Wave Energy Converter: Resonance & PTO Damping Tuning

Incoming Wave

Wave period T 8.0 s

Wave height H 1.5 m

Buoy Tuning

Natural period T_n (ballast) 8.0 s

PTO damping b_pto 180 kN·s/m

Live Output

Instantaneous power

0 kW

Time-avg. power

0 kW

Heave amplitude

0.0 m

Capture efficiency

0 %

How it works

The buoy is a single degree-of-freedom heaving oscillator driven by the wave and resisted by radiation damping and the power take-off (PTO):

(m + m_a)·z" + (b_rad + b_pto)·z' + k_hs·z = F0·cos(ωt)
k_hs = ρ·g·A_wp          (hydrostatic stiffness)
ω_n = √(k_hs / (m + m_a)) (natural frequency)

Power absorbed by the generator at any instant is P(t) = b_pto·z'(t)². Two conditions maximise the time-averaged power:

Resonance: the buoy's natural period T_n (set by ballast/mass) matches the wave period T, so the response amplitude peaks — exactly like pushing a swing at its own frequency.
Damping match: for a linear PTO, average power is maximised when b_pto ≈ b_rad(ω), the buoy's own radiation damping at that frequency — too little damping wastes the motion, too much stalls it.

Even at perfect resonance and matched damping, a heaving point absorber cannot out-capture more energy than the "capture width" limit from linear wave theory, CW_max = λ/(2π) (Budal/Falnes bound), where λ = gT²/(2π) is the deep-water wavelength. The capture efficiency readout compares the buoy's actual capture width (average power ÷ incident wave power per metre of crest) against this theoretical ceiling — real point-absorber WECs (e.g. Powerbuoy-class devices) typically reach 40–70% of it once losses are included.

Buoy heave motion Sea surface PTO power (glow)

Resonance match

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