Matrix Converter Technology
advertisement
IECON 2005 Matrix Converter Tutorial November 2005 Matrix 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. Pat.wheeler@Nottingham.ac.uk Presentation 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Presentation 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Matrix Concept Input filter 3-phase supply Bidirectional switch Load Variable frequency Variable voltage 3-phase output Basic 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Nomenclature Phase Labelling Convention A B SAa C a b c Load Example Switching Pattern Possible arrangement SAa (on) SCa (on) SBa (on) tBa tAa tCa SCb (on) SBb (on) SAb (on) tAb tBb SAc (on) tCb SBc (on) tAc tBc SCc (on) tCc Tseq (sequence time) Output phase a Output phase b Output phase c Repeats Switching frequency = 1/Tseq 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. School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Illustrative Output Waveforms Fin > Fout Output line to supply neutral voltage 360 Volts 50Hz in - 25Hz out switching frequency 500Hz 240 120 0 -120 -240 -360 0 Volts Time (ms) 40 Output line to line voltage 600 Low switching frequency shown for visual clarity 20 400 200 0 -200 -400 -600 0 10 Time (ms) 20 Illustrative Output Waveforms Fin < Fout Output line to supply neutral voltage 360 Volts 50Hz in - 100Hz out switching frequency 1kHz 240 120 0 -120 -240 -360 0 10 Time (ms) 20 Output line to line voltage 600 Low switching frequency shown for visual clarity Volts 400 200 0 -200 -400 -600 0 School of Electrical and Electronic Engineering, University of Nottingham, UK 10 Time (ms) 20 IECON 2005 Matrix Converter Tutorial November 2005 Illustrative Input Waveforms 1.2 0.8 Input current (unfiltered) 50Hz in - 25Hz out 0.4 0 -0.4 -0.8 Low switching frequency shown for visual clarity -1.2 0 20 40 60 Time(ms) 80 0 5 10 15 Time(ms) 20 1.2 0.8 Input current (unfiltered) 50Hz in - 100Hz out 0.4 0 -0.4 -0.8 -1.2 Example Spectra 100 % 80 50Hz in - 25Hz out Output voltage 25Hz Sidebands around multiples of the switching frequency 60 40 2kHz switching 20 0 0 Exact nature of spectra depends on modulation method 1 100 50Hz % 80 2 3 4 kHz 5 Input Current Sidebands around multiples of the switching frequency 60 40 20 0 0 School of Electrical and Electronic Engineering, University of Nottingham, UK 1 2 3 4 kHz 5 IECON 2005 Matrix Converter Tutorial Modulation 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 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 School of Electrical and Electronic Engineering, University of Nottingham, UK November 2005 IECON 2005 Matrix Converter Tutorial November 2005 Alternatives Rectifier DC link Inverter 3-Phase Supply 3-Phase Load 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 Alternatives “Back to Back” DC link Inverter 3-Phase Supply 3-Phase Load 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Perceived 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 Count Topology Fully Controlled Devices Fast Diodes Rectifier Diodes Large Electrolytic Capacitors Large Inductors Matrix Converter 18 18 0 0 0 Back-toBack 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 School of Electrical and Electronic Engineering, University of Nottingham, UK Back to back inverter • • • Provides regenerative capability Has sinusoidal supply currents Requires a DC link capacitor IECON 2005 Matrix Converter Tutorial November 2005 Pat Wheeler Presentation Outline Power Circuit Implementation • Bi-directional switch implementation and available semiconductor device products • Current Commutation strategies • Practical circuit layout issues • Power circuit protection School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Matrix Concept Bidirectional Switch Motor The Bi-directional Switch • Must be able to conduct positive and negative currents • Must be able to block positive and negative voltages Possible Switch Configurations Diode Bridge • High conduction losses » Two diodes and a switching device conducting • Only one switching device per switch School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Possible 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 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Possible 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 Device 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 A Bi-directional Switch in a Single Package Dynex 200Amp Bi-directional Module DIM200MBS12-A Nine packages for a 3-phase to 3-phase Matrix Converter Used for larger converters, say >200Amps Common Emitter A Matrix Converter Output Leg in a Single Package 600V, 300A (SEMELAB) 1700V, 600A (DYNEX) Three packages for a 3-phase to 3-phase Matrix Converter Used for medium converters, say 50Amps to 600Amps School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 A Complete Matrix Converter in a Single Package EUPEC 35 Amp Matrix Converter Module One package for a 3-phase to 3-phase Matrix Converter Used for small converters, say >50Amps A Complete Matrix Converter in a Single Package EUPEC 35 Amp Matrix Converter Module A three phase to three phase matrix converter 7.5kW from a 400V supply School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 The Current Commutation Problem 3-phase input Motor Two Rules • Do not short circuit input lines » will short circuit the supply • Do not open circuit output lines » will open circuit inductive load The Two Rules for Safe Current Commutation • Do not short circuit input lines 2-phase input Load • Do not open circuit output lines 2-phase input Load School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Switch Cells for a 2-Phase to 1-Phase Converter SA1 A1 A2 B1 B2 SA2 SB1 RL Load SB2 2-Switch Converter Commutation 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 V1 V2 Io School of Electrical and Electronic Engineering, University of Nottingham, UK 1 1 1 1 V1=V2 1 1 1 0 V1>V2 1 0 1 1 V1<V2 0 1 1 1 V1>V2 1 0 1 0 Io +ve 0 1 0 1 Io -ve 1 1 0 0 Any 0 0 1 1 Any 0 0 0 0 Io = 0 1 0 0 0 Io +ve 2 0 1 0 0 Io -ve 0 0 1 0 Io +ve 1 0 0 1 V1<V2 0 1 1 0 V1>V2 1 1 0 1 V1<V2 0 0 0 1 Io -ve IECON 2005 Matrix Converter Tutorial November 2005 2-Switch Converter Commutation Options The possible commutation routes for a 2-switch Matrix Converter 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 Matrix Converter Phase Labelling Convention A SAa B C a b Motor School of Electrical and Electronic Engineering, University of Nottingham, UK c IECON 2005 Matrix Converter Tutorial November 2005 Switch Cells for a 2-Phase to 1-Phase Converter SA1 A1 A2 B1 B2 C1 C 2 SA2 SB1 RL Load SB2 SC1 SC2 3-Switch Converter Allowable Switch State Options School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Current 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 Dead-Time Current Commutation SA1 SA2 SB1 • Open circuit of motor windings during switch commutation • Have to clamp output voltages due to open circuit on the motor windings RL Load • SB2 • SA1 SA2 SB1 SB2 td School of Electrical and Electronic Engineering, University of Nottingham, UK Output voltage clamping circuits such as a diode bridge Two step commutation strategy IECON 2005 Matrix Converter Tutorial November 2005 Four-Step Current Commutation SA1 Extra hardware • SA2 RL Load SB1 • • SB2 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 • SA1 50% of switch commutations will be soft commutations Four step commutation strategy SA2 • SB1 • SB2 td1 td2 td3 Bi-directional switch current flow No action required when output current changes direction Four Step, Semi-soft Current Commutation IL SA2 SA1 SA1 SA1 SA2 SA2 SB1 SB2 SB2 SB2 SA1 SA2 SA1 SA2 SB1 SB2 School of Electrical and Electronic Engineering, University of Nottingham, UK SB1 SB1 SB1 SB2 IECON 2005 Matrix Converter Tutorial November 2005 Three-Step Current Commutation SA1 SA2 Device Turn-on delays are shorter than the device turn-off delays (true for most common power electronic switching devices) RL Load SB1 The middle delay can therefore be reduced to zero without causing an input line short circuit or output line open circuit SB2 Minimization of the output voltage distortion as the output voltage will change on one of these switching edges depending on the output current direction. SA1 SA2 SB1 SB2 td3 td1 Three-Step Current Commutation 1400V, 600A IGBT 6us commutation time 3 2 Amps 1 0 -1 -2 -3 0 20 40 60 80 100 120 140 160 180 200 T ime, milliseconds 2us commutation time 3 2 Amps 1 0 -1 -2 -3 0 20 40 60 80 Time, milliseconds School of Electrical and Electronic Engineering, University of Nottingham, UK 100 120 140 IECON 2005 Matrix Converter Tutorial November 2005 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 Direction Self Sensing S1 D1 IL V1 Uses Device Currents to Make Current Commutation Decisions • V2 • D2 S2 If IL > 0 • V1 = +2.5 Volts and V2 = -1.2 Volts If IL < 0 and V2 = +2.5 Volts School of Electrical and Electronic Engineering, University of Nottingham, UK Only devices which are conducting are turned on Forms a Two Step Commutation Strategy • • S2 and D2 are conducting • S1 and D1 are reverse biased • V1 = -1.2 Volts Turns off all Devices Which are Not Conducting • • S1 and D1 are conducting • S2 and D2 are reverse biased Direct measurement of actual current flowing Current direction information passed between cells Minimisation of switch state change delays IECON 2005 Matrix Converter Tutorial November 2005 Current Direction Current [mA] Current Detection Circuit Output During Increasing Current 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Time [ms] Current [mA] Current Detection Circuit Output During Decreasing Current 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Time [ms] Experimental Results 40 30Hz Output 30 Loa d Curre nt (A) 20 2kHz Switching 10 0 -10 -20 -30 -40 0 5 10 15 20 25 Time (ms) 30 35 40 45 50 5 10 15 20 25 Time (ms) 30 35 40 45 50 400 300 Loa d Volta ge (V) 200 100 0 -100 -200 -300 -400 0 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Input Voltage Based Commutation 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 4-Step Voltage Based Commutation SA1 SA1 SA1 0V SA2 SA2 SA2 SB1 SB1 SB1 100V SB2 SB2 SB2 SA1 SA2 SA1 SA2 SB1 SB2 School of Electrical and Electronic Engineering, University of Nottingham, UK SB1 SB2 IECON 2005 Matrix Converter Tutorial November 2005 4-Step Voltage Based Commutation Critical areas VB VA VC Problems may occur when voltages are very close • Critical areas • Could commutated via the other voltage • Could rearrange commutation sequence − − Extra losses and unwanted pulses Waveform quality issues unless inherent in control algorithm 4-Step Voltage Based Commutation VA VA VB VB VC VC …A …A – C – B – B – C – A… B – C – A \ / B – C… \ C / C Extra states Critical Step Prevention Method • Rearrange commutation sequence School of Electrical and Electronic Engineering, University of Nottingham, UK Critical Step Replacement Method • Commutated via the other voltage IECON 2005 Matrix Converter Tutorial November 2005 Comparison of Commutation 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 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Matrix Converter Protection a b c Input filter Cin CClamp Lin Clamp circuit line A B C 3x3 matrix of bi-directional switches Auxiliary circuits supply unit (gate-drivers, transducers, control) SMPS IM 3~ motor Capacitor is typically very small depends on nature of load For a 3kW Matrix Converter Drive for an Aircraft Actuator (shown later) machine inductance = 1.15mH maximum output current is, say, 30Amps capacitor required is 2µF Power Circuit Layout Minimisation of mutual inductance between input lines Inclusion of local capacitance between input lines Laminated input line bus bars • Simplifies power circuit assembly Lstray Clocal Lstray Clocal Clocal Lstray School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 IGBT Turn-off Voltage when using Laminated Input Power Planes Device Voltage (V) 600 500 400 300 200 100 0 0 200 400 600 800 Time (ns) Jon Clare School of Electrical and Electronic Engineering, University of Nottingham, UK 1000 IECON 2005 Matrix Converter Tutorial November 2005 Presentation 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 vA Input vB vC iA iB SAa iC va vb vc ia ib ic Output 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Mathematical Model Assuming instantaneous and perfect commutation v a ( t ) S Aa ( t ) v ( t ) = S ( t ) b Ab v c ( t ) S Ac ( t ) S Ba ( t ) S Bb ( t ) i A ( t ) S Aa ( t ) i (t ) = S (t ) B Ba i C ( t ) S Ca ( t ) S Ab ( t ) S Ca ( t ) v A ( t ) S Cb ( t ) v B ( t ) S Cc ( t ) v C ( t ) S Bc ( t ) S Ac ( t ) i a ( t ) S Bc ( t ) i b ( t ) S Cc ( t ) i c ( t ) S Bb ( t ) S Cb ( t ) where the switching function S Kj ( t ) is 1 when the switch joining input line K to output line j is ON and is 0 otherwise. Voltage and current constraint ∑S K = A ,B ,C Ka (t ) = ∑S K = A ,B ,C Kb (t ) = ∑S K = A ,B ,C rules require that : Kc ( t ) =1 Example Switching Pattern SBa =1 SAa=1 (on) tBa tAa SAb=1 tCa SBb=1 tAb SCb=1 tBb SAa=1 tBc Output phase a Output phase b tCb SBc=1 tAc Sca=1 SCc=1 tCc Tseq (sequence time) Output phase c Repeats Switching frequency fsw = 1/Tseq 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Low Frequency Modulation Model 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 v a (t ) v b (t ) = v c (t ) mAa (t ) mBa (t ) mCa (t ) v A (t ) mAb (t ) mBb (t ) mCb (t ) v B (t ) mAc (t ) mBc (t ) mCc (t ) vC (t ) i A (t ) iB (t ) = iC (t ) mAa (t ) mAb (t ) mAc (t ) ia (t ) mBa (t ) mBb (t ) mBc (t ) i b (t ) mCa (t ) mCb (t ) mCc (t ) i c (t ) ∑m K = A,B,C Ka (t ) = ∑m K = A,B,C Kb (t ) = ∑m K = A,B,C Kc Compact notation [v o (t )] = [M (t )][v i (t )] [i i (t )] = [M (t )]T [i o (t )] (t ) = 1 The Modulation Problem Find a modulation matrix M(t) such that the following are satisfied: cos(ω i t ) [v i (t )] = Vim cos(ω i t + 2π / 3) cos(ω i t + 4π / 3 ) cos( ω o t ) [v o (t )] = qVim cos( ω o t + 2π / 3 ) cos( ω o t + 4π / 3 ) where q = voltage ratio If the output currents are sinusoidal and balanced, then it follows that: cos( ω i t + φ i ) cos(ω o t + φ o ) cos( φ i ) cos( ω i t + φ i + 2π / 3 ) [i o (t )] = Iom cos(ω o t + φo + 2π / 3) [i i (t )] = qI om cos( φ o ) cos( ω i t + φ i + 4π / 3 ) cos(ω o t + φ o + 4π / 3 ) School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Basic Algorithms (Venturini & Alesina) Two basic solutions to the modulation problem 1 + 2q cos(ω m t − 2π / 3) 1 + 2q cos(ω m t − 4π / 3) 1 + 2q cos(ω m t ) 1 + 2q cos(ω m t − 2π / 3) 3 1 + 2q cos(ω m t − 2π / 3) 1 + 2q cos(ω m t − 4π / 3) 1 + 2q cos(ω m t ) 1 + 2q cos(ω m t ) [M1(t )] = 1 1 + 2q cos(ω mt − 4π / 3) with ω m = (ω o − ω i ) This yields φi = φo, ie the input phase displacement is the same as the load phase displacement. The alternative solution is: 1 + 2q cos(ω mt − 2π / 3) 1 + 2q cos(ω mt − 4π / 3) 1 + 2q cos(ω m t − 4π / 3) 1 + 2q cos(ω m t ) 1 + 2q cos(ω mt ) 1 + 2q cos(ω m t − 2π / 3) 1 + 2q cos(ω m t − 4π / 3) with ω m = −(ω o + ω i ) 1 + 2q cos(ω m t ) [M 2(t )] = 1 1 + 2q cos(ω mt − 2π / 3) 3 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 [M ( t ) ] = α 1 [M 1( t ) ] + α 2 [M 2 ( t ) ] Input Displacement Factor 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: mKj = 1 2v K v j 1 + 2 3 Vim School of Electrical and Electronic Engineering, University of Nottingham, UK for K = A, B,C and j = a, b, c IECON 2005 Matrix Converter Tutorial November 2005 Voltage Ratio Limitation Average output voltage taken over each switching sequence equals the target voltage Target voltage must fit within input voltage envelope Input voltage envelope Target output voltages 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 0 90 180 270 360 Basic algorithm has a voltage ratio limitation of 0 < q < 0.5 Optimised Voltage Ratio Modify target output voltages to use all the input volt-second area. Target voltages become: 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 cos(ωot ) − 61 cos(3ωot ) + 1 cos(3ωi t ) 2 3 [vo (t )] = qVim cos(ωot + 2π / 3) − 61 cos(3ωot ) + 2 13 cos(3ωi t ) cos(ω t + 4π / 3) − 1 cos(3ω t ) + 1 cos(3ω t ) o o i 6 2 3 Target output voltages with q=0.866 0 90 180 270 360 Input voltage envelope Maximum voltage increased to 87% of input Added triple harmonics cancel in the output line to line voltages School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Added Voltage Cancellation Vim cos(ω i t ) Matrix Converter qVim 6 cos(3ωot ) im − qV cos(3ωi t ) 2 3 qVim cos(ω o t ) Venturini Optimum Amplitude Method Extension to original method to allow use of the modified target waveform set Input displacement factor control is at the expense of voltage ratio Algorithm can be simplified for unity displacement factor to yield: m Kj = 1 2v K v j 4q + sin( ω i t + β K ) sin( 3 ω i t ) 1 + 3 Vim 2 3 3 for K = A, B,C and j = a, b, c β K = 0,2 π/3,4 π/3 for K = A,B,C respectively and v j includes the triple harmonic addition School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Cyclic Venturini Method (1) Original Venturini method uses a “single-sided” fixed switching sequence S11 t11 S21 S12 S13 t12 t13 S23 t21 S22 t22 t23 S31 S32 S33 t31 t32 t33 tseq S11 ≡ SAa, S12 ≡ SBa etc Cyclic Venturini Method (2) Cyclic Venturini method uses a “double-sided” switching sequence S13 S12 S12 S11 t12/2 t12/2 t11/2 S21 S11 t11/2 t13/2 S23 S21 t23/2 S33 t33/2 t21/2 S31 t31/2 tseq/2 S22 t22/2 S32 t32/2 S22 t22/2 S32 t32/2 t21/2 S13 t13/2 S23 t23/2 S31 S33 t31/2 t33/2 tseq/2 “Cyclic” refers to the fact that the selection order of input voltages (3-12-2-1-3 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. School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Cyclic Venturini Method (3) Line to Line Voltage Non-cyclic (standard) Cyclic Cyclic method eliminates sub-optimal vectors Space 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: 2 Vo (t ) = v a (t ) + v (t )e j 2π / 3 + v c (t )e j 4π / 3 b 3 Geometrically, this amounts to plotting the instantaneous values of the three voltages along axes displaced by 120O School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Space Vector Illustration Assume target voltages are: v a = qVim cos(ω o t ), v b = qVim cos(ω o t + 2π / 3), v c = qVim cos(ω o t + 4π / 3) 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 2 I (t ) = ia(t ) + i (t )e j2π / 3 + ic (t )e j 4π / 3 i b 3 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 Vectors 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Group II Space Vectors Vector Number +1 -1 +2 -2 +3 -3 +4 -4 +5 -5 +6 -6 +7 -7 +8 -8 +9 -9 Conducting Switches SAa SBa SBa SCa SCa SAa SBa SAa SCa SBa SAa SCa SBa SAa SCa SBa SAa SCa SBb SAb SCb SBb SAb SCb SAb SBb SBb SCb SCb SAb SBb SAb SCb SBb SAb SCb SBc SAc SCc SBc SAc SCc SBc SAc SCc SBc SAc SCc SAc SBc SBc SCc SCc SAc Output Phase Voltages vb vc va vB vB vA vA vA vB vB vC vC vB vB vC vA vA vC vC vC vA vA vB vB vB vA vA vB vC vC vC vB vB vC vA vA vA vC vC vB vA vB vA vB vA vC vB vC vB vC vB vA vC vA vC vA vC Output Line to Line Voltages vab vbc vca 0 -vAB vAB -vAB 0 vAB vBC 0 -vBC 0 -vBC vBC 0 -vCA vCA 0 -vCA vCA -vAB vAB 0 0 vAB -vAB 0 -vBC vBC 0 vBC -vBC -vCA vCA 0 0 vCA -vCA 0 -vAB vAB 0 vAB -vAB 0 -vBC vBC 0 vBC -vBC 0 -vCA vCA 0 vCA -vCA Input Line Currents IA Ia Ib+Ic 0 0 Ib+Ic Ia Ib Ia+Ic 0 0 Ia+Ic Ib Ic Ia+Ib 0 0 Ia+Ib Ic IB Ib+Ic Ia Ia Ib+Ic 0 0 Ia+Ic Ib Ib Ia+Ic 0 0 Ia+Ib Ic Ic Ia+Ib 0 0 IC 0 0 Ib+Ic Ia Ia Ib+Ic 0 0 Ia+Ic Ib Ib Ia+Ic 0 0 Ia+Ib Ic Ic Ia+Ib 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. School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Target Vector Synthesis ±4, ±5, ±6 ±2, ±5, ±8 ±7, ±8, ±9 ωo ±1, ±4, ±7 Target vector ±1, ±2, ±3 ±3, ±6, ±9 Input current space vectors Target ±1, ±2, ±3 vector Output voltage space vectors ±3, ±6, ±9 ±4, ±5, ±6 ±7, ±8, ±9 ±1, ±4, ±7 ωi ±2, ±5, ±8 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 Vector Sequences S13 S11 t13/2 S23 t23/2 S33 t31/2 t33/2 01 V1 S12 S12 t12/2 t12/2 S22 S22 t22/2 t22/2 S32 S32 t32/2 t32/2 t11/2 S21 t21/2 S31 V2 02 V3 V4 03 03 S11 S12 t11/2 S21 t12/2 S22 t23/2 t21/2 t22/2 S32 t32/2 t33/2 01 V1 V2 S23 t23/2 V4 V3 02 S33 t33/2 V2 V1 01 tseq/2 t13/2 S23 S33 S13 t13/2 t21/2 S31 t31/2 tseq/2 S13 S11 t11/2 S21 V3 V4 tseq/2 School of Electrical and Electronic Engineering, University of Nottingham, UK 02 S12 t12/2 S22 t22/2 S32 t32/2 02 S11 t11/2 S21 t21/2 V4 V3 V2 tseq/2 S13 t13/2 S23 t23/2 S33 t33/2 V1 Double sided 3-zero states V1 → V4 are active states 01 → 03 are zero states Double sided 2-zero states 01 IECON 2005 Matrix Converter Tutorial November 2005 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 Min-Mid-Max Method Oyama et al Attempts to minimise switching loss Minimise commutations by having only 2 output phases switched in each sampling period Minimise voltage change at each commutation through optimum selection of switching sequence S11 S11 t11/2 t11/2 S21 S22 S23 S23 S22 S21 t23/2 t22/2 t23/2 t23/2 t22/2 t21/2 S31 S32 t31/2 t32/2 tseq/2 School of Electrical and Electronic Engineering, University of Nottingham, UK S33 S33 S32 t33/2 t33/2 t32/2 t31/2 tseq/2 S31 IECON 2005 Matrix Converter Tutorial November 2005 Fictitious DC Link Modulation 1 Modulation considered as a two step process [v o (t )] = ([A][v i (t )])[B ] First step - multiply by A, second step - multiply result by B [A] and [B] are given by: cos(ω i t ) [A] = α cos(ω i t + 2π / 3) cos(ω i t + 4π / 3) T cos(ω o t ) [B ] = β cos(ωo t + 2π / 3) cos(ω o t + 4π / 3) Fictitious DC Link Modulation 2 First step yields the “fictitious DC link” and is analogous to rectification 3αVim [ A][v i (t )] = 2 Second step modulates this DC constant at the output frequency and is analogous to conventional inversion using PWM cos(ω o t ) [A][v i (t )][B ] = 3αβVim cos(ωot + 2π / 3) 2 cos(ω o t + 4π / 3) Theoretical maximum values of a and b are: α MAX = 4 3 2 , β MAX = 2π π yielding a maximum voltage transfer ratio of 1.053! School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial Fictitious 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 - Observations 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 School of Electrical and Electronic Engineering, University of Nottingham, UK November 2005 IECON 2005 Matrix Converter Tutorial November 2005 Modulation - Conclusions 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial Presentation Outline Design Issues • Comparison of modulation methods • Input Filter design • Matrix Converter losses and comparisons with other topologies Comparison - Introduction 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 School of Electrical and Electronic Engineering, University of Nottingham, UK November 2005 IECON 2005 Matrix Converter Tutorial November 2005 Comparison (1) Comparison of output voltage weighted THD for equal commutation frequency (8kHz) WTHD = n max ∑ n =2 f1 I (fn ) fn I (f1 ) Sampling frequencies Vent (8kHz – single sided) SVM 3z (6kHz – double sided) SVM 2z (7kHz – double sided) MMM (9kHz – double sided) Comparison (2) Comparison of input current weighted THD for equal commutation frequency (8kHz) School of Electrical and Electronic Engineering, University of Nottingham, UK 2 IECON 2005 Matrix Converter Tutorial November 2005 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 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Simple Filter Analysis Iin L Assume harmonic current flows entirely in C to calculate distortion on Vin Vin In C 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 ∑ ((f ITHD1 = / f n )I (f n )) fn ≠ fi I (f i ) ∑ ((f ITHD 2 = Power I C = THD1 2 VinTHD 6π fiVll 2 i i / fn )2 I(fn ) ) I 1 L = THD2 3C (2π f )2 I in THD i 2 I (f i ) fn ≠ fi Simple Example 4.5 0.40 Input current weighted (1/f) THD Venturini optimum method, q =0.8 Weighted THD % 3.5 Input current weighted (1/f 2) THD Venturini optimum method, q =0.8 0.35 Weighted THD % 4.0 0.30 3.0 0.25 2.5 I THD2 0.20 I THD1 2.0 0.15 1.5 1.0 0.10 0.5 0.05 0.0 0.00 0 50 100 150 f sw /f i 200 0 50 100 150 f sw /f i 200 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Comparison of AC to AC Converter 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 Drive application supplying a 30kW induction motor is considered A 400V induction motor load is used with the inverter drives Ls Ls 400V 50Hz IM 400V 50Hz IM ≡ ≡ Rectifier input PWM Inverter Drive Active front-end Inverter Drive School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 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 v1i 400V 50Hz v2i v3i i1i i2i i3i S11 S21 S31 S12 S22 S32 S13 S23 S33 340V 30kW ≡ OR IM Bi-directional Switch 1200V, 200A IGBTs Matrix Converter Drive 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. School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 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) 3000 Total ) ( loss W t (w) pu t u O d et a R t a s e s s o L r et r ev n o C DB-Inverter AFE-Inverter Venturini M.C. S VM 2z S VM 3z 2500 2000 Note: 1500 THD of SVM method < Venturini at equal sampling frequency 1000 500 0 0 5 10 15 Modulation fre que ncy (kHz) Variation of total converter loss against sampling frequency at rated load School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 75 Load Current (%) 50 25 0 0 2.5 5 7.5 10 15 12.5 Frequency (kHz) Rectifier Input PWM Inverter 4500 4000 3500 3000 2500 2000 1500 1000 500 0 150 125 100 Total Converter Losses (W) 4500 4000 3500 3000 2500 2000 1500 1000 500 0 150 125 100 Total Converter Losses (W) Total Converter Losses (W) Results (2) 75 50 Load Current (%) 25 0 0 2.5 5 7.5 10 15 12.5 Frequency (kHz) 4500 4000 3500 3000 2500 2000 1500 1000 500 0 150 125 100 75 50 25 Load Current (%) Active front-end Inverter 0 0 2.5 5 7.5 10 15 12.5 Frequency (kHz) Matrix Converter Total Converter Loss against load current and sampling frequency 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Pat Wheeler Presentation Outline Two-Stage Matrix Converters (Sparse) • Basic Principle of Operation • Circuit topologies and device count reduction • Comparison of Sparse Matrix Converter Topologies • Modulation Schemes School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Two-Stage Matrix Converters ‘DC’ Link Voltage Bi-directional Switches Output Line Voltage 3-Phase Supply 3-Phase to 2-phase Matrix Converter 3-Phase Load Also known as the ‘Sparse’ Matrix Converter Same Functionality as a Matrix Converter Exception: 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 Two-Stage Matrix Converters Input Voltage [Volts/10] Unfiltered Input Current [Amps] ‘DC Link’ Voltage [Volts] Output Voltage (L-N) [Volts] Output Currents [Amps] School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Sparse Matrix Converters Single-Stage and Two-Stage Converters a b c Input filter Cin CClamp Lin Clamp circuit A B C IM 3~ 3x3 matrix of bi-directional switches Auxiliary circuits supply unit (gate-drivers, transducers, control) SMPS line Clamp circuit Lin Cin CClamp IM 3~ Auxiliary circuits supply unit (gate-drivers, transducers, control) SMPS motor line Both Converters need LC input filter, clamp circuit, Vout/Vin < 0.87! ☺ 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 Cannot produce rotating vectors ZCS ⇒ Rectifier stage decrease max. voltage transfer ratio Higher conduction losses at rated power School of Electrical and Electronic Engineering, University of Nottingham, UK motor IECON 2005 Matrix Converter Tutorial November 2005 Indirect Modulation Model 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 Rectification stage p a b c Inversion stage A B C Upn [R]=[Sa, Sb, Sc] n [T] = [R]⋅[I] [I]=[SA, SB, SC]T Known PWM modulation methods may apply easily Rectifier Stage SV-Modulation Combine adjacent current vectors for sharing the constant output power to the input lines ⇒ sine wave Va ab Line c b a REC = ca P=c Lin Cclamp Cin ac Iδ dδ⋅Iδ θ*in cb N=a Iin dγ⋅Iγ Rectification Stage ⇒VPN bc Iγ Vc Vb ca ba π d γ = mI ⋅ sin − θ*in 3 ( ) dδ = mI ⋅ sin θ * in School of Electrical and Electronic Engineering, University of Nottingham, UK Sector γ-sequence: 1 2 3 4 5 ac 0 bc ba ca cb ab VP Va Vb Vb Vc Vc Va VN Vc Vc Va Va Vb Vb Vline- γ Vac Vbc Vba Vca Vcb Vab ab ac bc ba ca cb VP Va Va Vb Vb Vc Vc VN Vb Vc Vc Va Va Vb Vline- δ Vab Vac Vbc Vba Vca Vcb δ-sequence: IECON 2005 Matrix Converter Tutorial November 2005 Inverter Stage SV-Modulation Line Combine adjacent voltage vectors for accurate generation of the reference voltage vector REC = ca c b a P=c INV=011 Lin 001 101 Vβ Vout dβ⋅Vβ θ*out 011 Cclamp Cin IDC =“acc” 100 dα⋅Vα Inversion Stage Vα α-sequence β-sequence 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 Sector 010 110 π dα = mU ⋅ sin −θ*out 3 * dβ = mU ⋅ sin θ out ( C=c B=c A=a N=a ) IDC [0-α-β -α-0] Pulse Width Generation Removing the Zero Current Vector from REC Stage = maintain dutyREC proportion Rectification stage duty-cycles d γR = VPN = dγ d δR = d γ + dδ dδ dγ + dδ π dα = mU ⋅ sin −θ *out 3 dβ = mU ⋅ sin (θ *out ) d γR⋅Vline- γ + d δR ⋅Vline- δ dγ Rectifier Stage - - d1 d0 = dγR ⋅ 1 − ( dγ + dδ ) ⋅ ( dα + d β ) δ - d2 α 0 Inversion stages duty-cycles dδ γ d0 Inverter Stage mU = 2 ⋅Vout VPN - β d3 - d4 α d1 = dγ ⋅ dα 0 Overflow d 2 = (dγ + dδ ) ⋅ d β Reload d3 = dδ ⋅ dα Timer Equivalent switching sequence 0 - αγ - School of Electrical and Electronic Engineering, University of Nottingham, UK βδ -βγ - αγ -0 d4 = dδR ⋅ 1 − ( dγ + dδ ) ⋅ ( dα + d β ) IECON 2005 Matrix Converter Tutorial November 2005 Pat Wheeler Matrix 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Matrix Converter Modules 600V, 300A SEMELAB Leg Module 1200V, 35A EUPEC Matrix Converter Module 1200V, 200A Dynex Switch Module 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 School of Electrical and Electronic Engineering, University of Nottingham, UK 1700V, 600A DYNEX Leg Module IECON 2005 Matrix Converter Tutorial November 2005 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 An EHA using a Matrix Converter Permanent Magnet Motor Drive (2) EHA Control Loops Voltage transducers Matrix Converter Supply Supply Voltage LEMs PM Motor Resolver Actuator Motor Current Control (DSP and FPGA) Motor Speed Ram Position Demand School of Electrical and Electronic Engineering, University of Nottingham, UK Ram Position LVDT IECON 2005 Matrix Converter Tutorial November 2005 An EHA using a Matrix Converter Permanent Magnet Motor Drive (3) Matrix converter driving two 400Hz induction motor fans, V/f mode 10 24 5 20 A 16 0 12 -5 8 -10 4 -15 A Output current (400Hz) -20 Input 0 current -25 (360Hz) -4 -8 0.001 0.0015 0.002 0.0025 0.003 -30 0.004 0.0035 An EHA using a Matrix Converter Permanent Magnet Motor Drive (4) Supply Loss Operation Speed reversal at 9600rpm 15000 Motor shaft speed (rpm) 5000 0 -5000 -10000 Iq ref[Amps] -15000 0.00 4 2 0 -2 -4 -6 -8 -10 -12 0.00 0.05 0.10 0.15 0.20 0.25 0.30 7500 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0.10 0.15 0.20 0.25 0.30 Phase A current 5 Iq 15 10 5 0 .0 0 .1 0 .2 0 .3 0 .4 0.10 0.15 0.20 0.25 0.30 Phase B current Io 2 [Amps] 10 5 0 -5 -10 0.05 0.10 0.15 0.20 15 0.25 0.30 0 .6 0 .7 0 .8 Input supply voltages 5 0 -5 -10 0.05 0.10 0.15 0.20 Time [secs] School of Electrical and Electronic Engineering, University of Nottingham, UK 0.25 200 150 100 50 0 -50 -100 -150 -200 0.0 0.1 0.2 0.3 0.4 T ime [secs] Phase C current 10 Input Supply [Volts] 0.05 15 Io 3 [Amps] 0 .5 -5 -10 -15 0.00 0 .8 0 0 -5 -15 0.00 0 .7 20 q-axis current 0.05 10 -15 0.00 0 .6 25 15 Io 1 [Amps] Motor speed 8000 7000 Iq [Amps] Speed [rpm] 10000 Motor Speed [rpm] 8500 0.30 0.5 0.6 0.7 0.8 IECON 2005 Matrix Converter Tutorial November 2005 Integrated Electromechanical Actuator (EMA) Technology Demonstrator Electronics Motor 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 EMA Technology demonstrator 30kW matrix converter integrated with ballscrewheatsink Switching Signals Gate Drive Circuits Voltage Clamp Capacitors Voltage Clamp Diodes Input Filter Capacitors Ballscrew housing School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Integrated EMA Technology demonstrator Bespoke PM motor designed and constructed Speed limited to 4950rpm by use of existing actuator for demonstrator Integrated EMA Technology demonstrator School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 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 Preliminary results Dynex/Nottingham collaboration Entire system designed and developed at Nottingham Control system Control electronics Detailed modelling Power circuit 100kW Direct Converter PM Motor Drive Input Current [Amps] 200 150 100 50 0 -50 -100 -150 -200 0 0.002 0.004 0.006 0.008 0.01 Time [secs] Converter on test in USA, May 2005 Input Voltage [Volts] 400 300 200 100 0 -100 -200 -300 -400 0 0.002 0.004 0.006 Time [secs] School of Electrical and Electronic Engineering, University of Nottingham, UK 0.008 0.01 IECON 2005 Matrix Converter Tutorial November 2005 An Integrated Matrix Converter Induction Motor Drive (1) Power Electronics house in the motor end plate = + IGBTs, diodes and filter capacitors Redesigned end plate Induction Motor Matrix Converter Integrated Motor Drive (Power Electronics housed in a redesigned End Plate) Extra fins to cool the devices Specially packaged devices (Dynex Semiconductors) 200 Amp Bi-directional Switch module 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 Bi-directional Switch Modules Redesign Motor End Plate Integrated Motor Drive Bi-directional Switches and Output Connections Power Planes and Input Filter Capacitors Complete Converter with Gate Drives School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 An Integrated Matrix Converter Induction Motor Drive (3) Output Voltages Power Circuit fits in available space 2500 2000 Output Voltages [Volts] 1500 Input inductor fits into a slightly modified terminal box 1000 500 0 Cooling requirement known – design for appropriate end plate exists -500 -1000 -1500 -2000 -2500 0 5 10 15 20 25 30 35 40 45 50 Viability of 30kW integrated drive using matrix converter has been demonstrated Time [ms ecs ] Output Current Input Currents 80 Output Currents [Amps] 60 40 20 0 -20 -40 -60 -80 0 5 10 15 20 25 30 35 40 45 50 Time [msecs] A 130kW Matrix Converter Vector Controlled Induction Motor Drive Control Platform • Infineon C167 control platform • FPGA based Current Commutation control • Fibre-optic connections from control card to to gate drives Power Circuit • Water cooled heat sinks • Laminated input power planes Controller Board Gate Drivers Work done in collaboration with the US Army Research Labs Design and construction of a large Matrix Converter power circuit FPGA Micro Contr. (6) PWM (6) Bidirectional Switches Current Direction (3) Current Direction Sensor School of Electrical and Electronic Engineering, University of Nottingham, UK Input voltage (6) Results from 150kVA tests with an Induction Motor Load under v/f control Closed loop vector control of a 150HP Induction Motor D/A Motor Speed Encoder Fiber Optic Links (27) Desired voltage, freq. PC Controller Serial Link IECON 2005 Matrix Converter Tutorial November 2005 A 130kW Matrix Converter Vector Controlled Induction Motor Drive (2) Results from a 600Amp, 1200V IGBT Matrix Converter Output Currents 500 400 150HP Induction Motor Load, 480Volt supply Output Power 129kW (156kVA) 300 200 Amps 100 0 -1 0 0 Switching Frequency: 4kHz -2 0 0 -3 0 0 -4 0 0 -5 0 0 0 5 1 0 1 5 2 0 2 5 30 35 40 4 5 5 0 Output Voltages 1750 1500 1250 134.0kW Output Power 129.5kW Total converter losses 1000 750 500 250 Volts Input Power 0 -250 -500 -750 -1000 -1250 -1500 -1750 0 5 10 15 20 25 30 35 40 45 50 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 Time, m illiseconds A 130kW Matrix Converter Vector Controlled Induction Motor Drive (3) Speed Demand ωref id Compensation terms * input voltages * Id Current Control vd Iq Current Control vq jθ e Speed Control iq * 3-Phase Supply MICRO-CONTROLLER Infineon SAB80C167 Flux Current Demand vα 2/3 vβ * va vb vc vAB vBC Closed Loop Vector Control of a 150HP Induction Machine Voltage A to D Input Filter Matrix Converter Control Algorithm Matrix Converter Power Circuit Gate Drives • Natural regeneration • Low cost Micro-controller control platform ωr i q* ωsl ωe τ i d* PWM dt id iq e-jθ iα iβ 3/2 ia ib FPGA Current A to D ic 1000 ωr A⊕B Timers Up/Down 800 FPGA A Closed Loop Motor Control Closed Loop Vector Scheme applied to the Matrix Converter Induction Motor Drive B motor Speed [rpm] Rotor Speed 600 400 200 Encode 0 800 Id, Iq [Amps] 600 400 200 0 -200 -400 Output Currents [Amps] 600 400 200 0 -200 -400 -600 0 1 2 3 Time [secs] Control Platform School of Electrical and Electronic Engineering, University of Nottingham, UK 4 5 IECON 2005 Matrix Converter Tutorial November 2005 Field Power Supply Using a Four-Output Leg Matrix Converter 250 200 • • • • • 150 Matrix Converter Power Circuit Variable Speed Diesel Engine Permanent Magnet Generator Designed for 10kVA Load 50Hz, 60Hz or 400Hz Output Frequency Output Line to Line Voltages [V] Field power supply 100 50 0 -50 -100 -150 -200 DIESEL ENGINE Matrix 10kW Gen Load -250 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 Time [s] 400Hz Output Voltage Waveforms FILTER FILTER MATRIX CONVERTER Input Voltage Space Vector Modulator Output Current Modulation D,Q, Control and Engine Demand Engine Speed Control Output Voltage • • • • • 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 Conclusions 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 School of Electrical and Electronic Engineering, University of Nottingham, UK IECON 2005 Matrix Converter Tutorial November 2005 Book 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 School of Electrical and Electronic Engineering, University of Nottingham, UK
