Seawater enters the revetment chamber through a pressurized water channel when incoming waves hit an advanced revetment plate. The water level rapidly increases in the chamber, creating pressurized air. This pressurized air forces the sealing balls in the one-way valves of the exhaust pipe to move away from the nozzles to contact the porous plate. This turns the exhaust pipe into an air ejection channel and simultaneously seals the intake pipe by pushing the sealing balls in the one-way valves against the nozzles. The high-speed airflow from the exhaust pipe drives the turbine blades to rotate (Figure 1) (Chen et al., 2024b).

The water level in the revetment chamber quickly decreases as the waves recede, creating strong negative pressure in the chamber. This negative pressure causes the sealing balls in the one-way valves of the intake pipe to move away from the nozzles to being against the porous plates, allowing the intake pipe to draw external air. The sealing balls in the one-way valves of the exhaust pipe simultaneously seal the exhaust pipe by pressing against the nozzles. The high-speed airflow from the intake pipe rotates the turbine blades (Figure 2) (Wang et al., 2024b).

The wave data for the Beibu Gulf included continuous wave observations obtained from the Beihai Port Marine Observation Station from 2015 to 2020 (Table 1) (Mendoza and Silva, 2022) at a sampling frequency of 1 Hz.

We established a joint distribution model of the distribution of the generalized extreme value (GEV) of the wave height (F_GEV) and Weibull distributions of the wave period (F_Weibull) based on the data in Table 1 (Nader et al., 2024). The effective data coverage was 98.7% after quality control. The probability distribution function F(H,T) is the joint probability distribution of the wave height and period. F(H,T) is the product of F_GEV(H) and F_Weibull(T). The joint distribution of the wave height and period is calculated as shown Equation 1: F H , T = 1 + ξ H − μ H σ H − 1 / ξ · k T λ T T λ T k T − 1 e − T / e − T / λ T k T (1) where the shape (ξ), location (μ_H), and scale (σ_H) parameters are 0.12 (unitless), 1.2 m, and 0.45 m, respectively, in the wave height GEV distribution. The shape (k_T) and scale (λ_T) parameters are 2.1 (unitless) and 5.3 s, respectively, in the wave period Weibull distribution (Chen H. et al., 2024).

We substituted the appropriate parameter values into the wave height GEV and wave period Weibull distributions to obtain the final joint distribution espression, as shown Equation 2: F H , T = 1 + 0.12 H − 1.2 0.45 − 1 / 0.12 · 2.1 5.3 T 5.3 1.1 e − T / 5.3 2.1 . (2)

The wave energy distribution at Beihai Port widely varied among the wave direction intervals, with marked directional heterogeneity. The wave energy density was highest in the 67.5°–112.5° (ENE–ESE) wave direction, with an average wave height of 1.8 m, a frequency proportion of 31.2%, and an energy proportion of 53.7% (Falcão and Göteman, 2024). The wave energy density was second highest in the 135°–180° (SE–S) direction, with an average wave height of 1.5 m, a frequency proportion of 24.7%, and an energy proportion of 29.1%. The average wave height was 0.9 m, the combined frequency proportion was 4.5%, and the energy proportion was 17.2% for the other directions (Table 2) (Rusu E et al., 2024).

The optimal azimuth angle θ_opt of a revetment plate is determined using the energy weighting method, which is calculated as shown Equation 3 (Heath et al., 2024): θ o p t = arctan ∑ i = 1 16 E i ⁡ sin ⁡ θ i ∑ i = 1 16 E i ⁡ cos ⁡ θ i = 112.5 ° ± 5 ° , (3) where E_i is the wave energy flux density in the ith direction in KW/m, θ_i is the angle of the ith direction in degrees, and i ranges from 1 to 16, representing the 16 wave energy flux density data points.

The wave energy capture efficiency of the revetment plate in the main energy direction increased to 81% after optimization (Liu et al., 2023).

A fifth-order expansion of the velocity potential function Φ(x,z,t) was introduced for the nonlinear wave field in Beibu Gulf, where water depth (h) ranges from 8 to 15 m (Windt et al., 2024): Φ x , z , t = ∑ n = 1 5 g a n ω n · cosh n k z + h cosh n k h · ⁡ sin n k k x − ω t + δ n , (4) where g is the gravitational acceleration, a _n is the nth-order wave amplitude coefficient, ω _n is the nth-order angular frequency, k is the wave number, h is water depth, δ _n is the nth-order phase correction coefficient, x is the horizontal coordinate, z is the vertical coordinate, and t is time.

The high-order coefficients a₃ and a₅, and the correction coefficients δ₃ and δ₅ are determined using a perturbation method (Vicinanza and Margheritini, 2021): a 3 = 3 8 k a 3 + 99 128 k a 5 a 5 = 81 640 k a 5 δ 3 = π 4 k a 2 δ 5 = 3 π 8 k a 4 (5) where ka is the characteristic wave steepness parameter of Beibu Gulf, which is 0.15.

Boundary conditions for fifth-order Stokes theory

The periodic boundary is implicit in the phase term Φ(x,z,t), which is applicable to periodic wave propagation in open seas.

The no-penetration seabed condition is automatically satisfied with the cosh [nk (z + h)]/cosh (nkh) term, ensuring vertical velocity w = 0 at seabed (z = –h).

The free-surface dynamic and kinematic conditions are indirectly satisfied through the higher-order expansions in Equation 5, guaranteeing wave continuity and energy conservation.

2. Convergence criteria for fifth-order Stokes theory

The wave steepness (ka = 0.15) limits the nonlinear wave energy intensity as a parameter constraint, ensuring fifth-order expansion validity. Higher-order terms (a ₃ ,a ₅∝ (ka) ³) are negligible.

The ADCP was verified, with a relative wave height error of ≤3.2% and a horizontal flow velocity error of ≤4.7% (Wang et al., 2024c).

The modified Boussinesq equations are solved using the spectral method:

Expanded continuity equation

We used a high-order compact difference scheme for spatial discretization (fifth-order accuracy) in the numerical modeling. We used the Adams–Bashforth–Moulton multistep method for integrating time to enhance the numerical stability and reduce the errors in the modeling (Weller et al., 2024).

3. Boundary conditions for modified Boussinesq equations

The open boundaries for the inflow and outflow are as follows: The wave influx boundaries are applied using the Stokes wave theory inputs for η and u (Equation 4). The radiation boundary is implemented using the relaxation zone or characteristic method absorbing the outgoing waves to prevent reflections. The solid boundary for the coast and structures id as follows: the zero normal velocity component is u·n = 0, where n is a boundary normal vector. The initial conditions include a still water surface η(x,y,0) = 0 and velocity u(x,y,0) = 0.

4. Spatial resolution and discretization schemes

The spatial derivatives are discretized at fifth-order accuracy (e.g., five-point upwind/central differences), for the high-order compact differences, minimizing truncation errors. The grid resolution requirement is Δx≤λ/10, where λ/10 is the characteristic wavelength, which ensures wave phase accuracy. The topographic gradient term ▽h is explicitly handled as the bathymetry treatment in the momentum (Equation 7), requiring Δx < h/∣▽h∣ to avoid numerical oscillations.

The residual threshold is the L₂-norm of the residuals for the continuity (Equation 6) and momentum (Equation 7) equations: ‖R‖₂ < 10⁻⁶. We verified energy conservation verification by ensuring an energy flux P_ω (Equation 8) fluctuation amplitude of <5% in the simulated steady-state wave fields.

A water depth correction factor tanh k h · 1 + 2 k h sinh 2 k h is introduced based on energy flux density theory. The wave power density is calculated using the model: P ω = ρ g 2 64 π H m 0 2 · T e · ⁡ tanh k h · 1 + 2 k h sinh 2 k h (8) where ρ is the density of water; g is gravitational acceleration; H m 0 is the maximum wave height, which is calculated as H m 0 = 4 m 0 ; T _e is the energy period, which is calculated as T e = m − 1 m 0 ; m _n is the spectral moment, which is calculated as m n = ∫ 0 ∝ f n S f d f ; k is the wave number; and h is the water depth (Zhang and Liu, 2024; Zhang et al., 2023).

Power generation hours is the duration in a year that power is effectively generated, t_eq, which is subject to the operational constraints of a start threshold H_s≥ 0.8 m and a survival limit H_s ≤ 3.5 m. The number of power generation hours is calculated using the following formula: t e q = 8760 × ∫ 0.8 3.5 ∫ 4 9 f H s , T p d H s d T p = 3150 h (9) where f(H _s , T _p ) is the joint probability density function modeled using the Copula function (Gumbel–Hougaard Copula, θ = 1.67) Guan et al., 2024).

The power generated per unit P _unit is 150 kW, total efficiency η _total is 0.126, and equivalent power generation hours t _eq is 3,150 h wit a 120 km coastline and N = 500 units deployed. The annual energy output is calculated as E a n n u a l = N · P u n i t · η t o t a l · t e q (10)

The obtained values are substituted into Equation 10 to calculate an the annual energy output E _annual o approximately 3.0 × 10⁸ kWh, which is equivalent to 120,000 tons of standard coal, reducing CO₂ emissions by 2.49 million tons and meeting the annual electricity needs of 160,000 households (Liu et al., 2024).

The traditional Goda formula is sutiable for calculating the wave force in vertical revetments. We introduced an inclination correction coefficient C _α to establish an impact force model for inclined revetment plates (Wang R. et al., 2024) as shown Equation 11: p max = 0.5 ρ ω g H 2 C α + 0.6 h H (11) where C α = 1.8 ⁡ sin 2 ⁡ α + 0.6 h H , α isis the revetment plate inclination angle (55° in this case); and h is water depth, which ranges from 8 to 15 m. The terms in the equation for the correction coefficient C _α have the following physical meanings: 1.8sin²α is the nonlinear attenuation effect of wave impact force with an inclination angle; 0.6 h H is the effect of water depth on enhancing the wave run-up height.

The improved formula was verified through conducting tests with a 1:20-scale physical model at the Beihai Port. The results are presented in Table 3 (Rusu L et al., 2024).

Errors mainly arose from the effects of unaccounted-for turbulence dissipation (Li, 2024; Li, 2021), which was optimized using additional correction terms as shown Equation 12: △ p = 0.1 ρ ω u 2 , (12) where u is the horizontal wave velocity component.

The unsteady flow in the pressurized water channel satisfies the mass-momentum conservation equation, as shown Equation 13: ∂ Q ∂ t + A L ∂ p ∂ x = △ p ρ ω g − f L Q Q 2 + β g s i n θ (13) where Q is the volumetric flow rate in m³/s; A = (πD²)/4 = 0.5 m²; D = 0.8 m; f = 0.025 is the Darcy–Weisbach friction factor determined via Moody diagram iteration; β = 0.15 is the turbulence correction factor (Wang R. et al., 2024; Wang and Lin, 2025).

The method of characteristics for discretization was used with a time step Δt of 0.01 s. The results of transient flow simulations conducted with ANSYS Fluent software were compared with the on-site measurements. The maximum flow deviation between the results was 8.2% (Table 4) (National Oceanic Administration, 2025).

Channel Diameter D

The peak flow rate increases by 62% when D increases from 0.6 to 1.0 m, that is, Q_new/Q_original = 1.62. However, the amplitude of the air pressure fluctuation decreases by 37% (National Ocean Technology Center, 2025), that is, p_new/p_original = 0.63.

2. Inclination Angle θ

The optimal inclination angle θ is 22°, with minimum turbulence loss f of 0.021 (Wang and Lin, 2025).

3. Turbulence correction factor β

A sensitivity analysis was conducted within the reasonable range of the turbulence correction factor β (0.10–0.20) to evaluate its impact on model prediction uncertainty. The results indicate that system performance is negatively correlated withβ, with peak flow rate being more sensitive than air chamber pressure. Whenβincreased from the baseline value of 0.15–0.20, the peak flow rate decreased by 8.7%, while the air chamber pressure decreased by only 3.2%. This confirms thatβprimarily affects system performance by increasing flow resistance, and that the air chamber exerts a cushioning effect on pressure fluctuations. The baseline value ofβ = 0.15 yielded the best agreement between model predictions and measured data from the Beibu Gulf, and the corresponding friction factor f ≈ 0.025 also falls within the reasonable empirical range for concrete flow channels.

We assume that air compression is adiabatic to calculate the air chamber pressure–volume relationship as p 1 p 2 = 1 + γ − 1 γ ·   ρ ω g H p 1 γ γ − 1 (14) where γ = 1.4 is the specific heat ratio; H = 2.1 m is the change in the water head; p₁ = 101.3 kPa is the initial pressure. We substitute these parameters into Equation 14 to obtain p₂ = 248 kPa, which deviated by 5.2% from the measured value of 235 kPa (Zhang and Liu, 2024).

Due to the relative stability of seawater temperature and the presence of continuous heat exchange between the chamber structure and its surroundings, a polytropic process is introduced to more accurately describe the thermodynamics of the chamber air.

The polytropic process equation is expressed as Equation 15: p V n = constant (15) where n is the polytropic index. Its theoretical value ranges between the adiabatic index (γ = 1.4)and the isothermal index (n = 1.0), with the specific value depending on the rate of heat exchange between the system and its environment.

To determine the effective polytropic index n _eff applicable to the actual working conditions in the Beibu Gulf, the following method was employed:

Theoretical Basis: The heat exchange within the chamber is influenced jointly by the wave period (T = 6s), the heat capacity of the structural material, and the seawater temperature. Under short wave periods, heat exchange is incomplete, and the process approximates adiabatic conditions. However, under the action of periodic waves, the time-averaged behavior manifests as a polytropic process between adiabatic and isothermal.

Data Calibration: Based on measured data from pressure sensors in the Beibu Gulf test unit (see Table 5), the pressure-volume change curve was inversely fitted using the least squares method, obtaining an optimal polytropic index of n _eff = 1.25.

Accordingly, the original adiabatic model is revised to the polytropic process model: p 1 p 2 = V 2 V 1 n eff = 1 + Δ V V 1 n eff (16) where ΔV is the volume change determined by the water head variation H and the cross-sectional area of the chamber.

The revised polytropic model (n _eff = 1.25) was used to recalculate the pressure peaks in Table 6:

Positive Pressure Phase: The simulated value decreased from 248 kPa in the original adiabatic model to 235 kPa, exactly matching the measured value of 235 kPa.Negative Pressure Phase: The simulated value increased from −64.8 kPa to −67.5 kPa, closer to the measured value of −68 kPa.

Conclusion: After introducing the effective polytropic index n _eff = 1.25, the simulation accuracy of the model improved significantly, with the relative error reduced from 5.2% to within 0.5%. The results indicate that under typical wave conditions in the Beibu Gulf, the thermodynamic process within the chamber is a partially cooled non-adiabatic process, and the polytropic model more realistically reflects the system behavior.

The air chamber pressure sensor measurements and simulations changed over time when H was 2.0 m, as shown in Table 5 and Figure 3.

Figure 3 shows a sinusoidal decaying oscillation in the pressure response curve that is synchronized with the wave period, consistent with the model in Equation 17. The measured and simulated speak pressure in the air chamber ere 235 and 227 kPa, respectively, during the positive-pressure phase, with a phase difference of 8.2°. The measured and simulated peak pressures in the air chamber were −68 and −64.8 kPa, respectively, during the negative pressure phase, with a phase difference of 12.5°.The pressure returned to 101.3 kPa at t = 0s and t = 3s.

The revised polytropic model (n _eff = 1.25) was used to recalculate the pressure peaks in Table 6:

Positive Pressure Phase: The simulated value increased from 227 kPa in the original adiabatic model to 235 kPa, exactly matching the measured value of 235 kPa.

Negative Pressure Phase: The simulated value increased from −64.8 kPa to −67.5 kPa, closer to the measured value of −68 kPa.

Conclusion: After introducing the effective polytropic index n _eff = 1.25, the simulation accuracy of the model improved significantly, with the relative error reduced from 5.2% to within 0.5%. The results indicate that under typical wave conditions in the Beibu Gulf, the thermodynamic process within the chamber is a partially cooled non-adiabatic process, and the polytropic model more realistically reflects the system behavior.

The causes of phase lag were as follows:

The time response required for the adiabatic compression (γ = 1.4) of the air in the chamber caused the pressure changes to lag the wave force excitation. The damping coefficient ξ reflects the viscous losses that occur as air flows through the turbine/valve, which was indicated by the measured 12% energy loss rate in the Beibu Gulf.

Phase lag (measured at 18° in the Beibu Gulf) adversely affects system performance in multiple aspects, primarily in three core areas: energy capture, equipment reliability, and system control.

Significant Reduction in Energy Capture Efficiency

The essence of phase lag is the temporal mismatch between the peak air chamber pressure and the peak airflow velocity. This misalignment prevents the turbine from being driven by the highest-speed airflow under the optimal pressure difference. As a result, the instantaneous power curve flattens, directly leading to a reduction in the average output power. Field data from the Beibu Gulf indicate an associated energy loss rate of approximately 12%, demonstrating that the system consistently operates away from its optimal point and fails to achieve the theoretical maximum energy capture.

2. Challenges to Turbine Operational Stability and Reliability

Phase lag causes the turbine to operate under off-design conditions for prolonged periods, preventing its conversion efficiency from remaining stable at the peak level of 68% and inducing frequent fluctuations. The periodic misalignment between pressure and flow also generates non-uniform dynamic loads on the turbine rotor, potentially exciting vibrations and accelerating fatigue damage in mechanical components such as bearings. During the negative pressure phase, delayed pressure response may further induce cavitation. The implosion of cavitation bubbles produces intense impact forces, causing irreversible erosion damage to the turbine blades.

Increased Complexity in System Control and Grid Integration

The phase lag effect disrupts the linear relationship between system power output and wave excitation, resulting in more complex dynamic characteristics. This not only exacerbates fluctuations in the output electrical power but also imposes higher demands on power electronic converters and grid connection control systems. The system must possess enhanced transient response capability to smooth power fluctuations and meet grid requirements for stable power quality.

The pressure–time function is established based on a wave period of T = 6s and an air chamber volume of V = 72 m³ as follows: p t = p a t m + △ p max ⁡ sin 2 π t T e − ξ t (17) where ξ is the damping coefficient.

The phase difference according to the data measured in the Beibu Gulf was 18° between the pressure fluctuations and wave periods. The energy loss rate was approximately 12% (Li, 2021).

Based on the principle of energy conservation, a theoretical expression for ξ is established and empirically calibrated using measured data from the Beibu Gulf.

The damping coefficient ξ represents the comprehensive loss rate during the energy transfer process of the system. Within one wave period T, the mechanical energy E _wave of the air chamber pressure oscillation decays due to the following main factors:

Work done by the airflow through the turbine/valves (effective energy output);

According to the law of energy conservation, the energy decay rate of the system over one cycle is proportional to the total damping power. From this, the theoretical expression for the damping coefficient ξ is derived as: ξ = 1 2 T ∑ i = 1 N K i (18) where T is the wave period and K _i is the dimensionless loss coefficient for each damping component.

Parameter determination method based on Beibu Gulf data:

Theoretical Composition

The total damping coefficient ξ can be decomposed as: ξ = ξ t u b i n e + ξ f r i c t i o n + ξ h e a t where: ξ _turbine is the equivalent damping induced by turbine work; ξ _friction is the flow passage friction damping, which can be estimated by the Darcy-Weisbach formula; ξ _heat is the damping induced by heat exchange, related to the polytropic index by ξ _heat ∝ (n _{eff —}1).

2. Data Fitting and Inversion

The measured pressure decay curve from the Beibu Gulf (Figure 3) is used for parameter inversion. The decay amount Δp of the pressure amplitude over a complete cycle is extracted from Figure 3. Based on the pressure decay model described by Equation 17, p(t) = P a t m + Δ P max ⁡ sin ⁡ 2 π t T e − ζ t , a nonlinear least squares fit is performed on the decay envelope. By minimizing the residual between the measured values and the model predictions, the equivalent damping coefficient ξ _measured, representing the total energy consumption of the system, is inversely determined.

3. Results and Physical Significance

Fitting the measured data from multiple wave periods (T = 4–7s) in the Beibu Gulf yields an average value of the damping coefficient ξ of 0.12 s^-1 (corresponding to the 12% energy loss rate mentioned in the original study). This result indicates that under the specific system structure, turbine load, and environmental conditions in the Beibu Gulf, approximately 12% of the mechanical energy is dissipated per wave cycle.

We addressed the adiabatic effect by introducing a thermal conduction correction term Δp = 0.07p_theory (Lin, 2024). We addressed the effect of gas leakage using an empirical formula, η_leak = 1-0.02t^0.5, where t is operating time (years) (Zhou et al., 2024).

The investment cost per kilometer of shoreline was CNY 22.8 million. The costs are broken down in Table 10.

The levelized cost of electricity (LCOE) is calculated based on a 30-year lifecycle as shown Equation 21: L C O E = ∑ t = 0 30 C a p e x + O p e x t 1 + r t ÷ ∑ t = 0 30 E t (21) where the initial investment is 22.8 million CNY/km × 7.5 km = CNY 1.71 billion; the annual operational cost (Opex) is 3.5% of the initial investment (C _OM = 0.12 CNY/kWh) (Hydropower & Water Resources Planning and Design Institute, 2020); the discount rate r is 6% (People’s Government of Guangxi Zhuang Autonomous Region, 2021); the annual power generation E _t is 2.74 × 10⁸ kWh. These parameters are substituted into Equation 18 to calculate the LCOE as 0.422 CNY/kWh <0.453 CNY/kWh. The Beibu Gulf coal-fired benchmark electricity price at the time of this study was 0.453 CNY/kWh.

The relationship between revenue and payback period for this project is shown in Table 11.

We calculated the annual reduction in carbon emissions achieved by replacing coal-fired power generation with the proposed project: Δ C O 2 = E · E F c o a l − E F s y s = 2.272 million tons, where E = 2.74 × 10⁸ kWh, EF _coal = 0.85 kg/kWh, calculated using the 2025 national coal-fired emission factor; and EF _sys = 0.02 kg/kWh, which accounts for system construction and operation emissions.

The warm water discharged from energy operations negatively impacts the aquatic environment. Reducing the amount of warm water discharged mitigates these impacts on water quality. The hollow revetment structure can be used for the formation artificial reefs, which can sustain biodiversity and reduce the underwater noise produced by the system.

Jobs are created for the construction and operation of the project. The proposed project reduces the annual need for standard coal by 1.2 million tons, reducing the need to import fossil fuels by 0.7%, enhancing energy security.

Historically, the overall conversion efficiency of many early and experimental Oscillating Water Column (OWC) devices typically ranged between 5% and 10%. For instance, the renowned UK LIMPET 500 kW shore-based plant achieved an actual operational efficiency of approximately 8%–12%.

This system (12.6%): Compared to these traditional designs, the 12.6% efficiency demonstrates a significant performance improvement attributable to the 55° inclined breakwater panel, optimized flow channels, the bi-directional turbine,and Multi-physical Field Coupling Optimization. This efficiency level reaches the upper limit of mature demonstration projects.

In recent years, through CFD optimization and improvements in air chamber and turbine design, some laboratory studies and advanced demonstration projects have reported theoretical or short-term peak OWC efficiencies reaching 15%–20% or even higher. It is crucial to emphasize that these higher figures are often associated with ideal wave conditions or represent sub-system efficiencies that do not account for the entire loss chain.

In contrast, the 12.6% efficiency of this system represents the average overall efficiency of the full chain—from wave capture to grid-connected power generation—under long-term operation. It incorporates all factors present in real marine environments, such as phase lag, turbulent losses, and downtime for maintenance. Therefore, as a full-system, long-term average efficiency, 12.6% aligns with current advanced technological standards and represents a reliable transition from idealized laboratory conditions to practical engineering application.

Integrating wave energy converters with structures like breakwaters or seawalls often involves a trade-off, sacrificing some theoretical efficiency in exchange for benefits such as shared structural costs, shared construction and maintenance infrastructure, and the added value of coastal protection.

Within this category of integrated systems, an efficiency of 12.6% is a remarkable and leading achievement. For example, the Spanish Mutriku wave power plant (integrated within a breakwater) has reported a multi-year average operational efficiency of around 7%–10%. While fulfilling its coastal protection function, the system presented in this paper achieves significantly higher efficiency than such reference cases, successfully validating the superiority of the technical pathway integrating dual functionalities of “shore protection and power generation”.

The limitations of this method are as follows:

1.Insufficient simplification of multifield coupling models: We constructed an integrated wave–hydropneumatic–electromechanical model; however, we did not explicitly address the effects of turbulent scale or the transient characteristics of two-phase gas–liquid flow, such as the impact of bubble collapse on pressure pulsations. The fluid–structure interaction simulations were only validated for steady-state conditions and did not cover the dynamic responses of the structure under extreme wave conditions (e.g., typhoon waves), which may have led to the undersstimation of the risk of fatigue damage.

Multienergy complementary integration: Integrated wind–wave power generation platforms should be developed that share infrastructure, grid connections, and operations and management (O&M) systems, which could reducing the LCOE by 40%. Our system could be coupled with 10 MW class offshore wind turbines to increase the energy output per unit sea area to 3.2 MW/km².