Study on effect of buoyancy modules on power connection cable for 15-MW based floating green-hydrogen production system

2.1 System Design

Figure 1 and Figure 2 show the top and side views of the floating green-hydrogen platform. The UMaine's FOWT was used with an IEC 15-MW reference provided by Orcina, as an example; for the FPSO, a 103-m long default vessel provided by OrcaFlex was used. Detailed properties of the configuration are given in references [15][16]. As shown in Figure 1, the power-producing FOWT was moored using a three-point mooring method, whereas the hydrogen-producing FPSO was moored using an eight-point mooring method. The FOWT’s mooring line used R4-grade studless chain with a bar diameter of 0.22 m, while the FPSO used oil rig quality (ORQ)-grade studless chain with a bar diameter of 0.18 m. Detailed properties of the mooring lines are listed in Table 1. Figure 2 also shows a connection cable between the FOWT and FPSO that transmits electricity. The connection cable was a power cable with an outer diameter of 0.17 m, and its detailed properties are listed in Table 2.

Figure 1:

Top view of floating green-hydrogen production platform.

Figure 2:

Side view of floating green-hydrogen production platform

Table 1 :

Properties of mooring line.

Table 2 :

Properties of power connection cable.

Table 3 :

Coordinate points according to the global coordinate system

The mooring lines for the FOWT and FPSO were 830 and 340 m long, respectively. Additionally, as shown in Figure 2, the total length of the power connection cable was 850 m. Two cases were considered in this study. In the first case, buoyancy modules were attached to the connection cable, while in the second case, they were not attached. In the former, the buoyancy modules were attached to connection cable at intervals of 25 m throughout its length. Therefore, the total length of the connection cable, with the buoyancy modules attached was 850 m. Detailed properties of the buoyancy module are listed in Table 4. Finally, Table 5 lists the natural frequencies of the system, calculated through modal analysis.

Table 4 :

Properties of buoyancy module.

Table 5 :

Natural frequency of floater.

2.2 Environmental Conditions

This study was conducted assuming normal operating conditions, under which power is produced by the FOWT. The water depth was set to 200 m, and environmental conditions, such as waves, wind, and currents, were considered.

Irregular waves were generated using the JONSWAP spectrum [17]. Additionally, the IEC Kaimal spectrum was used to consider turbulent wind speeds [18]. At this time, Turbsim v2.0, an open-source program, provided free of charge by National Renewable Energy Laboratory (NREL) in USA, was used to generate turbulent wind speeds; the generated turbulent wind speed model was loaded into OrcaFlex and numerical simulation was performed [18]. Finally, the sea-level speed of the current was set to 1.0 m/s, and the current profile was calculated using the 1/7 power law. Detailed properties of the environmental conditions are listed in Table 6 [11].

Table 6 :

Environmental conditions.

3.1 Static Analysis Results

First, the effective tension in the connection cable was checked under static conditions to determine whether the buoyancy module reduced the self-weight of the cables. Figure 3 shows the effective tension applied to the connection cable in the static analysis as a function of the arc length. As shown in Figure 3, when the buoyancy module was attached, the tension was reduced by approximately 100 kN across the entire line. This shows that attaching buoyancy modules to the connection cable can effectively reduce the self-weight of the cable. Additionally, the effective tensions at ends A and B of the connection cable were different because of the difference in the measurement locations with respect to the vertical axis.

Figure 3:

Effective tension in the connection cable in static analysis as a function of arc length

3.2 Dynamic Analysis Results

Next, a dynamic analysis was conducted to confirm the differences between the two aforementioned cases. The dynamic analysis time was set to 1800 s, with a ramp time of 250 s to gradually increase the wave height before 1800 s. Figure 4 shows the wave elevation and wind speed time series, and the spectra calculated from the simulation. The regenerated values obtained using the fast Fourier transform of the time series from the spectra were confirmed to be similar to the spectral input values. This means that all the design external forces were reflected, thus proving that the analysis time was reliable. Figure 5 shows the dynamic motion graph of the floater. In this study, only a 0° environmental heading was considered. In this case, the motion of the floater was dominated by surge, heave, and pitch. In the case of the FOWT, the yaw motion is also important for power generation; therefore, only the surge, heave, pitch, and yaw motions were considered in this study.

Figure 4:

Wave elevation, and wind speed time series and spectra (input vs re-generate)

Figure 5:

Floater dynamic motion (FOWT and FPSO)

Figure 5 shows that almost no difference existed in the dynamic response of the floater irrespective of whether the buoyancy module was attached to the connection cable or not.

Moreover. Figure 5 shows that, in the surge power spectral density graph, in the case of FOWT, the surge direction natural frequency and wave peak at approximately 0.02 and 0.09 Hz, respectively had dominant influence. In contrast, in the case of FPSO, wave loads distributed at approximately 0.09 Hz dominated the FPSO surge motion. In the case of heave motion, it could be confirmed through the spectra that the wave had a major influence on both the FOWT and FPSO. As regards the pitch response, it was confirmed that the power spectral density of the FPSO was much higher than that of the FOWT, indicating that the pitch response of the FPSO was larger. This was also confirmed from a time series graph. Finally, in the case of yaw, the yaw response was more noticeable in the FOWT than in the FPSO. Additionally, a peak was observed at approximately 0.03 Hz in the yaw spectra of the FOWT. In this study, system control of the FOWT was achieved through a reference open-source controller (ROSCO)-based controller developed by the NREL [19][20]. This controller controlled the rotor speed via a PI controller based on the blade pitch angle above the rated wind speed, and the natural frequency of the pole of the pitch controller corresponding to the rated load condition was designed to be 0.03 Hz [21]. Therefore, the controller operation caused a peak in the yaw at approximately 0.03 Hz.

Subsequently, the effective tension and bending moment of the connection cable were checked to determine the dynamic changes in the connection cable depending on whether the buoyancy module was attached.

Figure 6 shows the dependence of the effective tension and bending moment of the connection cable as a function of the arc length. The maximum and average values of the effective tension decreased noticeably across the entire line when the buoyancy module was attached. The minimum value also suggested that negative tension might have been applied across the entire line when the buoyancy module was attached.

Figure 6:

Maximum, minimum and average values of the effective tension and bending moment of the connecting cable depending on the arc length

Figure 6 suggests that attaching a buoyancy module might result in larger bending moments. It could be seen that a large bending moment was applied at 1.5 m close to the FOWT and 845.5 m close to the FPSO, based on the arc length. Furthermore, when the buoyancy module was not attached, in the vicinity of 1.5 m, the maximum value of the bending moment appeared to be almost nonexistent; however, when the buoyancy module was attached, the maximum value of the bending moment increased significantly. However, unlike around 1.5 m, the maximum bending moment around 845.5 m was observed to be greater than that around 1.5 m, even when the buoyancy module was not attached. Finally, the middle part of the cable was noticed to generate almost no bending moment compared with that at the ends.

Figure 7 shows the time series and spectra of effective tension at ends A and B, and middle of the connection cable. From the time-series graph, the effective tension appears to decrease when buoyancy module was attached to ends A, and B, and the middle. Additionally, from the spectra, the power spectral density was found to be larger when the buoyancy module was not attached. This again shows that attaching a buoyancy module to the connection cable would be effective in reducing the tension. Looking at the power spectral density graph in the frequency domain, it appears that the wave load around 0.09 Hz had a dominant influence on the effective tension of the connection cable.

Figure 7:

Effective tension time series and spectra of connection cable

Figure 8 shows the time series and spectra of the bending moments at the beginning, middle, and end of the connection cable. In this case, because the boundary conditions at both ends of the connection cable were set to “hinged” rather than “fixed”, the values at 1.5 and 845.5 m were analyzed instead of at 0 and 850 m, respectively. Moreover, as can be seen in Figure 6, 1.5 and 845.5 m were the locations, where the maximum bending moment was reached at both ends, when the buoyancy module was attached. From the time-series graph in Figure 8, the change in the bending moment was found to be greater when the buoyancy module was attached than when it was not. Additionally, almost no change was observed in the bending moment at the middle part of the cable compared with that at both ends; the bending moment around 845.5 m of the connection cable showed a larger change in bending moment than around 1.5 m. Additionally, in the spectrum around 845.5 m, in addition to the wave peak around 0.09 Hz, a low-frequency peak around 0.01–0.02 Hz occurred, which was believed to be a peak due to the natural frequency of the surge direction of the FOWT. This sudden change in the bending moment could have a significant negative impact on the fatigue damage of the cable. This suggests that further research is required on the fatigue damage caused by a change in the bending moment owing to the attachment of buoyancy modules.

Figure 8:

Bending moment time series and spectra of connection cable

In conclusion, in the dynamic analysis, attaching the buoyancy module to the connection cable did not significantly affect the floater motion. However, the effective tension of the connection cable was confirmed to be reduced when the buoyancy module was attached. This suggests that when designing a connection cable attaching a buoyancy module can be one way to reduce the effective tension in the cable without affecting the floater. However, the large change in the bending moment of the connection cable with the buoyancy module attached may precipitate cable fatigue damage; therefore, further research is needed on this issue.

Author Contributions

Conceptualization, S. M. Kim and W.C. Chung; Methodology, S. M. Kim and W.C. Chung; Software, S. M. Kim and W.C. Chung; Formal Analysis, S. M. Kim; Investigation, S. M. Kim and W.C. Chung; Resources, S. K. Lim and W.C. Chung; Data Curation S. M. Kim and W.C. Chung; Writing-Original Draft Preparation, S. M. Kim; Writing-Review & Editing, S. K. Lim and W.C. Chung; Visualization, S. M. Kim; Supervision, S. K. Lim and W.C. Chung; Project Administration, S. K. Lim and W.C. Chung; Funding Acquisition, S. K. Lim and W.C. Chung.