## 4 Simulation Results and Discussion
### Offshore Wind Farm Case  
A real-life offshore 20-turbine wind farm layout is designed in WFSim in Section 2.3 and it is assumed that the wind incident is perpendicular to the wind farm rows. In this paper, it is assumed that the wind direction stays intact. This wind farm configuration uses the AIC and WRC control methods discussed in Section 3. The lower and upper bounds of the yaw misalignment angle are \(0^{\circ}\) and \(30^{\circ}\), respectively, while the lower and upper bounds of the axial induction factor are 0 and \(1/3\), respectively. Simulations are carried out and outcomes are tabulated for various mean wind speeds, i.e., 5, 6, 7, and 8 m/s, in Table 2.  
From Table 2, it is inferred that the wind farm power output is improved by adopting WRC or by combining the WRC and AIC methods. In all scenarios in which wind speed is taken into account, the percentage increase in power output is around 17%. The power gain is not as noticeable when AIC is used. However, some studies [17] suggest that AIC could boost the power output on its own, and thus more research is needed.  
The real-life wind farm flow field diagram is shown in Figure 14 for the optimized control methods in place. In the figure, the upstream turbines are T5, T10, T15 and T20. Without WRC, the wake effect on the downstream turbines is more severe as can be seen in the flow field figure. Meanwhile, the wake is steered away from the downstream turbines with WRC, resulting in improved overall performance.  
Figure 13: Two-turbine case with and without WRC for 8D spacing.  
In Figure 15, the corresponding power output from each turbine in the wind farm is presented when WRC is used in comparison to when WRC is not used. It is clear from the figure that the upstream turbine power has been reduced due to WRC; however, at the same time, considerable power improvement is observed by the downstream turbine as expected. Thus, the total wind farm power output production is increased.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wind Speed—5 m/s** & **Farm Power** & **Wind Speed—6 m/s** & **Farm Power** \\ \hline Without Control & 7.2927 MW & Without Control & 12.602 MW \\ With WRC & 8.5491 MW & With WRC & 14.805 MW \\ With WRC-AIC & 8.5195 MW & With WRC-AIC & 14.784 MW \\ With AIC & 7.2917 MW & With AIC & 12.600 MW \\ \hline
**Percentage Increase *** & **17.2281\%** & **Percentage Increase** & **17.4813\%** \\ \hline
**Wind Speed—7 m/s** & **Farm Power** & **Wind Speed—8 m/s** & **Farm Power** \\ \hline Without Control & 20.011 MW & Without Control & 29.871 MW \\ With WRC & 23.475 MW & With WRC & 34.993 MW \\ With WRC-AIC & 23.462 MW & With WRC-AIC & 34.997 MW \\ With AIC & 20.007 MW & With AIC & 29.866 MW \\ \hline
**Percentage Increase** & **17.3104\%** & **Percentage Increase** & **17.1470\%** \\ \hline \hline \end{tabular}  
* Percentage increase is calculated between without control and with WRC.  
\end{table}
Table 2: Wind farm power at various wind speeds under various control methods.  
Figure 14: Flow field diagram from WFSim for real-life wind farm at 6 m/s mean wind speed.  
Figure 16 shows the corresponding time response of power produced by individual turbines in the wind farm with and without WRC. The green curve represents the power generated by the upstream turbine, which sacrifices its power generation for the downstream turbines while WRC is in operation; that is, when WRC is employed, the power produced by the upstream turbine decreases, but the power produced by downstream turbines increases as shown in Figure 16.  
Figure 16: Time response of power produced by individual turbine with and without WRC.  
Figure 15: Power produced by individual turbine with and without WRC.