The Use of Hydroelastic Structures in Wave Energy Converters

Abstract

The Wavepiston modular energy collector is a string of vertical ‘sails’, each comprising several vertical ‘paddles’, that respond primarily in surge to incident wave excitation. In an early device development stage, the sails were designed to allow spacing between the vertical paddles to minimise hydrodynamic forces, in extreme conditions, to improve survivability. However, the benefit for survivability was at the cost of energy absorption performance as a result of a substantial decrease in the sail excitation force. Therefore, flexible paddles, which can deform in response to large surge wave loads, are considered a feasible design strategy to minimise the energy-capture–survivability trade-off. An experimental wave tank test campaign was undertaken to investigate the response of paddle materials, with different paddle flexibility and overlaps, to wave-induced and forced motion excitation. This paper explores how different configurations of these hydroelastic structures affect the wave-induced load experienced by a fixed sail and the wave energy absorption potential of the sail. Two metrics are proposed to assess how different paddle overlaps and material properties affect device performance and survivability at particular deployment locations. The sail response is characterised and depicted through these metrics for increasing excitation amplitudes to provide initial insights into how the sail configuration design choices and materials impact the device capacity factor.

1. Introduction

Ocean wave energy offers a predictable, high-density energy [1] that can complement existing renewable energy sources [2]. Despite these advantages, progress in developing ocean wave energy technology has been relatively slow, particularly compared to wind energy, with large-scale commercial deployment of wave energy devices yet to be realised [3]. The slow pace of the commercial rollout of wave energy converters (WECs) has several causes, including the lack of convergence on a single WEC design [3], but the ultimate cause is an economic one; currently, wave energy is not commercially competitive [4,5,6]. One of the many obstacles to progress experienced by the wave energy industry is the challenge of ensuring the survivability of WECs while simultaneously maintaining low capital and operational costs to ensure a low lifetime cost of energy. In wind energy, reliability is reasonably high, with turbines designed to shed loads and operate near capacity factor in most environmental conditions. How can WEC technologies achieve similar levels of structural load compliance and performance efficiency?

WEC systems have a wide range of working principles, deployment locations, sizes, and designs and are typically classified according to working principles as oscillating bodies, oscillating water columns or overtopping devices [3,7]. Conventional oscillating body designs typically involve a rigid body energy collector (EC) interacting with incident waves and transferring the mechanical load to a power take-off (PTO) mechanism that harnesses the relative motion of the EC to a reference body/point to achieve energy extraction [3,8]. Such rigid body devices face economic feasibility challenges as a consequence of conflicting engineering device requirements for (i) survivability in extreme conditions, where high forces and structural stresses are experienced, and (ii) performance efficiency in operation conditions for a highly variable resource. That is, a significant challenge in WEC design and development is understanding how to optimise the capacity factor of the device.

Flexible and deformable structures in WECs are increasingly being considered as a solution to the design challenges posed by ocean energy conversion [9,10,11]. Several approaches have been proposed involving bulging membrane-type structures such as Anaconda [12], where electrical energy is generated using a hydraulic PTO, or electro-active polymer designs [13,14,15], which convert mechanical energy into electricity. However, conventional WEC designs based on rigid body operating principles have rarely harnessed hydroelastic behaviour in order to enhance performance and survivability.

The Danish wave energy developer Wavepiston A/S has designed a modular floating surge WEC technology comprising multiple, floating, energy collectors (ECs) coupled on a pipe or ‘string’ (see Figure 1b for a single EC deployment). Each EC has a vertical sail that moves back and forth in response to the surge motion of incident waves. The sails consist of multiple overlapping vertical ‘paddles’ attached to a rigid frame that can deform in response to incident wave excitation (Figure 1a). This horizontal movement drives hydraulic pumps generating pressurised seawater, which is piped through the string to a conversion station onshore or on a platform. A small-scale field deployment of a rigid-sail Wavepiston device comprising four ECs, in 2019, demonstrated the Wavepiston concept (WavePiston, 2019). The primary conclusion from this test deployment was that the capacity factor (defined as the mean produced power relative to maximum power) should be increased in order to achieve a competitive cost of energy. Integration of flexible and deformable paddles in the WEC shows promise in achieving a high capacity factor, while ensuring compliance with structural load ratings.

Wavepiston has commissioned physical tests of the hydrodynamic response of an experimental-scale single sail model to investigate how paddle flexibility and spacing affect sail response to provide validation data for high-fidelity numerical wave tanks [16]. In this analysis, the impact of different hydroelastic structure (paddle) configurations, defined by paddle flexibility and overlap, on the sail wave loads and energy capture capability is assessed. In particular, a wave-induced load metric and a wave energy absorption metric are developed to better understand and measure how each configuration modulates response gains, in response to increasing excitation amplitudes. The proposed metrics are used to illustrate the characteristic response curves of each configuration, and the potential application of these metrics in the sail design process to optimise the device capacity factor is considered.

2. Experimental Wave Tank Test Campaign

2.1. Wave Tank Facility Specifications

Experiments were conducted in the wave basin at the Ocean and Coastal Engineering Laboratory at Aalborg University. The wave basin is 1.5 m deep with an active test area that is 13.0 m long and 8.44 m wide [17] and is equipped with a segmented piston wavemaker and active wave absorption to minimise the influence of longitudinal wave reflections. The wave tank features an overhead gantry, which is used to support the main testing frame that holds the motor and instrumentation for the scale model sail, as shown in Figure 2a. Both wave excitation tests, with a stationary sail, and sail excitation (radiation) tests, in otherwise undisturbed water, were conducted for a range of sail configurations.

The physical model used in the wave tank tests is a 1:16 scale representation of the current Wavepiston sail design and comprises six vertical paddles of width $d_{wp}=0.0608$ m mounted on an outer sail ‘frame’, as illustrated in Figure 3. The sail, positioned equidistant from the basin side walls and 5 m from the wavemaker, is attached to a motor that can translate along a rail, oriented perpendicular to the wavemaker, as shown in Figure 2a. Four wave gauges were positioned in the vicinity of the sail, as shown in Figure 2b, to measure waves radiated by the sail in forced motion tests and incident and diffracted waves, in wave excitation tests. In equilibrium, the sail support structure suspends the frame and paddles, which are partially submerged in the water. Four load cells were positioned between each corner of the outer frame of the sail and the support structure to measure fluid and inertial forces exerted by the sail on the support structure. All sensor measurements are sampled at 200 Hz; see [16] for further details.

The six replaceable inner vertical paddles, shown in Figure 3, are hydroelastic structures that can deform in response to wave excitation and/or sail motion, allowing fluid through the sail, with the degree of flow transparency depending on the paddle bending stiffness and overlap.

Table 1. Sail configurations based on different paddle thickness (and hence flexibilities) and overlap.

Configuration	Material	Paddle Thickness (mm)	Overlap
FULL	Plexiglass	—	None
SLOT	Plexiglass	—	−15%
K1	PVC	0.3	0%
K2	PVC	0.4	0%
K3	PVC	0.5	0%
K2O	PVC	0.4	10%
K2O2	PVC	0.4	25%
K2O3	PVC	0.4	50%

lists the eight different sail configurations that were examined during the experimental campaign. Three different flexible paddle thicknesses were considered, with the $0.4$ mm case corresponding to the baseline bending stiffness and the $0.3$ mm and $0.5$ mm corresponding to 50% and 200% stiffness variations. Two configurations featuring rigid plexiglass material, with the same outer dimensions as the flexible sail configurations, were also examined: a solid sail (‘FULL’) representing zero deformation and a rigid slotted sail with 15% of its area open to flow, representing the full paddle-deformation scenario.

2.2. Wave Excitation Tests

The wave excitation tests comprised a total of 18 regular wave tests, for a range of amplitudes A and periods T, three irregular wave tests representing sea states with different peak periods, and three chirp tests for each sail configuration. Three linear chirp wave excitation signals were generated to excite a range of sail response frequencies at a specific input wave amplitude. Wave propagation-only tests, in the absence of the sail, were also conducted to obtain the undisturbed free-surface elevation ${\eta }_i\left(t\right)$ at the proposed sail location.

Chirp signals are widely applied in system identification [18], including recent applications in wave energy [19,20], because they allow constant-amplitude, broadband excitation of systems. In particular, linear chirp signals have an instantaneous excitation frequency that sweeps a specified frequency range according to $f=f_0+ct$, where $f_0$ is the minimum frequency, $c=\Delta f/T_c$ is the sweep rate across the frequency interval $\Delta f=f_1-f_0$, and $T_c$ is the signal duration. Chirp signals where $c>0$ are referred to as ‘up-chirp’ because frequencies are swept from low to high, whereas ‘down-chirp’ signals have $c<0$ and sweep from high to low frequencies. In wave energy system identification, chirp signals have mostly been used in forced motion tests; however, in this test campaign, the incident free-surface elevation at the sail was specified to have a linear chirp form, spanning the frequency range $(0.3,1.0)$ Hz over a duration of $T_c=100$ s for wave amplitudes of $0.011$ m, $0.023$ m, and $0.047$ m, as shown in

Table 2. Chirp excitation signal initial and final frequencies ($f_0$ and $f_1$, respectively) and chirp amplitude $A_c$ for PTO and wave excitation experiments. PTO excitation and wave excitation chirp signals are, respectively, specified in terms of velocity amplitudes and wave amplitudes. Full-scale excitation parameters, based on a 1:16 Froude scaling, are also provided as initial and final chirp periods ($T_0^{full}$ and $T_1^{full}$ and full-scale amplitudes $A_c^{full}$).

		Experimental Scale			Full Scale
	Chirp Signal	${\mathit{f}}_{\mathbf{0}}$ (Hz)	${\mathit{f}}_{\mathbf{1}}$ (Hz)	${\mathit{A}}_{\mathit{v}}$	${\mathit{T}}_{\mathbf{0}}^{\mathit{full}}$ (s)	${\mathit{T}}_{\mathbf{1}}^{\mathit{full}}$ (s)	${\mathit{A}}_{\mathit{c}}^{\mathit{full}}$
PTO	CH10	1.5	0.2	0.013 m/s	2.67	20	0.208 m/s
	CH11	1.5	0.2	0.052 m/s	2.67	20	0.803 m/s
	CH12	1.5	0.2	0.102 m/s	2.67	20	1.632 m/s
	CH13	1.5	0.2	0.205 m/s	2.67	20	3.280 m/s
Wave	CH00	0.3	1.0	0.011 m	13.3	4	0.176 m
	CH01	0.3	1.0	0.023 m	13.3	4	0.368 m
	CH04	0.3	1.0	0.047 m	13.3	4	0.752 m

. An example wave excitation test is shown in Figure 4. Specifically, the amplitude of the chirp signals employed is related to the amplitude of the tested regular waves (0.75 m and 1.5 m at full scale or 4.69 cm and 9.37 cm at lab scale, using Froude scaling with a scaling factor of 16). A smaller chirp (0.375 m at full scale), to have a less aggressive condition, was also introduced, while the 15.62 cm (2.5 m) amplitude chirp was not tested, since it would have resulted in wave breaking.

The employed frequency range is a combination of basin limitation (0.4 Hz—2.5 s is a limit to keep reflections low) and a limit inherited from the radiation test chirp (1 Hz). Moving toward higher frequencies would have resulted in steeper waves and poorer generation quality.

2.3. Forced Motion (PTO Excitation) Tests

A range of forced horizontal sail motion tests were also conducted, involving impulsive accelerations, sinusoidal oscillations, and chirp excitation signals. In the chirp excitation tests, the horizontal velocity of the sail was specified to follow down-chirp signals spanning the frequency range $(0.2,1.5)$ Hz and $(1.2,2.5)$ over a duration of $T_c=150$ s for four chirp velocity amplitudes $A_v=(0.013,0.052,0.102,0.205)$ m/s (see Table 2). A sample forced motion test is shown in Figure 5.

3. Wave-Induced Loads

3.1. Response Metric—Hydrodynamic Gain

The hydrodynamic gain concept [21] is introduced in order to characterise the system response, i.e., the wave-induced load experienced by the sail, to incident wave excitation. Hydrodynamic gain is defined as the ratio of excitation force (or torque) amplitude to incident wave amplitude in the frequency domain. In WEC studies, the excitation force in the primary floating body mode that contributes to power capture will be of most interest, which, for the Wavepiston device, is the surge mode. A key motivation for this study is to understand how the surge hydrodynamic gain is modulated by deformation of hydroelastic structures, as the amplitude of the incident waves increases. Therefore, the following metric is proposed

$$\overline{G}(A;\mathsf{\Theta })={\displaystyle \frac{{\sum }_i\sqrt{2S\left({\omega }_i\right)\Delta \omega }G({\omega }_i,A;\mathsf{\Theta })}{{\sum }_i\sqrt{2S\left({\omega }_i\right)\Delta \omega }}},$$

(1)

to characterise the hydroelastic-driven modulation of the excitation force gain $G(\omega ;A,\mathsf{\Theta })=\left|H\right(j\omega ;A,\mathsf{\Theta }\left)\right|$, where $H(j\omega ;A,\mathsf{\Theta })$ is the excitation force frequency response function, at a specific excitation amplitude A, for a certain hydroelastic structure configuration represented by $\mathsf{\Theta }$, including an amplitude weighting function $\sqrt{S\left(\omega \right)}$, where $S\left(\omega \right)$ is the wave energy spectrum at a deployment location. The mean gain is calculated over a prescribed set of discrete frequencies $\{{\omega }_i,i=1,\dots ,N\}$.

3.2. Metric Evaluation—System Identification

The surge excitation force response of the sail to wave excitation is modelled using system identification methods [22,23], which have previously been used to model WEC dynamics in experimental and numerical wave tank tests [24,25,26], to capture the most relevant wave-sail interaction dynamics.

System Identification Procedure

Prior to system identification, the experimental wave excitation sensor data are pre-processed to remove high-frequency contamination and ensure an appropriate time-step size for capturing system dynamics. All pre-processing and system identification tasks are conducted using the MATLAB R2025a (Version 25.1) system identification toolbox. A third-order polynomial Savitzky–Golay filter, applied to a fixed window of 45 time steps (0.225 s in duration), is used to smooth the signal without introducing a phase lag [27], and the filtered time signals are down-sampled to $0.25$ s intervals to provide a parsimonious signal representation.

A discrete-time system, comprising the load-cell measured surge force output $y\left(k\right)=F_1\left(t_k\right)$ and a free-surface elevation input $u_k=\eta \left(t_k\right)$, is identified using an ARX (Auto-Regressive with eXogenous inputs) model. ARX models are widely used discrete-time, black-box models that assume a linear relationship between system input and output [23,28], with the form

$$y\left(k\right)={\displaystyle \sum _{i=1}^{n_a}}{a}_{i}y(k-i)+{\displaystyle \sum _{i=0}^{n_b}}{b}_{i}u(k-n_d-i),$$

(2)

where $n_a$ is related to the autoregressive nature (memory) of the system and $n_d$ determines the system delay ($n_d>0$ for causality). ARX models are conceptually relatively simple, have low computational requirements, and have been employed as a first step in the system identification process; see [24,29] for examples in a wave energy context.

An important step in the identification/design of optimal ARX models is the estimation of optimal model order parameters $n_a$, $n_b$, and $n_d$ based on the model error criterion. In general, higher-order ARX models can capture more complex dynamics and can achieve lower fitting errors. However, the optimal model structure is the lowest-order model that captures all relevant dynamics and avoids over-fitting. The mean squared error (MSE) between the one-step-ahead model prediction $y_{1-k,i}$ and the experimental data $y_{\exp ,i}$ is the error criterion used for optimal model structure and subsequent parameter estimation. A systematic examination of the parameter space is undertaken to identify the optimal model. The optimal model order is the point at which further increases in model order yield progressively smaller reductions in the error criterion, e.g., $(n_a,n_b,n_k)=(2,2,1)$ for material K2 and $(n_a,n_b,n_k)=(3,2,1)$ for material SO, as shown in Figure 6. A black-box, nonlinear Kolmogorov–Gabor polynomial (KGP) model, which allows nonlinear dependence between the output and regressors (input and autoregressive terms) but is linear in the model parameters, was also explored but did not show improved predictive performance over the linear ARX, demonstrating the effective linear behaviour of the system dynamics.

This system identification approach is applied to each chirp-signal wave excitation dataset, comprising three different wave amplitudes, for each of the eight paddle configurations (material and overlap) shown in Table 1. The mean hydrodynamic gain metric is calculated by averaging the magnitude of the frequency response function of the dynamic system (ARX) model over 100 frequencies between $f=0.2$ Hz and $f=1.0$ Hz according to Equation (1). This approach assumes the system is potentially nonlinear in amplitude but can be described using a multi-linear approach, with different frequency responses at each amplitude. Therefore, the mean gain depends on the underlying experimental excitation data, the identified model, the frequency range of interest, and any weighting function identifying the most energetic frequencies at the deployment location.

3.3. Characteristic Response Comparison

Figure 7 shows the change in the weighted mean hydrodynamic gain with wave amplitude, for each sail configuration, in three reference sea states based on the wave energy spectra listed in

Table 3. Three Wavepiston reference sea states, assuming a Bretschneider spectrum, defined by the full-scale energy period $T_e$, significant wave height $H_s$, and experimental-scale energy frequency $f_{e,\exp }$.

Sea State	${\mathit{H}}_{\mathit{s}}$ (m)	${\mathit{T}}_{\mathit{e}}$ (s)	${\mathit{f}}_{\mathit{e}\mathbf{,}\mathbf{exp}}\mathbf{=}\mathbf{1}\mathbf{/}{\mathit{T}}_{\mathit{e}\mathbf{,}\mathbf{exp}}$ (Hz)
NEC1	1.0	5.0	0.8
NEC2	1.0	7.0	0.57
NEC3	2.0	9.0	0.44

. These reference sea-state spectra weight different frequency response bands excited by the chirp experiments, and, as a consequence, different sail configurations may exhibit different behaviours depending on the reference sea state.

The weighted mean hydrodynamic gain increases for both rigid paddle sail configurations (solid and slotted) as the wave amplitude increases from the lowest to the intermediate value, with saturation of the response at the highest amplitude for the sea states with shorter wave periods $T_{e1}=5.0$ s and $T_{e2}=7.0$ s. This contrasts with all flexible sail configuration responses, which exhibit a monotonic decrease in mean gain with increasing wave amplitude. It is also noticeable that all flexible sail configurations exhibit a higher response to the smallest wave excitation amplitude than either of the rigid sail configurations.

The nature of the average hydrodynamic gain response to incident wave amplitude is slightly modulated by the wave energy spectrum weighting function. Apart from the most flexible material (K1), all other configurations show a more gradual reduction in the weighted mean gain with increasing amplitude compared for the sea states $T_{e1}=5.0$ s and $T_{e2}=7.0$ s compared to $T_{e3}=9.0$ s.

4. Forced Motion (PTO Activation) Response

4.1. Response Metric—Wave Energy Radiation to Input Energy Ratio

The impact of hydroelastic deformations on the wave energy absorption of the various sail configurations is evaluated using a wave energy radiation metric, based on the forced motion test data. A wave energy radiation metric is considered appropriate for assessing wave energy absorption capability since, as stated by Falnes [30],

“Generally it can be said that a good wave absorber must be a good wavemaker.”

Based on this general principle, and with the goal of understanding how sail flexibility and panel spacing alter the wave generation and absorption capacity of the solid or ‘full’ sail, the proposed non-dimensional metric is

$${\displaystyle \frac{{\int }_{{\omega }_0}^{{\omega }_1}S\left(\omega \right)\times c_g\rho g{\left|A_{\eta }\left(\omega \right)\right|}^2{A}_{sub}d\omega }{{\int }_{{\omega }_0}^{{\omega }_1}S\left(\omega \right)\times c_g\rho g{\left|A_{\eta }^{FULL}\left(\omega \right)\right|}^2{A}_{sub}d\omega }},$$

(3)

where $A_{\eta }\left(\omega \right)=FT\left\{\eta (x,t)\right\}\left(\omega \right)$ is the Fourier transform of the radiated wave elevation at a representative location in the vicinity of the sail for any configuration, $A_{\eta }^{FULL}\left(\omega \right)$ corresponds to waves radiated by the FULL sail configuration, $\rho$ is the water density, g is the gravitational acceleration, $A_{sub}$ is the total submerged area of the full sail, and $c_g$ is the group velocity of radiated waves. This metric benchmarks the average wave energy flux radiated from a particular sail configuration undergoing forced motion against the (weighted) average wave flux radiated from a full, rigid sail undergoing the same motion. For a directional wave energy absorber, such as Wavepiston or an oscillating wave surge converter (OWSC), the location (or locations) x at which the wave elevation is measured should be along the axis of motion of the device.

4.2. Wave Energy Metric Evaluation—Fourier-Transform-Based

In order to evaluate the wave energy metric (3) for each sail configuration, the frequency-domain amplitude of the radiated waves is directly estimated from the wave gauge measurements of the free-surface elevation during the chirp excitation tests using the Fourier transform (i.e., the fft function in MATLAB). The sail velocity profile spans the frequency range $(0.2,1.5)$ Hz, corresponding to full-scale incident wave periods from $2.7$ s to 20 s, which includes all but the longest ocean waves. Note that the forced motion chirp tests are designed to give a constant velocity amplitude $U\left(\omega \right)=U$ over the chirp frequency range, although the actual input amplitude does vary slightly with $\omega$. All frequency integrals are approximated by summing over discrete frequencies in the range $({\omega }_0,{\omega }_1)=(0.0,2\pi \times 1.5)$ rad/s for $\Delta \omega =2\pi /T_c$ where $T_c=150$ s.

4.3. Characteristic Response Comparison

Figure 8 shows the weighted wave energy flux ratio metric for each sail configuration for sea states with three different energy periods (Table 3). Overall, the wave radiation flux from the flexible sail configurations decreases relative to the rigid, solid sail as the input excitation increases. Flexible panel deformations likely increase the ‘transparency’ of the sails and, hence, reduce wave energy generation relative to the solid sail, for increasing sail velocities. It is notable in Figure 8 that several of the flexible sail configurations (K2, K2O, K202, K3) generate more radiated wave power than the solid sail at the lowest velocity amplitudes. Configuration K3, based on the thickest flexible panels, exhibits the most similar wave radiation potential at the highest amplitudes compared to the full, rigid sail. Conversely, configuration K1, incorporating the thinnest flexible panels, has the lowest performance in terms of radiated wave flux, compared to the rigid, full sail. If the design goal is to achieve good power absorption (and hence generation) at low velocities and reduced power absorption and generation at higher velocities, then the K2O configuration shows a promising characteristic response compared to the full solid sail.

5. Design Evaluation Considerations

The mean hydrodynamic gain and wave energy radiation characteristic response curves, shown in Figure 7 and Figure 8, respectively, provide a useful foundation to evaluate and compare the performance of different hydroelastic configurations of Wavepiston sails. However, there are several areas to be addressed that will improve our understanding of the impact of hydroelasticity on performance and survivability. Comparison of the characteristic response curves will benefit from investigation of additional sail configurations. For example, the response of the sail with paddle K2 is explored for four different values of paddle overlaps (Table 1), whereas the sail response for paddle materials K1 and K3 is tested only for a single overlap. A multi-factorial design, involving all combinations of paddle types and overlaps, would improve insights into the roles of paddle overlap and flexibility in modulating extreme wave-induced loads and energy absorption capacity.

Improved sail design also requires selecting appropriate metrics to characterise the systems. Although the wave energy radiation metric (3) provides a useful proxy for wave energy capture, it would be more practical to compare device performance using a metric featuring a mechanical power absorption term. A parametric or multi-linear model of the sail response, similar to the approach used by Papillon [21] when examining a reconfigurable pitching flap, and ground-truthed by experimental data, may provide such an opportunity. Ultimately, this approach also requires a representation of the PTO force and consideration of how control can be used as an additional mechanism for mitigating extreme loads and optimising energy absorption. Furthermore, consideration of realistic PTO systems, including any load and displacement constraints, can benefit the overall design process by identifying the operational space of all sail configurations and restricting the device design space.

6. Conclusions

Wavepiston characteristic response curves show the potential to extend the operational region of the Wavepiston WEC by selecting an optimal sail material flexibility and overlap to achieve WEC excitation force and wave energy absorption saturation, below the maximum structural load or rated output, in high incident wave power conditions. Furthermore, the potential extension of the WEC operational region, without loss of energy capture in low incident wave power conditions, has been demonstrated by the ability of sails with flexible paddles to radiate more energy at lower sail velocities than rigid sails, as shown in Figure 8. Furthermore, the modulated amplitude-dependent behaviour displayed by sail configuration K2O could be exploited in a wave energy context to achieve saturation of power capture over a finite range of incident wave power.

Nevertheless, further refinement of the sail design and response characterisation approach is necessary to better understand and quantify the benefits of each paddle configuration in terms of performance and survivability. In terms of hydroelastic behaviours, exploring all combinations of paddle bending stiffness and overlap configurations can improve insights into how hydroelastic deformations can be harnessed to modulate extreme loads and benefit wave energy absorption in operational regimes. More detailed WEC system modelling should also be considered to obtain a more representative wave energy absorption metric that can support a quantitative design framework for selecting optimal configurations.