Modelling and Optimisation of Wave Energy Converters

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Cover Half Title Title Page Copyright Page Contents Preface Contributors Acronyms Nomenclature SECTION I: Introduction CHAPTER 1: Wave energy converter systems – status and perspectives 1.1. INTRODUCTION TO WAVE ENERGY CONVERTER SYSTEMS 1.1.1. The origins of wave energy technology development 1.1.2. Classifications of wave energy converter technologies 1.1.3. Oscillating water column 1.1.3.1. Floating OWCs 1.1.3.2. Fixed OWCs 1.1.4. Oscillating body systems 1.1.4.1. Floating oscillating bodies 1.1.4.2. Submerged oscillating bodies 1.1.5. Overtopping systems 1.1.6. Pressure differential systems 1.1.7. Summary 1.2. ECONOMIC ASPECTS OF WAVE ENERGY CONVERTERS 1.2.1. Development status of renewable energy 1.2.2. Role of wave energy in the renewable energy mix 1.2.2.1. Temporal and spatial availability 1.2.2.2. Environmental impact 1.2.2.3. Technology readiness level 1.2.2.4. Niche market for wave energy 1.2.3. Performance measures 1.2.3.1. Power production assessment 1.2.3.2. Techno-economic analysis 1.3. LATEST DEVELOPMENTS IN WAVE ENERGY HARVESTING RESEARCH 1.3.1. Integration with pre-existing and planned infrastructure 1.3.2. Prolonging the design life of the WEC technology 1.4. FUTURE DEVELOPMENTS IN WAVE ENERGY CONVERTER SYSTEMS 1.4.1. Efficiency augmentation 1.4.2. Integration with other renewable energy harvesting systems and technologies 1.4.3. Wave energy farms SECTION II: Fundamental Theories Applicable to Wave Energy Harvesting CHAPTER 2: Fluid dynamics and wave-structure interactions 2.1. FLUIDS AND WAVE-STRUCTURE INTERACTIONS 2.1.1. Ocean waves 2.1.1.1. Navier-Stokes equations 2.1.1.2. Linear potential flow theory 2.1.1.3. Dispersive waves 2.1.1.4. Wave spectra and wave parameters 2.1.2. Wave-structure interaction 2.1.2.1. Hydrodynamic forces 2.1.2.2. Hydrostatic forces 2.1.2.3. Hydrodynamic responses 2.2. LINEAR POTENTIAL FLOW THEORY SOLVERS 2.2.1. Analytical solutions 2.2.2. Boundary element method 2.2.2.1. Boundary integral equation 2.2.2.2. Removal of irregular frequencies 2.2.2.3. Calculating free-surface Green’s functions 2.2.2.4. Resolving linear algebraic system 2.2.2.5. Parallelisation on multi-core machines 2.2.2.6. Useful references and tools 2.3. COMPUTATIONAL FLUID DYNAMICS 2.3.1. Governing equations 2.3.2. Volume of fluid method for free-surface flows 2.3.3. Computational fluid dynamics software 2.3.4. Creating a computational fluid dynamics simulation 2.3.4.1. Numerical wave tank definition 2.3.4.2. Mesh generation 2.3.4.3. Boundary and initial conditions 2.4. WAVE TANK EXPERIMENTS 2.4.1. Objectives 2.4.2. Wave generation 2.4.3. Wave tank dimensions 2.4.4. Scaling 2.4.4.1. Scaling law 2.4.4.2. Scale issues 2.5. MODELLING OF INTERACTION BETWEEN OCEAN WAVE AND WAVE ENERGY CONVERTER CHAPTER 3: Wave energy converter modelling, control, and power take-off design 3.1. MODELLING OF WAVE ENERGY CONVERTER DYNAMICS 3.1.1. Time domain 3.1.2. Frequency domain 3.1.3. Statistical linearisation 3.1.3.1. Asymmetric non-linearities and constant loads 3.1.3.2. Multivariate normal probability density function 3.1.3.3. Iterative procedure 3.1.4. Alternative numerical methods 3.1.5. Case study 3.1.5.1. Time domain 3.1.5.2. Frequency domain 3.1.5.3. Statistical linearisation 3.1.5.4. Results 3.2. PRINCIPLES AND BOUNDS OF WAVE POWER ABSORPTION 3.2.1. Impedance matching 3.2.2. Phi-method 3.2.3. Theoretical power limit 3.2.3.1. Power limits in two-dimensional flows 3.2.3.2. Power limits in three-dimensional flows 3.2.3.3. Power absorption with motion constraint 3.3. CONTROL SYSTEM AND POWER TAKE-OFF DESIGN 3.3.1. Power take-off control strategy classification 3.3.1.1. Power flow 3.3.1.2. Causality 3.3.1.3. Model availability 3.3.1.4. Linearity 3.3.1.5. Multi-mode control 3.3.2. Power take-off machinery 3.3.2.1. Hydraulic power take-off machinery 3.3.2.2. Pneumatic power take-off machinery 3.3.2.3. Direct-drive power take-off machinery 3.3.3. Performance measures of power take-off machinery 3.3.3.1. Power conversion efficiency (mechanical-to-electrical) 3.3.3.2. Maximum values, or peak values 3.3.3.3. Peak-to-average values 3.3.3.4. Slew rate 3.3.3.5. Damage equivalent loading 3.3.3.6. Flicker severity 3.3.4. Challenges in power take-off design 3.3.5. Challenges in wave energy converter control SECTION III: Wave Energy Converters CHAPTER 4: Point absorber wave energy converters 4.1. INTRODUCTION 4.2. WORKING PRINCIPLES 4.2.1. One-body point absorbers 4.2.2. Two-body point absorbers 4.3. EXISTING PROTOTYPES 4.3.1. One-body point absorber prototypes 4.3.1.1. Seabased device 4.3.1.2. LifeSaver device 4.3.1.3. CorPower device 4.3.1.4. WaveStar device 4.3.2. Two-body point absorber prototypes 4.3.2.1. OPT PowerBuoy device 4.3.2.2. Wavebob device 4.3.2.3. SEAREV device 4.3.2.4. Penguin device 4.4. CASE STUDY – A HEAVING POINT ABSORBER 4.4.1. Force-to-motion modelling 4.4.1.1. Radiation force approximation 4.4.1.2. Linear force-to-motion modelling 4.4.1.3. Nonlinear force-to-motion modelling 4.4.1.4. Results and discussion 4.4.2. Wave-to-motion modelling 4.4.2.1. Excitation force approximation 4.4.2.2. Wave-to-motion modelling 4.4.2.3. Results and discussion 4.4.3. Wave-to-wire modelling 4.4.3.1. Modelling of a permanent magnet linear generator 4.4.3.2. Wave-to-wire modelling 4.4.3.3. Tracking control based on a wave-to-wire model 4.4.3.4. Results and discussion 4.5. SUMMARY CHAPTER 5: Multi-mode wave energy converters 5.1. INTRODUCTION 5.2. WORKING PRINCIPLE 5.2.1. Power absorption by a body oscillating in several modes of motion 5.2.2. Practical limits to the power absorption per mode 5.2.2.1. Heaving mode 5.2.2.2. Surging and pitching modes 5.3. EXISTING PROTOTYPES 5.3.1. Bristol cylinder, UK 5.3.2. Multi-tether spherical buoy 5.3.3. WaveSub by Marine Power Systems, UK 5.3.4. Triton WEC by Oscilla Power™, US 5.3.5. The NEMOS wave energy converter by NEMOS GmbH, Germany 5.3.6. The CETO system by Carnegie Clean Energy, Australia 5.3.7. Wave energy converter based on a Stewart-Gough platform, Mexico 5.3.8. Overview of existing multi-mode prototypes 5.4. CASE STUDY – SUBMERGED THREE-TETHER SYSTEM 5.4.1. Dynamic modelling 5.4.1.1. Kinematics 5.4.1.2. Forces 5.4.1.3. Time-domain model 5.4.1.4. Frequency domain 5.4.1.5. Power absorption 5.4.2. Modal analysis 5.4.2.1. Matrix eigenvalue problem for an undamped multiple DoF system 5.4.2.2. Natural frequencies and mode shapes 5.4.3. Power absorption potential 5.4.3.1. Power matrix 5.4.3.2. Power per power take-off system 5.4.3.3. Power per mode 5.4.4. Design optimisation 5.4.4.1. Approximation of levelised costs of electricity value 5.4.4.2. Optimisation routine 5.4.4.3. Optimisation results 5.4.5. Control system design 5.4.5.1. Controllability 5.4.5.2. Surge-pitch compromise 5.4.5.3. Review of advanced control strategies applied to multi-mode wave energy converters 5.4.6. Parametric instability 5.5. SUMMARY CHAPTER 6: Attenuator wave energy converters 6.1. INTRODUCTION 6.2. WORKING PRINCIPLE 6.2.1. Hinged-float-based devices 6.2.2. Flexible-tube-based devices 6.3. EXISTING PROTOTYPES 6.3.1. Cockerell raft 6.3.2. McCabe Wave Pump 6.3.3. Pelamis 6.3.4. The DEXA 6.3.5. Seapower Platform 6.3.6. M4 6.3.7. Anaconda 6.3.8. WEC S3 6.4. CASE STUDY – TWO HINGED FLOATS 6.4.1. Modelling methods of two hinged floats 6.4.1.1. Frequency domain 6.4.1.2. Time domain 6.4.2. Theoretical model for evaluating the maximum wave power absorption 6.4.2.1. Maximum wave power absorption without any constraints 6.4.2.2. Maximum wave power absorption with constraints 6.4.3. Frequency-domain analysis 6.4.3.1. Float length and linear power take-off damping 6.4.3.2. Float rotary inertia 6.4.3.3. Axis ratio of cross section 6.4.4. Time-domain analysis 6.4.4.1. Coulomb damping 6.4.4.2. Latching control 6.4.5. Maximum wave power absorption 6.4.5.1. Maximum power absorption with optimised power take-off damping 6.4.5.2. Maximum power absorption with optimised power take-off damping and stiffness/inertia 6.4.5.3. Wave power extraction with different optimisation principles 6.4.5.4. Performance of a device with a fixed optimised power take-off system 6.5. SUMMARY CHAPTER 7: Oscillating water column wave energy converters 7.1. INTRODUCTION 7.2. WORKING PRINCIPLE 7.2.1. Fixed oscillating water column 7.2.2. Floating oscillating water column 7.3. EXISTING PROTOTYPES 7.3.1. Fixed oscillating water column prototypes 7.3.2. Floating oscillating water column prototypes 7.4. CASE STUDY – OWC WEC 7.4.1. Modelling 7.4.1.1. Boundary Integral Equation 7.4.1.2. Pneumatic Model 7.4.1.3. Hydrodynamic Efficiency 7.4.1.4. Wave loads 7.4.2. Experimental investigation 7.4.3. Comparisons between measured and simulated results 7.4.4. Single chamber oscillating water column device 7.4.4.1. Hydrodynamic Efficiency 7.4.4.2. Wave Loads 7.4.5. Dual-chamber oscillating water column device 7.4.5.1. Hydrodynamic Efficiency 7.4.5.2. Wave Loads 7.5. SUMMARY SECTION IV: Wave Energy Converter Arrays/Farms CHAPTER 8: Large-scale computation of wave energy converter arrays 8.1. INTRODUCTION 8.2. REVIEW OF EXISTING ARRAY MODELLING METHODS 8.3. INTERACTION THEORY 8.3.1. The concept of partial waves 8.3.2. Ambient incident plane waves 8.3.3. Solution of the partial wave coefficients 8.3.4. Wave excitation forces and hydrodynamic quantities 8.3.5. Motion responses 8.4. LINEAR OPERATOR MATRICES 8.4.1. Diffraction transfer matrix 8.4.1.1. Alternative method I 8.4.1.2. Alternative method II 8.4.1.3. Comparison of accuracy and efficiency 8.4.2. Radiation characteristics 8.4.3. Force transfer matrix 8.5. BOUNDARY INTEGRAL EQUATIONS FOR PARTIAL WAVES 8.5.1. Indirect approach 8.5.2. Direct approach 8.5.3. Removal of irregular frequencies 8.6. EVALUATION OF THE ARRAY PROPERTIES 8.6.1. Interaction factor and directionality 8.6.2. Overall energy production of the WEC array 8.6.3. Case study 8.7. SUMMARY CHAPTER 9: Optimisation of wave farms 9.1. INTRODUCTION 9.2. MODELLING METHODS OF WAVE FARMS 9.2.1. Modelling of hydrodynamic interactions 9.2.1.1. Analytical modelling 9.2.1.2. Numerical modelling 9.2.1.3. Incident waves 9.2.2. Modelling full farms and power absorption 9.2.2.1. Power take-off and control in wave farms 9.2.2.2. Mooring systems 9.2.2.3. Solving the equations of motion 9.2.3. Experimental modelling 9.3. OVERVIEW OF OPTIMISATION METHODS 9.3.1. Grid search over specified solution subsets 9.3.2. Global optimisation algorithms 9.3.2.1. Non-linear optimisation and coordinated control 9.3.2.2. Metaheuristic optimisation algorithms 9.3.3. Optimisation objectives 9.3.3.1. Economic cost functions 9.3.3.2. Electricity quality 9.3.3.3. Survivability and other objectives 9.4. CASE STUDIES 9.4.1. Wave farm model 9.4.2. Economic optimisation of a wave farm 9.4.3. Comparison with similar studies 9.4.4. General trends 9.5. SUMMARY Bibliography Index