Patent Grant
8178775
The subject matter described herein relates to photovoltaic collection systems. More particularly, the subject matter described herein relates to methods, systems, and computer readable media for controlling orientation of a photovoltaic collection system to track apparent movement of the sun.
A photovoltaic collection system is a system that includes one or more photovoltaic cells that generate electric current in response to incident light. Types of photovoltaic collection systems include direct, non-concentrating photovoltaic collection systems that receive incident light directly and generate current. Direct, non-concentrating photovoltaic collection systems typically include large arrays of photovoltaic cells, which may be expensive to manufacture and/or maintain. Another type of photovoltaic collection system is a reflective, concentrating photovoltaic collection system where incident light is reflected and concentrated onto an array of photovoltaic cells. Because the incident light is concentrated on the cells, a smaller array of cells can generate more output power than the same number of photovoltaic cells in a direct, non-concentrating photovoltaic collection system.
The efficiency of both direct and reflective photovoltaic collection systems can be improved by controlling the orientation of the photovoltaic cells and/or the reflectors with respect to the light source. For example, if the light source is the sun, it may be desirable to control the orientation of the photovoltaic collection system to track apparent movement of the sun as the earth spins on its axis and rotates around the sun. If time, position on earth, and orientation of the photovoltaic collection system with regard to the earth's spin axis are known, known ephemerides can be used to control orientation of the photovoltaic collection system in an open loop manner. One problem with such an approach is that one or more of these variables may not be known, making accurate tracking using ephemerides that are based on these variables difficult. Another problem with approaches that require all of these variables to be known is that the equipment or method for determining the variables may unnecessarily increase the cost of the photovoltaic collection system.
Accordingly, in light of these difficulties, there exists the need for methods, systems, and computer readable media for controlling orientation of a photovoltaic collection system to track apparent movement of the sun.
The subject matter described herein includes methods, systems, and computer readable media for controlling orientation of a photovoltaic collection system to track apparent movement of the sun. According to one aspect, a method for controlling orientation of a photovoltaic collection system to track apparent movement of the sun using a photovoltaic-collection-system-derived tracking algorithm is provided. The method includes determining an initial orientation of a photovoltaic collection system. The method further includes automatically deriving, using output from the photovoltaic collection system as it tracks apparent movement of the sun across the sky caused by spinning of the earth on its axis and its orbit around the sun, a tracking algorithm for controlling orientation of the photovoltaic collection system to track the apparent movement of the sun. The method further includes controlling orientation of the photovoltaic collection system to track apparent movement of the sun using the photovoltaic collection system derived tracking algorithm.
According to another aspect, the subject matter described herein includes a system for controlling orientation of a photovoltaic collection system to track apparent movement of the sun using a photovoltaic-collection-system-derived tracking algorithm. The system includes a power unit including at least one photovoltaic array mounted on a pier. The system further includes a drive mechanism for controlling orientation of the power unit. The system includes a tracking module for automatically deriving, based on at least one signal output by at least a portion of the power unit, a tracking algorithm for controlling orientation of the power unit to track apparent movement of the sun across the sky caused by the spinning of the earth on its axis and its orbit around the sun. The tracking module controls the drive mechanism to vary orientation of the power unit to track the apparent movement of the sun using the photovoltaic-system-derived tracking algorithm.
According to another aspect of the subject matter described herein, a photovoltaic collection system is provided. The photovoltaic collection system includes a power unit having a photovoltaic array. A tilt sensor is coupled to the power unit for determining a tilt measurement for a tiltable portion of the power unit. A compass is coupled to the power unit for determining a compass reading from an azimuthally rotatable portion of the power unit. The system further includes a drive mechanism for moving at least a portion of the power unit. A tracking module uses the tilt measurement and the compass reading to determine an orientation of the power unit and controls the drive mechanism to vary the orientation of the power unit to track apparent movement of the sun across the sky caused by the spinning of the earth on its axis and its rotation about the sun.
The subject matter described herein can be implemented using a computer readable medium having stored thereon computer executable instructions that when executed by the processor of a computer perform steps. Exemplary computer readable media suitable for implementing the subject matter described herein include chip memory devices, disk memory devices, programmable logic devices, and application specific integrated circuits. In addition, a computer readable media that implements the subject matter described herein can be located on a single computing platform or may be distributed across multiple computing platforms.
According to another aspect, the subject matter described herein includes a computer readable medium having stored thereon computer executable instructions that when executed by the processor of a computer perform steps. The steps include determining an initial orientation of a photovoltaic collection system. The steps further include automatically deriving, using output from the photovoltaic collection system as it tracks apparent movement of the sun across the sky caused by the spinning of the earth on its axis and its orbit around the sun, a tracking algorithm for controlling orientation of the photovoltaic collection system to track the apparent movement of the sun. The steps further include controlling orientation of the photovoltaic collection system to track the apparent movement of the sun using the photovoltaic-collection-system-derived tracking algorithm.
Preferred embodiments of the subject matter described herein will now be explained with reference to the accompanying drawings which:
The subject matter described herein includes methods, systems, and computer readable media for controlling orientation of a photovoltaic collection system to track apparent movement of the sun.
Also illustrated in
Returning to
According to one aspect, the subject matter described herein includes automatically deriving a tracking algorithm for controlling orientation of power unit 100 to track apparent movement of the sun across the sky as the earth spins on its axis and revolves about the sun. In this example, the automatically derived tracking algorithm is defined in a coordinate system local to support pier 102. Deriving the tracking algorithm involves determining an initial orientation of power unit 100 in the pier centric coordinate system, initial sun acquisition, and initial sun tracking, and recording the changes in azimuth and elevation of power unit 100 with respect to time during initial sun tracking. Once the changes have been recorded with respect to time, the next time that power unit 100 is operated, for example, on a subsequent day, it can be operated open loop using the self-derived tracking algorithm. Sensor or power feedback can be used as appropriate to correct any tracking errors.
The initial orientation of power unit 100 in a pier-centric coordinate system can be determined using any suitable sensor that is capable of sensing the orientation of power unit 100 with respect to pier 102. In one exemplary implementation, Hall effect sensors are used to determine the azimuth and elevation of power unit 100 as defined by the stepper motors used to control azimuth and elevation. Each motor rotates from a stop position that can be sensed by a sensor through an angle or arc that defines an azimuth or elevation measurement. In another example, mechanical or optical encoders can be used to determine the azimuth and elevation.
In deriving the tracking algorithm, it is assumed that the power unit 100 is mounted on a celestial object that is spinning about its axis and orbiting the sun. The axis may be tilted with respect to the sun. The derivation of the tracking algorithm described herein relies on the equations of motion for such an object (like the earth) to be stable over time; in particular, it is assumed that deviations are negligible over the 20-year life cycle of a solar generator and are much smaller than deviations caused by clock drift.
An analysis of the system's sensitivity to other effects reveals that compensation for the apparent elevation shift at low elevations caused by the atmosphere would need to be considered. However, when power unit 100 is operated only at above 15 degrees elevation, this should not be a concern. If the apparent elevation shift is a concern, it can be modeled based only on elevation. Alternatively, the derivation of the tracking model can avoid using measurements in that region to build the model and the tracking algorithm could constantly optimize at low elevations. Other effects are much smaller than a 0.5-degree elevational tolerance for which the tracking model is designed and need not be considered herein.
The clocks installed on personal computers are not intended to be precision timepieces. It is not unusual for PC clocks to gain or lose up to minutes per day compared to standard time. Manufacturer specifications allow for up to an hour per week of drift. This means that the clock associated with the controller of power unit 100 cannot be relied upon to have a correct rate of time passage. The rates on PC clocks are also reported to vary with time (perhaps due to temperature effects or variations in power level).
The two most common solutions to the clock drift problem each require additional hardware or system complexity. If a computer is connected to a network, time provided by the Network Time Protocol (www.ntp.org) can be used to ensure that the clock of the computer is consistent with the NTP time. This is often used in a hierarchy to reference time back to an atomic clock or some other standard time source. To function precisely, this approach requires a communication channel with low latency and low jitter. The shared-bus serial, mesh-connected EKA radio system proposed for power unit installations does not meet these criteria. It also ties the power unit reliability to the communications mesh reliability, something that may not be desirable in some installations.
The second solution is to install a time source with a direct communication path to each power unit 100. The most appropriate version of this for equipment that sits in locations with clear sky views is probably a GPS radio receiver. We could consider adding to system cost and complexity by including GPS receivers, but relying on GPS receivers will also increase the failure rate of the system. Accurate timing is not required for system functionality in a system that automatically derives its tracking algorithm based on power or sensor feedback. That is, it is not required in order for the tracking system according to the present subject matter to be synchronized with respect to some other time source. Embodiments of the present subject matter can function with a local time source as long as the time between measurable time increments is substantially uniform. Other embodiments of the present subject matter that operate on a time and location-based ephemeris may use a GPS receiver to obtain both time and location data usable for tracking the sun.
In any case, having an accurate clock does not provide the ability to know the sun's location without also knowing the position of the pier on earth and its orientation with respect to the earth's spin axis.
In systems that do not have a time source whose accuracy can be relied upon, knowledge about the exact rotational speed of the earth cannot be effectively utilized. For earth-bound systems, we can certainly reject estimates of this speed that are off by more than a few percent of the expected value, but from the point of view of the computer (with its shifting clock) it will appear as if the sun is moving at an average rate that is slightly different from the actual rate and that this rate varies somewhat over time.
This requires the system to provide speed estimates based on its local clock that can vary somewhat over time, which indicates the use of a moving-average estimator of some sort. If the system is to work without modification on other celestial bodies orbiting stars, the check for the rotation speed being near earth-standard can be removed.
The orientation of the support pier with respect to the earth's spin axis (and one other specified coordinate direction, which could be the axis perpendicular to spin passing through Greenwich) must be known in order to determine the location of the sun. This orientation would have to be known to less than a half-degree tolerance in both directions for the embodiment described here and must not vary over the lifetime of the unit, if absolute location of the sun with regard to the earth's spin axis were used in the tracking algorithm.
Obtaining this information would require either careful placement of the support piers (increasing the labor cost of installation) or careful measurement (requiring either additional components in the system or additional labor cost of installation).
The design presented in this section, which uses the above-mentioned self-derived tracking algorithm, does not rely on such information. That is, one implementation of the present subject matter does not require that the orientation of the support pier of the assembly with respect to the earth's spin axis be known. Instead, this implementation requires only that the orientation of the array be known in a coordinate system local to the array. More particularly, the implementation described in this section requires only that the azimuth and elevation of the array in coordinate system centered about the support pier be known. Azimuth refers to the angle swept by the array in a plane perpendicular to the pier. For example, when looking down on the array, if the array is rotated clockwise or counterclockwise about the support pier, the azimuth will change. Elevation refers to the tilting of the array about an axis orthogonal to the support pier.
From the initial azimuth and elevation in the local coordinate system of the array, the present subject matter automatically develops a tracking algorithm for tracking the position of the sun. Because the tracking algorithm is automatically developed and does not require precise locating of the array with regard to the earth's spin axis, the tracking algorithm according the present subject matter allows arrays to be easily set up in any location and/or moved without requiring manual calibration by a skilled technician.
The automatically derived tracking algorithm is used to control a drive mechanism including at least one motor coupled to the support pier and to a member orthogonal to the support pier. In one implementation, the drive mechanism is fixedly attached to power unit 100 and rotationally attached to the support pier via wheels so that the drive can rotate about the support pier to control azimuth of power unit 100. In this implementation, the drive mechanism is rotationally coupled to the orthogonal member so that the orthogonal member rotates within an aperture defined by the drive to control elevation of power unit 100. An exemplary drive mechanism suitable for use with the subject matter described herein is illustrated in U.S. patent application Ser. No. 12/127,468 filed on May 7, 2008, the disclosure of which is incorporated herein by reference in its entirety.
When three of the following:
In the present implementation that uses the auto-derived tracking algorithm, a precise estimate of the pier orientation is not required. In addition, without a network connection or GPS receiver, power unit 100 has no accurate time estimate, so could not determine any of the other three. It has no intrinsic need for an accurate time measurement (the system is a solar generator rather than a clock), so having an accurate estimate of the position of the tracker on the earth is of no benefit.
The position on the earth of each pier could be known to within sufficient tolerance by storing the location explicitly on each power unit or having it communicated by a cluster controller. However, knowing this without knowing the orientation of the support pier is not useful.
Power unit 100 will operate most effectively when it has an estimate of the sun's location in its local pier-centered coordinate system that is accurate enough to let it to point its reflectors so that they reflect enough light onto its receivers to meet the power specifications of power unit 100. This requires the acquisition and maintenance of a sufficiently accurate local model of the sun's ephemeris.
Each power unit 100 will be capable of independently finding and tracking the sun using its instantaneous power output or other control feedback. In one implementation, each power unit 100 uses power output, i.e., the output of the array that would be fed to a power system in operation, rather than using a separate sensor to locate and track the sun. The use of power output as feedback for locating and tracking the sun eliminates the need for separate sensors to locate and track the sun. In an alternate implementation, each power unit 100 may use a measure of light incident on the collector arrays to track movement of the sun. Incident light may be measured using the same collectors that are used for power generation during operation of the power unit 100 or using separate sensors (perhaps also solar cells) mounted on each end of the collector assembly facing the same direction as the power generation solar cells. Separate solar cells on each end of the collectors can be used to produce a differential signal where the differential signal is the difference in voltage or power output by the separate solar cells mounted on opposite ends of the collectors. Assuming the image of the sun is somewhat symmetric, the sun can be located and tracked by determining and maintaining a differential signal that is zero or near zero. The procedures described herein for model generation and tracking apply (except as indicated below) both to the case where separate sensors or collectors are used and where the power generation collectors are use for sun image acquisition and tracking.
Onboard power unit control software design is divided into intercommunicating processes that manage control of each power unit 100 at two levels of abstraction. The control process constitutes the lowest level and is responsible for direct communication with the motors and power control and measurement unit. The control process is responsible for moving the unit to set points and for executing dedicated modes of operation such as stowing.
A higher-level tracker process (identified as tracking module 114 in
This section describes the procedure that each power unit 100 will use for initial set-up and also to recover from complete power loss, where even the system's Basic Input Output System (BIOS) has failed and it has no record of its location or the time. This procedure could also be used when a power unit 100 fails to locate the sun at a time when other inputs indicate that the sun is up (based on either external sun sensors or reports from other power units within a cluster).
In a system that has absolute encoders to determine its orientation, the limit and hysteresis measurement described below is not required. For example, absolute mechanical, electrical, or optical encoders could be positioned on each power unit 100 to sense the power unit's absolute elevation and azimuth in its pier centered coordinate system when each power unit 100 is powered on. In the alternative, as will be described in detail below, it may be desirable for cost and purposes to omit absolute encoders and instead use a procedure to determine the absolute elevation and azimuth of the system in its pier centered coordinate system. An exemplary procedure for determining azimuth and elevation of a power unit will now be described.
Upon cold boot, the system will initially determine its absolute position in azimuth and elevation using homing routines that rely on triggering of sensors when the unit reaches the end of the range of travel along each axis. If motions have been commanded that would have rotated by twice the available range for the unit without reaching the sensors, the system enters a failure state.
A hysteresis estimation procedure will be run that moves away from the home location until the sensor disengages; the distance traveled before this happens corresponds to one motion tick longer than the hysteresis in the ‘+’ direction. The motor will then travel back towards the stop until the sensor is triggered; the distance traveled before this happens corresponds to one tick less than the hysteresis in the ‘−’ direction. If needed, the hysteresis estimation can be repeated multiple times and can be performed at each end of travel to produce more reliable estimates.
The voltage generated by the unit when it is in daylight, even in the standby orientation, should be distinguishable from the (minimal) power generated at night. If this is not true, then a secondary assumption that an external computer (or a coarse local time measurement) is always able to determine the local time will enable the following procedure to continue. Failing that, the unit can run its initial sun acquisition process every four hours until the sun has been located.
When a cold-booted power unit is requested to begin energy collection, it will run its initial sun acquisition procedure followed by its initial sun-tracking procedure. If the initial sun acquisition procedure fails, it will wait until it is not dark and then repeat the acquisition routine at intervals of 30 minutes until it acquires lock on the sun or it gets dark again.
Assumption: The cylindrical parabolic dishes have a vertical axis of symmetry in the version of the power unit for which this was generated. If they do not, switch azimuth and elevation in many of the following sections and adjust the algorithm as needed.
When commanded to do initial sun acquisition, a power unit 100 will move to the center of its range in azimuth and elevation and then scan the sky using a linear Lissajous pattern that has relatively prime periods in azimuth and elevation such that it covers the entire sky with 4-degree coverage in azimuth (or with sufficient coverage to ensure detection of the sun). (A faster method is available if multiple power units are controlled consistently. Multiple power units could be used, each starting at a uniformly- or randomly spaced location along the Lissajous pattern.) It will scan at its maximum rate of motion, sampling the amount of power being generated at a rate sufficient to detect a peak at the maximum motor speed. If the unit ever reaches a specified fraction (perhaps 1/10th) of the maximum expected power, it will immediately switch to the initial sun-tracking procedure. If not, then the system reports a failure to find the sun and returns to its stow position.
Other acquisition procedures are possible, such as random sky searches or localized searches based on partial knowledge of time and/or orientation.
This mode will be entered when a power unit 100 reaches the specified fraction (perhaps 1/10th) of the maximum expected power (nearly pointed at the sun). This mode keeps the tracker centered on the maximum-power direction over time. The algorithm is designed to operate properly in the presence of variable cloud cover. It does not rely on an estimate of where the sun should be located for a particular time and location (time and location have not yet been determined by the power unit).
Assumption: There will be sufficient power reduction along the axis of symmetry on the graph of output power versus time to determine the sun location to within ⅛th degree. If this is not the case, then (1) the magnitude of the search will be larger along this axis, (2) the frequency of the search will be lower, and (3) a scan-and-fit-function approach will be taken instead of a local maximum estimation. The graph on the left hand side of
The algorithm proceeds serially on the two axes (azimuth and elevation), optimizing first one and then the other. The optimization procedure for one axis consists of reading the current position, ⅛th degree lower, and ⅛th degree higher (or some other appropriate fraction of a degree). The motors are driven to point power unit 100 in these directions and the power output at each is sampled. The maximum position is recorded. (To account for cloud-induced variation, this may be done multiple times. If the same location is the maximum for a majority of trials, it is assumed that the measurement is reliable and has not been corrupted by cloud-cover variation. Continuous cycling continues until three in a row agree or ten minutes has passed. After ten minutes without a consistent reading, the system will re-run the initial sun acquisition procedure and continue acquiring optimal orientations.)
Other optimization routines may be used, such as sweeping at a controlled rate along a longer arc on each axis or adjusting the step size as the optimum is sought.
When the center position on the graph is chosen as the maximum, the system will record that it has found the maximum location along this axis the system will switch to the other axis for optimization. The times and locations of axis maxima are recorded for later use by the model-based sun-tracking procedure, as well as the end-of-day and beginning-of-day estimation procedures.
If differential sensors are used to produce the above-described differential signal, they can be used directly to align the system to the sun without requiring either sweeping or the step-based optimization techniques described above. For example, the sun may be acquired and tracked by controlling azimuth and elevation to maintain a zero or near zero differential signal from sensors mounted on opposing ends of each collector array. The tracking may be used to generate a model in the local coordinate system of power unit 100, as described above. Model-based tracking with periodic optimization as described below may then be used to track apparent movement of the sun.
Once the initial sun-tracking procedure has operated for a specified range (perhaps 10 degrees of motion across the sky) (cloud cover will cause variation in how long this takes), the system will switch to a model-based sun-tracking procedure. The model assumes only that the sun takes a circular trajectory around an axis of rotation during the day, that the elevation of this circle varies less than ½ degree from day to day, and that the apparent elevation varies due to the effect of the atmosphere in a way that can be modeled accurately enough for our tracking needs). The speed of motion is calculated, and is expected to be near 24 hours for earth-mounted power units 100.
The estimated model parameters are: (1) period of repeat (estimated to compensate for CPU clock-speed inaccuracy and slight variation in day length as the earth orbits the sun), (2) peak power generation (varies based on season and condition of the generator), (3) axis of rotation (polar axis in the local coordinate system of power unit 100), (4) altitude of the orbit with respect to the polar axis, (5) change in altitude per day, and optionally (6) sunrise (defined as power crossing 15% of peak), and (7) sunset (defined as power crossing 15% of peak). The change in apparent elevation is expected to be modeled as a fixed function independent of pier-orientation estimate, but could be modeled if needed.
One method of estimating these parameters is as follows: The path of the sun is estimated by fitting a plane to the points swept out by the end of a unit Z axis rotated to point towards the sun at each measurement orientation; the normal to this plane is the polar axis. The average angle between these points and the polar axis provides an estimate of the altitude of the rotation. The angle and time of the initial and final measurements provide estimates for the initial position and speed of rotation. (Other estimation procedures may be used, including the fitting of a constant offset and speed to the various orientation points.) The change in altitude between days is to be estimated each day by subtracting the average altitude for the previous two days. Sunrise and sunset are estimated using the procedure described below. Peak power generation is estimated using the procedure described below.
During model-based tracking, the estimated trajectory of the sun acquired the previous day will be used to drive the system in an open-loop procedure (the stepper motors are used to provide closed-loop motion in azimuth/elevation space, but the sun is tracked open loop). During this time, the two-axis optimization routine described under the initial sun-tracking procedure is to be run less frequently (perhaps once every 15 minutes), as opposed to continuously as was done during initial tracking. The optimal orientations are stored, along with the times at which they occur. If no optimum is found within one minute, the system will go back to open-loop tracking and record a failure to optimize; such failures are not used in the curve fitting.
At the end of the day, these optimal orientations will be used to fit a new curve, which will be used to estimate the inter-day altitude change of the sun and to drive the model the following day. (Optionally, the curve may be updated based on each new measurement; taking into account either all measurements to date or a subset of the measurements that will enable the system to work in the presence of clock drift and changes in pier orientation or power unit configuration.)
If insufficient optimum points are found (perhaps fewer than 20) to fit the curve for five days in a row, or if a power unit does not find the sun when the other inputs reports that it should have, the power unit will re-run the cold-boot procedure.
Once power unit 100 has an estimated sun path, it will proceed open loop to the expected sun location and then run its optimization routine to determine the actual sun location. It re-optimizes and updates its estimate while tracking as described above.
Thus, the tracking algorithm according to the present implementation allows the sun to be accurately located and tracked using the orientation of the array in its local coordinate system and output power measurements or other estimates of optimal orientation. Because the tracking algorithm is developed automatically, arrays can be set up in different locations and/or move without requiring skilled technicians to recalibrate the arrays.
As indicated above, feedback for tracking module 114 may be provided based on power output from the same cells of power unit 100 that produce output power or using separate sensors.
The system illustrated in
In one implementation, a power unit 100 will consist of a set of collectors that are aimed by a pair of Anaheim Automation's (www.anaheimautomation.com) 23MDSI106S model stepping motors controlled by a local, dedicated Technologic System's (www.embeddedarm.com) TS-7250 200 Mhz ARM CPU tracking computer running embedded Linux. This computer will send commands to the two motors using an RS-485 bus and receive reports from them over this same bus. Each motor is a stepper motor to be connected to two limit switches (one at each end of its range of travel). The computer will receive (via a second serial communications connection) power-level reports from a Maximum-Power-Point Tracker (MPPT) unit or current+voltage measurement unit attached the output of the receivers. Each power unit may have a serial or Ethernet connection to an EKA radio transmitter (www.ekasystems.com) that communicates with its control cluster master. The computer, EKA radio, and power-point tracking electronics are to be packaged within NEMA-standard enclosures.
In the example illustrated in
In the example illustrated in
The second component useful in a reflective, concentrating power unit according to an embodiment of the subject matter described herein is an oversized reflector; i.e., a reflector that is greater in lateral dimension than a sensor array 104. This makes the linear image of the sun produced on each array 104 longer than the string of power producing cells, allowing simultaneous illumination of all four sensors 600. If the edge of the reflector is a sharp boundary, the resulting system will produce sensor cell voltages that drop abruptly when misalignments cause the image to move off any pair of sensor cells. By measuring which pair of cells has a lower voltage, the solar tracking software can determine the direction of the pointing correction required. However, for voltages that change very abruptly, the software will not be able to determine the size of the pointing correction to apply.
Although in the example illustrated in
To reduce the rate at which the voltage changes for a fixed pointing error, apodization can be applied to the edge of the reflector which causes the image brightness to drop slowly in a way that depends upon the apodization pattern. This pattern is confined to short enough regions at the reflector edge that power production is not reduced.
The apodization can be effected by taping the edge of the reflector with opaque tedlar tape that has been cut with a pattern. Tedlar tape or other edge treatment is a necessary element of our reflectors to prevent moisture from entering the edge of the reflective surface and oxidizing the metallized layer, so apodization is accomplished via this method with minimal added cost.
In the short dimension of the rectangular image of the sun produced by reflectors 106, no additional reflector treatment is required because the image produced by reflectors 106 is not sharp. Thus, one enhancement associated with reflectors 106 is to provide non-reflective patterns on the longer sides of reflectors 106 to reduce the rate of change in the current output of sensors 600 as the image of the sun appears across a pair of sensors 600 and off of the pair of sensors 600. For example, without any modification, reflectors 106 have straight edges. The resulting image of the sun will also have a straight edge, resulting in a high rate of change in output of a pair of sensors 600 as the image of the sun moves across a sensor pair. In order to reduce this rate of change so that the control system implemented by tracking module 114 can respond appropriately, it may be desirable to include an apodization or smoothing pattern on the longer lateral edges of each reflector 106. In one embodiment, as illustrated in
This section presents an evaluation of the effects of adding apodization tape to the reflector edges. It attempts to determine the optimal spacing for the tape, towards the following goals:
All tests were implemented using a 4-reflector power unit. The tests were performed on two reflectors that have a focal length of about (47.045″). In the tests, the two reflectors were on the same side of the power unit, one below and one above the other.
Two 2¾″ by 48″ pieces of dibond were cut and lines were drawn with about a 16th tolerance with respect to the outside edge of the cell row with a spacing of 45⅛″ from center to center on the line and a second set of lines were drawn to represent the inside edge line of the incident light sensor at a spacing of 46⅝″ from center to on those lines. The tolerance of these targets is as accurate as possible given float in reflow of both cells and sensors.
As seen in
Placement of these targets was by hand approximately centered in the receiver trays. The sun was then centered on the receiver by eye and verified by analysis of the signal and both ends of a reflector. The targets were backed off in depth ¼″ to match the focal location of the sensors. Two smaller white reflectors were added to the outside edges of each of these to collect light spilling past the ends of the targets.
The testing studied two cases: (1) a solid tape edge at ½″ from the reflector edge and (2) a ¾″ serration starting ¼″ from the reflector edge (total tape width of 1″).
This study was done with a band of tape overlapping the last ½″ of the reflector. The reflector was again aligned by eye to place the beam in the center of the receiver, with the tape shadow falling halfway to either side of the line indicating the receiver center.
A close-up view of the resulting light pattern on the left part of the reflector is shown on the left hand side of
A close-up view of the light pattern on the right part of the reflector is shown on the right hand side of
Discussion: The beam is much wider than the incident-light sensors, as expected.
This study was done with a serrated band of tape going from ¼″ to 1″ from each edge of the reflector. The reflector was again aligned by eye to place the beam in the center of the receiver. Only one reflector was outfitted with this tape (the lower reflector).
A close-up view of the resulting light pattern on the left end of the receiver is shown on the left hand side of
A close-up view of the resulting light pattern on the right end of the receiver is shown on the right hand side of
Discussion: The light band before it begins to fall off on the right end of the receiver appears to be about ¼″ to the right of the first useful location (½″ to the right of the optimal, which would place the incident-light sensor on the middle of the downward slope); indicating a desire for a narrower band.
The band appears to fall off at the left end about ¼″ to the left of the optimal location, again indicating a desire for a narrower band. There is an apparent rise in light levels just to the right of this fall off. This will cause a matching pairs of lower values at the present location and again about ½″ to the right of the present location so on a flat signal on the right sensor we would have two local minima to track on that are more than our tolerance apart.
This study indicates that for this reflector, a decrease in width of about ¾″ (increase in total tape width) would be optimal for tracking, placing the incident-light sensors about halfway down the slope on each end.
An initial study with a different reflector on a jig that had more flexation showed that taping with ½″ full coverage followed by ¾″ serration produced a light band that was too wide, and that ¼″ reduction was called for, which would produce an optimal spacing with ¼″ full tape followed by ¾″ serration at each edge.
A subsequent study on the 4-reflector gamma unit showed inconclusively that a ¼″ gap on each side was insufficient to produce sharp slopes on both light sensors, resulting in a recommendation to make the tape wider.
The present study on a second 4-reflector unit indicates that the optimal total tape width in this reflector would be near 2¾″, as compared to the 2″ used in the study; making the tape at each edge 1⅜″ wide, consisting of a ¾″ serration and a ⅝″ solid overlap.
To allow for ¼″ tolerance in tape placement, and the ½-degree misalignment called for in power unit tolerance (translates to another ¼″ offset), we'll need to keep a ½″ gap between the beginning of the light reduction and the outer edge of the last power-receiving cell. In each of the two most-recent studies (where both ends of the reflector were observed for the same incident sun), we were far from this limit. In the original study, there was discrepancy between the expected and seen location that can be explained by improper centering of the signal on the receiver.
The ¾″-serration tape on the reflector edge met both of its goals, but its signal is shifted with respect to its optimal placement. The serrated edge improves the incident-light sensor input without infringing on power production. For incident-light-sensor response, it does the following:
According to another aspect of the subject matter described herein, shielding may be included between adjacent sensor arrays to avoid interference from the reflected image of the sun from one reflector producing multiple sun images and thus multiple maxima that may affect the control of power unit 100.
According to another aspect of the subject matter described herein, a pointing model may be used with any of the methods described above for controlling the orientation of power unit 100 to track apparent movement of the sun. A pointing model suitable for use with the subject matter described herein may model the offset of pier 102 with respect to another coordinate system, such as a coordinate system centered about the axis of the earth or a coordinate system defined by the output of compass and tilt sensor 112. Such a pointing model may be used to map an ephemeris defined in the other coordinate system to the coordinate system of pier 102 or vice versa.
A pointing model can be developed without using iterative nonlinear optimizers which would be a downside because they are subject to local minima, need derivative info, initial guesses, etc. A two-Euler-angle pole tilt is still very accurate even to 5-10 degrees with a small angle approximation. So are the zero point offsets if you subtract the first estimation. This is how telescope pointing models work and remain numerically stable using linear optimization. Telescope pointing models typically correct mechanical defects to make the approximations even more valid, but they also require arc second precision. A percentage uncertainty in reduction ratio can be added to the model without sacrificing linearity. An advantage of modeling the geometrical system is that model parameters are directly meaningful and useful. It gives immediate feedback on how well piers are placed, aligned, calibrated, etc.
A full solar ephemeris is stable and easily testable/verifiable against other sources. It predicts the exact position (to desired any precision) of the sun for a thousand years. The advantage of this approach is that one day of data tells you exactly how to position power unit 100 until a free parameter, such as pier tilt, direction, sensor position, reduction ratio, etc., changes. It is expected that these parameters will remain constant with time, thus validating the models described herein.
A closed-loop mode is needed to gather the data, but just knowing the az/el offset parameters are sufficient local estimators for local tracking. Once the sun has been located once and azimuth and elevation offsets have been measured ignoring the other parameters still enables prediction of the path accurately enough for a few degrees of solar motion. After gathering just one point, tracking can be done through a cloud for 10 minutes. This removes the need for a large baseline of points to fit a plane; predictive capability comes after a single measurement. These linear Cartesian solutions have been validated using a spherical transform in parallel to produce the offset data points.
The following equations illustrate a method for mapping one coordinate system to another using the pointing model. The method described below can be used to map an ephemeris into the coordinate system of power unit 100 or vice-versa.
Define a coordinate transform C->C′ in Cartesian space that consists of a rotation about x (E) of alpha and then a rotation about the subsequent y (N) of beta:
To solve for the magnitude and azimuth of the tilt in C, multiply the vector (0, 0, 1) in the C′ by R inverse:
Transforming from Cartesian to spherical gives:
The measured azimuth and elevation are further offset from the C′ frame by linear encoder zero points such that:
α′=α″+α0
A′=A″+A0
Individually examine the Cartesian components of the transform defined by R:
x′=Cα′SA′=cβx+sβsαy−sβcαz
y′=cαy+sαz
z′=sβx−sαcβy+cβcαz
Expand the primed spherical coordinates using the identities below:
sin (a
±b)=sin(a)cos(b)±cos(A)sin(b)
cos(a±b)=cos(a)cos(b)∓sin(a)sin(b)
For example, x′ can be expanded and approximated as follows:
x′=Cα′SA′=[Cα″Cα
Make small angles for sin(x)˜x and cos(x)˜1, discarding any 2nd order terms:
Ca″SA″+AβCA″Ca″−a0SA″Sa″≅(CASα)−β(Sα)
Reordering terms and recognizing x and x″:
x″=x≅−A0CA″Ca″+a0SA″Sa″=β(Sα)
The same process yields small angle approximations for y″ and z″:
y′=[Ca″Ca
y″−y≅αSα+A0SA″Ca″+a0CA″S2″
z′=[Sa″Ca
z″=z≅−α0Ca″+βCαSA−αCACA
These three approximations can be expressed in matrix notation as:
Every measurement of (A″, a″) will correspond to an ephemeris derived pair (A,a) using time and location information. The free parameters can be solved for using simultaneous linear-least squares:
The matrix entries above denote full matrices corresponding to the ith pair of alt-az measurements. If N measurements are taken, X will be of size (3*N) by 4 and Y will be of size (3*N) by 1.
The best fit coefficient vector can be found in typical fashion for linear-least squares:
α=(XtX)−1XtY
Small angle approximation for the orthogonal rotations is good to the required pointing accuracy for as much as 5-10 degree tilt magnitude. The small-angle approximations for the zero-point offsets can be made arbitrarily accurate by iteratively applying the following technique:
It will be understood that various details of the presently disclosed subject matter may be changed without departing from the scope of the presently disclosed subject matter. Furthermore, the foregoing description is for the purpose of illustration only, and not for the purpose of limitation.
This application claims the benefit of U.S. Provisional Patent Application Ser. No. 60/998,871, filed Oct. 12, 2007; the disclosure of which is incorporated herein by reference in its entirety.
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