The Physics of Solar Concentration

Warren Morningstar
December 18, 2017

Submitted as coursework for PH240, Stanford University, Fall 2016


Fig. 1: The sun sets over the Crescent Dunes concentrated solar power plant. (Source: Wikimedia Commons)

Humanity consumes immense amounts of energy, most of which is gained through the combustion of fossil fuels. The environmental ramifications of using fossil fuels, combined with their expected remaining abundance on earth places limits on how much longer we as a species can rely on them as an energy source. If we are to continue to power our civilization, then alternative means of energy generation must become the new norm.

The Sun, a massive self-sustaining thermonuclear reactor, delivers substantially more energy to Earth than the entirety of humanity is able to consume, in the form of light. If we as a species are able to tap into this enormous source of energy, we could completely remove our dependence on fossil fuels. This is the motivation for technologies such as photovoltaic cells, which allow photons to be captured and used as a power source, with fairly high efficiency. [1-3] However increasing photovoltaic efficiency becomes harder as the efficiency gets higher. Here we present an incredibly simple alternative means of solar energy capture, concentrated solar power (CSP). A theoretical overview of solar concentration is provided, including some of the limitations at each step of the conversion process.

How it Works

Take a brief step outside. Can you see the world around you? Are you immediately freezing into a popsicle? If you answered no to either of these, it is likely that the sun is (in one way or another) responsible. Light from the sun carries a significant amount of energy. When sunlight reaches earth, some of this energy is deposited on the surface of our planet, keeping it from cooling to temperatures that would be unable to support human life, and providing the light that helps people to see the world around them. For a long time, humans have been trying to figure out ways of manipulating this light for our own purposes. In the last century, we have begun to devise means of harnessing this energy on large enough scales to potentially cause a noticeable impact in our full energy budget. One such device is a solar concentrator.

A solar concentrator (Fig. 1) at its core consists of a system of mirrors and an energy receiver. The mirrors are all oriented to reflect incoming sunlight toward the receiver. In doing so, the mirrors increase the amount of light, and thus the amount of energy, being sent to the receiver. As more energy is deposited to the receiver, it begins to heat up. This heat is used to power a heat engine, which extracts energy in the form of mechanical work, which can then be converted into electrical energy. This electrical energy can then be used or stored, completing the conversion from light to useful energy.

How does a solar concentrator work exactly? First, lets assume that the light from the sun carries with it a certain flux of energy, where flux just means that the light delivers some given amount of energy per unit time per unit area (the flux from the sun is about a kilowatt per square meter). For a given area, the sun delivers a certain amount of energy per unit time, and if we are able to double that area, then the amount of energy per unit time is itself doubled. Thus the goal of any solar power generator is to use as large of an area as possible, so that more energy can be produced.

For a solar concentrator, the collecting area is covered by mirrors which reflect sunlight from the full array into a much smaller receiver. Upon doing so, all the power incident on the full collecting area becomes sent to the receiver. So for an array of mirrors 100 square meters in size, roughly 100 kilowatts is sent to the receiver. The system of mirrors has concentrated the light, causing the flux of energy at the receiver to be significantly larger than the flux naturally incident upon the earth. If the receiver were 10 square meters, for example, then the flux of energy would be 10 kilowatts per square meter, a factor of 10 larger than it would be if unfocused. The ratio between the concentrated flux on the receiver and the ambient flux from the sun is called the concentration ratio (C). It is the same as the ratio of the area of the receiver to the total area of the reflectors (assuming the entirety of the receiver is illuminated). For the above concentrator, the concentration ratio is C=10.

Why is the concentration ratio an important metric of a solar concentrator? Simply put, the concentration ratio is an important ingredient in optimizing the efficiency of a concentrated solar power plant. By increasing the concentration, more light is focused onto the same collecting area, which causes more energy to be deposited in the same amount of time. For a solar concentrator to be useful, it needs to be able to generate large amounts of power. By this metric, the concentration should be increased as much as possible (while keeping to fundamental physics, engineering, and economic constraints, we'll get to this later).

An additional metric that should be considered in solar concentration is the temperature of the receiver. Because large amounts of energy are being deposited on the receiver fairly rapidly, the receiver heats up substantially. Water or a different fluid (like molten salt) is typically used to remove heat from the receiver, maintaining it at a stable temperature, and carrying the thermal energy to be used to power a heat engine. The amount of coolant being used to remove energy controls the temperature at which the receiver operates. This operating temperature also has an impact on the efficiency of a solar concentrator. This is due to energy losses because of thermal emission from the receiver. The physics principles here are straightforward. The receiver is approximately a blackbody (it is designed to be so that it absorbs light efficiently). Any blackbody loses energy by emitting blackbody radiation. The amount of energy lost due to blackbody radiation increases rapidly with temperature. Therefore, in order to minimize losses (and thus increase efficiency) it is advantageous to limit the operating temperature.

This second metric would seemingly suggest that the ideal operating temperature would be as low as possible, because then energy losses in the receiver are minimized. However, there is an additional source of wasted energy that must be examined: Energy lost as heat in the conversion to mechanical work. Carnot's theorem states that the maximum efficiency of an engine (ηcarnot) is determined by the ratio of the high temperature of your receiver (TH) and the cold temperature of your heat sink (TC).

ηcarnot = 1 - TC/TH (1)

The cold temperature of the heat sink is the ambient temperature of earth (which is roughly 300°K). Any temperature less than this will produce no energy at all, and the efficiency would thus be 0. In order to maximize efficiency in the heat engine, the temperature must be much higher (if run at infinite temperature for example, the efficiency will be 1). Combining thermal losses from the detector with the efficiency of the heat engine, it follows that we must run at some temperature sweet spot, between low and high. If we keep the temperature too high, then too much energy will be lost due to blackbody emission. If we run it too cold, then the efficiency of our heat engine goes to 0, negating any gain in efficiency due to minimizing blackbody radiation. Due to materials constraints, we are limited to a receiver temperature of roughly 900°K, which falls right into this sweet spot for concentrations of roughly 100. [5]

Practical Considerations

The above analysis focused exclusively on the physics involved and neglects a few practical considerations that can place additional limitations on solar concentration efficiency. These considerations come from the fact that thermodynamics is not the only constraint placed on a power plant: There are also optical, economic, and engineering constraints, as well as geographic constraints.

First, lets consider additional Optics constraints. In order to design a solar concentration plant with a large efficiency, you need a plant with a large concentration, in order to minimize losses due to blackbody emission from the receiver. However, there is a theoretical limitation to how much you can concentrate the sun, which exists due to its apparent size on the sky. Weinstein et al. calculate this limit to be C=210 for a 1-axis concentrator (a parabolic trough), and C = 4.3 × 104 for a 2-axis concentrator (an array of mirrors like that at Crescent Dunes). [4] While this limit may be constraining for 1-axis concentrators, it doesn't seem likely to be a significant constraint for 2-axis concentrators.

Second, lets consider economic and materials constraints. All of the above assumed that all of the incident sunlight is reflected by the mirrors, and that it was all absorbed by the receivers. However, realistic mirrors do not reflect all of their light (some is absorbed, some passes through). So in reality, the light incident on the array is not all reflected to the receivers. Optimizing this problem becomes an economic problem, because while certain metals have very high reflectances, they can be more expensive than materials with lower reflectance. [4] Cheap, reflective materials is an ongoing topic of research. [4] Similarly, the receiver needs to absorb as efficiently as possible at optical wavelengths, while being cheap and emitting inefficiently in the infrared (which can help to further reduce thermal losses). [4]

Additionally, producing a large concentration, and running the plant at a high temperature can become infeasible due to engineering constraints. As mentioned earlier, above a certain temperature the metals that you use become too hot, and can no longer be used to contain the steam necessary to power the plant. This temperature is in the neighborhood of 900°K. [5] So all solar concentrators must run below this temperature in order to avoid the onset of "creep" in their systems, which would lead to mechanical malfunctions that would prevent the plant from operating. This constraint becomes the strongest limit on 2-axis concentrators, because they are easily able to achieve concentrations large enough to increase the temperature to these levels.

Finally, CSP plants are limited by geographic constraints. In particular they need to be built in places that receive a lot of sunlight, and ideally a lot of sunlight from a high elevation. Elevation in this sense just refers to the height of the sun in the sky. If the sun is at low elevation (i.e. near the horizon), then the size of the array perpendicular to the sun is reduced. This limits the total amount of power able to be gained from a station. This is why CSP stations such as Ivanpah are typically found in sunny locations relatively close to the tropics (Southern California in the case of Ivanpah). Photovoltaic plants also suffer from this limitation. Additionally, the air quality can affect the utility of CSP stations, because any airborne refraction can defocus the light, lowering the concentration. Therefore, CSP stations aren't typically found in hazy places like the Persian gulf. Conventional photovoltaics do not suffer from this limitation, other than any attenuation of the light caused by the haze.


In conclusion, solar concentration is a well-established and promising idea for power production that utilizes simple technology to harness substantial amounts of energy. The efficiencies of solar concentrators are limited mostly by materials constraints, but also by economic and fundamental physics constraints. However, even subject to these constraints, concentrated solar power can be employed on large scales to generate significant amounts of power. Will solar concentration continue to increase in usage around the world, eventually replacing fossil fuels? Only time will tell.

© Warren Morningstar. 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.


[1] W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p-n Junction Solar Cells," J. Appl. Phys. 32, 510 (1961).

[2] A. De Vos, "Detailed Balance Limit of the Efficiency of Tandem Solar Sells," J. Phys. D-Appl. Phys. 13, 839 (1980).

[3] F. Dimroth et al. "Four-Junction Wafer-Bonded Concentrator Solar Cells," IEEE J. Photovolt. 6, 343 (2016)

[4] L. A. Weinstein et al., "Concentrating Solar Power," Chem. Rev. 115, 12797 (2015).

[5] H. J. French, H. C. Cross, and A. A. Peterson, "Creep In Five Steels At Different Temperatures," U.S. Bureau of Standards, Technologic Paper No. 362, 1928.