# Model Based Open-Loop Wind Farm Control Using Active Power for Power Increase and Load Reduction
## 3 Simulation Result
### Total Power  
Figure 8 shows the dynamic simulation results with both the baseline controller and the proposed controller. The turbulence intensity was fixed to be 0.075 and the control frequency was 0.1 Hz. The spacing of the wind turbines was 7 RD, which is the turbine spacing of the well-known Danish  
Figure 7: Wind speed variation for downstream wind turbines with the baseline and the proposed wind farm controllers: (**a**) ambient wind speed conditions: \(\overline{U}\) = 8 m/s, \(\overline{T}\) = 0.075; (**b**) ambient wind speed conditions: \(\overline{U}\) = 8 m/s, \(\overline{T}\) = 0.21; (**c**) ambient wind speed conditions: \(\overline{U}\) = 10.5 m/s, \(\overline{T}\) = 0.075; and (**d**) ambient wind speed conditions: \(\overline{U}\) = 10.5 m/s, \(\overline{T}\) = 0.21. Horms Rev offshore wind farm. The mean wind speed to the most upstream wind turbine was fixed to be 8 m/s. Power commands from the wind farm controller to individual wind turbines with both the proposed and the baseline control were calculated from Equations (4) and (5), respectively. Figure 8a,f shows the turbulent winds to three wind turbines in series. For two different wind farm controllers, the winds to the most upstream wind turbines are the same, but those to the subsequent wind turbines are slightly different. This is because the most upstream wind turbine is operated differently with different wind farm controllers and therefore the winds passing through the turbine are affected differently. Figure 8b,g shows the power commands to individual wind turbines by the wind farm controllers. For the baseline controller, the power command to the most upstream wind turbine is the rated power, 5 MW, and, therefore, the turbine will extract power from the wind as much as possible. The power commands to the downstream two turbines are much lower and dependent on their available powers. For the proposed controller, the power command to the most upstream wind turbine is less than 5 MW to pass slightly more wind to downstream wind turbines. In addition, the power commands to downstream wind turbines are both 5 MW, and therefore the downstream wind turbines will extract power from wind as much as possible. The blade pitch angles are presented in Figure 8c,h. For the baseline controller, the blade pitch angles are zero (fine pitch angle), and no blade pitch control is used. This is because the turbulent wind does not reach the rated wind speed of the wind turbine. All three wind turbines extract as much  
Figure 8: Dynamic simulation results in time domain with baseline and proposed wind farm controllers: (**a**,**f**) wind speed used in comparison of baseline controller and proposed controller for three wind turbines; (**b**,**g**) power command according to use of baseline controller and proposed controller to each wind turbine (**c**,**h**) blade pitch angle change of each wind turbine according to use of baseline controller and proposed controller; (**d**,**i**) generated power variation of wind turbines according to use of baseline controller and proposed controller ; and (**e**,**j**) total power variation of wind farm according to use of baseline controller and proposed controller. power from wind as possible. For the proposed controller, the pitch angles of the two downstream wind turbines are zero, but the pitch angle of the most upstream wind turbine varies within 0\({}^{\circ}\) and 4\({}^{\circ}\). This is because the most upstream wind turbine is slightly pitched to pass more wind to downstream wind turbines and the downstream wind turbines do their best to extract power from wind. This result is similar to the result obtained from a wind tunnel with miniature wind turbines with fixed blade pitching by other researchers that the pitch angle of 2\({}^{\circ}\) was the best to maximize the wind farm power [4; 7]. However, the optimum pitch angle found in this study was not fixed to be 2\({}^{\circ}\) but varied with wind speeds or available power.