Simulation of a Tidal Current-Powered Freshwater and Energy Supply System for Sustainable Island Development

Abstract

Sustainable development of islands cannot be achieved without the use of renewable energy to address energy and freshwater supply issues. Utilizing the widely distributed tidal current energy in island regions can enhance local energy and water supply security. To achieve economic and operational efficiency, it is crucial to fully account for the unique periodicity and intermittency of tidal current energy. In this study, a tidal current-powered freshwater and energy supply system is proposed. The marine current turbine adopts a direct-drive configuration and will be able to directly transfer the power of the turbine rotation to the seawater pump to improve the energy efficiency. Additionally, the system incorporates batteries for short-term energy storage, aimed at increasing the capacity factor of the electrolyzer. A simulation is conducted using measured inflow velocity data from a full 12 h tidal cycle. The results show that the turbine’s average power coefficient reaches 0.434, the electrolyzer’s average energy efficiency is 60.9%, the capacity factor is 70.1%, and the desalination system’s average specific energy consumption is 6.175 kWh/m³. The feasibility of the system design has been validated.

1. Introduction

The shortage and high cost of freshwater and energy supply in islands are multifaceted issues influenced by various factors, including geographical isolation, limited natural resources, and economic constraints [1]. Many remote islands, such as Limbo Island, face significant challenges in accessing freshwater due to the absence of local freshwater sources, necessitating the transportation of water from neighboring islands, which is both logistically complex and costly [2]. Similarly, the Mediterranean island of Skyros in Greece exemplifies the high costs associated with water transport and desalination, where 44% of expenses are related to the transportation of potable and residual water and 52% to the production of desalinated water, resulting in a total cost of water generation estimated at EUR 2.49/m³ [3]. Island electricity systems rely heavily on imported fossil fuels, making them particularly vulnerable to price fluctuations and supply disruptions. The cost of fuels on islands is significantly higher than on the mainland, often reaching 3–4 times the mainland price [4,5]. In the Maldives, fuel imports account for 10% of the country’s GDP. Additionally, the limited land area restricts the large-scale application of traditional renewable energy sources, severely constraining local development [6]. Transitioning to 100% renewable energy usage on islands can leverage local natural resources such as solar, wind, and ocean energy. This has been proven to be technically and economically feasible [7]. To achieve green energy transition and sustainable development, islands must utilize renewable energy to enable local energy supply, freshwater provision, and energy storage [8].

Hydrogen production is a critical component of the transition to sustainable energy systems, offering a clean alternative to fossil fuels. Hydrogen has a high energy density and is suitable for long-term energy storage [9]. Currently, proton exchange membrane (PEM) water electrolysis for hydrogen production is developing rapidly, offering high efficiency and the ability to quickly respond to fluctuations in input power [10]. When combined with renewable energy sources, it can effectively utilize excess renewable electricity. Ebba et al. reviewed large-scale hydrogen production using marine renewable energies, such as wind and tidal turbines. This approach highlights the potential of marine resources in achieving sustainable hydrogen production, focusing on the efficiency and cost-effectiveness of electrolyzers and fuel cells [11]. Li et al. [12] discuss the coupling of photovoltaic and photothermal systems for hydrogen production, emphasizing the economic and efficiency improvements of electrolytic cells. This integration addresses the intermittency of solar energy, enhancing the overall system’s viability. Abdelkareem et al. [13] identify several barriers to the widespread adoption of photovoltaic-based hydrogen production, including safety, storage, and commercialization challenges. Addressing these barriers is crucial for advancing solar-to-hydrogen conversion efficiency.

Seawater desalination has become an increasingly important technology for addressing global water scarcity, particularly in regions with limited freshwater resources such as arid coastal areas, islands, and densely populated cities. Reverse osmosis (RO), which uses a semi-permeable membrane to separate salts and impurities from seawater, is currently the most widely adopted method due to its relatively high efficiency and lower energy consumption compared to traditional thermal processes [14]. The integration of renewable energy with RO seawater desalination systems presents a promising solution to address global water scarcity while reducing reliance on fossil fuels. Cai et al. [15] investigated the effects of intermittent operation on membrane integrity in a photovoltaic-powered nanofiltration/RO system for brackish water desalination. They found that the system is robust under high pressure increase rates and frequent shutdowns, but observed membrane damage with increased permeate backpressure during osmotic backwash. Ba-Alawi et al. [16] proposed a coordinated sizing approach integrating demand-side water management to optimize a solar and wind-powered RO desalination system. Their method reduced the number of required photovoltaic panels and wind turbines, along with overall costs and emissions, compared to systems without this improvement. The study demonstrated that the new method significantly improves cost efficiency, environmental impact, and system reliability in renewable energy-powered desalination.

Some studies have explored the potential of using renewable energy sources to supply both freshwater and energy. Zhao et al. [17] proposed a renewable-driven standalone combined power and water supply system with cascade electricity and heat storage. The system uses wind and solar power as energy sources and employs humidification–dehumidification distillation to produce freshwater, while also incorporating underwater compressed air energy storage to mitigate renewable energy fluctuations. The simulation results indicate that the proposed system can adequately meet the electricity and freshwater demands with lower renewable configuration and total dumped energy. Mehrjerdi [18] modeled, designed, and optimized a joint water and energy supply system for a remote island without access to the utility networks. The optimal seawater desalination method was selected based on technical and cost factors. Battery storage was used to balance the time period of renewable energy production with the peak load demand. The simulation results indicate that a hybrid power and water supply system using RO seawater desalination is the most economical. Smaoui et al. [19] investigated an off-grid energy supply system based on photovoltaic energy, wind power, and hydrogen energy for a desalination system on Kerkennah Island. By establishing the models of the main hybrid system components and incorporating the hourly meteorological data and load profile for any site located worldwide, this study identified the optimal technical–economic configuration among a set of system components. Temiz et al. [20] designed a solar-based integrated offshore energy system for sustainable island communities. The proposed system utilizes an energy island concept where solar energy is the main source and provides electricity, freshwater, and hydrogen by integrating a floating photovoltaic system, a parabolic through collector system, the Cu-Cl cycle, a multi-effect desalination unit, and a fuel cell unit. A transient analysis is conducted to assess the performance of the proposed system in a case study focused on Northern Cyprus, considering its annual electricity demand.

Tidal current energy is a renewable energy source that utilizes the movement of seawater caused by the gravity of the moon and sun on the oceans. Abundant and predictable, tidal current energy is a cost-effective alternative to fossil fuels [21]. Li et al. [22] designed and tested a 600 kW tidal current turbine to verify the design methods for large tidal current turbines with high reliability and efficiency. They implemented a maximum power point tracking control strategy and conducted onshore and sea trials, showing good agreement between theoretical analyses and test results. O Connell et al. [23] used four open-access software tools to analyze critical elements of tidal energy projects, focusing on array configurations, foundation and mooring design, O&M strategies, and techno-economic analysis. They modeled scenarios for various project sizes and turbine types, demonstrating the potential to achieve lower levelized costs of energy for fixed and floating tidal technologies. According to the study by Neto et al. [24] on the impact of incorporating tidal, photovoltaic, and wind energy into off-grid hybrid energy systems, the average results show that integrating tidal current energy can reduce fuel consumption by 5.26%, extend battery lifespan by 172%, and increase renewable energy penetration by 2.21%. However, the lack of profitability is preventing the large-scale commercialization of tidal energy [25]. In the application scenarios for remote island supply, tidal current energy has unique advantages, including its widespread local availability, scalability, and flexibility [26]. Current research on systems providing freshwater and energy to islands primarily focuses on the established technologies of wind power and photovoltaics. These systems, which include renewable energy generation, desalination units, and energy storage solutions, are integrated as part of island microgrids. The focus is on optimizing capacity and operational strategies. There is limited research on utilizing tidal current energy, a naturally abundant renewable resource in island regions, to supply islands. Additionally, there is a lack of studies focusing on developing new technological solutions that consider the operational characteristics of renewable energy systems. Designing a low-cost, high-efficiency tidal current energy system to provide freshwater and power for islands will enhance energy security and sustainability, boosting resilience to climate change and extreme weather.

In this study, a tidal current-powered freshwater and energy supply system is proposed. One of the most significant innovations is the direct-drive configuration, which directly couples the tidal turbine with the seawater pump without the need for a separate motor or gearbox. This design reduces energy conversion losses and mechanical complexities. The integration of a hybrid energy storage system combining batteries and a PEM electrolyzer allows for better management of the fluctuating power generated by the tidal turbine. The advanced control strategy distributes power efficiently between short-term storage and long-term storage, enhancing the system’s capacity factor. A simulation analysis is conducted using measured inflow velocity data over a complete 12 h tidal cycle.

2. System Design

Figure 1 shows a schematic diagram of the proposed system. It mainly consists of three parts: the tidal current turbine, the hydrogen production system, and the desalination system. The tidal current turbine employs a three-bladed horizontal-axis floating structure. The turbine’s main shaft is connected to a low-speed permanent magnet synchronous generator (PMSG) without a gearbox. The rotor speed of the PMSG matches that of the turbine, offering simplicity in structure and ease of installation. The PMSG provides electrical power for the hydrogen production system. Unlike traditional transmission designs, a direct-drive configuration is proposed. The seawater pump of the RO desalination is not driven by a motor, but is installed in the nacelle and can be driven directly by the turbine through the gearbox. The mechanical energy captured by the turbine is used by the seawater pump to pressurize pre-treated seawater, creating the osmotic pressure for the RO desalination process. By directly coupling the energy source to the driven components, the direct-drive configuration reduces energy losses associated with intermediate conversion processes, achieving higher energy efficiency. It also minimizes the use of components such as hydraulic motors and electric motors, resulting in a more compact and reliable system structure, effectively lowering capital and maintenance costs. The desalination system includes seawater pretreatment equipment, RO elements, and an energy recovery device (ERD). Seawater is extracted locally, desalinated, and used as potable water and feedwater for the electrolyzer. The seawater pretreatment equipment purifies the raw seawater by removing solid particles, preventing biological fouling and deposition and ensuring that the feedwater meets the requirements of key components like the seawater pump and RO membrane. The high-pressure brine discharged from the RO element contains a large amount of pressure energy that can be recovered and utilized by the ERD. The ERD uses this energy to assist the seawater pump in pressurizing the seawater, which effectively reduces the energy consumption of the desalination system. The hydrogen production system includes power electronic devices, batteries, and a PEM electrolyzer. The power electronic devices distribute the electrical energy output from the PMSG between the batteries and the electrolyzer. Here, the batteries and electrolyzer form a hybrid energy storage system. The batteries handle short-term storage, absorbing most of the fluctuating electrical energy from the PMSG. When energy is abundant, the batteries transfer energy to the electrolyzer for hydrogen production, enabling long-term energy storage. In addition to improving energy availability, this approach also reduces the required capacity of the electrolyzer, thereby lowering capital costs. The key technical parameters of the system are detailed in

Table 1. The key technical parameters of the system.

Element	Parameter	Value
Tidal turbine	Rated inflow velocity	1.5 m/s
	Rotor radius	1.236 m
	Theoretical Cpmax	0.44
	Optimal TSR	5.5
Generator	Rated power	4 kW
	Rated efficiency	75%
Seawater pump	Transmission ratio	1:35.88
	Efficiency	90%
	Displacement	15.4 mL/r
RO element	Model	SW30HRLE-4040
	Array	single-stage one element in one vessel
Energy recovery device	Cross-sectional area ratio	10%
Power electronics	Rated efficiency	75%
PEM electrolyzer	Number of cells in series	4
	Rated voltage	9 V
	Rated current	36 A
	Rated production rate	1 SLPM
Battery	Capacity	128 V/50 Ah

.

2.1. Tidal Current Turbine

Similarly to wind turbines, tidal current turbines convert the kinetic energy of flowing seawater into the mechanical energy of rotating turbines. The power captured from the tidal current can be expressed by the following formula [22]:

$$P={\displaystyle \frac{1}{2}}\rho \pi R_r^2{C}_{\mathrm{p}}(\lambda ,\beta )v^3$$

(1)

where ρ is the density of seawater, R_r is the radius of the turbine, and v is the tidal current inflow velocity. C_p is the power coefficient, which represents the efficiency of capturing energy from seawater. For a given turbine blade, this coefficient is determined by two parameters, the tip speed ratio λ (TSR) and the pitch angle β, representing the theoretical design performance of the blades. The turbine used in this study is a fixed-pitch type, where the energy capture performance is determined by the installation angle of the blades, without considering variable pitch control. The TSR is defined by the following formula:

$$\lambda ={\displaystyle \frac{{\omega }_r{R}_r}{v}}$$

(2)

where ω_r is the rotor speed of the turbine.

The system is equipped with a three-bladed turbine, with a radius of 1.236 m and a hub diameter of 0.3 m. The turbine was provided by the manufacturer as shown in Figure 2.The relationship between the power coefficient and the tip speed ratio was obtained through blade element momentum theory, as shown in Figure 3. It can be observed that the maximum power coefficient reached 0.435 at a tip speed ratio of 5.4.

Figure 4 shows the functional relationship between the power captured by the turbine and the rotor speed at different inflow velocities. For any inflow velocity, there is an optimal TSR (λ_opt) that allows the turbine to capture the maximum power at the current inflow speed, also known as the maximum power point tracking (MPPT) for tidal current energy.

From Equation (2), it can be derived that by varying the turbine rotor speed, the optimal TSR can be tracked under different inflow velocities to achieve the MPPT control. However, in actual system operation, the measurement of tidal current speed is affected by turbulence and cannot be directly introduced into the control system. Therefore, in practical applications, power signal feedback (PSF) control is commonly used to improve the energy efficiency of the turbine at varying inflow velocities. Based on the energy capture characteristics of the turbine blade, the PSF control method adjusts the operation of the turbine by controlling the output power of the generator, thereby achieving optimal TSR tracking. The target output power for the generator in PSF control is given by the following formula [27]:

$$P_{opt}={\displaystyle \frac{1}{2}}\rho \pi R_r^2{C}_{p\max }{\left({\displaystyle \frac{R_r^2}{{\lambda }_{opt}}}\right)}^3{\omega }_r^3=K_{opt}\cdot {\omega }_r^3$$

(3)

where C_pmax is the power coefficient corresponding to the optimal TSR and K_opt is the coefficient used in PSF control to calculate the target power, derived from blade characteristics. Under this control method, the output power of the PMSG increases with the cube of the turbine’s rotor speed. This method does not require the measurement of the inflow velocity, thereby providing high stability and enabling maximum power capturing under various complex inflow conditions. After determining the energy capture characteristics of the blades, the next step is to identify the maximum inflow velocity at which the turbine operates under MPPT control based on the tidal characteristics of the experimental area. This information is then used to establish the required installed capacity and operational speed range of the generator. If the rotational speed is too low, a gearbox will be needed to increase the speed.

Considering the energy efficiency and availability of the system, the transmission chain structure of the tidal current turbine has been further improved, as shown in Figure 5. An electromagnetic clutch is installed between the seawater pump and the gearbox to control the engagement and disengagement of the seawater pump from the turbine main shaft transmission system. Although this increases the system’s complexity, it is necessary for improving the self-starting performance and energy efficiency during low-inflow-velocity operation of the turbine.

The strong fluctuations in marine current velocity result in unstable output power from the turbine. According to Equation (1), when the marine current velocity decreases to 0.8 times its original value, the capturable power is reduced to half of the original. Based on experience with tidal power generation in the Zhoushan sea area, to ensure the generator has sufficient allocable power for continuous MPPT control, the power allocated to the desalination system should be less than that of the hydrogen production system. This approach ensures that the generator can maintain continuous operation even under fluctuating flow velocities. This allows us to determine the operating power range of the desalination system, specifically the input power of the seawater pump.

Figure 6 illustrates the layout of the system performance testing setup. This configuration is used to measure the frictional forces, evaluate the performance of the generator and pump, and conduct on-site testing. Based on the measurement results of the generator, its parameters are provided in

Table 2. The key technical parameters of the tested generator.

Parameter	Value	Parameter	Value
Moment of Inertia	1.16 kg·m2	Quadrature Axis Inductance	6.24 mH
Stator Resistance	4.81 Ω	Flux Linkage	5.09 Wb
Direct Axis Inductance	3.05 mH	Number of Pole Pairs	12

.

Due to the inferior lubricating properties of water compared to hydraulic oil, high-pressure plunger pumps used for seawater have higher friction torque, which is amplified by the gearbox and acts on the turbine’s main shaft, resulting in significant friction losses. Figure 7 shows the experimentally measured friction torque during pump engagement and disengagement compared to the hydrodynamic torque of the turbine at the MPPT operating point. When the pump is disengaged, the friction torque includes the friction from the dynamic seal assembly, the PMSG, and the gearbox. The friction torque increases significantly when the pump is engaged. At 30 rpm, the driving torque provided by the turbine operating at maximum power capture state is only enough to overcome the friction torque, severely reducing the energy efficiency and availability under low inflow velocity conditions. By disengaging the seawater pump when the system is only generating power for hydrogen production, friction losses can be nearly halved, enhancing the overall performance of the system at low inflow velocity. Lower friction also means the turbine can self-start at lower flow speeds, improving the system’s availability.

The dynamic performance of the transmission system can be expressed by the following equation:

$$J{\dot{\omega }}_r+F_f{\omega }_r+T_f=T_h-T_e-T_p$$

(4)

where J is the equivalent rotational inertia, including the turbine blades, main shaft, generator, gearbox, and pump. Friction is modeled as the combined viscous and Coulomb friction, F_f is the coefficient of viscous friction, and T_f is the static friction torque. T_e is the electromagnetic torque of the generator, and T_p is the mechanical torque transmitted from the seawater pump through the gearbox.

2.2. PEM Electrolyzer

PEM electrolyzers represent a promising technology for efficient hydrogen production through water electrolysis. The PEM electrolyzer employs a solid polymer electrolyte, which facilitates the transfer of protons from the anode to the cathode while maintaining the separation of the produced gases [28]. This system offers several advantages, including high efficiency, rapid response times, and the ability to operate at high current densities, making it well-suited to accommodate the fluctuating energy input from renewable sources [29]. The reactions occurring in a PEM electrolyzer are as follows [30]:

$$Anode\hspace{0.33em}:\hspace{0.33em}\hspace{0.33em}{H}_2{O}_{(l)}\to {\displaystyle \frac{1}{2}}{O}_{2(g)}+2{H^{+}}_{(g)}+2e^{-}$$

(5)

$$Cathode\hspace{0.33em}\hspace{0.33em}:\hspace{0.33em}\hspace{0.33em}2H^{+}+2e^{-}\to H_{2(g)}$$

(6)

$$Overall reaction\hspace{0.33em}\hspace{0.33em}:\hspace{0.33em}\hspace{0.33em}{H}_2{O}_{(l)}\to H_{2(g)}+{\displaystyle \frac{1}{2}}{O}_{2(g)}$$

(7)

The voltage characteristics of a PEM electrolyzer can be represented by the following equations [31]:

$$u_{cell}=u_{ocv}+u_{act}+u_{ohm}+u_{con}$$

(8)

where u_cell is the operating voltage for a single cell, u_ocv is the open circuit voltage, u_act is the activation overvoltage, u_ohm is the ohmic overvoltage, and u_con is the concentration overvoltage. Multiple overvoltages in the equation can be modeled using various electrochemical empirical equations to determine the relationship between the electrolyzer voltage and its characteristics, input current, and temperature as shown below [32]:

$$u_{cell}=u_{rev}+{\displaystyle \frac{RT}{2F}}\ln ({\displaystyle \frac{p_{H_2}{p}_{O_2}^{0.5}}{p_{H_{2}O}}})+{\displaystyle \frac{RT}{2{\alpha }_{an}F}}a\sinh ({\displaystyle \frac{i}{2i_{0,an}}})+i\cdot (R_{elec}+{\displaystyle \frac{\delta }{\sigma }})+i\cdot {({\beta }_1{\displaystyle \frac{i}{i_d}})}^{{\beta }_2}$$

(9)

where the corresponding empirical equations and parameters can be found in Ref. [32].

The production of hydrogen and oxygen from the electrolyzer can be calculated using the following equations [33]:

$$f_{O_2}={\displaystyle \frac{N\cdot I_{cell}}{4F}}{\eta }_f$$

(10)

$$f_{H_2}={\displaystyle \frac{N\cdot I_{cell}}{2F}}{\eta }_f$$

(11)

where N is the number of cells connected in series, I_cell is the input current, and η_f is Faraday’s efficiency, which is affected by side reactions such as the production of hydrogen peroxide and the gas cross-permeation phenomena under pressure operation [34]. A critical metric for evaluating the performance of a PEM electrolyzer is its operating voltage, particularly in relation to the theoretical decomposition voltage of water, which is 1.23 V [35]. In practical applications, PEM electrolyzers typically operate at a higher voltage due to overvoltages associated with the oxygen evolution reaction and hydrogen evolution reaction, as well as resistive losses within the system [36]. The commonly used efficiency calculation method in engineering is given by the following formula [35]:

$${\eta }_{EL}={\displaystyle \frac{f_{H_2}HH{V}_{H_2}}{P_{EL}}}={\displaystyle \frac{1.48}{u_{cell}}}{\eta }_f$$

(12)

where HHV_H2 is the higher heating value of hydrogen, which is 285.8 kJ mol⁻¹, and P_EL is the input power of the electrolyzer. The thermoneutral voltage of 1.48 V takes into account both the electrical energy needed to drive the electrolysis reaction and the heat absorption, simplifying the calculations.

The polarization curve data measured using the PEM electrolyzer at 40 °C were used to validate the model’s fitting performance, as shown in Figure 8. The root mean square error (RMSE) of the model fitting was less than 0.064. The model exhibited a high-accuracy fitting performance for the nonlinear voltage–current characteristics of the PEM electrolyzer. The parameter identification results, based on the experimental data from Ref. [37], are provided in

Table 3. Identification parameters of the PEM electrolyzer model.

Parameter	Value	Parameter	Value
αan	0.5947	Relec	0.2312
i0,an,ref	4.9723 × 10−5	β1	2.2903
Eexc	5.1569 × 104	β2	4.6720
σref	0.0091	id	1.9550
Epro	2.4170 × 104	ηf	0.87

.

By introducing batteries as short-term energy storage devices, the installed capacity of the PEM electrolyzer can be reduced from being equivalent to that of the generator. Consequently, the battery’s maximum charging power needs to be at least equal to the generator’s output power. The energy storage capacity must also be sufficient to store at least the amount of energy generated by the generator during one power generation cycle. The potential generated energy can be estimated using flow velocity data. The installed power of the electrolyzer can be selected based on the requirement that the stored energy in the battery is fully consumed within a complete tidal cycle, including both the flood and ebb tides.

2.3. RO Element

The solute-diffusion transport model is widely used for modeling RO membranes, providing high-precision fitting results [38]. In this model, the mass transport equation typically neglects the concentration gradient along the direction of the membrane channel, using average values instead for the calculation of the transport equation. The modeling parameters for the SW30HRLE-4040 (Dow Chemical Company, Midland, MI, USA) RO membrane were obtained directly from The Open Membrane Database [39], ensuring the reliability and accuracy of the parameter values used in this study. The water transport equation for feed water permeating through the RO membrane to the freshwater side is as follows [40]:

$$Q_{p\mathrm{e}}=A\cdot (\Delta p-\Delta \pi )\cdot S_m$$

(13)

where Q_p is the permeate flow rate, A is the water permeability coefficient of the membrane, Δp is the transmembrane pressure difference, Δπ is the osmotic pressure difference, (Δp-Δπ) is referred to as the net driving pressure, and S_m represents the effective working area of the membrane. The rate of salt transfer through the membrane can be calculated using the following equation [41]:

$$Q_s=B\cdot TCF\cdot PF\cdot (C_{fb}-C_{pe})\cdot S_m$$

(14)

where Q_s is the mass flow rate of solute through the membrane, B is the solute permeability coefficient of the membrane, and TCF is the temperature compensation factor (set to 1 for a constant operating temperature of 25 °C). PF is the concentration polarization factor, compensating for the effect of increased local salt concentration on the feed side of the membrane, and C_fb is the average salt concentration on the feed side. C_pe is the permeate (freshwater) concentration.

The net driving pressure is given by [40]:

$$\Delta p-\Delta \pi =P_f-{\displaystyle \frac{P_{drop}}{2}}-P_p-{\pi }_m+{\pi }_p$$

(15)

where P_f is the feed pressure supplied to the RO membrane, P_p is the pressure on the permeate side, P_drop is the pressure drop along the membrane, π_m is the osmotic pressure on the feed side of the membrane, and π_p is the osmotic pressure on the permeate side.

The pressure drop P_drop along the membrane can be given by [38]:

$$P_{drop}={\lambda }_f\cdot L\cdot {\displaystyle \frac{{\rho }_{fb}}{d_h}}\cdot {\displaystyle \frac{v_{fb}}{2}}$$

(16)

where λ_f is the friction factor, L is the effective length of the membrane, ρ_fb is the density of the feed water, v_fb is the water flow velocity in the feed channel, and d_h is the hydraulic diameter of the feed channel. The friction factor λ_f is given by [38]:

$${\lambda }_f=2.3\cdot R{e}^{-0.31}$$

(17)

where R_e represents the Reynolds number inside the brine channel.

The empirical formula for calculating osmotic pressure from salt concentration is as follows:

$$\pi =2\times 0.0787\times 0.98\times 298\times C/MW$$

(18)

where C is the salt concentration in the liquid and MW is the molar mass of the salt (58.44 kg/kmol for NaCl).

The osmotic pressure of the salt water on the surface of the RO membrane can be given by the following equation:

$${\pi }_m={\pi }_f{\displaystyle \frac{C_{fb}\cdot PF}{C_f}}$$

(19)

The concentration polarization factor PF can be calculated as [40]:

$$PF=\exp (0.7Y)$$

(20)

where Y is the recovery rate of the RO membrane and represents the percentage of feed water that is converted into permeate.

The efficiency of an RO system can be assessed using the specific energy consumption (SEC). The SEC is an important metric for evaluating the energy efficiency of a RO system. Focusing on evaluating the recovery efficiency of the ERD, the SEC is calculated by the following equation [42]:

$$SEC={\displaystyle \frac{W_{pump}}{Q_p}}$$

(21)

where W_pump is the mechanical power of the pump. Using the pump input power takes into account the additional energy demand caused by friction losses within the pump.

The selection of the RO membrane can be determined based on the performance of the ERD and the input power range of the seawater pump. For seawater desalination, the operating pressure must be at least above 35 bar. The rated feed flowrate range of the RO membrane can be roughly determined according to the power range of the seawater pump.

In industrial applications, RO systems typically operate under constant pressure and flow conditions to ensure stable and efficient water production while minimizing the impact on membrane lifespan. However, for tidal energy seawater desalination systems, both pressure and flow fluctuate with the varying incoming tidal current speeds. Real-time adjustments are needed to achieve maximum power capture while ensuring efficient and stable water production. To evaluate the operating conditions of RO membranes, the concept of a Safe Operating Window (SOW) is introduced [43]. The SOW restricts the pressure and flow variations within the system to reduce the impact of changing conditions on membrane lifespan. The operational limits for the selected SW30HRLE-4040 RO element are as follows (assuming an inlet seawater temperature of 25 °C and a salt concentration of 31,000 ppm):

(1)

The highest allowable permeate concentration according to the World Health Organization guidelines is 500 mg/L.

(2)

The maximum permissible feed flowrate based on the membrane’s mechanical load capacity is 3.63 m³/h.

(3)

The upper limit for permeate flow per membrane element is 0.5 m³/h.

(4)

The highest recovery rate achievable per element is 13%.

(5)

The minimum brine flow to prevent salt precipitation and fouling is 0.91 m³/h.

(6)

The maximum feed pressure of 83 bar determined by the mechanical strength.

Using these boundary conditions, the SOW for the RO membrane in the desalination system can be developed, as shown in Figure 9.

2.4. ERD

In RO desalination systems, the ERD plays an important role in enhancing the system’s operational efficiency. Seawater RO desalination can operate at around 50 bar pressure, while the pressure drop between the brine discharge and the feed inlet of the RO element is usually less than 1 bar. The brine exiting the RO element still contains a significant amount of pressure energy. Effectively recovering this energy can substantially reduce the SEC of RO desalination and lower the input power required for the seawater pump. Figure 10 illustrates the working principle of the Clark pump-type ERD used in this study [44]. The Clark pump achieves self-pressurization by utilizing the difference in cross-sectional area between the rod and rodless chambers. The high-pressure brine discharged from the RO element, along with the pre-pressurized seawater from the seawater pump, boosts the feedwater pressure to multiple times the seawater pump’s outlet pressure. Two double-acting hydraulic cylinders enable continuous pressurization, achieved by controlling the piston direction through valve mechanisms.

Under ideal conditions, the pressure-flow relationship of the Clark pump can be described by the following equation [45]:

$$P_H=P_L+P_B(1-Y_R)$$

(22)

$$Q_H=Q_L=Q_B/(1-Y_R)$$

(23)

where P is the pressure, Q is the flow rate, and Y_R represents the ratio of the cross-sectional area of the hydraulic cylinder piston rod to the effective area of the piston. The subscripts H, L, and B represent the high-pressure feed seawater, the pre-pressurized feed seawater from the seawater pump, and the high-pressure brine, respectively.

Based on these relationships, the recovery rate of the RO system is determined by the characteristics of the Clark pump to Y_R, which is typically 10%. This means that, for a given feed flowrate, the feed pressure of the RO element will adjust to ensure a constant recovery rate is maintained. This facilitates the dynamic operational control of the RO system. This facilitates dynamic operational control of the RO element, linking the operating power of the system directly to the output flowrate of the seawater pump and the rotor speed.

As shown in Figure 11, tests were conducted using the constructed desalination system. The results indicate that the desalination system is able to maintain a 10% recovery rate. However, compared to the pressure-flow operating point at a 10% recovery rate in the theoretical model, the actual system requires approximately 5 bar less feed pressure to achieve the same recovery rate. There are two potential reasons for this phenomenon. Firstly, the product manual of the Dow reverse osmosis membrane states that the water production performance of actual membrane modules may vary by ±20%. This implies that performance differences between membrane elements could lead to variations in permeability, resulting in different permeate flow rates under the same feed pressure. Secondly, temperature changes can significantly affect the permeability of the reverse osmosis membrane, with an increase of 4 °C leading to a 10% increase in water production.

2.5. Control System

The turbine used in this system is of a fixed-pitch type and is not equipped with a yaw system, making it designed to generate power in a single tidal flow direction, meaning the generating system is operational for only half of the day, which poses a challenge in terms of maintaining a stable and continuous energy supply, especially for the electrolyzer. To improve the capacity factor of the PEM electrolyzer and the energy availability of the system, batteries have been introduced for short-term energy storage. By absorbing fluctuating electrical energy during high inflow velocity periods, the batteries allow the system to store excess power generated by the PMSG. This stored energy can then be used during low-inflow-velocity or non-generating periods, ensuring that the electrolyzer can operate continuously even when the turbine is not capturing sufficient tidal current energy. The primary benefit of adding batteries is the increase in the electrolyzer’s capacity factor. Without batteries, the electrolyzer would only operate intermittently, depending directly on the turbine’s real-time power output. This intermittent operation would lead to lower utilization rates, increased operational downtime, and potential inefficiencies in hydrogen production. However, with batteries, the system can smooth out these fluctuations by storing excess energy when available and releasing it when needed. A higher capacity factor translates into more consistent hydrogen output relative to the electrolyzer’s installed capacity, improving the return on investment. By maintaining continuous operation, the system maximizes hydrogen production without the need for a larger, more expensive electrolyzer.

Figure 12 illustrates the state machine diagram of the system. The system will assess whether the current tidal conditions are suitable for power generation, thereby selecting between operating in generating mode and supply mode. In generation mode, the system will determine whether to use the electrolyzer or the batteries to absorb fluctuating power based on the current captured power. The power electronic devices regulate the input power of the chosen load to match the target output power of the PMSG, as determined by the PSF control method. When the captured power is sufficiently high and the rotor speed satisfies the SOW constraints, the system will engage the electromagnetic clutch to initiate the operation of the desalination system. As the tidal flow gradually decreases, the system will shut down and switch to supply mode. In this mode, the system will assess whether the battery capacity is sufficient and decide whether to operate the electrolyzer. In this way, the electrolyzer can maintain continuous operation, thereby effectively improving its utilization. This is crucial for reducing the overall capital cost of the system.

Figure 13 illustrates the power distribution of the system, including the power captured by the turbine operating at the MPPT point, the hydraulic power of the seawater pump, and the frictional loss power. It can be observed that when the rotor speed is about 16 rpm, the power captured by the impeller just overcomes the frictional loss. This rotor speed is designated as the cut-out speed of the turbine, marking the entry into stop mode. The cut-out speed for the desalination system is 35 rpm, where a significant fluctuation in frictional loss power occurs due to the engagement and disengagement of the electromagnetic clutch. Due to the operation of the seawater pump, the frictional losses nearly double. At this speed, the desalination system is in operation. Since the Clark pump sets the recovery rate at 10%, the feed pressure and feed flowrate characteristics of the RO element are well-defined. The mechanical power of the seawater pump, excluding frictional losses at different speeds, is indicated in the figure. At a rotational speed of 35 rpm, there remains a surplus of power captured by the turbine available for consumption by the PMSG. When the inflow velocity decreases to or below this value, timely disengagement of the desalination system ensures the safe and stable operation of the system. By calculating the power capture characteristics of the turbine and the load characteristics of each component, the target power expression for the improved PSF control can be obtained as shown in Equation (24).

$$P_{PMSG\_target}=\left\{\begin{array}{cc}0\hfill & \hfill Idle\hfill \\ {\eta }_{PMSG}\cdot (K_{opt}\cdot {\omega }_r^3-6.35\cdot {\omega }_r^2-38.8\cdot {\omega }_r)\hfill & \hfill MPPT\hfill \\ {\eta }_{PMSG}\cdot (\underset{PSF\hspace{0.17em}control}{\underbrace{K_{opt}\cdot {\omega }_r^3}}\underset{Friction\hspace{0.17em}power}{\underbrace{\hspace{0.17em}-\hspace{0.17em}24.19\cdot {\omega }_r^2-58.33\cdot {\omega }_r}}\underset{Pump\hspace{0.17em}power}{\underbrace{\hspace{0.17em}-\hspace{0.17em}6.38\cdot {\omega }_r^2-37.05\cdot {\omega }_r}}\hfill & \hfill Desalination\hfill \end{array}\right.$$

(24)

3. Simulation Analysis

A full-system simulation model was built in Matlab/Simulink 2019b software as shown in Figure 14, and simulations were conducted using the measured flow velocity data.

The Zhoushan sea area, characterized by its complex topography and numerous islands, exhibits a unique hydrodynamic environment. This region features a multitude of narrow channels, particularly in areas with dense island distribution, which serve as the primary conduits for tidal and current flows. Influenced by tidal forces and topographical constraints, the flow velocity near these channels is typically high, especially in regions where significant topographical variations occur along the channel boundaries. As shown in Figure 15, the location corresponds to Zhejiang University’s tidal energy testing base, which also serves as the measurement site for flow velocity data. Figure 16 shows the inflow velocity data used in the simulation model. The inflow velocity data were collected from the Zhoushan archipelago using a Doppler current sensor, measuring the surface seawater velocity at a frequency of 1 Hz. The tidal cycle is approximately 12 h, with ebb tide from 0 to 6 h and flood tide from 6 to 12 h. During the ebb tide, the inflow velocity exhibits greater fluctuations compared to the flood tide. The inflow velocity varies in a “sine wave” pattern, with the maximum inflow velocity exceeding 1.5 m/s.

Figure 17 shows the rotor speed obtained from the simulation results, as well as the corresponding operating modes at different times. At the beginning of the simulation, during the ebb tide period, the system remains in idle mode, awaiting the increase in inflow velocity to self-start. The inflow velocity starts from 0 m/s and gradually increases, but initially is insufficient to overcome the frictional resistance. The turbine begins rotating once the inflow velocity approaches 0.75 m/s, and the system enters the generating mode, with the PMSG, converter, and electrolyzer starting to operate and undergo MPPT control. At around 1 h into the simulation, the inflow velocity reaches approximately 1.1 m/s, and the rotor speed reaches 45 rpm, meeting the startup requirements of the desalination system. The electromagnetic clutch is engaged, and the desalination system starts operating. At about 4.5 h into the simulation, the inflow velocity drops below 1 m/s, causing the rotor speed to fall below the desalination system’s cut-out speed of 35 rpm. The electromagnetic clutch is disengaged, and the desalination system ceases to operate. At approximately 5.5 h into the simulation, with a further decrease in inflow velocity, the system goes into shutdown mode, triggering the brake load and shutting down the system. Subsequently, the tide transitions into its flood tide period. During the flood tide period, the turbine remains shut down. However, the hydrogen production system continues to operate, using the stored energy in the battery to power the electrolyzer at a constant power output until the battery voltage drops below its discharge cutoff voltage.

Figure 18 shows the power coefficient of the turbine during simulation. It can be observed that the power coefficient remains around 43.5%, which is very close to its maximum value. Compared to the mid-period of the ebb tide, the power coefficient fluctuates and decreases during the early and late ebb tide periods. The PSF algorithm controls the generator output power based on the rotor speed, which always lags behind changes in the inflow velocity. As a result, the turbine can only operate near the MPPT operating point, leading to fluctuations in the power coefficient.

Figure 19 illustrates the total power captured by the turbine during the simulation and its distribution. Overall, friction losses account for a significant proportion, with the activation of the seawater pump roughly doubling the friction losses. The dynamic seals and the selected seawater pump have relatively high friction torque, necessitating further design optimization to improve operational efficiency. It can be observed that the input power to the PMSG fluctuates considerably. This is because the PMSG is responsible for controlling the maximum energy capture of the turbine, adjusting the load power based on rotor speed variations to keep the turbine operating at the optimal TSR. Around 1.5 h into the simulation, the input power allocated to the PMSG drops to less than 200 W. This explains the fluctuations in the power coefficient at the corresponding simulation time shown in Figure 18. Due to insufficient available adjustable power margin for the PMSG, its ability to control the turbine’s operating state diminishes, causing the turbine to deviate from the optimal TSR, resulting in a decrease in the power coefficient.

Figure 20 presents the simulation results of the battery and electrolyzer power. It can be observed that during the ebb tide, the electrolyzer remains in operation, with the input power to the electrolyzer fluctuating along with the rotor speed, contributing, to some extent, to the MPPT control functionality. Given that the installed rated capacity of the electrolyzer is only 300 W, most of the electrical energy output by the PMSG is absorbed by the battery. During the power generation process, the battery’s SOC increases from 0% to approximately 44%, absorbing 3.02 kWh of energy. During the flood tide, the electrolyzer continues to operate, with the battery supplying energy to the electrolyzer, which continues to produce hydrogen at a power level of 300 W. At around 12 h into the simulation, the battery’s SOC decreases to 0%, causing the hydrogen production system to cease operation.

Figure 21 shows the simulation results of the electrolyzer’s energy efficiency. The electrolyzer used consists of four membrane electrode assemblies, with a theoretical reversible voltage of 5.92 V for the water electrolysis process. As the input current increases, the overpotentials also increase, resulting in a decrease in efficiency as the input voltage rises. During the ebb tide period, the power of the electrolyzer fluctuates with the rotor speed, and its efficiency varies between 57.9% and 73.5%. During the flood tide period, the electrolyzer operates at a constant power of 300 W, with an input voltage reaching 9 V and an operational efficiency of 57.9%. Throughout the simulation, a total of 2.86 kWh of electrical energy is input into the electrolyzer, producing approximately 492.91 SL of hydrogen, with an average electrolysis efficiency of 60.9%. The capacity factor of the electrolyzer reaches 70.1%.

Figure 22 illustrates the simulation results of the feed pressure and feed flowrate for the RO element. It can be observed that only a small portion operates outside the SOW boundaries, corresponding to the startup process of the desalination system around 1.5 h into the simulation. The RO element operates at a constant recovery rate of 10%, validating the working characteristics of the energy recovery device.

Figure 23 depicts the relationship between the SEC and the rotor speed. It can be observed that as the rotor speed increases (i.e., as the feed flowrate increases), the SEC rises from approximately 4.0 kWh/m³ to about 7.7 kWh/m³. This SEC calculation considers the friction losses of the pump, which increase with higher speeds.

Figure 24 shows the energy flow diagram for the simulation, illustrating energy flow and material transfer in different parts of the system. During the entire simulation, the power coefficient of the turbine remains consistently above 0.4 and can be maintained near the theoretical maximum value over a long period. The turbine captured 9.37 kWh of tidal current energy. The PMSG consumed 4.37 kWh, while the seawater pump used 1.01 kWh as loads, and friction losses accounted for 3.95 kWh of energy consumption. The electrolyzer produced 492.91 SL of hydrogen, consuming 2.86 kWh of electricity and 0.45 L of water, with an average energy efficiency of 60.9%. The SEC for hydrogen production was 64.96 kWh/kg_H2. Compared to the 2022 PEM electrolyzer technical target of 51 kWh/kg_H2 set by the U.S. Department of Energy [46], there is a notable gap, primarily due to the limited performance of the selected electrolyzer. At a cell voltage of 2.25 V, the current density only reached 0.64 A/cm², resulting in significant overvoltage losses. However, compared to the 25% capacity factor of electrolyzers reported in wind-powered hydrogen production systems in the literature [47], this system undoubtedly improved the utilization rate of the electrolyzer. By replacing it with a high-performance electrolyzer, the SEC of the hydrogen production system can be effectively improved. During the approximately 12 h tidal cycle, the electrolyzer’s capacity factor was 70.1%. The seawater desalination system produced 521.46 L of freshwater, with an average SEC of 6.175 kWh/m³. Compared to the SEC of 3.65–5.25 kWh/m³ recorded for small seawater desalination systems in the literature [48], the higher friction losses considered for the seawater pump in calculations resulted in a significantly increased SEC. The selected equipment had relatively high friction losses, accounting for 42.2% of the turbine’s captured power, which reduced the system’s energy efficiency.

4. Conclusions

This study proposes a tidal current-powered freshwater and energy supply system designed to enhance the sustainability of island communities by integrating tidal energy, hydrogen production, and desalination. The simulation results demonstrate the technical feasibility and potential benefits of the system. During the power generation period, the average power coefficient of the turbine reached 0.434, indicating good MPPT control performance. The proposed system achieved a high average energy efficiency of 60.9% for the PEM electrolyzer and a capacity factor of 70.1%, demonstrating effective utilization of tidal current energy and short-term energy storage to maintain stable hydrogen production. Due to the high friction losses of the seawater pump, the SEC of the desalination system was relatively high, at 6.175 kWh/m³. This can be improved by optimizing the pump selection. The proposed system offers a promising approach to improving energy security and reducing dependency on imported fuels for remote and off-grid island communities. The integration of hydrogen production further adds value by providing a clean energy storage solution that can be used for various applications, including power generation and transportation. Further work is needed to optimize the selection of the electrolyzer and seawater pump to reduce energy losses and improve the overall operational efficiency of the system. Future research should focus on experimental validation of the system, including small-scale pilot projects or field testing in real tidal environments. This will provide critical data to validate simulation results and identify practical challenges that may not be fully captured in the simulations.