# Temperature and Solar Energy

## Katie Malone November 28, 2010

### Submitted as coursework for Physics 240, Stanford University, Fall 2010

The relationship between temperature and solar energy is a multifaceted one. Two primary means of harnessing power from the sun are photovoltaic (PV) cells and thermal energy collectors; high temperature drives down efficiency for the former but is the very basis for the latter. So while temperature is an enemy of efficiency for a PV array, thermal energy collectors provide a complementary means of harnessing solar power in hot climates.

## Photovoltaic Cells

PV cells are generally made of silicon, and when the photons from the sun hit the silicon atoms, they knock loose electrons to create electron-hole pairs. The silicon is fabricated such that it has positively-doped p-type material that is adjacent to negatively-doped n-type material, so there is an electric field that causes the electron-hole pairs to drift apart. Electrodes are then attached to the ends of the cell and the drifting electrons and holes are the current that the cell produces.

One of the quantities that characterizes a solar cell is the open circuit voltage, which is the voltage drop across a cell when there is a current that is the same magnitude as the photovoltaic current but not from the sun. In other words, it is the voltage drop when no external load is applied, and it is the maximum possible voltage that the cell can support. The open circuit voltage obeys the equation

Voc = ( kT / e ) ln(Isc/Io + 1)

where Isc is the max current (the short circuit current), Io is the saturation current, and T is the temperature of the cell. The maximum power that the cell generates is given by

Pmax=IscVocFF

where FF is the fill factor, a parameter that describes the real current and voltage characteristics (it typically has a value around 0.7 and decreases as cell temperature increases). [1]

What all this means is that the maximum power that a PV cell can generate decreases as the cell temperature increases, and since efficiency is power generated divided by power incident, the efficiency of a PV cell will decrease linearly with temperature. The exact amount of this decrease obviously depends on the details, and there is much research into how to minimize this efficiency hit, but sources estimate that a typical efficiency decrease is 0.5% per degree Celsius. [2] It is worth noting that even if efficiency goes down, overall power collected may go up if there is more sunlight on a cell, but the fact remains that a hot sunny day is a double-edged sword for a PV cell.

## Solar Heat Collectors

But that's not the whole story on solar energy collection. Anyone who has touched a metal bench on a hot sunny day knows that the sun is excellent for heating materials; an entire class of solar collectors is based around collecting and concentrating heat energy and using this to produce power. Solar energy can be used to heat a material and supply the thermal energy to run a turbine generator. In most cases, the solar collectors themselves are parabolic, which focuses the light rays along a line, along which runs a pipe carrying the heat transfer fluid so that the fluid absorbs more heat than in a flat panel collector.

The exact performance of these types of collectors obviously varies with the details of a particular system. Parabolic trough collectors, and other similar types of collectors, have thermal fluid lines that are coated with materials that, in a typical system, might absorb 97% of incident radiation but emits only 18% back out in blackbody radiation (at 80 °C). [1] These systems also typically can be controlled to track the sun as it travels across the sky; the exact details of orientation and tracking can be adjusted, for example, to supply more power in summer or in winter.

This technology is the method behind the nine arrays that were built in the Mojave desert after the California energy crisis [3], so the technology is developed enough to deploy on a commercial scale. Perhaps more intriguing is the accompanying technology that uses molten salt as the thermal fluid; the salt can be heated during the day and then stored until the night. The ability to store the power for later use is very important because it means that solar energy can be used when the sun isn't shining, making it commercially much more viable; you can use solar energy stored during the day, for example, to watch TV at night. [4,5]

Entire books can (and have) been written to explore these issues in more depth and breadth. The sun is a phenomenal source of energy (a back-of-the-envelope calculation shows that it supplies on order 1000 W/m2 around the equator at noon!) and it's as renewable of an energy supply as we can get. Other means of harnessing this energy, like solar water heaters and solar space heaters, hint at the amount of progress already made on this front. At the same time, though, it's important to remember the limitations on current technology. Solar photovoltaic and thermal energy collection methods demonstrate that something as elementary as the heat from the sun can have complicated and important effects on the viability of solar as a major alternative source of energy.

© Caitlin Malone. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] S. A. Kalogirou, Solar Energy Engineering: Processes and Systems (Elsevier, 2009).

[2] R. A. Messenger and J. Ventre, Photovoltaic Systems Engineering (CRC Press, 2004).

[3] German Solar Energy Society, Planning and Installing Solar Thermal Systems: A Guide for Installers, Architects and Engineers (James and James, 2005).

[4] C. Barile, "Solar Thermal Energy Storage Systems," Physics 240, Stanford University, 28 Nov 10.

[4] R. W. Bradshaw and N. P. Siegel, "Molten Nitrate Salt Development for Thermal Energy Storage in Parabolic Trough Solar Power Systems," in Proc. of the 2nd Int. Conf. on Energy Sustainability - Vol II (Am. Soc. Mech. Eng., 2009), p. 631.