For flat-panel photovoltaic systems, trackers are used to minimize the angle of incidence between the incoming sunlight and a photovoltaic panel. This increases the amount of energy produced from a fixed amount of installed power generating capacity. In standard photovoltaic applications, it was predicted in 2008-2009 that trackers could be used in at least 85% of commercial installations greater than one megawatt from 2009 to 2012. However, as of April 2014, there is not any data to support these predictions.
In concentrator photovoltaics (CPV) and concentrated solar power (CSP) applications, trackers are used to enable the optical components in the CPV and CSP systems. The optics in concentrated solar applications accept the direct component of sunlight light and therefore must be oriented appropriately to collect energy. Tracking systems are found in all concentrator applications because such systems do not produce energy unless pointed at the sun.
- 1 Basic concept
- 2 Types of solar collector
- 3 Non-concentrating photovoltaic (PV) trackers
- 4 Concentrator photovoltaic (CPV) trackers
- 5 Single axis trackers
- 6 Dual axis trackers
- 7 Tracker type selection
- 8 Multi-mirror concentrating PV
- 9 Drive types
- 10 Rotating buildings
- 11 Disadvantages
- 12 See also
- 13 Notes and references
Sunlight has two components, the "direct beam" that carries about 90% of the solar energy, and the "diffuse sunlight" that carries the remainder - the diffuse portion is the blue sky on a clear day and increases proportionately on cloudy days. As the majority of the energy is in the direct beam, maximizing collection requires the sun to be visible to the panels as long as possible.
The energy contributed by the direct beam drops off with the cosine of the angle between the incoming light and the panel. In addition, the reflectance (averaged across all polarizations) is approximately constant for angles of incidence up to around 50°, beyond which reflectance degrades rapidly.
|i||Lost = 1 - cos(i)||i||hours||Lost|
For example trackers that have accuracies of ± 5° can deliver greater than 99.6% of the energy delivered by the direct beam plus 100% of the diffuse light. As a result, high accuracy tracking is not typically used in non-concentrating PV applications.
The sun travels through 360 degrees east to west per day, but from the perspective of any fixed location the visible portion is 180 degrees during an average 1/2 day period (more in spring and summer; less, in fall and winter). Local horizon effects reduce this somewhat, making the effective motion about 150 degrees. A solar panel in a fixed orientation between the dawn and sunset extremes will see a motion of 75 degrees to either side, and thus, according to the table above, will lose 75% of the energy in the morning and evening. Rotating the panels to the east and west can help recapture those losses. A tracker rotating in the east–west direction is known as a single-axis tracker.
The sun also moves through 46 degrees north and south during a year. The same set of panels set at the midpoint between the two local extremes will thus see the sun move 23 degrees on either side, causing losses of 8.3% A tracker that accounts for both the daily and seasonal motions is known as a dual-axis tracker. Generally speaking, the losses due to seasonal angle changes is complicated by changes in the length of the day, increasing collection in the summer in northern or southern latitudes. This biases collection toward the summer, so if the panels are tilted closer to the average summer angles, the total yearly losses are reduced compared to a system tilted at the spring/fall solstice angle (which is the same as the site's latitude).
There is considerable argument within the industry whether the small difference in yearly collection between single and dual-axis trackers makes the added complexity of a two-axis tracker worthwhile. A recent review of actual production statistics from southern Ontario suggested the difference was about 4% in total, which was far less than the added costs of the dual-axis systems. This compares unfavourably with the 24-32% improvement between a fixed-array and single-axis tracker.
Types of solar collector
Different types of solar collector and their location (latitude) require different types of tracking mechanism. Solar collectors may be:
- non-concentrating flat-panels, usually photovoltaic or hot-water,
- concentrating systems, of a variety of types.
Solar collector mounting systems may be fixed (manually aligned) or tracking. Tracking systems may be configured as:
- Fixed collector / moving mirror - i.e. Heliostat
- Moving collector
Domestic and small-scale commercial photovoltaic and hot-water panels are usually fixed, often flush-mounted on an appropriately facing pitched roof. Advantages of fixed mount systems (i.e. factors tending to indicate against trackers) include the following:
- Mechanical simplicity, and hence, lower installation and maintenance costs.
- Wind-loading: it is easier and cheaper to provision a sturdy mount; all mounts other than fixed flush-mounted panels must be carefully designed having regard to wind loading due to greater exposure.
- Indirect light: approximately 10% of the incident solar radiation is diffuse light, available at any angle of misalignment with the sun.
- Tolerance to misalignment: effective collection area for a flat-panel is relatively insensitive to quite high levels of misalignment with the sun – see table and diagram at Accuracy Requirements section below – for example even a 25° misalignment reduces the direct solar energy collected by less than 10%.
Fixed mounts are usually used in conjunction with non-concentrating systems, however an important class of non-tracking concentrating collectors, of particular value in the 3rd world, are portable solar cookers. These utilize relatively low levels of concentration, typically around 2 to 8 Suns and are manually aligned.
Floating ground mount
Solar trackers can be built using a “floating” foundation, which sits on top of the ground without the need for invasive concrete foundations. Instead of placing the tracker on concrete foundations, the tracker is placed on a gravel pan that can be filled with a variety of materials, such as sand or gravel, to secure the tracker to the ground. These “floating” trackers can sustain the same wind load as a traditional fixed mounted tracker. The use of floating trackers increases the number of potential sites for commercial solar projects since they can be placed on top of capped landfills or in areas where excavated foundations are not feasible.
Even though a fixed flat-panel can be set to collect a high proportion of available noon-time energy, significant power is also available in the early mornings and late afternoons when the misalignment with a fixed panel becomes excessive to collect a reasonable proportion of the available energy. For example, even when the Sun is only 10° above the horizon the available energy can be around half the noon-time energy levels (or even greater depending on latitude, season, and atmospheric conditions).
Thus the primary benefit of a tracking system is to collect solar energy for the longest period of the day, and with the most accurate alignment as the Sun's position shifts with the seasons.
In addition, the greater the level of concentration employed, the more important accurate tracking becomes, because the proportion of energy derived from direct radiation is higher, and the region where that concentrated energy is focused becomes smaller.
Fixed collector / moving mirror
Many collectors cannot be moved, for example high-temperature collectors where the energy is recovered as hot liquid or gas (e.g. steam). Other examples include direct heating and lighting of buildings and fixed in-built solar cookers, such as Scheffler reflectors. In such cases it is necessary to employ a moving mirror so that, regardless of where the Sun is positioned in the sky, the Sun's rays are redirected onto the collector.
Due to the complicated motion of the Sun across the sky, and the level of precision required to correctly aim the Sun's rays onto the target, a heliostat mirror generally employs a dual axis tracking system, with at least one axis mechanized. In different applications, mirrors may be flat or concave.
Trackers can be grouped into classes by the number and orientation of the tracker's axes. Compared to a fixed mount, a single axis tracker increases annual output by approximately 30%, and a dual axis tracker an additional 6%.
Photovoltaic trackers can be classified into two types: standard photovoltaic (PV) trackers and concentrated photovoltaic (CPV) trackers. Each of these tracker types can be further categorized by the number and orientation of their axes, their actuation architecture and drive type, their intended applications, their vertical supports and foundation
Non-concentrating photovoltaic (PV) trackers
Photovoltaic panels accept both direct and diffuse light from the sky. The panels on standard photovoltaic trackers always gather the available direct light. The tracking functionality in standard photovoltaic trackers is used to minimize the angle of incidence between incoming light and the photovoltaic panel. This increases the amount of energy gathered from the direct component of the incoming sunlight.
The physics behind standard photovoltaic (PV) trackers works with all standard photovoltaic module technologies. These include all types of crystalline silicon panels (either mono-Si, or multi-Si) and all types of thin film panels (amorphous silicon, CdTe, CIGS, microcrystalline).
Concentrator photovoltaic (CPV) trackers
The optics in CPV modules accept the direct component of the incoming light and therefore must be oriented appropriately to maximize the energy collected. In low concentration applications a portion of the diffuse light from the sky can also be captured. The tracking functionality in CPV modules is used to orient the optics such that the incoming light is focused to a photovoltaic collector.
CPV modules that concentrate in one dimension must be tracked normal to the sun in one axis. CPV modules that concentrate in two dimensions must be tracked normal to the sun in two axes.
- Accuracy requirements
The physics behind CPV optics requires that tracking accuracy increase as the systems concentration ratio increases. However, for a given concentration, nonimaging optics provide the widest possible acceptance angles, which may be used to reduce tracking accuracy.
In typical high concentration systems tracking accuracy must be in the ± 0.1° range to deliver approximately 90% of the rated power output. In low concentration systems, tracking accuracy must be in the ± 2.0° range to deliver 90% of the rated power output. As a result, high accuracy tracking systems are typical.
- Technologies supported
Concentrated photovoltaic trackers are used with refractive and reflective based concentrator systems. There are a range of emerging photovoltaic cell technologies used in these systems. These range from conventional, crystalline silicon-based photovoltaic receivers to germanium-based triple junction receivers.
Single axis trackers
Single axis trackers have one degree of freedom that acts as an axis of rotation. The axis of rotation of single axis trackers is typically aligned along a true North meridian. It is possible to align them in any cardinal direction with advanced tracking algorithms. There are several common implementations of single axis trackers. These include horizontal single axis trackers (HSAT), horizontal single axis tracker with tilted modules (HTSAT), vertical single axis trackers (VSAT), tilted single axis trackers (TSAT) and polar aligned single axis trackers (PSAT). The orientation of the module with respect to the tracker axis is important when modeling performance.
- Horizontal single axis tracker (HSAT)
The axis of rotation for horizontal single axis tracker is horizontal with respect to the ground. The posts at either end of the axis of rotation of a horizontal single axis tracker can be shared between trackers to lower the installation cost. Field layouts with horizontal single axis trackers are very flexible. The simple geometry means that keeping all of the axes of rotation parallel to one another is all that is required for appropriately positioning the trackers with respect to one another. Appropriate spacing can maximize the ratio of energy production to cost, this being dependent upon local terrain and shading conditions and the time-of-day value of the energy produced. Backtracking is one means of computing the disposition of panels. Horizontal trackers typically have the face of the module oriented parallel to the axis of rotation. As a module tracks, it sweeps a cylinder that is rotationally symmetric around the axis of rotation. In single axis horizontal trackers, a long horizontal tube is supported on bearings mounted upon pylons or frames. The axis of the tube is on a north–south line. Panels are mounted upon the tube, and the tube will rotate on its axis to track the apparent motion of the sun through the day.
- Horizontal single axis tracker with tilted modules (HTSAT)
In HSAT, the modules are mounted flat at 0 degrees, while in HTSAT, the modules are installed at a certain tilt. It works on same principle as HSAT, keeping the axis of tube horizontal in north–south line and rotates the solar modules east to west throughout the day. These trackers are usually suitable in high latitude locations but does not take as much land space as consumed by Vertical single axis tracker (VSAT). Therefore, it brings the advantages of VSAT in a horizontal tracker and minimizes the overall cost of solar project.
- Vertical single axis tracker (VSAT)
The axis of rotation for vertical single axis trackers is vertical with respect to the ground. These trackers rotate from East to West over the course of the day. Such trackers are more effective at high latitudes than are horizontal axis trackers. Field layouts must consider shading to avoid unnecessary energy losses and to optimize land utilization. Also optimization for dense packing is limited due to the nature of the shading over the course of a year. Vertical single axis trackers typically have the face of the module oriented at an angle with respect to the axis of rotation. As a module tracks, it sweeps a cone that is rotationally symmetric around the axis of rotation.
- Tilted single axis tracker (TSAT)
All trackers with axes of rotation between horizontal and vertical are considered tilted single axis trackers. Tracker tilt angles are often limited to reduce the wind profile and decrease the elevated end height. With backtracking, they can be packed without shading perpendicular to their axis of rotation at any density. However, the packing parallel to their axes of rotation is limited by the tilt angle and the latitude. Tilted single axis trackers typically have the face of the module oriented parallel to the axis of rotation. As a module tracks, it sweeps a cylinder that is rotationally symmetric around the axis of rotation.
- Polar aligned single axis trackers (PASAT)
This method is scientifically well known as the standard method of mounting a telescope support structure. The tilted single axis is aligned to the polar star. It is therefore called a polar aligned single axis tracker (PASAT). In this particular implementation of a tilted single axis tracker, the tilt angle is equal to the site latitude. This aligns the tracker axis of rotation with the earth’s axis of rotation.
Dual axis trackers
Dual axis trackers have two degrees of freedom that act as axes of rotation. These axes are typically normal to one another. The axis that is fixed with respect to the ground can be considered a primary axis. The axis that is referenced to the primary axis can be considered a secondary axis. There are several common implementations of dual axis trackers. They are classified by the orientation of their primary axes with respect to the ground. Two common implementations are tip-tilt dual axis trackers (TTDAT) and azimuth-altitude dual axis trackers (AADAT). The orientation of the module with respect to the tracker axis is important when modeling performance. Dual axis trackers typically have modules oriented parallel to the secondary axis of rotation. Dual axis trackers allow for optimum solar energy levels due to their ability to follow the sun vertically and horizontally. No matter where the sun is in the sky, dual axis trackers are able to angle themselves to be in direct contact with the sun.
A tip–tilt dual axis tracker (TTDAT) is so-named because the panel array is mounted on the top of a pole. Normally the east–west movement is driven by rotating the array around the top of the pole. On top of the rotating bearing is a T- or H-shaped mechanism that provides vertical rotation of the panels and provides the main mounting points for the array. The posts at either end of the primary axis of rotation of a tip–tilt dual axis tracker can be shared between trackers to lower installation costs.
Other such TTDAT trackers have a horizontal primary axis and a dependent orthogonal axis. The vertical azimuthal axis is fixed. This allows for great flexibility of the payload connection to the ground mounted equipment because there is no twisting of the cabling around the pole.
Field layouts with tip–tilt dual axis trackers are very flexible. The simple geometry means that keeping the axes of rotation parallel to one another is all that is required for appropriately positioning the trackers with respect to one another. Normally the trackers would have to be positioned at fairly low density in order to avoid one tracker casting a shadow on others when the sun is low in the sky. Tip-tilt trackers can make up for this by tilting closer to horizontal to minimize up-sun shading and therefore maximize the total power being collected.
The axes of rotation of many tip–tilt dual axis trackers are typically aligned either along a true north meridian or an east–west line of latitude.
Given the unique capabilities of the Tip-Tilt configuration and the appropriated controller totally automatic tracking is possible for use on portable platforms. The orientation of the tracker is of no importance and can be placed as needed.
An azimuth–altitude dual axis tracker (AADAT) has its primary axis (the azimuth axis) vertical to the ground. The secondary axis, often called elevation axis, is then typically normal to the primary axis. They are similar to tip-tilt systems in operation, but they differ in the way the array is rotated for daily tracking. Instead of rotating the array around the top of the pole, AADAT systems can use a large ring mounted on the ground with the array mounted on a series of rollers. The main advantage of this arrangement is the weight of the array is distributed over a portion of the ring, as opposed to the single loading point of the pole in the TTDAT. This allows AADAT to support much larger arrays. Unlike the TTDAT, however, the AADAT system cannot be placed closer together than the diameter of the ring, which may reduce the system density, especially considering inter-tracker shading.
Tracker type selection
The selection of tracker type is dependent on many factors including installation size, electric rates, government incentives, land constraints, latitude, and local weather.
Horizontal single axis trackers are typically used for large distributed generation projects and utility scale projects. The combination of energy improvement and lower product cost and lower installation complexity results in compelling economics in large deployments. In addition the strong afternoon performance is particularly desirable for large grid-tied photovoltaic systems so that production will match the peak demand time. Horizontal single axis trackers also add a substantial amount of productivity during the spring and summer seasons when the sun is high in the sky. The inherent robustness of their supporting structure and the simplicity of the mechanism also result in high reliability which keeps maintenance costs low. Since the panels are horizontal, they can be compactly placed on the axle tube without danger of self-shading and are also readily accessible for cleaning.
A vertical axis tracker pivots only about a vertical axle, with the panels either vertical, at a fixed, adjustable, or tracked elevation angle. Such trackers with fixed or (seasonally) adjustable angles are suitable for high latitudes, where the apparent solar path is not especially high, but which leads to long days in summer, with the sun travelling through a long arc.
Dual axis trackers are typically used in smaller residential installations and locations with very high government feed in tariffs.
Multi-mirror concentrating PV
This device uses multiple mirrors in a horizontal plane to reflect sunlight upward to a high temperature photovoltaic or other system requiring concentrated solar power. Structural problems and expense are greatly reduced since the mirrors are not significantly exposed to wind loads. Through the employment of a patented mechanism, only two drive systems are required for each device. Because of the configuration of the device it is especially suited for use on flat roofs and at lower latitudes. The units illustrated each produce approximately 200 peak DC watts.
A multiple mirror reflective system combined with a central power tower is employed at the Sierra SunTower, located in Lancaster, California. This generation plant operated by eSolar is scheduled to begin operations on August 5, 2009. This system, which uses multiple heliostats in a north–south alignment, uses pre-fabricated parts and construction as a way of decreasing startup and operating costs.
Active trackers use motors and gear trains to direct the tracker as commanded by a controller responding to the solar direction. In order to control and manage the movement of these massive structures special slewing drives are designed and rigorously tested. The technologies used to direct the tracker are constantly evolving and recent developments at Google and Eternegy have included the use of wire-ropes and winches to replace some of the more costly and more fragile components.
Counter rotating slewing drives sandwiching a fixed angle support can be applied to create a "multi-axis" tracking method which eliminates rotation relative to longitudinal alignment. This method if placed on a column or pillar will generate more electricity than fixed PV and its PV array will never rotate into a parking lot drive lane. It will also allow for maximum solar generation in virtually any parking lot lane/row orientation, including circular or curvilinear.
Active two-axis trackers are also used to orient heliostats - movable mirrors that reflect sunlight toward the absorber of a central power station. As each mirror in a large field will have an individual orientation these are controlled programmatically through a central computer system, which also allows the system to be shut down when necessary.
Light-sensing trackers typically have two or more photosensors, such as photodiodes, configured differentially so that they output a null when receiving the same light flux. Mechanically, they should be omnidirectional (i.e. flat) and are aimed 90 degrees apart. This will cause the steepest part of their cosine transfer functions to balance at the steepest part, which translates into maximum sensitivity. For more information about controllers see active daylighting.
Since the motors consume energy, one wants to use them only as necessary. So instead of a continuous motion, the heliostat is moved in discrete steps. Also, if the light is below some threshold there would not be enough power generated to warrant reorientation. This is also true when there is not enough difference in light level from one direction to another, such as when clouds are passing overhead. Consideration must be made to keep the tracker from wasting energy during cloudy periods.
The most common Passive trackers use a low boiling point compressed gas fluid that is driven to one side or the other (by solar heat creating gas pressure) to cause the tracker to move in response to an imbalance. As this is a non-precision orientation it is unsuitable for certain types of concentrating photovoltaic collectors but works fine for common PV panel types. These will have viscous dampers to prevent excessive motion in response to wind gusts. Shader/reflectors are used to reflect early morning sunlight to "wake up" the panel and tilt it toward the sun, which can take nearly an hour. The time to do this can be greatly reduced by adding a self-releasing tiedown that positions the panel slightly past the zenith (so that the fluid does not have to overcome gravity) and using the tiedown in the evening. (A slack-pulling spring will prevent release in windy overnight conditions.)
A newly emerging type of passive tracker for photovoltaic solar panels uses a hologram behind stripes of photovoltaic cells so that sunlight passes through the transparent part of the module and reflects on the hologram. This allows sunlight to hit the cell from behind, thereby increasing the module's efficiency. Also, the panel does not have to move since the hologram always reflects sunlight from the correct angle towards the cells.
A chronological tracker counteracts the Earth's rotation by turning at the same speed as the Earth relative to the Sun. around an axis parallel to the Earth's, but in the direction opposite to the Earth's rotation. To do this, a simple rotation mechanism, turning at a constant speed of one revolution per day or 15 degrees per hour, is adequate for many purposes, such as keeping a photovoltaic panel pointing within a few degrees of the Sun, but for accurate tracking, such as may be needed to keep a telescope aimed at the Sun, the equation of time must be taken into account, so the tracker moves according to apparent solar time, often called "sundial time". The speed of the apparent motion of the Sun in the sky varies slightly, depending on the time of year, for reasons which are explained in the article Equation of time#Explanations for the major components of the equation of time. This causes the reading of a sundial to advance at a varying rate. The tracker contains a mechanism that takes account of the equation of time and makes the tracker move according to sundial time. For example, it turns 15 degrees in one hour as measured by a sundial, which may be slightly longer or shorter than an hour as measured by a clock. So the tracker's movement is governed by sundial time, which in turn is governed by the movement of the Sun in the sky. This makes the tracker accurately keep pace with the Sun.
In addition to following the daily East-West apparent motion of the Sun in the sky, the tracker must follow the Sun's seasonal apparent movements in the North-South direction. Around the equinoxes, the Sun moves about 0.4 degrees North or South per day, which is almost as great as its apparent diameter in the sky. The graph of this movement against time appears approximately to be a sine wave, with a period of one year and a peak-to-peak amplitude of 46.9 degrees - twice the tilt of the Earth's axis. A simple mechanism that produces this sinusoidal movement can be used in a tracker that will work well enough for many purposes. However, accurate tracking must take into account the fact that the Sun's North-South movement is not exactly sinusoidal. The peaks and troughs of its graph are more sharply "pointed" than those of a sine wave. A mechanism that contains a cam, rotating once a year and shaped according to the correct waveform, provides one way of achieving accurate tracking.
A chronological tracker is a very simple yet potentially a very accurate solar tracker specifically for use with a polar mount (see above). In theory the tracker may rotate completely, assuming there is enough clearance for a complete rotation, and assuming that twisting wires are not an issue, otherwise a simple reset to the dawn position may be performed at anytime between dusk and dawn.
In some developing nations, drives have been replaced by operators who adjust the trackers. This has the benefits of robustness, having staff available for maintenance and creating employment for the population in the vicinity of the site.
The Gemini House is a unique example of a vertical axis tracker. This cylindrical house in Austria (latitude above 45 degrees north) rotates in its entirety to track the sun, with vertical solar panels mounted on one side of the building, rotating independently, allowing control of the natural heating from the sun.
ReVolt House is a rotating, floating house designed by TU Delft students for the Solar Decathlon Europe competition in Madrid. The house would be realized in September 2012. A closed façade turns itself towards the sun in summer to prevent the interior space from direct heat gains. In winter, the glass façade faces the sun to get direct sunlight in the house.
Trackers add cost and maintenance to the system - if they add 25% to the cost, and improve the output by 25%, the same performance can be obtained by making the system 25% larger, eliminating the additional maintenance. Tracking was very cost effective in the past when photovoltaic modules were expensive compared to today. Because they were expensive, it was important to use tracking to minimize the number of panels used in a system with a given power output. But as panels get cheaper, the cost effectiveness of tracking vs using a greater number of panels decreases.
Tracking is also not suitable for typical residential rooftop photovoltaic installations. Since tracking requires that panels tilt or otherwise move, provisions must be made to allow this. This requires that panels be offset a significant distance from the roof, which requires exepnsive racking and increases wind load. Also, such a setup would not make for a very aesthetically pleasing install on residential rooftops. Because of this (and the high cost of such a system), tracking is not used on residential rooftop installations, and is unlikely to ever be used in such installations. This is especially true as the cost of photovoltaic modules continues to decrease, which makes increasing the number of modules for more power the more cost-effective option. Tracking can (and sometimes is) used for residential ground mount installations, where greater freedom of movement is possible.
Tracking can also cause shading problems. As the panels move during the course of the day, it is possible that, if the panels are located too close to one another, they may shade one another due to profile angle effects. As an example, if you have several panels in a row from east to west, there will be no shading during solar noon. But in the afternoon, panels could be shaded by their west neighboring panel if they are sufficiently close. This means that panels must be spaced sufficiently far to prevent shading in systems with tracking, which can reduce the available power from a given area during the peak sun hours. This is not a big problem if there is sufficient land area to widely space the panels. But it will reduce output during certain hours of the day (i.e. around solar noon) compared to a fixed array.
Notes and references
- Customers Recognize the Power of Solar Tracking Accessed 4-3-2012
- Tracking Systems Vital to Solar Success Accessed 4-3-2012
- Antonio L. Luque; Viacheslav M. Andreev (2007). Concentrator Photovoltaics. Springer Verlag. ISBN 978-3-540-68796-2.
- Ignacio Luque-Heredia et al., "The Sun Tracker in Concentrator Photovoltaics" in Cristobal, A.B.,Martí, A.,and Luque, A. Next Generation Photovoltaics, Springer Verlag, 2012 [ISBN 978-3642233692]
- For example Figure 6 (Si+SiO2 SLAR) at Bio-mimetic nanostructured surfaces for near-zero reflection sunrise to sunset, Stuart A. Boden, Darren M. Bagnall, University of Southampton, retrieved 5-June-2011
- Hours of rotation away from a time (e.g. noon) when the collector is accurately aligned.
- Greater due to higher reflectance at high angles of incidence.
- Maximum seasonal variation (at summer or winter solstice), as compared with accurate alignment at equinox.
- William David Lubitz, "Effect of Manual Tilt Adjustments on Incident Irradiance on Fixed and Tracking Solar Panels", Applied Energy, Volume 88 (2011), pp. 1710-1719
- David Cooke, "Single vs. Dual Axis Solar Tracking", Alternate Energy eMagazine, April 2011
- 900 W/m2 direct out of 1000 W/m2 total as per Reference Solar Spectral Irradiance: Air Mass 1.5 NREL, retrieved 1 May 2011
- Table at Air mass coefficient
- Gay, CF; Wilson, JH & Yerkes, JW (1982). "Performance advantages of two-axis tracking for large flat-plate photovoltaic energy systems". Conf. Rec. IEEE Photovoltaic Spec. Conf. 16: 1368. Bibcode:1982pvsp.conf.1368G.
- King, D.L.; Boyson, W.E. & Kratochvil, J.A. (May 2002). "Analysis of factors influencing the annual energy production of photovoltaic systems". Photovoltaic Specialists Conference, 2002. Conference Record of the Twenty-Ninth IEEE: 1356–1361. doi:10.1109/PVSC.2002.1190861.
- Chaves, Julio (2008). Introduction to Nonimaging Optics. CRC PressI Llc. ISBN 978-1-4200-5429-3.
- Roland Winston; Juan C. Miñano; Pablo Benítez (2005). Nonimaging Optics. Academic Press. ISBN 0-12-759751-4.
- example of HTSAT
- "Backtracking", Lauritzen Inc.
- "Portable solar trackers", Moser, LLC
- Solar Trackers: Pros & Cons Accessed 4-3-2012
Optimum Trackers builds innovative solar trackers that increases solar plant production up to 27% compared with a fixed-tilt installation : 
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