Solar and Renewable Energies -...

Physics 162:

Solar and Renewable Energies

Prof. Raghuveer Parthasarathy

[email protected]

Winter 2010

Physics 162: Solar and Renewable Energies R. Parthasarathy Winter 2010

January 28, 2010

Lecture 8: Announcements

• Reading: Wolfson 10.2

• Homework: Problem Set 4, due Thurs. Feb. 4.

• Homework: Microwave Exercise Part II, due Thurs. Feb. 4.

• No, we haven’t graded the quiz yet.

• Midterm Exam: Thursday Feb. 11


Recently:

• We learned about Conservation of Energy: Energy can be converted from one form to another but cannot be created or destroyed


Question• Q Two marbles, one twice as massive as the other, are dropped from a tall building. (Ignore air resistance.) Just before hitting the ground, the heavier marble has...


A. as much kinetic energy as the lighter oneB. twice as much kinetic energy as the lighter oneC. half as much kinetic energy as the lighter oneD. four times as much kinetic energy as the lighter oneE. impossible to determine

Start: All grav. potl. energy. (mgh). 2×mass → 2× PE.End: PE → Kinetic Energy. Conservation of energy, so the ball with the greater PE has the greater KE.Note that we don’t have to figure out speed, etc.

Last lecture: Hydroelectric power• Hydropower (part 1): Converting gravitational potential energy to kinetic energy. How much? We figured out how to calculate the power.

• Power = ΔEgrav / Δt , and Egrav = Mgh, so

• Power = ΔMgh / Δt =

• What is ΔM/Δt ? the mass flow rate, e.g. measured in kg/s.

• Calculations (last time)


M ght

Δ⎛ ⎞⎜ ⎟Δ⎝ ⎠

Hydroelectric power• How much hydropower could we use?

• Depends on what sorts of flows we harness (e.g. only large dams, or also “micro‐hydro power*” for small streams, individual houses...)

• Roughly:We (U.S.) are already using 10‐50% of the max. possible hydroelectric power. (i.e. 10‐50% of the grav. potential energy stored in high altitude water.) (Graph)


*Lots of good work on developing small scale hydropower generators for small streams, small & remote populations.

Estimates of average hydroelectric potential (tall bars) and actual average production (short bars) for five continents.

Hydroelectric power

Can hydroelectric power solve our energy problems?

Yes and no:

It’s certainly a significant source of power, especially in places like Oregon.

But we’re not going to be able to make our hydroelectric power fraction increase by orders of magnitude (e.g. from 3% to 100%).


Hydroelectric power

• More issues:

• “Good” things about hydropower– Renewable

– Clean (no pollution, emissions)

– Efficient (80‐90% of the gravitational potential energy → electrical energy). It’s fundamentally impossible to get efficiencies this high from, e.g., burning fossil fuels (converting chemical energy to thermal energy to electrical energy), for thermodynamic reasons we’ll see soon.


Hydroelectric power

• More issues:

• “Good” things– Renewable

– Clean (no pollution)

– Efficient

– Very low* greenhouse gas emissions. No combustion. No CO2 generated.

– Fairly constant, reliable, easy to control output.


* wait a few slides

Hydroelectric power

• “Bad:” “Local” environmental consequences – Blocking natural river flows (river → series of lakes)– Requires lots of area for the reservoir

– Displacing populations (> 1 million people for the Three Gorges dam in China)

– Disturbs wildlife (e.g. salmon), both in terms of migrations, and changing the oxygen content of the water (higher in fast‐flowing rivers)

– Human health effects: parasites in stagnant reservoir waters; deaths from dam failures, etc.


Hydroelectric power• “Bad:” Some greenhouse gas emissions (methane)

– Submerged vegetation can “anaerobically” decay (w/o oxygen), producing methane, a strong infrared absorber and hence a strong greenhouse gas.

– Insignificant for temperate zones (e.g. Oregon); over 100×smaller greenhouse gas emission factor* than e.g. coal plant of similar power.

– Can be significant (comparable to fossil fuel burning) for tropical, high vegetation areas (e.g. Brazil). Needs to be considered!


* accounts for the difference between methane & CO2 also (Phys 161)

Hydroelectric power• No power source is completely benign.

• Is hydroelectric power “good” or “bad?” This is a question I can’t answer for you – it’s yours.

• But I will stress that the “good” things about hydropower....– Renewable

– Clean (no pollution)

– Efficient

– Very low greenhouse gas emissions

• are really good!


Kinetic energy conversion• 1 Convert gravitational potential energy to kinetic energy (High, slow water → lower, faster water)

• 2 Convert kinetic energy to electrical energy.

• How do we convert kinetic energy to electrical energy?

• The flowing water turns a turbine...


Kinetic energy conversion• The flowing water turns a turbine in a generator...


A turbine used in the Three Gorges Dam, China [Wikipedia / Voith‐Siemens ]

Kinetic energy conversion• So: how does a generator convert kinetic energy into electrical energy?

• An electric current (e.g. that runs through all your appliances) is a flow of electrons, driven by an electric field.

• An electric field is what causes charged particles (like electrons) to move.

The force on the electron = charge × field, by the way

• How can we generate an electric field?


Kinetic Energy → Electrical Energy• Electromagnetic Induction

• Michael Faraday, in the 1800s, discovered that: A changing magnetic field creates an electric field.

• (& vice versa)

• This electric field can drive, for example, a current of electrons in a loop of wire

• [Demo: coil...]

• ...the magnetic field crossing the loop changes with time, generating an electric field and current

• visualizing magnetic fields (demo)


Kinetic Energy → Electrical Energy

• Consider this setup...

• then this...

• If you want a more precise statement: Electric field × L = rate of change of (B × A)


magnetic field, B

loop: length L, area A

the loop is rotating, so the amount of magnetic field crossing it is changing, generating an electric field in the loop


• Electric generator: Magnet + Rotating Loop

• My hand / falling water / etc. provides kinetic energyto make the loop rotate.

• The magnetic field crossing the loop changes as the loop rotates, generating electrical energy.

• Demo: my coil

Wolfson Fig. 3‐05a



• A large electric generator (650 MW):

Wolfson Fig. 3‐05b


Demo: Falling mass + generator → electricity.

Kinetic energy conversion• The flowing water turns a turbine in a generator...

• Which is also what happens in – a windmill (the wind turns a turbine)

– a coal plant (burning coal heats water into steam; hot steam pushes a turbine)

– a nuclear plant (nuclear fission heats water into steam; hot steam pushes a turbine)

– this hand crank (demo)


Sources of Electrical Energy

• All (except solar cells): something turns a generator → electricity.

• This is how we generate electricity from kinetic energy.

Wolfson Fig. 3‐6

U.S., 2004


Hydroelectric power

• So now we know how hydropower works.



• This discovery of induction was a “purely scientific” one that turned out to have profound technological consequences – a recurring theme in science!


• By the way: when Faraday discovered induction, there were certainly no electrical appliances, wall outlets, etc. –i.e. nothing for which it was apparent that this would be at all useful.

• Faraday, when asked by the minister of finance what practical use electricity had: “I don’t know, but one day you’ll be able to tax it.”

Wind Power• The essence of wind power is simply kinetic energy → electrical energy.

• Wind turns windmill blades, running a generator, generating electricity.

• How much? What does this depend on?


istockphoto.com

Wind Power Question• Suppose the average wind speed in area B is twice that in area A. You have funds to build either two identical windmills in area A, or one in area B, and want to maximize how much electrical power you can generate. Where do you build? (Guess; you’re not expected to know this yet.)

A. 2 in A

B. 1 in B

C. These are equivalent


Wind Power• The essence of wind power: kinetic energy (wind) → kinetic energy (blades) → electrical energy (generator).

• Our equation: KE = (½)Mv2, describes the kinetic energy of a “block” of mass Mmoving with velocity v.

• So if each “block” of air were to transfer all its kinetic energy to the windmill, it would transfer (½)Mv2.


Wind Power• Each “block:” kinetic energy (½)Mv2.

• All the blocks hitting the blades of the windmill: N(½)Mv2, where N is the number of blocks.

• So: the power generated should be proportional to the square of the wind speed, i.e. Power ∝ v2, where “∝” means “proportional to.” Right??


A. Yes

B. No – something seems wrong Energy ≠ Power

Wind Power• Power is the rate of energy transfer (or use, or consumption)

• Each block transfers energy (½)Mv2. How many “blocks per second” hit the blades?

• This rate depends on the wind speed: Doubling vwould double the “blocks per second.”

• So Power ∝ v2 × v, i.e. Power ∝ v3.


from kinetic energy

from rate (We’ll put M back in later.)

Wind Power• Wind Power ∝ v3 = v×v×v• We could look up & memorize charts of wind power vs. wind speed, e.g.

• ... but this would be silly; it implies that there are lots of “things” to know


from “Energy for Sustainability,” J. Randolph and G. M. Masters (Island Press, 2008)

Wind Power• Rather: the “scaling relation” Wind Power ∝ v3

describes all this behavior.

• Knowing one pt. on the chart, we know all pts.

• E.g. power = 75 W/m2 at v= 8.9 mph.

• So we expect at v = 17.8 mph (= 2 × 8.9), P=


A. 150 W/m2 (=2×75)

B. 300 W/m2 (=4×75)

C. 450 W/m2 (=6×75)

D. 600 W/m2 (=8×75)

And in fact, the chart says P=599 W/m2 at v=17.9 mph!

(The slight discrepancy is irrelevant; ask if you want.)

Wind Power• Wind Power ∝ v3 describes all this behavior.

• i.e. Wind Power ∝ v× v× v

• So if v doubles, we have 3 factors of 2: 2v× 2v×2v = 23v3=8× as much power


Wind Power• Plot Power vs. v3, which should look like a line...


We see why: wind speed is very important to wind power.

Wind Power Question 2• Suppose the average wind speed in area B is three times that in area A. You have funds to build either nine identical windmills in area A, or one in area B, and want to maximize how much electrical power you can generate. Where do you build?

A. 9 in A

B. 1 in B

C. These are equivalent


3× speed → 33× power = 27× power

People of course map wind speeds. “Class 3” and higher is considered sufficient for large‐scale power generation.

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