# Wind Turbines Optimal Operation at Time Variable Wind Speeds
## 7 Conclusions  
In this paper, the operation of one wind turbine within a wind farm, the data for which is collected in [21], is analyzed for wind speed values measured with a sampling step of 30 s.  
The operation of the wind turbine was analyzed at MPP, in which case the PMSG's angular speed tends towards its optimal value. The PMSG's optimal power values are determined by employing the values of the wind speed and its derivative in the mathematical model of the wind turbine. Since the wind turbine's mathematical model is used to calculate the PMSG's optimal angular speed's dependence on the wind speed, its moment of total inertia should be considered.  
For the actual PMSG's angular speed, the wind turbine's moment of total inertia behaves like a damper. Due to its high value, it is not possible for the PMSG to permanently operate at MPP, which, from the energy point of view, imposes the optimal value of the PMSG's angular speed, because the PMSG's angular speed is not capable of following the rapid variation of the wind speed in time.  
Therefore, in order to capture the maximum wind energy, the wind turbine should be controlled to operate at the PMSG's optimal angular speed, imposed by the wind speed value. This condition is checked periodically, and if there are large differences between the PMSG's angular speed and its optimal value, the wind turbine is brought into the MPP operation by inserting the necessary amount of electric energy, provided by the national power system. If the value of the wind speed is decreasing, its derivate becomes negative, and the PMSG's power becomes greater than the wind turbine's power, while in the case of the wind speed increasing, its derivative becomes positive, and the PMSG's power becomes lower than that of the wind turbine's power value.  
Thus, two methods to direct the PMSG's power towards its optimal value were proposed herein, both of them based on the same principle, using either a PI-type regulator or a PID-type regulator.  
The values of the regulator coefficients are determined by successive simulations, so that the oscillations of the power are reduced. The simulations are actually the numerical solutions obtained by using the MAPLE core of the Scientific Workplace simulation environment, and they are based on the wind speed measurements.  
In conclusion, it can be said that the proposed controls can bring the wind turbine within the MPP operation area. However, the PMSG's power, based on either the PI- or PID-type control, is not identical to the theoretical PMSG's optimal power based on the kinetic motion equation, but close to it, depending on the applied control method.  
For the presented case study, where the moment of total wind turbine inertia is large and leads to reduced dynamics in the wind turbine's operation, the PID regulator is recommended.  
For practical application, the obtained PMSG's optimal power curve is useful for monitoring and increasing the performance of the wind turbines. As was shown in this paper, the PMSG's optimal power curve can be extracted from the wind speed measurements data. This curve can be used as a reference curve. The actual PMSG's power curve to be monitored can be compared with the reference one, and the wind turbine can then be controlled, so that the deviation of the actual values from the expected ones will be as small as possible, which increases the wind turbine's efficiency.  
Writing--original draft preparation, M.-C.A.; Conceptualization, S.M.; Methodology, S.M.; Software, C.S.; Validation, M.-C.A., M.D. and C.S.; Formal analysis, G.M.E.; Investigation, M.D.; Resources, G.M.E.; Data curation, C.S.; Writing--review and editing, M.-C.A.; Visualization, M.D.; Supervision, M.-C.A.; Project administration, S.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by University POLITEHNICA Timisoara, GNaC2018 ARUT, no.1357/01.02.2019.  
The authors declare no conflict of interest.