Energy Storage I

Energy storage must consider both the amount of energy that can be stored (energy density of the material) and the efficiency at which it can be recovered. Some materials have high energy storage capacity but low rate of recovery.

Energy Density of Some Materials (KHW/kg)

 Gasoline  --------------------------> 14
 Lead Acid Batteries ----------------> 0.04
 Hydrostorage -----------------------> 0.3 (per cubic meter)
 Flywheel, Steel --------------------> 0.05
 Flywheel, Carbon Fiber -------------> 0.2
 Flywheel, Fused Silica -------------> 0.9
 Hydrogen ---------------------------> 38
 Compress Air -----------------------> 2 (per cubic meter)

Energy density storage drives the choices that can be made:

At the turn of the century electric vehicles were commonplace (using basically lead-acid batteries). Since gasoline has much higher energy density it quickly dominated the way vehicles were propelled.

In fact, gasoline has one of the highest energy density storage capacities known. This makes it very difficult to duplicate the convenience that gasoline has traditionally provided (e.g. 350 kg of batteries is equivalent to 1 kg of gasoline !).

Direct conversion into electricity Photovoltaics; conversion of solar photons into electrons that flow down a semi-conductor.

But this all started with THE PHOTOELECTRIC EFFECT:

Wave-Particle Duality of Light.

click here to see a wave experiment

The dark and light regions are called interference fringes, the constructive and destructive interference of light waves.

So Light acts like a wave, but ...

The Photoelectric Effect

Testing the wave-particle duality of light.

Light knocks electrons out of metal surfaces as if it were made of particles --- photons. For light of frequency f, each photon has energy hf.

In 1902, P.Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light.

He used a carbon arc light, and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination.

To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current.

Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it V_stop. This means that there is a threshold kinetic energy that the electrons must have in order to reach the detector.

Contrary to intuition, Lenard found that V_stop did not depend at all on the intensity of the light! Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons.

But Lenard did something else. With his very powerful arc lamp, there was sufficient intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color --- the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. This was, however, a fairly qualitative conclusion as his experimental apparatus lacked good the means to make a reliable measurement. Still this was a puzzling result at the time.

Let's examine some of the implications of Lenard's experiment in terms of whether light is a wave or a particle:

If its a wave, then:

Wave Theory: Light is an oscillating electric field. Only the electric field strength should affect electrons.

Prediction: Sufficiently intense light should eject electrons no matter what the frequency.

But this is not what was observed.

No Time delay:

Wave Theory: The power in a light beam is spread out. The area near an electron intercepts very little.

Prediction: It should take some time for an electron to absorb enough energy to be ejected.

Again, this is not observed.

Particle model works:

Particle theory: A photon with energy hf strikes an electron and ejects it from the metal.
hf = K.E. + w

w = work to remove electron from metal
K.E. = kinetic energy of ejected electron.

Einstein won the Nobel Prize for this Explanation!

Particle model explains threshold effect:

In the wave theory, greater light intensity simply means more photons.

Each photon ejects electrons in the same way, so more intensity means more electrons.

Threshold frequency and electron K.E. should not be affected by intensity.

For each metal, there is a threshold frequency. Light frequencies below the threshold eject no electrons, no matter how intense the light.

Light frequencies above the threshold eject electrons, no matter how low the intensity.

When the light source is turned on, the electrons begin to be ejected immediately.

No matter how weak the light source, if the frequency is above the threshold, there is no time delay.

Voltmeter measures reverse potential V₀ to stop the current.
eV₀ = K.E._max

So Light is also a particle. Energy of light is in the form of a particle. Transport of the energy through space is in the form of a wave.

Charge Generation Photoelectric Effect

This is the principle behind many digital cameras, otherwise known as CCD cameras . These kinds of cameras are used in astronomy to take digital pictures . Incoming photons are converted into units of electric charge and stored at individual pixel locations. Different amounts of charge represent different intensity levels. This encoded information is a digital image.

To make use of the photoelectric effect, we need material that is a good conductor of electricity and which can be manufactured in bulk at reasonable cost. This conditions strongly constrain the available choices. For most practical aspects, Silicon is the material of choice.

Silicon:

• is abundant on the earth and readily found in the crust. It is a direct product of fusion inside stars. It can be easily recovered from the crust and mass-produced. Computers are cheap because silicon works well for circuit boards and is an easily recoverable material from the earth's crust. The result is a world-wide economy centered around semi-conductor technology.

• Has four outer (valence) electrons to bond silicon atoms together in a crystal

• Under normal circumstances, there are no free electrons available in silicon to conduct electricity. All the electrons are used to bind the atoms in place to form the crystal.

• The conduction band is empty and therefore no current can be carried by the material.

Schematic structure of energy bands in Silicon:

Hence, if a silicon atom receives at least 1.11 Electron Volts from some source, a valence electron will move to the conduction band. Once an electron is in the conduction band, the material can carry a current and the material is now a conductor.

So much energy is 1.11 Electron Volts?

• 1.11 eV corresponds to the energy that a photon of wavelength 1.12 microns has.
• 77% of the energy from the sun is carried in photons with wavelength less than this and therefore can move a valence electron in silicon into the conducting band

This does not mean that the efficiency of silicon in converting solar photons to electrons is 77%!

Energy Losses:

• Photons with energy greater than 1.11 eV heat the crystal
• 43% of average absorbed photon energy goes into heating
• Some photons are reflected by the exposed surface of the crystal
• There is some internal resistance in the crystal that inhibits the flow of electrons. This internal resistance increases as the crystal is heated.

The efficiency is strongly temperature dependent. As the temperature is raised, the internal resistance of the material increases and the electrical conductivity decreases.

• At 0 degrees C silicon has efficiency of 24%
• At room temperature the efficiency is 12%
• Highest efficiency is achieved (at 0 degrees) in CdTe (Mercate-Telluride) but this is only 28%

The fundamental physical limitation in production photovoltaic cells is then this decrease in efficiency as the temperature of the cell increases. Because of this, for a material like silicon, the operating efficiency of a photovolatic array will probably never be higher than 20% and will most likely be between 5 and 15%.

This doesn't mean that production is not possible. It does mean that relatively large collection areas must be obtained which means high capital costs. If those costs can not be subsidized, then PV arrays can never be competitive in the commercial energy market place.

To have a production photovoltaic cell, one must mix impurities into silicon (like boron). This will create an internal electric field which will allow the liberated electrons to move down the material.

Over the last 40 years, the effort has gone into increasing the efficiency of PV cells and bringing down the manufacturing costs.

• $100 per kilogram of pure silicon then the crystals have to be grown in a carefully controlled environment from the molten silicon. impurities lower overall conductance and reduce the efficiency

• Present Costs of solar cells is about $5,000 per Kilowatt compared to $1,000 per Kilowatt from a coal-fired plant.
• Typically solar PV cell grids have enough components to produce 20-25 Volts per grid
• In California, there are some Production line PV facilities 350 Megawatts are generated in PV arrays which are about 11% efficient.

Recent Advances:

Advances in Amorphous Silicon technology has led to continuous thin-film deposition process.

• Uses very little silicon
• Inexpensive manufacturing process
• used in watches and calculators today

Can increase efficiency by using solar cells in conjunction with focussed systems (parabolic collectors).

• Increase gain by a factor of 100 per unit area
• For a given energy requirement, can then reduce collecting area by a factor of 100.

BUT

• Heat load on cells causes temperature to rise and efficiency to lower
• Need a cooling system (water - could then be used as alternative space heating source).
• Price of focusing system is quite high

Current Economics:

Consumer cost for energy from newly constructed coal-fired plant in the US ranges from 8-20 cents per KWH

PV power generation would cost the consumer 25-50 cents per KWH.

Costs might be equivalent when pollution from coal is also considered but still, the structure is not here for the consumer to pay the true cost of energy