Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia

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 ColumbiaPhysics 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 ColumbiaPhysics 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 ColumbiaPhysics 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 ColumbiaPhysics 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 ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia

/sm 1300

)s 3.15x10

year 1)(yearm0.6)(

kmm(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 ColumbiaPhysics 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 ColumbiaPhysics 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 ColumbiaPhysics 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 ColumbiaPhysics 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 ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia

Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics 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/environment/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=297338f7-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/ps/1.112.pdf [12 May 2010].

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