A New Family of Matrix Converters R. W. Erickson and O. A. Al-Naseem Colorado Power Electronics Center University of Colorado Boulder, CO 80309-0425, USA rwe@colorado.edu Abstract A new family of matrix converters is introduced, that employs relatively simple voltage-clamped buses and can generate multilevel voltage waveforms of arbitrary magnitude and frequency. The basic configuration includes a nine-cell matrix that uses fourquadrant switch cells. Each four-quadrant switch cell resembles a full-bridge inverter and can assume three voltage levels during conduction. Semiconductor devices in a switch cell are clamped to a known constant dc voltage of a capacitor. Control of the input and output voltage waveforms of the proposed converter can be achieved through space vector modulation. Simulation results show how the converter can operate with any input and output voltages, currents, frequencies, and power factors while maintaining constant dc voltages across all switch cell capacitors. 1
Comparison of conventional matrix converter with proposed new family of converters Voltage conversion ratio V out /V in Switch commutation Conventional matrix converter Buck only: V out 0.866V in Coordination of 4-quadrant switches Proposed new matrix converters Buck boost: 0 V out < Simple transistor + freewheeling diode Bus bar structure Complex Modular and simple Multilevel operation No Possible Utility-side filter elements Machine-side filter elements AC capacitors Inductive Inductive Inductive 2
II. Converter Derivation and Operation Basic Configuration of New Matrix Converter Basic converter Modular switch cell n + + + Three-phase ac system 1 Symbol Realization a A i a i b i c D 1 D 2 a b c A i A Three-phase ac system 2 + + + Q 1 Q 2 a A D 3 D 4 Q 3 Q 4 B C i B i C N Converter contains a matrix of switch cells Switch cells include dc capacitors Input and output ports include inductive elements 3
Operation of Switch Cell DC capacitor voltage = V When semiconductor devices conduct, switch cell can produce instantaneous voltages v aa of +V, 0, or V Switch cell can block voltages of magnitude less than or equal to V Diodes clamp maximum transistor voltage to V Break-before-make operation: it is allowed to turn off all transistors in the converter; diodes are able to provide a conducting path for inductor currents D 1 D 2 Q 1 Q 2 a A D 3 D 4 Q 3 Q 4 Modular switch cells lead to modular bus structure: simple H-bridges 4
Branch connections To avoid interrupting the input and output inductor currents, five of the nine branches of the matrix must conduct at any instant n + + + i a i b i c Three-phase ac system 1 81 valid combinations of conducting branches At rated voltage: two-level operation At low voltage: three-level operation is possible a b c A B C i A i B i C Three-phase ac system 2 + + + N 5
Example Three valid choices of switching combinations, for V = 240 V and all for the same choice of conducting branches In each case, the four nonconducting branches block voltages less than or equal to 240 V When a line-to-line voltage of 2V = 480 V is produced at one side of the switch matrix, then the voltages at the other side must be zero Number of valid switching combinations: 19683 6 UTILITY SIDE (a) Phase A V AB = 0V V CA = 0V Phase B (b) V CA = 0V (c) V CA = 0V V BC = 0V Phase C Phase A V AB = 0V Phase B V BC = 0V Phase C Phase A V AB = 0V Phase B V BC = 0V Phase C Branch Aa Branch Ba Branch Ca Branch Cb Branch Cc 0V +240V- MACHINE SIDE Phase a V ab = 0V Phase b V ca = 0V V bc = 0V Phase c Phase a V ab = 0V Phase b V ca = -240V V bc = 240V Phase c Phase a V ab = 0V Phase b V ca = -480V V bc = 480V Phase c
Increasing the number of levels Series connection of switch cells n + + + Three-phase ac system 1 For this example i a i b i c At rated voltage: three-level operation a b c Three-phase ac system 2 At low voltage: five-level operation is possible A i A Sharing of voltage stress: semiconductor blocking voltages are reduced by factor of two B C i B i C + + + N 7
III. Control Derived space-vector control algorithm for proposed new converters Showed that dc capacitor voltages can be controlled Developed extensive computer program to verify operation of control algorithms Space vectors of basic converter q (0, 2 3 V cap ) (1.5V cap, 1.5 3 V cap ) (0, 3 V cap ) (3V cap, 3V cap ) (1.5V cap, 0.5 3 V cap ) (3V cap,0) d 8
Space Vector Control q-axis V REF = d 1 V 1 + d 2 V 2 + d 0 V 0 V 1 (0, 3V cap ) 60 d 1 V 1 3 2 = V REF sin (φ) d 1 V 1 (0,0) d 0 V 0 V 0 V REF φ d 2 V 2 V 2 (1.5V cap, 0.5 3V cap ) d-axis d 1 = 2 3 V REF V 1 sin (φ)=m sin (φ) d 2 V 2 3 2 = V REF sin (60 φ) d 2 = 2 3 V REF V 2 sin (60 φ)=m sin (60 φ) Space vector control can be applied to the proposed new converters d 0 =1 d 1 d 2 M = 2 V REF = 2 3 V 1 3 V REF V 2 9
Simulated Waveforms: Basic converter in a wind power application Space vector control algorithm Operating point #1 Utility side: 60 Hz, 240 V, p.f. = 1 Generator side: 25 Hz, 240 V, p.f. = 1 Smooth waveforms: line currents PWM waveforms: lineline voltages 10
Simulated Waveforms Regulation of capacitor voltages within switch cells Dashed lines show nominal voltages ± 12% Operating point #1 11
Simulated Waveforms Switching states of each cell Operating point #1 12
Spectrum, utility-side voltage Operating point #1 Low switching frequency of 1 khz Utility frequency = 60 Hz Harmonics are sidebands of switching frequency Harmonic order 13
Spectrum, utility-side voltage Operating point #1 Switching frequency increased to 20 khz Utility frequency = 60 Hz Harmonic order 14
Simulated Waveforms Change of operating point Operating point #2 Utility side: 60 Hz, 240 V, p.f. = 0.5 Generator side: 6.25 Hz, 60 V, p.f. = 1 Smooth waveforms: line currents PWM waveforms: lineline voltages 15
Simulated Waveforms Operating point #2 Regulation of capacitor voltages is maintained at nonunity power factor 16
IV. Conclusions Introduction of a new family of matrix converters, that are fundamentally different from the traditional matrix converter New converters can both increase and decrease the voltage amplitude and can operate with arbitrary power factors Extension to multilevel switching can be attained with device voltages locally clamped to dc capacitor voltages Demonstration of space vector modulation to control the input and output voltage waveforms It is also demonstrated that the controller can stabilize the dc voltages of the capacitors Operation of the basic version of the new family of matrix converters has been confirmed. 17
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