Marine Energy Challenge. Marine Energy Glossary July 2005

Transcription

1 Marine Energy Challenge Marine Energy Glossary

2 Disclaimer Whilst the Carbon Trust has taken reasonable steps to ensure that the information contained in this Glossary is correct, it gives no warranty and makes no representation as to its accuracy and accepts no liability for any errors or omissions. The information in the Glossary is being made available to you as part of the Carbon Trust s general activity of promoting deployment of, and investment in, low carbon technology. The Carbon Trust does not give investment advice and you must take your own view on the merits of, and the risks attached to, any investment decision you may undertake. You may wish to obtain professional advice. An independent company set up the Government to help the UK meet its climate change obligations through business-focused solutions to carbon emission reduction, the Carbon Trust is funded by Defra, the Scottish Executive, the Welsh National Assembly and Invest Northern Ireland. This document is compiled by Entec UK Ltd. The information is provided by a number of parties. It is a working document that may be revised and published from time to time. The Carbon Trust 2005

3 i Foreword The Marine Energy Challenge (MEC) was established in response to the Carbon Trust s strategic work highlighting the potential for wave and tidal stream development in the UK. The main driver was to establish in the medium term if these technologies can become cost competitive. Through partnering large engineering design organisations with existing wave and tidal stream technology developers, the Challenge aims to accelerate the development of marine energy in the UK. By carrying out detailed engineering assessment in the MEC, it has become evident that the Carbon Trust and the marine energy stakeholders have a need to compare many different technologies and applications that could significantly benefit from a common set of terms and definitions. With this in mind the Carbon Trust has worked with Entec UK Ltd. to produce this Glossary as both a permanent record of the MEC understanding and a possible starting point for the wave and tidal stream sectors to further develop a Marine Energy language understandable by all. The terms in this Glossary are mostly adapted or borrowed from other fields of engineering but we have attributed meanings to them specifically for use in Marine Energy. This has given us the means to discuss complex ideas and varied options clearly and reduced misunderstandings of some crucial terms. Whilst this glossary is very useful to the Carbon Trust we hope that much of the industry would benefit from it too. Of course not all terms can be defined clearly and certainly new terms will be formed and others adapted as time passes, but the Carbon Trust has chosen to publish our understanding of the terms to date and welcome others to use, improve and extend the Glossary. The Marine Energy Industry offers a path to a more sustainable future and this Glossary represents one clear marker along that path. Paul Jordan Programme Manager Marine Energy Challenge The Carbon Trust

4 ii Contents 1. Introduction Background Using the glossary 1 2. Glossary 2 3. Symbols and abbreviations Symbols Abbreviations Units Notes Acknowledgements Figures 30 Figure 1 Wave nomenclature, wave crest and direction 30 Figure 2 Definition of amplitude and phase of a wave 30 Figure 3 Wave nomenclature 31 Figure 4 Wave nomenclature 31 Figure 5 Example of a time series of wave positions showing the significant wave height in red 32 Figure 6 Example of a power spectral density function showing the three main average periods and frequencies 32 Figure 7 Example of an un-smoothed time-series transformed using Fast-Fourier Transforms into the frequency domain. This shows the spectral density of the wave train showing which frequencies contain the most energy. Also shown is a Pierson Moskowitz spectrum that best describes the data. 33 Figure 8 An example of a wave rose 33 Figure 9 Example scatter diagram (joint probability distribution of significant wave height and energy period) showing occurrence of sea states in parts per thousand. Also shown are contours of constant mean wave power level [kw/m] 34 Figure 10 Depth of water and circular water motions for deep-water approximations of wave 35 Figure 11 An example of a power surface (power matrix), for illustration the scatter diagram in Figure 9 is overlaid. The product of these two matrices gives the energy output. 36 Figure 12 Example of a wide and narrow-band spectral response of an untuned device. The red curve has a wide (half-peak power) bandwidth and the blue has a narrow (half-peak power) bandwidth. Not that by tuning the peak frequency can also be moved. 37

5 iii Figure 13 Comparison of Pierson Moskowitz and JONSWAP spectral density functions for the same peak frequency 37 Figure 14 Definition of water-plane area 38 Figure 15 From left to right: Cross-flow tidal turbine, horizontal axis axial-flow turbine, the straight arrows indicate the tide flow direction 38 Figure 16 Darrieus turbine showing rotation and incident fluid flow 39 Figure 17 Cross-axis turbine; water flows through the centre of the turbine. Only three blades are shown here but other designs can have many more blades 39 Figure 18 An example of a duct, in this simple example the water flow from left to right is enhanced by the duct and speeds up 40 Figure 19 Principal axes in wave energy 40

6 1 1. Introduction 1.1 Background The Marine Energy Challenge has studied a wide cross-section of marine energy technologies. During the studies it became clear that there was an increasing need for clarity on the terms used to describe the technology. The Carbon Trust thus developed a set of terms as understanding improved. This glossary is intended primarily for use by the Carbon Trust but it is recognised that it might have benefit to technology developers, investors and other stakeholders. The terms contained are not exhaustive, but reflect those that have found most value on the Challenge thus far. Many engineering terms are not included since we believe that these are covered adequately in other texts. 1.2 Using the glossary The definitions in this glossary are intended to provide a useful tool for all involved in the marine energy sector to communicate. Many of the terms are borrowed from other fields. The definitions provided here though are specific to Marine Energy. Some technical terms that are in common usage in other industries and have the same meaning in marine energy are omitted from this glossary. This glossary is intended for readers with a good technical knowledge. Where units are suggested these can always be changed for their International Organization for Standardization (ISO) or imperial equivalents. The magnitudes of the units are chosen as the ones most likely to be used in the industry for a given task. Thus kilowatt-hours [kwh] are given as a measure of energy when terawatt-hours [TWh] or Joules [J] could be used instead. Where applicable, units and fundamental dimensions are given in squared brackets. Units are written in plain text e.g. [m], whereas fundamental units are written in serif text e.g. [ L ]. Equations follow as far as possible standard notation. Variables are shown in italic serif font e.g. y = mθ + AΩ. Terms used in definitions that are defined elsewhere in the glossary are shown in bold.

7 Accumulator - Alternating current 2 2. Glossary Term Definition Accumulator A device for storing energy for long or short periods and which can release the stored energy in the same form as it was supplied. There are several forms of accumulator. Mostly the term is used to describe a device that stores pressurised hydraulic or pneumatic fluids. Other types of accumulator include a battery. Added mass An equivalent mass, which represents the component of the wave excitation force that is in phase with the acceleration of the device. The hydrodynamic forces due to waves on an immersed object vary with time. The response of the device to those forces is not exactly in phase with the force itself. (The object either leads or lags the waves). This is because to move the device must impart some kinetic energy to the fluid. This hydrodynamic force can be expressed in terms of two complex components, one in phase with the acceleration of the device and one in phase with the velocity of the device (i.e. 90 lagging). These two force components can be expressed in terms of two useful quantities. The force in phase with the acceleration of the device can be expressed in terms of an extra point mass fixed to the device. This is known as the added mass. The force in phase with the velocity of the device can be expressed in terms of a velocity force as an applied damping. This is known as added damping, or since it is also the force that causes waves to be generated by the device, it is also known as the radiation damping. Both added mass and radiation damping are dependent on the frequencies of the waves creating the hydrodynamic forces. The effect of frequency on the added mass and damping is also related to the shape of the device. Added mass and radiation damping for an object can be calculated from computer diffraction codes or calculated from wave tank tests. Because of this frequency dependency, added mass cannot simply be interpreted as the mass of water moving with the structure in the fluid. Alternating current (AC) An electrical current which periodically changes or reverses its direction of flow.

8 3 Amplitude - Attenuator Amplitude The maximum extent or magnitude of a vibration or other oscillating phenomenon, measured from the equilibrium position or average value. From the equation for simple harmonic motion, the displacement x at time t from the equilibrium position is given by: x () t = Acos( ω t + φ) A = amplitude, ω = angular frequency, t = time, φ = phase constant This can also be written in complex form and an amplitude quantity can be a complex number. Anchor To fix to a point of support. Wave energy devices are often anchored to the seabed by means of a strong cable or chain, which is attached to a heavy anchor object. This anchor can provide its support through its own mass alone (gravity anchors), by being grouted into the seabed or embedded (dragged) into the seabed. Array An arrangement of similar devices. In renewable energy devices this means a number of similar devices arranged into a single group to provide a combined energy output. Also known as a farm. Attenuator A device that reduces the amplitude of a vibration or other oscillating phenomenon. A term borrowed from radio theory attenuator describes the way that a wave energy device may extract energy from the waves. An attenuator can produce a wave field that is highly focussed in one direction; conversely it can absorb energy from a focussed direction. An attenuating wave energy device is aligned horizontally and in the direction of the wave field. As waves pass the device they are focussed in on the device. In calm water if the device were run backwards it would produce a directionally focussed wave field from both the front and back of the device. A modern ultra-high-frequency (UHF) terrestrial television aerial behaves similarly to a water wave attenuator at absorbing radio waves. It is postulated that a perfect attenuator could achieve a capture width of 3 λ 2π compared to a point absorber s capture width of λ 2 π (where λ is the wave length).

9 Availability - Bathymetry 4 Availability The degree to which a system is free from degradation or interruption in its output resulting from component failures, maintenance or operational scheduling. Availability is often expressed as a annual percentage derived from the following equation: Availabili ty = Time available for operation Total time in period The time available for operation is regardless of whether the prevailing conditions are suitable for energy production. So it includes all times when the machine is turned off during storms for example, but when no fault is present. Availability Reliability Maintainability (ARM) Bandwidth A formal analysis process conducted to determine the likely availability, reliability and maintainability of a system. This process recognises the connections between all these aspects. This allows a traceable analysis that can be used to predict the life costs of any system. Bandwidth describes the range of wave frequencies over which a wave energy device responds. In wave energy different devices respond differently to different ranges of wave frequencies. Some might have a high response in a small range of frequencies and others might have a lower response over a wider range of frequencies. In either case these ranges can be changed by tuning the device. However, the width of the range is known as the bandwidth of the device. Bandwidth is defined variously depending on how it is most useful in a given context. For example if we tune two devices to the same natural frequency and then compare the difference between the two frequencies that give half the maximum response for each device we get a frequency band; the half-response bandwidth. Figure 12 shows two devices tuned to the same natural frequency (the peaks of the response curves are at the same frequency). The red curve is said to have a wide bandwidth and the blue curve has a narrow bandwidth. Both devices have the same response at their natural frequency. Whether a wave energy converter designer chooses a wide or narrow bandwidth solution depends on their view of the economics of their device, (e.g. the choice between say lower energy capture with less capital cost or higher energy capture with greater costly technical complexity). However, to explain the importance we will use an example. Taking the two devices in Figure 12 and assuming that they are tuned optimally for a given sea state to give maximum energy capture; the narrow bandwidth device would give a lower overall energy production. This is because its average response across all frequencies is lower than for the wide bandwidth device. (Note than in some circumstances a narrow bandwidth device might be the right economic solution), thus bandwidth alone is not a good differentiator between devices in terms of economics. Bathymetry The measurement of water depth and the shape of the seabed often as shown on a map of the sea or hydrographic chart.

10 Bretschneider spectrum - Constructive interference 5 Bretschneider spectrum A theoretical power spectral density function that has been found to be suited to some well developed (long-fetch) deep-water seas. The Bretschneider spectrum has two parameters of significant wave height ( H S ) and zero-up-crossing period ( TZ ). The spectral density S [m ² /Hz] for a given frequency f is ( ) 5 4 f = Af exp( Bf ) S where A = H 2 S 4π TZ4 and B = πt 4 1 Z The Bretschneider spectrum is a two-parameter extension of the Pierson Moskowitz spectrum. This is more useful since most historically recorded scatter diagrams are presented in terms of significant wave height ( H ) and zero-up-crossing period ( T ) S Z Buoys An anchored floating device. Traditionally these have served as navigation marks or for mooring but now can be incorporated to wave energy devices. They are typically small compared to the incoming wavelengths, thus are a common form of point absorber. Capacity factor The ratio of the mean generation to the peak generation on a renewable energy generator. The capacity factor, sometimes referred to as the load factor, of a renewable energy farm is the energy produced during a given period as a proportion of the energy that would have been produced had the device been running continually and at maximum output, e.g. Electricity production during the period[kwh] Capacity factor = Installed capacity [kw] time in period[h] Capture width Capture width ratio Energy in a uni-directional wave is expressed in terms of power per unit wave crest, i.e. per unit width (see wave power level). The capture width of a device is the width of wave front containing the same energy as the device can capture in that same wave field. For some devices the capture width can be wider than the device itself. The maximum theoretical capture width of a device can be defined by proposing an analogy that approximates the device operation. In a sense this defines the radiation field generated by the device when oscillated at a given frequency in calm water. The capture width ratio is the ratio of the device s actual capture width to the maximum theoretical capture width. This measure is only useful if the device is described correctly by the analogy in the first place. For example approximating an attenuator as a point absorber could give capture width ratios of greater than one. This would mean that more energy left the far field than entered through it thus not conserving energy. Clearly in such an example it is the analogy that is incorrect. Constructive interference The phenomenon of superposition where several waves travelling through the same point combine to increase the resultant wave amplitude above that of any of the original individual waves.

11 Conversion efficiency - Cross axis tidal turbine 6 Conversion efficiency The conversion efficiency (η ) of a device is the proportion of energy converted to a useful form (e.g. electricity) compared to the total energy available to the device. The definitions differ greatly between wave energy converters and tidal stream energy converters devices. η = E E OUT AVAILABLE It is sometimes difficult to define the energy available since it depends on how the device is best described mathematically. See discussion on capture width of wave devices. Also since it is the cost of energy produced (in both monetary and environmental terms) that is of primary importance the conversion efficiency of the waves or tides to useful power is of less interest. The conversion efficiency of different components in the power train however (power take-off) is of interest. The conversion efficiency of the power take off can often be described by a conversion efficiency, e.g. an average electrical generator efficiency for all normal operating conditions can be given as say 95%. This would mean that 95% of the mechanical power transmitted to the generator is converted to electricity. The total conversion efficiency η of a chain of can often be expressed conveniently as the product of their individual efficiencies ( η is the conversion efficiency of the n -th component). n η = η η η η N N Coriolis Cross axis tidal turbine An effect whereby a mass moving in a rotating system experiences a force perpendicular to the direction of motion and to the axis of rotation. In tidal energy the coriolis force is important. The main forces acting on the water masses on earth are gravitational. Since the earth also spins relative to these forces coriolis acceleration is also felt. This enhances the tidal ranges and flows at certain locations. A configuration of tidal stream turbine rotor that rotates such that blades move around an axis perpendicular to the flow. The blades at different rotational positions travel with the flow, across it and again into the flow. The flow of water thus passes a series of upstream blades then through the middle of the rotor and leaves through the downstream blades. See Figure 17. (Similar in principle to the Banki turbine used in hydropower).

12 7 Damping - Displacer Damping A mechanism for bringing about a reduction in the amplitude of a vibration or oscillation by extracting energy. In a power plant the damping is the part of the load that acts in phase with the velocity. Damping is usually expressed as the force per unit velocity [N/(m/s)]. Where a system operates in a quasi-stable state the damping is directly proportional to the load and thus the power produced. In an oscillating system the damping is specifically the component of the applied load that acts in phase with the velocity of the power-producing component. Damping can arise from methods to produce useful work, (such as in a generator) or by losses and friction forces. For most power systems the power-producing damping must be adjusted to achieve maximum energy conversion efficiency. If the damping is too high then the motions are limited and little power is produced. If the damping is too light then little power is absorbed by the damper and little power is taken off. Darrieus turbine A cross-axis turbine type common in early wind turbine designs, which may have application in tidal stream energy. The original wind turbine design was a vertical axis cross-axis turbine with curved blades (see Figure 16). These blades were given a troposkein (spinning rope) shape and are commonly referred to as egg-beaters. Destructive interference Diffraction The combination of two waves such that one wave in some part cancels the other. The phenomenon, when waves are obstructed by a still object, of the wave disturbance spreading beyond the limits of the geometric shadow of the object. The spreading effect of waves passing a still object in water. The frequency response of a wave energy device can be broken into three parts; the incoming wave field, the radiation problem and the diffraction problem. Computer codes and tank testing can be used to predict the radiation and diffraction relationships for a particular object. The diffraction and radiation characteristics are a function of the size and particularly shape of the object. Diffraction program Dimensional analysis Direct current Displacer A computer code used to calculate the frequency-dependent diffraction and radiation characteristics of a floating body. Used also to calculate added mass and damping functions. An analysis that can be performed on an equation, to describe the resultant quantity with respect to elementary dimensions, e.g. length [ ], time [ T ], mass [ ]. For example power has fundamental units L ML 2 3 T of. M An electric current flowing in one direction only. The part of a wave energy device that moves in response to the waves. Power is usually taken off (see power take-off) from the relative motions of the reactor and displacer.

13 Distribution system - Equation of motion 8 Distribution system Drag Duct An electrical grid network that is used to distribute power to a number of loads. The system can be composed of cables operating at several set voltages. In England and Wales the electricity distribution is composed of cables operating below 275kV and in Scotland, below 132kV. The retarding force exerted on a body moving relative to a fluid. Drag is usually an energy loss process. It can arise in water movements as friction on wetted surfaces or as vortex shedding from fluid flowing past solid object corners. With particular application to tidal stream turbines; a duct is a cowling placed around a turbine to enhance the flow through the rotor. The intention is to increase the flow such that a smaller rotor can be used for the same power production, or to gain more power from the same size rotor. Ducts can also be used to adjust the direction of a flow. These advantages must be balanced against possible increased flow direction sensitivity of the device and possible pressure drop across the duct. See also Figure 18. The term duct can also apply to the part of oscillating water columns where the air turbine is placed. Eigenfrequency Energy frequency ( ) f e See natural frequency. The frequency corresponding to the energy period, f = 1 T [Hz]. e e Energy period ( ) T e Real sea waves can be described as a series of superimposed waves of different periods and amplitudes. The energy period is the period of a monochromatic (single frequency) wave containing the same energy as the real sea state. It can be described mathematically as M M 1 0 where M n is the n -th spectral moment of the power spectral density function. See Figure 7. The energy period is usually measured in seconds. See also energy frequency. Energy storage Equation of motion Storing energy in a form so that it can be used at a time after it was originally generated. An equation that can be used to describe the motion of an object. These are typically derived from fundamental equations such as Newton s laws of motion. A simplified example of the equation of motion for a single-degree-of-freedom vibrating system is: m& x + cx& + kx = F0 sinωt where x is the displacement from the mean position, m is the effective mass of the system, c is the effective linear damping of the system, k is the stiffness of the system, F0 is the modulus of the applied harmonic force, ω is the frequency of the applied force and t is the time.

14 Equivalent linearization - Fast Fourier Transform 9 Equivalent linearization Many problems can be simplified by only considering situations where the describing functions are linear. Non-linearities might be ignored or approximated. Equivalent linearization is a process of approximating a non-linearity so that it can be included as a linear term. An example of such an approach is to produce an equivalent constant damping force to approximate drag on a floating buoyant body. In a real sea drag is not constant and is proportional to the square of the velocity and thus is not linear. However equivalent linearization can be used to produce a constant value of drag. In such an example the energy lost due to drag can be used for equivalence. So the average energy lost due to drag in the real sea equals the energy lost due to drag in the linearized model. This technique is especially useful in the frequency domain where time-averaged values are required. Excursion Far field Farm Fast Fourier Transform (FFT) The distance moved relative to the instantaneous water surface level is the excursion. The excursion of a device is the distance between a floating device s mean water position and the surface of the water. The mean water position is the point on the device level with the water surface in calm water and when the device is at rest in equilibrium. Since the device will not always move in phase with the waves it is possible for the device to move relative to the water surface. In a wave field a boundary distant from a certain point can be defined. The energy passing through this boundary must be in equilibrium. This boundary is known as the far field. Describing energy fluxes in the far field is much simpler than describing those near the body (see near field). See array. Fast Fourier Transforms are a computationally efficient means of transforming large quantities of data. They have particular application in analysing water waves. FFTs are used to convert time-series wave position information (such as wave height) into power spectral density functions. Thus from the time-domain into the frequency domain. The full process retains information about the energy and frequency content of the waves, but loses the phase-relationships between the waves. Whilst complex Fourier transforms can be reversed, their presentation of power or amplitude spectra normally cannot be reversed. This means that a time-series of wave positions can be transformed into the frequency domain, but can only be transformed back into the time-domain if the original intermediate calculations (the complex imaginary parts of the FFT) are available. In such cases it is highly likely that the original wave train data are available anyway.

15 Fast tuning - Froude number 10 Fast tuning Fast tuning requires changing characteristics of a device to adjust (or ideally to maximise) the energy capture. Fast tuning means adjustments for each wave or loosely over a period of around 1 second for real-sea waves. Also known as wave-by-wave tuning or better event-to-event tuning. Fast tuning requires that the device has a characteristic mode that can be altered to change its response. This may mean changing the effective system stiffness, or delaying or locking device against its natural motion. Fast tuning is required for systems that use stiffness modulation and latching to control their response to real sea waves. Fast tuning can be either predictive (feed-forward) or reactive (feedback) and usually requires complex software algorithms, sensors and controllers. Fetch Free surface Frequency Frequency domain Frequency response Froude number The distance travelled by wind or waves with no obstruction. In marine energy often this means the surface of the water. It is free to move. Often it is approximated by assuming that it is only affected by incoming wave fields and gravitational forces. The effects of the air above are ignored. In particular application to wave energy the frequency is the water/sea wave frequency. It is measured in Hertz [Hz] or [radians/s]. When analysing periodic information it is sometimes beneficial to consider using the frequency domain. Such analyses transform the problem into one of frequency components. An example of a frequency-domain presentation is the power spectral density function. The Power Spectrum Density (PSD) function shows the energy contained in each frequency of wave. The PSD was created by averaging a great number of waves in real time. (See time domain.) An oscillating system such as a resonant wave energy device can be excited by a varying force such as that from interactions with waves. The degree to which the system is affected by the force is its response. The frequency response of a system is particularly the extent to which that system is affected by particular frequencies of forcing. Thus it can be said that a wave energy device responds differently to different frequencies of waves. The relationship between the device s response and the frequency of the incoming waves is its frequency response. Also referred to as the Response Amplitude Operator (RAO). The Froude number is a non-dimensional scaling parameter used by hydrodynamicists. It is the ratio of the modulus of the inertia force to the gravity force. It is often expressed as l u lg where u is a g reference velocity, is a reference length and is a reference gravitational force (i.e. approximately 9.81m/s on earth). See also scaling.

16 11 Generator - JONSWAP Generator A device that converts mechanical power into electrical power. There are several forms of generator including synchronous, asynchronous, permanent magnet, linear and hydraulic types. Gravity foundation Grid Harmonic A foundation design that holds a structure in place primarily using the force of a mass under gravity. A network of interconnected cables for transmitting and/or distributing electricity. A harmonic is a single frequency that is an exact integer multiple of the fundamental or natural frequency of a system. Heave Vertical motions of a buoyant body (see Figure 19). Horizontal axis turbine Hydraulics Installed capacity Joint-probability distribution JONSWAP A tidal stream turbine mounted such that it rotates about a horizontal axis. See Figure 15. The use of fluids to convert motions from one form to another. The installed capacity of a device is the total power that the device can produce when operating correctly and at full power output. Traditionally this is the installed capacity of the electrical generator in a device. Installed capacity is usually measured in kilowatts [kw] or megawatts [MW]. See scatter diagram. A theoretical power spectral density function suggested by the Joint North Sea Wave Project (from the acronym of which JONSWAP derives) that has been found to be suited to some short-fetch seas, particularly the North Sea for which is was developed. This is an adaptation of the Pierson Moskowitz spectrum where the peak frequency is enhanced. One formulation of the JONSWAP spectrum is below in terms of the peak frequency: S 2 ( f ) αg ( π ) ( f f ) 2 4 P exp f 2σ f P 2 f exp γ = [m ² /Hz] ( ) 4 Where S f is the spectral density at a given frequency f, and γ is the peak-enhancement factor chosen to best suit the prevailing conditions and σ has different values above and below the peak frequency ( f P ). Various values for the literature for different conditions e.g. γ = 2 and σ = ( f f P ) and for σ = ( f > f P ). f P γ and σ have been proposed in In this formulation the JONSWAP represents a Pierson Moskowitz distribution with an extra enhancement of the peak and adjustments to the high and low-frequency tails. Thus the spectrum has a narrower band of high-energy frequencies than a Pierson Moskowitz distribution of the same peak period. See Figure 13.

17 Keulegan-Carpenter number - Monopile 12 Keulegan-Carpenter number The non-dimensional Keulegan-Carpenter number is defined as UMT KC = D Where U M [m/s] is the amplitude of the harmonically varying velocity D [m] and where T [s] of the water relative to a cylinder of diameter is the period of the velocity oscillations. The Keulegan-Carpenter number provides a basis for comparing the relative dominance of drag and inertia forces and is useful in the prediction of the onset of vortex shedding. Latching Linear Load factor Latching is a method of control. The aim is to deliberately hold back or latch a device in a particular position during a wave cycle. For example one might hold a heaving buoy lower in the water for part of the cycle than it would naturally assume under wave action alone. The aim is to make the device which is not naturally tuned to the sea state behave more like one that is. Latching is a form of fast tuning. In mathematical descriptions of oscillating systems such as wave energy devices the term linear means that all oscillating variables are sinusoidal and proportional (in the case of waves) to wave height. Linear often implies relatively small motions or amplitudes The ratio of the mean load to the peak load on a generator. Often used in the place of capacity factor. Load factor is traditionally used to describe the duty on a conventional power generation system where it is the load on the system that varies rather than the fuel. In renewable energy it is assumed that it is the fuel (the waves or tides) that varies and the load remains present at all times. Thus capacity factor is the term normally used. Marine current Mean wave power See tidal stream. Mean power is the average power in a real (polychromatic) sea. It is usually measured in kilowatts or megawatts. Even over relatively short periods such as the length of a persisting sea state (minutes to hours) it is common to use average powers rather than instantaneous powers. The mean power output over the year is a useful measure of a wave energy device performance since it gives a single figure by which the device can be compared with others. (Conventionally the mean power output is calculated as the installed capacity multiplied by the capacity factor). See also wave power level. Monochromatic Consisting of a single wavelength or frequency. In the real sea exists a set of waves in a range of different frequencies. However, during design and testing of wave devices it is often useful to analyse the device at a single known frequency and thus a much simpler wave train. Such a wave would be described as a monochromatic wave. Monopile A foundation design consisting of only one pile to support a structure.

18 13 Natural frequency - Panchromatic Natural frequency The frequency of vibration of an oscillating system when vibrating freely. If an oscillating system is moved out of the equilibrium position and then allowed to return to that equilibrium position over time then the frequency of the oscillations it produces during that time is the natural frequency of the system. Also the natural frequency of any oscillating system is the frequency of forcing that gives rise to the highest response from the device. Also known as the eigen-frequency. Near field Nearshore Ocean thermal energy conversion (OTEC) Offshore Operation and maintenance (O&M) Oscillating water column (OWC) Overtopping Panchromatic The region near to a point where calculation of energy flux can be complex and difficult to determine. The near field contrasts with the far field, which is much simpler to describe mathematically. The region of sea between but not including the shoreline and the offshore. Nearshore is typically defined in terms of water depth, distance to shore or both. The precise definition of nearshore in terms of water depth, distance to shore and other parameters is flexible to allow it to be used for different marine energy technologies. Thus the nearshore definition for one particular application might differ from another. Ocean thermal energy conversion technologies exploit large temperature gradients (where there is sufficient temperature difference between the surface and the depths) to extract power from the oceans. The offshore zone is usually the area of sea that is either distant from land, in deep water or both. Its precise definition is flexible, see nearshore. A term used to describe the combined activities for operating and maintaining a system. Also refers to the manuals supplied by the technology supplier to the system operator to provide all the necessary information on the proper, efficient and safe operation of a system or device. A hollow, open-ended inclined or vertical tube partially submerged in a body of water. As waves arrive at the partially submerged openended column the water in the tube is forced to oscillate. This movement is used to drive a power take-off. Most Oscillating Water Columns to date have used the water column to pressurise and depressurise an air volume that is passed back and forth through a turbine. Power is extracted then by a torque applied to the turbine. As used in marine energy: Overtopping is the method by which energy from the sea is extracted by allowing waves to impinge on a structure such that they force water up over that structure thus raising its potential energy (hydraulic head), kinetic energy or both. An overtopping device may or may not include a reservoir to contain the overtopped water. Often high specific-speed water turbine-generators (e.g. Kaplan turbines) are used to convert the hydraulic head to electricity. See polychromatic.

19 Peak frequency - Phase 14 Peak frequency ( ) f P The frequency corresponding to the peak period, f = 1 T [Hz]. P P Peak period ( ) T P Real sea waves can be described as a series of superimposed waves of different periods and amplitudes. The peak period is the period of the wave containing the most power. This is also the peak of the power spectrum (see Figure 7). The peak period is usually measured in seconds. Some real sea states do occur where two wave trains caused by different conditions meet. These can produce bi-modal seas that appear to have two (localised) peak frequencies. Clearly in such circumstances peak period can be of limited use and is often more meaningful in spectra that have a single peak frequency. See also peak frequency. Period (T ) Phase The interval of time between successive occurrences of the same state in an oscillatory or cyclic phenomenon. In wave energy there are several different periods that can be used to describe a wave train. In monochromatic waves all periods are the same, but in real sea conditions where we often describe average conditions several different periods are required. Three useful average wave periods are the zero-up-crossing period, the energy period and the peak period. See Figure 7. The period of a wave is the inverse of its frequency, T = 1 f [s]. See also amplitude. Phase is a relative position of two parts of the same wave or between two waves. It is measured as an angle [either degrees or radians]. For example waves are considered in phase when two corresponding parts of the wave e.g. their peaks, coincide at the same time. Another example is a simple wave with a crest and a trough. The trough follows the crest and is out of phase with the crest. The trough in a simple sinusoidal wave (see Figure 2) is out of phase with the crest; it lags the crest by Since many of the other quantities in wave energy also vary with time such as forces, accelerations and velocities, phases are often used to describe the relationship between them. For example we often talk about a device accelerating out of phase with its velocity. Imagine forcing a mass to oscillate on a spring. At the top of the movement the mass is stationary and has no velocity and yet it is accelerating downwards fully. As the mass passes the halfway point it begins to decelerate and thus the acceleration is zero, at this time though the velocity is maximum. We say that the velocity lags the acceleration by 90 phase.

20 Pierson Moskowitz spectrum - Polychromatic 15 Pierson Moskowitz spectrum A theoretical power spectral density function that has been found to be suited to some fully developed (long-fetch) deep-water seas. It does not strictly apply to all sea states in a real sea. The Pierson Moskowitz spectral density frequency f was originally defined as S spectrum for a given S( f ) = where 3 g 2 exp 0.74 g fu ( ) 4 5 2π f 2π 19.5 is the wind speed at 19.5m above the mean sea level. (The wind measurements in Pierson and Moskowitz s original study were made using weather ships whose instruments were mounted at 19.5m above mean sea level.) For the sea states that represent fully developed seas can be related to the significant wave height H S. U 19.5 U 19.5 Since the original Pierson Moskowitz definition does not apply to all sea states it is common to use the multi-parameter equivalent called the Bretschneider spectrum instead. 4 Pile Pitch Point absorber A heavy post driven into the ground to support the foundations of structure. A motion about an axis in the horizontal plane and perpendicular to the wave propagation. See Figure 19. (Note that in naval architecture the ship direction is used in the place of wave direction). A wave energy device that is small compared to the incident wave length. It can be sized in various ways to tune it to the sea conditions. One crucial aspect of a point absorber is its ability to focus energy onto itself. To do this the device radiates waves, which in part cancel the incoming waves. In the case of a heaving point absorber the radiated waves are circular when viewed from above whereas the incoming waves are straight. Under such conditions and in a monochromatic sea a point absorber can capture energy from a width of wave equal to λ 2 π where λ is the incoming wavelength. What is important here is that the capture width relates to the shape of the wave and not the size of the device. Thus a point absorber can be very small and still generate the same power. Note that to do so it would need to move a long distance to manage this feat. In reality seas are polychromatic and so a device needs to be able to cope with a range of different waves arriving at the same time as well as different wave combinations arriving at different times. In practice size is important and point absorbers are designed in such a ways as to optimise the power take-off, mass and more crucially the bandwidth which allows them to capture some energy from all frequencies and not just those to which they are tuned. Polychromatic Composed of more than one wavelength or frequency. Real seas contain polychromatic waves. Also known as panchromatic.

21 Power chain - Radiation 16 Power chain Power matrix Power spectral density (PSD) Power surface Power take-off (PTO) See power train. See power surface. The power spectral density is the amount of power contained in each frequency in a wave spectrum. In wave energy this can be calculated by transforming a wave train from the time-domain to the frequency domain using Fourier Transforms (see Fast Fourier Transforms). It is presented as power per unit frequency or specifically in water waves as m ² /Hz since the power in the waves is proportional to the square of the wave height. Also known as a power matrix. A power surface describes the timeaveraged mean power performance of a device in each sea state. A scatter diagram can thus be multiplied by a power surface to produce a mean energy production. The power surface is analogous to a power curve for wind turbines. As defined here this is a system incorporated to a renewable energy device that allows energy to be converted from the physical motions of the device to a useful form such as electricity. For example an energy extraction device might directly convert water motions to rotating shaft power. A power take-off might then convert this torque to electrical power via a gearbox and electrical generator. The power take-off is thus a subset of the complete wave-to-wire power train converting the main motions of the device to a useful form at the exit to the farm. It does not include the prime mover, or the electricity transmission system. A power take-off usually interfaces with a control system that is capable of adjusting the load to controller power extraction, controlling the quality of the power and changing the operation of the device for high and low energy conditions, etc. See also System Control and Data Acquisition. Power train Programmable Logic Controller (PLC) Radiation See also power take-off. Also known as power chain. The power train is a series of components that convert power from one form to another. For example rotating mechanical power can be converted from low-speed high torque by a gearbox, this mechanical rotation can then be turned into electricity using a low-voltage electrical generator and this electrical power can thence be converted to high voltage by an electrical transformer. The combination of gearbox, generator and transformer in this case comprise the power train. A system that can be programmed to respond to different input signals and provide control signals to other systems. PLCs are commonly used to control a range of different industrial plant. Can comprise part of a System Control and Data Acquisition system and offering the system control functions. See also diffraction for a more detailed explanation. In wave energy radiation can be considered the energy spread away from the device by its interaction with the water. It is the wave pattern that would be produced by the device when oscillated in calm water.

22 Radiation damping - Response amplitude operator 17 Radiation damping Rated capacity Radiation damping is the damping felt by a floating body as a result of the waves generated by it as it responds out of phase to the incoming wave field. See added mass for a more detailed explanation. See installed capacity. Also the maximum continuous point of operation at which an item of electrical or mechanical equipment is designed to operate. Reaction Reaction mass Reactive power A force exerted in opposition to an applied force. In terms of energy extraction devices it is the reaction force that is applied to the power take-off to produce useful energy (see reactor). A means of providing a reaction force. The reaction force results from accelerating and decelerating the reaction mass. Some reaction masses can be very large and have large inertia and thus move little and other reaction masses are small and move considerable distances. Reaction masses can be incorporated inside the working parts (such as the displacer) or outside the device. They can comprise solid materials such as concrete or steel or sometimes entrapped water. Reaction masses are often used where devices cannot gain useful reaction forces directly from the land or seabed. An abstract quantity used to describe the effects of a load, which on average neither supplies nor consumes real power. Reactive power, Q, uses the unit volt-ampere reactive (VAR) and is defined as: Q = VI sinθ Where: V = voltage (V) I = current (A) θ = impedance angle Reactor Reflection Resonance Response amplitude operator (RAO) A device relative to which some part of the wave energy device moves and against which it reacts. The reaction force generated is then used to generate useful power. Where forces arise from interactions between two or more components that then do not produce useful power then none of these components is considered a reactor. The phenomenon of propagating wave energy being thrown back from or bouncing off a surface. Energy reflection is a special case of diffraction. An increase in the oscillatory energy absorbed by a system when the frequency of the oscillations matches the system s natural frequency of vibration. The response amplitude operator (RAO) is a measure of the frequency response of a device relative to the wave causing the motion. RAOs can describe power and amplitude ratios. See frequency response.

23 Reynolds number - Scaling 18 Reynolds number Roll Root-mean-square (RMS) A dimensionless number used in fluid mechanics to indicate whether a fluid flow is steady or turbulent. The Reynolds number is the ratio of the inertia force to the viscous flow force. It can be described as: ρlu Re =, where ρ is the fluid density [kg/m³], l is a characteristic µ length [m], u is a related characteristic velocity [m/s] and µ is the fluid viscosity [Pa s]. See also scaling. To move by turning on an axis in the horizontal plane and in the direction of the wave propagation. (Note that in naval architecture the ship direction is used in the place of wave direction). In an oscillating system a useful average quantity is the root-meansquare quantity defined as: x RMS = 2 x for clarity this can also be expressed for x 1 n = N 2 RMS = x n N n= 1 N values of x as (For example the RMS amplitude of an integer number of sine waves cycles is half the amplitude squared). Salinity gradient Scaling Between two bodies of water of different salt concentrations (salinity) there can exist a pressure difference. This is known as the osmotic pressure difference. Energy can be extracted from the sea where large changes or salinity gradients exist. A semi-permeable membrane is placed between the two bodies of water. Slowly the less salty water moves into the salty water by osmosis. Energy can in theory be extracted by exploiting the pressure difference across the membrane. The determination of the interdependency of variables in a physical system. Scaling is relevant to the development of marine energy systems since most new devices will be developed as small models and tested at part-scale. However, this presents difficulties in extrapolating the results to full size. If one doubles the size of a device then not all forces on it will double. The method of scaling used can greatly affect the results and care must be taken to confirm that the most appropriate combination of methods is used. Some scales such as the Froude and Reynolds numbers are commonly used. However, they both scale differently and so predictions of forces, power output and non-linearities predicted using Froude scaling will be different from those predicted using Reynolds scaling. Neither approach will give truly accurate results. Model testing, and thus scaling, is a specialist area of knowledge.

24 19 Scatter diagram - Shoreline Scatter diagram Sea (as distinct from sea state) Also known as a joint probability distribution. The scatter diagram is a table that shows the frequency of occurrence of different sea states. Each sea state can be defined by a representative height (usually significant wave height ) and a representative period ( T, T or T ). The table therefore has axes of height and period. Z e P H S The number of occurrences of each combination is shown in the table cells corresponding to each height and period. Since not all combinations of height and period occur in a real sea some of the cells are left empty. The remainder of the cells are distributed across the table, thus the name scatter diagram. Seas are the margins of the oceans that cover most of the Earth s surface. They contain shallower water compared to oceans and have a semi-enclosed physiography. In wave energy a sea is a combination of sea states. Often a sea is an average condition likely to occur during a given period, such as a year. It is often represented as a scatter diagram. Sea state Shallow water Shoal Shoreline A numerical measure of the character of the sea for a given period of time. The sea state is typically described by its significant wave height ( H ) and period (usually either T, T or T ). A sea-state is S assumed to persist for minutes to hours and most sea state calculations are based on time periods of 2-4 hours. Over a year at a given location a range of sea-states are encountered. These are often summarised statistically in a joint probability distribution showing the occurrence of different sea-states over a long period (say one year or more), see scatter diagram. A sea can be described as a combination of a number of different sea states and a sea state can be described as a combination of waves characterised by the two parameters of wave height and period. In wave energy or wave forces shallow water is usually defined relative to the incoming wavelength. Most of the energy in the waves is contained in the top layers of the water. The decay in energy with depth is a function of the wavelength λ. The energy reduces exponentially with depth. Shallow water is therefore considered to be less than λ 2 π deep. A shallow place in a body of water. Shoals or changes in water depth can cause the direction of waves to change. This is known as wave refraction. (A similar effect is observed in light waves as the light passes into a more optically dense material it bends. This is what happens in a lens.) The line along which a large body of water meets the land. Z e P

25 Significant wave height - Survivability 20 Significant wave height ( ) H S The significant wave height is defined here as four times the rootmean-square water elevation. It can be calculated as it can be 4 M where is the zeroth M 0 describe mathematically as 0 spectral moment of the power spectral density function. The significant wave height was originally defined as the average height of the highest one-third of waves and is sometimes written as H. However, as defined here is derived from the zeroth 1 3 spectral moment of the wave train. This definition is also properly denoted as. H M 0 H S Skin friction Slow tuning Spectral moment ( ) M n Stiffness Drag due to friction with wetted surfaces. Slow tuning requires changing characteristic parameters of a device to adjust (or ideally maximise) the energy capture. Such characteristics could for example be the device s buoyancy or power take-off damping level. Slow tuning means typically adjustments over minutes to hours or sea state to sea state. Slow tuning is usually reactive and based on peak power tracking. The n -th spectral moment (about f = 0, S = 0 ) is defined as M n n = f S( f ) df f ( ) 0 power spectral density function. where is the frequency [Hz], S f is the The restoring force per unit displacement of a spring [N/m]. Note: A floating body can be thought of as having a buoyancy stiffness since when displaced downwards by small distance from the equilibrium position (such that any change in water-plane area is negligible) the restoring force is proportional to the distance displaced. Thus the buoyancy stiffness is the restoring force per unit displacement. Stiffness modulation Stiffness modulation is the means by which a wave energy converter in step or resonance with irregular waves. The technique treats the device as a mass/spring system in which the stiffness of the spring is modulated to achieve resonance. In the simplest form of the stiffness-modulation approach, the spring stiffness can be varied between two values, the higher giving a natural frequency f 2 and the lower a frequency f1, the required bandwidth being between the two. By switching between the two values of natural frequency at the right instants in a cycle, resonance with the waves can be maintained. Stiffness modulation is a form of fast tuning. Surge Motions in and out of the direction of wave travel. See Figure 19. (Note that in naval architecture the ship direction is used in the place of wave direction). Survivability A measure of a device s ability to remain intact and operational in extreme environmental conditions.

26 21 Survival mode - Transformer Survival mode Sway System Control and Data Acquisition (SCADA) Temperature gradient Terminator Tidal stream Tidal stream energy converter Time-domain Transformer An operation mode for a device that reduces the likelihood of damage being sustained during extreme/uncommon environmental conditions such as storms. Horizontal motions perpendicular to direction of wave travel. See Figure 19. (Note that in naval architecture the ship centreline is used in the place of wave direction). An automatic system that allows data collection and control of a system. Such systems are usually accessible by users remote from the system via telecommunications systems. In the oceans there can often be found a temperature difference between water near the surface and that deeper down. Where this temperature difference occurs over a relatively short distance (where there is a noticeable temperature gradient) it can be used to capture energy using a Rankine cycle. See also ocean thermal energy conversion (OTEC). A device which is long and oriented perpendicular to the wave direction. One example of a terminator is a wall. A wall however reflects all wave energy from it and consequently does not extract any power. An efficient wave energy device configured as a terminator would create waves exactly in anti-phase with those arriving at it. As with a wall no waves would be transmitted beyond the structure under such conditions. An imperfect terminator would reflect some wave energy, transmit some and extract the remainder. In theory a terminator can extract 100% of the energy in the waves. Since a terminator is by definition long, its capture width is equal to its length and is unrelated to wavelength. (This is unlike point absorbers and attenuators). In reality terminators are of finite length and the shorter they get the more they behave like point absorbers and thus the more sensitive they become to wavelength. The tides are generated by the rotation of the earth within the gravitational fields of the moon and sun. The relative motions of these bodies cause the surface of the oceans to be raised and lowered periodically and the water to move. Where these moving bodies of water meet land masses, channels or other underwater features they can be enhanced forming a tidal stream. The processes by which these currents are formed depend on the local topography and vary widely. Also referred to as marine currents. A tidal stream energy converter turns energy in tidal streams to a useful form such as electricity. Calculations or control systems that make use of second-by-second data streams operate in the time domain. A time-series of water elevation such as shown Figure 5 is an example of data presented in the time domain. This is to be contrasted with calculations completed in the frequency domain. A device that transfers energy from one electrical circuit to another via a magnetic coupling. Transformers are often used to transfer energy between circuits that operate at different voltages.

27 Tripod foundation - Wave-by-wave tuning 22 Tripod foundation Tuning Vertical axis tidal stream turbine Viscous drag Water-plane area Wave Wave crest Wave energy converter Wave power level Wave rose Wave steepness Wave tank Wave-by-wave tuning A foundation structure based upon three poles fixed to the ground in different locations, which are all joined together at the same point. The process of matching one oscillation to another. In oscillating wave energy systems a device can be sized or controlled in such a way as to change its oscillation frequency. This is known as tuning. A device may be tuned to resonate with the incoming waves. Under such conditions the maximum energy from the waves can be extracted. Conversely a device can be de-tuned so that it moves little under the influence of the waves. (For some devices this is an important survival mode). A tidal stream turbine mounted such that it rotates about a vertical axis. See Figure 15. Drag caused by interaction with viscous fluids such as water. See drag. When a body pierces the surface of the water the area of the intersection between the body and the surface is the water-plane area. See Figure 14. Ocean waves are caused by winds blowing over the earth s surface. These winds transfer energy in shear to the water in the seas and oceans. This energy causes waves to form. It is from these waves that carry the energy with no net transfer of water in deep water. Energy can be extracted by marine energy technologies. The wave crest is the peak of the wave. Since many water waves are wide compared with their height. The crests of successive waves proscribe parallel lines on the surface. Measurements of wave energy are usually related to a certain length of wave crest [kw/m]. See Figure 1. A system to convert the energy in surface water waves to a useful form such as electricity. See mean wave power. A graphical plot describing the wave climate of a location usually in terms of mean wave energy in given wave directions. Wave roses can also be produced from measurements taken by wave-rider buoys. Wave steepness is a gradient used to describe the shape of a wave. It is defined as the wave height divided by the wavelength ( H λ ). Wave steepness is important when considering extreme waves or waves that do not behave linearly and is thus is often an important survival parameter. Note that the wave steepness is not the slope of the water surface. A test facility capable of producing (wide) waves of a known shape and type. See fast tuning.

28 23 Wavelength - Zero-up-crossing period Wavelength Wave-rider buoy The distance between two successive zero-up-crossing motions. Wavelength is usually measured in meters and is often represented mathematically as the symbol λ. A device used to measure wave properties. The buoy rides the waves and estimates the wave positions and directions based on measurements of its own accelerations in different directions. Data from wave-rider buoys can be used to form time-series for different sea-states of water surface position in given directions and these can then be used to create power spectral density functions using fast-fourier-transform techniques, wave roses and scatter diagrams. Wave-to-wire efficiency Wells turbine The conversion efficiency from the wave energy in the sea to a useful power form e.g. electricity. A turbine with a zero-pitch rotor designed to rotate in a single direction regardless of the direction of fluid flow through it. Known for its use in several oscillating water column designs. Yaw Rotation of a buoyant body about the vertical axis. See Figure 19. Zero up-crossing frequency ( ) f Z Zero-up-crossing period ( ) T Z The frequency corresponding to the zero-up-crossing period, f = 1 [Hz]. Z T Z Real sea waves can be described as a series of superimposed waves of different periods and amplitudes. The zero-up-crossing period (often incorrectly called the zero-crossing period) is the average time between successive movements of the water surface through the mean position in the upward direction. The zero-upcrossing period is usually measured in seconds. It can be calculated as D / n zˆ where D is the duration in seconds and nˆ z is the number of times in that duration that the water surface passed through the mean position in the upwards direction. The zero-up-crossing period can also be defined in terms of spectral moments as M 0 M 2 where M is the n -th spectral moment of the power spectral density function. n See also zero-up-crossing frequency.

29 24 3. Symbols and abbreviations 3.1 Symbols λ f e Wavelength Energy frequency f Modal frequency, see peak frequency M f P f Z H Peak frequency Zero up-crossing frequency Wave height H See significant wave height M 0 H S KC Significant wave height Keulegan-Carpenter number M n n -th spectral moment S ( f ) Spectral density function T T e Period Energy period T P T Z x x& & x& Peak period Zero-up-crossing period Mean of all x First time derivative of x Second time derivative of x 3.2 Abbreviations AC ARM DC Alternating current Availability Reliability Maintainability Direct current

30 25 FFT ISO O&M OTEC OWC PLC PSD PTO RMS SCADA Fast Fourier Transform International Organization for Standardization Operation and Maintenance Ocean Thermal Energy Conversion Oscillating water column Programmable Logic Controller Power spectral density Power Take-Off Root-mean-square System Control and Data Acquisition 3.3 Units Degrees (of heat) Degrees (of angle) = radians A GW GWh Hz J K km kv kw kwh m MW MWh N Pa rad s TW TWh Amperes Gigawatts = 1,000 Megawatts = 1,000,000,000 Watts Gigawatt-hours = 1,000 megawatt-hours = 1,000,000,000 watt-hours Hertz (cycles per second) Joules Kelvin kilometres = 1,000 metres kilovolts = 1,000 Volts Kilowatts = 1,000 Watts Kilowatt-hours = 1,000 Watt-hours metres Megawatts = 1,000 kilowatts = 1,000,000 Watts Megawatt-hours = 1,000 kilowatt-hours = 1,000,000 watt-hours Newtons [kgms ²) Pascals [N/m²] Radians = degrees seconds Terawatts = 1,000 Gigawatts = 1,000,000,000,000 Watts Terawatt-hours = 1,000 Gigawatt-hours = 1,000,000,000,000 watt-hours

31 26 V VAR W Wh Volts Volt-Amperes-Reactive Watt Watt-hours = 3600 Joules

32 27 4. Notes Calculation of power from the frequency response of a wave energy device and the spectral density of the sea-state In wave energy a simple useful example of a frequency-domain calculation of mean wave power is shown below: P = 0 c H 2 ( f ) S( f ) d f where P is the mean power produced by the device in a given wave train before losses, is the spectral density function of that wave train, ( f ) S( f ) H is the complex response of the displacer to a complex wave of unit amplitude and frequency ( f ), and c is the useful powerextracting damping applied to the displacer. In other words if we know how a device responds to waves of different frequencies we can calculate the mean power produced by the device in a wave that contains a range (spectrum) of different frequencies by convoluting the response function with the spectral density function. Note that this gives a mean power.

33 28

34 29 5. Acknowledgements The author would like to thank the following people for providing commentary and discussion on this glossary. Rod Rainey from Atkins engineering consultancy helped check all the draft definitions and was particularly helpful in his discussion useful definitions of the added mass and damping terms. Rod s contribution helped shape the glossary in its early stages of development. Tony Lewis director of University College Cork Hydraulics and Maritime Research Centre suggested the need for this Glossary during the running of the European Commission-funded WaveNet project. He also provided a number of tighter definitions and more precise meanings for the glossary terms. His input is greatly appreciated since it greatly enhanced the clarity of the glossary. Michael French of Emeritus Professor of Engineering from Lancaster University provided some very important insights to the engineering behind the glossary. Michael s progressive and clear thinking is evident in many of the terms in the glossary. Many of these terms were devised and expounded by Michael. Michael has also suggested that glossaries such as this one do not simply record the current state of play but offer progressive terminology to help move the industry on. I hope future revisions of this glossary will allow that to happen. The Carbon Trust would like to thank Richard Boud for editing and compiling this glossary.

35 30 6. Figures Wave direction Wave crest Figure 1 Wave nomenclature, wave crest and direction A x > φ θ > Figure 2 Definition of amplitude and phase of a wave

36 31 water position wavelength mean water position height distance > Figure 3 Wave nomenclature water position upcrossing period height mean water position up-crossing time > Figure 4 Wave nomenclature

37 32 Water surface level [m] h Significant wave height Time [s] Figure 5 Example of a time series of wave positions showing the significant wave height in red Density [m2/hz] > fp Peak frequency = 1/Tp fe Energy frequency = 1/Te fz Zero-upcrossing frequency = 1/Tz Frequency [Hz] > Figure 6 Example of a power spectral density function showing the three main average periods and frequencies

38 33 Power spectral density [m 2 /Hz] Power spectral density Pierson Moskowitz approximation Zero-upcrossing frequency Energy frequency Peak frequency Frequency [Hz] Figure 7 Example of an un-smoothed time-series transformed using Fast-Fourier Transforms into the frequency domain. This shows the spectral density of the wave train showing which frequencies contain the most energy. Also shown is a Pierson Moskowitz spectrum that best describes the data Figure 8 An example of a wave rose

39 Significant wave height [m] Energy period [s] Figure 9 Example scatter diagram (joint probability distribution of significant wave height and energy period) showing occurrence of sea states in parts per thousand. Also shown are contours of constant mean wave power level [kw/m]

40 35 D Figure 10 Depth of water and circular water motions for deep-water approximations of wave

41 36 Figure 11 An example of a power surface (power matrix), for illustration the scatter diagram in Figure 9 is overlaid. The product of these two matrices gives the energy output.