*5.2. Aerodynamic Performance*

In this section, the aerodynamic performance in dynamic conditions is discussed. Figure 10 shows the generator power as a function of the wind speed for the two turbines in the conditions specified by IEC 61400-2 DLC 1.2 [12] and discussed in Section 4. The

error bars show the maximum and the minimum calculated values, while the filled areas represent the standard deviation. The analysis of the mean values shows that the power produced by the pitch-regulated turbine was higher than that generated by the stallregulated turbine. This was largely because the pitch-regulated turbine was more efficient below the rated wind speed (Figure 8a). Furthermore, the standard deviation was generally lower for the pitch-controlled turbine at all wind speeds, and power output seemed to be better controlled, especially at high wind speeds. With their respective differences, these results show how the control systems of both turbines were able to adequately regulate the turbine in turbulent inflow conditions. The oscillation of the minimum power values for both turbines was due to the strong wind speed oscillations during turbulent simulations. This is in fact a key aspect of SWTs, whose installation contexts are often characterized by very turbulent winds.

**Figure 10.** Generator power mean, standard deviation (shaded areas), and maxima and minima.

When comparing the power predicted in steady and dynamic conditions, some interesting considerations can be drawn. Figure 11a,b compares the power curves in steady and dynamic conditions for the pitch- and stall-regulated turbines. The effects of vertical up-flow, yaw-misalignment, and turbulence intensity can be globally evaluated.

**Figure 11.** Power curves of the pitch- (**a**) and stall-controlled (**b**) variable speed concept.

For the pitch-regulated turbine, especially, there was a tendency to increase power output below rated power, while both the pitch- and stall-regulated turbines drastically decreased power around the rated wind speed. This was mainly an effect of turbulence intensity, as many authors have shown [57–60], and underlines the importance of taking realistic operating conditions into account in the design process of a wind turbine (while in the past, this was discarded in many small wind turbines). For instance, in Figure 11b, one can notice how in turbulent flow conditions, the rated power was not reached until 20 m/s average wind speed; this could lead the designer to modify the turbine design, e.g., by compensating for this effect by reducing the fixed pitch angle.

By comparing the performance obtained in steady conditions with that in dynamic conditions, it can be noticed how the gap between the pitch-regulated and stall-regulated power curves widened in turbulent wind. This is very visible in Figure 12. Referring to this figure, the area between the curves in steady conditions was 27.06 kW\*m/s (Figure 12a) and 55.26 kW\*m/s in dynamic conditions (Figure 12b). This was a consequence of the flatter TSR–Cp curve of the stall-regulated case, as shown above in Figure 9. For this reason, the pitch-regulated turbine was less sensitive to variations in TSR and could operate near peak Cp for longer time. This is again a consideration that was often unclear in the old generation of stall-regulated SWTs, and it seems to suggest that the real benefits of pitch regulation are higher than expectations and thus possibly able to compensate for the increased cost.

**Figure 12.** Power curves for the pitch- and stall-regulated turbines in steady conditions (**a**) and dynamic inflow conditions (**b**).

In above-rated flow speed operation, the stall-regulated turbine was able to selfregulate power output, as previously shown in Figure 7a. Unfortunately, as shown in Figure 13, the result was an increase in axial load for the stall-regulated rotor—more force was transferred into axial loading rather than into rotating the blade. In fact, as wind speed increased in the stall-regulated rotor, the force vector rotated downwind to decrease the torque component and increase the thrust component. Therefore, a potential advantage of pitch regulation over its stall counterpart is decreased peak axial loads, which decrease rotor structural requirements and may lower the risk of failure during high-wind events.

**Figure 13.** Average rotor thrust curves in dynamic conditions.

#### *5.3. Annual Energy Production (AEP)*

Differences in power delivery and efficiency discussed in the previous sections result in different annual energy production values. The AEP was calculated according to IEC 61400-2 standard turbine classes from the results of the dynamic simulations. A Weibull wind speed distribution with shape factor of 2 and an average value of 8.5 m/s was used to model sites of IEC wind class IIA, with medium wind speed and high turbulence intensities.

The results of AEP estimations are displayed in Figure 14. It can be noted that the energy capture was very low at low wind and high wind speeds, though for different reasons. At low wind speeds, a wind turbine cannot deliver enough power, while high wind speeds occur only for short times during a year.

**Figure 14.** Annual energy production per wind average wind speed in dynamic conditions.

In the analyzed case study, the pitch-regulated turbine produced 12.36% more energy (kWh) annually than the same stall-regulated turbine. The annual energy production calculated for the stall-regulated turbine was 46.058 MWh/year, while the pitch-regulated turbine produced 52.554 MWh/year.

#### *5.4. Results in the Time Domain*

In order to do a comparative analysis between pitch and stall control strategies, it was also useful to look at time characteristics. The first reason for this is to show that the controllers and simulation models worked properly. The second is to show the impact of the two control methods on power output, which also has an effect on global energy capture. Finally, the third is to get an impression of the power quality of the different controls.

In the following, below, above, and at around rated wind speed simulations are discussed, and the results for a 600 s time interval are shown. For the partial load time characteristics, an average wind speed of 7 m/s was selected. In this scenario, wind speed rarely reached its rated value, and power limiting did not occur. In this area, the main goal was to maximize energy harvesting.

In Figure 15a, the generated power is shown for the two turbines. In the 600 s time interval, the power of the pitch-regulated turbine was always slightly higher than that produced by the stall-regulated turbine, as was expected given the higher Cp. The power output was globally similar for the two turbines, as power regulation did not kick in until higher wind speeds were reached.

**Figure 15.** Generator power for a (**a**) 7 m/s average wind speed simulation, (**b**) a 12 m/s average wind speed simulation, and (**c**) a 16 m/s average wind speed simulation.

For the near rated wind speed time characteristics, an average wind speed of 12 m/s was selected. The main interest lies in the transitions from partial load to rated power and vice versa. In this area, a smooth transition between the power maximization and the power limiting was of interest. In Figure 15b, the power output for the two turbines at 12 m/s average wind speed is shown.

The stall-controlled variable-speed concept showed very steep power changes when entering and leaving region 3. While power overshoots were similar in magnitude for the two regulation concepts, power output dropped significantly as wind speed dropped below rated for the stall-regulated variant. When the turbine was operating at rated power, the blades were in partial or total stall; therefore, due to dynamic effects, power dropped significantly as the blade gradually exits stalled.

In Figure 15c, the behavior of the two different concepts at wind speeds above rated wind speed is shown; in particular, an average wind speed of 16 m/s was selected. At these wind speeds, there is always much more power in the wind than the wind turbine can handle. Therefore, the power output must be curtailed. Overall, the pitch-controlled turbine appeared to be able to regulate power more efficiently, although both control systems provided satisfactory results. As noted also when analyzing operation around rated wind speed, the generator power dropped significantly more on the stall-regulated turbine at the 180 s mark, an effect that could be again related to the stall state the blade is in.

Some interesting trends can also be inferred from the rotor speed of the same simulations at 7, 12, and 16 m/s shown in Figure 15; these trends are shown in Figure 16.

**Figure 16.** Generator speed for a (**a**) 7 m/s average wind speed simulation, (**b**) a 12 m/s average wind speed simulation, and (**c**) a 16 m/s average wind speed simulation. Results for the same simulations shown in Figure 15.

At 7 m/s, the two turbines behaved similarly, with the stall-regulated turbine producing more power and operating at a higher rotor speed. The stall-regulated turbine operated at a lower TSR, as intended and shown in Figure 9. At 12 and 16 m/s, the average rotor speed was higher for the pitch-regulated turbine and both turbines were operating at their nominal rotor speed, thus indicating that the controllers were performing as intended. It can be noted how the stall-regulated turbine was able to maintain a nearly constant rotor speed. The differences between control systems can be explained as follows: the pitch controller employed in this study maintained a constant torque above rated and regulated rotor speed and power trough blade-pitch feathering. Thus, fluctuations in power were caused by variations in rotor speed and vice-versa. The stall controller, on the other hand, was set to operate in region 2.5 at a wind speed above rated (further details are discussed previously in Section 3.3), and controlled rotor speed at the expense of fluctuations in torque and power. Keeping rotor speed in check is very important for a stall controller because if rotor speed could increase, the turbine would increase its TSR and quickly accelerate out of control.

#### **6. Conclusions**

In this study, the design process of a 50 kW turbine from blade selection to performance assessment was used to show how modern engineering codes and recent tools for turbine control can be effectively used to design an efficient small wind turbine.

Focusing first on aerodynamic design, it must be noted that he intended final control strategy (i.e., pitch or stall control) needs to be defined early on in the design process because the resulting final blade shape may be significantly influenced by the choice. In the case of SWTs, it is preferable to use a family of airfoils that targets a high glide ratio with moderate lift coefficients, as this helps to increase blade chord and, hence, operating Reynolds number. Furthermore, although these effects are not fully understood and their inclusion in the design process is somewhat uncertain, it is very important to consider 3D-effects. Such phenomena play a key role in the inner parts of the blade and have been shown, as expected, to significantly influence the stall-regulation capabilities of an SWT. The presented guidelines and aerodynamic design procedure are general and can be applied to all turbine sizes, not only to SWTs. It must be noted, however, that when designing very large wind turbines (10–20 MW), pitch control is the undisputed choice and focus is placed mainly on structural loads. In fact, these rotors operate at extremely high Reynolds numbers, therefore achieving high peak aerodynamic performance almost effortlessly. On the other hand, structural optimization is extremely important to keep blade cost and weight down, as well as to guarantee robust blade design. For this class of rotors, a more integrated design procedure, focusing on loads in addition to aerodynamics and control in the initial stages of rotor design, should be considered.

Focusing on control, the study showed the basic approaches and methods to implement both pitch and stall control in small wind turbines. In this sense, even though existing books and reports very often only focus on the stationary power curve, it has been shown

here that in dynamic conditions, i.e., in a power-production DLC case from international design standards, the power curve of the turbine significantly changes, thus indicating the importance of accounting for such conditions in the design process and, especially, in the selection of the best control strategy.

For the stall-regulated turbine, an overall good level of performance was achieved. The peak aerodynamic power coefficient for the selected case study was around 0.4, which is in line with turbines of this class. When adopting a pitch regulation strategy, however, fewer compromises to the blade design have to be made in order to ensure good power regulation; in this case, no fixed blade pitch angle needed to be set, and the ideal blade twist distribution could be used. As a consequence, the aerodynamic power coefficient improved significantly, reaching a value of nearly 0.5, which is in line with most modern utility-scale turbines. Furthermore, rotor thrust continued to increase above rated wind speed for the stall-regulated turbine, as opposed to the trend observed when using pitch regulation. This points to the possibility that pitch regulation also has the added benefit of lowering axial blade loads. In this sense, this work has shown how the use of a modern, pitch-to-feather control strategy has the potential to significantly improve SWT performance through more effective power regulation and due to the fact that many compromises to the aerodynamic design can be avoided.

**Author Contributions:** Conceptualization, A.B. and F.P.; methodology, F.P.; software, A.N.; validation, A.N., F.P.; investigation, A.N.; data curation, A.N.; writing—original draft preparation, A.N.; writing—review and editing, F.P. and A.B.; supervision, A.B., G.F.; project administration, G.F.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available on request due to restrictions.

**Conflicts of Interest:** The authors declare no conflict of interest.
