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Scientific Reports volume 14, Article number: 29920 (2024)
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An Author Correction to this article was published on 21 February 2025
This article has been updated
With the expansion of floating photovoltaics, rigid connectors offer advantages over polyester ropes by reducing the relative motion of floats and simplifying the layout of the connection system. However, the overall stability and safety of the floating photovoltaic system may be compromised if a wave crest occurs at the connection point of the rigid connector during motion. Furthermore, the rigid connectors with different degrees of freedom significantly impact the motion of the floats and their connection loads. In this study, three types of single-rod rigid connector models with varying constraints are established through numerical simulation to explore the feasibility of applying single-rod rigid connectors with different degrees of freedom in photovoltaic systems. Based on their degrees of freedom, these connectors are classified as cardan, purely rigid, and hinged. An analysis of float motion and connector loads in two-floating, four-floating, and eight-floating systems shows that as the number of floats increases, the axial distance between them decreases, resulting in more intense motion. Despite this, the eight-floating system maintains a certain safety distance. The maximum load on the connectors occurs in the middle of the multi-floating system, and releasing degrees of freedom can help mitigate some of the load effects.
As global energy demand continues to rise, solar energy is poised to become a primary source of new energy, according to the International Energy Agency’s (IEA) World Energy Outlook1. Due to land constraints for terrestrial photovoltaics, floating photovoltaic (FPV) has entered a developmental phase. Emerging as a new industry, the world’s first floating photovoltaic power station is established in Aichi Prefecture, Japan, in 2007 2. Since then, floating photovoltaics have progressed and gradually advanced into the oceanic realm3. Currently, many floating photovoltaic (FPV) floats are connected using polyester ropes. However, as the photovoltaic deployment area increases, the number of polyester ropes and the complexity of their arrangement also increase, leading to potential issues. In comparison to polyester ropes, steel structural connectors offer advantages such as simplifying their arrangement. Therefore, applying steel structural connectors to connect photovoltaic floats is a promising approach.
Due to the nascent stage of development of floating photovoltaics4,5, research on photovoltaic connectors is relatively scarce. The connection of photovoltaic floats through connectors results in indirect interactions between floating structures due to their radiation and diffraction effects6,7 conducted a numerical simulation to study the motion response of multi-floating system under wave action and verified the accuracy of this conclusion. Therefore, in simulations involving multiple floats, the mutual influence between modules cannot be ignored.
By drawing on the study of very large floating structures connectors8. Wang et al. verified the accuracy of the numerical simulation method through experimental and numerical comparisons, and the influence of waves on the connectors is explored9. In the context of multi-floating simulations, Yang et al. established a Boussinesq-Hydroelasticity coupling method based on the Boussinesq equation and Cummins theory. The motion response and connector load of a single module in a multi-floating is investigated by numerical simulation10. Releasing the degree of freedom of the connector can effectively reduce the connection load, and the hinged connectors can be applied. Results demonstrated that hinged connectors can be effectively applied to connect large-scale multi-floating system11. Additionally, when considering the influence of connector stiffness, the longitudinal loads are found to exceed the transverse and vertical loads due to multi-floating motion processes12.
Compared to large floating structures, floating photovoltaic floats are smaller in size. To ensure the reliability of numerical methods applied to photovoltaic floats, the motion characteristics and mooring responses of photovoltaic arrays are analyzed separately through experimental and simulation comparison methods. The results show that the calculation error is within the allowable range, confirming the feasibility of the method13,14. In terms of the connection between photovoltaic floats, several researchers have proposed a new method to establish multi-floating photovoltaic power stations by connecting photovoltaic modules through the application of constraints. Based on this, they analyzed the impact of wave period and direction on the response of the photovoltaic float, and found that the wave direction has a significant impact on the motion response of the float15.
The applicability of rigid connectors in floating photovoltaic systems requires further study. Building on research related to very large floating structures, three types of single-rod rigid connectors suitable for floating photovoltaic systems are proposed. These single-rod connectors are more effective at maintaining safety between the floats compared to other types of connectors. Numerical models of these connectors are used to investigate the loads experienced by connectors with different degrees of freedom, as well as the relative motions of neighboring connected floats in multi-floating systems composed of varying numbers of modules. It is important to emphasize that the overall analysis considers the interaction between the floats. The results offer valuable guidance for the application of rigid connectors in floating photovoltaics.
In order to analyze the impact of rigid connectors on the interaction between multiple floats and the load borne by the connectors, it is necessary to perform a coupled analysis. It has been proven through validation that the three-dimensional potential flow theory can be well applied to the motion of floating photovoltaics, with the overall coupling of the floats shown in Fig. 1. In the rigid connectors between the floats, different joints are simulated by imposing constraints. The connection used in the article is a single-rod connector. Therefore, constraints are imposed on both sides. In numerical simulation, the joints of connectors are simplified into constraints, and different forms of connectors are simulated by releasing degrees of freedom in different directions.
Coupling analysis of multi-floating photovoltaic system.
Each individual module of the photovoltaic platform is supported by four small floats, each designed in an octagonal shape to facilitate bundling onto the upper platform. These floats are constructed from high-density polyethylene (HDPE), which ensures adequate buoyancy while minimizing platform costs. Each float can be conceptualized as the intersection of eight cylinders, each with a diameter of 0.8 m, resulting in an outer diameter of 2.8 m and an inner diameter of 1.2 m. Within the assembled module, the floats can be flexibly arranged to achieve controlled eccentricity. The upper platform is designed as a rigid structure, capable of withstanding bending or tearing under rough sea conditions. The selected materials are corrosion-resistant, thereby eliminating the need for anti-corrosion treatment or ongoing maintenance. Detailed parameters of the individual modules are presented in Table 1.
The schematic diagram of the model is shown in Fig. 2.
Schematic diagram of FPV system.
The module is deployed in waters with a depth of 12.68 m and initially consists of two basic modules connected at the center via connectors, with the floats primarily constructed from high-density polyethylene (HDPE). A six-line mooring system is employed, utilizing a dual-component pendant chain-type anchor chain. This system incorporates a pre-tension of less than 3 tons to facilitate project implementation. The effect of the pre-tension of about 2 tons is mainly to improve the anchorage stability of the multi-floating platform16. To mitigate excessive platform movement and prevent vertical forces at the anchor points, a weight chain is installed to enhance the overall safety of the system. This configuration ensures that the safety factor of the mooring line subjected to windward forces exceeds the specified threshold17,18.
The analysis of rigid connectors primarily includes purely rigid connectors, hinged connectors, and cardan connectors. Among these, purely rigid connectors, which do not release any degrees of freedom, represent a weak point in the overall float system, resulting in significant loads at the connector location that can easily lead to failure and damage. However, they are relatively simple to construct and easy to connect. Hinged connectors allow for relative rotation between modules, which can result in substantial material wear at the connector, complicating maintenance. Nevertheless, compared to purely rigid connectors, hinged connectors release the pitch degree of freedom, thereby reducing vertical loads and bending moments. Cardan connectors, on the other hand, further amplify the load on the connector due to the continuous action of waves on the module, exhibiting a long-term cyclic response that increases susceptibility to material fatigue and connection failure. However, they do release both the pitch and lateral rotational degrees of freedom, thus decreasing vertical and lateral bending moments. Additionally, if two or more cardan joint connectors are employed, interlocking between degrees of freedom may occur, leading to jamming. This can result in the re-emergence of the originally intended fully released bending moment value. Diagrams of the three types of connectors are presented in Fig. 3.
Schematic simulation of the three different forms of connectors.
Building on the degrees of freedom provided by hinged and cardan connectors, further investigation is necessary. The lightweight nature of HDPE material used in the photovoltaic floats raises questions regarding its compatibility with purely rigid connectors. Therefore, it is essential to conduct additional research on photovoltaic floats under three specific conditions: when no degrees of freedom are released, when one degree of freedom is released, and when two degrees of freedom are released.
If the interaction between floats is not considered, the time-domain motion equation of the floating photovoltaic platform under the coupled action of wind and waves is as follows:
where, (left( {{varvec{M}}+{varvec{m}}} right)) is the mass matrix of the photovoltaic floats, ({varvec{K}}) is the hydrostatic stiffness matrix, the external load acting on the float generates forces, which include wave force ({{varvec{F}}_{wav}}(t)), wind force ({{varvec{F}}_{win}}(t)), current force ({{varvec{F}}_{cur}}(t)), and connection force ({{varvec{F}}_{con}}(t)), ({varvec{C}}) is damping matrix.
In the case of multi-floating photovoltaic system, the motion of the floats will be affected by other floats6. In the actual movement, taking a two-floating as an example, the hydrodynamic coupling effect is considered in the actual motion, the equations of motion can be rewritten as Eq. (2).
where, ({varvec{m}}) is the additional mass matrix, ({varvec{F}}(t)) is the force of external loads, ({{varvec{C}}_{coupled}}) is the coupling damping matrix, which represents the effect of the connectors on the relative velocity between the two floats, ({{varvec{K}}_{coupled}}) is the coupling stiffness matrix, which represents the effect of the connectors on the relative displacement between the two floats.
The dynamic response calculation of the mooring line is analyzed through the lumped mass method. The lumped mass method, also known as the lumped mass-spring method, mainly applies the concept of discretization19. In this method, the self-weight of the mooring line, the buoyancy it receives in the water, and the load of external forces all act directly on the mass nodes, as shown in Fig. 4.
Lumped mass method.
In conjunction with the thesis, the number of degrees of freedom can be categorized as (m=0({text{rigid}}),m=1({text{hinged}}),m=2({text{cardan}})).
Regarding the existence of a two-floating system:
where, ({(P)_n}) is denoted as the expression of P onto coordinate system of the connecting points, Z is the transformation matrix.
There is a relationship in the following coordinate system:
where, R is the matrix of (3 times 3), the matrices N and M are related to the angular distance of the float.
Firstly, at (m=0), since there is no release of degrees of freedom between the rigid connectors, the degrees of freedom between the floats are restricted, there exists Eq. (5).
Secondly, at (m=1), in contrast to a purely rigid connector, a hinged connector releases one degree of rotational freedom and other rotations are restricted, assuming that the structure rotates around the axis. Taking the two-floating system as an example, the transformation of the formulae combined with the relationship between the different coordinate systems can finally be obtained:
where,(A={left[ {begin{array}{*{20}{c}} {Z{Z_{11}}}&{Z{Z_{12}}} \ {Z{Z_{21}}}&{Z{Z_{22}}} end{array}} right]^{ – 1}}left[ {begin{array}{*{20}{c}} {{{({Z^{ – 1}}{R_2}^{{ – 1}}{R_1})}_y}} \ {{{({Z^{ – 1}}{R_2}^{{ – 1}}{R_1})}_z}} end{array}} right]),(B={left[ {begin{array}{*{20}{c}} {Z{Z_{11}}}&{Z{Z_{12}}} \ {Z{Z_{21}}}&{Z{Z_{22}}} end{array}} right]^{ – 1}}left[ {begin{array}{*{20}{c}} { – Z{Z_{13}}} \ { – Z{Z_{23}}} end{array}} right]), (Z{Z_{2 times 3}}=left[ {begin{array}{*{20}{c}} {{Z^{ – 1}}_{y}} \ {{Z^{ – 1}}_{z}} end{array}} right]Z), ({theta _n}^{2}=left[ {begin{array}{*{20}{c}} {{theta _x}^{2}}&{{theta _y}^{2}}&{{theta _z}^{2}} end{array}} right]), A is a (2 times 3) matrix, B is a (2 times 1) matrix.
When (m=2), unlike the previous two cases, the degrees of freedom of release are two. Assuming that the two-floating system can rotate about the y and z axes, and disregarding other relative motions:
With these preconditions and combining them with the case m = 1, the final transformation formula can be obtained:
where, (Z{Z_{1 times 3}}=left[ {{Z^{ – 1}}_{x}} right] cdot Z), N and M are the results obtained by rotating the two-floating system around the y and z axes.
The model accounts for the shielding effect and mutual interactions among multiple floats. Multi-degree-of-freedom connectors are utilized to link adjacent floats, and the motion response of the floats under different connector configurations is compared. To reduce the impact of wave randomness, various seeding methods are applied during the simulation process, with average values ultimately calculated. All results are derived from representative floats. Fig. 5 illustrates the motion response of the floats under different connection configurations at the 0° wave direction.
Maximum values of floats with different degree of freedom connections at 0°.
As shown in Fig. 5, the release of connector degrees of freedom results in an increased motion response, with more pronounced changes observed in rotational degrees of freedom. Purely rigid connectors, which do not release any degrees of freedom, cause the multi-floating system to approximate the motion of a single float, leading to smaller motion responses. Given the nonlinearity of second-order wave forces, the axial distance between floats is also a critical factor. Fig. 6 displays the axial distances between photovoltaic floats, demonstrating that, even under extreme conditions, a safe distance is maintained to prevent collisions between multiple photovoltaic floats. Attention must also be given to wave breaking on the photovoltaic panels, as this can significantly affect power generation efficiency and the overall lifespan of the photovoltaic system. Techniques such as applying wave-breaking methods, thickening the edges of support boards to disperse incoming waves, or erecting aluminum supports can effectively reduce air gap requirements. Fig. 7 illustrates variations in the minimum clearance under different connector degrees of freedom, ensuring wave overtopping is prevented within permissible limits. To address wave randomness, multiple wave seed numbers are incorporated in the results.
Minimum axial distance of floats connected in different degrees of freedom.
From Fig. 6, increasing the number of released degrees of freedom results in a reduction in the minimum axial distance between floats. This is primarily due to the additional degrees of freedom provided by the connectors, which expand the range of relative motion between floats and intensify the motion of the photovoltaic floats in the direction of wave propagation. The axial distance for purely rigid connectors remains effectively constant, consistently preserving the initial spacing between floats. For connectors with other degrees of freedom, the axial distance varies with the degree of freedom released; however, the values always remain above zero, thus preventing collisions between floats.
Minimum values of the float air gap for different degrees of freedom connections. (a) Float 1 air gap, (b) Float 2 air gap.
From Fig. 7, it is evident that for float 1, the air gap value with a released degree-of-freedom connection is greater than that of an unreleased degree-of-freedom connection. With the release of varying degrees of freedom, the float’s motion becomes more intense under a 45° wave direction, resulting in a smaller air gap for each type of connection. Due to the increased number of released degrees of freedom, the air gap value is minimized in the cardan configuration. Subsequently, as the wave angle increases, the air gap value demonstrates an upward trend.
In the multi-float configuration, the air gap is largest for the purely rigid connection in float 1. However, since there is no relative motion between floats 1 and 2, the difference in air gap between them is minimal, and the trend in clearance values remains consistent across different wave angles. As degrees of freedom are released, intensifying the motion between floats, the air gap value for float 1 gradually decreases. Due to connector influence, the clearance for float 1 decreases, indirectly impacting float 2’s motion and resulting in a higher clearance for float 2 than for float 1.
To reduce the likelihood of connector self-locking, the floats are arranged longitudinally in an “I-shaped” configuration, as shown in Fig. 2, which provides a schematic of the floats and connectors. Due to the presence of connectors and external environmental influences, connectors with different degrees of freedom exert various effects on three-axis loads and moments. To further examine the impact of multi-float configurations on load distribution for steel structural connectors, Fig. 8 provides load data for different degrees of freedom in connectors under various wave directions, using dual floats as an example. The positive and negative load values only denote direction, with the comparison focusing on load magnitudes. Load points are designated as point 1 and point 2, with results relative to the global coordinate system. To reduce computational error from wave randomness, simulations are conducted using five seed numbers.
Comparison of maximum values of loads at point 1 of connectors with different wave directions. (a) Longitudinal load, (b) Transverse load, (c) Vertical load, (d) Torsional moment, (e) Longitudinal moment, (f) Transverse moment.
In the analysis of the two-floating system, based on the load at Point 1 and in the scenario where the float faces the waves, the connector primarily bears longitudinal loads. The purely rigid connector generates the largest longitudinal load, primarily due to the absence of released degrees of freedom; the longitudinal load is also influenced by the mooring pretension, resulting in relatively high values. With the release of certain degrees of freedom, the corresponding directional moments are reduced. However, as the photovoltaic float uses two connectors, a minor self-locking effect may occur. Consequently, cardan connectors still experience moments, but the longitudinal moments are 4.86 times smaller than in the fully constrained setup. Due to the extensive release of degrees of freedom in the cardan connector, the float undergoes intensified motion, which can worsen the self-locking phenomenon. Influenced by these factors, the connector exhibits greater sensitivity to loads in oblique waves.
After completing the initial load calculations for the two-floating connectors, we have gained a clearer understanding of the loads borne by connectors with varying degrees of freedom. Considering the demands of floating photovoltaic systems and the increasing market requirements, it is clear that a two-floating configuration is no longer sufficient. Therefore, it is essential to build upon the existing framework by increasing the number of floats and examining the load effects on connectors in larger multi-floating systems. With a higher number of floats and no substantial changes to the basic mooring system structure, the relative motion between floats will become more pronounced, raising the potential for collisions. Fig. 9 provides the axial distance between floats; if this distance is greater than zero, it indicates a safe separation between the floats, thus preventing collisions.
Minimum axial distance between multiple floats. (a) Float 1 and Float 2, (b) Float 2 and Float 3, (c) Float 3 and Float 4, (d) Comparison of two-floating and four-floating.
With the increase in the number of floats, the relative motion among them intensifies, resulting in smaller axial distances between quadruple floats compared to those in a two-floating configuration. As the floats extend outward, the motion of the rear floats becomes comparatively more vigorous, further reducing axial distances. The computational results indicate that the release of connector degrees of freedom contributes to axial distance variations, with cardan-type connectors exhibiting the most significant effects. Additionally, using the two-floating setup as a reference, an investigation assesses whether the gap conditions maintained in the two-floating configuration persist under the quadruple-float configuration. Fig. 10 presents the results, revealing that while the air gap conditions are maintained in the two-floating system, wave overtopping occurs in the four-floating setup. This phenomenon is primarily observed in configurations with rigid and hinged connections, with rigid connections showing the most severe wave overtopping across all floats. In contrast, hinged connections result in only a slight wave overtopping in float 1 due to the characteristics of the connectors.
Minimum values of air gap between four-floating in different wave directions. (a) Float 1, (b) Float 2.
Similar to the two-floating system, the four-floating system can be regarded as two dual-floating units connected longitudinally. The overall structure requires six connection devices. To better illustrate the load variations on connection components following the expansion to a four-floating system, and with reference to the two-floating system’s results, Fig. 11 presents the load distribution at connection points 3 and 4 within the four-floating system.
Comparison of maximum values of loads at point 1 of connectors with different wave directions. (a) Longitudinal load, (b) Transverse load, (c) Vertical load, (d) Torsional moment, (e) Longitudinal moment, (f) Transverse moment.
Compared to the load generated by the two-floating connection, the loads in the four-floating system are larger, with a similar variation pattern. The maximum load occurs at the connection between floats 2 and 3. In analyzing the four-floating system, focusing on the load at connection point 3, the purely rigid connectors experience the most severe environment, mainly reflected in bearing a substantial longitudinal bending moment—4.7 times that of the two-floating system. Loads generated by cardan connectors increase gradually with the addition of floats due to self-locking phenomena. Relative to the two-floating configuration, both the bending moments and shear forces of connection devices show noticeable increases. Given the release of two rotational degrees of freedom in cardan connectors, if two joints are present, the probability of self-locking will exceed that in hinged connectors. Consequently, while cardan connectors release more degrees of freedom, they may bear higher loads than hinged connectors.
To maximize sea area utilization and expand the power generation zone, increasing the number of floats beyond the four-floating configuration is a feasible approach. As the float count rises, so does the inertial force generated by the floats, leading to a more pronounced motion response. These factors collectively contribute to more complex loads on the connections. Fig. 12 illustrates the axial distance between floats, where it is evident that the distance between floats 6 and 7 is approximately 0.3 m. Compared to the four-floating configuration, the axial distance among floats shows a reduction, particularly as the degrees of freedom in the connectors increase. This phenomenon primarily arises from the increased float counts, which diminishes the effectiveness of external constraints in limiting float motion, thereby decreasing the axial distance between adjacent modules.
Minimum axial distance between multiple floats. (a) Float 1 and Float 2, (b) Float 2 and Float 3, (c) Float 3 and Float 4, (d) Float 4 and Float 5, (e) Float 5 and Float 6, (f) Float 6 and Float 7, (g) Float 7 and Float 8, (h) Comparison of four-floating and eight-floating.
The air gap of the four-floating FPV model slightly exceeds the initial air gap criterion, and the eight-floating module, with greater motion inertia, requires an air gap value that surpasses this criterion. This adjustment can be achieved by installing an aluminum alloy bracket to accommodate the air gap requirement, though further details on this will not be discussed here. Excessive relative motion frequently results in increased loads on the connections. Analysis indicates that the highest connection loads occur in the central area of the multi-floating configuration. For the eight-floating model, the maximum load appears between floats 4 and 5, as shown by the load value at point 7 in Fig. 13.
Maximum values of loads at point 7 of connectors. (a) Longitudinal load, (b) transverse load, (c) vertical load, (d) torsional moment, (e) longitudinal moment, (f) transverse moment.
Fig. 13 shows that in the eight-floating system, the maximum load on the connectors between modules is significantly higher than that observed in the four-floating and two-floating systems. The torsional moment generated by purely rigid connectors is lower compared to hinged and cardan types, yet it bears substantial bending moments and vertical loads. While the cardan-type connector releases two rotational degrees of freedom, theoretically reducing its load, the self-locking effect between connectors causes the released degrees of freedom to regain stiffness, resulting in larger load values. To mitigate self-locking effects, reducing the number of connectors or degrees of freedom may be effective; however, further details will not be discussed here due to space constraints. Among the three connector types, the hinged connector bears the smallest load. By releasing one degree of freedom at each end, it reduces the bending moment on the central rod and is almost unaffected by the self-locking effect.
The length of the connectors is a critical factor influencing both the movement of the floats and the magnitude of the loads experienced. Using the two-floating photovoltaic system as a case study, three types of connector lengths of 0.5 m, 1.2 m and 1.9 m are analyzed to investigate the overall impact of connector length on system performance. The simulation process incorporates individual wave seeds. Fig. 14 illustrates the effects of different connector lengths on the relative distances between the floats and the loads on the connectors over a simulation duration of one hour.
Influence of connector length on relative distance and load of floats. (a) 0.5 m connectors, (b) 1.2 m connectors, (c) 1.9 m connectors, (d) Longitudinal load, (e) Transverse load, (f) Vertical load.
Analysis of Fig. 14, reveals that with connector lengths of 0.5 m, significant instantaneous longitudinal loads are generated, resulting in negative relative distances between the floats and leading to collisions. Therefore, it is critical to ensure that the distance between the floats does not become too small. As the length of the connectors increases, collisions between the floats are avoided; however, excessively long connectors may reduce their stiffness, thereby increasing the risk of fracture. The computational results indicate that the variations in motion displacement and load for connectors measuring 1.2 m and 1.9 m are relatively minor. Consequently, based on the calculated relative distances between the floats in the eight-floating photovoltaic system, the 1.2 m connectors are considered more suitable for systems with no more than eight floats.
At this stage, the connection system for FPV primarily utilizes polyester ropes. As the number of floats increases, the arrangement of these ropes becomes increasingly complex. To explore the differences between polyester ropes and rigid connectors, simulations are conducted separately for the two cases, based on the two-floating photovoltaic system, while disregarding the influence of wave randomness and ensuring consistency in external variables. Since the six degrees of freedom of the cable are fully available, there is no impact from bending moments. The simulation results are analyzed in terms of the axial forces in the different connection systems and the relative distances between the connected floats. The axial forces and relative distances between the floats are illustrated in Fig. 15.
Loads on polyester ropes and rigid connectors and relative distances between floats. (a) Relative distance between floats. (b) Load ratios for polyester ropes and rigid connectors.
The analysis presented in Fig. 15 indicates that the relative distances between floats connected by polyester ropes are the smallest, consistently remaining lower than those between floats connected by rigid connectors across various wave directions. Despite significant mooring pretension preventing collisions between the floats, the movement of those connected by polyester ropes intensifies as the number of floats increases, thereby sharply increasing the likelihood of collisions. This issue can be mitigated by increasing the spacing between the floats. In contrast, rigid connectors can effectively connect eight floats while maintaining a safe distance between them. From the point of view of load, unlike the rigid connector, the polyester ropes release six degrees of freedom without considering the influence of bending moments, while the axial forces generated by polyester ropes are significantly greater than those produced by rigid connectors.
This study primarily presents the application of rigid connectors in floating photovoltaic system. The FPV floats are simulated of three-dimensional potential flow theory. The polyester cable has the disadvantages of complex arrangement and large instantaneous axial force. The research aims to transition away from traditional polyester ropes connections, and instead investigates the load dynamics of various forms of rigid connectors. This investigation is based on parameters such as axial distance between floats, air gap, load, and expansibility. The objective is to thoroughly understand the application of single-rod rigid connectors, possessing different degrees of freedom, in FPV system. The research results provide valuable guidance for the subsequent design of rigid connectors and stress analysis in floating photovoltaics. Additionally, the study explores the interplay among multiple floats. The analysis yields the following results:
In the configuration of floating photovoltaic floats, a single-row arrangement is employed to avoid self-locking of connectors. A connector length of 1.2 m is used between the floats. The investigation into different connector types reveals that an increase in degrees of freedom results in decreased axial distances, more intense float movements, and reduced air gap values. Notably, purely rigid connectors experience significant longitudinal bending moments and vertical loads; however, the release of degrees of freedom leads to a corresponding reduction in bending moments and loads. It is important to highlight that, in cardan connectors, the self-locking effect reintroduces stiffness, generating additional bending moments. This suggests that connectors lacking released degrees of freedom are unsuitable for harsh offshore environments. To prevent self-locking, cardan connectors should be utilized individually in areas with lower wind and wave conditions.
The study of float expansion indicates that as the number of floats increases, the loads on the connectors progressively rise, and the likelihood of green water on deck also increases. The maximum loads on the connectors in eight-floating and four-floating configurations are significantly greater than those in the two-floating setup, with the maximum load point shifting toward the center as the float configuration expands. This finding indicates that the middle section of the multi-floating system is particularly vulnerable, suggesting that measures should be implemented to reduce the load on the central connector and mitigate fatigue damage.
Data is provided within the manuscript or supplementary information files.
A Correction to this paper has been published: https://doi.org/10.1038/s41598-025-91166-x
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This work is supported by the Key R&D Program of Shandong Province, China (Grant No. 2023CXGC010407), the Fundamental Research Funds for the Central Universities (Grant No. 3072024XX2705), the National Natural Science Foundation of China (Grant No. 52271268, 52471279, U24B2090), the Scientific and Technological Innovation and Development Plan of Yantai City, China (Grant No. 2023ZDCX018), the development and application project of ship CAE software.
Yantai Research Institute, Harbin Engineering University, Yantai, 264006, China
Gang Ma, Chang Zhang & Hailong Chen
Yantai CIMC Raffles Offshore Ltd, Yantai, 264670, China
Weiping Hou & Wenping Wang
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China
Jianhua Zhang
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G.Ma.: Funding acquisition, Methodology, Investigation, Visualization Resources, Project; C.Zhang.: Conceptualization, Software, Validation, Writing original draft; H.L.Chen.: Resources, Project administration; W.P.Hou. & W.P.Wang.: Validation. J.H.Zhang.: Data curation, Supervision. All authors reviewed the manuscript.
Correspondence to Hailong Chen.
The authors declare no competing interests.
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The original online version of this Article was revised: The original version of this Article contained an error in the acknowledgement section. Full information regarding the correction can be found in the correction published with this article.
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Ma, G., Zhang, C., Chen, H. et al. Hydrodynamic analysis of floating photovoltaic system constrained with rigid connectors. Sci Rep 14, 29920 (2024). https://doi.org/10.1038/s41598-024-81245-w
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DOI: https://doi.org/10.1038/s41598-024-81245-w
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