Wave Energy Converter (WEC) Power Estimation Simulator

Parameters

Significant wave height H_s

Mean height of the highest one-third of waves in a sea state

Peak period T_p

Period at the peak of the wave spectrum. T_e is approximately 0.857 T_p

Water depth d

Site water depth. Deep-water approximation holds for d/lambda > 0.5

WEC type

Capture width ratio (CWR) depends on device type

Device width (facing waves)

PTO efficiency η_PTO

Hydraulic to electrical conversion. Hydraulic 60-70%, direct-drive 70-80%

Array size (devices)

units

Results

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Wave power flux (kW/m)

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Capture width per device (m)

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Hydraulic power per device (kW)

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Electrical power per device (kW)

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Array total power (kW)

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Annual energy (MWh)

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WEC concept — wave to device to electricity

Animated sea surface, the selected WEC device, and the PTO-to-grid energy flow. Wave height and period follow the sliders.

Wave power flux vs significant wave height H_s (T_p fixed)

Device type comparison — capture width and electrical output

Theory & Key Formulas

$$P_{wave} = \frac{\rho g^2 H_s^2 T_e}{64\pi}, \qquad P_{elec} = P_{wave}\cdot CW\cdot \eta_{PTO}$$

H_s = significant wave height (m), T_e ≈ 0.857 T_p = energy period (s), CW = capture width (device width times CWR), η_PTO = power conversion efficiency. P_wave is the incident wave power per meter of wavefront (W/m).

$$\lambda = \frac{g T_p^2}{2\pi}, \qquad E_{annual} = P_{elec}\cdot 8760\cdot CF$$

λ = deep-water wavelength (m), CF = capacity factor (~0.30). Annual energy E_annual is rated electrical power times hours per year times capacity factor.

Wave Energy Converter (WEC) power estimation

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I have a rough mental picture of offshore wind — turbines bolted to the seabed — but wave energy looks more mysterious. How does a wave actually become electricity?

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Good question. Wave Energy Converters (WECs) split into four main families: (1) point absorbers — a buoy that rides up and down with the waves; (2) attenuators — a long string of segments that flex at the joints, like Pelamis; (3) oscillating water columns (OWC) — a partially submerged chamber where the water level pumps air through a turbine; and (4) overtopping devices — a ramp that catches water in a reservoir and lets it fall back through a low-head turbine. Try switching the WEC type on the left; you'll see the capture width ratio (CWR) and the output change immediately.

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The first stat says "wave power flux = 13.46 kW/m". How should I read that? The defaults are Hs = 2 m and T_p = 8 s.

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It means 13.46 kW of power crosses every meter of wavefront. So a 100 m wide stretch of coastline would receive about 1.35 MW. You can't grab all of it, of course; a point absorber has CWR ≈ 0.30, so for a 20 m device the capture width is 6 m. That gives 13.46 × 6 ≈ 80.7 kW of hydraulic power, and with a PTO efficiency of 65% you get about 52.5 kW of electricity — which is exactly what the default settings show.

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Japan is surrounded by sea, so I'd expect wave power to be big there. Why hasn't it taken off?

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The technical potential (~36 GW around Japan) is real, but commercialization is hard. The main reasons are typhoons and cost. Typhoon waves above 10 m hit the coast several times a year, and surviving them pushes CAPEX 3-5 times above onshore wind. Mooring and subsea cables are expensive too. Calmer test sites like EMEC in Orkney (UK) and Aguçadoura in Portugal have done most of the demonstration work. In Japan, OWCs built into harbor breakwaters look promising because they share the cost of an existing structure.

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There's a "capacity factor = 0.30" in the formulas. I've seen solar PV reported at 0.15 or so. What does it mean here?

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Capacity factor is the annual energy divided by (rated power × 8760 h). Hs = 2 m might be your rated point, but most of the year the waves are smaller, so the long-term average is only 20-35% of rated output. That puts wave between onshore wind (25-40%) and solar PV (10-20%). The number depends strongly on the local wave climate, so you really need at least one year of buoy measurements before you size a wave farm.

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If I add more devices in the array, does power scale linearly? I'd expect them to shadow each other.

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This tool just multiplies by N for simplicity, but in real arrays there's a mix of negative and positive interaction. Devices in the lee of the front row see weaker waves (shadowing), while constructive interference at certain spacings can actually boost output by 10-20%. Optimizing layout usually requires linear potential-flow tools like WAMIT, NEMOH or a boundary element solver — the simple N-times approximation is fine for a first-pass estimate.

Frequently Asked Questions

For a monochromatic deep-water wave the energy flux per meter of wavefront is P = rho g^2 H^2 T / (32 pi). Real seas, however, are irregular and contain many frequency components, so the convention is to use the significant wave height H_s and the energy period T_e. With those definitions the formula becomes P = rho g^2 H_s^2 T_e / (64 pi); the factor changes from 32 to 64 because H_s is defined as four times the surface-elevation standard deviation. For a Pierson-Moskowitz spectrum T_e is roughly 0.857 T_p (peak period). For Hs=2m and T_p=8s the flux is about 13.5 kW/m, which is the upper bound of electrical power that can fall on each meter of device frontage.

Capture width (CW) is the hydraulic power absorbed by the device divided by the incident wave power flux, expressed as a length. CWR = CW divided by device width is the non-dimensional efficiency. A well-tuned point absorber operating near resonance reaches CWR around 0.30, a Pelamis-style attenuator aligned with the wave direction sits around 0.40-0.50, an OWC around 0.20-0.30, and an overtopping device built into a breakwater around 0.30-0.50. Budal and others showed that small resonant absorbers can theoretically exceed CWR = 1 (the "point absorber effect"), but structural and PTO control limits keep commercial devices in the 0.3-0.5 range.

PTO (Power Take-Off) efficiency converts hydraulic power into electrical power instantaneously; hydraulic + generator chains achieve 0.6-0.7, direct-drive linear generators 0.7-0.8. Capacity factor, on the other hand, is the annual energy production divided by (rated electrical power times 8760 h) and reflects the long-term variability of the wave climate. The Hs=2m, T_p=8s case is a typical rated point, but most real sea states are smaller, so wave farm capacity factors are usually 0.20-0.35 (onshore wind 0.25-0.40, offshore wind 0.35-0.50, solar PV 0.10-0.20).

Although NEDO, the University of Tokyo and JAMSTEC have studied wave energy for decades, three barriers slow commercialization. First, structural cost to survive typhoons and long swells (wave loads can be 2-3 times wind loads). Second, subsea cable and mooring costs, which often make CAPEX 3-5 times that of onshore wind. Third, the lack of a large open-sea test facility comparable to EMEC in the UK, and immature certification/insurance frameworks. Even so, Japan's coastal flux is 5-15 kW/m and the total resource is estimated at about 36 GW. Hybrid OWC breakwaters that share construction cost with port infrastructure are now a focus area.

Real-world applications

EMEC (Orkney, UK): The European Marine Energy Centre on the Orkney Islands has hosted more than 20 international wave and tidal energy projects for full-scale, grid-connected open-sea testing. The annual average wave power flux is 20-30 kW/m. Carnegie's CETO buoys and Aquamarine's Oyster are well-known examples. Setting Hs = 3 m and T_p = 10 s in this tool reproduces the typical EMEC flux around 25 kW/m.

Aguçadoura Wave Farm (Portugal): The world's first commercially grid-connected wave farm (2008) used three 750 kW Pelamis-style attenuators for a total of 2.25 MW. Choosing "Attenuator" and a device width of 120 m (the actual P-750 length) in this simulator gives a capture width of 54 m and around 350 kW per device at Hs = 2 m, showing that Hs of 3-4 m is needed to approach the 750 kW rating.

Garden Island (Perth, Australia): Carnegie's CETO 6 demonstrator uses fully submerged point absorbers that drive seabed pumps for electricity and reverse-osmosis desalination on shore. This water-and-energy co-generation model is especially attractive for remote-island microgrids.

OWC breakwaters: The Mutriku port breakwater in the Basque Country, Spain integrates 16 OWC units for a total of 296 kW, the first grid-connected OWC wave farm in the world. Sharing the breakwater's construction cost with the wave plant reduces CAPEX by 30-50%. Japan studied similar ideas in the 1980s with NEDO's Kaimei and Mighty Whale projects.

Common misconceptions and pitfalls

The biggest trap is judging a site solely by its wave power flux. The 13.5 kW/m on the dashboard is the incident power per meter of wavefront, not the electricity you can sell. For a point absorber the overall chain is CWR 0.30 × PTO 0.65 × CF 0.30, which is only about 6% of the incident energy on an annual average. Bigger waves are not automatically better either — extreme waves above 10 m force the device into survival mode and stop generation. A proper site assessment looks at the full wave-height distribution and the 50- or 100-year design wave, not just the mean flux.

A second pitfall is applying the linear deep-water flux formula in shallow water or breaking zones. P = rho g^2 H_s^2 T_e / (64 pi) is a linear, small-amplitude, deep-water expression. Once the depth is less than half a wavelength, phase and group velocities change and the general form is P = rho g H_s^2 c_g / 8 (c_g is the group velocity). In the breaking zone (H_s/d above roughly 0.7) energy is dissipated as turbulence and never reaches the device. Overtopping devices are designed to make use of breakers, but point absorbers and OWCs typically operate just outside the breaking zone. Treat this tool as a screening estimate, not a final design.

The third pitfall is confusing PTO efficiency with isolated component efficiency. PTO efficiency is the full "wall-to-wall" ratio of electrical to hydraulic power and includes pump volumetric losses, piping pressure drops, generator and power-electronic losses. A 95% generator can sit inside a chain whose overall efficiency is only 70-80%, and low-wave idling losses pull the annual average down further. A realistic plant-level η_PTO is 0.55-0.65. The 65% default here is on the optimistic side; for initial concept screening, also run a conservative case at 0.5 to see how sensitive your AEP is.

Wave Energy Converter (WEC) Power Estimation Simulator