Three-Level Z-Source Hybrid Direct AC-AC Power Converter Topology Francis Boafo Effah, BSc. MSc. Submitted to the University of Nottingham for the degree of Doctor of Philosophy, November 2013. Abstract Voltage source inverter (VSI) is the traditional power converter used to provide vari- able voltage and frequency from a fixed voltage supply for adjustable speed drive and many other applications. However, the maximum ac output voltage that can be synthesized by a VSI is limited to the available dc-link voltage. With its unique structure, the Z-source inverter can utilise shoot-through states to boost the output voltage and provides an attractive single-stage dc-ac conversion that is able to buck and boost the voltage. For applications with a variable input voltage, this inverter is a very competitive topology. The same concept can equally be extended to the two-stage matrix converter, where a single Z-source network is inserted in its virtual dc-link. The topology formed is, thus, quite straightforward. Its modulation is, however, non-trivial if advantages like voltage buck-boost flexibil- ity, minimum commutation count, ease of implementation, and sinusoidal input and output quantities are to be attained simultaneously. This thesis presents two novel space vector modulation methods for controlling a three-level Z-source neutral point clamped VSI to enable the use of a boost function. The second of the two space vector modulation methods is then adopted and applied to a three-level, two-stage matrix converter with a Z-source network inserted in its virtual dc-link to increase the voltage transfer ratio beyond the intrinsic 86.6% limit. Simulation results are supported by experimental verification from two laboratory prototype converters. i Acknowledgements IwouldliketothankProf. PerttiSilventoinenandProf. PericleZanchettaforsparing their time to examine me on the work in this thesis. I would also like to express my most sincere gratitude to my supervisors Prof. Pat Wheeler, Prof. Jon Clare and Dr. Alan Watson for their guidance, patience and sup- port over the course of this project. Special thanks to the University of Nottingham for awarding me a “Dean’s Scholarship for Engineering Research” to undertake this project. Thanks also to the staff of the PEMC group at the University of Nottingham and all the technicians of the ground floor workshop, for providing the necessary help to carry out this work. I would especially like to thank Dr. Liliana de Lillo, Dr. Lee Empringham and Dr. Andrew Trentin for their help during the experimental testing of my rig - even when they were very busy. Thanks to all my friends and colleagues of the PEMC group for their friendship and support over the last few years. I would like to especially thank my dear wife Ellen and my sons Michael, Bryan and Philip for their patience, support and love over the course of this work and for generally being there when I needed them. Finally, I would like to thank God Almighty for giving me life and strength to carry out this work. All glory and honour be unto His name now and forever. Amen! ii List of Terms Notation Meaning Notation Meaning V Volt A Ampere Ω Ohm H Henry F Farad Hz Hertz ac Alternating current V Full dc-link voltage pn dc Direct current ASD Adjustable speed drive PWM Pulse width modulation NPC Neutral point clamped V DC supply SVM Space vector modulation DC NTV Nearest three vectors SVD Space vector diagram GTO Gate turn-off thyristor v Neutral point voltage o MOS Metal-oxide-semiconductor i Neutral point current o MCT MOS controlled thyristor VSI Voltage source inverter IGBT Integrated gate bipolar IGCT Integrated gate transistor commutated transistor V Average dc-link voltage v , v , v Diode voltage drop pn,avg D D1 D2 RB Reverse blocking p,n DC-link terminals o DC-link midpoint T Switching period sw V Zero voltage vector V , V Split dc-link voltages 0 po no V Small voltage vectors V Medium voltage vectors Si Mi ⃗ V Large voltage vectors V Amplitude of V (t) Li om out ⃗ m Modulation index of V (t) Reference output voltage I out inversion stage vector REC Reduced element count FST Full-shoot-through L , L Z-source inductors UST Upper-shoot-through 1 2 ˆ C , C Z-source capacitors V Effective dc-link voltage 1 2 i V , V , V Output line-to-load V , V , V Output line-to-dc link As Bs Cs Ao Bo Co neutral voltages midpoint voltages V , V Average values of V , V , V Output line-to-line po,avg no,avg AB BC CA V and V voltages po no MOSFET Metal-oxide-semiconductor m Modulation index of R Field-effect transistor Rectification stage LST Lower-shoot-through q Voltage transfer ratio DSP Digital signal processor SMC Sparse matrix converter iii iv Notation Meaning Notation Meaning PCB Printed circuit board R Damping resistor d ⃗ d ,d ,d Duty ratios of small, I (t) Reference input current VSi VMi VLi in medium, large vectors vector I Amplitude of reference θ Angle of reference output in out input current vector voltage vector NTVV Nearest three virtual V Virtual zero voltage V0 vectors vector V Virtual small voltage V Virtual medium voltage VSi VMi vectors vectors V Virtual large voltage d , d , d Duty ratios of VLi x y z vectors virtual voltage vectors i , i , i Three phase input ULST Upper-lower-shoot- a b c currents through T Full-shoot-through T Upper-shoot-through st u time time T Lower-shoot-through T Total upper-lower- l ulst time shoot-through time B Boost factor for B′ Boost factor for FST operation ULST operation ˆ ˆ V Peak fundamental ac V Peak fundamental ac xo xy phase-to-neutral voltage line-to-line voltage ˆ V , V , V Average Z-source capacitor V DC-link voltage C1 C2 C i UST voltage during UST states ˆ ˆ V DC-link voltage V DC-link voltage i LST i NST during LST states during NST states V , V , V Supply voltages I , I , I Output currents sa sb sc A B B V , V , V Three-phase input V , V , V Three-phase a b c A B C voltages to matrix converter output voltages ω Frequency of supply ω Frequency of output i o voltages voltages ϕ , ϕ Input and output V Amplitude of input i o im phase displacement angles phase voltages V Rectified input voltage ω Cut-off frequency env c envelope value of input filter d , d , d Duty ratios for d , d , d Duty ratios for γ δ 0,rec α β 0,inv input current vectors output voltage vectors L , C Input filter inductor C , R Clamp capacitor and f f c c and capacitor resistor TMC Two-stage matrix VSMC Very sparse matrix converter converter USMC Ultra sparse matrix FPGA Field programmable gate converter array Contents 1 Introduction 1 1.1 Background of dc-to-ac power conversion . . . . . . . . . . . . . . . . 1 1.2 Background of ac-to-ac power conversion . . . . . . . . . . . . . . . . 2 1.3 The Z-source converter . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.1 Target application areas for Z-source converters . . . . . . . . 5 1.4 Motivation and objectives of the project . . . . . . . . . . . . . . . . 6 1.5 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Three-Level Neutral Point Clamped Inverter 8 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Inverter configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 State of the art in modulation strategies . . . . . . . . . . . . . . . . 12 2.4 Space vector modulation . . . . . . . . . . . . . . . . . . . . . . . . . 16 v CONTENTS vi 2.4.1 Nearest three vector SVM . . . . . . . . . . . . . . . . . . . . 17 2.4.1.1 Calculation of duty cycles . . . . . . . . . . . . . . . 19 2.4.1.2 Switching sequences . . . . . . . . . . . . . . . . . . 20 2.4.2 Nearest three virtual vector (NTVV) SVM . . . . . . . . . . . 21 2.4.2.1 Definition of virtual space vectors . . . . . . . . . . . 21 2.4.2.2 Selection of virtual space vectors . . . . . . . . . . . 23 2.4.2.3 Switching states sequence . . . . . . . . . . . . . . . 24 2.5 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 Three-Level Z-Source Neutral Point Clamped Inverter 29 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Overview of Z-source inverter . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Three-level Z-source NPC inverter . . . . . . . . . . . . . . . . . . . . 31 3.3.1 Circuit configuration . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.2 Circuit analysis of the REC Z-source NPC inverter . . . . . . 34 3.3.2.1 Full-shoot-through operating mode . . . . . . . . . . 35 3.3.2.2 Upper-lower-shoot-through operating mode . . . . . 37 3.4 Selection of Z-source component values . . . . . . . . . . . . . . . . . 39 CONTENTS vii 3.5 Novel NTV SVM for Z-source NPC inverter . . . . . . . . . . . . . . 40 3.5.1 PWM switching pattern . . . . . . . . . . . . . . . . . . . . . 41 3.5.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.6 Novel NTVV SVM for Z-source NPC inverter . . . . . . . . . . . . . 48 3.6.1 PWM switching pattern . . . . . . . . . . . . . . . . . . . . . 48 3.6.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4 Two-Stage Direct AC-AC Power Converter 55 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 Conventional matrix converter . . . . . . . . . . . . . . . . . . . . . . 56 4.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.2 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . 58 4.2.3 Modulation techniques for the direct matrix converter . . . . . 60 4.2.3.1 The modulation problem and basic solution . . . . . 60 4.2.3.2 Venturini modulation methods . . . . . . . . . . . . 62 4.2.3.3 Scalar modulation methods . . . . . . . . . . . . . . 63 4.2.3.4 SVM methods . . . . . . . . . . . . . . . . . . . . . 64 4.2.3.5 Indirect modulation methods . . . . . . . . . . . . . 68 CONTENTS viii 4.3 Two-stage matrix converter . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.3.2 SVM for the two-stage matrix converter . . . . . . . . . . . . 71 4.3.2.1 The rectification stage - input current SVM . . . . . 72 4.3.2.2 Elimination of zero current vectors in the rectification stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.2.3 The inversion stage - output voltage SVM . . . . . . 74 4.3.2.4 Synchronisationoftherectificationandinversionstage switching . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.4 Bidirectional switch configurations . . . . . . . . . . . . . . . . . . . 82 4.4.1 Diode bridge bidirectional switch cell . . . . . . . . . . . . . . 82 4.4.2 Common-emitter bidirectional switch cell . . . . . . . . . . . . 83 4.4.3 Common-collector bidirectional switch cell . . . . . . . . . . . 83 4.4.4 Anti-parallel reverse blocking IGBTs (RB-IGBTs) . . . . . . . 84 4.5 Current commutation techniques . . . . . . . . . . . . . . . . . . . . 85 4.5.1 Basic current commutation . . . . . . . . . . . . . . . . . . . . 86 4.5.1.1 Dead-time commutation . . . . . . . . . . . . . . . . 86 4.5.1.2 Overlap commutation . . . . . . . . . . . . . . . . . 86 CONTENTS ix 4.5.2 Advanced commutation methods . . . . . . . . . . . . . . . . 87 4.5.2.1 Current-direction-based commutation . . . . . . . . . 88 4.5.2.2 Relative-voltage-magnitude-based commutation . . . 89 4.5.2.3 Selection of a suitable current commutation technique for the two-stage matrix converter . . . . . . . . . . 90 4.6 Practical issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.6.1 Input filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.6.2 Over-voltage protection . . . . . . . . . . . . . . . . . . . . . . 93 4.6.3 The clamp circuit . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.7 Advantages of the two-stage matrix converter over the conventional matrix converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.7.1 Safer commutation . . . . . . . . . . . . . . . . . . . . . . . . 95 4.7.2 Reduced number of switches . . . . . . . . . . . . . . . . . . . 96 4.7.3 Cost effective multi-drive system . . . . . . . . . . . . . . . . 97 4.8 Comparison of conventional and two-stage matrix converters . . . . . 98 4.8.1 Supply current quality . . . . . . . . . . . . . . . . . . . . . . 99 4.8.2 Voltage transfer ratio . . . . . . . . . . . . . . . . . . . . . . . 99 4.8.3 Semiconductor power losses . . . . . . . . . . . . . . . . . . . 99 4.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101