Turbine’s Unsteady Operation

Wind turbines continuously experience unsteady operating conditions with the main reason being unsteadiness in the wind hitting the blade due to both wind shear and atmospheric turbulence. The unsteady BEM solver enables the anal-ysis of the instantaneous loading on the rotor at a reasonable computational cost. In the following, three scenarios of unsteady operating condition of wind turbines are presented.

2.8.2.1 Blade Pitching

In pitch-controlled wind turbines, blade’s pitch angle (θ_p) is used to regulate the generated power. The Power could be decreased by pitching the blades out of the wind at higher wind speeds. As demonstrated in Fig. 2.17 the pitch angle in this example is increased from3^◦att= 25sto5^◦att= 25.5s. It is then decreased back to3^◦during0.5sstarting att= 35s. The wind speed is 8m/s.

Figure 2.17: Time-dependent pitch angle.

The change in Power and thrust as a result of changing the pitch angle can be seen in Fig.2.18. By increasing the pitch angle both the power and the thrust decrease. There is an initial overshoot right after changing the pitch angle, but after some time delay a new equilibrium state is reached. For this example, the time delay is about5sfor both the increase and the decrease of the pitch angle.

The time delay increases with the decrease of wind speed, it depends on the ratio of rotor diameter to the wind speed.

36 Chapter 2 Blade Element Momentum Method

Figure 2.18: Change in power and thrust as a result of changing the pitch angle.

2.8.2.2 Wind Shear

In this second example the pitch angle is fixed atθ_p = 5^◦ but wind shear is taken into account rather than assuming a uniform wind velocity profile. The logarithmic profile suggested in [31] is used for the mean wind profile:

U(z) =u_∗

Kln(z+z0

z₀ ), (2.105)

whereu∗is the friction velocity,z0is the roughness length, andKis the von Karman constant. The roughness length is set toz0 = 0.01m (which cor-responds to open areas covered with mown grass) and the friction velocity is calculated for a mean wind speed of8m/sat hub height. For this example, the velocity at the rotor plane ranges forms7.7m/sto8.3m/s. The difference between the minimum and maximum velocity is not very high (rotor diameter is10m), but it is still enough to observe oscillations in power and thrust at the frequency of rotor’s rotation. Fig2.19shows the oscillation in the generated power and Fig. 2.20 shows the thrust applied on each blade. By definition, blade 1 is positioned at an azimuth angle of0^◦att = 0s. As it is expected for a 2-bladed rotor, because of the180^◦angular distance between the blades, while the thrust of one blade is at its maximum value the other blade faces its minimum thrust.

2.8.2.3 Atmospheric Wind

This example takes both wind shear and atmospheric turbulence into account.

The pitch angle is fixed atθp = 5^◦and the mean wind speed at hub height is 8m/s. The described method in section2.6is used for generating the fluctuat-ing part of the velocity vector. Instantaneous wind field in front of the turbine is shown in Fig.2.21. The wind velocity vector for each section of each blade

2.8 Results 37

Figure 2.19: Influence of wind shear on the generated power.

Figure 2.20: Influence of wind shear on the thrust applied to individual blades.

is calculated for every time step via bi-linear interpolation. The change in wind velocity for the section at the middle of the first blade over time is shown in Fig.2.22. Because of the fluctuations in the wind field, the power output and the thrust applied on the blade have an oscillatory behavior. Next, they are compared with the case of using mean flow with no turbulent fluctuations.

The generated power by the rotor in plotted in Fig. 2.23. While for the mean wind profile the mean time-averaged power stays constant, the power oscillates about this mean value for the case of fluctuating wind.

Similar behavior is observed for the thrust applied on individual blades. The thrust applied on blade 1 is shown in Fig. 2.24. For the mean wind profile oscillation of the thrust force due to wind shear could be clearly observed, but it is not the case for the fluctuating wind case. Looking at the spectrum of

38 Chapter 2 Blade Element Momentum Method

Figure 2.21: Three dimensional wind field in front of the turbine.

Figure 2.22: Change in wind velocity over time for a selected monitor point.

Figure 2.23: Comparison of the generated power.

the thrust force (Fig. 2.25) it is seen that for the uniform wind case, there is only one dominating frequency in the signal atf = 1.196Hzwhich is the fre-quency of blade’s rotation. For the fluctuating wind case on the other hand, the

2.8 Results 39 frequency of blade’s rotation has still the maximum amplitude, but other fre-quencies have a higher contribution to the thrust force compared with the mean profile case. Taking all these frequencies into account is crucial for fatigue life analysis of the blade and other mechanical components of the turbine.

Figure 2.24: Comparison of the thrust force on blade 1.

Figure 2.25: Fourier transform of the thrust on blade 1.