# Model Based Open-Loop Wind Farm Control Using Active Power for Power Increase and Load Reduction
## 1 Introduction  
Offshore wind farms using fixed substructures are mostly constructed in seawaters having a depth of less than 40 m, and this often limits the number of wind turbines that can be installed in a wind farm. The spacing between wind turbines commonly range from 7 RD to 11 RD, where RD represents the rotor diameter of the wind turbine [1; 2]. Considering the fact that the rotor diameters of modern wind turbines commonly reach 100 m, the spacing between wind turbines seems large but it is still necessary to reduce the wake effects from upstream wind turbines on downstream ones which result in lower power and higher load [3]. Investigations on active induction wind farm control to reduce the wake strength by regulating the power of the upstream wind turbines less than their available power have been done by researchers. Earlier research articles were focused on the phenomenon itself, and the physical explanations of the power increase using one-dimensional momentum theory were presented [4; 5]. The simple model predicted an increase of 4.1% of the total power of two turbines in line when the induction of the first wind turbine was reduced from 1/3 to 1/5. In addition, to prove the idea, wind tunnel tests with micro scale wind turbine model arrays with manually adjustable blade pitches with a turbine spacing of 4.5 RD were used. From the scaled farm measurements, about 4.5% of increase in the total power was observed with a blade pitch angle of 2\({}^{\circ}\). However, later, the measurement uncertainty turned out to be greater than the power increase 6%, and the results were also found to be greatly affected by the Reynolds number effects occurring only in wind tunnel tests [5; 6]. In addition, a fewfield measurements with multi-MW wind turbines with a 3.8 RD spacing were tried but not very successful [5; 6] to make a quantitative conclusion. Later, the field data were reanalyzed for two 2.5 MW wind turbines with a spacing of 3.8 RD, and turned out to have a power increase of about 5% with a fixed pitch angle of 2\({}^{\circ}\)[7]. After that, the active induction wake control method based on the manual blade pitch adjustment (change of axial induction) was applied to a simple wind turbine model with an engineering wake model. The simulation concluded that the adjustment of the blade pitch angle can increase the total power of a wind farm by about 10% [8; 9; 10]. Later, articles focused on various wind farm control algorithms including genetic algorithms were presented [11; 12; 13; 14]. Some were wind farm model based methods and some were model free methods. Because it is very hard to prove the wind farm control effects on the farm power output in real wind farms, all validations were made with simulations. In addition, the facts that a wind farm simulation must deal with multiple wind turbines, and simulations with multiple wind turbines require large computational loads, limited the simulations to be the simulations of simple wind turbine models without any dynamics in conjunction with a simple wake model. The wind turbine models were simply algebraic equations with power coefficient and the simulations were made with constant wind speeds and no turbulence. The power gains from these simplified static analyses varied from 0.6% to 25% depending on the control method [11; 12; 13; 14]. In addition, some researchers tried to change the wind turbine operating point to reduce the wake effect based on simple wind turbine models with engineering wake models and they concluded with power increases of 1.86% to 6.24% [8]. However, the results are considered to be exaggerated due to the simple wind turbine model and the constant wind. Recently, an extremum seeking control as a model-free method was used to prove the algorithm. The simulation was done in turbulent winds with a few different turbulence intensities [15] but the wind turbine model was still a simple algebraic equation that does not have any system dynamics. In the study, the controller was successful with low turbulence intensity.