# Model Based Open-Loop Wind Farm Control Using Active Power for Power Increase and Load Reduction
## 2 Methodology
### Wind Farm Controller
To find the values that can minimize the objective function value, the method repeats reflection, contraction and expansion of the variables [30; 31] by comparing function values at \(n+1\) test points and by avoiding the test point that gives the worst function value. More explanation to understand the algorithm is available in [32]. In this study, the \(\mathrm{TSO}_{\mathrm{CMD}}\) in Equation (6) was chosen to be the rated power of the wind turbine multiplied by the number of wind turbines because the curtailment of the total power from the wind farm by the \(\mathrm{TSO}_{\mathrm{CMD}}\) is not considered. In addition, only one variable in the objective function, the power command to the most upstream wind turbine, was used to avoid the convergence at a local minimum. In this case, therefore, minimizing the objective function in Equation (6) means that the wind farm controller finds the optimal power command to the most upstream wind turbine to maximize the total power output (from three wind turbines) because the \(\mathrm{TSO}_{\mathrm{CMD}}\) will be always larger than the available power from the wind farm except the case when the wind speed is high enough to make all three wind turbines generate at their rated powers. The wind farm model in the wind farm controller was constructed to calculate the total power output from the wind farm for various operating conditions of the most upstream wind turbine and finally to find the optimal power regulation of the most upstream wind turbine by minimizing the objective function, Equation (6), using a function minimization algorithm. Basically, the wind farm model predicts the wind speeds for all downstream wind turbines using [PERSON]'s eddy viscosity wake model and estimates the power output and load variation according to the power command from the power command calculator to maximize the power output by minimizing the objective function. Changes based on the TSOCMD are calculated for all wind turbines. The wind farm model in the wind farm controller is a simplified version of the wind farm model for dynamic simulation in Section 2.1. Figure 3 shows the difference between the wind farm model used for the dynamic farm simulation and the simplified wind farm model applied to the controller. As shown in the figure, the wind farm model applied to the wind farm controller is similar to that used for the dynamic wind farm simulation in a point that the same wake and the wake merge models are applied to predict the wind speed inside the wind farm. However, the wind farm model in the wind farm controller differ from that for the dynamic wind farm simulation because it does not calculate the wind propagation at each time step and only calculates the steady state winds at the rotors of all downstream wind turbines by considering the wake and the wake superposition. Since the time-dependent wind propagation algorithm is not used in the wind farm model of the wind farm controller, a simple look-up table based wind turbine model without any wind turbine dynamics was used.