Modeling and Experimental Investigation on Performance of a Wave Energy Converter with Mechanical Power Take-Off

  • Tri Dung Dang
  • Cong Binh Phan
  • Kyoung Kwan AhnEmail author
Regular Paper


This paper presents an experimental investigation on the hydrodynamic performance and energy conversion efficiency of an efficient wave energy converter using a simple conceptual design. The system is based on a mechanical device power take-off (PTO) so-called a bidirectional rotary motion converter (BRMC), which can absorb wave energy by converting bidirectional motion of ocean waves into one-way rotation of an electric generator. First, a prototype system is designed, fabricated and assembled in the Research Institute of Small & Medium Shipbuilding (RIMS). The tests are carried out under different conditions, such as wave profiles, the resistive load coefficients and supplementary masses. A wave simulator is controlled to make harmonic waves with different amplitudes and frequencies. Metal plates are added and fixed on the buoy as supplementary masses. Closed-loop torque control has been applied on the Magneto-Rheological (MR) brake to simulate the induced torque of an electric generator. Moreover, the rotary angle compared to vertical direction, is adjusted to investigate the influence of surge mode and heave mode combination on the absorption energy. The output power is calculated and compared with maximum theoretical absorbed power in heave mode to evaluate the efficiency of the prototype under different conditions. Finally, at optimum condition, the efficiency of the PTO system can reach 80.4% including frictional loss, and the capture width ratio is up to 41.6%.


WEC Energy conversion efficiency Wave extraction test Construction of mechanical PTO test 

List of symbols

\( \alpha \)

Phase difference (rad)

\( a \)

Buoy radius (m)

\( A \)

Wave amplitude (m)

\( A_{0} \)

The water plane area of the buoy at rest (m2)

\( A_{d} \)

The characteristic frontal area (m2)

\( A_{w} \)

The water plane area of the buoy (m2)

\( b \)

The draft of initial position (m)

\( \beta \)

The angle between the buoy shaft and the vertical direction

\( C_{d} \)

The drag coefficient

\( c_{g} \)

The group velocity (m/s)

\( c_{vf} \)

Force transition approximation coefficient (s/rad)

\( c_{vt} \)

Torque transition approximation coefficient (s/rad)

\( D(kh) \)

The depth function

\( d \)

The captured width (m)

\( E \)

The mean wave energy density per unit horizontal area (J/m2)

\( E_{g} \)

The generated energy (J)

\( \varepsilon \)

The non-dimensionalised radiation resistance

\( F_{b} \)

Hydrostatic force (N)

\( F_{br} \)

The breakaway friction force (N)

\( F_{c} \)

The Coulomb friction force (N)

\( F_{e} \)

The excitation force (N)

\( F_{f} \)

Friction force from the PTO system (N)

\( F_{h} \)

The hydrodynamic force (N)

\( F_{pto} \)

The resistive force from the PTO system (N)

\( F_{r} \)

Radiation force (N)

\( F_{u} \)

User’s force (N)

\( F_{v} \)

Viscous force (N)

\( f \)

The excitation force coefficient

\( f_{v} \)

The viscous friction coefficient

\( g \)

Gravitational acceleration (m/s2)

\( H \)

Wave height (m)

\( h \)

Water depth (m)

\( I_{f\,l} \)

Equivalent inertia of the flywheel (kg.m2)

\( K \)

The memory function

\( k \)

The angular repetency (rad/m)

\( k_{g} \)

The gear ratio

\( \kappa \)

The dimensionless excitation force coefficient

\( l \)

Buoy displacement (m)

\( M_{a} \)

The added mass (kg)

\( M_{b} \)

The buoy mass (included support structure) (kg)

\( M_{r1} \)

The added mass in surge (kg)

\( M_{r3} \)

The added mass in heave (kg)

\( M_{s} \)

Supplementary mass (kg)

\( m \)

The flywheel mass (kg)

\( n \)

The rotational speed of driving shaft (rad/s)

\( \eta \)

Wave elevation (m)

\( \eta_{a} \)

The capture width ratio efficiency

\( \eta_{pto} \)

The PTO efficiency

\( \eta_{O} \)

The overall efficiency

\( R_{r} \)

The radiation damping coefficient

\( R_{u} \)

The electric torque coefficient (Nms/rad)

\( r \)

The flywheel radius (m)

\( r_{p} \)

Pinion radius (m)

\( P_{1} \)

The gravity on the surge displacement (N)

\( P_{a} \)

The absorbed power (W)

\( P_{c} \)

The capture power (W)

\( P_{g} \)

The generated power (W)

\( P_{w} \)

The mean wave power (W)

\( \rho \)

Water density (kg/m3)

\( S_{b} \)

The buoyancy stiffness (N/m)

\( T_{br} \)

The breakaway friction torque (Nm)

\( T_{c} \)

The Coulomb friction torque (Nm)

\( T_{f\,l} \)

Flywheel torque (Nm)

\( T_{in} \)

The input shaft torque (Nm)

\( T_{out} \)

The output shaft torque (Nm)

\( T_{u} \)

User’s torque (Nm)

\( \varphi \)

The phase angle (rad)

\( \omega \)

Angular frequency of wave (rad/s)

\( \theta \)

Angle of rotation of the output shaft (rad/s)



This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT, South Korea (NRF2017R1A2B3004625).


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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Graduate School of Mechanical EngineeringUniversity of UlsanUlsanSouth Korea
  2. 2.Faculty of Mechanical EngineeringHo Chi Minh City University of Technology and EducationHo Chi Minh CityVietnam
  3. 3.Department of Mechanical EngineeringUniversity of UlsanUlsanSouth Korea

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