Influence of Excitation by Idling Rotor on Wind Turbine Ultimate Loads in Storm Conditions

Abstract

Typical large scale pitch-controlled wind turbines idle their rotors during storm conditions. The design loads of wind turbines are calculated by aeroelastic simulations under various conditions. These include grid loss and failures, which can increase rotor speed and excite the first-mode of the tower bending. In this study, the influences of self-excitation by the idling rotor on the ultimate loads in storm conditions were investigated. Aeroelastic simulations were conducted for a three-bladed 5 MW upwind turbine as an example, under steady and extreme turbulent wind conditions according to the international design standard IEC61400-1 ed.4. As a result, we confirmed that yaw misalignment increases the idling rotor speed and 6P, second order harmonics of blade passing frequency, excites the first-mode tower bending, which can generate a large load on the tower. Pitch stick can increase the rotor speed but not as noticeably as yaw error. Although no clear provisions exist in wind turbine design standards or guidelines for the self-excited vibration during wind turbine idling, these results indicate that conditions must be set that consider self-excited vibration.

1. Outlines

Efforts are underway in most major countries to achieve carbon neutrality by 2050, with the aim of preventing further global warming. Among the technologies developed for this purpose, wind energy has a relatively low energy cost and CO₂ emissions per unit energy, contributing to energy security, industry, and employment. Due to its effectiveness, wind energy had been rapidly deployed in recent decades. Technological innovations related to wind turbines have also been promoted, such as increasing their size, lowering costs, increasing reliability, and so on. In addition to the development of design analysis methods and new technologies, advances in design standards and guidelines have considerably contributed to this process. In recent years, the hub height of wind turbines has increased, and higher design wind speeds are often required for deployment offshore or in typhoon areas; as such, storm conditions are becoming more important to consider. Given the above situation, the new wind class T (extreme wind speed of 57 m/s), which exceeds the conventional class I (extreme wind speed of 50 m/s), was specified in the international wind turbine design standard IEC61400-1 ed.4 [1].

The design load case (DLC) during idling or parking in a storm is described as follows, according to IEC61400-1 ed.4:

(DLC6.1) Idling in storm under normal conditions (normal conditions)—at extreme wind speeds with a recurrence period of 50 years. This involves pitch-controlled wind turbines, which are common for large scale wind turbines, idling in full feather. In addition, since active yaw control is normally used to follow wind direction change, an average yaw misalignment of up to ±15 and ±8 degrees are considered in the cases of steady and turbulent extreme wind conditions, respectively. Note that if the yaw is not controlled, an average yaw error of ±180 degrees must be taken into consideration.

(DLC6.2) Idling in a storm during grid loss (abnormal condition)—a case where a power outage is considered at extreme wind speeds with a recurrence period of 50 years. Most large wind turbines are designed to secure and hold the feather even without external power, but yaw will be fixed. Therefore, the wind direction is assumed in all directions with full feather and rotor idling. Note that, if yaw control can be performed for a sufficient period with an auxiliary power source, the conditions are the same as in DLC6.1.

(DLC6.3) Extreme yaw error during idling (normal condition)—extreme wind speed with a recurrence period of 1 year (0.8 times the extreme wind speed over 50 years), and the wind turbine in normal condition. Consider a yaw error of ±30 and ±20 degrees for steady and turbulent extreme wind conditions.

(DLC7.1) Parking in storm under fault conditions (abnormal condition)—conditions for idling or parking in storm under fault conditions of any of the non-safe-life design components at extreme wind speeds with a recurrence period of 1 year.

Among the above DLCs, the partial safety factors for loads (PSFLs) are 1.35 or 1.1 in the cases of normal and abnormal conditions, respectively. In either case, if yaw slippage occurs during idling or parking, or if the influence of resonance exceeds 5%, turbulent extreme wind conditions must be assumed in the analysis.

In the above DLCs, due to yaw error and pitch sticking, the rotor speed increases, and concerns arise regarding tower excitation. The above design standards and guidelines emphasize resonance and self-excited vibration during power generation, but no special consideration is given during idling in a storm. In addition, no report has been found regarding the self-excited vibrations caused by the rotor idling during storms.

Regarding loads and stability during idling in storms, Totsuka et al. [2] aeroelastically analyzed the DTU 10 MW reference wind turbine under extreme winds in all directions (DLC6.2). Severe damage to the blades occurred when the yaw error was 30 degrees, and severe vibrations generated a large blade root bending moment. This is caused by the known bending/torsion or stall flutter of the blades; self-excited vibration due to rotor rotation was not discussed in this study. Wang et al. [3] also studied stall induced instability of DTU 10 MW reference turbine blades, by non-linear time domain analysis and linear eigenvalue analysis. They showed good agreement. Bangga et al. [4] studied instability of an idling IEA 15 MW reference turbine. Estimations by blade element and momentum and vortex line methods and Beddoes–Leishman and IAG dynamic stall models were compared. The combination of vortex line methods and IAG dynamic stall model provided the most reasonable results. This research focused on the aeroelastic stability of the blades.

Regarding excitation by the rotor and the resonance, Lian et al. [5] conducted a sensitivity analysis for the influence of rotor speed (1P) and blade passing frequency (3P) on the dynamic response of a three-blade wind turbine. As a result, they found that the Sommerfeld effect does not occur in soft towers where the first-mode bending frequency of the tower is between 1P and 3P; in soft towers below 1P, the imbalance is substantial. They clarified that the Sommerfeld effect must be considered only when the tower is tall, but this is related to the characteristics during power generation. In addition, Tibaldi et al. [6] examined the resonance of wind turbines in the time and frequency domains for a 1.5 MW wind turbine with different natural frequencies. They confirmed the influence of turbulence intensity on fatigue loads. They also found that, even if the damping is positive, edgewise vibrations occur, and this tendency is more pronounced when the turbulence intensity is low; this also relates to the characteristics during power generation. In addition, Yoshida [7] investigated the rotor in-plane self-excitation caused by the gravity induced deformation of the blades. However, the excitation of the tower during low speed rotation while idling in storm conditions was not discussed.

As such, in this study, we investigated the influences of self-excitation of the tower due to the idling rotor in yaw errors (DLC6.1, DLC6.2, and DLC6.3) and one blade pitch stuck (DLC7.1). We examined the occurrence of vibration and the effect of its conditions at the tower base bending moment. Section 2 describes the analysis method; Section 3 and Section 4 present the analysis results under steady and extreme turbulent wind conditions, respectively; and Section 5 summarizes this study.

2. Simulation Outlines

2.1. Aeroelastic Analysis Method

Bladed ver. 4.7.066 [8] was used for aeroelastic analysis. This is a widely used and proven commercial software for wind turbine analysis and design, which considers most of the necessary aspects of the present study. The aerodynamic model is based on the well-established blade element and momentum theory, and the structural model is based on the multi-body dynamics to deal with the flexible structures of the wind turbine. In the present study, the wind turbine responses, such as rotor speed, nacelle accelerations, and loads of the tower, were calculated by setting conditions such as turbulent wind, yaw misalignment, and pitch angles of the wind turbine as the input.

2.2. Wind Turbine Model

The 5 MW wind turbine model, provided as a sample model in Bladed, was used in this study. The general specifications and appearance are shown in

Table 1. General specifications of the 5 MW turbine.

Rotor Position	Upwind
Rated Power	5 MW
Rotor Diameter	118 m
Hub Height	80 m
Number of Blades	3
Tilt Angle	4 degrees
Coning Angle	0 degree
Rotor Speed	7.5–13.9 rpm
Tower Diameter	4.4–6.0 m
Rotor Mass	92 t
RNA Mass	342 t
Tower First-mode Frequency	0.31 Hz
Rotor Mass Imbalance	264 kgm
Pitch Error	0, −0.3, +0.3 degrees

and Figure 1. This model was originally defined as an offshore wind turbine with a tripod foundation, but we modified it as an onshore turbine by removing the underwater substructure, and the bottom of the tower is fixed on the surface of the ground in this study. Here, the outer shape of the tower retained the original shape, and the tower wall thickness was adjusted so that the natural frequency of the tower first-mode bending was 0.31 Hz. Figure 2 shows the Campbell diagram of this wind turbine, which shows that the natural frequency of the tower first-mode bending was set between the excitation frequencies f produced by the rotor (1P) and blades (3P) to avoid resonance in power production.

2.3. Full Feather Pitch Angle

Typical large pitch-controlled wind turbines idle the rotor low speed at full feather to avoid excessive load while idling during storms. From the viewpoints of the lubrication of the main shaft bearing and protection of the gearbox, the rotor should not stop rotating and the rotational direction should not frequently reverse.

Figure 3 shows the analysis results of 10 min averaged rotor speed (n_R) at the feather pitch angle (θ_F) of 82 to 92 degrees. The average wind speed is 50 m/s with 11% of turbulence intensity, 0.11 of average wind shear, and 0 degree of average yaw error. The figure shows that the rotor speed in idling decreases as the pitch angle increases. The average rotational direction reverses around 90 degrees of pitch angle. No particular rule exists for the full feather pitch angle, but in this study, given the condition of almost no reverse rotation, 87 degrees was determined as the full feather pitch angle, which corresponds to an average value of −2σ (average − 2σ; exceedance probability 2.3%). Here, σ is the standard deviation. The pitch angle was taken as the pitch angle during feathering.

2.4. Conditions for Major Excitation Sources

The settings for the major sources of vibration due to rotor rotation are described below.

2.4.1. Rotor Aerodynamic Imbalance

The rotor aerodynamic imbalance is caused by the mutual deviations in the blade shapes and pitch angles, and mainly excites the tower in a direction out of the rotor plane. Recent design standards and guidelines do not specify the conditions, so in this study the pitch misalignment of one of the three blades was set to −0.3 degrees, and one of the other blades was set to +0.3 degrees, following to GL2010 [9].

2.4.2. Rotor Mass Imbalance

The rotor mass imbalance mainly excites the tower in the rotor in-plane direction. GL2010 stipulates that the rotor mass imbalance should be considered according to the specifications of the wind turbine manufacturer, and 264 kgm of rotor mass imbalance (equivalent to a shaft position deviation of 3 mm) was assumed as a realistic value, in this study.

2.4.3. Blade–Tower Aerodynamic Interaction

Blade–tower aerodynamic interaction applies an impulsive variable load to the blades passing around the tower. We applied the “load equivalent tower shadow model” by Yoshida et al. [10] in this study. This is similar to the “combined tower shadow model” in Bladed, defining the aerodynamic influence of the tower by two-dimensional potential theory. The wind speed distribution behind the tower is modelled by Gaussian-type distribution for the blade positions on the downwind of the tower; the depth and width of the wind speed distribution, which are neglected in the previous model, are defined considering the mutual interaction between the tower and the rotor in this model.

2.5. Analysis Conditions

IEC61400-1 ed.4 offers steady and extreme turbulent wind conditions. In this study, cases with no yaw slip were analyzed under both conditions.

Table 2. Steady extreme wind conditions of typical DLCs.

	DLC6.1	DLC6.2	DLC6.3	DLC7.1
WT Condition	Normal	Grid loss	Normal	Fault
Wind Speed	70 m/s	70 m/s	56 m/s	56 m/s
Average Yaw Error	−15–+15 degrees	−180–+180 degrees	−30–+30 degrees	0 degree
Turbulence Intensity	–	–	–	–
Turbulence Seed	–	–	–	–
Average Wind Shear	0.11	0.11	0.11	0.11
Average Inclination	0 degree	0 degree	0 degree	0 degree
Pitch Blade 1	87.0 degrees	87.0 degrees	87.0 degrees	0.0–85.0 degrees
Pitch Blade 2	86.7 degrees	86.7 degrees	86.7 degrees	86.7 degrees
Pitch Blade 3	87.3 degrees	87.3 degrees	87.3 degrees	87.3 degrees
Rotor	Idling	Idling	Idling	Idling
PSFL	1.35	1.1	1.35	1.1

and

Table 3. Turbulent extreme wind conditions of typical DLCs.

	DLC6.1	DLC6.2	DLC6.3	DLC7.1
WT Condition	Normal	Grid loss	Normal	Fault
Wind Speed	50 m/s	50 m/s	40 m/s	40 m/s
Average Yaw Error	−8–+8 degrees	−180–+180 degrees	−20–+20 degrees	0 degree
Turbulence Intensity	0.11	0.11	0.11	0.11
Turbulence Seed	6	6	6	6
Average Wind Shear	0.11	0.11	0.11	0.11
Average Inclination	0 degree	0 degree	0 degree	0 degree
Pitch Blade 1	87.0 degrees	87.0 degrees	87.0 degrees	0.0–85.0 degrees
Pitch Blade 2	86.7 degrees	86.7 degrees	86.7 degrees	86.7 degrees
Pitch Blade 3	87.3 degrees	87.3 degrees	87.3 degrees	87.3 degrees
Rotor	Idling	Idling	Idling	Idling
PSFL	1.35	1.1	1.35	1.1

show steady and turbulent extreme wind conditions, respectively. Here, the Kaimal model [1] was used as the turbulence model. The sampling time was set to 0.05 s (20 Hz), which is sufficiently short compared with the natural frequency of first-mode tower bending. The analysis duration was 3 min for each case under steady extreme wind conditions and 10 min for each case under extreme turbulent wind conditions, excluding 1 min at the beginning.

3. Simulation Results of Steady Extreme Wind Conditions

3.1. Rotor Speed

Figure 4 shows the rotor speed to yaw error (ψ) for DLC6.1, DLC6.2, and DLC6.3 under steady extreme wind conditions. It shows that the rotor rotates in the range of −75–+30 degrees of yaw error. The rotor speeds for DLC6.1 and DLC6.2 (both 70 m/s) were exactly the same, approximately 3.6 rpm at a yaw error of −25 degrees. Additionally, the rotor speed for DLC6.3 was 0.8 times that of DLC6.1 and DLC6.2, which was the same as the wind speed ratio. Note that the rotor speed was almost the same in the cases of an elastic body (“Flex” in the figure) and a rigid body (“Rigid”).

Figure 5 shows the rotor speed (1P), blade passing frequency (3P) and its harmonics 6P and 9P for DLC6.2 and DLC6.3, where the rotor speed is maximum, as well as the first-mode tower bending frequency. Generally, the rotor speeds are lower in DLC6.3, as the wind speed is 0.8 times those in DLC6.1 and DLC6.2. For DLC6.2, at yaw errors of −30 and −20 degrees, six times the rotor speed (6P) and the first-mode tower bending natural frequency almost match. In addition, for DLC6.3, excitation frequencies below 6P do not match the natural tower frequency.

Similarly, Figure 6 shows the rotor speed with the blade 1 stuck pitch angle (θ₁) for DLC7.1 under steady extreme wind conditions. The rotor speeds are almost 0 rpm around 0 and 90 degrees of the stuck pitch angles where the angle of attacks to the blade section are close to 90 and 0 degrees, respectively. The maximum rotor speed is approximately 2.2 rpm at 65 degrees of the stuck pitch angle. In addition, Figure 7 shows the excitation frequency and the first-mode bending frequency of the tower depending on the fixed pitch angle for DLC7.1. Under this condition, components below 6P barely excite the first-mode tower bending.

3.2. Tower Base Bending Moment

Figure 8 shows the maximum value of the ultimate bending moment at the tower base with respect to yaw error for each DLC. PSFLs were applied for each DLC. DLC6.2 shows a substantially large value around yaw error of −30 degrees. For DLC6.3, the rotor speed is 0.8 times that of DLC6.1 and DLC6.2, and 6P does not resonate, so it does not peak even at −30 degrees of yaw error. Additionally, even when the tower is rigid for DLC6.2, the peak at the yaw error of −30 degrees does not appear. The above shows that the peak value at a yaw error of −30 degrees of DLC6.2 is caused by the excitation of the first-mode tower bending by 6P. This peak occurs at 15 degrees in the yaw error range. Therefore, if resonance with this harmonic component is ignored, such as by conducting analyses at discrete angles that do not include this yaw error range, the ultimate load will be substantially underestimated.

Figure 9a shows the statistical values of the tower base bending moment to yaw error for DLC6.2. At −30 degrees of yaw error, the average value is also large, in addition to the large standard deviation. Figure 9b shows the similar data to stuck pitch angle of one of the blades for DLC7.1. The influence of the stuck pitch angle in DLC7.1 on the tower base’s bending moment is weaker than that in DLC6.1 and DLC6.2. Furthermore, even at a pitch angle of approximately 60 degrees, where the rotor speed is at its maximum, the resulting excitation is slight.

3.3. Yaw Center Shear Force

The ultimate yaw center shear forces to yaw error are shown in Figure 10. F_XK and F_YK are longitudinal and lateral shear forces, respectively. Although F_XK is generally positive, on the other hand F_YK changes direction at 0 degree of yaw error. Like tower base bending, large loads are generated around −30 degrees of yaw error, where the range of F_YK is large.

Figure 11 shows the power spectral density (PSD) of the yaw center shear forces at the yaw error of −30 degrees in DLC6.2. The thick and thin vertical lines are the tower first-mode bending frequency, and this is 1/2, at which second-order harmonics would excite the tower fist-mode bending.

A large peak appears in the first bending natural frequency (f_T1 = 0.31 Hz) of the tower in both longitudinal (F_XK) and lateral (F_YK) directions, and this component determines the range of the load vibration. Another peak appears at approximately 1/2 of this frequency (0.16 Hz), which corresponds to the blade passing frequency (3P); 6P, which is twice this frequency, also excites the first-mode tower bending. Furthermore, the excitation caused by 1P, which is caused by the mass or aerodynamic imbalances of the rotor, has almost no effect.

3.4. Effect of Analysis Conditions

As mentioned above, no clear regulations exist regarding the resolution of yaw error during idling or parking in a storm in the design standards and guidelines; as such, in this study, we considered the effects of resolution and phase.

Figure 12 shows the maximum values (ultimate load) of the tower base bending moment (M_XYT) with respect to the phase of the average yaw errors of 15 and 30 degrees regarding the resolution. The peak of the load sharply appears in the 15 degree range, so if discretization is inappropriate, the peak of the load may not be captured, and an optimistic design load may be calculated. In this case, the estimate is −40%.

4. Simulation Results of Turbulent Extreme Wind Conditions

4.1. Rotor Speed

Figure 13 shows the rotor speed ((a) average, (b) average + 1σ, and (c) maximum) against the average yaw error under extreme turbulent wind conditions. The points are the values of each seed, and the lines are the average values of each DLC’s yaw error from six seeds. Figure 13d is a summary only of the average values of Figure 13a–c. Additionally, the excitation frequencies for DLC6.2 and DLC6.3 are shown in Figure 14 and Figure 15, respectively. Overall, the rotor speed changes more slowly with respect to the average yaw error than in the case with steady extreme wind conditions. In addition, the rotor speed in DLC6.2 is between the average + 1σ (probability of exceedance 16%) and the maximum value, and the rotor speed in steady extreme wind conditions does not change for any frequency, even in turbulent extreme wind conditions. Additionally, because the wind speed is low in DLC6.3, the rotor speed is generally low.

4.2. Tower Base Bending Moment

Figure 16 shows the distribution of the ultimate load of the tower base’s bending moment under extreme turbulent wind conditions. These are the averages of six seeds’ maximum values for each condition multiplied by the PSFL for load in each case. Like the rotor speed, the change with respect to yaw error is small compared with that in steady extreme wind conditions but has a high load at approximately −30 degrees yaw error, where high rotor speeds are frequent.

4.3. Yaw Center Shear Force

Similarly, the statistical values of the yaw center shear force are shown in Figure 17. Like the tower base’s bending moment, the value of the yaw center shear force is high around the average yaw error of −30 degrees. Figure 18 shows the PSD of the yaw center shear force at a yaw error of −30 degrees. As in the case of steady extreme wind conditions, a large peak occurs at the first natural bending frequency (0.31 Hz) of the tower. Note that no clear peaks can be observed in this 1/2 blade passing frequency (3P) or the frequency corresponding to the rotor speed (1P). This is because the rotor speed is not constant in the case of extreme turbulent wind conditions, but the tower first-mode bending frequency is excited as the rotor speed changes.

4.4. Effect of Analysis Conditions

As in the case of steady extreme wind conditions, the influences of the resolution and phase of the average yaw error were investigated.

Figure 19 shows the maximum value of the tower base’s bending moment (ultimate load) with respect to the initial phase at yaw error resolutions of 15 and 30 degrees. Each load reaches a high value within a range of approximately 10 degrees, so the effect is not as pronounced as in the case of steady extreme wind conditions. However, if the resolution is low, and the initial phase is inappropriate, the ultimate load estimate is more than 5% lower.

5. Conclusions

The influences of self-excitation due to rotor idling under storm conditions were investigated for a 5 MW wind turbine with three blades. Under the designed load conditions DLC6.1, DLC6.2, DLC6.3, and DLC7.1 (one pitch stuck) for wind speed class 1, aeroelastic simulations were performed under the conditions of steady and extreme turbulent wind conditions The following details were obtained by calculating the bending moment at the base of the tower. The first-mode tower bending was set to 0.31 Hz, which is approximately halfway between the variable speed range of 1P and 3P, and the pitch angle at full feather was set to 87 degrees, which reduces the frequency of reverse rotation.

(1)

The results of the analysis under steady extreme wind conditions showed that the rotor speed is high at around −30 degrees of yaw error in DLC6.2, and the first-mode tower bending frequency is excited at twice the blade passing frequency (6P). In addition, under the conditions in DLC7.1 with one blade fixed, the rotor speed cannot reach a high enough speed to considerably excite the tower.

(2)

A similar trend was observed under turbulent extreme wind conditions, although the influence was not as pronounced compared with that under steady extreme wind conditions.

(3)

We confirmed that, unless the average yaw error is analyzed with an appropriate resolution, the excitation due to rotor rotation is not captured, and the ultimate load used in the design is therefore optimistic. In particular, the influence is stronger under steady extreme wind conditions. This result showed that analysis with sufficient resolution is necessary when twice the blade passing frequency during free rotation (6P) exceeds the first-mode tower bending frequency.

(4)

We recommend the resolution of yaw misalignment to be fine enough (5 degrees around the maximum idling speed in this study) to catch the resonance even in storm conditions with large yaw error, such as DLC6.2. This is not stated in design standards and design guidelines, nor considered carefully in the present design of wind turbines. This concern is more important for large offshore wind turbines designed for high wind speed and low turbulence conditions.

A 5 MW class 1 onshore upwind turbine with yaw control/fixed yaw, which is common for large scale wind turbines, was assumed in this study. If the wind speed is higher and less turbulent, the influences would be more critical. Here, downwind turbines with free yaw can avoid the most critical case, DLC6.2 with large yaw error, discussed in this study, but some conditions can be more critical for downwind turbines and two-blade wind turbines, as the impact is expected to increase due to aerodynamic/structural imbalance and aerodynamic interference with the tower. The influences of the foundation and substructures of the bottom fixed onshore and offshore turbines should be modelled appropriately for practical design analysis. Furthermore, an experiment concerning the present phenomenon is planned in future work.