CABLE STAYED WIND TURBINE

FIELD OF THE INVENTION

The present invention relates to a wind turbine comprising at least three stay cables, sometimes referred to as a cable stayed wind turbine. The wind turbine of the invention is positioned at a site with uneven terrain. The invention further relates to a method of constructing such a wind turbine.

BACKGROUND OF THE INVENTION

Wind turbines are sometimes provided with stay cables connected between a mounting position at the tower of the wind turbine and a stay cable foundation arranged at a distance from the tower of the wind turbine. The stay cables support the tower, in particular with respect to bending moments in the tower. Thereby it is possible to provide slender towers, possible with thinner walls, while ensuring that the strength of the wind turbine is sufficient to withstand expected loads during operation. Smaller foundations may also be used when the wind turbine is provided with stay cables.

When the wind turbine is positioned at a site with uneven terrain, stay cables extending from the wind turbine tower in different directions may have lengths which differ from each other. This gives rise to variations in stiffness of the cables, from one cable to another. This is highly undesirable, since it may result in uneven natural frequencies and uneven loads on the wind turbine, in particular on the tower.

EP 2 711 485 B1 discloses a hybrid tower structure comprising a plurality of stay cables connected to the tower structure and equipped with means for adjusting the tension of the cables for adjusting the stiffness of the tower structure and thereby obtaining specific frequencies for the tower structure. DESCRIPTION OF THE INVENTION

It is an object of embodiments of the invention to provide a cable stayed wind turbine which can be erected at a site with uneven terrain without introducing variations in eigenfrequencies or stiffness of the tower system. According to a first aspect the invention provides a wind turbine comprising a tower mounted on a foundation, a nacelle mounted on the tower and a rotor mounted on the nacelle, wherein at least three stay cables are connected, at a first end, to the tower, each stay cable further being connected, at a second end, to a stay cable foundation, wherein the stay cable foundations are positioned on a slope defined by a slope plane intersecting at least three of the stay cable foundations, wherein each stay cable has a length defined by a distance between its connecting point at the tower and its stay cable foundation, wherein the lengths of the stay cables differ from each other due to the slope of the slope plane, wherein each stay cable is configured in such a manner that the stiffness of the stay cables are substantially equal and with a tension in the stay cables that are substantially equal.

Thus, according to the first aspect, the invention provides a wind turbine comprising a tower mounted on a foundation. A nacelle is mounted on the tower and a rotor is mounted on the nacelle. The wind turbine is further provided with at least three stay cables, i.e. the wind turbine is a cable stayed wind turbine. Each stay cable is connected, at a first end, to the tower and, at a second end, to a stay cable foundation.

The wind turbine is positioned at a site with an uneven terrain, and therefore the stay cable foundations are not all positioned at the same level, and the foundation of the tower is not necessarily arranged at the same level as any of the stay cable foundations.

Therefore the stay cable foundations are positioned on a slope defined by a slope plane intersecting at least three of the stay cable foundations. In the present context the term 'slope plane' should be interpreted to mean an imaginary or mathematical plane which is defined by the positions of at least three of the stay cable foundations. Due to the uneven terrain, the slope plane may not be arranged horizontally, and thereby it will define a slope relative to horizontal, i.e. it will be inclined relative to horizontal. It is, however, not ruled out that the slope plane may be arranged horizontally, but in this case the foundation of the tower may be arranged above or below the slope plane.

Each stay cable has a length defined by a distance between its connecting point at the tower and its stay cable foundation. Due to the slope of the slope plane, caused by the uneven terrain, the lengths of the stay cables differ from each other.

Each stay cable is configured in such a manner that the stiffness of the stay cables are substantially equal and with a tension in the stay cables that are substantially equal. If cables of the same kind are used for the stay cables, the differing lengths of the stay cables would result in differing stiffness of the stay cables, and this would in turn result in variations in tower eigenfrequencies.

Equal cable frequencies of the stay cables can be obtained by adjusting the tension in the cables, e.g. as described in EP 2 711 485 Bl. However, this may result in uneven loads on the wind turbine, in particular on the tower.

Furthermore, the tower frequencies are typically not allowed to overlap with the wind turbine rotor frequencies. Therefore, variations in the frequencies may lead to a need for design changes, and possibly non-optimal material use, and it may even be impossible to make a single design which suits different sites.

It is an advantage of the wind turbine of the present invention that the stay cables are configured in such a manner that the stiffness of the stay cables as well as the tension in the stay cables are substantially equal, because thereby the differing lengths of the stay cables can be handled in a manner which does not affect the eigenfrequencies and without introducing uneven loads in the wind turbine. According to the invention, each stay cable is configured with due consideration to the length which is dictated by the uneven terrain, and in such a manner that the same stiffness, or at least approximately the same stiffness, is obtained for all of the stay cables.

The wind turbine may comprise exactly three stay cables. In this case the stay cables may advantageously be arranged with an angle of 120° there between. Such a configuration ensures that the tower is capable of withstanding loads caused by the incoming wind, regardless of the direction of the wind.

Alternatively, the wind turbine may comprise more than three stay cables, for instance an uneven number of stay cables and/or a multiple of three stay cables.

Each stay cable may have a cross-sectional area, and the cross-sectional areas of the stay cables may be configured to achieve a substantially equal stiffness of the stay cables.

According to this embodiment, the equal stiffness of the stay cables are obtained by carefully selecting appropriate cross-sectional areas for each of the stay cables. The longer a cable with a given cross-sectional area is, the smaller the stiffness of the cable will be. Therefore, a stay cable which is longer than another stay cable should be designed with a larger cross-sectional area than the shorter stay cable in order to obtain that the stiffness of the two cables are identical.

Thus, the cross-sectional area of at least one stay cable may be different from the cross sectional area of the other stay cables.

For instance, the cross sectional area of a given stay cable may be selected using the formula: k=E-A/L, wherein k is the stiffness of the stay cable, E is the Young's module of the stay cable, A is the cross sectional area of the stay cable, and L is the length of the stay cable. If a specific material is selected for the stay cables, the Young's module, E, is a constant. The length, L, of each of the stay cables is given by the positions of the stay cable foundations, i.e. by the distance between each of the connecting points on the tower and the corresponding stay cable foundation. A desired stiffness, k, which is to apply to all of the stay cables can be selected, and then the cross-sectional area, A, can easily be calculated for each of the stay cables, using the formula above.

Each stay cable may be formed from a plurality of strands, and the cross- sectional area of each stay cable may be selected by selecting the number of strands in each stay cable. This is a very easy way of adjusting the cross- sectional areas of the stay cables. According to this embodiment, the cross- sectional area of each stay cable may be selected from a plurality of discrete area steps, where the distance between the area steps corresponds to the cross- sectional area of a single strand. In other words, the cross-sectional area of a stay cable can be increased or decreased by one area step by adding or removing one strand to/from the cable. Thereby the resulting stiffness of the stay cables may not be exactly identical, but the differences in stiffness are sufficiently small to avoid the variations in eigenfrequencies and uneven loads described above.

As an alternative, each stay cable may be formed from a single strand.

According to this embodiment, the cross-sectional areas of the stay cables may be varied continuously, and thereby exactly identical stiffness of all of the stay cables may be obtained.

The cross-sectional area of each of the stay cables may be larger than a predefined minimum cross-sectional area. The minimum cross-sectional area may be selected in such a manner that it is ensured that each of the stay cables is capable of withstanding expected loads during operation of the wind turbine. For instance, the cross-sectional area of each of the stay cables should be sufficient to provide a required breaking force of the cable. Thus, according to this embodiment, the cross-sectional areas of the shorter stay cables should not be reduced below the minimum cross-sectional area in order to obtain equal stiffness of the stay cables. Instead the cross-sectional areas of the longer stay cables must be increased.

As an alternative to adjusting the cross-sectional areas of the stay cables, other parameters of the stay cables, such as choice of material, cable angle, use of reinforcement element, etc., could be varied from one stay cable to another. Alternatively or additionally, an additional element with a selected spring stiffness could be arranged in series with the cables, in order to keep the overall stiffness constant.

An angle defined between a stay cable and the tower may be substantially identical for each of the stay cables. As a stay cable extends from the connecting point on the tower to the stay cable foundation, which is arranged at a distance from the tower, the cable defines an angle with the tower, which is larger than 0° and smaller than 90°. The angle decreases if the stay cable foundation is moved closer to the tower, and it increases if the stay cable foundation is moved longer away from the tower.

By designing the wind turbine in such a manner that the angles defined between the stay cables and the tower are substantially identical, uneven loads on the tower caused by pull in the stay cables are minimised.

The angle defined between a given stay cable and the tower may

advantageously be approximately 45°.

One of the stay cables may be arranged along a direction which is directly downhill along the slope plane. The stay cable which is arranged directly downhill along the slope plane will typically be the one having its stay cable foundation arranged at the lowest level among the stay cable foundations.

Thereby this stay cable will also typically be the longest of the stay cables.

In the case that the wind turbine comprises exactly three stay cables, and in the case that the wind turbine is positioned on a sloping hill, the other two stay cables will be arranged along directions which are uphill along the slope plane. These two stay cable may be of substantially equal length. This orientation of the stay cables is the one which minimises the added material use when handling the uneven terrain.

The material for the stay cables may be selected such that Young's module of at least one stay cable is different from the Young's module of the other stay cables. According to this embodiment, the stiffness of the stay cables is adjusted by adjusting material properties of the stay cables, instead of or in addition to adjusting the cross-sectional area.

According to a second aspect the invention provides a method of constructing a wind turbine comprising a tower mounted on a foundation, a nacelle mounted on the tower, a rotor mounted on the nacelle, and at least three stay cables, each connected, at a first end, to the tower and, at a second end, to a stay cable foundation, the stay cable foundations being positioned on a slope, the method comprising the steps of: - identifying a position for the foundation,

- identifying positions for each of the stay cable foundations,

- defining a slope plane intersecting at least three of the stay cable

foundations,

- deriving a length of each stay cable from the distance between its

connecting point at the tower and its stay cable foundation, and

- selecting each of the stay cables in such a manner that a stiffness of the stay cables are substantially equal and with a tension in the stay cables that are substantially equal.

The method according to the second aspect is a method of constructing a wind turbine. The wind turbine could, e.g., be a wind turbine according to the first aspect of the invention, and the remarks set forth above are therefore equally applicable here.

In any event, the wind turbine being constructed comprises at least three stay cables, each being connected between a connecting point on the tower of the wind turbine and a stay cable foundation, and thereby the wind turbine is a cable stayed wind turbine.

In the method according to the second aspect of the invention, a position for the foundation of the wind turbine and positions for each of the stay cable

foundations are initially identified. The wind turbine is arranged in an uneven terrain, as described above, and the stay cable foundations are thereby positioned on a slope. Accordingly, once the positions for the foundation and the stay cable foundations have been identified, a slope plane intersecting at least three of the stay cable foundations is defined. In the case that the wind turbine comprises exactly three stay cables, the positions of the three stay cable foundations uniquely defines a plane

intersecting all of them. In the case that the wind turbine comprises more than three stay cables, all of the stay cable foundation may still be intersected by the slope plane, but it is not ruled out than one or more of them will not be intersected by the slope plane. In this case, the slope plane may be defined based on the three stay cable foundations which are regarded as the ones which most accurately reflect actual sloping conditions on the site of the wind turbine.

Next, a length of each of the stay cables is derived from the distance between its connecting point at the tower and its stay cable foundation.

Finally, each of the stay cables is selected in such a manner that a stiffness of the stay cables are substantially equal and with a tension in the stay cables that are substantially equal. This has already been described in detail above.

As a final step, the wind turbine may be erected, arranging the foundation and the stay cable foundations at the identified positions, and using the selected stay cables. Thereby a wind turbine with the advantages described above with reference to the first aspect of the invention is obtained.

The step of selecting each of the stay cables may comprise tailoring a cross- sectional area of each stay cable in order to achieve a substantially equal stiffness of the stay cables. This has already been described above.

One of the stay cable foundations may be arranged directly downhill along the slope plane relative to the foundation, and the step of selecting each of the stay cables may comprise selecting a cable with a baseline cross-sectional area for the stay cable foundation arranged directly downhill relative to the foundation, and calculating cross-sectional areas for each of the other stay cables based on the baseline cross-sectional area.

According to this embodiment, the stay cable being connected to the stay cable foundation which is arranged directly downhill relative to the foundation of the wind turbine is the one which is expected to be the longest of the stay cables. As described above, the longest of the stay cables should also be the one with the largest cross-sectional area when an equal stiffness of the stay cables is desired.

Thus, for the stay cable connected to the stay cable foundation arranged directly downhill of relative to the foundation of the wind turbine, the baseline cross- sectional area is selected. The length of the stay cable is defined by the position of the stay cable foundation, and the Young's module of the stay cable is defined by the material of the stay cable. Thereby the stiffness of the stay cable can be calculated using the formula: k=E-A/L, wherein k is the stiffness of the stay cable, E is the Young's module of the stay cable, A is the cross sectional area of the stay cable, and L is the length of the stay cable. The stiffness, k, calculated in this manner is then selected as the stiffness which all of the other stay cables must have. The lengths of the other stay cables are defined by the positions of the their respective stay cable foundations, and the Young's modules are defined by the selected material. Accordingly, the cross- sectional areas of each of the other stay cables can be calculated, using the formula above.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in further detail with reference to the accompanying drawings in which Fig. 1 is a perspective view of a wind turbine tower for a wind turbine according to an embodiment of the invention,

Fig. 2 shows side views of wind turbine towers for wind turbines according to three different embodiments of the invention,

Figs. 3-5 are graphs illustrating cable stiffness, tower bending frequencies, cable forces and strand forces for a prior art wind turbine, and

Figs. 6-8 are graphs illustrating cable stiffness, tower bending frequencies, cable forces and strand forces for a wind turbine according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE DRAWINGS Fig. 1 is a perspective view of a tower 10 for a wind turbine according to an embodiment of the invention. Three stay cables 11 are each connected, at a first end, to the tower 10, and, at a second end, to respective stay cable foundations 12. Accordingly, the tower 10 is a cable stayed tower. The stay cables 11 are labelled Ί', '2' and '3' in order to distinguish them from each other in the following. The tower 10 is positioned in an uneven terrain, and therefore the stay cable foundations 12 are arranged at various levels. Thereby a slope plane 13 is defined, the slope plane 13 intersecting each of the three stay cable foundations 12. Due to the uneven terrain, the slope plane 13 is inclined, i.e. it defines an angle with respect to horizontal.

The stay cables 11 have been positioned in such a manner that the stay cable 11 labelled Ί' is arranged along a direction downhill from the position of the tower 10. Accordingly, the stay cable foundation 12 of the stay cable 11 labelled Ί' is arranged at a lower level than stay cable foundations 12 of the stay cables 11 labelled '2' and '3', and the stay cable 11 labelled Ί' is arranged essentially along a slope defined by the slope plane 13. This is illustrated by insert 14, in that the slope plane 13 is tilted around the y axis shown in the insert 14.

Due to the inclined slope plane 13, the lengths of the stay cables 11 are not identical. Instead, the length of the stay cable labelled Ί' is the longest, since the stay cable foundation 12 of this stay cable 11 is the one which is arranged at the lowest level. The stay cables 11 labelled '2' and '3' may have substantially identical lengths, but this needs not be the case.

As described above, varying lengths of the stay cables 11 would result in variations in stiffness of the cables, and possibly in the tension introduced in the cables, from one cable to another, if the stay cables 11 were made from identical cable material. In order to avoid this, each of the stay cables 11 is configured in such a manner that the stiffness of each of the stay cables 11 are substantially equal and with a tension in the stay cables 11 that are substantially equal. Thus, the individual stay cable 11 is designed with due consideration to the length of the stay cable 11, and in such a manner that the stiffness and tension do not vary from one stay cable 11 to another.

For instance, a cross-sectional area of each stay cable 11 may be selected in such a manner that equal stiffness is obtained among the stay cables 11, without having to increase the tension in some of the stay cables 11. In this case, a longer stay cable 11 should be designed with a larger cross-sectional area than a shorter stay cable 11. Various cross-sectional areas may, e.g., be obtained by varying the number of strands used for forming the stay cable 11.

Fig. 2 shows side views of wind turbine towers 10a, 10b, 10c for wind turbines according to three different embodiments of the invention. The towers 10a, 10b, 10c are similar to the tower 10 illustrated in Fig. 1, and they will therefore not be described in detail here.

The tower 10b is arranged at a position where the slope plane is not tilted about the y axis illustrated in Fig. 1, indicated by 'Y=0°'. Accordingly, the stay cable foundations are, in this case, all arranged at the same level, and at the same level as the tower foundation, and the stay cables 11 have substantially identical lengths. Therefore, the stay cables 11 can be designed in an identical manner, e.g. with identical cross-sectional areas.

The tower 10a is arranged at a position where the slope plane is inclined with respect to horizontal, in such a manner that the stay cable foundation of the stay cable 11 labelled Ί' is arranged at a lower level than the stay cable foundations of the stay cables 11 labelled '2' and '3'. This is indicated by Ύ=- 10°', and can also be seen from the varying levels of the end points of the stay cables 11. The slope plane is indicated by a dotted line. This is the situation illustrated in Fig. 1 and described above. Accordingly, for the tower 10a the stay cable 11 labelled Ί' is longer than the stay cables 11 labelled '2' and '3', and should therefore be designed differently, e.g. with a larger cross-sectional area, in order to obtain substantially equal stiffness of the stay cables 11.

The tower 10c is arranged at a position where the slope plane is inclined with respect to horizontal, in such a manner that the stay cable foundation of the stay cable 11 labelled Ί' is arranged at a higher level than the stay cable foundations of the stay cables 11 labelled '2' and '3'. This is indicated by

Ύ= + 10°', and can also be seen from the varying levels of the end points of the stay cables 11. The slope plane is indicated by a dotted line. Accordingly, for the tower 10c the stay cable 11 labelled Ί' is shorter than the stay cables 11 labelled '2' and '3', and should therefore be designed differently, e.g. with a smaller cross-sectional area, in order to obtain substantially equal stiffness of the stay cables 11.

Figs. 3-5 show graphs illustrating various parameters of a prior art wind turbine. The wind turbine is a cable stayed wind turbine comprising three stay cables, and it is positioned in an uneven terrain, resulting in different lengths of the stay cables, essentially as described above with reference to Figs. 1 and 2. The stay cables are arranged in such a manner that a slope plane intersecting each of the stay cable foundations is tilted around a y axis as defined in the insert of Fig. 1. The stay cables are designed in an identical manner, i.e. from the same cable material, without taking the various lengths of the stay cables into account.

Fig. 3 is a graph illustrating cable stiffness of the three stay cables as a function of inclination angle of the slope plane. It is clear from the graph, that the inclination angle has a significant impact on the stiffness of the cables. This is due to the fact that a change in inclination angle changes the levels at which the stay cable foundations are arranged, and thereby the lengths of the stay cables.

Furthermore, it can be seen that tilting the slope plane towards negative inclination angles causes the stiffness of the stay cable labelled Ί' to decrease, while the stiffness of the stay cables labelled '2' and '3' increases. This is due to the fact that negative inclination angles increases the length of the stay cable labelled Ί' and decreases the lengths of the stay cables labelled '2' and '3', as illustrated in Fig. 2.

Similarly, tilting the slope plane towards positive inclination angles causes the stiffness of the stay cable labelled Ί' to increase, while the stiffness of the stay cables labelled '2' and '3' decreases. Thus, the difference in stiffness between the stay cable labelled Ί', on the one hand, and the stay cables labelled '2' and '3', on the other hand, increases as the inclination of the slope plane increases, regardless of whether the inclination angle is positive or negative. Fig. 4 is a graph illustrating tower bending frequencies originating from the three stay cables as a function of inclination angle of the slope plane. It is clear from the graph, that the inclination angle has a significant impact on the tower bending frequencies. This is due to the fact that the tower bending frequencies are closely related to the stiffness of the stay cables. Therefore, the difference in stiffness between the stay cable labelled Ί', on the one hand, and the stay cables labelled '2' and '3', on the other hand, caused by the difference in length of the stay cables and described above with reference to Fig. 3, results in a corresponding difference in tower bending frequencies. This is very undesirable, since it may lead to uneven loads on the wind turbine. Furthermore, tower frequencies are not allowed to overlap with the turbine rotor frequencies.

Fig. 5 shows three graphs illustrating minimum cable forces, maximum cable forces, minimum strand forces and maximum strand forces, respectively, introduced in the stay cables as a function of inclination angle of the slope plane. It can be seen from the graphs of Fig. 5 that these forces also vary as a function of the inclination angle of the slope plane. As a result, a cable design which is optimised to the limit level will lead to upper and/or lower limits being exceeded. The limit levels are indicated by dashed lines.

Figs. 6-8 are graphs illustrating various parameters for a wind turbine according to an embodiment of the invention. The wind turbine is a cable stayed wind turbine comprising three stay cables, and it is positioned in an uneven terrain, resulting in different lengths of the stay cables, essentially as described above with reference to Figs. 1 and 2. The stay cables are arranged in such a manner that a slope plane intersecting each of the stay cable foundations is tilted around a y axis as defined in the insert of Fig. 1. The stay cables are designed in accordance with the invention, i.e. in such a manner that the various lengths of the stay cables are taken into account, and in such a manner that the stiffness of the stay cables is substantially equal.

Fig. 6 is a graph illustrating cable stiffness of the three stay cables as a function of inclination angle of the slope plane, and is similar to Fig. 3. However, in this case the stiffness of each of the stay cables is substantially independent of the inclination angle of the slope plane. This is due to the design of the stay cables described above. Accordingly, regardless of the inclination angle of the slope plane, the stiffness of the stay cables remains substantially identical, i .e. no difference in stiffness occurs, as was the case in the prior art wind turbine illustrated in Fig. 3.

Fig. 7 is a graph illustrating tower bending frequencies originating from the three stay cables as a function of inclination angle of the slope plane, and is similar to Fig. 4. However, in this case the inclination angle has almost no impact on the tower bending frequencies, and thereby almost no difference in tower bending frequencies from one stay cable to another occurs, even for large inclination angles of the slope plane. This is due to the close relationship between the stiffness of the stay cables and the tower bending frequencies described above, and due to the design of the stay cables ensuring equal stiffness of the stay cables. This is very advantageous, because thereby it is obtained that the cable stayed wind turbine can be positioned at a site with uneven terrain, without introducing differences in tower bending frequencies originating from the stay cables, and thereby without increasing the risk of undesired uneven loads on the wind turbine. Fig. 8 shows three graphs illustrating minimum cable forces, maximum cable forces, minimum strand forces and maximum strand forces, respectively, introduced in the stay cables as a function of inclination angle of the slope plane, and is similar to Fig. 5. It can be seen from the graphs of Fig. 8 that these forces still vary as a function of inclination angle of the slope plane, and that the maximum and minimum limits are still exceeded. However, if a baseline cable thickness is selected which takes the load limits into account, the graphs of Fig.

8 could be moved to be within the design limits for most inclination angles.