Power Output Performance and Structural Design

For the assessment of the annual power output within defined operational limits and the determination of the indicative maximum structural loads on the hull for each device configuration, the ‘principle of superposition’, as first applied to hydrodynamics by [114], has been applied.

3.3.4.1 Power Matrices

In the following analysis, this principle is applied in the determination of the power matrix of each device from the IWS response and the representation of each sea state within which the device may operate as a summation of sinusoidal waves. A random phase shift is applied to each sinusoidal wave, and as a result a Monte Carlo simulation technique is applied in the determination of the mean result for the power output at each sea state to account for the variation in each realisation of sea state through the effect of the attributed random phase shift between sinusoidal waves in

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the principle of superposition. The number of simulations has been increased until convergence of the output is achieved. The resultant electrical power matrices are illustrated in Figure 3-52, Figure 3-53 and Figure 3-54 assuming a PTO efficiency of 54%. The annual power output of each device, at each site, is then determined by multiplying the power output in each cell of the power matrix by the hours of occurrence of that sea state determined from the scatter diagrams illustrated in Figure 3-34, Figure 3-35 and Figure 3-36. The results are tabulated in Table 3-8.

Figure 3-52: Electrical Power Matrix for the BBDB M1 Location

Figure 3-53: Electrical Power Matrix for the BBDB M5 Location

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Figure 3-54: Electrical Power Matrix for the BBDB M2 Location Table 3-8: Power Output Performance of the BBDB’s at each Site

Site Power (kW)

M1 310

M5 38

M2 13

3.3.4.2 Hull Structural Analysis

The extreme Hs,50 conditions used for the structural design of the hull and mooring system are as tabulated in Table 3-6 for each site. These values were readily available from internal studies in the HMRC. However, design codes typically require return periods for individual environmental conditions of 100 years. In the case of the sites named in this study, similar studies have shown that the Hs,100 is c.

4% higher than Hs,50 [140], which it was thought was within the range of uncertainty in the analysis carried out on the raw data from the offshore M buoys. Thus H_s,50 was deemed sufficient to provide initial estimates of the hull structural mass. In [127], the range of wave periods to use with the extreme wave height is given in Section 3.7.4.2. The ‘principle of superposition’ was applied to the hydrodynamic pressure RAO of each panel of the discretised wetted hull of the structure to determine the hydrodynamic pressures during extreme conditions. The maximum panel pressure experienced by the hull during the extreme sea states was used as the design pressure. The LRFD design method was applied. A FOS of 2 was applied to the load, while a FOS of 0.95 was used on the yield strength of steel which was taken to be 235MPa for all designs as denoted for NS in [128]. A further FOS is applied to the load to account for extreme response variability from different short term sea state realisations as detailed by [127]. For this study, a multiplier of 1.3 could be considered to inflate the short term response. An alternative to the use of this multiplier is the use of the MC simulation technique to carry out many simulations to take account of the short terms variations in sea state realisations in the structural design. A simple comparison of these methods is included in the results. The configuration of the steel hulls were assumed to be constructed of standard steel plate sizes, with ‘T’ beam longitudinal and lateral stiffener beams welded to the plates as illustrated in Figure 3-24.

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Based on the ‘Plate and Stiffener’ guidelines in [128], the minimum stiffener section modulus and stiffener spacing has been varied in order to achieve the optimum balance between steel plate thickness, stiffener size and spacing to achieve minimum steel mass for a specific simulation. The plots illustrating the variation in hull steel mass with stiffener spacing are shown in Figure 3-55, Figure 3-56 and Figure 3-57.

The maximum optimum calculated structural mass for the hull is tabulated in Table 3-9 for both the MC Simulation technique using 20 simulations and the use of the DNV multiplier.

Figure 3-55: M1 BBDB Hull Steel Mass for Optimum Stiffener Spacing

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Figure 3-56: M5 BBDB Hull Steel Mass for Optimum Stiffener Spacing

Figure 3-57: M2 Hull Steel Mass for Optimum Stiffener Spacing

3.3.4.3 Mooring System Design

The ‘principle of superposition’ was again applied to the surge motion RAO of the buoy to determine the mooring line loads during extreme conditions using the typical catenary line equations as listed in [129]. There was a FOS of 1.5 applied to the

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mooring loads, as well as the aforementioned multiplier of 1.3 to account for extreme response variability due to different short term sea state realisations. The MC Simulation technique was also applied to the mooring system design to compare results. Guidelines provided by [130] for mooring chain design have been used to design the mooring chain size and mass required to resist extreme loading. The total mooring line masses as determined for each device at each site are tabulated in Table 3-9.

Table 3-9: Structural Mass and Mooring Mass Summary Site Hull Mass