# Model Based Open-Loop Wind Farm Control Using Active Power for Power Increase and Load Reduction
## 3 Simulation Result  
### Flow Field in Wind Farm  
Figure 5 shows snapshots of wind fields obtained from the simulation for two different mean wind speeds with turbulence and with and without the wind farm control. Two different mean wind speeds are 8 m/s and 10.5 m/s. The former is the wind speed lower than the rated wind speed of the wind turbine, and the latter is the wind speed close to the rated wind speed of the wind turbine. The wind is propagating from the left to the right, and therefore the leftmost wind turbine is the most upstream wind turbine. The three short vertical lines represent the turbines. The spacing of wind turbines was 7 RD which is the spacing of the Danish Horns Rev 1 offshore wind farm. The turbulence intensity was 0.075. Because of the turbulence, the wind speed fluctuates and the plots of Figure 5 shows the wind speed distribution at a particular time at which the wind speed at the most upstream wind turbine is 8 m/s (for Figure 5a,c) or 10.5 m/s (for Figure 5e,g). The two plots in a row such as Figure 5a,b or Figure 5c,d show the wind field in the wind farm, and the steady wind fields normalized by the free stream wind speed, respectively. The latter figure includes numbers above and below the steady wind fields. The former represents the distance in rotor diameter from the most upstream wind turbine and the latter represents the largest wind speed deficit in the wake region. The wind speed deficit increases when the wind speed is further reduced in the wake region. In addition, it reduces as the wind speed in the wake region becomes recovered. In addition, a set of two rows such as the row with Figure 5a and the row with Figure 5c or the row with Figure 5e and the row with Figure 5g show the results without and with the wind farm control proposed, respectively. In this case, without wind farm control means the greedy control shown in Equation (7), and it is the baseline control used in this study to validate the performance of the proposed wind farm control. \begin{table}
\begin{tabular}{c c} \hline
**Items** & **Properties** \\ \hline Rotor, Hub Diameter & 126 m, 3 m \\ Hub Height & 90 m \\ Cut-in, Rated, Cut-out wind speed & 3 m/s, 11.4 m/s, 25 m/s \\ Cut-in, Rated Rotor Speed & 6.9 rpm, 12.1 rpm \\ \hline \end{tabular}
\end{table} 
Table 1: Specification of NREL 5-MW wind turbine model [21]. It can be seen in Figure 5a,c that the wake area of the wind turbine is clearly shown in the downstream direction and the influence continues to a relatively long distance. Because the [PERSON]'s eddy viscosity model neglects the pressure gradient in the near-wake region, the solution is not defined within 2 RD from the upstream wind turbine [25]. Therefore, the wakes begin at 2 RD behind the wind turbine. In addition, it can be found from the figures that, with the wind farm control (Figure 5c), the wind speed becomes higher in the wake region than the wind speed without the wind farm control. This is because when the wind farm control is turned on, the most upstream wind turbine is forced to generate slightly lower power than the power that it can generate by the wind farm controller. Without the wind farm control (or with the baseline control), the most upstream wind turbine generates electricity with its best. This means that if the farm control is applied to the most upstream wind turbine, the wake impact on the downstream wind turbines is reduced. This is also clearly shown in Figure 5b,d, which shows pure wind speed deficit only in the space excluding the turbulent components of the wind without and with the wind farm control, respectively.