Predictive Control of Three Phase AC/DC Converters

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56 CHAPTER 4. PREDICTIVE DIRECT POWER CONTROL ( )) 1 Q err = Q ref − Q − 2 (f q1 t 1 + f q2 t 2 + f q3 2 T s − t 1 − t 2 (4.39) To minimize power errors, least square optimization method has been introduced. The cost function J has been defined as a sum of squared errors: and after replacing (4.38) and (4.39) into (4.40): J = P 2 err + Q 2 err (4.40) J = [ P ref − P − 2 ( f p1 t 1 + f p2 t 2 + f p3 ( 1 2 T s − t 1 − t 2 ))] 2 + [ Q ref − Q − 2 ( f q1 t 1 + f q2 t 2 + f q3 ( 1 2 T s − t 1 − t 2 ))] 2 (4.41) The optimal application times t 1 , t 2 , t 3 , which minimize cost function value J, during sampling time T s , satisfies minimum value condition: ⎧ ⎪⎨ ⎪⎩ ∂J ∂t 1 = 0 ∂J ∂t 2 = 0 (4.42) Partial differences of J function are expressed as: ∂J ∂t 1 = 4 [ (P ref − P − f p3 T s ) (f p3 − f p1 ) + (Q ref − Q − f q3 T s ) (f q3 − f q1 ) ] + 8 [ (f p3 − f p1 ) 2 + (f q3 − f q1 ) 2] t 1 + 8 [ (f p3 − f p2 )(f p3 − f p1 ) + (f q3 − f q2 )(f q3 − f q1 ) ] (4.43) t 2 ∂J ∂t 2 = 4 [(P ref − P − f p3 T s ) (f p3 − f p2 ) + (Q ref − Q − f q3 T s ) (f q3 − f q2 )] + 8 [(f p3 − f p1 )(f p3 − f p2 ) + (f q3 − f q1 )(f q3 − f q2 )] t 1 + 8 [ (4.44) (f p3 − f p2 ) 2 + (f q3 − f q2 ) 2] t 2 The J gets minimum value when (4.43), (4.44) are equal to zero (4.42). The solution of sets of conditions are application times given by: [ t 1 = (P ref − P )(f q2 − f q3 ) + (Q ref − Q)(f p3 − f p2 ) + (f p2 f q3 − f p3 f q2 )T s ]/ [ ] 2((f q2 − f q3 )f p1 + (f q3 − f q1 )f p2 + (f q1 − f q2 )f p3 ) (4.45) t 2 = [ (P ref − P )(f q3 − f q1 ) + (Q ref − Q)(f p1 − f p3 ) + (f q1 f p3 − f q3 f p1 )T s ]/ [ ] 2((f q2 − f q3 )f p1 + (f q3 − f q1 )f p2 + (f q1 − f q2 )f p3 ) (4.46) t 3 = 1 2 T s − t 1 − t 2 (4.47) Appendix C shows an example operation of presented control method for specified conditions.
fqi fpi Qref Sabc 4.6. CONSTANT SWITCHING FREQUENCY PREDICTIVE DIRECT POWER CONTROL 57 4.6.5 Control Scheme of CSF-P-DPC Control scheme of proposed method has been presented in Fig. 4.11. System uses linear PI controller in outer DC-link voltage stabilization loop. Instantaneous active P and reactive Q powers are calculated on the basis of line voltages U L , and line currents I L measurement (3.13), (3.14). Also, line voltage space vector U Lαβ is delivered to switching table (Tab. 4.4), which selects sequence of VSC input vectors (Fig. 4.10). Next, the power predictive model, calculates power time derivatives f pi , f qi (4.25), (4.26) for appropriate voltage vectors U P . The goal of the control is to determine U P application times t 1 , t 2 and t 3 (4.45) – (4.47) in order to minimize cost function value J defined as a sum of squared instantaneous power errors (4.40). αβ uLab ULαβ abc Active & Reactive Power Calculation ILαβ iLab Q P Switching Table ULαβ Cost Function Minimization Criteria Power Predictive Model VSC PI - LOAD Figure 4.11: Control scheme of Constant Switching Frequency Predictive Direct Power Control CSF-P-DPC Pref UDC UDCref
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WARSAW UNIVERSITY OF TECHNOLOGY Fac
Page 5 and 6:
Contents Contents i 1 Introduction
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CONTENTS iii List of Symbols and Ab
Page 11 and 12:
Chapter 1 Introduction AC/DC Voltag
Page 13 and 14:
Based Trajectory Based Deadbeat Con
Page 15 and 16: 5 which properties are deteriorated
Page 17 and 18: Chapter 2 Voltage Source Converter
Page 19 and 20: (Sa=1, Sc=0) UP2 (Sa=1, UP1 Sb=1, S
Page 21 and 22: IL UL jωLIL UL jωLIL 2.2. MATHEMA
Page 23 and 24: ILα 1 sL+RSα - ULα 32IDC 1 sCUDC
Page 25: 2.3. SUMMARY 15 2.3 Summary In this
Page 28 and 29: Iqref Idref ILq ILd ILq φ uLab UDC
Page 30 and 31: UDC Filter 20 CHAPTER 3. CONTROL ST
Page 32 and 33: Qref dP dQ uLab UDC Sabc 22 CHAPTER
Page 34 and 35: 24 CHAPTER 3. CONTROL STRATEGIES FO
Page 36 and 37: Qref Pref uLab UDC Sabc 26 CHAPTER
Page 38 and 39: UDC Filter 28 CHAPTER 3. CONTROL ST
Page 40 and 41: ILq φ ωL 30 CHAPTER 3. CONTROL ST
Page 42 and 43: Lα 32 CHAPTER 3. CONTROL STRATEGIE
Page 51 and 52: Chapter 4 Predictive Direct Power C
Page 53 and 54: 4.3. VARIABLE SWITCHING FREQUENCY P
Page 55 and 56: UPdqUDC Qref UDCSabc uLab iLab 4.3.
Page 57 and 58: UPdqUDC UDCSabc uLab iLab 4.4. CURR
Page 59 and 60: UPdqUDC Qref Pref UDCSabc uLab iLab
Page 61 and 62: 4.6. CONSTANT SWITCHING FREQUENCY P
Page 63 and 64: PP1 fq1 fq2 PP4 PP5 PP6 PP3 fp3 fp3
Page 65: Sb Sc Sa Sb Sa Sc Sb Sa 4.6. CONSTA
Page 69 and 70: 4.7. VF BASED CSF - PREDICTIVE DIRE
Page 71 and 72: Qref fpi Sabc iLab 4.7. VF BASED CS
Page 73 and 74: 4.8. SIMULATION RESULTS 63 200 150
Page 77 and 78: 4.8. SIMULATION RESULTS 67 Mag (% o
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
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6.4. SUMMARY 107 Control Method t s
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110 CHAPTER 7. SUMMARY AND FINAL CO
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112 BIBLIOGRAPHY [11] K. Hyosung an
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114 BIBLIOGRAPHY [38] A. Nasiri,
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116 BIBLIOGRAPHY [66] F. Morel, J.
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118 BIBLIOGRAPHY 13. A. Lopez de He
Page 131 and 132:
Appendix A Coordinate transformatio
Page 133 and 134:
q β A.2. ROTATING SYSTEM 123 A.2 R
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Appendix B Predictive Current Contr
Page 137 and 138:
∆ILαβP6 ∆ILαβP5 Figure B.2:
Page 139:
Figure B.4: Vector diagram of predi
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132 APPENDIX C. PREDICTIVE DIRECT P
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List of Symbols and Abbreviations S
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137 Symbols Description Definition
Page 149 and 150:
List of Figures 1.1 Conjunction bet
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LIST OF FIGURES 141 5.3 Line curren
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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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