Predictive Control of Three Phase AC/DC Converters

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a α ka kα kαβ a α kα kαβ ka 122 APPENDIX A. COORDINATE TRANSFORMATIONS where: ⎡ ⎢ ⎣ 1 0 − 1 2 √ 3 2 − 1 2 − √ 3 2 ⎤ ⎥ ⎦ = A αβ2abc (A.5) is called matrix transformation. Figures A.1 and A.2 show graphical transformation between coordinate systems. kβ kc β kb Figure A.1: Transformation from natural to stationary coordinate system c b kβ kc kb β Figure A.2: Transformation from stationary to natural coordinate system c b
q β A.2. ROTATING SYSTEM 123 A.2 Rotating system Let consider space vector k in stationary αβ system, which will be transformed into rotating with angular frequency coordinate dq system. Ω r = dγ r dt where: γ r is an angle between real axes: α and d <strong>of</strong> coordinate systems. (A.6) Figure A.3: Transformation from stationary to rotating coordinate system kβ α kd kq γr Ωr γ d The expressions can be written as: kkα k r = ke −jγ r (A.7) = (k α + jk β )(cos γ r − j sin γ r ) = k α cos γ r + k β sin γ r + j(−k α sin γ r + k β cos γ r ) (A.8) or as a matrix: [ ] [ k d = k q ] [ ] cos γ r sin γ r k α − sin γ r cos γ r k β (A.9) where: [ ] cos γ r sin γ r = A αβ2dq (A.10) − sin γ r cos γ r is matrix transformation. The inverse equation: k = k r e jγ r = (k d + jk q )(cos γ r + j sin γ r ) (A.11) = k d cos γ r − k q sin γ r + j(k d sin γ r + k q cos γ r ) (A.12)
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WARSAW UNIVERSITY OF TECHNOLOGY Fac
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Contents Contents i 1 Introduction
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CONTENTS iii List of Symbols and Ab
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Chapter 1 Introduction AC/DC Voltag
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Based Trajectory Based Deadbeat Con
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5 which properties are deteriorated
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Chapter 2 Voltage Source Converter
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(Sa=1, Sc=0) UP2 (Sa=1, UP1 Sb=1, S
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IL UL jωLIL UL jωLIL 2.2. MATHEMA
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ILα 1 sL+RSα - ULα 32IDC 1 sCUDC
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2.3. SUMMARY 15 2.3 Summary In this
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Iqref Idref ILq ILd ILq φ uLab UDC
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UDC Filter 20 CHAPTER 3. CONTROL ST
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Qref dP dQ uLab UDC Sabc 22 CHAPTER
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24 CHAPTER 3. CONTROL STRATEGIES FO
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Qref Pref uLab UDC Sabc 26 CHAPTER
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UDC Filter 28 CHAPTER 3. CONTROL ST
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ILq φ ωL 30 CHAPTER 3. CONTROL ST
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Lα 32 CHAPTER 3. CONTROL STRATEGIE
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Chapter 4 Predictive Direct Power C
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4.3. VARIABLE SWITCHING FREQUENCY P
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UPdqUDC Qref UDCSabc uLab iLab 4.3.
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UPdqUDC UDCSabc uLab iLab 4.4. CURR
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UPdqUDC Qref Pref UDCSabc uLab iLab
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4.6. CONSTANT SWITCHING FREQUENCY P
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PP1 fq1 fq2 PP4 PP5 PP6 PP3 fp3 fp3
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Sb Sc Sa Sb Sa Sc Sb Sa 4.6. CONSTA
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fqi fpi Qref Sabc 4.6. CONSTANT SWI
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4.7. VF BASED CSF - PREDICTIVE DIRE
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Qref fpi Sabc iLab 4.7. VF BASED CS
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4.8. SIMULATION RESULTS 63 200 150
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4.8. SIMULATION RESULTS 67 Mag (% o
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Page 81 and 82: 4.8. SIMULATION RESULTS 71 2500 200
Page 83 and 84: 4.8. SIMULATION RESULTS 73 650 600
Page 85 and 86: 4.9. SUMMARY 75 Control Method t se
Page 87 and 88: Chapter 5 Investigations of Control
Page 89 and 90: 5.1. ROBUSTNESS TO PARAMETERS MISMA
Page 91 and 92: Sabc UDC UPαβ UPαβ Lest Lest UP
Page 93 and 94: 5.4. LINE VOLTAGE DISTURBANCES 83 (
Page 95 and 96: 5.4. LINE VOLTAGE DISTURBANCES 85 (
Page 97 and 98: 5.4. LINE VOLTAGE DISTURBANCES 87 C
Page 99 and 100: Chapter 6 Experimental Study Experi
Page 101 and 102: 6.1. STEADY STATE OPERATION 91 (a)
Page 103 and 104: 6.1. STEADY STATE OPERATION 93 Cont
Page 105 and 106: 6.2. TRANSIENT OPERATION 95 (a) ST-
Page 111 and 112: 6.3. OPERATION WITH LOW SWITCHING F
Page 117: 6.4. SUMMARY 107 Control Method t s
Page 120 and 121: 110 CHAPTER 7. SUMMARY AND FINAL CO
Page 122 and 123: 112 BIBLIOGRAPHY [11] K. Hyosung an
Page 124 and 125: 114 BIBLIOGRAPHY [38] A. Nasiri,
Page 126 and 127: 116 BIBLIOGRAPHY [66] F. Morel, J.
Page 128 and 129: 118 BIBLIOGRAPHY 13. A. Lopez de He
Page 131: Appendix A Coordinate transformatio
Page 135 and 136: Appendix B Predictive Current Contr
Page 137 and 138: ∆ILαβP6 ∆ILαβP5 Figure B.2:
Page 139: Figure B.4: Vector diagram of predi
Page 142 and 143: 132 APPENDIX C. PREDICTIVE DIRECT P
Page 145 and 146: List of Symbols and Abbreviations S
Page 147 and 148: 137 Symbols Description Definition
Page 149 and 150: List of Figures 1.1 Conjunction bet
Page 151 and 152: LIST OF FIGURES 141 5.3 Line curren
Page 153: LIST OF TABLES 143 B.2 An example o
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Predictive Control of Three Phase AC/DC Converters

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