Tài liệu Handbook of ocean wave energy

Ocean Engineering & Oceanography 7 Arthur Pecher Jens Peter Kofoed Editors Handbook of Ocean Wave Energy Ocean Engineering & Oceanography Volume 7 Series editors Manhar R. Dhanak, Florida Atlantic University, Boca Raton, USA Nikolas I. Xiros, New Orleans, USA More information about this series at http://www.springer.com/series/10524 Arthur Pecher Jens Peter Kofoed • Editors Handbook of Ocean Wave Energy Editors Arthur Pecher Wave Energy Research Group, Department of Civil Engineering Aalborg Universtiy Aalborg Denmark Jens Peter Kofoed Wave Energy Research Group, Department of Civil Engineering Aalborg Universtiy Aalborg Denmark ISSN 2194-6396 ISSN 2194-640X (electronic) Ocean Engineering & Oceanography ISBN 978-3-319-39888-4 ISBN 978-3-319-39889-1 (eBook) DOI 10.1007/978-3-319-39889-1 Library of Congress Control Number: 2016943821 © The Editor(s) (if applicable) and The Author(s) 2017. This book is published open access. Open Access This book is distributed under the terms of the Creative Commons AttributionNoncommercial 2.5 License (http://creativecommons.org/licenses/by-nc/2.5/) which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. The images or other third party material in this book are included in the work’s Creative Commons license, unless indicated otherwise in the credit line; if such material is not included in the work’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt or reproduce the material. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland Preface This Handbook for Ocean Wave Energy aims at providing a guide into the field of ocean wave energy utilization. The handbook offers a concise yet comprehensive overview of the main aspects and disciplines involved in the development of wave energy converters (WECs). The idea for the book has been shaped by the development, research, and teaching that we have carried out at the Wave Energy Research Group at Aalborg University over the past decades. It is our belief and experience that it would be useful writing and compiling such a handbook in order to enhance the understanding of the sector for a wide variety of potential readers, from investors and developers to students and academics. At the Wave Energy Research Group, we have a wide range of wave energy related activities ranging from teaching at master and Ph.D. level, undertaking generic research projects and participating in specific research and development projects together with WEC developers and other stakeholders. All these activities have created a solid background in terms of theoretical knowledge, experimental and numerical modeling skills as well as a scientific network, which is why we found that the idea of putting this book together seemed realistic. With this as a starting point, we gathered a group of authors, each an expert within their specific research topic. It was clear from the beginning that the ambition was to make a high-quality publication but still ensuring that it would have a high level of accessibility. Therefore, we wanted the book to be freely available in digital form. To make this happen, we sought and received funding from the Danish EUDP program (project no. 64015-0013), for which we are extreme thankful. The ten chapters of the handbook present a broad range of relevant rules of thumb and topics, such as the technical and economic development of a WEC, wave energy resource, wave energy economics, WEC hydrodynamics, power take-off systems, mooring systems as well as the experimental and numerical simulation of WECs. It covers the topic of wave energy conversion from different perspectives, providing the readers, who are experts in one particular topic, with a clear overview of the key aspects in other relevant topics in which they might be less specialized. v vi Preface We would especially like to thank our co-authors, who have contributed enthusiastically to the content and without whom we would never have been able to realize this handbook. We would also like to thank our colleagues at the Department of Civil Engineering for supporting us, especially Kim Nielsen who patiently helped us getting all the small final details in place as well as reading through all the chapters for final corrections and comments, and Vivi Søndergaard who gave the final touch to the English language. Last but not least, we would like to thank our wives, Marie Isolde Müller and Kirsten Aalstrup Kofoed, for their endless patience and support. We have enjoyed working with you all and we are very grateful for each of your contribution. Aalborg, Denmark 2016 Arthur Pecher Jens Peter Kofoed Contents 1 2 3 Introduction . . . . . . . . . . . . . . . . . . . . . . Arthur Pecher and Jens Peter Kofoed 1 Introduction. . . . . . . . . . . . . . . . . . . . . 2 The Successful Product Innovation . . . . . 3 Sketching WECs and Their Environment 4 Rules of Thumb for Wave Energy . . . . . 4.1 The Essential Features of a WEC . . 4.2 Economic Rules of Thumb . . . . . . 4.3 WEC Design Rules of Thumb . . . . 4.4 Power Take-Off Rules of Thumb . . 4.5 Environmental Rules of Thumb . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 5 5 6 9 12 13 14 ................... 17 . . . . . . . . . . . . . . . . . . 17 19 22 22 23 24 37 39 41 ...................... 43 ...................... ...................... Energy Resource . . . . . . . . . . 43 43 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . The Wave Energy Sector . . . . . . . . . . . . Jens Peter Kofoed 1 Introduction. . . . . . . . . . . . . . . . . . . . 2 Potential of Wave Energy . . . . . . . . . . 3 Wave Energy Converters. . . . . . . . . . . 3.1 History . . . . . . . . . . . . . . . . . . . 3.2 Categorization of WEC’s. . . . . . . 3.3 Examples of Various WEC Types 3.4 The Development of WECs . . . . . 4 Test Sites . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . The Wave Energy Resource . . . . . . . Matt Folley 1 Introduction to Ocean Waves. . . . . 1.1 Origin of Ocean Waves. . . . . 1.2 Overview of the Global Wave .................. . . . . . . . . . vii viii Contents 2 Water Wave Mechanics . . . . . . . . . . . . . . . . . . . . . . . 2.1 Definition and Symbols. . . . . . . . . . . . . . . . . . . . 2.2 Dispersion Relationship. . . . . . . . . . . . . . . . . . . . 2.3 Water Particle Path and Wave Motions . . . . . . . . . 3 Characterisation of Ocean Waves and the Wave Climate . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Temporal, Directional and Spectral Characteristics of the Wave Climate. . . . . . . . . . . . . . . . . . . . . . 3.3 Spectral Representation of Ocean Waves . . . . . . . . 3.4 Characterization Parameters . . . . . . . . . . . . . . . . . 3.5 Challenges in Wave Climate Characterisation. . . . . 3.6 Coastal Processes . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Case Study—Incident Wave Power. . . . . . . . . . . . 4 Measurement of Ocean Waves . . . . . . . . . . . . . . . . . . . 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Surface-Following Buoy . . . . . . . . . . . . . . . . . . . 4.3 Sea-Bed Pressure Sensor . . . . . . . . . . . . . . . . . . . 4.4 Acoustic Current Profiler . . . . . . . . . . . . . . . . . . . 4.5 Land-Based and Satellite Radar . . . . . . . . . . . . . . 5 Modelling of Ocean Waves . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 General Spectral Wave Models . . . . . . . . . . . . . . 5.3 Third Generation Spectral Wave Models . . . . . . . . 5.4 Grid Definition. . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Techno-Economic Development of WECs . . . . . . . . . . . . Arthur Pecher and Ronan Costello 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Continuous Evaluation of the WEC Potential . . . . . 1.2 Overview of the Techno-Economic Development . . 2 The WEC Development Stages . . . . . . . . . . . . . . . . . . 3 Techno-Economic Development Evaluation . . . . . . . . . . 3.1 The Technology Readiness and Performance Level. 3.2 The WEC Development Stages and the TRL Scale . 3.3 The TRL-TPL R&D Matrix . . . . . . . . . . . . . . . . . 3.4 Uncertainty Related to the TRL-TPL Matrix . . . . . 3.5 Valuation of R&D Companies . . . . . . . . . . . . . . . 4 Techno-Economic Development Strategies . . . . . . . . . . 4.1 R&D Strategy as TRL-TPL Trajectories . . . . . . . . 4.2 Extreme Cases of Techno-Economic Development Strategy . . . . . . . . . . . . . . . . . . . . . 4.3 Efficient Techno-Economic Development. . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 46 47 48 50 50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 55 57 60 62 66 67 67 68 69 69 70 71 71 72 74 76 77 ....... 81 . . . . . . . . . . . . . . . . . . . . . . . . 81 81 82 83 85 85 87 88 90 91 92 92 ....... ....... ....... 93 95 97 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents ix 6 Overview of Some of the Leading WECs . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 7 Economics of WECs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ronan Costello and Arthur Pecher 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Power Is Vanity—Energy Is Sanity . . . . . . . . . . . . . . . . 3 Economic Decision Making. . . . . . . . . . . . . . . . . . . . . . 3.1 Cash Flow Terminology . . . . . . . . . . . . . . . . . . . . 3.2 Time Value of Money (and Energy) . . . . . . . . . . . . 3.3 Economic Metrics . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Effect of Depreciation on Discounting. . . . . . . . . . . 3.5 Effect of Inflation on Discounting. . . . . . . . . . . . . . 3.6 Setting the Discount Rate . . . . . . . . . . . . . . . . . . . 3.7 Economic Decision Making—Which Metric to Use?. 3.8 Expert Oversight and Independent Review. . . . . . . . 4 Economic Analysis in Technology R&D . . . . . . . . . . . . . 5 Techno-Economic Assessment and Optimisation . . . . . . . 6 WEC Cost-of-Energy Estimation Based on Offshore Wind Energy Farm Experience . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Definition of the Categories . . . . . . . . . . . . . . . . . . 6.3 Wind Energy Project Case. . . . . . . . . . . . . . . . . . . 6.4 Wave Energy Case . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Cost Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Revenue and Energy Yield . . . . . . . . . . . . . . . . . . 7 Strategic Support Mechanisms . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 98 . . . . . . 101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 102 103 104 105 106 112 112 113 114 116 117 118 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 119 120 121 124 131 133 133 135 Hydrodynamics of WECs . . . . . . . . . . . . . . . . . . . . . . . . . . . Jørgen Hals Todalshaug 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Wave Energy Absorption is Wave Interference . . . . . . 1.2 Hydrostatics: Buoyancy and Stability . . . . . . . . . . . . . 1.3 Hydrodynamic Forces and Body Motions . . . . . . . . . . 1.4 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Oscillating Water Columns—Comments on Resonance Properties and Modelling . . . . . . . . . . . 1.6 Hydrodynamic Design of a Wave Energy Converter . . . 1.7 Power Estimates and Limits to the Absorbed Power . . . 1.8 Controlled Motion and Maximisation of Output Power . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 . . . . . . . . . . . . . . . . . . . . 139 139 140 143 146 . . . . . . . . . . . . . . . . . . . . 147 149 153 156 157 Mooring Design for WECs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Lars Bergdahl 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 x 8 Contents 1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Mooring Design Development Overview . . . 1.3 Wave-Induced Forces on Structures . . . . . . 1.4 Motions of a Moored Device in Waves . . . . 2 Metocean Conditions . . . . . . . . . . . . . . . . . . . . 2.1 Combinations of Environmental Conditions . 2.2 Design Wave Conditions . . . . . . . . . . . . . . 2.3 Environmental Data at DanWEC . . . . . . . . 2.4 Example Design Conditions. . . . . . . . . . . . 3 Estimation of Environmental Forces . . . . . . . . . . 3.1 Overview and Example Floater Properties . . 3.2 Mean Wind and Current Forces . . . . . . . . . 3.3 Wave Forces . . . . . . . . . . . . . . . . . . . . . . 3.4 Summary of Environmental Forces on Buoy 4 Mooring System Static Properties. . . . . . . . . . . . 4.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Catenary Equations. . . . . . . . . . . . . . . . . . 4.3 Mean Excursion . . . . . . . . . . . . . . . . . . . . 5 Alternative Design Procedures . . . . . . . . . . . . . . 5.1 Quasi-Static Design . . . . . . . . . . . . . . . . . 5.2 Dynamic Design . . . . . . . . . . . . . . . . . . . 5.3 Response-Based Analysis . . . . . . . . . . . . . 6 Response Motion of the Moored Structure. . . . . . 6.1 Equation of Motion . . . . . . . . . . . . . . . . . 6.2 Free Vibration of a Floating Buoy in Surge . 6.3 Response to Harmonic Forces . . . . . . . . . . 6.4 Response Motion in Irregular Waves . . . . . 6.5 Equivalent Linearized Drag Damping . . . . . 6.6 Second-Order Slowly Varying Motion . . . . 6.7 Wave Drift Damping . . . . . . . . . . . . . . . . 6.8 Combined Maximum Excursions . . . . . . . . 7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Power Take-Off Systems for WECs . . . . . Amélie Têtu 1 Introduction, Importance and Challenges . 2 Types of Power Take-Off System. . . . . . 2.1 Overview . . . . . . . . . . . . . . . . . . 2.2 Air Turbines . . . . . . . . . . . . . . . . 2.3 Hydraulic Converters . . . . . . . . . . 2.4 Hydro Turbines . . . . . . . . . . . . . . 2.5 Direct Mechanical Drive Systems . . 2.6 Direct Electrical Drive Systems . . . 2.7 Alternative PTO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 160 162 162 162 162 163 165 166 166 166 167 169 178 179 179 180 182 183 183 187 188 189 189 190 191 194 196 197 198 198 199 200 . . . . . . . . . . . . . . . . . . 203 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 205 205 206 210 211 213 213 214 Contents xi 3 Control Strategy of Power Take-Off System 3.1 Introduction . . . . . . . . . . . . . . . . . . . 3.2 Types of Control Strategy . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Testing and Evaluation of WECs. . . . . . . . . . . Arthur Pecher 1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Tank Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Representative Sea States . . . . . . . . . . . . . . . . . . . . . 2.3 Hydrodynamic Response . . . . . . . . . . . . . . . . . . . . . . 2.4 Power Performance Evaluation. . . . . . . . . . . . . . . . . . 2.5 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Structural and Mooring Loads . . . . . . . . . . . . . . . . . . 2.7 Parametric Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Sea Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Performance Assessment of WECs Based on Sea Trials References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Wave-to-Wire Modelling of WECs Marco Alves 1 Introduction. . . . . . . . . . . . . . . 2 Wave-to-Wire Models. . . . . . . . 2.1 Equation of Motion . . . . . 2.2 Excitation Force . . . . . . . . 2.3 Hydrostatic Force . . . . . . . 2.4 Mooring Loads . . . . . . . . 2.5 Radiation Force . . . . . . . . 2.6 PTO Force . . . . . . . . . . . 2.7 End Stops Mechanism. . . . 3 Benchmark Analysis. . . . . . . . . 4 Radiation/Diffraction Codes . . . . 5 Conclusion . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 214 215 218 218 . . . . 221 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 223 223 224 229 234 242 247 249 250 250 251 258 . . . . . . . . . . . . . . . . . . . . . . . . 261 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 264 265 265 267 268 270 272 281 281 283 284 285 Abbreviations AEP BoP CapEx CF CFD CHP CoE CRL CWR Dec DevEx DoF DPP EMEC FCF FV IRF IRR IW LCoE MAEP NPV OpEx OWC PI PLC PP PTO PV RADR Annual Energy Production Balance of Plant Capital Expenditure Cash Flow or Capacity Factor Computational Fluid Dynamics Combined Heat and Power Cost of Energy Commercial Readiness Level Capture Width Ratio Decommissioning Development Expenditure Degree of Freedom Discounted Payback Period European Marine Energy Centre Free Cash Flow Future Value Impulse Response Function Internal Rate of Return Irregular Waves Levelized Cost of Energy Mean Annual Energy Production Net Present Value Operational Expenditure Oscillating Water Columns Profitability Index Programmable Logic Controller Payback Period Power Take-Off Present Value Risk Adjusted Discount Rate xiii xiv RANSE R&D RAO RW SS TPL TRL VoF WAB WACC WEC Abbreviations Reynolds-Averaged Navier-Stokes Equation Research and Development Response Amplitude Operator Regular Waves Sea State Technology Performance Level Technology Readiness Level Volume of Fluid Wave Activated Body Weighted Average Cost of Capital Wave Energy Converter Symbols a A A(ω) Ac Ae AEP ai Awp A∞ B Be11 C c ca Cd CD Cg CI Cm Contrib D Db Des Dh Dt E F f F F3 Amplitude of incident wave (m) Cross-sectional area (m2) Frequency-dependent added mass (kg) Effective cross-sectional area of a pair of cylinders (m2) Electric loading (A/m) Annual energy production (MWh/year) Amplitudes at each frequency (m) Water plane area (m2) Limiting added mass coefficient at infinite frequency (kg) Air gap magnetic flux density (Tesla) or center of buoyancy (m) Equivalent damping coefficient (surge) (–) Shape coefficient (–) Wave celerity (m/s) Speed of sound in atmospheric conditions (m/s) Wave drift force coefficient (–) Drag coefficient (–) Group velocity (m/s) Confidence interval (–) Added mass coefficient (–) Contribution to the available wave power (–) Damping coefficient (kg/s) Float draft below the water surface (m) Damping constant for the end stop mechanism (kg/s) Float height above surface (m) Turbine rotor diameter (m) Electromotive force (V) Fetch length (m) Frequency (Hz) Force (N) Restoring force (N) xv xvi Fb Fc Fe fexc Fexc Ff Fhs Fm Fpto Fr fw(f) G g G ɣ Gm GZ h H H1/3 Hmax Hp Hs h(t -τ) Hm0 I Io i,j J K k k k/D KC Kes Kt l Ll Lm Lp,0 Ls m m M Symbols Buoyancy force (N) Current force (N) Excitation force (N) Excitation impulse response function (–) Excitation force (N) Friction force (N) Hydrostatic force (N) The Mooring force (N) PTO force (N) Radiation force (N) Wave force ratio (–) Center of gravity (m) Gravitational acceleration (m/s2) Hydrostatic matrix (N/m) Peak enhancement factor (–) Constant (–) Righting arm (m) Water depth (m) Wave height (m), heaviside step function (–) or horizontal force (N) Significant wave height (m) Max wave height within a given duration of a sea state (m) Horizontal pretension (N) Significant wave height (m) Impulse-response function (–) Significant Wave Height estimate from wave spectrum (m) Current density in the conductor (A) Incident momentum (–) Mode of motion (–). Translations: 1: Surge, 2: Sway, 3: Heave. Rotations: 4: Roll, 5: Pitch, 6: Yaw Wave power flux or wave power level (equal to Pwave) (kW/m) Roughness height (mm) Spring coefficient or Stiffness (N/m) Wave number (m−1) Relative roughness (–) Keulegan–Carpenter number (–) Spring constant for the end stop mechanism (N/m) Constant that depends only on turbine geometry (–) Length (m) Leakage inductance (H) Main inductance (H) Wave length based on peak wave period and deep water (m) Synchronous inductance (H) Body mass (kg) Mass (kg) Mass matrix (kg) Symbols MAEP m0 mn mr ṁ mn N N N or ώ Nc NL p pa Pabs Pavailable Pel Pmech Prob Pt Pu Pwave Q q q0 Qm r R Re Rg Rl S s Sf Smbs Sp,0 t T T0 T01 T02 TB Te Tp xvii Mean annual energy production (MWh/year) Variance of the wave spectra or ‘zeroth’ moment of the wave spectra (m2) Spectral moment of the nth order (n = 0, 1, 2, …) (m2 s−n) Added mass (kg) Mass flow rate of air through the turbine (kg/s) Spectrum moments (–) Number of coil turns (–) Number of harmonic wave components (–) Rotational speed (radians per unit time) (rad/s) Number of pairs of cylinders (–) Length scaling factor (–) Differential pressure in the pneumatic chamber (Pa) Atmospheric pressure (Pa) Primary absorbed power from the waves (kW) Available power (kW) Generated electrical power (kW) Available mechanical power (kW) Probability of occurrence (–) Turbine power output (kW) Useful power (kW) Wave power flux or wave power level (equal to J) (kW/m) Volume flow rate of liquid displaced by the piston (m3/s) Volume flow rate of air (m3/s) Mass per unit unstretched length (kg/m) Flow rate (m3/s) Amplitude of reflected wave (m) Damping (kg/s) Reynolds number (–) Resistance inside the generator (Ω) Resistance (Ω) Stiffness (N/m), spectral density function (m2/Hz) or scaling ratio (S) Wave steepness or sample standard deviation (–) Spectral density at frequency component f (m2/Hz) Minimum breaking strength (N) Wave steepness for the peak wave period and deep water (–) Time or amplitude of transmitted wave (s) or (m) Wave period or wave record with duration (s) Resonance period (s) Spectral wave period based on 0th and 1st moment (s) Spectral wave period based on 0th and 2nd moment (spectral estimate of Tz) (s) Breaking load (N) Wave energy period (s) Peak wave period (s) xviii TQS Tz u U U10 U10min,10m Uc Uf Um umax ur V Vs w x Xc ẋ ẍ z ż λ Δf Δpc Φ Π Ψ αi β ϕ γ μ0 ν ρ ρcu ω ξ ∇ ζ(z) ξ(z) η g_ € g η3 Symbols Quasi static tension (N) Mean zero down crossing wave period (s) Horizontal water velocity (m/s) or usage factor (–) Velocity (m/s) Wind speed at a height of 10 m (m/s) Mean wind speed over 10 min at 10 m height (m/s) Current speed (m/s) Full scale velocity (m/s) Model scale velocity (m/s) Maximum water velocity (m/s) Relative speed (m/s) Volume (m3) Available stroke volume (m3) Distance between the poles (m) Horizontal position of the body (m) Quasi static line extension (m) Velocity of the body (m/s) Acceleration of the body (m/s2) Vertical displacement (m) Vertical velocity (m/s) Wave length (m) Frequency interval (Hz) Pressure difference between the accumulators (–) Flow coefficient (–) Power coefficient (–) Pressure coefficient (–) Phases of each frequency (Hz) Wave direction (degree) Permanent magnet induced flux per pole or Constant for fixed entropy (B) or (–) Specific heat ratio for the gas (–) or peak enhancement factor (–) Magnetic permeability (H m−1) Specific volume of gas (m3) or kinematic viscosity (m2/s) Density (kg/m3) Resistivity of the conductor material (Ω) Angular frequency (rad/s) Acceleration vector (m/s2) Submerged volume (m3) Vertical displacement of the water particles (m) Horizontal displacement of the water particles (m) Free surface elevation (m) or non-dimensional performance (also called CWR or efficiency) (–) Velocity of water surface (m/s) Acceleration (m/s2) Body displacement (m) Symbols ηi ηlim ηoverall ηPTO ηss ηw2w ε0 xix Position in mode (m) Excursion limit for which end stop mechanism starts acting (m) Overall non-dimensional performance (efficiency) (–) PTO efficiency (–) Non-dimensional performance (efficiency) in individual sea state (–) Wave-to-wire efficiency (–) Spectral bandwidth (–) Chapter 1 Introduction Arthur Pecher and Jens Peter Kofoed 1 Introduction The widespread usage of affordable electricity converted from ocean waves would be a fabulous achievement. Besides that the wave energy converting (WEC) technology would be particularly interesting, it also would have several significant benefits to society, such as: • It is another sustainable and endless energy source, which could significantly contribute to the renewable energy mix. In general, increasing the amount and diversity of the renewable energy mix is very beneficial as it increases the availability and reduces the need for fossil fuels. • Electricity from wave energy will make countries more self-sufficient in energy and thereby less dependent on energy import from other countries (note: oil is often imported from politically unstable countries). • It will contribute to the creation of a new sector containing, innovation and employment. • Electricity from ocean wave can be produced offshore, which thereby does not require land nor has a significant visual impact. As the world energy needs will keep on increasing while the fossil fuel reserves are depleting, wave energy will become of significant importance. The demand for it will start when its price of electricity will be right and will then only increase with time. A. Pecher (&)
J.P. Kofoed (&) Department of Civil Engineering, Aalborg University, Thomas Manns Vej 23, 9220 Aalborg Ø, Denmark e-mail: [email protected] J.P. Kofoed e-mail: [email protected] © The Author(s) 2017 A. Pecher and J.P. Kofoed (eds.), Handbook of Ocean Wave Energy, Ocean Engineering & Oceanography 7, DOI 10.1007/978-3-319-39889-1_1 1