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Study of scale modelling, verification and control of a heaving point absorber wave energy converter

Guo, Bingyong


Bingyong Guo


J. M. (James Michael) Gilbert


This study focuses on scale modelling of a heaving Point Absorber Wave Energy Converter (PAWEC), model verification via wave tank tests and power maximisation control development. Starting from the boundary element method simulation of the wave-PAWEC interaction, linear and non-linear modelling approaches of Wave-To-Excitation-Force (W2EF), Force-To-Motion (F2M), Wave-To-Motion (W2M) are studied. To verify the proposed models, a 1/50 scale PAWEC has been designed, simulated, constructed and tested in a wave tank under a variety of regular and irregular wave conditions. To study the coupling between the PAWEC hydrodynamics and the Power Take-Off (PTO) mechanism, a Finite Element Method (FEM) is applied to simulate and optimise a Tubular Permanent Magnet Linear Generator (TPMLG) as the PTO system and control actuator. Thus linear and non-linear Wave-To-Wire (W2W) models are proposed via combining the W2M and PTO models for the study and development of power maximisation control.

The main contributions of this study are summarised as follows:

Linear and non-linear F2M models are derived with the radiation force approximated by a finite order state-space model. The non-linear friction is modelled as the Tustin model, a summation of the Stribeck, Coloumb and damping friction forces, whilst the non-linear viscous force is simulated as the drag term in the Morison equation. Thus a non-linear F2M model is derived considering the non-linear friction and viscous forces as a correction or calibration to the linear F2M model. A wide variety of free-decay tests are conducted in the wave tank and the experimental data fit the non-linear F2M modelling results to a high degree. Further, the mechanism how these non-linear factors influence the PAWEC dynamics and energy dissipations is discussed with numerical and experimental results.

Three approaches are proposed in this thesis to approximate the wave excitation force:
(i) identifying the excitation force from wave elevation, referred to as the W2EF method, (ii) estimating the excitation force from the measurements of pressure, acceleration and displacement, referred to as the Pressure-Acceleration-Displacement-To-Excitation-Force (PAD2EF) approach and (iii) observing the excitation force via an unknown input observer, referred to as the Unknown-Input-Observation-of-Excitation-Force (UIOEF) technique. The W2EF model is integrated with the linear/non-linear F2M models to deduce linear/non-linear W2M models. A series of excitation tests are conducted under regular and irregular wave conditions to verify the W2EF model in both the time- and frequency-domains. The numerical results of the proposed W2EF model show a high accordance to the excitation test data and hence the W2EF method is valid for the 1/50 scale PAWEC. Meanwhile, a wide range of forced-motion tests are conducted to compare the excitation force approximation results between the W2EF, PAD2EF and UIOEF approaches and to verify the linear and non-linear W2M models. Comparison of the PAWEC displacement responses between the linear/non-linear W2M models and forced-motion tests indicates that the non-linear modelling approach considering the friction and viscous forces can give more accurate PAWEC dynamic representation than the linear modelling approach.

Based on the 1/50 scale PAWEC dimension and wave-maker conditions, a three-phase TPMLG is designed, simulated and optimised via FEM simulation with special focus on cogging force reduction. The cogging force reduction is achieved by optimise the TPMLG geometric design of the permanent magnets, slots, pole-shoe and back iron. The TPMLG is acting as the PTO mechanism and control actuator. The TPMLG is connected with the buoy rigidly and hence the coupling is achieved by the PTO force. Linear and non-linear W2W models are derived for the study of power maximisation control. To investigate the control performance on the linear and non-linear W2W models, reactive control and phase control by latching are developed numerically with electrical implementation on the TPMLG. Further, a W2W tracking control structure is proposed to achieve power maximisation and displacement constriction under both regular and irregular wave conditions.


Guo, B. (2017). Study of scale modelling, verification and control of a heaving point absorber wave energy converter. (Thesis). University of Hull. Retrieved from

Thesis Type Thesis
Deposit Date Jun 21, 2018
Publicly Available Date Feb 23, 2023
Keywords Engineering
Public URL
Additional Information School of Engineering and Computer Science, The University of Hull
Award Date Oct 1, 2017


Thesis (8 Mb)

Copyright Statement
© 2017 Guo, Bingyong. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

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