## 3 Comparison of Power Generation of Wind Farm between MPPT and MPG
### Optimal Tip Speed Ratio Selection at 270\({}^{\circ}\) Wind Direction  
As shown in Figure 2, in the case of the wind direction \(\alpha\) at 270\({}^{\circ}\), no energy loss is induced by the WT\({}_{2}\), as there is no wind turbine along with this wind direction. Therefore, to maximize the total active power of the wind farm, the pitch angle and tip speed ratio for WT\({}_{1}\) can be optimized, while WT\({}_{2}\) is controlled according to the MPPT method. It starts with the optimization of the tip speed ratio of WT\({}_{1}\), where the pitch angle of WT\({}_{1}\) is assumed to be the same with the MPPT method.  
At the ambient wind speed of 9 m/s, the active power of WT\({}_{1}\), the wind speed of WT\({}_{2}\), the active power of WT\({}_{2}\), and the total active power of the wind farm are shown in Figure 6 at the various tip  
Figure 5: Layout of the wind farm with two NREL 5 MW wind turbines.  
speed ratio of WT\({}_{1}\). The active power of WT\({}_{1}\) and WT\({}_{2}\) are calculated by (1), where the wind speed of WT\({}_{1}\) is equal to the ambient wind speed, and the wind speed of WT\({}_{2}\) is calculated by (3). In Figure 6d, it can be observed that the maximum total active power of the wind farm is obtained with the tip speed ratio of 6.5. Thus, the optimal tip speed ratio of WT\({}_{1}\) can be selected at 6.5.  
Compared with the MPPT method, where the wind turbine operates at the tip speed ratio of 7.55, in the case that the wind turbine operates at the tip speed ratio of 6.5, the active power of WT\({}_{1}\) is reduced (as shown in Figure 6a) due to the reduction of the power coefficient of WT\({}_{1}\); however, the wind speed of WT\({}_{2}\) is increased (as shown in Figure 6b) due to the reduction of the thrust coefficient of WT\({}_{1}\), and as a consequence the active power of WT\({}_{2}\) is increased (as shown in Figure 6c). In total, the active power of the wind farm is increased from 0.37 pu to 0.38 pu.  
Similarly, the optimal tip speed ratio for WT\({}_{1}\) can be selected from the cut-in wind speed to the cut-out wind speed by the exhausted search method. This method first calculates the total active power of the wind farm at each possible tip speed ratio of WT\({}_{1}\). Then, the maximum total active power of the wind farm can be selected and the corresponding optimal tip speed of WT\({}_{1}\) can be obtained. The optimized tip speed ratio, the turbine speed, and active power of WT\({}_{1}\) are shown in Figure 7 in the cases that the MPG and the MPPT are adopted, respectively. It can be seen that the tip speed ratio of the MPG is relatively smaller than the MPPT in the range that the wind speed is below the rated value.  
One of the active power control schemes for the DFIG wind turbine is shown in Figure 1. The pitch angle is regulated by the pitch controller, and the tip speed ratio is controlled by the power controller by changing the active power reference. In Figure 1, the pitch angle reference and the  
Figure 6: Comparison between WT\({}_{1}\) operating at the tip speed ratio of 7.55 and 6.5, at the wind direction of 270\({}^{\circ}\) and ambient wind speed of 9 m/s: (**a**) the active power of WT\({}_{1}\), where the base value is 5 MW; (**b**) the wind speed of WT\({}_{2}\); (**c**) the active power of WT\({}_{2}\), where the base value is 5 MW; (**d**) the total active power of the wind farm, where the base value is 10 MW.  
Figure 7: Comparison of the tip speed ratio, rotor speed and active power of WT\({}_{1}\) between the MPPT method and the Maximum Power Generation (MPG) method at 270\({}^{\circ}\) wind direction.  
active power reference are obtained from the pitch angle curve and the active power curve according to the wind speed. With the optimized pitch angle and tip speed ratio, the pitch angle curve and active power curve in terms of the wind speed are optimized, as shown in Figure 7. And the optimized pitch angle curve and active power curve can be implemented as look-up table by the pitch angle controller and the power controller.