Natural Period

TECHNICAL FIELD

[0001] The present disclosure relates in general to wind turbines and more specifically to shallow floats supporting offshore wind turbines and providing stability by exhibiting a high natural frequency of rigid motions in the water.

BACKGROUND

[0001] A wind turbine is a rotating machine that, converts kinetic energy from wind into mechanical energy that is converted to electricity. Utility-scale, horizontal-axis wind turbines have horizontal shafts that are commonly pointed into the wind by a shaft and generator assembly within a nacelle, at the top of a tower that is yawed relative to the tower in order to align the rotor with the wind. The nacelle commonly houses a direct drive generator or a transmission and generator combination.

[0002] The state of the art includes offshore wind turbines that are anchored to the ocean bottom and are neither built nor intended to be moved. In waters shallower than 60m, wind turbines used for offshore applications commonly include single-tower systems mounted to the sea bed But in deeper waters such towers are too expensive, so the turbines must float, using submersible or semi-submersible platforms employing spars or spar buoys, tension legs, or a large-area barge-type construction. Offshore turbines are usually connected to am onshore power grid and electrical energy produced is transferred and conditioned by ocean-floor grid structures.

[0003] Waves are created by wind blowing across the water. A wave pattern on the ocean’s surface is defined as sea when it is generated locally and traveling in various directions at varying speeds. Waves generated by remote wind in the open ocean are called swell, these travel in a single direction and are somewhat more regular than sea waves. But they still present a very irregular aspect, being formed as the instantaneous summation of many different small waves traveling at different speeds and adding elevations at each point.

[0004] A wave's crest is its point of maximum elevation. A wave trough is the point of minimum elevation. A wave amplitude A equals one half the wave's height H, which is the distance between the crest and the trough.

[0005] In deep water, wavelength X is the distance between two crests, troughs or inflection points with the same curvature above and below the points. Period, T, is the time it takes one wavelength to pass by a fixed position. A swell is formed of many different wavelengths, each with its own height and starting time; mathematically the most complete description is with a ‘spectrum’.

[0006] The wave of a specific wavelength L (in meters) has a period T in seconds related by the following equation. The speed of a wave is defined by L/T, so each wavelength travels at a different speed. :

T ² L = 9.81 — 2n

[0007] The heave response amplitude operator (heave RAO) for a floating structure or vessel is a plot of heave amplitude divided by wave amplitude as a function of every possible wave frequency or wavelength. RAOs describe a vessel’s response to wave-frequency excitation. RAOs are typically determined by diffraction analysis.

[0008] The resonance of a floating structure is of concern when medium or large waves have a frequency similar to the natural frequency of the floating structure. Damaging ocean wave energy tends to occur in waves where period, T, is between T = > 5 and T = < 20 seconds, so L is between L = 39m and 625m.

[0009] For every wave L or T, the resulting motion of a floating body may be approximated as a multiplier of wave height. When Heave RAO = 1, a body will move vertically to match wave motion at that wave frequency. When RAO is <1, a floating body will move up and down less than the waves of those frequencies. When RAO >1 , the body may be said to be resonant, meaning that it moves up and down at the frequency of the wave but with greater amplitude, in other words higher than the height of the wave and lower than the trough of the wave. It is commonly desirable to avoid an RAO >1 particularly where T is between T = 5s and T = 20s.

[0010] One conventional approach to keep RAO <1 is to build a structure that has a natural frequency that is lower than the wave frequency of the intended environment. In one example a natural period of a structure being > 20s will typically suffice. Some common examples exhibit a natural period of 30s. A relatively long natural period may be achieved by a relatively large mass and a relatively small water-plane area. The heave radian frequency of a slender vertical cylinder is determined as the square root of the heave stiffness divided by the draft; divide by 2n to give frequency in Hz. Heave stiffness may be expressed as water density times g, times the water-plane area. For a slender cylindrical body, radian frequency simplifies to the square root of g/draft. The natural period in seconds is expressed in the following equation where D = draft in meters and g = 9.81 m/s ^A 2:

For example, a draft of 100 meters gives a period of 20 seconds. One skilled in the art understands that an appropriate practice is to design a structure to have a period longer than 20 seconds and in many cases close to 30 seconds.

### this should be para 0011 ### In contrast, when a flat cylindrical float has a large radius R compared to its draft, the heave period is T = 2n^R/g . These formulas may be combined approximately to give the period for any cylindrical float defined in terms of radius and draft: = 2n^R + D)/g .

When the object is a short natural period for a given float volume, the optimum cylinder shape is a draft of half the radius, and the period becomes T = 2n^ 1.29 V ^1/3 /g

[0011] What is not common in the state of the art is a floating wind turbine structure having a natural period (i .e., the period of a possible RAO peak) that is less than most wave periods, with a submerged shape exhibiting no RAO peak. This will lead to RAO = 1 in most waves, but never greater. [0012] A floating body may be said to be equi-axed when the vertical dimension d (approximately the cube root of the submerged volume) of the underwater part is approximately equal to the horizontal dimension. In general a float of given volume displacement achieves the shortest period when it is near to equi-axed, in other words neither far wider or far slenderer than its diameter.

SUMMARY

[0013] A structure for supporting an offshore wind turbine employs shallow draft floats supporting a wind turbine structure.

[0014] In an example embodiment, an apparatus has at its central portion a horizontal structure that is configured to support a rotating shaft at both ends. Energy from the shaft driven by a wind-turbine rotor is transferred to electrical-generation equipment . In one embodiment, this central portion is supported on a plurality of legs, each with a shallow float at the base.

[0015] In one embodiment a structure is designed to move vertically as a wave passes, rather than the common approach of designing to avoid wave-induced movement. An equi-axed shape supporting a minimum weight per float provides a relatively high natural frequency. In one embodiment a shallow float is formed by two conical sections joined at their bases.

[0016] In one embodiment a float is an equi-axed form, a 90 degree cone supporting approximately 250 tons providing a four second heave period. A set of 4 floats support a turbine structure. Each float supports <250 tons. One skilled in the art understands that reducing the weight per float will reduce the period.

[0017] Other equi-axed float shapes will also maintain a short natural period, for example a hemisphere, a short cylinder, or a pointed cone with apex angle around 90 degrees.

[0018] Drawings are designed as an illustration and not as a definition of the limits of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] FIG. 1 is a perspective view of an example embodiment of the present disclosure;

[0020] FIG. 2 is a side view thereof;

[0021] FIG. 3 is a perspective view of a turbine supported by the example embodiment.

DESCRIPTION

[0022] FIG. 1 shows a perspective view of an example embodiment 100. A frusto-conical section 1 10 is joined at its base with the top of a second frusto conical section 1 12 forming an equatorial plane 130. Except in extreme conditions, the upper section 110 is not submerged; heave response is defined by the lower section 112.

[0023] FIG. 2 shows a side view of the embodiment. The equatorial width 114 of the portion 112 is a little greater than its height 122, providing an equi-axed form. In some embodiments the width 114 of the apparatus 100 is approximately equal to the height 116, providing an equi-axed form. The diameter 118 of the top 111 of the upper frusto conical section 110 is approximately equal to the distance 120 from the equatorial plane 130 to the top 111. The diameter 124 of the base 113 of the lower frusto-conical section 112 is approximately equal to the distance 122 from the base 113 of the second frusto-conical section, to the equatorial plane 130.

[0024] FIG. 3 shows an example embodiment 100 in situ on a floating turbine 101. In the example embodiment, four floats are used to support the turbine structure. The upper frusto- conical section 110 is designed to remain above the water and half or more of the lower frusto- conical section 112 resides under water. The weight of the turbine 101 is distributed across the floats 100. The distributed weight and equi-axed underwater volumes provides a relatively high natural frequency. A stiff mooring line 132 can further assist in providing a relatively high natural frequency.