## 4 Results  
The wave energy farm is simulated for the WEC design wave state, which is defined as 2.75 m significant wave height \(hs\) and 6.5 s zero-crossing period \(Tz\). Production from each of the 48 WECs is simulated for the same 20 minute window, and the actual power output from each WEC is stored. Figure 12(a) shows the simulated raw output power from each of the 48 WECs. The power from each absorber is individually colored with a rainbow color map, and the power scale is normalized to rated average output power for one WEC. The plot illustrates the time-shifting effect of the power peaks as the waves propagate through the array. It also clearly shows the lack of power smoothing as the wave trains passes through the farm in that the power peaks do not reach maximum power for some portion of the time. By adding up the power from each WEC according to the array and farm configuration, the aggregated power from each of the six arrays is calculated and plotted in Figure 12(b) by applying the same plot method as in the previous figure. The plot demonstrates the improvement in power quality as the power fluctuations within a single wave is smoothed out with a reduction in peak-to-average ratio from ten to three. As the rated capacity of an inverter may be exceeded for short periods, an array inverter with double power capacity of the rated power is likely to suffice. Still, this will require a converter with twice the cost compared to an average exported power, and measures to further improve the power quality should be kept in mind. Our previously published paper [14] indicates a final peak-to-average ratio for the array between 1.5 and 3 after energy storage is included, the exact figure being a result of economic optimization. Figure 12: Simulation results. All values are normalized to the average output power of the unit (WEC/array/farm). (**a**) Individual power output from all 48 WECs; (**b**) Aggregated power output from each of the six arrays; (**c**) Aggregated power output from the entire wave farm. The red curve shows the output power smoothed with a 10-second low pass filter; (**d**) Illustration of the power quality improvement as the power is aggregated in the farm; (**e**) Output power in frequency domain; (**f**) Output power distribution. The total aggregate wave farm power is calculated by adding up the six array outputs. The result is plotted in Figure 12(c) and shows a further improvement of power quality. The resulting peak-to-average power ratio is 1.56 in this case, which is higher than the target of 1.25. However, it can be seen that there is a high frequency distortion on the power signal that seems to relate directly to the wave fluctuations from the WECs. These rapid fluctuations can be filtered down quite easily with a small energy storage, and the red curve in Figure 12(c) shows the total farm output power smoothed with a 10-second filter. In this case, the peak-to-average ratio is reduced to a healthy 1.28, which is regarded as satisfactory. At this level, almost the whole of the installed conversion and transfer capacity can be utilized with negligible cost impact due to reduced power quality. The calculated rms value of the output power is only 1.63% higher than the average power. In Figure 12(d) a power time series from WEC, array and farm are plotted together to illustrate the power quality improvement as power is aggregated. The power in each case is normalized to the rated power of the unit. A small energy storage seems favorable given the high fluctuations still present on the farm power output, but it is not necessarily required to be located in the farm connection point. If distributed energy storages were instead installed on each of the arrays, and controlled or tuned to compensate the aggregated fluctuations on the farm output, the energy storage could serve dual purposes by also reducing the array peak-to-average power, which would further improve the power quality before transformation to AC.