EE535: Renewable Energy: Systems, Technology &

EconomicsTidal (1)

Nature of the Resource

• Tidal energy is the result of the gravitational pull of the moon, and to a lesser extent the sun

• Tidal energy schemes rely on the twice daily tides which produce the ebb and flow of large volumes of water in estuaries and at sea

• Other factors such as ocean depths, landmass shapes etc, can accentuate tidal flow

• Energy can be extracted from the tidal flow in 2 principal ways:

1. Tidal Barges2. Tidal Streams

Lunar Induced Tide

• Centrifugal Effect• Gravitational Effect• As the earth rotates

on its axis, 2 high tides are drawn around the globe as it rotates - 2 high tides every day (24.8 hour period)

moon

moon

Influence of Solar Effects• The solar tide moves in and out

of phase with the lunar tide• Lunar and solar tides are in

phase when sun, earth and moon are aligned– Produces tides of maximum

range– These are spring tides– Occur twice per month at full

and new moons• When sun/earth and

moon/earth directions are perpendicular– Produces tides of minimum

range– These are neap tides

s em s me

or

s e

m

s e

m

Tidal Currents

(a) Tidal current over a 21-day period at a location where the maximum current at spring tide is 2.9 knots (1.5 m/s) and the maximum current at neap tide is 1.8 knots (0.9 m/s).

(b) The power per unit sea-floor area over a nine-day period extending from spring tides to neap tides. The power peaks four times per day, and has a maximum of about 27 W/m2.

The average power of the tide farm is 6.4 W/m2.

http://www.inference.phy.cam.ac.uk/withouthotair/cG/page_315.shtml

Power density of tidal pools / barges / Tidal Range Power

• Tide pool filled rapidly at high tide and emptied rapidly at low tide

• So, change in potential energy every 6 hours is mgh (where h is half the range)

• The mass per unit area covered by the tide pool = ρ 2h

• So, power per unit area generated by a tide pool– P = 2 ρghgh / 6 hours

• Let h = 2meters, density of water = 1000kg/m3, g = 9.81m/s/s

• Power per unit area ≈ 3.6 W/ m2

• Assume 90% efficiency: 3W/m2

sea

Tidepool

h

Ran

ge (

R)

Low water

High water

turbine

Power = E/T = ρ A R2g/2T

Tidal Streams / Tidal Flow Power

• Near coastlines and between islands, tides may produce strong water currents

• Tidal flow power conversion is similar to wind power conversion, – Advantage of predictable velocity and greater fluid density

(x1000)– Disadvantage of low fluid velocity and an aquatic environment– Power density for in water = ½ ρ v3

– Only a fraction of the power available can realistically be converted (typically about 40%)

• Tidal current velocities vary with time approximately as :• V = Vo sin (2πt / τ), where τ is the period of the natural tide

(12h 25min for semidiurnal tide), and Vo is the maximum velocity of the current

• If η is the efficiency of the conversion device, the electric power per unit cross section = 0.25 η ρ Vo

3

Tidal Current Power Device

turbine

Electric generator

TidalFlow

seabed

Drawbacks of Tidal Energy

• Mismatch of principal lunar driven periods of 12h 25mins and 24hrs50 mins with the human (solar) period of 24hrs – optimum generation not in phase with demand

• Tidal range changes over a 2 week period – producing changing power production

• Large volume of water at low head necessitates many specially constructed turbines in parallel

• Very high capital costs of installations• Potential ecological harm to estuaries and

marine regions

Resonance Enhancement• Resonant enhancement on the

tides in estuaries and bays occurs in the same manner as the resonance of sound waves in a closed pipe

• Resonance with the open sea tide occurs when L = jλ/4, j is an odd integer

• Natural frequency of the resonance :

• fr = 1/Tr = c/λ

• Wave of velocity c = √(gh)• So, Tr = λ/c = 4L /jc = 4L/j√(gh)• L/√h = (j/4) √(g)Tf

λ/4

Open Sea Land

River Severn Example

• The River Severn estuary between Wales and England has a length of about 200km and a depth of 30m.

• So L/√h = 200x103m / √(30m) = 36000m1/2

• The semidiurnal tidal period is about 12hrs 25mins. • So, resonance for j = 1 occurs when :• L/√h = (45000s/4) √(9.81ms-2) = 36000m1/2

• Hence there is a close matching of the estuary’s resonance frequency with the normal tide frequency.

• Large amplitude tidal motions of 10 – 14m range occur

Open Hydro

http://www.openhydro.com/technology.html