MODULATION AND CONTROL OF MATRIX CONVERTER FOR AEROSPACE APPLICATION by Keyhan Kobravi A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto Copyright ⃝c 2012 by Keyhan Kobravi Abstract MODULATION AND CONTROL OF MATRIX CONVERTER FOR AEROSPACE APPLICATION Keyhan Kobravi Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2012 In the context of modern aircraft systems, a major challenge is power conversion to supply the aircraft’s electrical instruments. These instruments are energized through a fixed-frequency internal power grid. In an aircraft, the available sources of energy are a set of variable-speed generators which provide variable-frequency ac voltages. Therefore, toenergizetheinternalpowergridofanaircraft,thevariable-frequencyacvoltagesshould be converted to a fixed-frequency ac voltage. As a result, an ac to ac power conversion is required within an aircraft’s power system. This thesis develops a Matrix Converter to energize the aircraft’s internal power grid. The Matrix Converter provides a direct ac to ac power conversion. A major challenge of designing Matrix Converters for aerospace applications is to minimize the volume and weight of the converter. These parameters are minimized by increasing the switching frequency of the converter. To design a Matrix Converter operating at a high switching frequency, this thesis (i) develops a scheme to integrate fast semiconductor switches within the current available Matrix Converter topologies, i.e., MOSFET-based Matrix Converter, and (ii) develops a new modulation strategy for the Matrix Converter. This Matrix Converter and the new modulation strategy enables the operation of the converter at a switching-frequency of 40kHz. Toprovideareliablesourceofenergy, thisthesisalsodevelopsanewmethodology for robust control of Matrix Converter. To verify the performance of the proposed MOSFET-based Matrix Converter, mod- ulation strategy, and control design methodology, various simulation and experimental results are presented. The experimental results are obtained under operating condition present in an aircraft. The experimental results verify the proposed Matrix Converter provides a reliable power conversion in an aircraft under extreme operating conditions. ii The results prove the superiority of the proposed Matrix Converter technology for ac to ac power conversion regarding the existing technologies of Matrix Converters. iii Dedication To my parents and my beloved brother Sepehr, iv Acknowledgements I am very grateful for the opportunity provided for me by both of my supervisors, Professor Reza Iravani and Doctor Hassan Kojori to work on a project that I loved. This projectcouldnothavebeenaccomplishedwithout(i)thebrilliantideasthatwasprovided to me by my both supervisors and (ii) the leadership skills and strategies of my both supervisors. The idea of using output-current measurement to develop a generalized PWM strategy was solely developed during my weekly meetings with Professor Reza Iravani. The idea of developing an optimized switching-pattern to reduce the output- current ripple was provided by Doctor Hassan Kojori. The idea of extending these ideas to 4-Leg Matrix Converter was provided by my both supervisors. Professor Reza Iravani, have learned me a great lesson during my life: A thesis, paper, or report should have both a comprehension of substance and a good style. Two words that I heard later on in speech by the winner of Nobel Memorial Prize in Economic Sciences, Paul Krugman. I would never forget his efforts to improve my style of thinking, writing, and putting various ideas into perspective. His dedication to hard work during the week and weekends, motivated me to work hard all through the years that I had been at University of Toronto. He represented to me a source of unmistakable technical knowledge. His views represented to me magical, as I realized his views importance some years or months afterwards. There has been so many Matrix Converter projects in the world. Rarely, the Matrix Converter projects targeted specifically an aerospace application. It was Doctor Hassan Kojori’s brilliant ideas and exceptional engineering talent that made such a complicated converter to be built for aerospace application. The knowledge for design of such con- verter is fairly complex. I have tried to provide this knowledge as much as possible in this thesis, as they had been taught to me by Doctor Hassan Kojori. I also want to thank Doctor Nabavi for our discussion on the difficulty of various commutation strategies for the Matrix Converter. Special thanks to Honeywell to provide us the opportunity to use their facilities along other equipments of the lab. I would also like to thank my parents to support me financially and spiritually during my PhD studies. I should also thank my long term friend Dr. M. Hajiaghayi who inspired me to do more math work in my thesis and helped me through various convex optimization concepts. I am also very grateful for the knowledge that I gained through my courses at Uni- versity of Toronto. The courses had played a major role in preparing and providing the skills that I needed to accomplish my Ph.D. v Contents 1 Introduction 1 1.1 An Introduction to Aerospace Power Conversion . . . . . . . . . . . . . . 1 1.2 Background and Literature Review . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 MC Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 MC Switch Configurations . . . . . . . . . . . . . . . . . . . . . . 4 1.2.3 MC Commutation Strategies . . . . . . . . . . . . . . . . . . . . . 6 1.2.4 MC Pulse-Width Modulation Strategies . . . . . . . . . . . . . . 9 1.2.5 MC Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Statement of the Problem and Proposed Solution . . . . . . . . . . . . . 10 1.4 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Commutation Strategy 16 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 Organization of this chapter . . . . . . . . . . . . . . . . . . . . . 16 2.2 MC Control-Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Switching Strategy of the MOSFET-Based MC . . . . . . . . . . . . . . 17 2.3.1 Single-Step Commutation Strategy . . . . . . . . . . . . . . . . . 18 2.3.2 The Gate-Driver Structure . . . . . . . . . . . . . . . . . . . . . . 18 2.3.3 Integrated-Capacitor-Snubber-Circuit (ICSC) . . . . . . . . . . . 20 2.3.4 Voltage and Current Waveforms of MC AC-switches during Single- Step Commutation Process . . . . . . . . . . . . . . . . . . . . . . 21 2.3.5 Dead-Time Selection . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4 Performance Evaluation and Verification of the Dead-Time Commutation Strategy with Minimum T . . . . . . . . . . . . . . . . . . . . . . . . . . 24 c 2.4.1 Time-Domain Simulation Using HSPICE . . . . . . . . . . . . . . 25 2.4.2 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . 27 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 vi 3 Generalized PWM Strategy of Matrix Converter 32 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.1.2 Organization of this chapter . . . . . . . . . . . . . . . . . . . . . 33 3.2 Switching-Pattern Generation . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 DCSV-based Generation of Switch Duty Cycles . . . . . . . . . . . . . . 37 3.3.1 DCSV-based Representation of Switch Duty-Cycles . . . . . . . . 37 3.3.2 Triple-Coordinate Representation of a DCSV . . . . . . . . . . . . 38 3.3.3 Surrounding-Triangle of a set of DCSVs . . . . . . . . . . . . . . 39 3.3.4 Duty-cycle Generation of a Set of Translated DCSVs . . . . . . . 41 3.4 Generalized DCSV-Based PWM Strategy of 1-Leg MC . . . . . . . . . . 41 3.4.1 Averaged Input-Currents and Output-Voltage of 1-Leg MC . . . . 43 3.4.2 FormulationofModulationConditionsBasedonControl-Command- Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4.3 Summary of DCSV-based PWM Strategy of the 1-Leg MC . . . . 46 3.5 Generalized PWM Strategy for the 3-Leg MC . . . . . . . . . . . . . . . 47 3.5.1 Averaged Input-Currents and Output-Voltages of the 3-Leg MC . 47 3.5.2 FormulationoftheModulation-ConditionsBasedonControl-Command- Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.5.3 DCSV-based PWM Strategy for the 3-Leg MC . . . . . . . . . . 50 3.6 Generalized PWM Strategy for 4-Leg MC . . . . . . . . . . . . . . . . . 53 3.6.1 Averaged Input-Currents/Output-Voltages of the 4-Leg MC . . . 54 3.6.2 FormulationofModulationConditionsBasedonControl-Command- Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.6.3 DCSV-based PWM Strategy of the 4-Leg MC . . . . . . . . . . . 57 3.7 Implementation of Digital DCSV-based PWM Strategy on a DSP-FPGA- Based Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.7.1 Digital DCSV-based PWM Algorithm for the 3-Leg and the 4-Leg MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.8 Performance Evaluation and Verification of DCSV-based PWM Strategy of 3-Leg and 4-Leg MCs . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.8.1 Computational Performance of DCSV-based PWM Strategy . . . 64 3.8.2 PerformanceEvaluationandVerificationoftheDigitalDCSV-based PWM Strategy of 3-Leg MC . . . . . . . . . . . . . . . . . . . . . 65 3.8.3 PerformanceEvaluationoftheDigitalDCSV-basedPWMStrategy of the 4-Leg MC . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 vii 4 Minimum-Commutation PWM Strategy 82 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.1.1 Organization of this chapter . . . . . . . . . . . . . . . . . . . . . 82 4.2 Minimizing Number of Commutations per Switching-Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3 MinC-PWM Strategies of 3-Leg MC . . . . . . . . . . . . . . . . . . . . 84 4.3.1 DCSV-based MinC-PWM Strategy of 3-Leg MC . . . . . . . . . . 90 4.4 Performance Evaluation and Verification of MinC-PWM . . . . . . . . . 93 4.4.1 Performance Evaluation and Verification of MinC-PWM for 3-Leg MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4.2 Performance Evaluation of MinC-PWM for 4-Leg MC . . . . . . . 104 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5 Minimum Output-Current Ripple PWM Strategy 116 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.1.2 Organization of this Chapter . . . . . . . . . . . . . . . . . . . . . 117 5.2 Space-Vector of Output-Current Ripple . . . . . . . . . . . . . . . . . . 117 5.2.1 Instantaneous Output-Current Ripple RMS (Ins-OCRrms) . . . . 122 5.3 Instantaneous Output-Current Ripple RMS of MinC-PWM (Ins-OCRrms) 123 5.4 MinOCR-PWM Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.5.1 Averaged Output-Current Ripple RMS of MinOCR-PWM, SVM, and SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.5.2 Output-Current Ripple in Frequency-Spectrum . . . . . . . . . . 130 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6 Control of Matrix Converter for Power Supply Application 138 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.2.1 Organization of this Chapter . . . . . . . . . . . . . . . . . . . . . 140 6.3 Abc-frame based control strategy of MC-Based Power Supply . . . . . . 140 6.3.1 Dynamical Equations of the Output-Filter Variables . . . . . . . . 141 6.4 Observer-Based Design of the Resonant Controller . . . . . . . . . . . . . 143 6.4.1 Reference signal generation using an exodus model . . . . . . . . 144 6.4.2 Design of Resonant Controller . . . . . . . . . . . . . . . . . . . . 146 6.4.3 Summary of Design Process . . . . . . . . . . . . . . . . . . . . . 150 6.5 Discrete Time-Domain Realization of Resonant Controller . . . . . . . . 150 viii 6.6 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.6.1 Balanced Full-Load Condition . . . . . . . . . . . . . . . . . . . . 157 6.6.2 No-Load Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.6.3 Single-Phase Non-linear Load Condition . . . . . . . . . . . . . . 162 6.7 conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 7 Conclusions 168 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 7.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 7.4 Suggested Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Appendices 174 A Quasi-stationary Model of Power MOSFET 175 B Switching Process 177 B.1 Turn-off Process of S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Aa B.2 Open Circuit Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 B.3 Turn-on Process of S . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Ba B.4 Summary of Switching Process . . . . . . . . . . . . . . . . . . . . . . . . 184 C Modeling of Low-Frequency Harmonic-Distortions 186 C.1 Input/Output Current Distortions Due to Commutation Process . . . . . 191 C.1.1 Losses due to Commutation Processes . . . . . . . . . . . . . . . 193 D Space-Vector Definition 194 E 3-Leg MC Generalized Set of DCSVs 195 F 4-Leg MC Generalized Set of DCSVs 197 G Method to Determine m(2) , m(2) , and m(2) 200 y;+ y;− y;c H MinC-PWM Strategies of the 4-Leg MC 203 H.1 Method to Find m(2) , m(2) , and m(2) . . . . . . . . . . . . . . . . . . . . 209 y;+ y;− y;c H.2 DCSV-based MinC-PWM Strategy of 4-Leg MC . . . . . . . . 209 H.3 Digital Implementation of the DCSV-Based MinC-PWM of 3-Leg and 4- Leg MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Bibliography 216 ix List of Tables 2.1 The signal propagation components . . . . . . . . . . . . . . . . . . . . . 24 2.2 The parameters of the circuit in Fig. 2.2 used for HSPICE simulation for T = 125o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 2kW Single-Phase MC Specifications . . . . . . . . . . . . . . . . . . . . 27 3.1 Execution Time of Some Basic Algebraic Calculations . . . . . . . . . . . 64 3.2 Execution Time of Modulation-Algorithm in DSP and FPGA . . . . . . 65 3.3 2kW 3-Leg MC Experimental Setup Parameters . . . . . . . . . . . . . . 65 3.4 4-Leg MC Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.5 THD Analysis of DCSV-based PWM Strategy . . . . . . . . . . . . . . . 75 3.6 THD Analysis of DCSV-based PWM Strategy with Unbalanced Load . . 79 3.7 THD Analysis of DCSV-based PWM Strategy with Unbalanced Load . . 81 4.1 THD Analysis of MinC-PWM Strategy . . . . . . . . . . . . . . . . . . . 99 4.2 THD Analysis of MinC-PWM Strategy . . . . . . . . . . . . . . . . . . . 104 4.3 THD Analysis of MinC-PWM Mode-R Strategy for 4-Leg MC . . . . . . 107 5.1 THD Comparison of SVM and MinOCR-PWM . . . . . . . . . . . . . . 136 6.1 4-Leg MC Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.2 Comparison of Output-Voltage v THD for SVM and MinOCR-PWM . 157 f;an x