1. EE535: Renewable Energy: Systems, Technology & Economics
Session 7: Wave Energy (1)

2. European Theoretical Wavepower
IEA (International Energy Association) estimates that there is a potential to generate 1500TWh per year (10% of global demand) from wave power
No commercial wave farms yet exist but there are several beta installments
European Wave Energy Atlas, Average
Theoretical Wave Power (kW))

3. Irish Context
Estimated power of Atlantic coastline is 40kW per meter of exposed coastline
Highest energy points are Northwest Mayo, West Galway, West Cork, Kerry
Trade-off between the available energy (which increases with distance from land), and practicalities of harnessing and connecting to grid

4. Waves Storm Waves Swell Waves Wave size depends on:
Waves located close to the location where they were generated
Form complex irregular sea
Swell Waves
Waves can travel a great distance with minimum loss of energy to produce a swell
Wave size depends on:
Wind speed
Duration
Fetch

5. Wave Formation
Ocean waves are generated by wind passing over stretches of water
3 main processes give rise to wave formation and growth:
Air flowing over the seas exerts a tangential stress on the water surface
Turbulent air close to the water surface creates rapidly varying shear stresses and pressure fluctuations. Where these processes are in-phase with existing waves, further wave development occurs
When waves have reached a certain size, the wind can exert a stronger force on the up-wind face of the wave, causing additional growth

6. Waves
It is important to realise that there is no net motion of water in deep water waves
Waves contain energy in two forms:
Potential energy – energy required to move the water from the trough to the crest
Kinetic Energy – energy associated with water moving around (circular motion)

7. Difficulties facing wave power developments
Wave patterns are irregular in amplitude, phase and direction. Difficult to design devices to extract power efficiently over such a wide range of variables
Probability of extreme gales or hurricanes – devices need to be able to withstand conditions which are ~ 100 times the power density for which they are normally matched
Peak power normally available in deep water from open swells. Very difficult conditions to construct, fix, and maintain devices

8. Difficulties facing wave power developments
Wave periods are typically low frequency (circa 0.1Hz). Difficult to efficiently couple this slow irregular motion via an electrical generator.
Many different device types in the public domain – which to choose?
Economy of scale?
Peak power is generally only available far from land and remote from dense populations
Capital costs of structures very high due to necessity to withstand harsh environments

9. Advantages of Wave Power
Large energy fluxes available
Predictability of wave conditions over a period of days
Low environmental impact – little visual impact
Since only a small fraction of wave power is extracted, impact on coastline is minimal
Chemical pollution is minimal
No obvious problems for marine life
Load factor of energy supply from ocean waves matches demand for electricity – wave power largest in winter when demand is increased
Economies can be achieved by installing wave generators in groups and connecting to shore via a single submarine cable

10. Properties of Deep Water Waves
Surface waves are sets of unbroken sine-waves of irregular wavelength, phase and direction
Motion of any particle of water is circular. Surface form of the wave shows progression, but water particles have no net progression
Water on the surface remains on the surface
The amplitudes of water particle motion decreases exponentially with depth
The amplitude of the wave is independent of λ, c or T
A wave will break into white water when the slope of the surface exceeds about 1 in 7 – dissipating energy potential

11. Wave Motion Wave direction Wave Surface Tangent mrw2 Resultant F F mg
Water surface perpendicular to resultant of gravitation and centrifugal
Forces acting on an element of water of mass m λ a H w
Wave Motion
Wave Characteristics

12. Wave Particle Motion a

13. Water Particle Acceleration
Wave direction x s g
Resultant
acceleration
aw2 g s Ф
aw2
aw2 sinώ
Note: force due to gravity = mg, centrifugal force = maw2

15. (particle velocity)

24. +z crest
-z trough

27. Summary for Deep Water Waves

29. Power
From earlier, we know that the energy per unit wavelength in the direction of the wave is given by E = ½ ρa2gλ
Phase velocity c = λ/T, so E = ½ ρa2g cT
To calculate the power we need to consider the group behaviour of the waves. Specifically the velocity u at which the energy in the group of waves is carried forward is related to the phase velocity by u = c/2
This property comes about due to the dispersive nature of waves
So,
Power P = E/(time) = ½ ρa2g (c/2) = ¼ ρa2g c = ¼ ρa2g λ/T

30. Question
What is the power in a deep water wave of wavelength 100m and amplitude 1.5m?
We know from earlier that c = 13m/s
(group velocity) u = c/2 = 6.4m/s
P = ½ (1025kg/m2)(9.81ms-2)(1.5m)2(6.5m/s)
P = 73 kW/m