead to higher

switching losses

• Simpler Power Semiconductor Module Design» Increase in theoretical reliability?

• Can Control Direction of Current Flow within each Switch

Matrix Converter Matrix Converter Device PackagingDevice Packaging

A Bi-directional Switch in a Single Package• Two IGBTs and associated diodes• A rearranged ‘Inverter leg’• 200Amp samples available from Dynex Semiconductors

A Matrix Converter Output Leg in a Single Package• Possible to have 3 bi-directional switches in a single package

» One package per output leg of the converter» Possible advantages in the minimisation of inductance between devices

• Can be built as specials by Dynex and Semelab• Products from Fuji, IXSY and Mitsubishi using Reverse blocking

IGBTs

A Complete Matrix Converter in a Single Package• Suitable for lower power levels• Eupec had a 400V, 7.5kW matrix converter ‘ECONOMAC’ module



A BiA Bi--directional Switch directional Switch in a Single Packagein a Single Package

Dynex 200Amp Bi-directional ModuleDIM200MBS12-A

Common Emitter

Nine packages for a 3-phase to 3-phase Matrix ConverterUsed for larger converters, say >200Amps

A Matrix Converter Output Leg in a Single Package

Three packages for a 3-phase to 3-phase Matrix ConverterUsed for medium converters, say 50Amps to 600Amps

600V, 300A

(SEMELAB)

1700V, 600A

(DYNEX)



A Complete Matrix Converter A Complete Matrix Converter in a Single Packagein a Single Package

One package for a 3-phase to 3-phase Matrix ConverterUsed for small converters, say >50Amps

EUPEC 35 Amp Matrix Converter Module

EUPEC 35 Amp Matrix Converter Module

A three phase to three phase matrix converter 7.5kW from a 400V supply

A Complete Matrix Converter A Complete Matrix Converter in a Single Packagein a Single Package



The Current The Current Commutation ProblemCommutation Problem

Two Rules• Do not short circuit input lines

» will short circuit the supply• Do not open circuit output lines

» will open circuit inductive load

3-phaseinput

Motor

The Two Rules for The Two Rules for Safe Current CommutationSafe Current Commutation

• Do not short circuit input lines

• Do not open circuit output lines

2-phaseinput

Load

2-phaseinput

Load



Switch Cells for a 2Switch Cells for a 2--Phase Phase to 1to 1--Phase ConverterPhase Converter

RL Load

SA1

SA2

SB2

SB1

2121

BBAA

22--Switch Converter Switch Converter Commutation OptionsCommutation Options

Switch states for a 2 to 1 matrix Converter• Allowable conditions for each state is given

Commutation path just has to follow the allowable conditions

1111

V1=V2

0101

Io +ve

1100

Any

1010

Io -ve

0000

Io = 0

0001

Io +ve 2

0010

Io -ve

0100

Io +ve

0011

Any

0111

V1>V2

1110

V1>V2

1101

V1<V2

1000

Io -ve

1011

V1<V2

0110

V1>V2

1001

V1<V2

V1

V2

Io



22--Switch Converter Switch Converter Commutation OptionsCommutation Options

The possible commutation routes for a 2-switch Matrix Converter

1111

0101

1100

1010

0000

0001

0010

0100

0011

0111

1000

1101

1110

1011

0110

1001

Matrix ConverterMatrix Converter

Motor

SAa

A

a

B

C

b c

Phase Labelling Convention



Switch Cells for a 2Switch Cells for a 2--Phase Phase to 1to 1--Phase ConverterPhase Converter

RL Load

SA1

SA2

SB2

SB1

SC2

SC1

212121

CCBBAA

33--Switch Converter Allowable Switch Converter Allowable Switch State OptionsSwitch State Options



Current Commutation MethodsCurrent Commutation Methods

Output Current Commutation Methods• Rely on measurement of the output current

direction on each output leg

Input Voltage Commutation Methods• Rely on measurement of the relative input

voltages

Resonant Techniques• Use an auxiliary resonant circuit to achieve

safe commutation

DeadDead--Time Current Time Current CommutationCommutation

td

SA1

SA2

SB1

SB2

RL Load

SA1

SA2

SB2

SB1

• Open circuit of motor windings during switch commutation

• Have to clamp output voltages due to open circuit on the motor windings

• Output voltage clamping circuits such as a diode bridge

• Two step commutation strategy



FourFour--StepStepCurrent CommutationCurrent Commutation

SA1

SA2

SB1

SB2

td1 td2 td3

RL Load

SA1

SA2

SB2

SB1

Extra hardware• Require knowledge of output

current direction in each output line

• Increase in gate drive complexity to allow independent control of devices

• Control logic complexity

Reduction in device losses• 50% of switch

commutations will be soft commutations

Four step commutation strategy

• Bi-directional switch current flow

• No action required when output current changes direction

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

IL

Four Step, SemiFour Step, Semi--soft soft Current CommutationCurrent Commutation



ThreeThree--StepStepCurrent CommutationCurrent Commutation

SA1

SA2

SB1

SB2

td1 td3

RL Load

SA1

SA2

SB2

SB1

Device Turn-on delays are shorter than the device turn-off delays (true for most common power electronic switching devices)

The middle delay can therefore be reduced to zero without causing an input line short circuit or output line open circuit

Minimization of the output voltage distortion as the output voltage will change on one of these switching edges depending on the output current direction.

ThreeThree--StepStepCurrent CommutationCurrent Commutation

2us commutation time

-3

-2

-1

0

1

2

3

0 20 40 60 80 100 120 140

Time, milliseconds

Amps

1400V, 600A IGBT 6us commutation time

-3

-2

-1

0

1

2

3

0 20 40 60 80 100 120 140 160 180 200

Time, milliseconds

Amps



Current Direction Sensing Current Direction Sensing

External Measurement of Load Current• Hall effect current transducers

» Cost of extra hardware • Current sense resistors

» Extra energy losses

Back to Back Diodes• Direction of voltage across diodes gives current

direction• Additional Conduction losses

Internal Switch Current Direction Detection• Direct measurement of current direction information• No external hardware required• Information acquired at point of use• Reliable at very low current levels

» Current as low as 100µA can be detected

Switch Current Switch Current Direction Self SensingDirection Self Sensing

If IL > 0• S1 and D1 are conducting• S2 and D2 are reverse biased

• V1 = +2.5 Volts and V2 = -1.2 Volts

If IL < 0• S2 and D2 are conducting• S1 and D1 are reverse biased

• V1 = -1.2 Volts and V2 = +2.5 Volts

S1

S2

V2IL

D2

D1

V1

Uses Device Currents to Make Current Commutation Decisions

• Direct measurement of actual current flowing

• Current direction information passed between cells

Turns off all Devices Which are Not Conducting

• Only devices which are conducting are turned on

Forms a Two Step Commutation Strategy

• Minimisation of switch state change delays



Current DirectionCurrent Direction

Current Detection Circuit Output During Decreasing Current

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

0.2

0.4

0.6

Time [ms]

Cur

rent

[mA

]

Current Detection Circuit Output During Increasing Current

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

0.2

0.4

0.6

Time [ms]

Cur

rent

[mA

]

Experimental ResultsExperimental Results

30Hz Output

2kHz Switching

0 5 10 15 20 25 30 35 40 45 50-400

-300

-200

-100

0

100

200

300

400

Time (ms)

Load

Vol

tage

(V)

0 5 10 15 20 25 30 35 40 45 50-40

-30

-20

-10

0

10

20

30

40

Time (ms)

Load

Cur

rent

(A)

0 5 10 15 20 25 30 35 40 45 50-400

-300

-200

-100

0

100

200

300

400

Time (ms)

Load

Vol

tage

(V)

0 5 10 15 20 25 30 35 40 45 50-40

-30

-20

-10

0

10

20

30

40

Time (ms)

Load

Cur

rent

(A)



Input Voltage Based Input Voltage Based CommutationCommutation

Uses Input Voltages to Make Current Commutation Decisions• Relies on knowledge of relative magnitude order of the input

voltages• Requires accurate and balanced measurement of input voltage

waveforms required

Example:

4-Step Voltage Commutation• Must avoid critical areas where input voltages are close

» Prevention method» Replacement method

44--Step Voltage Based Step Voltage Based CommutationCommutation

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

SA1

SA2

SB2

SB1

0V

100V




V A V CV B

Critical areas

Problems may occur when voltages are very close• Critical areas• Could commutated via the other voltage

− Extra losses and unwanted pulses

• Could rearrange commutation sequence− Waveform quality issues unless inherent in control algorithm

VA

VB

VC

… A – C – B – B – C – A …

Critical Step Prevention Method• Rearrange commutation sequence

VA

VB

VC

… A B – C – A B – C …

\ /C

\ /C

Extra states

Critical Step Replacement Method• Commutated via the other voltage




Comparison of Comparison of Commutation MethodsCommutation Methods

Output Current Commutation Methods• Relies on measurement of the output current direction

on each output leg• Output line open circuit if a commutation error occurs

» Overvoltage clamp used

Input Voltage Commutation Methods• Relies on measurement of the relative input voltages• Longer commutation times• Input line short circuit is a commutation error occurs

» ?

Some Protection IssuesSome Protection Issues

Fault conditions

• Overcurrent due to short circuit

» Commutation failure

• Loss of supply

• Output power overload

Protection strategies

• No natural freewheeling paths

• Have to provide energy storage in event of turning-off all devices

» Overvoltage clamp

» Freewheeling with the matrix converter circuit



Matrix Converter ProtectionMatrix Converter Protection

Capacitor is typically very smalldepends on nature of load

For a 3kW Matrix Converter Drive for an Aircraft Actuator (shown later)machine inductance = 1.15mHmaximum output current is, say, 30Ampscapacitor required is 2µF2µF

Auxiliary circuits supply unit (gate-drivers, transducers, control)

Inpu

t filt

er

line

a b c

A B C

IM 3~

Clamp circuit

3x3

mat

rix o

f b

i-dire

ctio

nal s

witc

hes

SMPS

motor

CClamp

Lin

Cin

Power Circuit LayoutPower Circuit Layout

Minimisation of mutual inductance between input linesInclusion of local capacitance between input linesLaminated input line bus bars

• Simplifies power circuit assembly

Lstray

Clocal

Lstray

Lstray

Clocal

Clocal



IGBT TurnIGBT Turn--off Voltage when using off Voltage when using Laminated Input Power PlanesLaminated Input Power Planes

0 200 400 600 800 10000

100

200

300

400

500

600

Time (ns)

Device Voltage (V)

Jon Clare




Modulation Algorithms• Mathematical model

• Basic Modulation problem and solution

• Voltage ratio limitation

• Principal modulation methods» Venturini, Space vector, Max-mid-min, Fictitious DC Link

Ideal Switch Matrix Ideal Switch Matrix

vASAa

vC

vB

va vb vc

iC

iB

iA

ia ib ic

Assume voltage fed input and current sink output - inductors represent inductive load

Measure all voltages with respect to a hypothetical star (wye neutral) point of the supply

Input

Output



Mathematical ModelMathematical Model

1)()()(

:that require rules constraint current and Voltage otherwise. 0 is and ON is line output to line input joining

switch the when1is)( function switching thewhere

)()()(

)()()()()()()()()(

)()()(

)()()(

)()()()()()()()()(

)()()(

,,,,,,∑∑∑

===

===

=

=

CBAKKc

CBAKKb

CBAKKa

Kj

c

b

a

CcCbCa

BcBbBa

AcAbAa

C

B

A

C

B

A

CcBcAc

CbBbAb

CaBaAa

c

b

a

tStStS

jK tS

tititi

tStStStStStStStStS

tititi

tvtvtv

tStStStStStStStStS

tvtvtv

Assuming instantaneous and perfect commutation

Example Switching Example Switching PatternPattern

Switching frequency fsw = 1/Tseq

Tseq (sequence time)

SAb=1

SBa =1 Sca=1SAa=1 (on)

SBb=1 SCb=1

SAa=1 SBc=1 SCc=1

tAa tBa tCa

tAb tBb tCb

tAc tBc tCc

Outputphase a

Outputphase b

Outputphase c

Repeats

Many different ways of sequencing the switches are possible – depends on modulation strategy

Define the modulation duty cycle for each switch as mAa(t) = tAa/Tseq etc



Low Frequency Low Frequency Modulation ModelModulation Model

v tv tv t

m t m t m tm t m t m tm t m t m t

v tv tv t

i ti ti t

m t m t m tm t

a

b

c

Aa Ba Ca

Ab Bb Cb

Ac Bc Cc

A

B

C

A

B

C

Aa Ab Ac

Ba

( )( )( )

( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )

( )( )( )

( )( )( )

( ) ( ) ( )( )

=

= m t m tm t m t m t

i ti ti t

m t m t m t

Bb Bc

Ca Cb Cc

a

b

c

KaK A B C

KbK A B C

KcK A B C

( ) ( )( ) ( ) ( )

( )( )( )

( ) ( ) ( ), , , , , ,

= = == = =∑ ∑ ∑ 1

Switching function model gives instantaneous relationships - not immediately useful for studying modulation

Assume that the input frequency and output frequency (fi, fo) << fsw

Low frequency input-output relationships can then be defined in terms of the modulation duty cycle matrix

Compact notation

[ ] [ ][ ]

[ ] [ ] [ ])()()(

)()()(

titMti

tvtMtv

oT

i

io

=

=

The Modulation ProblemThe Modulation Problem

Find a modulation matrix M(t) such that the following are satisfied:

( )[ ]

++=

)3/4cos()3/2cos(

)cos(

πωπω

ω

tt

tVtv

i

i

i

imi

( )[ ]

+++++

=)3/4cos()3/2cos(

)cos(

πφωπφω

φω

oo

oo

oo

omo

tt

tIti

( )[ ]

++=

)3/4cos()3/2cos(

)cos(

πωπω

ω

tt

tqVtv

o

o

o

imo

( )[ ]

+++++

=)3/4cos()3/2cos(

)cos(

)cos()cos(

πφωπφω

φω

φφ

ii

ii

ii

o

iomi

tt

tqIti

If the output currents are sinusoidal and balanced, then it follows that:

where q = voltage ratio



Basic Algorithms (Venturini &Basic Algorithms (Venturini &AlesinaAlesina))

[ ] [ ] [ ])(2)(1)( 21 tMtMtM αα +=

[ ]

)( with)cos(21)3/4cos(21)3/2cos(21

)3/2cos(21)cos(21)3/4cos(21)3/4cos(21)3/2cos(21)cos(21

31)(1

iom

mmm

mmm

mmm

tqtqtqtqtqtqtqtqtq

tM

ωωωωπωπω

πωωπωπωπωω

−=

+−+−+−++−+−+−++

=

[ ]

)( with)3/2cos(21)cos(21)3/4cos(21

)cos(21)3/4cos(21)3/2cos(21)3/4cos(21)3/2cos(21)cos(21

31)(2

iom

mmm

mmm

mmm

tqtqtqtqtqtq

tqtqtqtM

ωωωπωωπω

ωπωπωπωπωω

+−=

−++−++−+−+

−+−++=

Two basic solutions to the modulation problem

This yields φi = φo, ie the input phase displacement is the same as the load phase displacement. The alternative solution is:

This yields φi = - φo, ie the input phase displacement is the reverse of the load phase displacement. Combining the two solutions provides the means for input displacement factor control

Input Displacement Input Displacement Factor ControlFactor Control

Combined solution allows input displacement factor control

For example, assuming an inductive load:

a1 = a2 : input is resistive (unity displacement factor)

a1 > a2 : input is inductive (lagging displacement factor)

a1 < a2 : input is capacitive (leading displacement factor)

Assuming unity displacement factor solution, allows the switch duty cycle calculation to be reduced to:

cbajCBAKV

vvm

im

jKKj ,,and,,for

21

31

2 ==

+=



Voltage Ratio LimitationVoltage Ratio Limitation

Input voltage envelopeTarget output voltages

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0 90 180 270 360

Average output voltage taken over each switching sequence equals the target voltage

Target voltage must fit within input voltage envelope

Basic algorithm has a voltage ratio limitation of 0 < q < 0.5

Optimised Voltage RatioOptimised Voltage Ratio

-1.2-0.8-0.4

00.40.81.2

0 90 180 270 360

Modify target output voltages to use all the input volt-second area. Target voltages become:

( )[ ]

+−++−+

+−=

)3cos()3cos()3/4cos()3cos()3cos()3/2cos(

)3cos()3cos()cos(

321

61

321

61

321

61

tttttt

tttqVtv

ioo

ioo

ioo

imo

ωωπωωωπω

ωωω

Target output voltages with q=0.866

Input voltage envelope

Maximum voltage increased to 87% of input

Added triple harmonics cancel in the output line to line voltages



Added Voltage Cancellation Added Voltage Cancellation

MatrixConverter

)cos( tV iim ω

)cos( tqV oim ω)3cos(

)3cos(

32

6

t

t

iqV

oqV

im

im

ω

ω

−

Venturini Optimum Amplitude Venturini Optimum Amplitude MethodMethod

Extension to original method to allow use of the modified targetwaveform set

Input displacement factor control is at the expense of voltage ratio

Algorithm can be simplified for unity displacement factor to yield:

mv vV

qt t

K A B C j a b c

0,2 /3,4 /3 K A,B,C

v

KjK j

imi K i

K

j

= + + +

= =

= =

13

12 4

3 332 sin( )sin( )

for , , and , ,

ω β ω

β π π for respectively

and includes the triple harmonic addition



Cyclic Venturini Method (1)Cyclic Venturini Method (1)

Original Venturini method uses a “single-sided” fixed switching sequence

S22

S11

S21

S31 S32

t11

t21 t22

t31 t32

S23

S33

t23

t33

tseq

S13

t13

S12

t12

S11 ≡ SAa, S12 ≡ SBa etc


Cyclic Venturini method uses a “double-sided” switching sequence

tseq/2

t13/2

S13 S11 S12

S23 S21 S22

S33 S31 S32

t11/2 t12/2

t23/2 t21/2 t22/2

t33/2 t31/2 t32/2

t12/2

S12S11 S13

S22S21 S23

S32 S31S33

t11/2 t13/2

t22/2 t21/2 t23/2

t32/2 t31/2 t33/2

tseq/2

“Cyclic” refers to the fact that the selection order of input voltages (3-1-2-2-1-3 above) is changed every 60O of input period.

Input voltage with largest absolute magnitude (1 above) is always placed in the middle.

Duty cycle calculations are identical to standard (optimum) Venturini method.




Line to Line Voltage

Non-cyclic (standard) Cyclic

Cyclic method eliminates sub-optimal vectors

Space Vector ConceptSpace Vector Concept

Space vector concept allows a 3-phase set of quantities to be represented by a single vector on a complex plane

Define space vector of (Va, Vb, Vc) as:

++= 3/4)(3/2)()(

32)( ππ jetcvjetbvtavtoV

Geometrically, this amounts to plotting the instantaneous values of the three voltages along axes displaced by 120O



Space Vector IllustrationSpace Vector Illustration

++= 3/4)(3/2)()(32)( ππ jetci

jetbitaitiI

)3/4cos(),3/2cos(),cos( πωπωω +=+== tqVvtqVvtqVv oimcoimboima

Assume target voltages are:

Result is that Vo(t) - the target output voltage space vector has constant length qVim and rotates at ωO when plotted in the complex plane imd0046.html

Space vector of input current is defined in the same way

Target space vector of input current is normally chosen to line up with the input voltage space vector (unity displacement factor), and rotates at ωi

Matrix Converter Space Matrix Converter Space VectorsVectors

27 possible vectors can be split into 3 groups

Group I: each output line is connected to a different input line.

Space vectors of output voltage rotate at ωi

Space vectors of input current rotate at ωO

Group II: two output lines are connected to a common input line, the remaining output line is connected to one of the other input lines.

Space vectors of output take one of 6 fixed positions (varying amplitude)

Space vectors of input current take one of 6 fixed positions (varying amplitude)

Group III: all output lines are connected to a common input line.

All space vectors are at the origin (zero length)

Group I is not useful, only Groups II (18 vectors) and III (3 vectors) are used



Group II Space VectorsGroup II Space Vectors

Output Phase

Voltages Output Line to Line Voltages

Input Line Currents Vector Number

Conducting Switches va vb vc vab vbc vca IA IB IC

+1 SAa SBb SBc vA vB vB vAB 0 -vAB Ia Ib+Ic 0 -1 SBa SAb SAc vB vA vA -vAB 0 vAB Ib+Ic Ia 0 +2 SBa SCb SCc vB vC vC vBC 0 -vBC 0 Ia Ib+Ic -2 SCa SBb SBc vC vB vB -vBC 0 vBC 0 Ib+Ic Ia +3 SCa SAb SAc vC vA vA vCA 0 -vCA Ib+Ic 0 Ia -3 SAa SCb SCc vA vC vC -vCA 0 vCA Ia 0 Ib+Ic +4 SBa SAb SBc vB vA vB -vAB vAB 0 Ib Ia+Ic 0 -4 SAa SBb SAc vA vB vA vAB -vAB 0 Ia+Ic Ib 0 +5 SCa SBb SCc vC vB vC -vBC vBC 0 0 Ib Ia+Ic -5 SBa SCb SBc vB vC vB vBC -vBC 0 0 Ia+Ic Ib +6 SAa SCb SAc vA vC vA -vCA vCA 0 Ia+Ic 0 Ib -6 SCa SAb SCc vC vA vC vCA -vCA 0 Ib 0 Ia+Ic +7 SBa SBb SAc vB vB vA 0 -vAB vAB Ic Ia+Ib 0 -7 SAa SAb SBc vA vA vB 0 vAB -vAB Ia+Ib Ic 0 +8 SCa SCb SBc vC vC vB 0 -vBC vBC 0 Ic Ia+Ib -8 SBa SBb SCc vB vB vC 0 vBC -vBC 0 Ia+Ib Ic +9 SAa SAb SCc vA vA vC 0 -vCA vCA Ia+Ib 0 Ic -9 SCa SCb SAc vC vC vA 0 vCA -vCA Ic 0 Ia+Ib

Modulation Calculations Modulation Calculations

Calculations are performed at a regular sampling frequency.

Target output voltage space vector rotates, but can be assumed to be fixed at a particular magnitude and position during each sampling period.

Output voltage space vectors that the converter can produce are fixed in position (or zero).

Time weighted switching between adjacent vectors, produces the correct target “average” output voltage vector during each sampling period.

Use of 4 (non-zero) vectors in each sampling period allows input current space vector direction to be controlled as well (for unity displacement factor).

Any extra time in the sampling period not occupied by active vectors is filled with zero vectors.

Sequence of the 4 active vectors is chosen to minimise commutations.



Target Vector Synthesis Target Vector Synthesis

±1, ±2, ±3

±4, ±5, ±6

±7, ±8, ±9

ωo

ωi

±1, ±4, ±7±3, ±6, ±9

±2, ±5, ±8

Output voltage space vectors

Input current space vectors

Target vector

Target vector

For any condition, using 4 vectors allows control of output voltage magnitude and angle and input current angle (displacement factor)

In this case vectors are 5, 6, 8, 9

±1, ±2, ±3

±7, ±8, ±9

±4, ±5, ±6

±3, ±6, ±9±1, ±4, ±7

±2, ±5, ±8

Vector Sequences Vector Sequences

tseq/2

t13/2

S13 S11 S12

S23 S21 S22

S33 S31 S32

t11/2 t12/2

t23/2 t21/2 t22/2

t33/2 t31/2 t32/2

t12/2S12

S11 S13

S22S21 S23

S32 S31S33

t11/2 t13/2

t22/2 t21/2 t23/2

t32/2 t31/2 t33/2

01 02 03 03 02 01V1 V2 V3 V4 V4 V3 V2 V1

tseq/2

tseq/2

t13/2

S13 S11 S12

S23 S21S22

S33 S32

t11/2 t12/2

t23/2 t21/2 t22/2

t33/2 t32/2

t12/2S12 S11 S13

S22 S21 S23

S32 S33

t11/2 t13/2

t22/2 t21/2 t23/2

t32/2 t33/2

01 02 02 01V1 V2 V3V4 V4

V3 V2V1

tseq/2

Double sided

3-zero states

Double sided

2-zero states

V1 → V4 are active states

01 → 03 are zero states



Space Vector Comments Space Vector Comments

Selection of vector sequence is not unique - different implementations possible

Different implementations give different high frequency (distortion) characteristics at the input and output port

Common mode addition to output target is inherent with space vector method → 87% voltage ratio

Freedom to control input current vector position can be beneficial under distorted/unbalanced load/supply conditions

MinMin--MidMid--Max MethodMax MethodOyama Oyama et alet al

Attempts to minimise switching lossMinimise commutations by having only 2 output phases switched in each sampling periodMinimise voltage change at each commutation through optimum selection of switching sequence

t11/2

S23

tseq/2

S11

S21 S22

S31 S32 S33

t23/2 t22/2 t23/2

t31/2 t32/2 t33/2

S11

S23 S22 S21

S33 S32 S31

t11/2

t23/2 t22/2 t21/2

t33/2 t32/2 t31/2

tseq/2



Fictitious DC Link Modulation 1 Fictitious DC Link Modulation 1

Modulation considered as a two step process

[ ] [ ][ ]( )[ ]BtvAtv io )()( =

First step - multiply by A, second step - multiply result by B

[A] and [B] are given by:

[ ] [ ]

++=

++=

)3/4cos()3/2cos(

)cos(

)3/4cos()3/2cos(

)cos(

πωπω

ω

πωπω

ωβα

tt

tB

tt

tA

o

o

oT

i

i

i

Fictitious DC Link Modulation 2Fictitious DC Link Modulation 2

Theoretical maximum values of a and b are:

πβ

πα 2,

234 == MAXMAX

yielding a maximum voltage transfer ratio of 1.053!

First step yields the “fictitious DC link” and is analogous to rectification

[ ] [ ]A v tV

iim( ) =

32

α

Second step modulates this DC constant at the output frequency and is analogous to conventional inversion using PWM

[ ][ ][ ]

++=

)3/4cos()3/2cos(

)cos(

23)(

πωπω

ωαβ

tt

tVBtvA

o

o

oim

i



Fictitious DC Link Modulation 3Fictitious DC Link Modulation 3

For q > 0.87 the mean output voltage in each sequence

cannot equal the target voltage → Increased low

frequency distortion in output and/or input

As q → 1.05 input current and output voltage approach

quasi-square wave

For q < 0.87, method is similar to others

Sparse Matrix Converter makes the distinction between

[A] and [B] in hardware - but still without DC energy

storage

Modulation Modulation -- ObservationsObservations

Practical implementation of switching schemes (any of

them) with a modern DSP is straightforward

Switch duty cycles are normally calculated at each sampling

instant based on input voltage measurement (all methods)

Low frequency distortion/unbalance in input voltage does

not appear at output

(Instantaneous power out) = (Instantaneous power in) at all

instants in a matrix converter



Modulation Modulation -- ConclusionsConclusions

No restriction on input and output frequency within limits imposed by switching frequency

Inherent bi-directional power flow in all modes with 4 quadrant voltage-current characteristics at both ports

“Sinusoidal” input and output currents

Input displacement factor can be controlled

Output voltage limited to 87% of input voltage (for most modulation schemes)

Schemes for which q > 0.87 have significant performance penalties

Jon Clare




Design Issues• Comparison of modulation methods

• Input Filter design

• Matrix Converter losses and comparisons with other topologies

Comparison Comparison -- IntroductionIntroduction

Define:• Modulation frequency (fm) = frequency at which switching

pattern repeats• Sampling frequency (fsamp) = frequency at which modulation

duty cycles are calculated• Switching frequency (fsw) = average frequency at which each

bidirectional switch commutates

Comparison of modulation methods not straightforward since:• Often fm ≠ fsamp ≠ fsw • Ratio fm/fsw, fsamp/fsw etc depends on modulation method• Even for equal fsw, different modulation methods can give

vastly different switching losses



Comparison (1)Comparison (1)

( )( )

2

1

max

2

1

= ∑

= fIfI

ff

WTHD nn

n n

Comparison of output voltage weighted THD for equal commutation frequency (8kHz)

Sampling frequencies

Vent (8kHz – single sided)

SVM 3z (6kHz – double sided)

SVM 2z (7kHz – double sided)

MMM (9kHz – double sided)


Comparison of input current weighted THD for equal commutation frequency (8kHz)




Comparison of losses for 30kW converter

Balance between conduction and switching loss depends on devices chosen –relatively slow devices used in this example

Input Filter DesignInput Filter Design

R

L

C

Matrix Converter

C chosen to limit voltage distortion at converter terminals

L chosen to limit current distortion at supply

R chosen to give adequate damping

• Limit overshoot on turn-on

• Avoid excitation of resonance by supply or converter



Simple Filter AnalysisSimple Filter Analysis

Assume harmonic current flows entirely in C to calculate distortion on Vin

Use calculated distortion on Vin to determine distortion on Iin

Enables C and L to be determined directly from weighted THD curves and target THD for Iin and Vin

VinC

LIin

In

( )

( )in

i

nniTHD

ini

nniTHD

fffI

fIffI

fffI

fIffI

≠=

≠=

∑

∑

)(

)()/(

)(

)()/(

22

2

2

1

( )

=

=

22

21

23

1

6

iTHDin

THD

lliTHDin

THD

fCII

L

Vf

PowerVI

C

π

π

Simple ExampleSimple Example

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 50 100 150 200f sw/f i

Wei

ghte

d TH

D %

Input current weighted (1/f) THDVenturini optimum method, q =0.8

I THD1

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 50 100 150 200f sw/f i

Wei

ghte

d TH

D %

Input current weighted (1/f2) THDVenturini optimum method, q =0.8

I THD2

Example: 415V line to line input at 50Hz, 15kW power level at q=0.8, 8kHz switching frequency

Target distortions: Input current THD 5%, Converter input voltage THD 5%

Data from curves at fsw/fi = 160: ITHD1 = 0.35%, ITHD2 = 0.004%

Component values: C = 6µF, L = 210µH

Space vector or cyclic Venturini modulation would yield smaller values



Comparison of AC to AC Comparison of AC to AC Converter LossesConverter Losses

Research programme looking at 30kW integrated matrix

converter induction motor drive

3 configurations studied

Rectifier PWM drive

Active front-end PWM drive

Matrix converter drive

Conduction and commutation losses considered in detail

Voltage Source Inverter Drives

IM

≡

Ls

IM

≡

Ls

400V50Hz

400V50Hz

Rectifier input PWM Inverter Drive

Active front-end Inverter Drive

Drive application supplying a 30kW induction motor is

considered

A 400V induction motor load is used with the inverter drives



Matrix Converter Drive

• Maximum voltage transfer ratio of matrix converter is 0.866

• A 340V induction motor load is therefore used for the matrix converter drive

≡

OR

v1i

i3i

S11 S21 S31

S12 S22 S32

S13 S23 S33

i2i

i1i

v2i

v3i

IM340V30kW

400V50Hz

Matrix Converter Drive

Bi-directional Switch

1200V, 200A IGBTs

Device Conduction Losses

• Fit curve to the IGBT and diode forward voltage drop characteristics.

• Matrix Converter - output current flows through a series combination of an IGBT and a diode at all times.

• Inverter – Dependant on the output fundamental displacement angle.

• Diode bridge – Dependant on supply impedance.



Device Commutation Losses

• Simulations for each converter were used to identify switching instants

• IGBT turn-on, turn-off losses and diode recovery energy loss included

• Soft turn-on, turn-off instances due to zero current switching

• Matrix Converter – switching voltage dependant upon the switching instants

• A linear relationship of switching loss with voltage and current at commutation instant was assumed

Results (1)

0 5 10 150

500

1000

1500

2000

2500

3000

Modulation fre que ncy (kHz)

Converter Losses at Rated Output (W)

DB-InverterAFE-InverterVenturini M.C.S VM 2zS VM 3z

Variation of total converter loss against sampling frequency at rated load

Total loss (w)

Note:

THD of SVM method < Venturini at equal sampling frequency



Results (2)

02.5

57.5

1012.5

15

025

5075

100125

1500

50010001500200025003000350040004500

02.5

57.5

1012.5

15

025

5075

100125

1500

50010001500200025003000350040004500

02.5

57.5

1012.5

15

025

5075

100125

1500

50010001500200025003000350040004500

Tota

l Conve

rter

Loss

es (

W)

Tota

l Conve

rter

Loss

es (

W)

Tota

l Conve

rter

Loss

es (

W)

Load Current (%)

Load Current (%) Load Current

(%)Frequency (kHz)

Frequency (kHz)

Frequency (kHz)

Total Converter Loss against load current and sampling frequency

Rectifier Input PWM Inverter Active front-end Inverter Matrix Converter

Loss Comparison - Conclusions

• Highest efficiency obtained with diode rectifier PWM inverter

• Matrix converter is more efficient than the active front-end drive that has similar characteristics



Pat Wheeler


Two-Stage Matrix Converters (Sparse)• Basic Principle of Operation

• Circuit topologies and device count reduction

• Comparison of Sparse Matrix Converter Topologies

• Modulation Schemes



TwoTwo--Stage Stage Matrix ConvertersMatrix Converters

3-Phase Load

3-Phase Supply

Also known as the ‘Sparse’ Matrix Converter

Same Functionality as a Matrix ConverterException: rotating vectors are not possible,

ie. different input phase connected to each output phase

In this form it has the same number of devices as a Matrix Converter

Output Line Voltage

‘DC’ Link Voltage

3-Phase to 2-phase Matrix Converter

Bi-directional Switches

TwoTwo--Stage Stage Matrix ConvertersMatrix Converters

Input Voltage [Volts/10]

Unfiltered Input Current [Amps]

‘DC Link’ Voltage [Volts]

Output Voltage (L-N) [Volts]

Output Currents [Amps]



Sparse Matrix ConvertersSparse Matrix Converters

☺ Save diodes for clamp circuit on load side☺ Flexible design of rectifier stage☺ Dead-time commutation in inversion stage☺ Possible ZCS of rectifier stage during a zero-voltage vector☺ Conduction losses are load dependent

Both Converters need LC input filter, clamp circuit, Vout/Vin < 0.87!

Cannot produce rotating vectors ZCS ⇒ Rectifier stage decrease max. voltage transfer ratioHigher conduction losses at rated power

Auxiliary circuits supply unit (gate-drivers, transducers, control)

Inpu

t filt

er

line

a b c

A B C

IM 3~

Clamp circuit

3x3

mat

rix o

f b

i-dire

ctio

nal s

witc

hes

SMPS

motor

CClamp

Lin

Cin

line

Lin

CinCClamp

Clamp circuit

IM3~

Auxiliary circuits supply unit(gate-drivers, transducers, control) SMPS motor

SingleSingle--Stage and Stage and TwoTwo--Stage ConvertersStage Converters



Indirect modulation model for MC = two stage transformation • a rectification stage, to provide a (constant) DC-link voltage

• an inversion stage, to produce the three output voltages

ABC

abc

p

n

Upn

[R]=[Sa, Sb, Sc] [I]=[SA, SB, SC]T

Rectification stage Inversion stage

[T] = [R]⋅[I]

Known PWM modulation methods may apply easily

Indirect Indirect ModulationModulation ModelModel

Rectification Stage ⇒VPN

Sector 0 1 2 3 4 5

γ-sequence:

VP

VN

Vline- γ

δ-sequence:

VP

VN

Vline- δ

ac

Va

Vc

Vac

ab

Va

Vb

Vab

bc

Vb

Vc

Vbc

ac

Va

Vc

Vac

ba

Vb

Va

Vba

bc

Vb

Vc

Vbc

ca

Vc

Va

Vca

ba

Vb

Va

Vba

cb

Vc

Vb

Vcb

ca

Vc

Va

Vca

ab

Va

Vb

Vab

cb

Vc

Vb

Vcb

cba

Lin

Cin

Cclamp

LineP=c

N=a

REC = ca

Rectifier Stage SVRectifier Stage SV--ModulationModulation

Iγ

Iδ

Iin

θ*in

dγ⋅Iγ

dδ⋅Iδ

bc

acab

cb

baca

Va

VbVc

*sin3I ind mγπ = ⋅ − θ

( )*sinI ind mδ = ⋅ θ

Combine adjacent current vectors for sharing the

constant output power to the input lines ⇒ sine wave



Inversion Stage

Sector α-sequence β-sequence IDC [0-α-β-α-0]

0 100 = IA 110 = -IC 0 IA -IC IA 0

1 110 = -IC 010 = IB 0 -IC IB -IC 0

2 010 = IB 011 = -IA 0 IB -IA IB 0

3 011 = -IA 001 = IC 0 -IA IC -IA 0

4 001 = IC 101 = -IB 0 IC -IB IC 0

5 101 = -IB 100 = IA 0 -IB IA -IB 0

cba

Lin

Cin

Cclamp

Line

C=cB=c A=a

P=c

N=a

INV=011

IDC

=“acc”

REC = ca

001

011

110010

Vα

Vβ

Vout

θ*out

dα⋅Vα

dβ⋅Vβ

100

101

Combine adjacent voltage vectors for accurate

generation of the reference voltage vector

Inverter Stage SVInverter Stage SV--ModulationModulation

*sin3U outd mαπ = ⋅ −θ

( )*sinU outd mβ = ⋅ θ

δγ

γγ +

=dd

dd R

δγ

δδ +

=dd

dd R

Removing the Zero Current Vector from REC Stage = maintain dutyREC proportion

*sin3U outd mαπ θ = ⋅ −

1d d dγ α= ⋅

2 ( )d d d dγ δ β= + ⋅

3d d dδ α= ⋅

( ) ( )0 1Rd d d d d dγ γ δ α β = ⋅ − + ⋅ +

( ) ( )4 1Rd d d d d dδ γ δ α β = ⋅ − + ⋅ +

Inversion stages duty-cycles

Rectification stage duty-cycles

VPN = ⋅Vline- γ + ⋅Vline- δRdδ

Rd γ

2U out PNm V V= ⋅

0 α β α 0

Rectifier Stage

0 - αγ - βδ -βγ - αγ -0

Inverter Stage

γ δ

ReloadEquivalent switching sequence

Overflow

Timer

d0 - d1 - d2 - d3 - d4

dγ - dδ

Pulse Width Generation Pulse Width Generation

( )*sinU outd mβ θ= ⋅



Pat Wheeler

Matrix Converter ProductMatrix Converter Product

The Yaskawa Matrix Converter

• The first commercial Matrix Converter product

• Launched in 2004

• Aimed at Lift and hoist applications

• An important milestone in the development of Matrix Converter

• Some circuit optimisation still required, for example in size and wieght



Matrix Converter ModulesMatrix Converter Modules

1200V, 35A EUPEC Matrix Converter Module

1200V, 200A Dynex Switch Module

600V, 300A SEMELAB Leg Module

1700V, 600A DYNEX Leg Module

Applications?Applications?

Integrated Motor Drives• No DC link capacitor• Voltage ratio not a limitation

Industrial Applications• Lifts and Hoists• Power density• Regeneration

Aerospace• Power density• Temperature tolerance

Electric Military Vehicles• Weight and volume• Bi-directional power flow



An EHA using a Matrix Converter Permanent Magnet Motor Drive

Aims

• Produce a 3kW Matrix Converter to drive an EHA

• Demonstrate the actuator as part of the TIMES programme

Testing

• Prototype EHA has been tested on 400Hz and variable frequency supplies over a range of realistic loading conditions

• Converter has also been tested as a motor drive under various supply conditions found on aircraft

EHA Control Loops

Matrix Converter

PMMotor

Actuator

Control (DSP and FPGA) Ram Position

Motor Current

Motor Speed

SupplyLVDTResolverLEMs

Supply Voltage

Ram Position Demand

Voltagetransducers

An EHA using a Matrix Converter Permanent Magnet Motor Drive (2)



-8

-4

0

4

8

12

16

20

24

0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004-30

-25

-20

-15

-10

-5

0

5

10

A

A

Matrix converter driving two 400Hz induction motor fans, V/f mode

Output current (400Hz)

Input current (360Hz)


Speed reversal at 9600rpm

-15000

-10000

-5000

0

5000

10000

15000

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Spee

d [rp

m]

-12-10-8-6-4-2024

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Iq re

f[Am

ps]

-15

-10

-5

0

5

10

15

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Io 1

[Am

ps]

-15

-10

-5

0

5

10

15

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Io 2

[Am

ps]

-15

-10

-5

0

5

10

15

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Time [secs]

Io 3

[Am

ps]

Motor shaft speed (rpm)

q-axis current

Phase A current

Phase B current

Phase C current

7000

7500

8000

8500

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8

Mot

or S

peed

[rpm

]

-5

0

5

10

15

20

25

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8

Iq [A

mps

]

-200-150-100

-500

50100150200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8T ime [secs]

Inpu

t Sup

ply

[Vol

ts]

Motor speed

Iq

Input supply voltages

Supply Loss Operation




MotorMotor

Electronics

MotorMotor

Electronics

Integrated Electromechanical Actuator (EMA) Technology Demonstrator

To design and build an Integrated Electro Mechanical Actuator (EMA) intended as a technology demonstrator for a rudder actuator on a large, twin-engined, civil aircraft.

Need to continuously deploy rudder under some flight conditions drives thermal design (stationary motor with high torque)Natural cooling considered

Integrated EMATechnology demonstrator

Gate Drive Circuits

Ballscrew housing

Input Filter Capacitors

Switching Signals

Voltage Clamp Diodes

Voltage Clamp Capacitors

30kW matrix converter integrated with ballscrew-heatsink




Bespoke PM motor designed and constructedSpeed limited to 4950rpm by use of existing actuator for demonstrator




100kW Direct Converter PM Motor Drive

Water-cooled direct power converter

100kW vector controlled PM motor

360Hz-800Hz input, dc-1200Hz output

230V phase voltage input

120kVA rating

Aerospace power quality targets

Bespoke semiconductor packaging

Dynex/Nottingham collaboration

Entire system designed and developed

at Nottingham

Control system

Control electronics

Detailed modelling

Power circuit

Preliminary results

100kW Direct Converter PM Motor Drive

Converter on test in USA, May 2005

-200

-150

-100

-50

0

50

100

150

200

0 0.002 0.004 0.006 0.008 0.01

Time [secs]

Input

Curr

ent

[Am

ps]

-400

-300

-200

-100

0

100

200

300

400

0 0.002 0.004 0.006 0.008 0.01

Time [secs]

Input

Voltage [

Volts]



Integrated Drives above 7.5kW are not feasible within the same motor space envelope

DC Link Capacitors form about 40% of the volume

Matrix Converter will give same functionality as a back-to-back inverter drive

Regeneration to supply

Input current waveform quality

BUT no large capacitors or inductors

+ =Matrix ConverterInduction Motor Integrated Motor Drive

(Power Electronics housed in a redesigned End Plate)

An Integrated Matrix Converter Induction Motor Drive (1)

Power Electronics house in the motor end plate

IGBTs, diodes and filter capacitors

Redesigned end plate

Extra fins to cool the devices

Specially packaged devices (Dynex Semiconductors)

200 Amp Bi-directional Switch module

Bi-directional Switch Modules Redesign Motor End Plate

Integrated Motor DriveIntegrated Motor Drive

Bi-directional Switches and Output Connections

Complete Converter with Gate Drives

Power Planes and Input Filter Capacitors



An Integrated Matrix Converter Induction Motor Drive (3)

-80

-60

-40

-20

0

20

40

60

80

0 5 10 15 20 25 30 35 40 45 50

Time [msecs]

Outp

ut

Curr

ents

[Am

ps]

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

0 5 10 15 20 25 30 35 40 45 50

Time [msecs ]

Outp

ut

Voltages

[Volts]

Input CurrentsOutput Current

Output VoltagesPower Circuit fits in available space

Input inductor fits into a slightly modified terminal box

Cooling requirement known – design for appropriate end plate exists

Viability of 30kW integrated drive using matrix converter has been demonstrated

A 130kW Matrix Converter Vector Controlled Induction Motor Drive

PC Controller

GateDrivers

FiberOpticLinks(27)

Current Direction Sensor

Desiredvoltage, freq.

SerialLink

InputvoltageD/A

PWM

FPGA MicroContr.

BidirectionalSwitches

Controller Board

(6)

(6)

(6)

CurrentDirection

(3)

Motor Speed Encoder PC Controller

GateDrivers

FiberOpticLinks(27)

Current Direction Sensor

Desiredvoltage, freq.

SerialLink

InputvoltageD/A

PWM

FPGA MicroContr.

BidirectionalSwitches

Controller Board

(6)

(6)

(6)

CurrentDirection

(3)

Motor Speed Encoder

Work done in collaboration with the US Army Research Labs

Design and construction of a large Matrix Converter power circuit

Results from 150kVA tests with an Induction Motor Load under v/f control

Closed loop vector control of a 150HP Induction Motor

Control Platform• Infineon C167 control platform• FPGA based Current Commutation

control• Fibre-optic connections from control card

to to gate drivesPower Circuit

• Water cooled heat sinks• Laminated input power planes



A 130kW Matrix Converter Vector Controlled Induction Motor Drive (2)

Results from a 600Amp, 1200V IGBTMatrix Converter

150HP Induction Motor Load, 480Volt supplyOutput Power 129kW (156kVA)

Switching Frequency: 4kHz

Output Currents

Output Voltages

-1750

-1500

-1250

-1000

-750

-500

-250

0

250

500

750

1000

1250

1500

1750

0 5 10 15 20 25 30 35 40 45 50

Time, milliseconds

Volts

- 5 0 0

- 4 0 0

- 3 0 0

- 2 0 0

- 1 0 0

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0

Am

ps

Input Power 134.0kW Output Power 129.5kW Total converter losses 4530W

Output Power Factor 0.835

Efficiency 96.2%

Input Voltage (L to L) 475V

Input Current 172A

Input Power Factor 0.985

Output Voltage 362V

Output Current 256

A 130kW Matrix Converter Vector Controlled Induction Motor Drive (3)

vc

va

vbvβ

vα vd

*

vq*

Rotor Speed

Flux Current Demand Compensation terms

iq*

ωsl ωe

ωr

id

iq

iα

iβ ic

ia ib

Speed Control

Id Current Control

ejθ

e-jθ

Timers

3/2

2/3Iq Current Control

*

*

d

q

i

i

τ dt

ωr

ωref id* Speed Demand

inputvoltages

Matrix Converter

Control Algorithm

PWM

MICRO-CONTROLLER Infineon SAB80C167

motor

3-Phase Supply

Input Filter

Matrix

Converter Power Circuit

FPGA

CurrentA to D

Gate Drives

VoltageA to D

FPGA

Encode

A B

A ⊕ B

Up/Down

vAB

vBC

Closed Loop Vector Scheme applied to the Matrix Converter Induction Motor Drive 0

200

400

600

800

1000

Spee

d [

rpm

]

-400

-200

0

200

400

600

800

Id, Iq

[Am

ps]

-600

-400

-200

0

200

400

600

0 1 2 3 4 5

Time [secs]

Outp

ut

Curr

ents

[Am

ps]

0

200

400

600

800

1000

Spee

d [

rpm

]

-400

-200

0

200

400

600

800

Id, Iq

[Am

ps]

-600

-400

-200

0

200

400

600

0 1 2 3 4 5

Time [secs]

Outp

ut

Curr

ents

[Am

ps]

Closed Loop Vector Control of a 150HP Induction Machine

• Natural regeneration• Low cost Micro-controller

control platform

Control Platform

Closed Loop Motor Control



Field Power Supply Using a Four-Output Leg Matrix Converter

LoadMatrix10kWGenDIESEL

ENGINE

FILTER

EngineSpeed Control

ModulationD,Q, Control

and Engine Demand

MATRIXCONVERTER

FILTER

SpaceVector

ModulatorInput Voltage

Output Voltage

Output Current

-250

-200

-150

-100

-50

0

50

100

150

200

250

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Time [s]

Out

put L

ine

to L

ine

Vol

tage

s [V

]

Field power supply• Matrix Converter Power Circuit• Variable Speed Diesel Engine• Permanent Magnet Generator• Designed for 10kVA Load• 50Hz, 60Hz or 400Hz Output Frequency

• IGBT based Matrix Converter• 25kHz Sampling Frequency• DSP/FPGA Control Platform• LC Output Filter• Output Voltage Control Loop designed using a Genetic Algorithm Optimisation

• A collaborative project with the US Army Research Labs

400Hz Output Voltage Waveforms

ConclusionsConclusions

Matrix converters can offer advantages

• Size

• Regenerative operation

• Sinusoidal input/output

Modulation control is not difficult

New power devices (eg Silicon Carbide) will increase the attractiveness of matrix converters

Current research is application orientated

Ongoing research into derived circuits



BookBook

A Book entitled “Matrix Converters” is due for publication in 2006

• Authors:

» Prof Jon Clare

» Dr Pat Wheeler

» Dr Christian Klumpner

» Dr Lee Empringham

• Publisher:

» Springer

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