Distributed Energy Resources - Lectures 9-10: Thermal Storage and Water Heaters & Solar Energy

Other notes in this series from Kevin Kircher’s Distributed Energy Resources class are here.

Thermal Storage and Water Heaters

An overview of three kinds of thermal storage.

• Lumped sensible thermal storage: we heat something up to a uniform temperature, eg: a storage heater full of bricks.
• Stratified sensible thermal storage: we heat different parts up the storage unit to different temperatures, eg: a hot water tank.
• Latent thermal storage: we melt/freeze (or sometimes vaporise/condense) a material as a way of storing/releasing energy, eg: freezing/thawing ice to “store” cooling.

Here is a nice picture of heat-pump/resistance hybrid water heater:

Solar Energy

A little spherical geometry gives us a model to estimate solar irradiance at different locations at different times of year with different solar panel orientation.

This gets a little more interesting when you have time-varying electricity costs and net-metering since the value of solar energy also now varies with time.

Here is a nice picture of a solar photovoltaic cell:

Notes

• Thermal Storage and Water Heaters
  • Three types of thermal storage
    • Lumped sensible thermal storage
      • Lumped means all one temp through the entire tank
      • Sensible refers to temp change vs phase change (which is called “latent”)
      • 
    • Stratified sensible thermal storage
      • Two zones with different temperatures rather than the same temp through the tank.
      • 
    • Latent thermal storage
      • freeze/melt a material instead of heating/cooling it
  • Typical domestic hot water cylinder holds up to ~9-13kWh
• Solar Energy
  • Empirical equation of time converts GMT to $t_{gm}$, local solar time
    • $\tau \approx (0.165h)\sin (2\gamma )-(0.126h)(\cos (\gamma )-(0.025h)\sin (\gamma ))$ (only an approximation)
    • $\gamma =\frac{360(d-81)}{365}$ where day # $d$ is 1 on Jan 1
    • solar time, $t_{gm}+\tau$ , equals 12 h when sun is highest
  • On a clear day, ~75% of solar constant, $S_0$ (the irradiance at top of earth’s atmosphere) reaches the surface.
    • ∼70% transmitted through atmosphere (beam)
    • ∼5% scattered to earth by air, dust, water vapour (diffuse)
    • ∼20% absorbed by atmosphere
    • ∼5% scattered back to space
  • As cloud cover increases
    • less of $S_0$ reaches surface (as little as ∼10%)
    • beam % of total surface sunlight falls, diffuse % rises
  • Solar cell efficiency scales ~linearly with cell temperature $T_c$ $\eta \approx \tilde{\eta }(1-\frac{T_c-\tilde{T}}{T_0-\tilde{T}})$
    • where
      • $\tilde{n}$ is the effiency at rated cell temp $\tilde{T}\approx 25C$
      • $T_0\approx 270C$ is the cell temp at which generation stops
      • $T_c\approx T_a+(35C{m}^2/kW)S_{tot}$ where $S_{tot}$ is incident irradiance