# Development of a CFD-Based Wind Turbine Rotor Optimization Tool in Considering Wake Effects
## 3 Results and Discussion
### Rotor Optimizations
#### 3.4.2 Optimization Studies  
The wind turbine rotor type of the Horns Rev I wind farm is chosen for the aerodynamic optimization. The selected wind turbines are located at the first and second rows (T1, T2 as depicted in Figure 8). It is worth noting that with the present method, it is possible to optimize the whole column of 8 wind turbines together. First, a larger number of wind turbines involve more design variables and thus a larger computational demand; second, it is the first two rows of wind turbines that have the major aerodynamic differences, as widely observed from measurements in several wind farms. According to the different optimization objectives, four optimization cases are carried out during the blade aerodynamic design. **Case 1**: Baseline optimization for a single rotor. Using the optimization objectives of AEP and ATP, optimize the upstream wind turbine (the 1 st row of rotors). **Case 2**: Optimization of the 2 nd row of rotors considering the wake effect from the 1 st row of wind turbines. Using the optimization objectives of AEP and ATP, perform optimization for the 2 nd wind turbine optimization. **Case 3**: Further optimization of the rotational speed of the 1 st row of wind turbines. The optimization objectives are the AEP and ATP for the two rows of wind turbines. The blade shape of the two types of rotors is obtained from Case 1 and Case 2, respectively, but the rotational speed of the 1 st row of rotors will be optimized further. Figure 13: Distribution of the control points and the sample line of blade geometry. (**a**) Chord; (**b**) Twist angle. **Case 4**: Based on Case 3, further optimization is performed for the two rows of wind turbines. Using the optimization objectives of both AEP and ATP, the two rows of wind turbines are optimized together. To summarize these optimization cases: Case 1 follows a classical blade optimization routine; Case 2 only focuses on a downwind rotor, its blade shape is optimized; Case 3 optimizes the rotational speed of the first row of rotors to seek the global maximum energy production for two rows of rotors; Case 4 optimizes both the rotational speed of the first row of rotors and the blade geometry of the second row of rotors. By performing the 4 steps analysis, it expected that after the Case 4 study a more realistic optimization can be achieved for such a typical multiple wind turbine system. The optimization Pareto fronts are shown in Figure 14 with the resulted Pareto front that measures how the solutions are distributed. The four subfigures (a-d) represents the above mentioned four cases. In the figures, the areas marked with \(A\), \(B\) and \(C\) indicate the regions of feasible optimal solutions. The trend of area \(A\) suggests the solutions with high AEP, whereas low thrust is more focused in area \(C\). As a multi-objective method, balance is then needed to weight between the high AEP and low ATP. In Figure 14a, Case 1 represents the standard optimization of a single rotor (the 1 st row of rotors) without any wake effect. The high AEP and high ATP region is marked as area \(A\), whereas area \(B\) finds good balance between low ATP and high AEP. In Figure 14b, the second row of wind turbine is optimized. Due to the wake effect from the first row of wind turbine, both the ATP and AEP are reduced comparing with Case 1 results. In Figure 14c, a high AEP area can hardly be achieved. The reason is that in Case 3 the AEP from the upstream rotor is reduced to increase the energy output for the downwind rotor. Such that, it is necessary to further optimize the downwind rotor. In Figure 14d, the optimization is continued such that the two rows of wind turbines are fully optimized with satisfactory results obtained. Figure 14: Pareto fronts of AEP and ATP in the 4 different cases. (**a**) Case 1; (**b**) Case 2; (**c**) Case 3; (**d**) Case 4. Some key numbers are shown in Tables 2 and 3 after each optimization. For the Case 1 design, the upstream rotor is first optimized.