# Why torsional stiffness of Jacket-type structures has a low influence in WTG dynamics

Wind turbine towers are traditionally based on steel tubes of large diameter and thickness. This configuration provides an excellent torsional stiffness, and therefore torsional modes are very fast (usually allocated between the 3P and the 6P excitation frequencies band) and torsional deflection on tower top is highly restrained.

Alternatively, two alternative framed structures have been used in the industry:

- Lattice towers, in two variants:
- Full lattice up to the yaw interface
- Hybrid lattice, using a tubular part on top of the tower

- Jacket-type structures, such as:
- Offshore jackets
- Nabralift tower solution

*Tubular, lattice (std & hybrid) and jacket-type (offshore & Nabralift) towers*

Lattice tower (both full lattice and hybrid solutions) have a very low torsional stiffness, (60-70% lower than a conventional tubular steel tower) that may cause:

- Interferences with the 3P forbidden band
- Large torsional deflections on tower top affecting aerodynamics

On the other side, jacket-type structures have a high torsional stiffness, similar to standard steel towers.

Hereinafter the justification of the difference between the torsional stiffness of lattice and jacket-type tower is discussed and justified.

**Torsional stiffness of thin-walled closed sections**

Torsional stiffness of thin-walled closed sections is given by:

where

- A is the area enclosed by the mean perimeter P
- t is the wall thickness
- G is the material shear modulus

According to this expression, the combination of the section geometry (circular, square, triangular…), section size and wall thickness define the torsional stiffness of the structure.

**Effect of section geometry**

Section geometry affects to the torsional stiffness, due to the different ratio between area and perimeter.

To illustrate this effect, torsional stiffness has been calculated for three sections (circular, square, triangular) of equivalent perimeter:

*Effect of Section Geometry on the Torsional Stiffness*

*Iso-perimeter Sections: Circular, Square & Triangular*

Results confirm that circular sections have the highest torsional stiffness, whereas triangular sections have the lowest stiffness. Other polygonal geometries, such as square sections, have an intermediate torsional stiffness.

**Effect of wall thickness**

Torsional stiffness is proportional to wall thickness, as illustrated in the following table:

**Effect of section size**

Torsional stiffness is significantly affected by section size: it increases to the third power in respect to the section diameter/side, as shown in the following table.

Therefore, __section size is the variable that most influences torsional stiffness of the structure__.

**Evaluation of torsional stiffness of WTG towers**

Coming back to the tower comparison, the torsional stiffness of the uppermost, central, and lowermost sections is analyzed to have a full understanding of the structures.

*Uppermost, central and lowermost sections identification*

At these sections, torsional stiffness is calculated for representative designs of lattice and jacket-type typologies (140 m high in all cases), according to the following criteria:

- Tubular tower:
- Maximum diameter limited to 4.3m for logistic constraints

- Lattice tower:
- A lattice with 4 legs is considered (square section). Results do not change significantly if number of legs is increased.
- Section size is limited in the central section to guarantee blade clearance (i.e. side of 5m).
- An equivalent wall thickness is calculated from the design of the bracing of the structure.

- Jacket-type:
- Nabralift 2.0 design is used as a representative example
- An equivalent wall thickness is calculated from the design of the bracing of the structure.

Results of the analysis are shown in the following table:

Next figure compares the torsional stiffness along the height of the three towers:

Comparison between the tower alternatives shows that:

- Tubular towers have a high torsional stiffness along the full structure.
- Lattice towers
__have a very low torsional stiffness in the upper and central part of the structure__. In the lower part, as the distance between the legs increases, the torsional stiffness rises to high values. - Jacket-type towers
__do not have any zone of low torsional stiffness__, since the transition piece connects the upper tubular part with a frame structure with a high torsional stiffness due to the large distance between columns.

Note that WTG dynamics are mostly driven by the tower sections with lowest stiffness, so tubular and jacket type towers (as shown in next section) will have similar dynamics, whereas lattice tower will have dynamics with larger nacelle rotations and lower torsional frequencies.

**Evaluation of torsional stiffness of WTG dynamics**

Wind turbine towers need high torsional stiffness to:

- Avoid large rotations of tower top in operation, that would increase inertial loads and would create interferences with the WTG aerodynamics (causing additional loads and energy losses)
- Avoid interferences between the 1
^{st}torsional mode of the WTG and the 3P excitation frequency

Both the rotation and the frequencies are analyzed hereinafter for the three tower alternatives described in the previous section.

**Tower top rotation**

Tower top rotation has been evaluated under a reference torque on top (Mz=3 000 kNm) for the three tower typologies. The following figure shows the rotation of each tower in this condition.

*Uppermost, central and lowermost sections identification*

Results of this analysis confirm that:

- tubular and jacket type towers have low deflection on tower top
- lattice towers have large torsional deflections on tower tow, that may generate load increases and loss of production

Note that results are mainly driven by the more flexible zone of the tower (the central and upper sections). Differences in the stiff lower zone of the towers (i.e. between the tubular tower and the Nabralift tower) are not affecting significantly the tower top rotation.

To reduce tower top rotation, lattice towers may be transformed to hybrid-lattice structures with tubular segments on top. However, this solution would still have a very flexible section in the zone right under the transition piece that would make this solution more flexible than tubular or jacket type towers.

**Torsional mode excitation**

Torsional frequencies have been calculated for the three tower typologies. The following table shows the frequencies obtained in this analysis.

*1 ^{st} Torsional Mode Frequencies (140 tall towers)*

1^{st} torsional mode must be far from the 3P excitation frequency. Modern turbines have a nominal rated speed of 10-12 rpm. Therefore, torsional frequencies must be out of a band of 0.45-0.65Hz to avoid rotor induced vibrations. Next figure compares both torsional mode frequencies with this forbidden zone:

*1 ^{st} Torsional Mode Frequencies (140 tall towers) vs 3P forbidden band*

Tubular and jacket type tower do not have problems in staying over the forbidden band, whereas lattice towers may not fulfil this requirement due to the low torsional stiffness of the upper and central part of the structure.

As proposed above, lattice towers can be transformed to hybrid-lattice structures with tubular segments on top to increase torsional frequency, but the solution would have more flexibility than tubular or jacket type towers due to the flexible section in the zone right under the transition piece.

**Conclusions**

Wind turbine tower with low torsional stiffness sections may face challenges regarding tower top rotation and low torsional frequencies.

Low torsional sections happen with the concurrence of the following factors:

- Polygonal tower sections
- Frame structures
- Small section side

The following figure illustrates the stiff and flexible sections of tubular, lattice and jacket-type towers:

*Stiff (green) and flexible (red) sections of WTG towers*

Tubular tower and jacket-type (such as Nabralift) towers are widely used in onshore and offshore applications. Both tower typologies show good torsional stiffness along the full structure, what restrains the rotation of the tower top and keeps the 1^{st} torsional mode far from the rotor induced vibrations frequencies.

On the other hand, the upper and central part of the lattice towers has a low torsional frequency. This may lead to excessive rotations of the tower top during operation and makes more complicated to avoid rotor resonance frequencies due to the closeness of the 1^{st} torsional mode with the 3P excitation frequency.

To mitigate problems related to the torsional stiffness of lattice towers, hybrid-lattice solutions with tubular segments on top may be used. However, this typology would still have a very flexible section in the zone right under the transition piece that would make this solution more flexible than tubular or jacket type towers.