## 3 Simulation Model  
The simulations are performed on the basis of the WEC prototype test site _Wavehub_ located west of Cornwall, England as shown in Figure 5. The test site is funded and supported by the renewable energy program administrated by the British government. The site includes a sub-sea power substation that allows for electrically connecting the WECs to the grid. Wavehub has been surveyed and monitored for an extensive period and work is still ongoing to calculate true statistical wave data for the site. The wave scatter diagram and the directional spectrum for Wavehub is plotted in Figure10(a) and Figure 10(b), respectively. The directional scatter is heavily dominated by waves from the west, and the directional plot must be logarithmically scaled to show all the directions observed.  
The model used for the farm simulation is based on the single absorber model for Lifesaver ([PERSON] _et al._, 2007, [PERSON] _et al._, 2008) [15,16]. The simulation model solves Equation (1) for \(\zeta\left(t\right)\) in the time domain. The index denotes the mode of motion, given by the six _degrees of freedom_  
Figure 9: Wave farm design. (**a**) Farm configuration; (**b**) Electrical configuration.  
(DOF) of motion for the floater. The excitation force matrix \(F_{e,i}\) is the time-dependent force due to incident waves, and M denotes the mass of the system.  
\[F_{e,i}\left(t\right)-F_{D,i}\left(t\right)=M\frac{d^{2}\zeta\left(t\right)}{dt^ {2}} \tag{1}\]  
\[F_{D,i}\left(t\right)=F_{r,i}\left(t\right)+F_{d,i}\left(t\right)+C_{i}\cdot \zeta_{i}\left(t\right)+F_{PTO}\left(t\right) \tag{2}\]  
\(F_{D,i}\) accounts for the sum of all the damping forces in Equation (2), where \(F_{r,i}\) accounts for the time-dependent forces on the floater due to radiation of waves. The term \(F_{d,i}\) accounts for non-linear damping terms, mainly the drag forces. \(\zeta_{i}\) is the time-dependent motion of the floater, \(C_{i}\) is the restoring force matrix accounting for the hydrostatic pressure acting on the floater, and \(F_{PTO}\) is the time-dependent force applied from the PTO. The PTO is modeled as a rope and winch system that is tightly moored to the sea floor. Detailed performance curves for Lifesaver are presented in our previous article [17].  
Since the simulation is based on a detailed 6 DOF model for Lifesaver, FO keeps the simulation model confidential. However, such high level of complexity is not essential for this study, and a simplified 1 DOF model would produce almost the same result. It is therefore possible for a third party to qualitatively verify the results published here without detailed knowledge of the simulation model used.  
To simulate a wave state, a 20-minute time series of irregular waves is generated based on the JONSWAP wave spectrum [18]. The wave state is defined by the significant wave height \(h_{s}\), the zero crossing period \(t_{z}\), and the wave direction \(\theta\). The subsequent excitation forces are then calculated and the simulation is performed for the full length of the time series. The simulation model also takes into account PTO and generator losses, and the model outputs a 20-minute time series of exported electrical power from the WEC. The simulation model has undergone many years of development and testing, and is verified against real production data from several prototypes, including Bolt\({}^{\circled  
Array and farm simulations are performed by running the simulation model separately for each absorber in the array/farm. All absorbers are simulated for the same wave scenario, and the wave propagation through the array is modeled in detail to produce an authentic result. The simulation model does not take interference between the WECs into consideration. This is handled by separate modeling work and is described in the next section.