| name | wave-energy |
| description | Wave energy conversion — ocean wave power density (P = ρg²H²T/(32π)), point absorber (Froude-Krylov force, heave resonance, power take-off PTO), oscillating wave surge converter (OWSC), attenuator (Pelamis), oscillating water column (OWC, Wells turbine), resource assessment (significant wave height Hs, energy period Te), capture width ratio, WEC array design, mooring, and leading projects (Wave Dragon, Corpower, MARMOK-A-5). |
| metadata | {"priority":7,"promptSignals":{"phrases":["wave energy","wave energy converter","WEC","ocean wave power","oscillating water column","point absorber wave"],"minScore":3}} |
Wave Energy Conversion — Complete Skill
Ocean Wave Resource
Wave Power Density
Regular wave power (per unit crest width):
P = ρ × g² × H² × T / (32π) [W/m; H = wave height; T = wave period; ρ = 1,025 kg/m³; g = 9.81 m/s²]
For irregular waves using Hs (significant wave height) and Te (energy period):
P = ρ × g² × H_s² × T_e / (64π) [W/m; Hs = 4√m₀ = 4×standard deviation of surface elevation; Te = m₋₁/m₀]
Simplified: P ≈ 0.5 × H_s² × T_e [kW/m; with ρg²/64π ≈ 0.491 kW·s/m³ ≈ 0.5]
Example:
North Atlantic: H_s = 3 m; T_e = 10 s → P = 0.5 × 9 × 10 = 45 kW/m of wave crest
Excellent resource sites:
- West Scotland, Orkney (EMEC): 40–70 kW/m annual mean
- West Ireland: 50–65 kW/m
- Peru/Chile (Humboldt Current): 25–40 kW/m
- Oregon Coast: 40–50 kW/m
Wave resource assessment:
Scatter diagram: joint probability distribution of (H_s, T_z) pairs from measured data or ERA5 reanalysis
Annual mean power P_annual = ΣΣ p(Hs, Tz) × P(Hs, Tz) [probability-weighted average]
Wave Spectrum
JONSWAP spectrum (North Sea and similar):
S(ω) = (αg²/ω⁵) × exp(−5/4 × (ω_p/ω)⁴) × γ^(exp(−(ω−ω_p)²/(2σ²ω_p²)))
ω_p = 2π/T_p (peak angular frequency); γ = peak enhancement factor (γ = 3.3 for North Sea; γ = 1 for Pierson-Moskowitz)
Pierson-Moskowitz (fully developed sea):
S(ω) = (αg²/ω⁵) × exp(−0.74 × (g/(ω × U₁₉.₅))⁴) [U₁₉.₅ = wind speed at 19.5 m height]
WEC Types and Operating Principles
Point Absorber
Point absorber: small buoy (diameter << wavelength); heaves in response to wave
Froude-Krylov force (exciting force for heave):
F_FK = ρg × V_submerged × k_FK [k_FK = Froude-Krylov coefficient; depends on frequency and geometry]
Or: F_exc = A_WL × ρg × η_surface [simple piston approximation; A_WL = waterplane area]
Equation of motion (heave):
(m + m_a) × ẍ + (B_PTO + B_rad) × ẋ + (k_hydrostatic + k_PTO) × x = F_exc(t)
m_a = added mass; B_rad = radiation damping; k_hydrostatic = ρg × A_WL
Resonance condition:
ω_n = √(k_hydrostatic / (m + m_a)) [natural heave frequency]
Maximum power at resonance: ω_exc = ω_n (wavelength matches buoy response)
Typical T_n = 8–12 s → matches swell periods at good wave sites
Maximum capturable power per unit incident power (theoretical):
P_max = |F_exc|² / (8 × B_rad) = P_incident × D_capture [capture width per unit wave energy]
For 3D point absorber: D_capture_max = λ/(2π) = L/(2π) [capture width ratio CWR = D_capture / D_buoy]
CWR (Capture Width Ratio):
CWR = P_absorbed / (P_incident × D_buoy)
Point absorber: CWR = 0.15–0.30 (practical); maximum theoretical 1/(2π) × λ/D ≈ 2–10 for buoy
Power Take-Off (PTO)
Linear generator (direct drive):
Buoy heave drives linear generator (magnet/coil assembly)
Direct PTO: no mechanical conversion; efficient; high capital cost per kW; used by CorPower, AWS
Hydraulic PTO:
Heave drives hydraulic cylinder → high-pressure fluid → hydraulic motor → generator
Advantages: energy storage in accumulator (smooths power); flexible; established technology
Disadvantages: sealing in marine environment; efficiency ~60–80%
Optimum PTO damping (matched to radiation damping for maximum power):
B_PTO_opt = B_rad [at resonance; or more generally: B_PTO_opt = √(B_rad² + (ω(m+m_a) − k/ω)²)]
Oscillating Water Column (OWC)
Principle: fixed or floating structure with air pocket above internal water surface
Waves cause water to rise/fall → air pumped through turbine → electricity
Internal free surface acts as secondary oscillator
Air turbine options:
Wells turbine: self-rectifying (works in both directions); constant rotation; poor efficiency at off-design; η ≈ 0.65–0.70
Impulse turbine (Dennis-Auld): self-rectifying; better off-design; η ≈ 0.75–0.80
Biradial turbine: rotating valve rectification; η ≈ 0.80–0.85
OWC power:
P = η_turbine × ṁ_air × Δh [ṁ_air = air mass flow; Δh = enthalpy change through turbine]
Or: P = η_turbine × p_chamber × Q_air [Q_air = volumetric flow through turbine]
Shore-based OWC: LIMPET (Scotland, 500 kW); Pico (Azores, 400 kW); Mutriku (Spain, 300 kW)
Oscillating Wave Surge Converter (OWSC)
Example: Oyster, BioWave:
Hinged flap near seabed; surge (horizontal) waves drive flap rotation
Amplified by proximity to seabed (shallow water compression of wave orbits)
Drives hydraulic pumps to shore-based turbine (no moving parts offshore except flap)
Surge force:
F_surge = C_m × ρ × π × D²/4 × ∂u/∂t + C_d × 0.5 × ρ × D × u|u| [Morison; u = horizontal velocity]
Attenuator (Pelamis-type)
Pelamis: long snake-like machine; segments connected by hydraulic joints
Waves pass along length; segments articulate; relative motion drives hydraulic pumps
Capture width proportional to length; length 150 m (Pelamis P2)
Power: 750 kW rated; decommissioned 2014 (commercial challenges)
Array Design and Performance
Spacing:
WECs absorb and radiate waves → wake effects on downstream devices
Optimal spacing depends on wave direction spread; typically 3–10 × device diameter
Array interaction can be constructive or destructive at specific frequencies
Capacity factor:
Wave energy Cf_wave ≈ 25–40% (better than wind at same site; more consistent)
Seasonal variation: higher in winter storms; lower in summer swells
Grid connection:
Subsea cable to shore; voltage: 11–33 kV typical; HVDC for remote locations
Power quality: smoothed by array diversity; storage (flywheel, battery) for further smoothing
Mooring Design
Key loading:
Extreme survival storm: design wave Hs_100yr; mooring must withstand peak load without failure
Fatigue: millions of wave cycles; chain and polyester fatigue data per DNV-ST-0437
Catenary mooring:
Water depth > 50 m: catenary chain (steel or polyester tether)
Water depth < 50 m: taut-leg mooring; stiffer; less horizontal excursion
Mooring horizontal restoring force:
F_moor = (EA/L) × (ε − ε₀) + catenary weight term [ε = strain; EA = axial stiffness; L = mooring line length]
Typical: 500–2,000 kN horizontal force in survival storm
Resource-to-Grid Efficiency Chain
η_total = η_WEC × η_PTO × η_generator × η_cable × η_transformer
η_WEC: 20–35% (wave → mechanical)
η_PTO: 70–85% (mechanical → hydraulic → mechanical)
η_generator: 90–95%
η_cable: 98–99%
η_total: 15–30% overall wave-to-grid
Leading Projects and TRL
| Project | Type | Rated Power | Status |
|---|
| CorPower C4 | Point absorber | 300 kW | TRL 6; wave trial completed 2023 |
| MARMOK-A-5 (IDOM) | OWC buoy | 30 kW | TRL 5; Biscay Marine Energy Platform |
| Wavepiston (Denmark) | Point absorber chain | Modular | TRL 5 |
| AWS Ocean E1 | Submerged point absorber | 1 MW | TRL 5 |
| Mutriku OWC | Shore-based OWC | 300 kW | Operational commercial |
| Wave Dragon | Overtopping attenuator | 4–11 MW | TRL 6; demonstrated |
Standards and References
| Standard | Scope |
|---|
| IEC 62600-100 | Wave energy — WEC power performance assessment |
| IEC 62600-200 | (Marine energy — resource assessment) |
| DNV-ST-0437 | Loads and site conditions for WTGs (applicable to WEC mooring) |
| EMEC guidelines | Wave energy device testing protocol |
| Cruz "Ocean Wave Energy" (Springer) | Comprehensive reference |
Output
Provide: site data (location; H_s [m] and T_e [s] at annual mean and 1-yr/50-yr return; water depth [m]; resource P [kW/m]; predominant direction; seabed type), WEC type selection (point absorber/OWC/OWSC/attenuator; basis: water depth, wave climate, technology maturity), device design (for point absorber: D [m]; m [t]; m_a [t]; ω_n [rad/s]; resonance T_n [s]; vs. T_e match), PTO (linear/hydraulic/pneumatic; rated force or pressure; rated power [kW]; PTO damping B_PTO [kN·s/m]; energy storage buffer [kWh]), capture width ratio (CWR = [value]; P_absorbed per device [kW] at annual mean sea state; vs. incident P × D), annual energy production (AEP per device [MWh]; capacity factor [%]; array of N devices; total AEP [GWh/year]), mooring (type: catenary/taut; water depth [m]; line material; survival tension at H_s_100yr [kN]; fatigue life [years]), grid connection (cable voltage [kV]; length [km]; array layout; cable losses [%]), economics (capex estimate [$/kW]; LCOE [$/MWh]; comparison to offshore wind [$/MWh]; path to cost reduction), and applicable standard (IEC 62600-100 for performance; EMEC protocol for testing; DNV-ST-0437 for mooring).
