Physics and Astronomy Outreach Program at the University of British Columbia

Renewable

& Clean

Energy

Hydro-Electric Dams

Lecture Notes

Hydro-Electric

Dams

• Hydro-electricity can be generated in

numerous ways: dams, rivers, tides

and waves.

• Here we describe the simplest and

oldest method, the dam.

• The analysis can easily be applied to

run-of-the-river power generation.

Physics and Astronomy Outreach Program at the University of British Columbia

Hydro-Electric

Dams

• The energy transformations are:

• Solar radiation evaporates water

from the ocean

• Rain falls on mountains, and runs

into lakes

• The runoff is interrupted by a

reservoir and dam

• Water is extracted at the base of

the dam to turn generators

Physics and Astronomy Outreach Program at the University of British Columbia

Hydro-Electric

Dams

• A reservoir (may be a natural lake):

• h – height below water level the

water is extracted

• Q – flow rate (in m3/s)

• A - surface area

Physics and Astronomy Outreach Program at the University of British Columbia

Hydro-Electric

Dams

• In principle, one can calculate a

maximum value of Q from h and the

size of the hole using Bernoulli’s

principle.

• In real hydro-electric dams Q is

determined by the amount of rainfall

landing on the catchment area A of

the lake.

Physics and Astronomy Outreach Program at the University of British Columbia

Hdro-Electric

Dams

• Let’s look at the W.A.C. Bennett Dam

in north-eastern BC.

• A = 70 000 km2

• Rainfall = 600 mm/year

Physics and Astronomy Outreach Program at the University of British Columbia

/sm 1300

)s 3.15x10

year 1)(

year

m0.6)(

km

m(10)km 70,000(

3

72

26 2

Q

Hydro-Electric

Dams

• Potential energy per unit volume at

the surface is ρgh (in J/m3)

• Potential energy at the turbines

is ρghQ

• ρ = density of the water = 1000 kg/m3

• h = 186 m

• Efficiency = η

Pturbines= ηρghQ

Physics and Astronomy Outreach Program at the University of British Columbia

Hydro-Electric

Dams

• Assuming ηgenerators = 1

• The calculated maximum available

power is 2.4 GW

• The maximum power rating of the

dam and its 10 turbines is 2.73 GW

• The maximum power cannot be

sustained as it is greater than the

calculated value when assuming

100% efficiency and no evaporation

Physics and Astronomy Outreach Program at the University of British Columbia

Hydro-Electric

Dams

• The annual average power generated

is given to be 13 100 GWh per year.

• This is of the same order as, but

comfortably less than, our “ideal”

maximum value of 2.4 GW

Physics and Astronomy Outreach Program at the University of British Columbia

GW 1.5)h 8760

year 1)(

year 1

GWh 13,100(

Hydro-Electric

Dams

• GHG emissions from hydro-electric

dams are small to other means of

electricity generation, but not negligible

• They arise from the construction and

decay of biomass in the flooded valley

(if that is how the project is constructed)

Physics and Astronomy Outreach Program at the University of British Columbia

Hydro-Electric

Dams

• The proposed “Site-C” dam is just

downstream of the Bennett Dam

• This project has a rated power of ~1

GW and flood 10 000 hectares

• A study predicts ~150 000 tonnes of

CO2 will be emitted for the first 20

years, half from construction and half

from biomass decay in the artificial lake.

• 10 000 000 tonnes/GWh of electricity is

produced by coal-fired plants Physics and Astronomy Outreach Program at the University of British Columbia

Physics and Astronomy Outreach Program at the University of British Columbia

1. BC Hydro. The Peace/Williston Fish and Wildlife Compensation

Program (PWFWCP) (online).

http://www.bchydro.com/pwcp/program.html [12 May 2010].

2. Natural Resources Canada. The Atlas of

Canada (online). http://atlas.nrcan.gc.ca/site/english/maps/environme

nt/climate/precipitation/precip [12 May 2010].

3. The Vancouver Sun. Site C Dam No Green Power Project, Critics

Say (online).

http://www.canada.com/vancouversun/news/business/story.html?id=2

97338f7-f072-47d5-babb-1a20e58664ab&k=49198 [9 April 2010].

4. MacKay DJC. Sustainable Energy - Without the Hot Air (online). UIT

Cambridge.http://www.inference.phy.cam.ac.uk/sustainable/book/tex/p

s/1.112.pdf [12 May 2010].

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