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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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
Low switching frequency shown for visual clarity
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
Low switching frequency shown for visual clarity
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
Possible Switch ConfigurationsPossible Switch Configurations
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
Possible Switch ConfigurationsPossible Switch Configurations
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
Possible Switch ConfigurationsPossible Switch Configurations
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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)
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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)
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
44--Step Voltage Based Step Voltage Based CommutationCommutation
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
44--Step Voltage Based Step Voltage Based CommutationCommutation
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
Presentation OutlinePresentation Outline
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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 ==
+=
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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 (2)Cyclic Venturini Method (2)
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.
IECON 2005 Matrix Converter Tutorial November 2005
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Cyclic Venturini Method (3)Cyclic Venturini Method (3)
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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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.
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
Presentation OutlinePresentation Outline
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
IECON 2005 Matrix Converter Tutorial November 2005
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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 (2)Comparison (2)
Comparison of input current weighted THD for equal commutation frequency (8kHz)
IECON 2005 Matrix Converter Tutorial November 2005
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Comparison (3)Comparison (3)
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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
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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.
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
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Pat Wheeler
Presentation OutlinePresentation Outline
Two-Stage Matrix Converters (Sparse)• Basic Principle of Operation
• Circuit topologies and device count reduction
• Comparison of Sparse Matrix Converter Topologies
• Modulation Schemes
IECON 2005 Matrix Converter Tutorial November 2005
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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]
IECON 2005 Matrix Converter Tutorial November 2005
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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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
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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= ⋅
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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)
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
-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)
An EHA using a Matrix Converter Permanent Magnet Motor Drive (3)
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
An EHA using a Matrix Converter Permanent Magnet Motor Drive (4)
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
Integrated EMATechnology demonstrator
Bespoke PM motor designed and constructedSpeed limited to 4950rpm by use of existing actuator for demonstrator
Integrated EMATechnology demonstrator
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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]
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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
IECON 2005 Matrix Converter Tutorial November 2005
School of Electrical and Electronic Engineering, University of Nottingham, UK
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