The Physics of Energy, page 97
As an example of this limit, consider again the linear parabolic concentrator. We found in Examples 24.3 and 24.4 that a linear parabolic concentrator with height equal to focal length has , and . In this case, , which clearly satisfies the limit eq. (24.16). In fact, the linear parabolic concentrator undershoots the maximum possible effective concentration by a factor greater than π. Nonetheless, linear and dish parabolic concentrators are frequently used in practice due to the difficulty of designing and implementing a practical concentrator with closer-to-optimal concentration.
For solar energy applications, the Sun is the source of the incident radiation on a concentrator. For the Sun, m and m, so the sun subtends a half-angle in the sky of rad, or about 1/4°. Thus, it is not useful to have a solar concentrator with acceptance angle below . This limits the effective concentration of a 3D solar concentrator to approximately
(24.17)
24.3.4 Compound Parabolic Concentrators
Several other concentrator designs are of interest either for their theoretical properties or for their applications to solar thermal energy. In this section we describe one class known as compound parabolic concentrators (CPCs), which are of particular theoretical interest because they can in principle come arbitrarily close to the optimal effective concentration. While based on the parabolic shape, the CPC combines opposing parts of parabolas at different angles to increase the effective concentration. The key feature of the parabola that is exploited in the CPC is the fact that light incident on one side of the parabola coming from an angle away from the parabola axis is always reflected below the focus. This feature can be seen in Figure 24.10, where it is clear that it is a consequence of specular reflection.
Acceptance Angle and Maximum Concentration
The maximum concentration possible for a concentrator with acceptance angle is
For 2D geometries (extended into the third dimension by linear translation of a planar geometry), the maximum is
Figure 24.10 Light incident on one side of the parabola at an angle away from the parabola axis is always reflected below the focus.
A (2D) CPC is constructed by mounting identical (congruent) parabolic surfaces on either side of a central symmetry plane, rotated at equal but opposite angles away from the vertical. The basic geometry is depicted in Figure 24.11(a), where the two sides of the concentrator are constructed from two distinct but congruent parabolic segments. The right-hand side of the concentrator follows parabola 1, with focal point A and symmetry axis rotated counterclockwise from the vertical by an angle θ. Similarly, the left-hand side of the concentrator follows parabola 2, with symmetry axis rotated by θ clockwise to the vertical, and focal point B chosen to be the point on parabola 1 at an equal height to point A. By symmetry, focal point A lies on parabola 2. Both parabolic curves continue up to the points where their tangents become vertical, parallel to the collector's axis of symmetry. It follows from simple geometric reasoning (see Problem 24.15) that the line from the top of parabola 1 to its focus (QA) is parallel to the axis of parabola 2 (and the corresponding line on parabola 2 is parallel to the axis of parabola 1). The absorber is placed along the line segment connecting the two foci A and B.
Using the observation that light incident from an angle away from the parabola axis goes below the focus, it is straightforward to show that all incident light within an angle less than θ of normal is reflected by one side or the other of the CPC to the absorber along line . This is illustrated in Figure 24.11(b). Light ray grazes the edge of parabola 2 and goes to the focus at B. A light ray such as , which is parallel and to the right of , hits parabola 1 and goes to its focus at A. The light ray labeled is incident at an angle less than θ, and is therefore reflected from parabola 1 towards a point to the right of A and hits the absorber along AB. Any such ray incident on parabola 1 at any angle less than θ either hits the absorber along AB after one reflection, or hits parabola 1 again at an angle even further clockwise rotated from the parabola axis, and is reflected again, with the process continuing until the light ray eventually hits the absorber. Finally, a light ray incident at an angle greater than θ – ray for example – misses the absorber and eventually exits the collector. Thus the angle θ by which the parabolas are rotated away from the vertical is also the acceptance angle of the CPC, .
The CPC can be adjusted to achieve arbitrarily high concentration C, with correspondingly small acceptance angle. Remarkably, the linear concentrator based on the 2D CPC achieves the ideal concentration limit (24.16), at least in the limit of an infinitely long “trough” in the third dimension. In other words, the ratio (see Figure 24.11(a)) equals (Problem 24.17). The 3D CPC is constructed by rotating the 2D CPC cross section depicted in Figure 24.11 around the vertical axis. In the 3D geometry, however, the ray-tracing argument is more subtle, and in fact some incoming rays within the acceptance angle are sent back out of the collector after a number of bounces. Thus, the 3D CPC does not realize the maximal concentration for a given acceptance angle. For a more detailed discussion of CPCs and other novel concentrator designs, see [143].
While CPCs are very intriguing due to their high effective concentration for a given acceptance angle, they have not yet seen widespread use – in part because of the difficulty of inexpensively manufacturing them to the exacting specifications needed for very high concentrations.
24.3.5 Dynamical Adjustment
In §24.2, we discussed the idea that a flat-panel solar collector may be mounted at a fixed angle towards the southern horizon in order to increase effective insolation on the collector. With a solar concentrator, the relative orientation of the concentrator to the Sun becomes even more crucial. For a system with a high effective concentration, the acceptance angle is small, and as the Sun moves through the sky from morning to night over trajectories varying with the seasons, it is necessary to adjust the orientation of the collector in order to keep the Sun within the acceptance angle. The inverse relationship between concentration and acceptance angle leads to a trade-off: for concentrators with large acceptance angle and small effective concentration C, the concentrator achieves a lower temperature, but does not need much, if any, adjustment. For concentrators with small acceptance angle and large effective concentration C, the concentrator can achieve a very high temperature, but needs to be dynamically adjusted to track the Sun through the day. There are a variety of strategies used for adjusting solar collectors to optimize energy collection for minimal adjustment effort. Broadly, these strategies fit into three categories:
Figure 24.11 A compound parabolic concentrator is constructed from opposing surfaces based on parabolas with different focal points and non-parallel axes. The significance of the geometry depicted in (a) and the light rays traced in (b) is explained in the text.
Fixed orientation For concentrators with very low effective concentrations ( 1–3), and high acceptance angle (), it is often possible to use a collector with a permanently fixed orientation (fixed-angle mounting). Generally such collectors are either flat (as in §24.2.2), or are linear concentrators with the trough axis aligned in the E–W directions and a tilt towards the equator.
Periodic/seasonal adjustment For slightly larger concentrations ( 3–6), and smaller acceptance angles ( 10°), a fixed orientation is inadequate to deal with the seasonal variation of the Sun’s trajectory across the sky. Often, linear concentrators in this range are periodically or seasonally adjusted, with the trough axis aligned E–W, and the tilt adjusted through the year to match the seasonally changing declination.
Continuous tracking For concentrators with very high effective concentration (for which C could be as high as 200 for a linear concentrator, or 10 000 for a 3D concentrator such as a parabolic dish), and small acceptance angle, it is necessary to continuously track the motion of the Sun through the day. Configurations of this type typically employ (i) a linear concentrator aligned on a N–S axis with tilt and continuously changing trough angle ranging from east in the morning to west in the evening to follow the Sun (1-axis tracking) or (ii) a 3D concentrator like a parabolic dish or 3D CPC with 2-axis tracking of the Sun's direction from sunrise to sunset. Some energy is needed to run the tracking system for these types of concentrators, but generally the power involved is negligible compared to the total power gathered by the collector.
24.4Solar Thermal Electricity (STE)
24.4.1 Challenges and Technologies
One of the most promising technologies for large-scale electricity production from solar energy is solar thermal electricity generation, also known as concentrated solar power (CSP). This is a simple and relatively low-technology approach to power generation from the Sun. The basic idea is to use concentrators to reflect solar energy at high concentration to a fluid such as water, molten salt, or oil. The fluid is heated to a high temperature, generally between 200℃ and 1000℃, and can be used to run a relatively high-efficiency heat engine (for example by transferring the heat to water to run a Rankine steam turbine). As mentioned earlier, concentrators require direct exposure to the Sun and cannot make use of light diffused through or reflected from clouds or haze. STE generation is therefore impractical in regions where cloudy days are common and is typically sited in deserts and at relatively low latitudes.
Technology for solar thermal electricity generation was developed in the 1970s and 1980s. A few plants were built at that time, such as the SEGS (Solar Energy Generating Systems) facility in California's Mojave Desert. The 9 individual SEGS plants that have been running since that time have a total capacity of 354 MW, with output around 75 MW when averaged over the year. These plants utilize a total land area of about 6.5 km, and have a gross conversion efficiency (electric power output divided by total insolation on land area used for the plant) of about 3–4%. The actual field area covered by mirrors is somewhat smaller – about 2.25 km – so efficiency relative to insolation on the field area is higher, above 10%. Recently, there has been renewed interest in solar thermal electricity generation. The first commercial solar thermal power plant in Europe was the Andasol solar power station, a set of three plants in Andalusia, Spain. Each plant has a 50 MW capacity, with actual output averaging around 20 MW/plant (capacity factor , see Box 24.3). Andasol 1 went online in 2009 and uses a total land area of roughly 2 km, with total collector area of roughly 0.5 km; efficiency factors are similar to those of the SEGS plants. Construction of many new plants is underway around the world. We briefly summarize here a few of the issues encountered in solar thermal electricity production and some of the main technologies used.
One of the main challenges in solar electricity production is the large area needed. The gross conversion efficiency of ~3–4% realized by existing systems such as SEGS could be pushed higher by newer technologies. Smaller parabolic trough plants have been built with efficiency approaching 20%, and individual parabolic dishes with Stirling engines have surpassed 40% conversion efficiency, but developing large-scale plants with high gross conversion efficiency remains a challenge. At a gross conversion efficiency of 3% and average insolation of 300 W/m in an ideal arid environment, net output of such a plant averages only ~10 W/m. So, a plant producing a time-averaged 1 GW of electrical power output would require around 100 km. Obviously, constructing a large number of such plants is a substantial engineering undertaking, though not impossible. Related challenges in large-scale solar thermal electricity production include the difficulty of mass-producing highly reflective mirrors and keeping them clean and undamaged over years of exposure to dust, rain, wind, sandstorms, etc. Cooling is also an issue. Standard steam turbine plants require a large amount of water or other resource to act as a heat sink into which to dump entropy, though systems have been developed that use less water by employing air cooling to condense steam. Storage and transmission are also substantial challenges, discussed further in §37 and §38. Some recent STE plant designs, such as the Andasol plants (see Figure 37.4), employ a molten nitrate salt mixture that is inexpensive, has a high heat capacity (see Problem 5.8), and can be stored at high temperature for days, allowing nighttime and peak energy distribution independent of the time of energy collection. Other materials with high heat capacities and relatively low cost, such as graphite, have been incorporated in solar thermal storage systems (see §5, Problem 5.9). Research is ongoing for optimal solar thermal storage media (see for example [145]).
Solar Thermal Electricity (STE)
Solar thermal electric power plants use concentrators in various geometries to focus direct sunlight on an absorber. The resulting thermal energy is used to generate electricity. STE has the significant advantage that thermal energy can be stored for later use, thus reducing the variability of solar power. Siting of STE plants is limited to locations with the least cloud cover and haze by the fact that only direct sunlight can be concentrated.
Some of the main technologies that have been developed for solar thermal electricity plants involve the following configurations (see Figure 24.12):
Parabolic trough This is the most established technology, used in the SEGS plants in California. A linear parabolic concentrator is used to heat liquid in absorber tubes. The heat transfer fluid that is circulated through the solar field is used to provide thermal energy to a steam turbine. Numerous solar thermal plants using this technology are currently operating around the world.
Power tower In this design, an array of flat mirrors called heliostats are arranged on the ground around a central tower. Each mirror is independently oriented with a dual-axis control to reflect the sunlight onto the tower, where a fluid is heated. This design was used in the Solar 1, Solar 2, and Solar Tres (Gemasolar) plants in California and Spain, using high-temperature molten salt as the heating fluid and for storage. As of the time of writing, there were several further plants of this type operating in the US and other countries.
Parabolic dish In this design, 3D parabolic dish concentrators individually track the Sun and reflect to absorbers mounted on each dish. The highest-efficiency solar thermal electricity generators designed so far combine a parabolic dish concentrator with a Stirling engine mounted on the dish. Though several systems using this design have been developed, there has as yet been no large-scale deployment of this technology.
Box 24.3. Capacity Factor
The capacity factor of a power plant is the ratio of actual output (averaged over time) to its maximum output power capacity. The capacity factors of different power plants vary widely, and depend upon the power source, design features, and usage patterns. Nuclear power plants, for example, which are generally used as 24/7 baseload power, often run at capacity factors of 90% or higher. Due to the daily cycle of insolation, solar thermal power plants without storage tend to run at capacity factors of 30% or lower, while plants with storage can realize significantly higher capacity factors (up to 75% reported for existing plants) by storing thermal energy collected during daylight hours for power generation at night.
Figure 24.12 Some solar thermal electricity generation technologies: (a) parabolic trough; (b) power tower; (c) parabolic dish. (Credit: (a) DLR, (b) SOLUCAR PS1O reproduced under CC-BY-SA 2.0 license via Wikimedia Commons (c) National Renewable Energy Laboratory, David Hicks)
Other technologies Other design approaches for solar thermal electric plants include compact linear Fresnel reflectors (CLFRs), in which an array of long rectangular mirrors with single-axis control reflect sunlight onto a linear absorber fixed in place over the reflector field. Though the efficiency of this design is lower than that of the parabolic trough, the implementation is simpler, and it is much easier to mass-produce flat mirrors than parabolic mirrors. Fresnel lenses, which are cheaper than mirrors, can also be used for concentrators. For the most part, solar thermal electricity production is designed as a utility-scale operation, though there is some development of smaller systems, such as individual Stirling engine + parabolic dish configurations.
24.4.2 Efficiency Optimization
The use of solar concentrators makes it possible to heat the working fluid in an STE plant to a high temperature. This increases the maximum (Carnot) efficiency possible for conversion of the solar thermal energy to electricity. On the other hand, at higher temperatures, the absorber reradiates a higher fraction of the incident energy. This leads to an optimization problem: given a concentrator geometry, the temperature of the absorbing material should be raised high enough for efficient thermal to electric conversion, but not so high that too much incoming radiation is re-emitted.
To analyze this situation quantitatively, we consider an idealized situation where a solar concentrator with concentration C is used to heat the working fluid to a temperature T. We are interested in determining the temperature T at which the theoretical upper bound on overall conversion efficiency is as high as possible, assuming that the absorber radiates as a black body at temperature T. For an ambient temperature of , we assume that the conversion of available thermal energy to electricity can take place at the Carnot efficiency,
(24.18)
If the incident power per unit area is then the total power hitting the absorber is , where A is the surface area of the absorber. The power reradiated by the absorber is , so the available power is
(24.19)
Assuming Carnot efficiency, the output electric power (per unit absorber surface area) is
(24.20)
