ChEn 433 Solar

Class 21-22

Solar energy

What are the major themes and issues with solar power?

  • Intermittent
  • Cloud cover
  • Energy storage
  • Materials availability
  • Land use requirements

Solar Energy

  • Two major types
    • solar thermal
    • photovoltaic
  • Wind and hydro power may be considered indirect solar energy.
  • Outline
    • Solar radiation physics
    • Solar thermal
    • Photovoltaics
    • Implementation and contributions to world energy
    • Economics

World solar energy

Solar is growing fast, and is 4.5% of world electricity

World solar energy

Economics

“The levelized cost of energy (LCOE) is a measure of a power source that allows comparison of different methods of electricity generation on a consistent basis. The LCOE can also be regarded as the minimum constant price at which electricity must be sold in order to break even over the lifetime of the project.”

LCOE

Economics

1 CMO

2 kW solar plant

3.5 CMO

If all the highways, streets, buildings, parking lots and other solid structures in the 48 contiguous United States were pieced together like a giant jigsaw puzzle, they would almost cover the state of Ohio (Reference)

Rate of growth (articles)

Human cost (article)

Greenhouse gases from metals (article)

Large solar installations take one to seven years to “break even” with coal power on the greenhouse scorecard

Break even (article)

The Sun

Nuclear fusion \[4^1_1p \rightarrow _2^4\alpha + 2e^+ + 2\nu_e +\Delta E\]
\[\Delta E = 3.955\times 10^{-12}\, J\, = 24.687 MeV\]

  • Energy released = \(3.8\times 10^{26}\) W
  • E per Area = \(63.3\) MW/m\(^2\)

E at Earth = \(1361\) W/m\(^2\) solar constant

Radiative Spectrum

Radiative Spectrum

  • \(E = \sigma T^4\rightarrow T=5777\) K
  • Distribution
    • 7% ultraviolet (UV)
    • 47% visible
    • 46% infrared (IR)
  • Atmospheric losses
    • reflection
    • absorption: O\(_3\), H\(_2\)O, O\(_2\), CO\(_2\)
    • Rayleigh scattering: molecules \(d\ll\lambda\)
    • Mie scattering: particles (pollution) \(d\gg\lambda\)

Air mass

  • \(\gamma_s\) is angle of sun from horizontal (elevation)
  • \(\alpha_s\) is the solar azmuth

Air mass

Air mass

Effect of solar angle

  • plot is for Athens
  • June:Dec = 40:1 in Bergen, Norway
  • June:Dec = 3.3:1 in Lisbon, Portugal

Tracking solar panels

Earth energy balance

Albedo

Rank order the albedo of the following surfaces:

Surface
Forest
Fresh Snow
Water (\(\gamma_s > 45^o\))
Bare ground
Clean cement

Albedo is the proportion of incident light or radiation that is reflected by a surface, typically a planet or moon.

Albedo

Rank order the albedo of the following surfaces:

Surface Albedo
Water (\(\gamma_s > 45^o\)) 0.05
Forest 0.1
Bare ground 0.2
Clean cement 0.55
Fresh Snow 0.85

Albedo is the proportion of incident light or radiation that is reflected by a surface, typically a planet or moon.

Albedo

Solar irradiance

Solar irradiance

Glossary of terms

  • Convert units: 7.4 kWh/m\(^2\) to W/m\(^2\), compare to the solar constant.
  • What is the reason for the difference?
  • How is this information useful?

Solar thermal

  • Key types
    • non-concentrated
      • e.g., hot water heating
    • concentrated
      • high temperature, power generation
  • Focus on concentrated here
  • Concentrate solar energy using reflectors
  • Higher temperatures for heat engine efficiency
  • Energy storage benefits over PV
    • Store the existing high T fluid, versus batteries
  • Higher costs than PV
    • See also the LCOE chart.


Solar thermal

  • Linear recievers:
    • Parabolic trough
      • oil, molten salt, pressurized steam
      • most common
    • Enclosed trough
      • sheltered from wind, dust
    • Fresnel reflector: lower costs
    • efficiencies 8-18%
    • only need one axis tracking
  • Point recievers:
    • Power tower
      • higher temperatures
      • allows uneven ground
      • 1st in Spain, 2007, 11 MW
      • Largest = Mohammad bin Rashid, UAE, 600 MW.
      • 3rd largest is Ivanpah in California, 392 MW.
      • About 60 plants that are larger than 50 MW.
      • consolidated operations
    • Dish
    • efficiencies 20-40%
    • dual axis control needed


Concentration factor

Question: how much can the sun be concentrated? What are the limits?

Question: what is the maximum temperature a solar reciever can have?

\[C = \frac{A_C}{A_R}\]

Concentration factor

Power (P) emitted from the sun’s surface of radius \(r_S\): \[P_s = \sigma T_s^4 \cdot 4\pi r_s^2\] Power of the sun at solar collector distace \(R_{SE}\) from the sun \[P_c = \sigma T_s^4 \cdot 4\pi r_s^2 \cdot\frac{A_c}{4\pi R_{SE}^2}\] \(\frac{A_c}{4\pi R_{SE}^2}\) is the fraction of power reaching the collector. The best reciever will have power: \[P_r = \sigma T_s^4 A_r\] And \(P_c = P_r\) by conservation of energy. This gives

\[C_\text{max} = \frac{A_c}{A_r} = \frac{R_{SE}^2}{r_s^2} = 46152 \]

Concentration factor

Absorber tubes


\(\rho\): reflectivity \(\gamma\): intercept factor
\(\tau\): transmissivity \(\alpha\): absorptivity

\[\dot{Q}_S = A_\text{A}\epsilon\sigma(T_\text{A}^4 - T_U^4)\] \[\dot{Q}_K = hA_\text{A}(T_\text{glass} - T_U)\]

Cerro Dominador Plant

  • Chile
  • 110 MW
  • June 2021
  • 1.9 GWh energy storage
  • Aperature area = 1,484,000 m\(^2\)
  • 250 m tower heats salts 560 \(^o\)C
  • 100 MW PV component

Photovoltaic effect

  • Atomic energy levels are quantized
  • Photon (light) energy \(E=hc/\lambda\)
    • 13.59 eV (91 nm) light (UV) ionizes hydrogen
      • external photovoltaic effect
    • Lower energies \(\rightarrow\) internal PV effect
  • Molecules, atoms, solids \(\rightarrow\) many energies \(\rightarrow\) bands
  • electrons occupy the lower bands, and are excited into upper bands

   

Conductors, semi-conductors, insulators

“The valence band is simply the outermost electron orbital of an atom … that electrons actually occupy”

“The conduction band is the band of electron orbitals that electrons can jump into from the valence band when excited. When the electrons are in these orbitals, they have enough energy to move freely in the material.”

Visible light \(\lesssim\) 3 eV

Semiconductors

  • PV cells use semi-conductors
  • Group IV elements: Si, Ge, Sn; 4 valence electrons \(\rightarrow\) in the crystal shared electrons in covalent bonds fill the valence band.
    • Light can raise electrons to the conduction band: free electron + a hole
  • Groups III + V, II+VI

Semiconductors

  • PV cells use semi-conductors
  • Group IV elements: Si, Ge, Sn; 4 valence electrons \(\rightarrow\) in the crystal shared electrons in covalent bonds fill the valence band.
    • Light can raise electrons to the conduction band: free electron + a hole
  • Groups III + V, II+VI

p,n Doping

  • n electrons, p holes; \(n=p\)
  • \(n\cdot p\) is the intrinsic carrier density.
  • n-Doping
    • replace some Si with Group V elements like phosphorus (P) or antimony (Sb)
    • five valence electrons \(\rightarrow\) one left over, weakly bound
    • more free electrons than holes; electrons are the majority carriers
  • p-Doping
    • replace some Si with Group III elements like Boron (B) or aluminum (Al)
    • three valence electrons \(\rightarrow\) one missing
    • holes are the majority carriers
  • p-n junction:
    • electrons move from the n-region to the p-region, and vice-versa for the holes
    • an electric field is formed that opposes continued motion
  • voltage ~0.5 V open circuit silicon single junction

p-n Junction


Video

Losses

  • Shading
  • Transmission
  • Reflection
  • Absorption
  • Heat losses
    • photons energy > band gap lost to heat

Efficiency

\[\eta = \frac{\text{electrical power}}{\text{incident solar power}}\]

  • Shockley-Queisser limit:
    • \(\eta\) = 33%
    • single p-n junction
  • Multiple junctions
    • differing band gaps optimize to different parts of the spectrum

Efficiency

Video

Solar panel

  • Series arrangment
  • 0.5 V \(\cdot\) 36 = 18 V
  • ~17% efficient
  • 25-30 years
  • textured surfaces

Example panel

PV module prices

Swanson’s law