The most common modes of motion (in terms of energy capture are heave, surge and pitch, while yaw, roll and sway are rarely used. The natural frequency if the device is the square root of all the spring terms divided by all inertia terms.
𝜔𝑛 = √
∑ 𝐶
∑ 𝑀 (2.112)
Heaving buoys and bodies that pitch about an axis close to the mean surface level naturally have high hydrostatic stiffness. Unless provided with some means of reducing the stiffness or controlling the motion, such heaving or pitching systems will have quite narrow response bandwidth, which makes them hydrodynamically inefficient wave absorbers in varying irregular seas. This flaw may be mitigated by active use of the machinery through a proper control strategy, or by including mechanical components to counteract the hydrostatic stiffness (Todalshaug, 2017). Control refers to any methods taken to achieve better power absorption, through the variation of physical parameters.
Figure 2:17: The pitch, heave and surge responses of a floating object to incident waves (source Open University (2018)
Pitching about an axis close to the surface is less volumetric efficient than surging When it comes to absorbing power. This is because such pitch motion gets its excitation from an area distributed along the direction of propagation for the wave. Surge motion on the in contrast gets its excitation mainly from areas of opposing vertical walls a distance apart (see Figure
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2:17). On the other hand, it may be easier to design a practical machinery for pitching bodies than for surging bodies.(Todalshaug, 2013)Todalshaug, (2017) states that for small bodies, heaving motion is the most volumetric efficient. This is because the heave excitation comes from a difference between atmospheric pressure at the top of the body and the full amplitude of hydrodynamic pressure at the bottom, see Figure 2:17. Surging and pitching take their excitation from a difference in hydrodynamic pressure along the wave, which is quite weak when the body is small. For large bodies the opposite is true, such that pitching and in particular surging motion are favoured over heaving motion. Systems combining power extraction from two or three modes of motion have the potential of giving a more efficient use of the installed structure.
Figure 2:18: Sketch showing complete absorption of the incoming wave (source Falnes (2002))
To absorb waves means to generate waves. In Figure 2:18 curve (a) represents an undisturbed incident wave. Curve (b) illustrates symmetric wave generation (on otherwise calm water) by means of a straight array of evenly spaced, small floating bodies oscillating in heave. Curve (c) illustrates antisymmetric wave generation. Curve (d), which represents the superposition (sum) of the above three waves, illustrates complete absorption of the incident wave energy Falnes (2002). To absorb energy from an incident wave, the radiated waves emitted from the surface(s) of an oscillating system must destructively interfere with the incident wave (Wypych et al (2012))
The surge, sway and yaw modes have no restoring forces, and station-keeping forces must be supplied by moorings or other mechanisms. University of Exeter (Parish, 2015 for
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example) are conducting interesting work into the use of dynamic moorings with a view to increase energy yield. This is a potentially advantageous avenue of research although the reliability of such systems as well as the economic considerations of mooring installation and operation and maintenance are crucial. Connecting moorings at sea is a difficult task and the larger the operational load the more expensive the charter vessel.The fundamental purpose of control is to force the device to move in such a way as to increase power capture. For maximum power extraction, there exists an optimum motion path (position and velocity) that should be followed, and such a path depends on the incident wave. The response is governed by the combination of inertia, stiffness, damping and machinery (PTO) forces. This means that the response may be improved either by the design of the buoy (inertia, stiffness and wave damping), or by using the machinery to get closer to the optimum trajectory. In practice we often use a combination of the two (Todalshaug, 2017).
Geometry control
Geometry control relates the first option mentioned above whereby some fundamental property of the device is physically changed as opposed to using the PTO directly. For example the spring constant of the AWS device can be changed by changing the air pressure and volume inside the submerged chamber (Polinder, Damen, & Gardner, 2004). Likewise, the sloped IPS device can change its spring constant by restraining the motion of the device to an intermediate direction between surge and heave (Payne, 2006). Altering the angle of the device varies the natural frequency and bandwidth of the device. The submerged pressure differential CalWave (2018) device is another interesting WEC which utilises geometry control, coming second in a recent U.S Dept. of Energy Wave Energy Prize, (2018). Another example of geometric control would be the use of ballast to change the mass of a floating structure (which also changes the draft and hydrodynamic parameters of the device) Nolan, (2006)
Complex conjugate control
Complex conjugate control relates to the other option which is to implement machinery forces for the purposes of control. The method can be accredited to Nebel (1992) who
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implemented the strategy using an experimental model Salters Duck. In order to maximize wave-energy input to an oscillating body, one necessary condition is that the body’s velocity should be in phase with the wave’s excitation force acting on the body. This condition is automatically fulfilled at resonance, that is, if the wave frequency equals the natural frequency of the oscillating body. At resonance, the oscillator’s mechanical reactance vanishes, off resonance, however, the oscillator has a finite mechanical reactance. Complex conjugate control cancels out this intrinsic reactance by using the PTO to supply external reactance of an opposite sign, thus the oscillation velocity is in phase with the excitation force (Falnes & Bjarte-larsson, 2006). This optimal control method requires advanced knowledge of the incoming wave profile as well as the requirement to input power at very high efficiency to the WEC at certain instances in time. The method simultaneously satisfies the optimum amplitude trajectory and the optimum phase conditionLatching (phase) control
Another method which seeks primarily to satisfy the optimum phase control, such the buoys velocity is in phase with the excitation force is known as latching or phase control. The principal of the method is shown in
Figure 2:19: Latching principal, (a) is the wave elevation, (b) the optimum displacement of the body and (c) the actual displacement using latching. (Source Falnes (2002))
The method works by holding the device in position at certain moments during the wave cycle (when the velocity is nil) and releasing the device at a later stage such that the velocity is now in phase with the excitation force. In doing so, the amplitude of the device is increased along with power capture. The method can be accredited to Budal & Falnes (1975).