GB2494188A

GB2494188A - Controlling parametric resonance in a wave energy conversion system

Info

Publication number: GB2494188A
Application number: GB1115202.2A
Authority: GB
Inventors: Carol Villegas
Original assignee: Wavebob Ltd
Current assignee: Wavebob Ltd
Priority date: 2011-09-02
Filing date: 2011-09-02
Publication date: 2013-03-06
Anticipated expiration: 2031-09-02
Also published as: GB2494188B; GB201115202D0; WO2013030359A3; WO2013030359A2

Abstract

A wave energy conversion system comprising a wave energy absorber, a power take off (PTO), a sensor and a controller for determining a force at the PTO in response to a sensed operating parameter of the wave energy absorber and dynamically varying at least one of the operating parameters to provide the required PTO force so as to either reduce or reach parametric resonance. In the arrangement configured to reach parametric resonance the wave energy absorber also has a variable water piercing area (Fig 17). The operating parameter varied by the controller may be the metacentric height, centre of gravity or displacement of the absorber or the pretension, width or stiffness of the mooring of the absorber. The controller may include an adaptive filter such as a notch band-stop filter with parameters which change according to the wave conditions and applied to a signal representing the force acting on the PTO.

Description

A Wave Energy Conversion System

Field of the Invention

The present invention relates to a wave energy conversion system. In particular the present invention relates to a wave energy conversion system whichin a first arrangement is configured to reduce parametric resonance which causes large pitch motion in thesystem, and thus optimise power conversion efficiency. In a second arrangement, the wave energy conversion system is configured to have a variable water piercing area so as to experience parametric resonance, which can be exploited to increase power capture.

Background

Wave energy conversion systemsare known in the art. Examples of such arrangements include those described in our earlier patents EP1439306, EP1295031 and EP1036274. Such arrangements are usefully deployed in a maritime environment and generate energy from wave motion.

The technical challenges involved in the conversion of ocean wave energy into useful electrical power are substantial. There is a perceptible convergence towards floating, offshore systems that are adapted to respond in accordance with the incident wave climate and thus maximize energy absorption.

Theavailable energy in the oscillating system may be transformed, via a power take-off (PlO), to useful electrical or other power. The interaction between the oscillating bodies and the P10 is therefore of vital importance to the optimization of energy conversion. In particular, large pitch motion in a heaving buoy wave energy conversion system may affect the available useful powerat the PTO.

As mentioned above, one type of wave energy conversion systemcomprises a point absorber or heaving buoy wave energy absorber. Point absorbers may be comprised of one or more buoys and extract energy from the motion of each buoy and/or their relative motion. Each of such buoys has its own resonance frequency given mainly by its mass and geometry. The resonance frequency is particularly important for devices with more than one body as they tend to capture power mainly available between the highest and the lowest resonance frequencies. Such wave energy absorbers have normally either a very short draught to become a wave follower (high resonance frequency) or a constant water piercing area for their operational range.

Design of point absorbers have been based mainly on the selection of the natural frequencies of the buoys and their resonance based on linear wave theory. As a result, most buoys have a constant water piercing area close to the static water level. Motions of the buoys can be adequately characterised using linear methods such as Response Amplitude Operators (RAO) or transfer functions.

The main source of large pitch motions of a heaving buoy wave energy absorbercan be associated with parametric resonance, whichis a nonlinear behaviour that affects floating bodies. Parametric resonance has beenwidely investigated for ships and offshore platforms andhas been analyzed using various non-linear approaches such asdescribing functions, the circle criterion or the extended Popovcriterion. Such behavior in the context of a heaving buoy wave energyabsorber arises from harmonic variations in the pitch restoringcoefficient caused by large heaving motions close to twice thepitch resonance frequency. While there are various approachesto deal with parametric resonance for wave energy absorbers -such as shape adjustments and specific mooring designs -there are still problems associated with the effect that parametric resonance has on the efficiencies of wave energy absorbers.

Sum mary These and other problems are addressed in accordance with the present teaching by an adaptive approach which in a first arrangement allows for a reduction in the effect of parametric resonance to optimise wave energy absorption, and in a second arrangement achieves parametic resonance which can be exploited in order to increase power capture. This has a number of advantages including an improvement in design flexibility.

Accordingly, in the first arrangement, there is provided a system which reduces parametric resonance in order to optimise wave energy absorption.Such a system comprises acontrolled power take off system that reduces parametric resonance of a wave energy absorber by using the concept of harmonic balance.

In the second arrangement, a wave energy absorber is provided with a variable water piercing area such that the absorber experiences parametric resonance under certain sea conditions. Such geometry together with suitable control means allows the non-linear effects of parametric resonance to be exploited in order to increase power capture.

Accordingly, the present teaching provides a wave energy conversion system as detailed in claim 1. Further, another wave energy conversion system is provided according to claim 39. Advantageous features are provided in the dependent claims These and other features will be better understood with reference to the following drawings which are provided to assist in an understanding of the teaching of the invention.

Brief Description Of The Drawings

The present invention will now be described with reference to the accompanying drawings in which: Figure 1 is a block diagram showing the main components of a wave energy conversion system according to the present teaching; Figure 2 is aview of aheaving buoy wave energy absorber; Figure 3is a graph showing a transfer function of vertical motion to wave amplitude for a highdamping coefficient and a low damping coefficient; Figure 4is a graph illustrating the amplitude of a pitch transfer function G(s) plotted as a functionof frequency; Figure 5is a graph showing wave elevation for experimental results with typical North Sea waveconditions; Figure 6is a graph showing pitch motion for experimental results with typical North Sea wave conditions; Figure 7is a graph showing mechanical power capture for experimental results with typical North Sea wave conditions; Figure8a is a block diagram illustrating how a notch filter is applied to a FTO force signal in a wave energy conversion system for reducing parametric resonance, according to the present teaching; Figure 8b illustrates Bode diagrams showing the frequency response of the notch filter of Figure 7a, according to the present teaching; Figure 9 is a graph illustrating the region where dangerous frequencies are excited at twice the resonance frequency in a wave energy absorber; Figures 10 and 11 are graphs illustrating methods of reducing parametric resonance by decreasing and increasing the natural frequency of a wave energy absorber, respectively, according to the present teaching; Figure 12 is a graph illustrating a method of reducing parametric resonance by increasing the damping factor in a wave energy absorber, according to the present teaching; Figures 1 3a and 1 3b respectively illustrate a side view and a top view of a wave energy absorber with fins and plates to increase damping in pitch, according to the present teaching; Figures 14a and 14b illustratea wave energy absorber wherein the parametric resonance in pitch can be reduced by varying the water piercing area of the wave energy absorber; Figure 15 illustrates an exemplary wave energy conversion system for harnessing wave energy; Figure 1 6a illustrates a buoy with a constant area and Figure 1 6b illustrates a buoy with a variable area relative to wave height and heave; Figure 17 illustrates examples of buoys with varying surface piercing area; Figure 18 is a Bode diagram illustrating the excitation force to heave transfer function for both heaving buoys in Figures 16 and 17; Figures 19a and 19b are graphs illustrating a comparison of heave motion and mechanical power for both heaving buoys for a wave excitation at the natural frequency; Figures 20a and 20b are graphs illustrating a comparison of heave motion and mechanical power for both heaving buoys for a wave excitation at twice the natural frequency; Figures 21 a and 21 b are graphs illustrating a comparison of heave motion and mechanical power for both heaving buoys for a panchromatic wave excitation; Figures 22a and 22b respectively illustrate a two-body point absorber with constant area and with variable area relative to wave height and heave; Figures 23a and 23b respectively illustrate a spar platform with an array of heaving buoys with constant area (a) and with variable area (b); and Figures 24a and 24b respectively illustrate a two-body point absorber with one body tethered to the sea floor with constant area (a) and with variable area (b) relative to wave height and heave.

Detailed Description Of The Drawings

The invention will now be described with reference toexemplary systernswhich are provided to assist in an understanding of the teaching of the invention.

Through adopting a mathematical approach to model the factors that influence the conversion efficiency of a wave energy conversion system, the present inventor has realised that the mathematical equations arising from such modelling give rise to possibilities for implementing an adaptive control method for reducing the effects of pitch motion on the efficiency of the wave energy conversion system. Such analysis has also shown that the parametric resonance of a wave energy absorber can be exploited to improve the power capture from the system.

Accordingly, in a first embodiment, the present teaching provides a wave energy conversion system which reduces parametric resonance due to pitch motion using a number of techniques. In another embodiment of the present teaching, a wave energy conversion system having a variable surface piercing area is provided which is configured to achieve parametric resonance in order to improve power capture.

Figure 1 is a block diagram of an exemplary wave energy conversion system according to the present teaching. Referring to Figure 1, the system includes a wave energy absorber 110 coupled to a power take off (PTO) 115. A sensor 130 is provided for sensing operating parameters of waves 150 and the wave energy absorber 110. A controller 120 is provided for determining the force at the PTO 115 in response to the sensed parameters of the waves 150 and the wave energy absorberl 10. The controller 120 may be configured to allow a dynamic varying of at least one of the operating parametersto provide the required PTO force to vary the parametric resonance of the wave energy absorber 11 0.The sensor 130 senses the operating parameters of the waves and the wave energy absorberl 10 which are then read by the controller 120. The controllerl 20, in response to the sensed operating parameters of the waves 150 and the wave energy absorberl 10, appropriately dynamically varies the operating parameters ofthe wave energy absorberl 10 so as to reduce the parametric resonance of the wave energy absorberl 10 in order to optimise power conversion efficiency or to achieve parametric resonance in order to maximise the power captured from the system. Thus the controller 120 is co-operable with the sensor 130 for selectively controlling the system. The system may further include a calibration module 140 for calibrating the data read by the sensor 130. It will be appreciated therefore that the present teaching provides a feedback system whereby sensed operating parameters of the system and the waves are used to dynamically vary the parametric resonance of elements or components of the convertor, thereby maximising the power conversion efficiency. It will be appreciated that in certain configurations the controller 120 can also use the sensed operating parameters of the wave energy absorber to estimate and/or predict the current and future parameters of the waves 150.

In order to provide some mathematical basis for the problem addressed we firstly detail a brief discussion of instability mechanisms in the Mathieu equation.

We consider the following equation: y1-:yH (a-bcos(w))y=U (1) It will be appreciated that on ignoring some important mathematical details concerning the existence of transforms, this equation may be written (in a generic form) using Laplace transforms as: 1) b Y(s) = 2 (Y(s -jw) ± Y(s + j2) (2) s -l--çs-4--a Once the equation is in this form, one may apply Harmonic balance arguments to postulate the existence of periodic motion to characterize the boundary of instability. It will be appreciated that the effect of the cosine is to split the feedback signal into two sidebands. Using Harmonic balance arguments, the condition for instability is that some frequency has a unity amplification and a phase shift of 2ff in the feedback loop.

The present insights into the parametric instability of a wave energy conversion system are based on a Mathieu-like equation. For example, for a wave energy absorber with moorings, the pitch dynamics can be approximated by the Mathieu-like equation: d+O+(a-bcos(cot-i-çb3)9 =u where is the phase angle of at that frequency and: tJ+tJzo a -pgV/GM + Fmoo/ + 2kjiioorE

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b= pgVE-rjj 2(J+JJ ]+F, = J+Jnc -A1z1+A2z2 4+A2 Referto Table Ibelow for a description of the notation used. a

The instability occurs for excitations at twice the transfer function (b / 2)G(s), in situations where G(.c) = I / (s2 +s + a) has a magnitude amplification greater or equal to one.

By assuming that one of the sidebands is filtered out as a result of low-pass filter characteristics, and by using standard harmonic balance arguments (akin to describing function analysis) the present inventor has realized that given certain approximations that this may be achieved for any modulation frequency that is twice the frequency at which the bode plot of0' / 2)GC) has a magnitude amplification greater or equal to one. It will be appreciated that: (i) This is an argument based on Harmonic balance. It isidentical in spirit to describing function analysis and canbe mathematically justified on this basis.

(U) The technique can be applied to any periodic multiplierf(t) by replacing f(t) with its Fourier series.

(Di) The analysis clearly identifies the importance of theresonance frequencies of G(s) and identifies mechanismsthat excite these modes using a time-varying multiplier.

Using the above analysis the present inventor has realized that by avoiding excitation of specific frequencies it is possible to mitigate the effect of resonance.

A. Modelling of a wave energy absorber Figure 2 is a view of a heaving buoy wave energy absorberl. The heaving buoy wave energy absorberl comprises an inner body 10, an outer floating body 11, wherein the outer floating body 11 is annular and surrounds the inner bodyl 0. A significant portion ba of the inner body 10 is located below the surface 20 of the body of liquid. Consider the simplified heave and pitch equations of motion of theheaving buoy wave energy absorberl: * tmii)z1 ± :vi22+hizi ± pg*.i = } ± Fçj ± FETo nQO!P \ (m2±ni22)32±rrl2lzl H-b2z2+ y)9A2± 47 ThA)OT) (4) = :F ± lia PPTO (j Jca)O ± bO ± (k9 ± Fmoor (5: 9 ô± P;1d9 where keis the time-varying pitch restoring coefficient. Referto Table Ibelow for a description of the notation used. The restoringcoefficient can be represented as a function of the displacedvolume and the metacentric height: k0 pVGM but once there is heave motion of the wave energy absorberand a wave elevation, both the volume and the metacentricheight change approximately by: CMEW CM --bY (7) Vtww = V 77) ) g)

TABLE I

NoT ATIQN

Symbol Description

11 Way elevation Em] 0 Pitch apgle [degrees] Heave motion of i-tb body [mJ Mass of i-tb body [kqi J Mass moment of ineitta [kjm2] Infloite added inertia [kgrn2] Infinite added mass of i-Lb body relative to j Ui body [kg] p Density of water Lkq/m] g. Acce1ratioñ of gravity [m/s2] CIV Metacennic height [in] nab/a Submeiged volume [m] F Dictance betweell moonug connecting points [7Th] Pretensinn mooring force EN I Damping iii heave for i1h body ENS/rn Damping in pitch fJVm] Waterplane area of i-Ui body [rz2J Excitation force in heave f or i-th body [Nj FO Excitation moment in pitch [N7aJ pac Radiation force in heave for i-tb body [NJ Radiation moment in pitch [Nm] FpTQ PIG force [NI kojr Mooring stittnesb [N/rn] Length ot horizontal mooring hue [m] Vertical distnace from M to morning connection tim] Aj.z1 4-Az2 The new rest ring coefficient k9 c-an, be written as: = p9VGM -El 5pg (V H-20M(A1 ± A2)(. (10) H-1).5pI(Ai H--A2)( --In order to illustrate the effect of the Power Take-Off (PTO)force on the heave motion of the two bodies (zi,z2), consider a typical P10 force defined as 5.:FPTO -D(1. -.Z2) where D is a damping coefficient. The P10 force is the force linking the two bodies. The frequency response of the two bodies to a wave (transfer function amplitude) is depicted in Figure 3. The damping value (D) clearly affects the vertical response of the bodies by shifting the resonance from their individualeigenvalues (no PTO force) to the single eigenvalue of the bodies when locked together (no relative motion: z1 = z2).

B. Parametric resonance of a wave energy absorber As was discussed above, it is known in the art that the Mathieu system may be used in analysing floating devices. While waves are not really periodic, it will be appreciated that given certain assumptions that they may be considered periodic, and given that the Mathieu analysiscan be extended to general periodic multipliers, the present inventor has realized that a study of this equation gives insights that can be used for the design of wave energy converters and their controllers. In particular, the Mathieu analysis shows that periodic multipliers that have significant frequency components at twice the resonant frequency of the pitch dynamics are most dangerous. The present teaching provides a simple control design that is based on reducing the loop gain at this frequency. In particular, the present teaching provides an approach to reduce the harmonic excitations at half the resonance period by using the PTO force. In the next section, we present an experimental validation of the approach leading to a reduced pitch motion and increased power capture of the wave energy absorber.

First of all note that in this simplified model there is coupling from equations (3) and (4) to (5) but not in the other direction. Furthermore, note that the inputs to equations (3) and (4) are a function of the wave elevation that we assume to be a combination of sinusoids. Thus, since equations (3) and (4) are both linear equations, we assume that in steady-state the outputs z1 and z2 are both combinations of sinusoids. It will be appreciated that this assumption is consistent with simulations and experimental observations.

For the following analysis, let us consider that the variations of the pitch restoring coefficient are mainly affected by the variations of GM (7). As a result, the variations in the pitch restoring coefficient are a function of 2 and the wave elevation i (defined in 9):

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If we assume a sinusoidal wave affecting the wave energy absorber at a frequency w, that the input from the waves restoring coefficient k9can be rewritten as a one term harmonic and the pitch equation of motion in (5) can be approximated as a Mathieu equation: 9+cO+(a-bcos(wt+Ø))9u (11) where& is the phase angle of 5 at that frequency and: a = pgV/GM + noor + 2kmoor C J+J andu='° 2(J+Jj cC It is well known that the Mathieu equation could be subject to parametric instability for harmonic excitations around half the resonance period of the linear time invariant system G(s)= The amplitude of G(s) is plotted as a function of frequency in Figure 4.

In order to assess the simulation data above, experiments were conducted in a wave tank using a small scale wave energy absorber. In the wave tank, the wave energyabsorber was subjected to wave conditionsrepresentative ofthe same North Atlantic sea conditions for three different tests. Figure 5 is a graph showing wave elevation for experimental results with typical North Sea wave conditions. Referring to Figure 5, the solid line represents high damping, the dashed line represents low damping, and the dotted line represents application of a notch filter. Initially, simulations not involving parametric motion suggested using a high damping. However, experimental tests with such damping resulted in higher than expected pitch and much lower mechanical power capture, as illustrated in Figures 6 and 7. Figure 6 is a graph showing pitch motion for experimental results with typical North Sea wave conditions, and Figure 7 is a graph showing mechanical power capture for these experimental results. To remove parametric resonance, the present inventor provided a first and second approach. The first approach was a reduction in the overall PTO damping D and the second involved application of a notch filter at half the resonance period to the reference PTO force. Both approaches reduced pitch motion and increased power. By using a notch filter, mainly the damping at half the resonance period of pitch was affected leading to higher power output and capacity factor than a reduced damping. A description of the implementation of the notch filter is provided below.

Figure 15 illustrates an exemplary wave energy conversion systemloo for harnessing wave energy. The systemloo comprises a power take-off (FTO) device in the form of a mechanical energy converter 102. The mechanical energy converter 102 may be a linear switch reluctance (LSR) generator configured to convert mechanical energy into electrical energy. However, it will be appreciated by those skilled in the art that instead of a linear switch reluctance (LSR) generator, the PTO may comprise another type of mechanical energy converter such as the application of actuators in the form of hydraulic pumps.

Referring to Figure 15, the mechanical energy convertor 102 is coupled to and driven by a wave energy absorber 105. It will be understood that wave energy absorbers are known in the art, an example of which is shown in European Patent No. 1,295,031 of which the present applicant is the proprietor. This exemplary wave energy absorber 105 comprises at least two devices (floats) 110, 111. While it is not intended to limit the teaching of the present invention to such a specific type of wave energy absorber, this specific absorber is described to assist in an understanding of a mechanical to electrical energy converter.

In the exemplary wave energy absorber 105, each of the two devices comprises aninner surface float 110, an outer surface float 111, and/or at least one submerged wave driven body 115 below the surface of the body of liquid. The outer surface float 111 is annular and surrounds the inner surface float 110.

Linkages 139 are provided between the at least two devices 110, 111. By configuring each of the two devices 110, 111 to oscillate at different frequencies relative to one another in response to passing waves, relative movement between the at least two devices 110, 111 may be used to generate an energy transfer which may be harnessed by the linkages 139 between the at least two devices 110, 111. The linkages 139 are coupled to the generator 102 which harnesses the mechanical energy generated by the wave energy absorber 105 and converts the mechanical energy into electrical energy.

The mechanical energy converter 102 may be a linear switched reluctance(LSR) generator and is directly coupled to the wave energy absorber 105. However, the mechanical energy converter 102 may also be a rotary switched reluctance generator with a linear to rotary conversion mechanism such as a rotary switched reluctance generator with a rack and pinion.

Referring to Figure 15, the converter 102 comprises a translating member 120 of electrical steel which is moveable axially and intermediate to a pair of spaced apart stator members 125 also of electrical steel. The translating member 120 includes first and second sets of teeth 132 of rectangular cross section on its respective opposite sides which define translator poles. Each stator member includes teeth 138 on one side thereof of rectangular cross section which define stator poles. The respective sides of the translating member 120 are associated with the corresponding stator members 125 such that the translator poles 132 and the stator poles 138 define opposing pole arrangements. The translating member 120 is operably coupled to the wave driven body 115 via linkages and is axially moveable along rails (not shown) such that the translating member 120 reciprocates in tandem with the oscillating wave driven body 115. The opposing pole arrangements are dimensioned such that air gaps exist between the translator poles 132 and the stator poles 138. The translating member 120 is coupled to the inner surface float 110, and each stator member 125 is coupled to the annular outer surface float 111.

Copper coils 141 are wound around the stator poles 138. The sequential energisation of these poles creates a magnetic field and a steady aligning force between opposing stator poles 138 and translator poles 132. The translating member 120 moves against the steady aligning force thereby converting mechanical energyinto electrical energy. The aligning force may be considered to be an operating characteristic of the generator 102. A person skilled in the art will appreciate that, in motoring operation, a forwardelectromagnetic force (forward EMF) is produced when electric current flowing in a coil 141 coincides with rising coil inductance. In generating operation, a backward electromagnetic force (back EMF) is produced when the coil 141 current coincides with falling coilinductance.

As mentioned above, large pitch motion in a heaving buoy wave energy absorber may affect the available useful powerat the PTO.

The main source of large pitch motions can be associated with parametric resonance. The present teaching provides various approachesto deal with parametric resonance for wave energy absorbers -such as shape adjustments, specific mooring designs, and pitch stability control means.

The system according to the present teaching includes a controller or control means that is configured for reducing such parametric resonance of the wave energy absorber. The control means incorporates a number of techniques for reducing the parametric resonance, as will be described below. It will be appreciated that any of the below methods of reducing parametric resonance may be utilised alone or in conjunction with each other.

In one embodiment, as mentioned above, the control means comprises a filter which may be applied to the PTO force setpoint signal or any other operating parameter associated with the waves and/or wave energy converter such as the velocity and position sensed parameters of the translating member 120 of the wave energy conversion system 100 of FIG. 15. The filter is applied to a signal representing force of the PTO, the PTO force setpoint signal. Figure 8a is a block diagram illustrating a control means for reducing parametric resonance of a wave energy conversion system, according to an embodiment of the present teaching. Referring to Figure 8a, the system includes an adaptive filter 750, an actuator control 710, a PTO control means 720, a PTO 700, a wave energy converter73o, and signal conditioning means 740. The signal conditioning means 740 may be a band-stop filter in the form of a notch filter. The notch filter tested by the inventors is mainly a filter for the velocity signal of the translating member 120 of Figure 15.The filter 740 may be applied to a signal representing the force to be applied by the PTO 700. As described above, the notch filter is applied at half the resonance period of the wave energy absorber to a signal representing the FF0 force. By using a notch filter, mainly the damping at half the resonance period of pitch motion is affected leading to higher power output and capacity factor than a reduced damping.

A typical frequency response of the notch filter 740 is illustrated in Figure 8b.

Note that all the filters in Figure 8b have a notch roughly at 0.075 Hz. A linear damping would be a constant value for all frequencies. For example, in the present teaching, a hnear damping of roughly 1,800,000 N is used (Plot I without notch).

Alternatively, the parametric resonance may be reduced by changing the resonance frequency in pitch motion of the wave energy absorber. As the instability is due to excitations at twice the resonance frequency of (b/2)G), and with previous knowledge of the frequency content of the wave climate at the location where the wave energy absorber will be stationed (e.g. via Fourier analysis), the resonance frequency of the WEC can be adjusted such that the frequency content of is away from twice the resonance frequency of (b/2)G(s). Figure 9 is a graph illustrating the region where dangerous frequencies are excited at twice the resonance frequency in a wave energy absorber.The resonance frequency wrof G(s) is determined by co = I7. For example, as shown in FIGS. 10 and 11, the resonance frequency co, can be reduced or increased away fromtwice the resonance frequency of (ii / 2)G(s) G(s) = 1 / (s2 + s + a) , having a magnitude amplification greater or equal to one.

The resonance frequency of a wave energy absorber with moorings can be adjusted in a number of ways. Referring to FIG. 2 and Table 1 above, the resonance frequency co of the wave energy absorber can be increased or decreased by varying at least one of the following: a) the metacentric height GM for the WEC by lowering the centre of gravity b) the WEC displacement V (i.e. submerged volume) c) the pretension mooring force F d) the width of the mooring attachment £ e) the mooring stiffness f) the distance of the mooring attachment from the metacentre t.

Normally, the main changes can be obtained by adjusting the product of centre of gravity and displacement \7GM Thus, the control means may comprise configuring the moorings, ballast and shape of the system to adjust the resonance frequency of the pitch resonance.

In another embodiment for reducing the parametric resonance, the damping term of the linear pitch dynamicsG(s) may be increased. By increasing the damping term in pitch of a wave energy absorber, the amplitude of G(s) at the resonance frequency is reduced. As a result, the parametric resonance can be reduced as it would be less likely to satisfy the conditions for (h / 2)G(s) being equal or larger than unity. FIG. 12 is a graph showing the effect of increasing the damping term, showing how the amplitude of G(s) at the resonance frequency is reduced.

One approach to increase damping is the addition of long fins and/or plates that present little resistance in heave, as depicted in Figure 13. Figures 13a and 13b respectively illustrate a side view and a top view of a wave energy absorber with one or more fins 4 and plates 5 to increase damping in pitch, according to the present teaching. Referring to Figure 13a, both fins 4or plates 5 could be attached to either body 1 or body 2 such that pitch damping (e.g. viscous drag) is increased mainly in pitch and roll with little effect on heave motion. The fins may be disposed in a substantially vertical orientation. Note that the b9 term of the damping coefficient of pitch can be seen as a first order linearization of viscous drag. In Figure 13b, one or more plates 5 may project outwardly from the outer portion of the body 2 of the wave energy absorber and are disposed in a substantially vertical orientation. The long fins 4 or plates 5 present little drag in heave while they increase drag in roll and pitch motion. Note that the b9 term of the damping coefficient of pitch can be seen as a first order linearization of viscous drag.

Another method for reducing parametric resonance is to vary the water piercing area of the wave energy absorber such that the time-varying effects in the metacentric height GMof the wave energy absorberare reduced. Figures 14a and 1 4b illustrate a wave energy absorber wherein the parametric resonance in pitch motion can be reduced by varying the water piercing area of the wave energy absorber. By decreasing the surface piercing area of at least one of the inner and outer surface floats 2 and 3, changes in metacentric height due to wave elevation can be reduced.Referring to Figure 14a, at least one of the inner and outer surface floats 2 and 3 may be configured to have a variable water piercing area. At least one of the inner and outer surface floats 2 and 3 comprises an upper portion above the surface of the water 4, a lower submerged portion, and a water piercing portion between the upper and lower portions, wherein the horizontal cross sectional area of the water piercing portion is reduced from the lower portion towards the upper portion.

As mentioned above, the present inventor has also realised that the phenomenon of parametric resonance of a wave energy absorber may be used to improve the power captured from the absorber. Accordingly, in a second arrangement of the present teaching, a wave energy absorberwhich comprises a variable water piercing area is provided such that the absorber experiences parametric resonance under certain sea conditions. Such geometry together with suitable control means allow the non-linear effects of parametric resonance to be exploited in order to increase power capture. As parametric resonance implies that oscillations will grow exponentially, control means are required to maintain stability and parametric oscillation. While resonance of typical wave energy absorbers is excited by waves at that same resonance frequency, parametric resonance is excited by waves at roughly twice the resonance frequency of the body. For example, waves of 2 Hz could cause parametric resonance of a body with resonance frequency of 1 Hz.

In a preferred embodiment, the variable water piercing area changes linearly with respect to the water level. Nevertheless, parametric resonance may be achieved with other variable piercing areas including discrete area variations. In addition, the wave energy absorber may be designed with natural frequencies away from critical sea conditions and capture such power using parametric resonance such that it would be easier to detune these frequencies from harsh sea conditions.

Consider the surface buoys illustrated in Figures 16a and 16b. Both wave energy conversion systemscomprise a power take off (PTO) fixed to the sea-bed 1, a connecting element 2 and a surface buoy 3. The surface piercing area of the surface buoy 3 in Figure 16a is relatively constant with the waves 4 while the surface piercing area of the surface buoy 3 in Figure 16b varies with the waves 4.

On the assumption of similar masses and surface piercing areas for static equilibrium, both surface buoys will have a similar frequency response with a natural frequency w0. With waves close to the natural frequency of the buoy, the amplitude of the oscillations will be large while for waves away from the natural frequencies will be less. With the wave energy absorber in Figure 17, the use of a variable piercing surface area at the buoy together with control means 6 allow for the extraction of additional power at frequencies away from the natural frequency of the body. The control means 6 uses sensor means 5 to measure the wave height and obtain the buoy elevation. The control means 6 may also use means to predict wave elevation and wave energy converter parameters a few seconds ahead. Those variables are used to achieve parametric resonance and maintain overall stability.

Figure 17 illustrates examples of buoys with varying surface piercing area.

Referring to Figure 17, the buoys are described as a surface of revolution around an axis 6. In such cases, the area with no waves is given by the water level 5 and it changes linearly with changing wave elevation. Parametric resonance can be excited either with smooth changing areas as in 1 and 2 or discrete changes as in 3 and 4. For heaving buoys where pitch parametric stability is a concern, the variations 2 and 4 may be employed.

Consider that the buoys in Figures 1 7a and 1 7b have the same excitation force to heave transfer function as depicted in the Bode diagram of Figure 18. That means that both buoys have the same mass and area at the level position. The natural frequency of both buoys in this case is around 0.18 Hz.

Figures 19a and 19b are graphs illustrating a comparison of heave motion and mechanical power for both heaving buoys for a wave excitation at the natural frequency (height=0.5 and period=5.6). Figures 20a and 20b are graphs illustrating a comparison of heave motion and mechanical power for both heaving buoys for a wave excitation at twice the natural frequency (height=0.5 and period=2.8). Figures 21a and 21b are graphs illustrating a comparison of heave motion and mechanical power for both heaving buoys for a panchromatic wave excitation (Hs=0.75 and Tp=2.75) Referring to Figures 19a and 19b, a sinusoidal wave excitation at the natural frequency is depicted. For that case, the power capture between buoys (a) and (b) in Figure 16 would be similar. Nevertheless, at wave excitations at twice the natural frequency of the buoys (Figure 20), the buoy (a) of Figure 16 will capture practically no power while buoy (b) will resonate and capture power from such waves. The effect for real sea conditions is clear in Figure 21 where much more power is captured from the waves once the buoy starts to resonate (due to a parametric instability).

Other tested realisations of the invention enhance various wave energy technologies including nearshore buoys, two-body point absorbers and offshore platforms fitted with heaving buoys. Such technologies are depicted in Figures 221024.

Figures 22a and 22b respectively illustrate a two-body point absorber with constant area and with variable area relative to wave height and heave.

Referring to Figures 22a and 22b, the shape also reduces parametric pitch as the metacentric height change due to incoming waves is reduced.

Figures 23a and 23b respectively illustrate a spar platform with an array of heaving buoys with (a) constant area and (b) with variable area.

Figures 24a and 24b respectively illustrate a two-body point absorber with one body tethered to the sea floor (a) with constant area and (b) with variable area relative to wave height and heave.

It will be understood that what has been described herein are exemplary embodiments of a system which adoptscontrol, shape changes and mooring configuration approaches to reduce parametric resonance of a wave energy absorber. By usinginsights from the Mathieu equation, it was found that byapplying a notch filter at half the resonance period to thePlO force it was possible to reduce parametric instability.Experimental results in a wave tank demonstrated the approach with such notch filter leading to lower pitch motions andhigher mechanical power output. Other methods of reducing the parametric resonance have also been described above. In another arrangement, it was found that by configuring a wave energy absorber to excite parametric resonance, the power captured from the wave energy absorber was increased.lt will be understood that the invention is to be limited only insofar as is deemed necessary in the light of the appended claims.While the present invention has been described with reference to exemplary arrangements it will be understood that it is not intended to limit the teaching of the present invention to such arrangements as modifications can be made without departing from the spirit and scope of the present invention.

The words comprises/comprising when used in this specification are to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more other features, integers steps, components or groups thereof.

Claims

<claim-text>Claims 1. A wave energy conversion system comprising: a wave energy absorber being moveable in response to passing waves; a power take off (P10) being driven by the wave energy absorber for converting wave energy to another form of energy, a sensor for sensing operating parameters of the wave energy convertor, and a controller for determining a force at the PTO in response to the sensed operating parameters of the wave energy absorber, the controller being further operable for selectively dynamically varying at least one of the operating parameters to provide the required P10 force to reduce parametric resonance.</claim-text> <claim-text>2. The system of claim 1, wherein the PTO comprises a mechanical energy converter which is directly coupled to the wave energy absorber.</claim-text> <claim-text>3. The system of claim 2, wherein the mechanical energy converter comprises an actuator, the wave energy absorber being operably coupled to the actuator for facilitating driving the actuator.</claim-text> <claim-text>4. The system of any preceding claim wherein the PTO comprises one of a linear switched reluctance generator, a rotary switched reluctance generator with a linear to rotary conversion mechanism; or a rotary switched reluctance generator with a rack and pinion.</claim-text> <claim-text>5. The system as claimed in any preceding claim, wherein the wave energy absorber comprises a reciprocating wave driven body, the sensor being operable for sensing an operating characteristic of the reciprocating wave driven body.</claim-text> <claim-text>6. The system of claim 4, wherein the controller is configured to operably dynamically vary an operating characteristic of the actuator in response to the sensed operating parameters of the wave energy absorber.</claim-text> <claim-text>7. The system of any one of claims 4 to 6, wherein the operating characteristic of the actuator comprises a velocity signal.</claim-text> <claim-text>8. The system of any preceding claim, wherein the controller comprises an adaptive filter whose parameters are variable according to the wave conditions.</claim-text> <claim-text>9. The system of claim 8, wherein the controller is configured to apply the filter to a signal representing a force acting on the PTO.</claim-text> <claim-text>10. The system of claim 8 or 9, wherein the output of the filter is applied to a PTO force setpoint signal where the parameters of the controller are variableaccording to the wave conditions.</claim-text> <claim-text>11. The system of any of claims 8 to 10, wherein the filter comprises a band-stop filter.</claim-text> <claim-text>12. The system of claim 11, wherein the band-stop filter comprises a notch filter.</claim-text> <claim-text>13. The system of any of claims 8 to 12, wherein the controller is configured to apply the filter at half the pitch motion resonance period of the wave energy absorber.</claim-text> <claim-text>14. The system of any preceding claim, further comprising moorings for fixing the wave energy absorber.</claim-text> <claim-text>15. The system of claim 14, wherein the controller is configured to modify the characteristics of the moorings.</claim-text> <claim-text>16. The system of any preceding claim, wherein the parametric resonance is determined by one or more of the following parameters: the metacentric height of the wave energy absorber; the centre of gravity of the wave energy absorber; the wave energy absorber displacement; the pretension mooring force of the wave energy absorber; the width of the mooring attachmentof the wave energy absorber; the mooring stiffness of the wave energy absorber; and the distance of the mooring attachment from the metacentre of the wave energy absorber.</claim-text> <claim-text>17. The system of claim 16, wherein the controller is configured to control the parametric resonance by varying one or more of the listed parameters.</claim-text> <claim-text>18. The system of any preceding claim, wherein the controller is configured to vary the resonance frequency of the wave energy absorber in response to pitch motion of the wave energy absorber.</claim-text> <claim-text>19. The system of claim 18, wherein the resonance frequency is configured by setting the metacentric height of the wave energy absorber.</claim-text> <claim-text>20. The system of claim 19, wherein the metacentric height of the wave energy absorber is set by configuring the centre of gravity of the wave energy absorber.</claim-text> <claim-text>21. The system of claim 18, wherein the resonance frequency is configured bysetting the wave energy absorber displacement.</claim-text> <claim-text>22. The system of claim 18, wherein the resonance frequency is configured by setting the pretension mooring force of the wave energy absorber.</claim-text> <claim-text>23. The system of claim 18, wherein the resonance frequency is configured by setting the width of the mooring attachmentof the wave energy absorber.</claim-text> <claim-text>24. The system of claim 18, wherein the resonance frequency is configured by setting the mooring stiffness of the wave energy absorber.</claim-text> <claim-text>25. The system of claim 18, wherein the resonance frequency is configured by setting the distance of the mooring attachment from the metacentre of thewave energy absorber.</claim-text> <claim-text>26. The system of any preceding claim, wherein the controller is configured to provide a damping of the movement of the wave energy convertor.</claim-text> <claim-text>27. The system of claim 26, comprising at least one of fins and plates configured to increase drag in roll and pitch motion of the wave energy convertor.</claim-text> <claim-text>28. The system of claim 27, wherein the at least one of fins and plates are attached to the wave energy absorber.</claim-text> <claim-text>29. The system of claim 27 or 28, the fins comprising one or more longitudinal fins attached to an outer surface of the wave energy absorber and extending in a substantially vertical direction.</claim-text> <claim-text>30. The system of any of claims 27 to 29, the plates comprising one or more plates extending radially from an outer surface of the wave energy absorber and disposed in a substantially vertical direction.</claim-text> <claim-text>31. The system of any preceding claim, wherein the wave energy absorber comprises an annular outer surface float and an inner surface float surrounded by the outer surface float, the PTO being operably coupled to the outer surface float and the inner surface float.</claim-text> <claim-text>32. The system of claim 31, wherein the inner and outer surface floats are configured to oscillate at different frequencies relative to one another in response to passing waves.</claim-text> <claim-text>33. The system of claim 31 or 32 when dependent on claim 5, wherein the reciprocating wave driven body is suspended from the inner surface float.</claim-text> <claim-text>34. The system of any of claims 5 to 33, wherein the reciprocating wave driven body is operably provided below the surface of the waves.</claim-text> <claim-text>35. The system of any of claims 31 to 34, wherein the one or more plates extend from an outer surface of the outer surface float.</claim-text> <claim-text>36. The system of any preceding claim, wherein the controller is configured tooperably vary the water piercing area of the wave energy absorber.</claim-text> <claim-text>37. The system of claim 36, wherein at least one of the inner and outer surface floats is configured to have a variable water piercing area.</claim-text> <claim-text>38. The system of claim 36 or 37, wherein the at least one of the inner and outer surface floats comprises an upper portion above the surface of the water, a lower submerged portion, and a water piercing portion between the upper and lower portions, wherein the horizontal cross sectional area of the water piercing portion is reduced from the lower portion towards the upper portion.</claim-text> <claim-text>39. A wave energy conversion system comprising a wave energy absorber being moveable in response to passing waves with a geometry such that the surface piercing area of the wave energy absorber varies according to the wave elevation; a power take off (P10) being driven by the wave energy absorber for converting wave energy to another form of energy; a sensor for sensing operating parameters of the wave energy convertor; and a controller for determining a force at the PTO in response to the sensed operating parameters of the wave energy absorber, the controller being further operable for dynamically varying at least one of the operating parameters to provide the required PTO force to reach parametric resonance.</claim-text> <claim-text>40. The system of claim 39, wherein the P10 comprises a mechanical energy converter which is directly coupled to the wave energy absorber.</claim-text> <claim-text>41. The system of claim 40, wherein the mechanical energy converter comprises an actuator, the wave energy absorber being operably coupled to the actuator for facilitating driving the actuator.</claim-text> <claim-text>42. The system as claimed in any of claims 39 to 41, wherein the wave energy absorber comprises a reciprocating wave driven body, the sensor being operable for sensing an operating characteristic of the reciprocating wave driven body.</claim-text> <claim-text>43. The system of claim 41, wherein the controller is configured to operably dynamically vary an operating characteristic of the actuator in response to the sensed operating parameters of the wave energy absorber.</claim-text> <claim-text>44. The system of any of claims 39 to 43, wherein the operating parameters of the wave energy absorber comprise at least one of velocity, acceleration and wave elevation of the wave energy absorber.</claim-text> <claim-text>45. The system of any of claims 39 to 44, wherein the surface piercing area of the wave energy absorber varies linearly according to the wave elevation.</claim-text> <claim-text>46. The system of claim 45, wherein the surface piercing area varies continuously.</claim-text> <claim-text>47. The system of claim 45, wherein the surface piercing area varies discretely.</claim-text> <claim-text>48. The system of any of claims 39 to 47, wherein the wave energy absorber comprises an annular outer surface float and an inner surface float surrounded by the outer surface float, the PTO being operably coupled to the outer surface float and the inner surface float.</claim-text> <claim-text>49. The system of claim 48 wherein the inner and outer surface floats are configured to oscillate at different frequencies relative to one another in response to passing waves.</claim-text> <claim-text>50. The system of claim 48 or 49, wherein at least one of the inner and outer surface floats has a surface piercing area that either increases or decreases with the wave elevation.</claim-text> <claim-text>51. The system of any of claims 48 to 50, wherein at least one of the inner and outer surface floats has a tethered mooring.</claim-text> <claim-text>52. The system ot any of claims 48 to 50, wherein at least one of the inner and outer surface floats has a slack mooring.</claim-text> <claim-text>53. The system of any of claims 39 to 52, wherein the operating parameters of the wave energy absorber comprise velocity, acceleration and wave elevation of at least one of the inner and outer surface floats.</claim-text> <claim-text>54. The system of any preceding claim, wherein the PTO is an electrical PTO.</claim-text> <claim-text>55. The system of any of claims 3 to 38 and 41 to 54, wherein the actuator comprises a translating member.</claim-text> <claim-text>56. The system of claim 55, wherein the translating member is axially moveable.</claim-text> <claim-text>57. The system of claim 55 or 56 when dependent on any of claims 31 to 38 and 49 to 56, wherein the translating member is associated with the inner surface float of the wave energy absorber.</claim-text> <claim-text>58. The system as claimed in any of claims 55 to 57, wherein the mechanical energy converter further comprises a pair of stator members, the translating member being arranged relative to the stator members so as to be moveable therebetween.</claim-text> <claim-text>59. The system as claimed in claim 58, wherein each stator member is associated with the outer surface float of the wave energy absorber.</claim-text> <claim-text>60. The system as claimed in claim 58 or 59, wherein each stator member comprises a plurality of stator poles.</claim-text> <claim-text>61. The system as claimed in any of claims 58 to 60, wherein each stator member comprises at least one coil.</claim-text> <claim-text>62. The system as claimed in claim 61, wherein a corresponding coil is wound on the respective stator poles.</claim-text> <claim-text>63. The system as claimed in any of claims 58 to 62, wherein the translating member reciprocates relative to each stator member.</claim-text> <claim-text>64. The system as claimed in claim 63, wherein the translating member is moveable intermediate a pair of spaced apart stators members.</claim-text> <claim-text>65. A system as claimed in any of claims 60 to 64, wherein the translating poles and the stator poles define opposing pole arrangements.</claim-text> <claim-text>66. A system as claimed in claim 65, wherein an air gap is provided between opposing translating poles and stator poles.</claim-text> <claim-text>67. A system as claimed in any of claims 58 to 66, wherein each stator member is associated with the outer surface float of the wave energy absorber.</claim-text> <claim-text>68. The system of any preceding claim, wherein the PTO is fixed to the sea floor.</claim-text> <claim-text>69. The system of any preceding claim, wherein the PTO is fixed to a spar platform.</claim-text> <claim-text>70. The system of any of claims 39 to 69, wherein the PTO comprises one of a linear switched reluctance generator, a rotary switched reluctance generator with a linear to rotary conversion mechanism; or a rotary switched reluctance generator with a rack and pinion.</claim-text> <claim-text>71. The system of preceding claim, wherein the PTO comprises hydraulic pumps.</claim-text> <claim-text>72. A system substantially as described hereinbefore with reference to the accompanying drawings.</claim-text>