1. Introduction
To reduce the use of fossil fuels and protect the environment, it is urgent to vigorously develop clean energy such as solar energy. At present, terrestrial photovoltaic (PV) energy faces many problems, such as the loss of agricultural land due to the high demand for land area, the abandonment of light due to the large distance from the load center, and the system risk to the power grid due to the distributed photovoltaic energy [
1]. On the contrary, the development of floating photovoltaic (FPV) technology in the ocean is very advantageous for overcoming the above problems, and it provides a method to optimize the energy structure for the high electricity demand in economically developed coastal areas.
The FPV array consists of floating platforms, PV modules, connectors, mooring systems, and related electrical components [
2]. Compared to terrestrial PV, the cooling effect of water can effectively reduce the service temperature of the PV modules, which increases the energy conversion efficiency and, thus, outputs more electricity [
3]. For example, the FPV array arranged in the Straits of Johor, with an area of 5 hectares, is expected to generate 6.02 million kWh of electricity per year, which is about the annual electricity consumption of 1380 four-roomed HDB flats, while reducing the carbon emissions by close to 4258 ton [
4]. It can be seen that FPV technology has great economic and environmental benefits. It should be noted that the composition of ocean loads is complex, and the continuous action of wind, waves, and currents will pose great challenges to the safe service of the FPV array. In 2019, an FPV power station in Japan was damaged by a hurricane, and a fire was triggered [
5]. To prevent further accidents, it is crucial to study the hydrodynamic characteristics of FPV arrays under ocean loads. In recent years, a series of effective studies have been carried out, one after another.
In the field of wind load, Choi et al. [
6] and Bei et al. [
7] measured the distribution of wind loads within a PV array. The results show that, due to the shielding effect of the outer structures, the wind loads acting on the structures located in the middle of the PV array are significantly reduced, and the influence gradually weakens and tends to stabilize as the number of rows increases. Wood et al. [
8] and Warsido et al. [
9] investigated the effects of transverse and longitudinal spacing between structures on the wind loads acting on PV panels, and the results indicated that the transverse spacing has little effect on the wind loads, while the increase in longitudinal spacing will lead to an increase in wind loads. The studies by Shademan et al. [
10], Bitsumlak et al. [
11], and Jubayer et al. [
12] indicated that PV panels will withstand greater drag and lift when the incident wind is parallel to the array direction. Aly et al. [
13] explored the influence of PV panel dimensions on the wind loads and found that there is no obvious relationship between average wind load and PV panel dimension, while the peak wind load is significantly affected. The research of Choi et al. [
5] revealed that the lift and drag on PV panels gradually increased with the turbulence intensity. In addition, the numerical study of Honaryar et al. [
14] indicated that the wind load on an FPV array is 458% higher than that on a terrestrial PV array of the same scale. Therefore, the interaction between water and wind is extremely important.
In the field of wave load, Ikhenniche et al. [
15] calculated the total loads on the FPV system in three environments and found that wind dominates in inland water, while waves contributes significantly in the ocean. Kim et al. [
16] analyzed the hydrodynamic characteristics of the FPV array under waves with different incident angles, and the results showed that the mooring forces reach the maximum when the wave direction coincides with the mooring direction. Lee et al. [
17] obtained the distribution of wave loads within the FPV array by numerical simulation, and the results showed that the minimum occurs at the corner, while the maximum occurs at the front and rear of the FPV array. In the study of Song et al. [
18], the influences of the arrangement angle of the FPV array, the dimensions of floating structures, and the axial stiffness of tensioned mooring lines on the supporting frames were examined. The results showed that the overall stiffness of the FPV array is mainly controlled by the mooring stiffness. Song et al. [
19] compared the effects of a fixed connection and a hinged connection on the dynamic response of the FPV array under wave conditions, and the results indicated that the fixed connection can effectively reduce the mooring forces. Al-Yacouby et al. [
20] and Friel et al. [
21] carried out parametric studies on the dynamic response of the single horizontal cylindrical floating platform under the action of regular and irregular waves, including the immersion depth, diameter of the pontoon, wave height, and wave period. Gharechae et al. [
22] proposed a semi-analytical method for solving the vertical acceleration of an elastic circular floating system, and the research indicated that, as the wave number increases, the hydroelastic interactions between the floating structures become increasingly significant. Zhang et al. [
23] systematically investigated the influence of module number, external constraint, and internal hinge on the motion of the array. The study by Wang et al. [
24] indicates that modular floating structures can effectively attenuate incident waves when the wave has a short period. In addition, the action mechanism of the current load is similar to that of the wind load, but the presence of the current will affect the characteristics of the wave load. Currently, there is a lack of research on the action mechanism of current on the FPV array.
In summary, the existing research focuses mostly on the hydrodynamic characteristics of an FPV array under one single load; however, in engineering, wind, waves, and currents often exist simultaneously. In addition, the study should be based on the entire FPV array rather than a single PV panel [
20,
21]. At present, there is a lack of research in this field. On the other hand, existing studies have shown that the FPV array is subjected to the maximum force when the direction of loads is parallel to the FPV array [
10,
11,
12,
16]. In this case, it could be expected that the dynamic response mechanism of each row of the FPV system located in the middle part of the FPV array (
Figure 1a) is similar, and the transverse force is significantly smaller than the longitudinal force within the FPV array. Therefore, the single-row FPV system, located in the middle part of the FPV array (marked with a red block in
Figure 1a), can be selected as the simplified research object. In this study, based on the potential theory, a numerical model of a single-row FPV system with ten floating platforms is established using the software ANSYS-AQWA. Following this, the hydrodynamic coefficients of a single floating platform are calculated and evaluated. After that, the dynamic responses of the FPV system under different load combinations are explored. Finally, the influence mechanism of wave parameters on the hydrodynamic characteristics of the FPV system is discussed in detail, including the wavelength and wave height. This study explores the dynamic response mechanism of the FPV system under typical ocean loads, which can provide useful guidance for the safety design of the FPV system.
3. Hydrodynamic Coefficients
As the important parameters for predicting the seakeeping and stability of floating platforms, the hydrodynamic coefficients are of great significance for accurately predicting the dynamic response of floating platforms under waves. In this section, the hydrodynamic coefficients of a single floating platform, including added mass, radiation damping, wave excitation force, and response amplitude operators (RAOs), are calculated and analyzed.
The added mass of a single floating platform is shown in
Figure 8, which represents the variation of the added water mass of the floating platform in six degrees of freedom (DOFs) under waves with different frequencies. It can be seen that the added mass in surge, sway, and yaw reaches the maximum in the wave frequency range of 0.40~0.50 rad/s, and the added mass in heave, roll, and pitch has little change with wave frequency, especially after 0.45 rad/s. The radiation damping of a single floating platform is shown in
Figure 9. The radiation damping in surge, sway, and yaw varies significantly with wave frequency. When the wave frequency is small (less than 0.30 rad/s), the radiation damping approaches 0, and it reaches the maximum in the wave frequency range of 0.70~0.80 rad/s. In addition, the radiation damping in heave, roll, and pitch does not vary significantly with wave frequency and is generally close to 0.
The floating platform is in a static state in still water without moving speed, so the added mass and radiation damping in six DOFs are all symmetric matrixes. In addition, the projection of the center of the floating platform on the X–Y plane is located at the origin, and the floating platform is symmetrical around the X–Z plane and the Y–Z plane, so the added mass and radiation damping of the floating platform in surge, sway, pitch, and roll are basically consistent.
Under the action of waves, the floating platform and wave will interfere with each other. Based on the diffraction theory, the wave excitation forces, including the Froude–Krylov force and the diffraction wave force, can be solved. The wave excitation forces of a single floating platform are shown in
Figure 10. It can be seen that the floating platform will withstand the wave excitation forces in three DOFs (surge, heave, and pitch), and the wave excitation forces in sway, roll, and yaw approach 0 when the wave is incident at 0°. Under the moderate wave of this study (frequency of 0.0215 rad/s), the wave excitation force in heave is significantly greater than that in surge. In addition, the wave excitation forces in surge and pitch of the floating platform vary significantly with wave frequency, but, as the wave frequency increases, the wave excitation forces exhibit a “decreasing” trend in general. The wave excitation force in surge reaches the maximum in the wave frequency range of 0.45 rad/s to 0.55 rad/s, while the wave excitation force in pitch reaches the maximum in the wave frequency range of 0.40 rad/s to 0.50 rad/s.
The motion responses of the floating platform under a unit wave can be described by the response amplitude operators (RAOs), which represent the transfer function of wave amplitude in various positions. The RAOs of a single floating platform are shown in
Figure 11. It can be seen that the floating platform will generate significant motion responses in surge, heave, and pitch, and the motion responses in sway, roll, and yaw approach zero when the wave is incident at 0°. The response amplitude operator (RAO) in surge of the floating platform is obvious under waves with low frequency, which means it can resist the waves for short periods. Moreover, as the wave frequency increases, the RAO in surge significantly decreases. The RAO in heave exhibits a maximum in the wave frequency range of 0.40 rad/s to 0.50 rad/s. The RAO in pitch shows a trend of first increasing and then decreasing, with the maximum occurring in the wave frequency range of 0.30 rad/s to 0.45 rad/s. It should be noted that the RAOs of the floating platform in surge, heave, and pitch tend to approach 0 as the wave frequency increases.
In summary, referring to the environmental loads in
Section 2.1.1, the floating platform has good seakeeping and stability. Therefore, this design of the floating platform can be used to construct an FPV system for time-domain analysis to explore the hydrodynamic characteristics under ocean loads.
4. Load Coupling Analysis
The ocean environment is dynamic and variable, and an FPV array arranged in the ocean is highly susceptible to the continuous effects of waves, wind, and currents, and the coupling mechanism is very complex. In this section, based on typical sea conditions (
Table 1), three different load combinations, namely “wave only”, “wave and current”, and “wave, current and wind”, are set up to discuss the dynamic response mechanism of the single-row FPV system. The loads are parallel to the FPV system.
4.1. Motion Responses
Due to the action of waves, the floating platforms will generate motions in surge (translation along the X-axis), heave (translation along the Z-axis), and pitch (rotation around the Y-axis). After the stabilization of loads and the FPV system, the motion variation of floating platforms (structure 1, 5, 10) at typical positions are selected for analysis, as shown in
Figure 12. It can be seen that: (1) Determined by the periodicity of wave, the motion responses of floating platforms exhibit periodic characteristics. When the wave acts alone, the motion period of floating platforms is consistent with the wave period. (2) The existence of current affects the motion period of floating platforms, with the motion period changing from 7.4 s to 7.3 s. This is mainly due to the changes in relevant parameters of the wave when the wave interacts with the current. Barltrop et al. [
31] pointed out that the wave period can be expressed as Equation (12) when wave and current interact together. Therefore, when the wave and current are in the same direction, the period of the wave decreases to 7.3 s. It should be noted that, in this study, the current has only a slight impact on the motion amplitude of floating platforms and is mainly reflected in the motion of the surge. The average increases in the maximum and minimum values are 0.3% and 0.7%, respectively, which can be ignored in terms of quantity. This is mainly because the current is relatively small, only 0.15 m/s; therefore, its impact on the wave is mainly reflected in the change of wave period.
where
is the wave period relative to the stationary observer,
is the wavelength,
is the wave period relative to the current,
is the velocity amplitude of the current, and
is the angle between the wave and current.
(3) The existence of wind only affects the motion amplitudes of floating platforms. The surge amplitude exhibits a slight increase, and the average increases in its maximum and minimum are 0.9% and 0.8%, respectively. This can be attributed to the wind acting in the X-direction, the wind speed is relatively small, and the height of the floating platforms is also small; therefore, the wind has a smaller force on the FPV system. (4) The motion responses of floating platforms in a period are not completely symmetric. This is mainly because the wave in this study belongs to the Stokes second-order wave [
32] with an asymmetric wave surface; its crest is steeper, and its trough is slower.
4.2. Force Characteristics
In this section, the external loads applied to the FPV system are wave force, wind force, and current force. Three floating platforms at typical positions are selected, and the force characteristics are explored. The variation of wave forces acting on floating platforms are shown in
Figure 13. It can be seen that wave play is a dominant role in the force of floating platforms under the typical sea environment, and the contribution can reach over 99%. The current affects its periodic characteristics more, while the wind load does not have a notable impact on the force. It should be pointed out that the hydrodynamic characteristics of the FPV system will exhibit significant differences when encountering strong winds and huge currents, which will be explored in subsequent research.
In summary, within the scope of this study, wave loads exhibit a significant impact on the dynamic response of the FPV system, with a contribution of up to 99%. The current load has more influence on the periodic characteristics of the dynamic response due to the interaction between waves and currents. In addition, the wind load does not exhibit a notable effect on the dynamic response of the FPV system. It should be noted that the load acting on the floating platform depends on two aspects, i.e., the shape and dimension of the floating platform as well as the environmental loads. For different sea areas, there are significant differences in environmental loads, and the relative amplitudes of wind, waves, and currents can also vary obviously. Therefore, the contribution of wind, waves, and currents will vary with the ocean environment. The load in this study is taken from a moderate-intensity sea area, featuring moderate-intensity waves and relatively weak wind and currents, and the research findings of this study can effectively characterize the interaction mechanism of wind, waves, and currents for such sea areas. For other sea areas with significantly different features, it is expected that the contribution rate of wind, waves, and currents will vary accordingly, which needs further specific calculations based on practical sea loads.
6. Conclusions
In this study, a single-row FPV system with 10 floating platforms is taken as the object of study, based on the potential theory, and the hydrodynamic coefficients of a single floating platform are calculated through AQWA software. Then, the acting mechanisms of wind, waves, and currents are explored. Finally, the influences of wave parameters, including wavelength and wave height, are investigated in detail. The main conclusions obtained are as follows:
- (1)
The motion response of the floating platform is obvious under the wave with low frequency. As the wave frequency increases, the motion response decreases, in general, which means it can resist the waves for short periods. In addition, the design of the floating platform exhibits good seakeeping and stability under the moderate sea area of this study.
- (2)
The influence of the wave on the dynamic response of the FPV system dominates under the moderate sea area of this study, with a contribution of up to 99%. The wind and currents mainly affect the motion and force in the X-direction of floating platforms in this study, and, due to the small dimension of the floating platform, the influence of wind and currents is very limited and can be ignored. In addition, the presence of currents affects the period of dynamic response.
- (3)
When the wave height is constant, the motions of floating platforms and hinged joints increase at first and then decrease due to the resonance effect between the wave and the FPV system, and the variation mechanism in the connection forces with wavelength is the same. In addition, the wave forces gradually reduce due to the decrease in wave steepness (H/L). It should be pointed out that as the wavelength increases, the surge amplitudes of floating platforms increase at first, decrease later, and increase again as a whole.
- (4)
When the wavelength is constant, the wave energy increases with wave height. Therefore, the motion and force of floating platforms and hinged joints in the FPV system exhibit significant enhancement. Nevertheless, the mooring force on the rear side decreases as the wave height increases. As it is significantly smaller than the mooring force on the front side, it may not be a key consideration in design.
This study focuses on the hydrodynamic interaction between waves and the FPV system, and the influences of wavelength and wave height are systematically explored. It should be noted that the FPV system with ten floating platforms is investigated, considering the fact that, in practical engineering, there will be tens or even hundreds of floating platforms connected in a row. Hence, a study on an FPV system with more structures should be carried out in the future. In addition, the waves applied in this study mainly focused on moderate waves, in which the turbulence, splash, and wave-in-deck are not involved. Nevertheless, for high waves from storms or typhoons, it is expected that the potential theory would present obvious deviation due to its limitation. In this case, a CFD-based software is more suitable for this kind of simulation, which needs further studies in the future.