EE535: Renewable Energy:
Systems, Technology &
Economics
Session 7: Wave Energy (1)
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))
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
http://www.inference.phy.cam.ac.uk/withouthotair/c12/page_73.shtml
Waves
• Storm Waves
– 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
Wave Formation
•
•
Ocean waves are generated by wind passing
over stretches of water
3 main processes give rise to wave formation
and growth:
1. Air flowing over the seas exerts a tangential stress on the
water surface
2. 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
3. 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
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)
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
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
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
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
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
Wave Particle Motion
a
Water Particle Acceleration
Wave direction x
s
g
Resultant
acceleration
aw2
s
g
Ф
aw2
aw2 sinώ
Note: force due to gravity = mg, centrifugal force = maw2
(particle velocity)
+z crest
-z trough
Summary for Deep Water Waves
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
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