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On the Steady-State Harmonic Performance of Subsea Power Cables Used in Offshore Power Generation Schemes

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On the Steady-State Harmonic Performance of Subsea Power Cables Used in Offshore Power Generation Schemes On the Steady-State Harmonic Performance of Subsea Power Cables Used in Offshore Power Generation Schemes Chang-Hsin CHIEN A Thesis Submitted for the Degree of Doctor of Philosophy Department of Mechanical Engineering University College London June 2007 UMI Number: U592682 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U592682 Published by ProQuest LLC 2013. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 To my grandfather and in memory of my grandmother and to those who believe that education is invaluable asset which can never be taken from us 1 Statement of Originality I, Chang-Hsin CHIEN, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, 1 confirm that this has been indicated in the thesis. Chang-Hsin CHIEN University College London 20 June 2007 Singed: 2 Abstract This thesis reports upon investigations undertaken into the electrical performance o f high power subsea transmission cables and is specifically focused upon their harmonic behaviour, an understanding o f which is fundamental for developing accurate computer based models to evaluate the performance o f existing or new offshore generation schemes. A comprehensive literature search has been undertaken in the areas o f offshore generation, offshore power transmission schemes and harmonic performance o f subsea cable systems. Subsea cable configurations, types and anatomy are presented to give an appreciation o f the arrangement o f subsea power cables. Mathematical equations and computer based algorithms have been developed to model subsea transmission system behaviour where the electrical parameters derived from natural physical phenomena such as skin effects, proximity effects and mutual couplings are included. Proximity effect is examined to determine the consequences o f whether it needs to be considered for each subsea cable arrangement. Bonding solutions for subsea transmission are investigated to study the effect they have on resonance frequency and harmonic response for different cable lengths. The resulting analysis for various cable arrangements explains how geometric arrangements affect the harmonic impedance and harmonic resonance. The harmonic distortion in HVAC offshore transmission systems is also studied to demonstrate the importance o f considering all power components in a subsea power transmission system for harmonic evaluation. In addition, the harmonic distortions of the VSC- HVDC link and associated harmonic power loss are examined. The effects of switching frequency, smoothing capacitor bank size, cable materials and transmission method on harmonic performances o f the VSC -H VD C system w ith varying cable lengths is discussed and therefore subsea power cable harmonic behaviour interacted w ith subsea transmission systems is investigated. The novel contribution of this work is claimed to be in the development of superior models of subsea cables, transmission schemes and associated performance studies, which should lead to significant improvements over existing models and their results. Contents 3 Contents Statement of Originality 1 Abstract 2 Contents 3 List of Figures and Tables 9 Acknowledgments 12 Nomenclatures 13 Abbreviations 24 1. introduction 26 1.1 Background 26 1.2 Aims and Research Objectives 30 l .3 Publications 3 1 1.4 Contributions 32 1.5 Outline of Thesis 33 2. Literature Review 34 2.1 Introduction 34 2.2 A Brief History o f Offshore Power Generation 34 Contents 4 2.2.1 Offshore Renewable Energy 35 2.2.2 Offshore Gas Generation 37 2.3 A Review of AC and DC Offshore Power Link 39 2.4 A Review of Harmonics on Offshore Power Transmission 43 2.5 Summary 50 3. Subsea Power Cable Structures 52 3.1 Introduction 52 3.2 Subsea Power Cable Configurations 52 3.3 Subsea Power Cable Types 54 3.4 Subsea Power Cable Anatomy 56 3.4.1 Conductor 56 3.4.2 Insulation 57 3.4.3 Screening 57 3.4.4 M etallic Sheath 57 3.4.5 Arm our 57 4. Harmonic Calculation Models of Subsea Power Cable 58 4.1 Introduction 58 4.2 Constraints o f Software Package 60 4.3 Equivalent Circuit of Transmission Line 61 4.4 Harmonic Calculations of Overhead Transmission Line 62 4.4.1 Evaluations o f Lumped Parameters 62 4.4.2 Evaluations o f Distributed Parameters 64 4.4.3 Resonances Calculations of A Three-Phase Overhead Transmission Line 67 4.5 Skin Effect and Mutual Coupling 70 4.6 Subsea Power Cable Haimonic Model 72 4.6.1 Calculations o f Single-Core Subsea Power Cable Impedances 72 Contents 5 4.6.2 Calculations of Magnetic Amour Impedances 75 4.6.3 Boundary Condition 77 4.6.4 Calculations o f Single-Core Subsea Power Cable Admittance 78 4.6.5 Resonances Calculations o f Three-Phase Single-Core Subsea Power Cable 79 4.7 Validation of Single-Core Subsea Power Cable Harmonic Model 81 4.8 Summary 83 5. Proximity Effect on Harmonic impedance of Subsea Power Cable 84 5.1 Introduction 84 5.2 Proximity Effect 86 5.3 Calculations o f Harmonic Impedance o f Single-Core Subsea Cables with Proxim ity Effect 88 5.4 Calculations of Harmonic Impedance of Three-Core Subsea Cables with Proximity Effect 91 5.5 Proxim ity Effect on Single-Core and Three-Core Subsea Cables 94 5.5.1 Harmonic Analysis of Proximity Effect using Phase Domain 94 5.5.2 Harmonic Analysis of Proximity Effect using Sequence Domain 96 5.6 Summary 101 6. Harmonic Assessment on Bonding Methods of Subsea Power Cable 102 6.1 Introduction 102 6.2 Bonding Methods 103 6.3 Harmonic Considerations of Bonding Methods 105 6.3.1 Harmonic Equations for Solid Bonding 106 6.3.2 Harmonic Equations for Single-Point Bonding 107 6.3.3 Harmonic Equations for Cross Bonding 108 6.4 Simulation of Subsea Cable Harmonic under Different Bonding Methods 109 6.5 Harmonic Resonance Analysis of Subsea Cable under Different Bonding Methods 112 6.5.1 Resonance Magnitude Analysis 112 6.5.2 Resonance Frequency Analysis 116 Contents 6 6.5.3 Q Factor Analysis 116 6.6 Summary 119 7. Harmonic Performances of Subsea Power Cables in HVACTransmission Systems 120 7.1 Introduction 120 7.2 Arrangements o f AC Subsea Power Cable 122 7.3 Harmonic Calculations under Different Cable Configurations 124 7.3.1 Comparison o f Wedepohl and W ilcox’s Approach and Bianchi and Luoni’s Approach for Sea Return Path Impedance 125 7.3.2 Harmonic Resistance and Inductance for Subsea Power Cables for Each Case 128 7.3.3 Harmonic Resonance for Subsea Power Cables in Each Case 131 7.4 Harmonic Model for Offshore Power HVAC Transmission Systems 133 7.4.1 Harmonic Resonances o f the H VAC Test System 135 7.4.2 Harmonic Distortions of the HVAC Test System 137 7.5 Summary 141 8. Harmonic Analysis of Subsea Power Cables in VSC-HVDC Transmission Systems 142 8.1 Introduction 142 8.2 DC Subsea Cable Harmonic Calculations using Different Materials 144 8.3 Offshore VSC-HVDC Transmission Systems 148 8.3.1 Characteristics o f VSC-HVDC 148 8.3.2 Steady-State Control 149 8.3.3 Calculations Model for Harmonic Analysis 150 8.4 Resonance Evaluations o f VSC-HVDC Subsea Transmission Systems 152 8.5 Harmonic Analysis of VSC-HVDC Subsea Transmission Systems 154 8.5.1 Switching Frequency Effect 154 8.5.2 Capacitor Bank Effect 156 8.5.3 Cable Material Effect 158 Contents 1 8.5.4 Bipolar Transmission Effect 159 8.6 Summary 161 9. Conclusions and Further Work 162 9.1 Conclusions 162 9.2 Further W ork 166 References 168 A. Electrical Parameters of Transmission Lines 178 A. I Introduction 178 A.2 DC Transmission Parameters 178 A .3 AC Transmission Line Parameters 179 A.3.1 Resistance 179 A .3.2 Inductance 180 A.3.3 Capacitance 182 A.3.4 Shunt Conductance 184 B. Cable Dimensions and Materials for Case Studies 185 B. 1 Cable Dimensions and Materials o f Case Study 4.5 185 B.2 Cable Dimensions and Materials of Case Study 4.6 186 B.3 Cable Dimensions and Materials of Case Study 4.7 Validation of PSCAD/EMTDC 187 B.4 Cable Dimensions and Materials o f Case Study 5.2 187 B.5 Cable Dimensions and Materials of Case Study 6.4 188 B.6 Cable Dimensions and Materials o f Case Study 7.3 188 B.7 Cable Dimensions and Materials o f Case Study 8.2 189 B.8 Cable Dimensions and Materials of Case Study 8.5.4 189 Contents 8 C. Modelling of Skin Effect and Mutual Coupling using MathCAD 190 D. Modelling of Harmonic Impedance of Single-Core Subsea Cable using MathCAD 199 E. Transfer Matrices in Admittance Form for HVAC System Components 209 E. 1 Transfer Matrix of Power Transformers in Admittance Form 209 E.2 Transfer M atrix o f Passive Load in Admittance Form 210 E.3 Transfer Matrix of TCR in Admittance Form 210 F. Simulation of HVAC System Harmonics using MATLAB 212 F.l List of Main Program 212 F.2 List o f Sub-Routine o f Cable Harmonic Impedance and Admittance for Cable Type (a) Single-Core Trefoil Subsea Power Cable 215 F.3 List of Sub-Routine for Obtaining Transformer Impedance Matrices 221 F.4 List of Sub-Routine for Obtaining TCR Switching Functions 222 F.5 List of Sub-Routine for Obtaining Harmonic Content 224 G.
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