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

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## Abstract

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%.

## Keywords

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 (m

^{2})- \( A_{d} \)
The characteristic frontal area (m

^{2})- \( A_{w} \)
The water plane area of the buoy (m

^{2})- \( b \)
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/m

^{2})- \( E_{g} \)
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/s

^{2})- \( H \)
Wave height (m)

- \( h \)
Water depth (m)

- \( I_{f\,l} \)
Equivalent inertia of the flywheel (kg.m

^{2})- \( K \)
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/m

^{3})- \( S_{b} \)
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)

## Notes

### Acknowledgements

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).

## References

- 1.Yang, S. M., Ji, H. S., Shim, D. S., Baek, J. H., & Park, S. H. (2017). Conical roll-twist-bending process for fabrication of metallic archimedes spiral blade used in small wind power generator.
*International Journal of Precision Engineering and Manufacturing-Green Technology,**4,*431–439.CrossRefGoogle Scholar - 2.Garate, J., Solovitz, S. A., & Kim, D. (2018). Fabrication and performance of segmented thermoplastic composite wind turbine blades.
*International Journal of Precision Engineering and Manufacturing-Green Technology,**5,*271–277.CrossRefGoogle Scholar - 3.Kim, Y. W., Park, J. H., Lee, N. K., & Yoon, J. H. (2017). Profile design of loop-type blade for small wind turbine.
*International Journal of Precision Engineering and Manufacturing-Green Technology,**4,*387–392.CrossRefGoogle Scholar - 4.Johannes, F. (2007). A review of wave-energy extraction.
*Marine Structures,**20,*185–201.CrossRefGoogle Scholar - 5.Falcão, A. F. O. (2010). Wave energy utilization: A review of the technologies.
*Renewable and Sustainable Energy Reviews,**14,*899–918.CrossRefGoogle Scholar - 6.Iraide, L., Jon, A., Salvador, C., de Iñigo Martínez, A., & Iñigo, K. (2013). Review of wave energy technologies and the necessary power-equipment.
*Renewable and Sustainable Energy Reviews,**27,*413–434.CrossRefGoogle Scholar - 7.Leijon, M., Bernhoff, H., Agren, O., Jan, I., Jan, S., Marcus, B., et al. (2005). Multiphysics simulation of wave energy to electric energy conversion by permanent magnet linear generator.
*IEEE Transactions on Energy Conversion,**20,*219–224.CrossRefGoogle Scholar - 8.Colli, V. D., Cancelliere, P., Marignetti, F., Stefano, R. D., & Scarano, M. (2006). A tubular-generator drive for wave energy conversion.
*IEEE Transactions on Industrial Electronics,**53*(4), 1152–1159.CrossRefGoogle Scholar - 9.Binh, P. C., Truong, D. Q., & Ahn, K. K. (2012). A study on wave energy conversion using direct linear generator.
*12th International Conference on Control, Automation and Systems*.Google Scholar - 10.Richard, C., Helen, B., Markus, M., Edward, S., & Paul, M. (2013). Analysis, design and testing of a novel direct-drive wave energy converter system.
*IET Renewable Power Generation,**7,*565–573.CrossRefGoogle Scholar - 11.Silvia, B., Adrià Moreno, M., Alessandro, A., Giuseppe, P., & Renata, A. (2013). Modeling of a point absorber for energy conversion in Italian seas.
*Energies,**6,*3033–3051.CrossRefGoogle Scholar - 12.Danielsson, O., Eriksson, M., & Leijon, M. (2006). Study of a longitudinal flux permanent magnet linear generator for wave energy converters.
*International Journal of Energy Research,**30,*1130–1145.CrossRefGoogle Scholar - 13.Ocean power technologies. http://www.oceanpowertechnologies.com. Accessed 2015.
- 14.Wave star energy. http://www.wavestarenergy.com Accessed 2015.
- 15.Ahn, K. K., Truong, D. Q., Tien, H. H., & Yoon, J. I. (2012). An innovative design of wave energy converter.
*Renew. Energy,**42,*186–194.CrossRefGoogle Scholar - 16.Truong, D. Q., & Ahn, K. K. (2014). Development of a novel point absorber in heave for wave energy conversion.
*Renew. Energy,**65,*183–191.CrossRefGoogle Scholar - 17.Al-Habaibeh, A., Sub, D., McCague, J., & Knight, A. (2010). An innovative approach for energy generation from waves.
*Energy Conversion and Management,**51,*1664–1668.CrossRefGoogle Scholar - 18.Tri, N. M., Binh, P. C., & Ahn, K. K. (2018). Power take-off system based on continuously variable transmission configuration for wave energy converter.
*International Journal of Precision Engineering and Manufacturing-Green Technology,**5,*89–101.CrossRefGoogle Scholar - 19.Folley, M., & Whittaker, T. J. T. (2009). Analysis of the nearshore wave energy resource.
*Renewable Energy,**34,*1709–1715.CrossRefGoogle Scholar - 20.Lok, K. S., Stallard, T. J., Stansby, P. K., & Jenkins, N. (2014). Optimisation of a clutch-rectified power take off system for a heaving wave energy device in irregular waves with experimental comparison.
*International Journal of Marine Energy,**8,*1–16.CrossRefGoogle Scholar - 21.Albert, A., Giovanni, B., Luca, B., & Pietro, F. (2017). Mechanical design and simulation of an onshore four-bar wave energy converter.
*Renewable Energy,**114*(Part B), 766–774.CrossRefGoogle Scholar - 22.Liang, C., Junxiao, A., & Lei, Z. (2017). Design, fabrication, simulation and testing of an ocean wave energy converter with mechanical motion rectifier.
*Ocean Engineering,**136,*190–200.CrossRefGoogle Scholar - 23.Cummins, W. E. (1962). The impulse response function and ship motions.
*Symp. on Ship Theory, Inst.ffur Shiffbau*, Hamburg.Google Scholar - 24.WAMIT Version 6.3 User Manual. http://www.wamit.com. Accessed 2015.
- 25.Evans, D. V., & McIver, P. (1984). Added mass and damping of a sphere section in heave.
*Appl Ocean Res*,*6*, 45–53.CrossRefGoogle Scholar - 26.McIver, P. (1991). The added mass of bodies heaving at low frequency in water of finite depth.
*Appl Ocean Res*,*13*, 12–17.CrossRefGoogle Scholar - 27.Havard, E. (1995). Hydrodynamic parameters for a two-body axisymmetric system.
*Applied Ocean Research,**17,*103–115.CrossRefGoogle Scholar - 28.Falnes, J. (2002).
*Ocean waves and oscillating systems, linear interaction including wave-energy extraction*. Cambridge: Cambridge University.CrossRefGoogle Scholar - 29.Babarit, A., Hals, J., Muliawan, M. J., Kurniawan, A., Moan, T., & Krokstad, J. (2012). Numerical benchmarking study of a selection of wave energy converters.
*Renewable Energy,**41,*44–63.CrossRefGoogle Scholar - 30.Armstrong, B., & de Wit, C. C. (1995).
*Friction modeling and compensation: the control handbook*. Boca Raton: CRC Press.Google Scholar - 31.Lim, C. W. (2017). Design and manufacture of small-scale wind turbine simulator to emulate torque response of MW wind turbine.
*International Journal of Precision Engineering and Manufacturing-Green Technology,**4,*409–418.CrossRefGoogle Scholar - 32.Do, H. T., Dinh, Q. T., Nguyen, M. T., Phan, C. B., Dang, T. D., et al. (2015). Effects of non-vertical linear motions of a hemispherical float wave energy converter.
*Ocean Engineering,**109,*430–438.CrossRefGoogle Scholar - 33.Tri, N. M., Truong, D. Q., Binh, P. C., Dung, D. T., Lee, S., et al. (2016). A Novel control method to maximize the energy-harvesting capability of an adjustable slope angle wave energy converter.
*Renewable Energy,**97,*518–531.CrossRefGoogle Scholar - 34.Do, H. T., Dinh, Q. T., Nguyen, M. T., Phan, C. B., Dang, T. D., et al. (2017). Proposition and experiment of a sliding angle self-tuning wave energy converter.
*Ocean Engineering,**132,*1–10.CrossRefGoogle Scholar