MODELING AND ANALYSIS OF A 5 MW SEMI-SUBMERSIBLE WIND TURBINE COMBINED WITH THREE FLAP-TYPE WAVE ENERGY CONVERTERS

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1 Proceedings of the ASME rd International Conference on Ocean, Offshore and Arctic Engineering OMAE2014 June 8-13, 2014, San Francisco, California, USA OMAE MODELING AND ANALYSIS OF A 5 MW SEMI-SUBMERSIBLE WIND TURBINE COMBINED WITH THREE FLAP-TYPE WAVE ENERGY CONVERTERS Chenyu Luan Centre for Ships and Ocean Structures (CeSOS) and Centre for Autonomous Marine Operations and Systems (AMOS), NTNU Norwegian Research Centre for Offshore Wind Technology, NTNU Trondheim, Norway Chenyu.luan@ntnu.no Zhen Gao CeSOS and AMOS Norwegian University of Science and Technology (NTNU) Trondheim, Norway Zhen.gao@ntnu.no Constantine Michailides CeSOS and AMOS Norwegian University of Science and Technology (NTNU) Trondheim, Norway constantine.michailides@ntnu.no Torgeir Moan CeSOS and AMOS, NTNU Norwegian Research Centre for Offshore Wind Technology, NTNU Trondheim, Norway Torgeir.moan@ntnu.no ABSTRACT Semi-submersible floating structures might be an attractive system to support wind turbines and wave energy converters (WECs) in areas with abundant wind and wave energy resources. The combination of wind turbines and WECs may increase the total power production and reduce the cost of the power. A concept of a semi-submersible with a 5 MW horizontal axis wind turbine combined with three flap-type WECs is presented in this paper. The concept is named as Semisubmersible Flap Combination (SFC). The WECs of the SFC are inspired by an optimized bottom-fixed rotating flap-type wave energy absorber. Each WEC of SFC includes an elliptical cylinder, two supporting arms, a rotational axis and a power take off (PTO) system. A time domain numerical modeling method for the SFC is presented. The numerical model is using the state-of-the-art code Simo/Riflex/Aerodyn. Linear rotational damping is introduced to model the effects of the PTO system. The choice of a PTO damping coefficient and of the mass of the elliptical cylinders has a significant effect on the power generated by the WECs. Such effects have been addressed and discussed in the paper through a sensitivity study. INTRODUCTION The huge potential of offshore wind and wave energy are attractive to satisfy the increasing demand for electric power, to increase the ratio of renewable energy resource to nonrenewable energy resource and to reduce the emission of CO 2. Although the cost of on-shore wind energy has been reduced to a fairly competitive level when compared with traditional power such as thermal power and hydropower, the cost of offshore wind turbines is one of the main handicaps for harvesting offshore wind energy. Offshore wind turbines are much more expensive than on shore wind turbines due to the high cost of the supporting structures, sea transportation, installation, maintenance, operation and offshore grids and cables. In order to reduce the cost of generated power, developing large rated wind turbines is considered as a potential direction for offshore wind energy. Up to now, 6-MW wind turbines produced by Alstom have been working at the Belwind site off the coast of Belgium, while various other 6- MW offshore turbines are coming to the market [1]. Semisubmersible wind turbines are considered as a potential solution when the depth of the water is above 100m. Designs of 5-MW semi-submersible wind turbines, e.g. WindFloat [2] and the design of the OC4 semi-submersible wind turbine [3, 4] have been published. The displacement of the OC4 concept is Copyright 2014 by ASME

2 tonnes [3, 4]; however, the total mass of the 5-MW wind turbine itself is 600 tonnes [5]. The ratio of the mass of the wind turbine to the displacement is quite small. It indicates a big potential for the cost reduction of the hull. In addition to offshore wind energy, the potential use of wave energy is being explored. The research on wave energy converters focuses on maximizing the power harvested by the wave energy converters through optimizing the control and the geometrical configuration of the energy absorbers, while analysis and design of the supporting structures are simplified. In fact, however, an appropriate design for supporting structures is also a critical issue for the cost of the wave energy converters. This paper explores the possibility of combining wind turbines and wave energy converters on one semi-submersible platform. A combined concept of a 5-MW semi-submersible wind turbine and three rotating flap-type WECs is proposed and introduced in the present paper. The concept is named Semisubmersible Flap Combination (SFC). The SFC is described in detail in the next section. In addition to SFC, there are several combined concepts proposed by other researchers, such as Spar-Torus Combination (STC) ([6-8]) and other concepts [9-11]. Time domain numerical modelling for such novel designs is a new challenge since the available commercial codes, such as Simo/Riflex [12, 13], are initially designed for solving the motions of offshore vessels or solving the sea keeping problem of offshore platforms combined with slender structures such as mooring lines and risers. In this paper, the numerical model of SFC is based on Simo/Riflex/Aerodyn [14-17], which is a state-of-theart code. The modeling method is described in a subsequent section. A sensitivity study with respect to the effects of the mass of the WECs of the SFC and the PTO damping coefficients used in the numerical model on the generated power has been carried out. The mass of the WECs of the SFC and the damping coefficients are selected based on this sensitivity study. DESCRIPTION OF THE SFC CONCEPT The layout of the SFC is shown by Figure 1. It is seen that three WECs with elliptical cylinders and supporting arms are mounted on a semi-submersible wind turbine. The semisubmersible wind turbine is named 5-MW-CSC [25]. It includes a 5-MW NREL reference wind turbine [5], a hull and three catenary mooring lines. The hull is composed of a central column, three side columns and three pontoons. The wind turbine is located on the central column. The side columns are used to provide restoring stiffness to prevent capsizing. Pontoons are used to connect the side columns and the central column as an integrated structure. The hull of 5-MW-CSC is braceless and looks clean. The distance from the central line of the central columns to the central line of each side column, is 41 meter, which is large. This is because the 5-MW-CSC needs sufficient restoring stiffness from the second moment of water line area. Moreover this layout provides ample space for the WECs. The location and dimension of the three WECs are shown in Figures 2 and 3. The SFC is described in a body-related coordinate (XYZ) [18]. The positive direction of each axis of the body-related coordinate is shown in Figures 2 and 3. The origin (O) of the coordinate is located at the still water line (SWL). Figure 3 shows a single WEC mounted on a pontoon of the 5-MW-CSC. The WEC includes an elliptical cylinder, two supporting arms and a PTO system. The elliptical cylinder can oscillate about an axis which is mounted on the upper surface of the pontoon and is parallel to the longitudinal axis of the pontoon. The elliptical cylinder can absorb wave energy and transfer it into the kinetic energy through the rotational axis. The rotational axis is connected to the PTO system, which finally converts the kinetic energy to electrical power. The PTO system and the rotational axis are not shown in Figure 3. The effects of the PTO system and the rotational axis are simplified by a constant linear damping coefficient in the numerical model introduced in the next section. In the present paper, we focus on introducing the design of the elliptical cylinder and the design of the supporting arms. More information with respect to the physical design of the PTO system and the rotational axis will be available in 2014 (after the SFC concept has been tested in the Hydrodynamic and Ocean Engineering Tank of Ecole Centrale de Nantes (ECN)). Figure 1 Layout of the SFC 2 Copyright 2014 by ASME

3 cylinders are introduced in the WECs of the SFC. The length of one of the elliptical cylinders, in Figure 3, is 20m. The cross section of the elliptical cylinder is shown in Figure 4. Based on the coordinate described in Figure 4, the configuration of the cross section can be expressed by Equation (1). ( Y 1.75 )2 + ( Z 3.5 )2 = 1 (1) Figure 2 Location and dimensions of WECs (Top view), the unit is meter Figure 3 Location and dimensions of WECs (side view), the unit is meter Regarding the design of the WECs of the SFC, a rotating flap-type WEC concept has been selected. The geometrical optimization of rotating flap-type WECs oscillating about a fixed axis has been reported by [19]. Several geometries with different simple cross sections, i.e. vertical flap, inclined flap, curved flap, circular cylinder, submerged elliptical cylinders, have been systematically considered. Among the investigated cross sections, a submerged elliptical cylinder was found to have the best performance in minimizing the two simplified cost criteria specified in [19]. For this reason, the elliptical Figure 4 Cross-section of elliptical cylinder The major axis of the elliptical cross-section is 7m. It is about one third of the distance (24m) from the upper surface of the pontoon to the SWL. This choice is made as a simplified interpretation of the conclusions in [19] A common feature of the optimal configurations is that when the geometries are optimized over a uniform distribution of wave frequencies from 0.4 to 1.3 rad/s, the body generally spans from the free surface to no more than approximately one third of the water depth, while the rotation axis tends to be located close to the sea bottom. It should be noted that the conclusion is applicable to a bottom supported flap. The minor axis of the elliptical cross section is simply set to be 3.5m, which is half of the major axis of the elliptical cross section. The elliptical cylinder is close to SWL. The distance from the upper edge of the elliptical cylinder to SWL is 2m. The mass of the elliptical cylinder is selected as 100 tonnes based on a sensitivity study shown in a later section. The mass of the elliptical cylinder includes the mass of steel and the mass of ballast inside the elliptical cylinder. We assume that the mass of the elliptical cylinder is uniformly distributed along the surface of the elliptical cylinder. Therefore, the center of gravity of the elliptical cylinder is at the same position as the center of buoyancy. However, it should be noted that the gravity of the elliptical cylinder is not in balanced with the buoyancy of the elliptical cylinder. The displacement of the elliptical cylinder is 394.5tonnes. The elliptical cylinder is connected to the PTO system and the rotational axis through two supporting arms. Design of the supporting arms is a big challenge. The supporting arms should have sufficient stiffness and strength. The upper ends of the supporting arms are clamped to the elliptical cylinder, while the lower ends are hinged to the pontoon. The joints between the 3 Copyright 2014 by ASME

4 supporting arm and the elliptical cylinder or the pontoon are complex. Consequently, finite element models of the structure may be needed for ultimate limit state (ULS) and fatigue limit state (FLS) design checks. In the present paper, a conservative design of the supporting beams is introduced. Axis symmetrical pipe cross-section is used. The outer diameter is 1.5m. The thickness is 0.05m. The high strength steel (Density=7850 [kg/m^3]; Young s modulus=2.1e+11[pa]; Yield stress=355[mpa]; Poisson ratio=0.3; Structural damping ratio=1%) is the selected material. There is no ballast inside the supporting arms. The length of a single supporting arm is 18.5m. It is the vertical distance from the upper surface of the pontoon to the geometrical center of the cross-section of the elliptical cylinder, see ac and df in Figure 5. As a result, the mass of a single support arm is tonnes. The displacement of a single supporting arm is 33.5 tonnes. The design of the arms will be refined in the future. In summary, dimensions of a single WEC have been tabulated in Table 1. Three WECs are mounted on three pontoons of the 5-MW-CSC respectively. The arrangement of the three WECs is shown in Figure 2. The distance between the central line of the central column and the inner edge of an elliptical cylinder is 15m. The distance is used to prevent collisions between the WECs. The displacements of the WECs are larger than the mass of the WECs. If we want to make SFC have the same draft as the 5-MW-CSC, we need to reconsider the ballast water inside the side columns and the pontoons of the 5-MW-CSC. The three WECs introduce tonnes displacement, while the total mass of the elliptical cylinders and the supporting arms of the three WECs is tonnes. Consequently, the pontoons of the semi-submersible of the SFC are filled with ballast water, while the ballast water in the side columns of the SFC is from the position, which is 16.5m from the bottom of the side columns, to the bottom of the side columns. There is no ballast water in the central column. We assume that there is no free surface due to the ballast water. The mass of the hull of the supporting semi-submersible of the SFC (including the mass of steel and the mass of ballast water inside the hull) is tonnes. The position of the center of gravity (COG) of the hull with respect to the body-related coordinate is (0 m, 0 m, m). The mass matrix with respect to O of the body related coordinate is tabulated in Table 2. Table 1 Dimension of a single WEC Length of major axis of the elliptical cross-section [m] 7 Length of minor axis of the elliptical cross-section [m] 3.5 Length of an elliptical cylinder [m] 20 Mass of an elliptical cylinder [tonnes] 100 Displacement of an elliptical cylinder [tonnes] Length of a supporting arm [m] 18.5 Outside diameter of a supporting arm [m] 1.5 Inside diameter of a supporting arm [m] 1.4 Mass of two supporting arms [tonnes] Displacement of two supporting arms [tonnes] 67 Table 2 Mass matrix of the hull of the supporting semisubmersible of SFC with respect to O in the body-related coordinate; the unit is ttttt m 2. Ixx Iyy Izz Ixy Iyz Ixz NUMERICAL MODELLING Developing time domain numerical model for combined floating wind turbine and WEC concepts is a new challenge for researchers. Although the commercial codes used in the offshore oil and gas (O&G) industry have been used for developing numerical models of floating wind turbines, the commercial codes are initially designed for solving the motions of offshore vessels or the sea keeping problem of offshore platforms combined with slender structures such as mooring lines and risers. The difficulties of developing a numerical model for the SFC include 1) Each WEC should be able to rotate with respect to its rotational axis; 2) The motions and loads on the floating wind turbine and the WECs should be fully coupled; 3) The effects of PTO system should be included in the numerical model; 4) Environmental loads on the floating wind turbines and the WECs should be well represented. The authors use Simo/Riflex/Aerodyn [14-17] to develop the time domain numerical model of the SFC. Simo/Riflex/Aerodyn is a state-of-the-art code for time domain numerical simulation of floating wind turbines. For floating wind turbines, slender structures such as blades, shaft of drive train, wind turbine tower and catenary mooring lines, can be modelled by beam elements in Riflex [13-15]. The blades are connected to the tower through the shaft. The hub and nacelle are modeled as rigid bodies attached to the shaft and the top of the tower [14, 15]. Aerodynamic loads on the blades and tower are calculated by Aerodyn [17]. Hydrodynamic loads on the mooring lines are considered by Morison formula. Pitch control of the blades and the effect of the generator in the nacelle are added into the numerical model through a dll file [16]. The torque of the generator is calculated by the dll file based on the rotational speed of the shaft. A flex joint [13-15] is applied to the shaft to make the shaft able to rotate about the longitudinal axis of the shaft, while the loads on the blades, the hub and the shaft and the generator torque, can be transferred through the flex joint to the tower in the numerical model. The flex joint can also be applied to the arm structures of the WECs to make each elliptical cylinder of the WECs rotate about its rotational axis. Figure 5 shows a WEC attached to a pontoon. The elliptical cylinder is considered as a rigid body with 6 d.o.f. with respect to O of the body-related coordinate, which is denoted by x. x is a 6 1 vector. Based on linear potential theory, the hydrodynamic loads on the elliptical cylinder can be expressed in the frequency domain as: 4 Copyright 2014 by ASME

5 F hhhhhhhhhhhh = F ee (ω) A(ω)x C(ω)x KK (2) where: F hhhhhhhhhhhh denotes the hydrodynamic loads on the elliptical cylinder in the frequency domain. F ee (ω) denotes the frequency-dependent first order wave excitation loads on the elliptical cylinder A(ω) is frequency-dependent added mass matrix C(ω) is frequency-dependent potential damping matrix K is restoring stiffness matrix. It is noted that F ee (ω) is a 6 1 vector, while A(ω), C(ω) and K are 6 6 matrices. The terms in Equation (2) can be calculated by commercial hydrodynamic codes such as WAMIT [20]. By applying Fourier transformation to Equation (2), the linear potential hydrodynamic loads on the elliptical cylinder can be expressed in the time domain as [21]: L = R ppppppppp (t) + k(t τ)x (τ)dd C x (t) A x (t) KK(t) (3) where, R ppppppppp (t) denotes time-dependent first-order wave excitation loads. It is determined by F ee (ω). k denotes retardation function. It considers the memory effects of the wave loads and is determined by A(ω) or C(ω). A is added-mass matrix corresponding to high-frequency limit; C is potential damping matrix corresponding to high-frequency limit, which is equal to zero when the high-frequency limit is equal to infinite. The supporting arms of each WEC are modelled by beam elements. For the WEC shown in Figure 5, the upper ends of the supporting arms, which are point c and point f, are clamped to the elliptical cylinder. In the numerical model, the clamped relationship is modelled by applying master-slave relationship on x and the 6 d.o.f. of each upper end of the supporting arms. As a result, the beam elements of the supporting arms are coupled to the elliptical cylinder. If the reaction loads of the upper ends in the bodyrelated coordinate with respect to O are denoted by R bbbb (t, x, x ), the motion equation of the elliptical cylinder described in the body-related coordinate with respect to O can be expressed as: + (M + A )x (t) + C x (t) + k(t τ)x (τ)dd + KK(t) = R ppppppppp (t, x, x ) + R bbbb (t, x, x ) + R ooooo (t, x, x ) (4) where, M is the body mass matrix of the elliptical cylinder with respect to O. R ooooo (t, x, x ) denotes the viscous drag and other loads on the elliptical cylinder, such as gravity and buoyancy. R bbbb (t, x, x ) is given by the beam model of the supporting arms. An iterative process is needed. Figure 5 One of the WECs of the SFC attached to one of the pontoons of the SFC Regarding the lower ends of the arm structures, if we want to mount the WEC on the pontoon, we can model the hull of floating wind turbine as a rigid body, which is similar as what we did for the elliptical cylinder. Similarly, master-slave relationship is applied on the 6 d.o.f. of the hull and the one of each lower end of the supporting arms. In the numerical model of the SFC, the hull of the semisubmersible wind turbine and three WECs are modelled as rigid bodies. Each body has 6 d.o.f.. Consequently, the numerical model of SFC is considered as a four-body (multi-body) system. It is noted Equation (2), Equation (3) and Equation (4) are used for the system with single rigid body. As what has been illustrated in [22], we can express the loads and motions of the four-body system in the same form of Equation (2), Equation (3) and Equation (4) except the matrices and vectors in Equation (2), Equation (3) and Equation (4) should include all d.o.f. of each body of the four-body system. That means the 6 1 vectors should be updated to 24 1 since the four-body system has 24 d.o.f. in total. The 6 6 matrices should be updated to For example, in the four-body system A(ω) is expressed as: A1,1 A 1,2 1,3 A A 1,4 A 2,1 A 2,2 A 2,3 A 2,4 A(ω) = A 3,1 A 3,2 A 3,3 A 3,4 (5) A 4,1 A 4,2 A 4,3 A 4, A i,j (i = 1,2,3,4; j = 1,2,3,4) is 6 6 matrix. A i,j expresses the added mass on body i due to 6 d.o.f. motions of body j. The option of multi-body analysis of WAMIT can be 5 Copyright 2014 by ASME

6 used to calculate F ee (ω), A(ω) and C(ω) of the four body system. However, due to the limitation of the matrix solver, the current version of Riflex can only include the diagonal terms of the frequency dependent matrices. In another word, the cross terms, e.g. A i,j, (i j), are equal to zero in the coupled analysis of Simo/Riflex/Aerodyn. It means that part of the hydrodynamic interaction effects cannot be included in the numerical model of the SFC. This drawback will be fixed by a future version of Riflex. In addition, the effects of hydrodynamic interaction on the performance of the SFC will be investigated based on laboratory tests at the Hydrodynamic and Ocean Engineering Tank of Ecole Centrale de Nantes (ECN) within April-May, As has been mentioned above, flex joints are employed to make each of the elliptical cylinders and the supporting arms able to rotate about the rotational axis. In the numerical model, the flex joints cannot be applied on the lower ends of the arm structures, such as point a and point d, since master-slave relationships have been specified on these ends. In practice, each supporting arm is divided into two parts. For example, the support beam 1, in Figure 5, is divided as ab and bc. The flex joint is applied on point b. The length of ab is 0.1m. The effect of the PTO system is modelled in a simplified manner (as linear rotational damping) with respect to the rotational axis. Constant linear damping coefficient with respect to the rotational axis is specified in each of the flex joints on the arm structures. The constant linear damping coefficient is equal to 650 KN*m*sec/deg. It is selected based on a sensitivity study with respect to the effects of the mass of the elliptical cylinders and the damping coefficient on the power production of the three WECs of the SFC. The details are shown in the next section. The control mechanism of the WECs is not included in the current model of the SFC. That means that the linear damping coefficient due to the PTO system is considered as a constant value during the time domain simulation. The performance dependent damping coefficients should be considered in the future. In addition, it should be noted that the linear assumption of the hydrodynamic potential loads on the hull and the WECs means that the oscillation of each elliptical cylinder with respect to its rotational axis is expected to be relatively small, while the non-linear effects, i.e. the effects of WECs out of water and the effects of second order hydrodynamic loads, have not been included except for the viscous drag on the hull and mean drift forces on the WECs. Regarding hydrodynamic interaction, it is possible to carry out the frequency-domain hydrodynamic analysis in Wadam, but the inclusion of all of the cross terms of the hydrodynamic coefficients (such as added mass and potential damping) are not possible in the current version of the Riflex. However, if the Wadam analysis includes the hydrodynamic interaction, the excitation forces on each body accounts for the presence of other bodies and the hydrodynamic interaction for these forces is included. This is similar for the diagonal terms of the added mass and damping coefficients. But, as mentioned, only the cross terms of the added mass and damping (that is the wave loads acting on body i due to other bodies motions) are not included. In summary, the features of the numerical model of SFC are tabulated in Table 3. Table 3 Summary of the features of the numerical model of SFC Mass model Structure model External load model The hull of the semisubmersible floater Nacelle and hub Mooring lines and supporting arms Tower Three blades Three elliptical cylinders Integrated mass Distributed mass Integrated mass Rigid body Flexible body, beam element Rigid body 1) Gravity/Buoyancy 2) First order wave loads (potential theory) 3) Viscous force (Drag term of the Morison formula) 1) Gravity 1) Gravity/Buoyancy 2) Morison formula 1) Gravity 1) Gravity 2) Aerodynamic loads (Aerodyn) 1) Gravity/Buoyancy 2) First order wave loads (potential theory) 3) Mean drift force SENSITIVITY STUDY WITH RESPECT TO THE EFFECTS OF THE MASS OF THE ELLIPTICAL CYLINDERS AND THE DAMPING COEFFICIENTS ON THE POWER PRODUCTION OF THE WECS As mentioned above, the linear constant damping coefficients specified at the flex joints on the supporting arms of the WECs are used to model the effect of the PTO system. The damping coefficients and the mass of the elliptical cylinders have significant influence on the generated power. In order to illustrate this issue, a single WEC could be considered. Reference is made to Figure 5 to represent the WEC and introduce the following assumptions, 1) We remove the semi-submersible wind turbine and the master-slave relationships between the hull and point a and point d ; 2) We fix all the d.o.f. of Point a and point b at z = -24m in the body related coordinate. 3) We assume the elliptical cylinder and the two supporting arms rigidly rotate about the rotational axis which is pointed from point b to point e. 4) We establish a right-hand coordinate x y z. The origin (O ) is located at point e. x is in line with the direction of the 6 Copyright 2014 by ASME

7 rotational axis (from point b to point e ). z is parallel to z axis of the body related coordinate. x y z is fixed in space. Consequently, the WEC has only one rotational d.o.f. The rotational d.o.f. is denoted by x(t). In the x y z coordinate, the frequency domain expression of x(t) can be written as x(t) = R{X(ω)e iii }, while the moment induced on the rotational axis by the first-order wave loads on the WEC can be written as F ee (t) = R{F(ω)e iii }. X(ω) and F(ω) are frequency dependent complex numbers. R means the real part of the complex. x(t) and F ee (t) are sinusoidal functions corresponding to frequency ω. In the frequency domain, the motion equation of x(t) in the x y z coordinate can be expressed as: as: s ω 2 I + m a (ω) + iω(b(ω) + b PPP ) X(ω) = F(ω) (6) The mean generated power P mmmm (ω) is then expressed P mmmm (ω) 1 = 2 b PPP F(ω) 2 (b(ω) + b PPP ) 2 + ω 2 (I + m a (ω) sω 2 ) 2 (7) It should be noted all the terms in Equation (6) and Equation (7) are described in the x y z coordinate. m a (ω) is the integrated added mass moment with respect to the rotational axis of the WEC. It is frequency dependent, while it is induced due to the unit oscillation of the WEC system with respect to the rotational axis. Similarly, b(ω) is frequency dependent potential damping. I denotes the moment inertia of the system with respect to the rotational axis. s is a coefficient of the restoring moment. Since the effect of out of water of the elliptical cylinder during the operation is not considered, s x(t) denotes the restoring moments on x due to the gravity and buoyancy of the elliptical cylinder and the supporting arms when the WEC is rotated to x(t). From Equation (7) we can see that the variation of the mass of the elliptical cylinder and the variation of b PPP can significantly change P mmmm (ω), while F(ω), b(ω) and m a (ω) are determined by the geometrical configuration. In order to specify the mass of the elliptical cylinders of the WECs of the SFC and the damping coefficients of the flex joints in the numerical model, a sensitivity study has been done. In this study, we focus on the performance of a three-wec system The three WECs of the three-wec system are located at the same positions as the three WECs of the SFC. The three- WEC system does not include the floating wind turbine. Consequently, instead of being connected to the pontoons of the floating wind turbine, the lower ends of the supporting arms of the WECs are fixed at z = -24m. The waves come from zero direction shown in Figure 2. There is no wind loads. 9 load cases have been selected. They are tabulated in Table 4. A JONSWAP spectrum with a peakedness =3.3 is employed for these load cases. The significant wave height varies from 1m to 5m, while the peak period of the spectrum varies from 8s to 13s. The mass of an elliptical cylinder varies from 50 tonnes to 300 tonnes in intervals of 50 tonnes. The constant damping coefficient for a flex joint is varied from 333 KN*m*sec/deg to 3000 in intervals of 333 KN*m*sec/deg. Consequently, for each case, there are 6 9 = 54 models with different mass and damping coefficients. For each model, a 1-hour irregular wave time domain simulation with the same random seed has been done. In total, 9 54 = hour simulations with different load cases and different models have been carried out. For each simulation, the mean value and the standard deviation (std) of the generated power have been calculated. It should be noted that each of the WECs has two flex joints. As a result, If we denote the damping coefficient of one of the flex joints as b ffff jjjjj, the power generated by a WEC is expressed in KW as: P WWW _1 = 2 b ffff jjjjj Ω dddddd Ω rrr (8) where, Ω dddddd denotes the rotational speed of the rotational axis with the unit degree/second. Ω rrr denotes the rotational speed of the rotational axis with the unit rad/second. This is because the unit of b ffff jjjjj used in the numerical model is KN*m*sec/deg rather than KN*m*sec/rad. Table 4 Selected load cases Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case8 Case9 Hs (m) Tp (s) The mean value of the total power of the three WECs of Case4, Case5 and Case6 are shown in Figure 6, 7 and 8. It should be noted that the total power of the three WECs refers to kinematic power. An efficiency factor, which could be 0.5 for a hydraulic PTO system, should be considered if electrical power is to be calculated. The mean value and std of the total power of the three WECs vary with the damping coefficient and the mass of the elliptical cylinders. All the results for the 9 cases show the upper limit of the mean and std of the power decrease with the increasing of the mass of elliptical cylinders. We can tune the mean and std of the generated power by tuning the damping coefficients. The effect of the damping coefficients are related to the mass of the elliptical cylinders and the peak periods of the wave spectra. For the models with the mass of each elliptical cylinder equals to 50 tonnes, in Case 4 (Figure 7), the damping coefficients varying within the range roughly from 1000 KN*m*sec/deg to 2666 KN*m*sec/deg correspond to mean values of the total power for the three WECs larger than 200KW. However, in Case5 (Figure 7), the range is changed to from 333 KN*m*sec/deg to 1200 KN*m*sec/deg. From Case4 to Case5, Tp moves from 8 seconds to 11 seconds. If we increase Hs from 1m to 3m and 5m while we fix Tp, the results show the mean and std of generated power are proportional to the square of Hs. In addition, the std of the generated power follows the mean value of the generated power. Therefore, if 7 Copyright 2014 by ASME

8 the mean value of the power is large, the std of the power is large. However, the damping coefficients are constant during the simulation. An appropriate control mechanism could be helpful to reduce the std of the generated power. We should also be aware of the fact that the performance of the WECs could be more complex when they are combined with semi-submersible wind turbines. The responses of the SFC in irregular waves and the coupled effects between the semi-submersible wind turbine and the WECs have been discussed in [23]. For a given site, an optimal damping coefficient, which maximizes the total annual power absorption of the three-wec system with a given mass, could be identified. In summary, the mass of the elliptical cylinders and the damping coefficients of the SFC are selected based on the sensitivity study shown in the present section. The simulation results indicate that a relatively small mass of elliptical cylinders and a relatively small damping coefficient are preferable to increase the mean value of the generated power of the three WECs. However, it should also be noted that the standard deviation of the generated power will also increase at the same time. Finally, the mass of each elliptical cylinder is specified as 100 tonnes, while the damping coefficient of each flex joint in the numerical model is specified to be 650 KN*m*sec/deg. Figure 7 Contour lines of the mean value of the total power for the three WECs for 56 different models in Case 5 Figure 8 Contour lines of the mean value of the total power for the three WECs for 56 different models in Case 6 Figure 6 Contour lines of the mean value of the total power for the three WECs for 56 different models in Case 4 CONCLUSIONS A novel combined semi-submersible wind turbine and WECs concept, named SFC, has been described in the present paper. It consists of a 5-MW semi-submersible wind turbine and three flap-type WECs. A time domain numerical model of the SFC has been developed by using the Simo/Riflex/Aerodyn, which is a stateof-the-art code. The hull of the semi-submersible wind turbine and the three elliptical cylinders are considered as a multi-body system. They are modelled in Simo. The wind turbine blades, the tower and the supporting arms are modeled by beam elements in Riflex. The elliptical cylinders are connected to the hull through the arm structures. Flex joints are used to make the arm structures able to rotate around the relevant axes. Linear 8 Copyright 2014 by ASME

9 rotational damping is introduced to model the effects of the PTO system. Due to the limitation of the matrix solver of Riflex, part of the hydrodynamic interaction effects cannot be included in the current model. That means the cross terms of the added mass and damping (that is the wave loads acting on body i due to other bodies motions) are not included. The limitation will be remedied in a future version of Riflex, while laboratory tests and numerical simulations have been planned to investigate hydrodynamic interactions in The generated power of the WECs is sensitive to the mass of the elliptical cylinders and the damping coefficients of the flex joints. The results of the sensitivity study for the three- WEC system without the floating wind turbine show that 1) the upper limit of the mean and std of the power decreases with increasing mass of the elliptical cylinders. 2) The effect of the damping coefficients are related to the mass of the elliptical cylinders and the peak periods of the wave spectra. 3) The wave spectrum, the mean and std of generated power are proportional to the square of Hs when Tp is fixed. ACKNOWLEDGMENTS The authors acknowledge the financial support from the Research Council of Norway granted through the Centre for Ships and Ocean Structures, the Norwegian Research Centre for Offshore Wind Technology (NOWITECH), NTNU and the European Union Seventh Framework Programme theme FP7- ENERGY (MARINA Platform Marine Renewable Integrated application Platform, Grant Agreement no ). 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10 International Conference on Ocean, Offshore and Arctic Engineering, no, OMAE , Nantes, France. [23] Michailides, C., Luan, C., Gao, Z. and Moan, T., (2013), Effect of flap type wave energy converters on the response of a semi-submersible wind turbine, In 33rd International Conference on Ocean, Offshore and Arctic Engineering, no.omae , San Francisco, USA [24] Kurniawan, A. and Moan, T., (2013), Optimal geometries for wave absorbers oscillating about a fixed axis, IEEE Journal of Oceanic Engineering, 38: [25] Luan, C., Gao, Z., and Moan, T., Conceptual designs of a 5-MW and a 10-MW semi-submersible wind turbine with emphasis on the design procedure, Journal of Offshore Mechanics and Arctic Engineering (submitted, 2014). 10 Copyright 2014 by ASME