NL2013165B1 - Heliostat system and method. - Google Patents
Heliostat system and method. Download PDFInfo
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- NL2013165B1 NL2013165B1 NL2013165A NL2013165A NL2013165B1 NL 2013165 B1 NL2013165 B1 NL 2013165B1 NL 2013165 A NL2013165 A NL 2013165A NL 2013165 A NL2013165 A NL 2013165A NL 2013165 B1 NL2013165 B1 NL 2013165B1
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F24—HEATING; RANGES; VENTILATING
- F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
- F24S30/00—Arrangements for moving or orienting solar heat collector modules
- F24S30/40—Arrangements for moving or orienting solar heat collector modules for rotary movement
- F24S30/45—Arrangements for moving or orienting solar heat collector modules for rotary movement with two rotation axes
- F24S30/452—Vertical primary axis
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F24—HEATING; RANGES; VENTILATING
- F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
- F24S50/00—Arrangements for controlling solar heat collectors
- F24S50/20—Arrangements for controlling solar heat collectors for tracking
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F24—HEATING; RANGES; VENTILATING
- F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
- F24S50/00—Arrangements for controlling solar heat collectors
- F24S50/20—Arrangements for controlling solar heat collectors for tracking
- F24S2050/25—Calibration means; Methods for initial positioning of solar concentrators or solar receivers
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/40—Solar thermal energy, e.g. solar towers
- Y02E10/47—Mountings or tracking
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- Combustion & Propulsion (AREA)
- Mechanical Engineering (AREA)
- General Engineering & Computer Science (AREA)
- Mounting And Adjusting Of Optical Elements (AREA)
Abstract
The present invention relates to a heliostat system and method for reflecting incoming sunlight towards a target. According to the invention, the heliostat comprises a three-dimensional acceleration sensor fixedly attached to the mirror for measuring a direction of the Earth' s gravitational field relative to a coordinate system of the acceleration sensor, an optical sensor and aperture fixedly attached to the mirror, said optical sensor having an optical surface and an optical sensor normal vector arranged perpendicular to the optical surface. The zenith angle of the mirror normal vector is calculated using the measured direction of the Earth' s gravitational field, and the azimuth angle of the mirror normal vector is calculated using the measured direction of the Earth' s gravitational field and a position of a spot of sunlight formed by the aperture on the optical surface.
Description
Heliostat system and method
The present invention relates to a heliostat system and method for reflecting incoming sunlight towards a target.
An example of a known heliostat system is illustrated in figure 1. This heliostat system comprises a plurality of mirrors 1, of which only one is shown, to reflect incoming light from the Sun 2 towards a receiver 3, which is typically mounted in a tower 4. At the receiver, the sunlight is collected and the heat is transformed into other forms of energy, for instance electrical energy.
Actuators (not shown) are used to change the orientation of mirror 1. Here, mirror 1 has at least two degrees of freedom, i.e. rotation via arrow 5 about the zenith axis 6 and rotation via arrow 7 about azimuth axis 8. A heliostat system as defined in the preamble of claim 1 is disclosed in US 2011/0000478A1. This heliostat system employs an optical sensor that is fixedly attached to a mirror to record an image of the Sun during daytime. At night, a calibration run is performed that records the position of the receiver, which is for instance illuminated, for various orientations of the mirror. During daytime, the heliostat system uses this calibration to determine the desired orientation of the mirror to ensure that light is reflected to the receiver. A drawback of the known heliostat system is that it is susceptible to shifts in orientation and position of the heliostat system, and more in particular of the mirrors, as result of temperature changes or changes due to ground settling. The calibration for the known heliostat system, which is typically deployed in a desert, is executed at night when the temperature may be around or below freezing point. However, during daytime, the temperatures may rise in the order of 50 to 70 degrees centigrade. This may result in significant changes in the actual position and/or orientation of the mirror compared to the position and/or orientation during the calibration procedure. Consequently, a large error is obtained in the estimated position of the receiver, thereby reducing the overall efficiency of the system.
Alternatively, the calibration may be performed during daytime. However, during the calibration, the heliostat system of concern is essentially shut off and no power will be contributed at the receiver.
The object of the invention is to provide a heliostat in which the abovementioned problems do not occur or at least to a lesser extent. According to a first aspect, this object is achieved with a heliostat system as defined in claim 1.
According to the invention, the heliostat system comprises a mirror having a mirror normal vector perpendicular to a surface of the mirror or corresponding to an optical axis of the mirror. Within the context of the present invention, a mirror should be interpreted as an element or unit that is configured to reflect incoming sunlight. The mirror may have a flat surface in which case the normal vector is perpendicular to any part of the surface. Alternatively, the mirror may have a concave or other shape. In this case, the mirror normal vector coincides with the optical axis.
The heliostat system further comprises an actuator unit for changing the orientation of the mirror. The actuator unit may comprise one or more actuators corresponding to mechanical degrees of freedom. For instance, the actuator unit may comprise a first actuator to control the elevation of the mirror, i.e. the rotation about a horizontal axis of the mirror, a second actuator to control the rotation of the mirror about an axis parallel to the earth axis, and a third actuator to control the rotation of the mirror about a vertical axis. In most applications, the first and third actuators are the most important.
The heliostat system further comprises a position determination unit that comprises a Sun position determination unit for determining a position of the Sun. The position of the Sun may be expressed as an azimuth angle and a zenith angle.
Figure 2 illustrates a definition of the zenith angle and azimuth angle. Here, an observer standing on the Earth’s surface observes a star 9, such as the Sun, as being above a horizon 10. An observer is assumed to be at a center 11 of a sphere 12, wherein star 9 is positioned at the outer surface 13 of sphere 12. A vertical line 14 extending from center 11, opposite the gravitational force at center 11, intersect outer surface 13 of sphere 12 at the zenith 15. Horizon 10 is a curve on outer surface 13 which bounds a surface 16 that is perpendicular to vertical line 14. A point “N” can be identified that corresponds to the geographic north..
The zenith angle, indicated by arrow 17, can now be defined as the angle between vertical line 14 and a line 18 from center 11 to star 9. The position of star 9 may be projected on horizon 10 along a line 19 from zenith 15 through the position of star 9 towards horizon 10. In this case, the azimuth angle may be defined as the angle, indicated by arrow 20, between a line from center 11 to “N” and a line 21 from center 11 to projection 22 of the position of star 9.
The position determination unit further comprises an azimuth angle calculation unit for calculating an azimuth angle of the mirror normal vector, and a zenith angle calculation unit for calculating a zenith angle of the mirror normal vector.
The zenith angle of the mirror normal vector can be defined as the zenith angle corresponding to a fictional star being pointed at by the mirror normal vector when this vector is arranged at the center of the sphere in figure 1. An azimuth angle can be identified in a similar manner.
The heliostat system further comprises a difference calculation unit to calculate a difference between a desired and calculated azimuth and zenith angle of the mirror normal vector based on the determined position of the Sun and the position of the target. The position of the target, e.g. the receiver, is predetermined. Typically, the receiver is mounted in a stationary manner. On the other hand, the position of the Sun may be calculated a priori or it may be determined at the position of the mirror. This allows a desired orientation of the mirror, expressed as azimuth angle and zenith angle, to be calculated such that incoming sunlight is reflected to the target.
According to the invention, the heliostat system further comprises a controller for controlling the actuator unit in dependence of the calculated difference. The controller can be based on a feedback control system wherein the difference between the actual orientation of the mirror and the desired orientation is taken as an error signal to drive the actuator unit.
The invention is characterized in that the heliostat further comprises a three-dimensional acceleration sensor fixedly attached to the mirror for measuring a direction of the Earth’s gravitational field relative to a coordinate system of the acceleration sensor, and an optical sensor and aperture fixedly attached to the mirror, wherein the optical sensor has an optical surface and an optical sensor normal vector arranged perpendicular to the optical surface. Furthermore, the zenith angle calculation unit is configured to calculate the zenith angle using the measured direction of the Earth’s gravitational field, and the azimuth angle calculation unit is configured to calculate the azimuth angle using the measured direction of the Earth’s gravitational field and a position of a spot of sunlight formed by the aperture on the optical surface.
Compared to the known heliostat system, the position and orientation of the mirror are not determined using a calibration at the operation location. Instead, the position and orientation are determined during operation using incoming sunlight and a measurement of the Earth’s gravitational field. Any changes in orientation and position due to external causes, such as ground displacements, temperature changes, etc. can be accounted for in real-time. The down-time of the heliostat system can therefore be minimized.
The heliostat may further comprise a memory for holding a first calibration, wherein the first calibration comprises a representation of the mirror normal vector in the coordinate system of the acceleration sensor, wherein the zenith angle calculation unit is configured to determine the zenith angle based on the representation of the mirror normal vector and the measured direction of the Earth’s gravitational field.
The first calibration can be constructed by first arranging the mirror such that the mirror normal vector is horizontal with respect to the Earth’s gravitational field. Then, a first vector measurement of the Earth’s gravitational field is performed using the acceleration sensor. Subsequently, the mirror is rotated about its mirror normal vector such that a different orientation of the mirror is obtained. Then, a second vector measurement of the Earth’s gravitational field is performed using the acceleration sensor. Finally, the representation of the mirror normal vector can be determined based on a vector product of the first and second vector measurements.
Alternatively, the first calibration can be constructed by arranging the mirror such that the mirror normal vector is parallel with respect to the Earth’s gravitational field, and to subsequently perform a vector measurement of the Earth’s gravitational field using the acceleration sensor.
Then, the representation of the mirror normal vector can be based on this vector measurement.
The mirror normal vector can be arranged vertically or horizontally by using a light source that is arranged to emit a ray of light vertically or horizontally, respectively, and to ensure that the light reflected by the mirror follows the same path.
The azimuth angle calculation unit is preferably configured to determine the azimuth angle of the mirror normal vector using an azimuth angle corresponding to the determined Sun position and a calculated difference between an azimuth angle of the mirror normal vector and the azimuth angle corresponding to the determined Sun position, wherein the azimuth angle calculation unit is configured to calculate said difference using a spot of sunlight generated by the aperture on the optical surface.
The optical sensor may be configured to determine, relative to a coordinate system of the optical sensor, a first position of the Sun using a spot of sunlight generated by the aperture on the optical surface, a second position on the optical surface corresponding to light that would have been transmitted towards the optical sensor if a source of light would have been arranged on a line corresponding to the mirror normal vector, and a third position on the optical surface corresponding to light that would have been transmitted towards the optical sensor if a source of light would have been arranged on a line corresponding to the optical sensor normal vector. Furthermore, the memory may further comprise a second calibration comprising a representation of a horizontal edge vector of the optical surface in the coordinate system of the acceleration sensor, a representation of the optical sensor normal vector in the coordinate system of the acceleration sensor, and a value for a distance between the aperture and the optical surface. The azimuth angle calculation unit may be configured to determine the azimuth angle of the mirror normal vector based on the first, second, and third position, and said first and second calibration.
The second calibration may have been constructed using the steps of aligning the optical sensor normal vector horizontally with respect to the Earth’s gravitational field, performing a third vector measurement of the Earth’s gravitational field using the acceleration sensor, rotating the optical sensor about the optical sensor normal vector such that a different orientation of the optical sensor is obtained, performing a fourth vector measurement of the Earth’s gravitational field using the acceleration sensor, and determining the representation of the optical sensor normal vector based on a vector product of the third and fourth vector measurements. Arranging the optical sensor normal vector horizontally may comprise fixedly connecting the aperture to the assembly of the acceleration sensor and the optical sensor, if not connected, providing a light source that emits light on a horizontal path with respect to the Earth’s gravitational field towards the optical sensor, and orienting the optical sensor such that light reflected by the optical sensor follows the horizontal path backwards.
Alternatively, the second calibration may have been constructed using the steps of aligning the optical sensor normal vector vertically with respect to the Earth’s gravitational field, performing a vector measurement of the Earth’s gravitational field using the acceleration sensor, and determining the representation of the optical sensor normal vector based on this vector measurement.
The optical sensor normal vector can be arranged vertically or horizontally by using a light source that is arranged to emit a ray of light vertically or horizontally, respectively, and to ensure that the light reflected by the optical sensor follows the same path.
The second calibration may have been constructed using the steps of arranging the horizontal edge vector of the optical surface horizontally with respect to the Earth’s gravitational field, performing a fifth vector measurement of the Earth’s gravitational field using the acceleration sensor, rotating the optical surface about the horizontal edge vector such that a different orientation of the optical sensor is obtained, performing a sixth vector measurement of the Earth’s gravitational field using the acceleration sensor, and determining the representation of the horizontal edge vector of the optical surface based on a vector product of the fifth and sixth measurement. Arranging the horizontal edge vector of the optical surface horizontally may in turn comprise fixedly connecting the aperture to the assembly of the acceleration sensor and the optical sensor, if not yet connected, providing at least two light sources which are arranged horizontally with respect to the Earth’s gravitational field, recording spots of light generated by the aperture on the optical surface corresponding to the at least two light sources, and orienting the optical sensor such that the spots of light are positioned on a line parallel to the horizontal edge vector.
The second calibration may have been constructed using the further steps of fixedly connecting the aperture to the assembly of the acceleration sensor and the optical sensor, if not connected, arranging a light source on a line corresponding to the optical sensor normal vector and measuring a fourth position of a spot of light on the optical surface generated by that light source using the aperture, arranging a light source on a known position not on the line corresponding to the optical sensor normal vector and measuring a fifth position of a spot of light on the optical surface generated by that light source using the aperture, and calculating the distance between the optical surface and the aperture based on a difference between the fourth and fifth position and the known position.
The azimuth angle calculation unit may further be configured to correct the first, second, and third position for a difference between the actual orientation of the optical surface and an orientation of the optical surface in which the horizontal edge vector is horizontal with respect to Earth’s gravitational field using the second calibration and the measurement of the Earth’s gravitational field. More in particular, the azimuth angle calculation unit may be configured to shift the coordinate system of the optical sensor such that the third position is at the origin of the shifted coordinate system and to rotate the shifted coordinate system around the origin of the shifted coordinate system by an angle between the horizontal edge vector and a vector product of the measured Earth’s gravitational field and the optical sensor normal vector, wherein the corrected first, second, and third positions correspond to the first, second, and third positions in the rotated shifted coordinate system of the optical sensor, respectively. The azimuth angle calculation unit may further be configured to determine the azimuth angle using the distance between the aperture and the optical surface, the corrected first position, and a distance between the corrected first position and the corrected second position along a line on the optical surface through the origin and corresponding to a line horizontal with respect to Earth’s gravitational field.
The Sun position determination unit may be configured to determine the position of the Sun using the corrected first, second, and third position, and the first and second calibration. More in particular, the Sun position determination unit may be configured to determine a first vector expressed in the coordinate system of the acceleration sensor, said first vector having a first component in a direction corresponding to a vector product of the optical sensor normal vector and the horizontal edge vector, and a second component corresponding to the horizontal edge vector, wherein the length of the first component corresponds to the vertical component of the corrected first position and wherein the length of the second component corresponds to the horizontal component of the corrected first position, said Sun position determination unit being further configured to add the first vector to the optical sensor normal vector to find a vector indicating a direction towards the Sun in the coordinate system of the acceleration sensor, wherein the Sun position determination unit is configured to determine a zenith angle corresponding to the position of the Sun using the scalar product of the vector indicating the direction towards the Sun and the measured Earth’s gravitational field and to determine an azimuth angle corresponding to the position of the Sun using astronomic models or ephemerids.
The Sun position determination unit may further be configured to determine the position of the Sun using astronomic models or ephemerids. Consequently, the zenith angle corresponding to the position of the Sun may be determined in two different ways.
The heliostat may further comprise a three dimensional magnetic sensor, fixedly attached to the mirror, and configured to measure a direction of the Earth’s magnetic field, wherein the azimuth angle calculation unit is configured to determine the azimuth angle using the measured direction of the Earth’s magnetic field. In this case, the azimuth angle calculation unit may be configured to calculate a first horizontal projection of the measured direction of the Earth’s magnetic field with respect to the Earth’s gravitational field, calculate a second horizontal projection of the mirror normal vector with respect to the Earth’s gravitational field, and calculate the azimuthal angle using a difference in angle between the first and second horizontal projections and using the local value of the magnetic declination.
The controller may be configured to determine whether or not the sunlight is obstructed from reaching the optical sensor, and, if the sunlight is not obstructed, to use the sunlight to determine the azimuth angle of the mirror normal vector as described above, and to, if the sunlight is obstructed, use the magnetic sensor to determine the azimuth angle of the mirror normal vector as described above.
According to a second aspect, the present invention provides a method for reflecting incoming sunlight towards a target. This method comprises the steps of providing a mirror having a mirror normal vector perpendicular to a surface of the mirror or corresponding to an optical axis of the mirror, determining a position of the Sun, calculating an azimuth angle of the mirror normal vector, calculating a zenith angle of the mirror normal vector, calculating a difference between a desired and calculated azimuth and zenith angle of the mirror normal vector based on the determined position of the Sun and the position of the target, and controlling an orientation of the mirror in dependence of the calculated difference. The method is characterized by measuring a direction of the Earth’s gravitational field using a three-dimensional acceleration sensor fixedly attached to the mirror relative to a coordinate system of the acceleration sensor, providing an optical sensor and aperture fixedly attached to the mirror, said optical sensor having an optical surface and an optical sensor normal vector arranged perpendicular to the optical surface, wherein said calculating the zenith angle comprises calculating the zenith angle using the measured direction of the Earth’s gravitational field, and wherein said calculating the azimuth angle comprises calculating the azimuth angle using the measured direction of the Earth’s gravitational field and a position of a spot of sunlight formed by the aperture on the optical surface.
The method may further comprise holding a first calibration in a memory, said first calibration comprising a representation of the mirror normal vector in the coordinate system of the acceleration sensor, the method further comprising determining the zenith angle based on the representation of the mirror normal vector and the measured direction of the Earth’s gravitational field.
The method may even further comprise determining the azimuth angle of the mirror normal vector using an azimuth angle corresponding to the determined Sun position and a calculated difference between an azimuth angle of the mirror normal vector and the azimuth angle corresponding to the determined Sun position, said difference being calculated using a spot of sunlight generated by the aperture on the optical surface.
The method may still further comprise determining, relative to a coordinate system of the optical sensor, a first position of the Sun using a spot of sunlight generated by the aperture on the optical surface, a second position on the optical surface corresponding to light that would have been transmitted towards the optical sensor if a source of light would have been arranged on a line corresponding to the mirror normal vector, a third position on the optical surface corresponding to light that would have been transmitted towards the optical sensor if a source of light would have been arranged on a line corresponding to the optical sensor normal vector. The method may still further comprise holding a second calibration in said memory comprising a representation of a horizontal edge vector of the optical surface in the coordinate system of the acceleration sensor, a representation of the optical sensor normal vector in the coordinate system of the acceleration sensor, and a value for a distance between the aperture and the optical surface, and determining the azimuth angle of the mirror normal vector based on the first, second, and third position, and said first and second calibration.
Next, the invention will be described referring to the appended drawings, wherein:
Figure 1 illustrates an example of a known heliostat system;
Figure 2 illustrates definitions of the zenith and azimuth angles;
Figure 3 illustrates an embodiment of the heliostat system in accordance with the present invention;
Figure 4 depicts a general work flow of the heliostat system of figure 3;
Figure 5 illustrates the arrangement of the optical sensor and the mirror of the heliostat in figure 3;
Figure 6 shows how an angle between a cross-section of a horizontal surface and optical surface of the optical sensor of the heliostat in figure 3 can be compared to the horizontal edge vector;
Figure 7 shows the direction towards the sun and the direction of the normal of the sensor for the heliostat in figure 3;
Figure 8 visualises the coordinates of three points N, S and Ns and the rotated coordinate system on the optical surface of the optical sensor in the heliostat in figure 3;
Figures 9 and 10 illustrate different views of the vectors N, S and Ns with respect to the optical surface of the optical sensor in the heliostat in figure 3; and
Figure 11 illustrates a method in accordance with the present invention.
Figure 3 illustrates an embodiment of heliostat system 100 in accordance with the present invention. System 100 comprises a position determination unit 101, which comprises a Sun position determination unit 102, a zenith angle calculation unit 103, and an azimuth angle calculating unit 104. The output of position determination unit 101 is fed to a difference calculating unit 105, which calculates a difference between the actual and a desired orientation of mirror 108. This difference is fed to a controller 106, which drives an actuation unit 107 to change the orientation of mirror 108. At least during operation, an acceleration sensor 109, an optical sensor 110, and optionally a magnetic sensor 111 are fixedly attached to mirror 108.
Heliostat system 100 is one of a plurality of heliostat systems used in overall system as depicted in figure 1. Receiver 3 is configured for collecting and converting solar energy in what may be called a solar power plant that may be thermal or electric depending on the type of receiver. Heliostat system 100 is configured to ensure that mirror 108 tracks the Sun during the course of the day and reflects the incident light to receiver 3 where it may be converted to heat or electricity.
Mirror 108, actuators of actuator unit 107, and a support structure for changing the orientation of mirror 108 may be referred to as a heliostat. According to the invention, each heliostat comprises acceleration sensor 109, optical sensor 110 and, optionally, a magnetic sensor 111.
Throughout the day the orientation of each mirror 108 is periodically adjusted about two or three degrees of freedom to obtain the required orientation accuracy for continually reflecting the light onto receiver 3. The two axes may be the azimuth angle in the horizontal plane and the zenith angle in the vertical plane, as depicted in figure 1. Alternative schemes of freedom can be an axis turning around an axis parallel to the earth axis and a tilt angle that can adapt to the angle between the Sun direction and the Earth axis. The present invention is not limited to one particular scheme.
The heliostat is one out of many heliostats distributed in the area around tower 2 that supports receiver 3. Receiver 3 contains a system that can do useful activities based on the collected heat, like a water-steam boiler, a molten salt system, a heat engine, one or more photovoltaic cells, a biomass cooker, a water purification system, a syngas generation system or any combinations thereof.
Now referring to figure 4, which illustrates a general work-flow of heliostat system 100, the sun-tracking operation is controlled by controller 106 that calculates, in step S3, the current direction of the sun in terms of azimuth angle and zenith angle, see figure 2. The input for that calculation is the current time and the geographic position of the heliostat, determined in steps S1 and S2, respectively. The formulas used are derived from ephemerids or astronomic models. An alternative approach is that at the location of the heliostat a measurement system is measuring the actual azimuth and zenith angles corresponding to the observed sun position and communicates these angles to each heliostat or to the total group of heliostats. In this case, the position of the Sun is not determined by measurement but is calculated a priori.
In step S4, the position of receiver 3, expressed in zenith and azimuth angles with respect to the mirror position are calculated. The position of receiver 3 is fixed during operation.
In step S5, position determination unit 101 determines the required direction for the mirror normal vector, hereinafter referred to as the normal of the mirror, of the heliostat mirror after obtaining the position of the sun. The required direction of the normal of the mirror of the heliostat is obtained as the vector in the direction found by adding the unit vectors in the direction of the sun and the unit vector in the direction of receiver 3. For a curved mirror, such as a parabolic or concave mirror, the normal of the mirror should correspond to the optical axis direction.
In step S6, the zenith and azimuth angle of the normal of the mirror are calculated. This allows the difference calculation unit 105 to calculate a deviation in both the zenith and azimuth angles in step S7. Thus, having calculated the required vector orientation of the heliostat mirror, the controller is programmed, in step S8, to control the actuator unit such that the measured orientation of mirror 108 equals the calculated required orientation of mirror 108.
Hereinafter, an approach to measure the actual orientation of the mirror is described. The measurement of the orientation can be based on measuring the zenith angle and azimuth angle of the normal of the mirror. The zenith angle of the mirror (MZA) can be measured by using an acceleration sensor or a spirit level and an encoder. This however does not tell which line on a cone is the direction of the normal of the mirror. It is necessary to also measure the azimuth angle of the normal of the mirror (MA), which can be realised by determining the magnetic orientation using a compass sensor or an optical sensor looking at a fixed reference in combination with an encoder or an optical sensor looking at the sun. A method to calibrate the direction of the normal of the mirror in coordinate system of the acceleration sensor is described hereafter.
The data that a 3D acceleration sensor may provide are x, y and z values of the measured acceleration. If such a sensor is stationary at the earth surface, it still is subject to the acceleration caused by Earth’s gravitational field. Each set of x, y and z values can mathematically be represented by a vector in the coordinate system of the acceleration sensor. The coordinate system of the acceleration sensor is preferably a right-hand rotational orthogonal coordinate system.
Simple transformations are possible to make it satisfy this preference, would it not be the case. The acceleration sensor will provide the orientation of the gravitational acceleration, which lies on a line between centre 11 and zenith 15 in figure 2.
The objective is to measure the zenith angle of the mirror normal vector. So also the direction of the normal of the mirror is required. During a one-time calibration procedure the orientation of the normal of the mirror in the coordinate system of the 3D acceleration sensor is determined and this data is stored, preferably in a non-volatile memory of the zenith angle calculating unit. One way to find the direction of the normal is by placing the normal of the mirror horizontal. A first example of the calibration method makes use of the properties of the vector product of two vectors. As the sensor is rigidly attached to the heliostat mirror the direction of the normal of the mirror can be represented by a vector (having x, y and z values) in the coordinate system of the 3D sensor. For a flat mirror the normal of the mirror is in the same direction at any spot on the mirror. The direction of the normal of the mirror can be represented as a vector that has its origin at the origin of the coordinate system of the 3D acceleration sensor. If a focussed mirror is used, the surface is not flat and the normal of the mirror is in the direction of the optical axis and typically the direction normal to the surface of the mirror is in that direction at only one point of the mirror. Also in this case the direction can be represented by a vector having its origin at the origin of the coordinate system of the 3D acceleration sensor.
In the first example of the calibration, light is sent to the mirror via a horizontal path and it is tested that the reflected light follows the same path backwards. So during the calibration the normal of the mirror is horizontal. The mirror including the acceleration sensor can still be rotated around an axis that is parallel to the normal of the mirror. So measurements of the x, y and z values of the vertical acceleration for two or more positions of the mirror can be obtained. As for each set of x, y and z values the normal of the mirror is kept horizontal the sets of x, y and z values of each measurement represent accelerations that are perpendicular to the normal of the mirror, as the gravitational acceleration is by definition vertical.
Next, take two sets V1 and V2 of x, y and z values such that the mirror was turned anticlockwise as viewed in the direction of the normal. When turning anticlockwise the acceleration measured in the coordinate system of the 3D acceleration sensor will be turning clockwise. The sensor rotates including its coordinate system, while the measured gravitational acceleration does not change in the outside world.
Then, calculating the vector product of the two sets of measurement values, by vector multiplying the first measurement V1 and the second measurement V2, renders a new set of x, y and z values that represent a vector in the direction of the normal of the mirror.
According to the right hand rule, the vector product results in a vector that is perpendicular to the first two vectors and has a direction equal to the direction of the normal of the mirror if going from the first vector to the second vector requires rotating clockwise within the coordinate system. So after this procedure and calculation, it is possible to store a representation of the normal of the mirror in the coordinate system of the acceleration sensor.
Having this information, the angle between the normal of the mirror (N) and the direction of the gravitational acceleration can be determined. As both are vectors in the coordinate system of the acceleration sensor, finding the angle between those two vectors is a matter of calculating the scalar product of the two vectors. By dividing both vectors by their length, both become unit vectors. Their length is 1, so the result equals the cosine of the angle to be measured.
The useful zenith angles are always between 0 and 90 degrees, so this calculation is sufficient to find the mirror normal vector zenith angle. The zenith angle is known by means of the above measurement, but still it is required to measure the mirror normal vector azimuth angle too.
As a second example, a representation of the mirror normal vector in the coordinate system of the acceleration sensor can be obtained by arranging the mirror normal vector vertically and using the output of the acceleration as a representation of the vector. A light source configured to transmit light along a vertical path may be used during the calibration.
The mirror normal vector azimuth angle can be measured by measuring the magnetic orientation of the mirror normal. The earth magnetic field is not exactly pointing from north to south, and the deviation is called magnetic variation or magnetic declination. The magnetic declination depends on time and location and the value can be obtained from scientific institutes, so when this is stored in memory this correction is possible A 3D magnetic sensor, which is rigidly attached to the heliostat mirror and sharing the coordinate system of the acceleration sensor can provide magnetic measurements of the Earth’s magnetic field, that renders information about the azimuth angle. The azimuth angle is found as the angle between the horizontal component Mh of the magnetic vector M representing the measured direction of the magnetic field and the horizontal component Nh of the direction of the normal of the mirror represented by normal vector of the mirror N, wherein characters in bold refer to vectors. The horizontal components follow by subtracting the vertical components of those vectors from their corresponding vector.
The vertical components are obtained by calculating the scalar product of the vectors N or M with the unit vector in the direction of the acceleration vector g. The unit vector in the direction of the acceleration needs to be multiplied with the resulting value to obtain a vector in the correct direction that has the correct length. This way the calculation to find the two horizontal vectors can be noted as Mh=M-g-(M-g) and Nh=N-g-(N-g). The cosine of the angle between these two vectors is obtained by again determining the scalar product between the two vectors:
Mh-Nh=l Mh I I Nh I cos(mirror normal vector azimuth angle + magnetic declination)
This is however not sufficient as there are multiple angles that have the same result for the cosine. Thus the sine of the same angle is needed too. The vector product of the two vectors will reveal that value. The size of the vector product is:
Mh x Nh =1 Mh I I Nh I sin(mirror normal vector azimuth angle + magnetic declination)
Therefore the value of the cosine and the absolute value of the sine of the angle are known. The vector product has a direction that can be compared to the acceleration vector. The scalar product (Mh x Nh)-g is positive if both vectors are in the same direction, else negative. This information indicates if the sine of the angle resulted from turning clockwise or anticlockwise when viewed upward. The value of sine, cosine and the rotation direction can be combined to find the correct angle. One last correction has to be done to find the true azimuth of the normal of the mirror. The magnetic declination has to be subtracted.
The result of the calculations above is the true value of the azimuth angle for the mirror normal vector. Therefore the controller can drive the actuators to match the required values of the zenith and azimuth angles. As result the heliostats mirror can adapt to the sun position and deliver the reflected sunlight on spot without influence of installation deviations.
Unfortunately, the field strength of the Earth’s magnetic field is rather small. The measurements therefore include a significant contribution of noise due to the method of measuring. This may result in a variation of the measured azimuth angle that is of the same or larger magnitude than the size of the required accuracy. Also the metal parts of the support construction of the heliostat should not have any magnetic field associated with them. One can think of using a gyroscope as an alternative, but these today have price levels that do not result in an affordable design for the application described. So, for at least some applications, an alternative for determining the azimuth angle is desired. Such alternative can be found by utilizing optical information that can be used to determine the difference in azimuth angle between the direction of the sun and the direction of the normal of the mirror.
To use the alternative method for determining the azimuth angle of the mirror normal, the heliostat’s configuration is enhanced with a 2-dimensional optical sensor 120 in combination with a small aperture 121, see figure 5. Both are rigidly attached to mirror 108 or otherwise having a fixed orientation with respect to mirror 108 of the heliostat. The distance of aperture 121 to the optical surface of optical sensor 120 is chosen in a way to obtain a wide angle view.
Optical sensor 120 further comprises a distance holder 122 that simultaneously functions as a dark chamber. Distance holder 122 places optical surface 123 of optical sensor 120 at a distance ks from aperture 121. Mirror 108 may comprise a glass layer 130 covered on one side by a reflective surface 131.
In the notation of directions and light spot positions that follow hereafter bold font notations refer to a direction (a vector in the 3D coordinate system of the acceleration sensor). Regular font notations refer to a position of a light spot on the optical surface of the optical sensor (two dimensional vectors in the different 2D coordinate system of the optical sensor).
The light of the sun creates a bright area on optical surface 123. The average location of the bright elements is calculated and this results in a 2-dimensional position of the centre of the suns projection through the aperture. That position is noted as a horizontal or x value and a vertical or y value (S in figure 5). The x direction will later be referred to as the sensor horizontal axis Ha. These values can be regarded as the horizontal and vertical position of the centre of the image spot in the coordinate system of the 2D optical sensor. From this optical position of the projection of the sun the difference between azimuth of the sun and the azimuth of the mirror normal can be derived. A series of one-time calibrations need to be executed, before the optical information can be used to measure the azimuth difference of the sun and the mirror. The directions and positions of the normal to the optical sensor, the sensor horizontal axis and the normal of the mirror are needed for the measurement operation.
The first calibration step is executed with an assembly of the optical sensor together with the acceleration sensor that is not yet attached to the aperture and also not yet attached to the mirror. The first calibration step is aimed to get the direction of the normal to the optical surface of the optical sensor in the coordinate system of the acceleration sensor. This direction is perpendicular to the optical surface of the 2D optical sensor. This direction is noted as Ns and the projection of this direction through the aperture is noted as Ns, see figure 5. Ns is determined by projecting a light source horizontally onto optical surface 123 and making sure the reflected light is following the same path backwards. The direction Ns is horizontal during the calibration as a consequence. The assembly of the optical sensor and the acceleration sensor can still be rotated around the normal to the optical surface of the 2D optical sensor. So it is possible to collect the x, y and z data for the acceleration measurements for two orientations of the assembly, where the second position was obtained by turning the assembly anti-clockwise starting from the first position. After calculating the vector product of the two measurements the vector in the direction Ns is obtained.
Alternatively, optical surface 123 can be arranged vertically using a source of light as described above in conjunction with the calibration of the mirror normal vector. Then, the output of the gravitational sensor can be used as a representation of the optical sensor normal vector in the coordinate system of the gravitational sensor.
For the next calibrations the aperture is attached to the assembly too. It is mechanically made sure that the alignment of the assembly and the light source is the same as during the calibration of Ns. The coordinates on the optical surface of the direction Ns follow from the light spot that is projected through the aperture on the surface of the optical sensor. Ns is available now as its coordinates are at the centre of that light spot. The direction Ns can be used to determine information about the zenith angle of the optical surface.
It is also necessary to have information about the rotation of the optical surface around an axis parallel to its normal. The direction of the sensor horizontal axis (Ha) has to be calibrated in the coordinate system of the acceleration sensor to be able to get information about the rotation around the normal. To this purpose a second light source is placed horizontally in relation to the first light source and at a known distance to the first light source and to the aperture. In this situation both light sources and the aperture are at the same horizontal level in the earth coordinate system and the three distances are exactly known and Ns is still perpendicular to the surface of the optical sensor. Because the distances are known also the viewing angle between the two light sources is known. This allows the distance between optical surface 123 and aperture 121 to be computed, see figure 5.
Next, the orientation of the assembly of the optical sensor, aperture and acceleration sensor is manipulated such that the positions of the light spots that are projected on optical surface 123 have the same vertical coordinate. This way the projected direction from one light source to the other is essentially parallel to the sensor horizontal axis of the optical sensor. It should be noted that the sensor horizontal axis is represented by the horizontal edge vector discussed previously. As such, both terms will be used interchangeably. At the same time the light sources are at the same horizontal level. So the manipulation has made the sensor horizontal axis of the optical sensor parallel to the horizontal surface of the earth. Now the x, y and z values of the acceleration sensor can be measured. It is still possible to rotate the assembly around the sensor horizontal axis. The vertical coordinate of both projected light spots will move up or down, but the vertical position of each spot will be equal to the other. By rotating the assembly anticlockwise viewed in the direction of the sensor horizontal axis a second set of x, y and z values can be measured with the acceleration sensor. After calculating the vector product of the first measurement and the second measurement, a new set of x, y and z values is obtained that represents the direction of the sensor horizontal axis of the optical sensor in the coordinate system of the acceleration sensor. This direction is further referred to as the direction of the sensor horizontal axis Ha.
The total assembly is then attached to the mirror to calibrate the mirror normal vector as described above, but the calibration now also includes the optical measurement of the centre of a projected light spot. As mentioned above, the direction N of the normal of the mirror is obtained in the coordinate system of the acceleration sensor. In addition, the position of the light spot caused by the projection of a light source arranged in the direction of the normal of the mirror through the aperture is measured using the optical sensor. This location is further on noted as N.
The main purpose of the optical sensor is to accurately determine the azimuth angle difference of the direction to the sun and the horizontal direction of the normal of the mirror. The optical sensor only provides the 2D coordinates of the light spot that is projected through aperture 121. The position of the projection of the sun can be compared to the projection of the normal of the mirror that was obtained during the calibration procedure. If two requirements would be met, the horizontal difference of the two light spot positions is a direct measure of the azimuth difference. This requires that the surface of the optical sensor is parallel to the reflective surface of the mirror and that the sensor horizontal axis of the optical sensor is horizontal with respect to Earth’s gravitational field. These requirements may not always be met.
The sensor horizontal axis Ha is only accurately horizontal in the earth coordinate system during operation of the heliostat if extreme care would be taken. It is an object of the invention to avoid extreme care for installation and construction of the heliostat. So the sensor horizontal axis of the optical sensor will be at an angle with the horizontal plane. And the optical sensor may not be exactly parallel tot the surface of the mirror either. The already described calibration procedure has given the information that makes it possible to handle these deviations. The properties measured during the calibration procedure make it possible to correct for the non-horizontal arrangement of optical surface 123. A rotation of optical sensor 120 around the normal to its surface will create an angle between a horizontal line and the sensor horizontal axis of the optical sensor.
Figure 6 shows how an angle Θ between a cross-section 140 of a horizontal surface 141 and optical surface 123 of the sensor 120 can be compared to the direction of the sensor horizontal axis Ha of optical sensor 120.
It is allowed to translate vectors representing the directions to any point in the coordinate system. This is because only the directions are of interest, not the 3D locations. For simplicity the origin of the 3D acceleration sensor coincides with reference point Ns in the plane of the 2D acceleration sensor. Next, it is useful to make the point Ns the origin of the 2D coordinate system by subtracting the coordinate values of Ns from the coordinates of any other point of the 2D coordinate system. The direction of the real horizontal axis Hr is found as the vector product of two vectors. That direction must be horizontal, so it must be perpendicular to the unit vector in the direction of the gravitational acceleration g. It must also be in optical surface 123 of optical sensor 120, so it must be perpendicular to the normal of the optical sensor Ns. So according figure 6, Hr lies in the direction of vector product Ns x g.
Next, the angle between Hr and Ha can be found with the help of the scalar product between those two vectors. This angle is denoted as Θ, allowing the transformation of the found x and y positions of the geometric centre of any image spot into the corrected values x’ and y’ to be expressed as x’=xcos(0)-ysin(0) and y’=xsin(0)+ycos(0).
This transformation will be required for any point on the optical surface. This includes N and S, while Ns is at the origin after subtracting the coordinates of Ns from any of the other coordinates.
Light sources that have the same zenith angle will project light spots that are on a conic section on the surface of the optical sensor. Light sources that share the same azimuth value will project light spots that are on one vertical line in the rotated coordinate system. This can be seen in figure 7.
Figure 7 shows the direction towards the sun S, and the direction of the normal of the sensor Ns. The remainder of the drawing shows a polar coordinate system around the observation point (i.e. the centre of aperture 121), which acts as the origin of the coordinate system, oriented towards the surface of the earth on the location of the observation. A circle 150 on the horizontal plane through the observation point represents the collection of all directions that share a zenith angle of 90 degrees and the plane of that circle contains all azimuth directions. A circle 151 drawn at the height of the sun represents the cross-section of a cone that includes all directions that share the same zenith angle seen from the observation point as the sun and a sphere 152 around the observation point.
Plane 153 shows a flat surface that contains a line 154 in the direction of the sun and a line 155 in the direction of the optical sensor normal vector. Such a plane projects as a line onto optical surface 123 of optical sensor 120. However, circle 151 will not project as a line onto optical surface 123, but as a cone section. If the objective is to find the difference between the zenith-angle of the sun and the zenith angle of the mirror normal vector, it is necessary to take in account the curved shape of the projection of directions having equal zenith angle. Directions that have different zenith angle, but which share the same azimuth are essentially in plane 153 that goes through the observation point. Thus the collection of these directions projects as a line onto optical surface 123. It is therefore possible to calculate the azimuth difference between the direction of the normal of the sensor and the direction towards the sun by comparing projections on a horizontal line through the normal of the sensor. This statement is also valid for comparing the azimuth direction of the normal of the mirror to the azimuth direction of the normal to the sensor. It is therefore allowed to calculate the azimuth difference of the direction of the normal of the mirror to the direction of the sun in the optical projection, by observing the distances after projection onto a horizontal line through the projection point of the normal to the sensor.
Figure 8 visualises the coordinates of the three points N, S and Ns and the rotated coordinate system on optical surface 123. As the objective is to measure the difference in the azimuth angle it is possible to project the spots of interest on the real horizontal axis. The length of the projection of the azimuth difference is found between the transformed horizontal position of the mirror normal spot N and the transformed horizontal position of the sunspot S. It is possible to observe only the horizontal differences of the projections on the real horizontal axis. The new spots are simply obtained by only using the horizontal coordinate of the transformed position.
Figure 8 shows the points N’, S’ and Ns on the real horizontal axis 160. N’ and S’ are the projections of N and S to the real horizontal axis. In this example N’ is between S’ and Ns. The azimuth angle difference β between S and Ns follows from the distance between S’ and Ns on the real horizontal axis, see figure 9. The same is true for the azimuth difference δ between N and Ns, which follows from the distance between N’ and Ns. Because in this example N’ and S’ are on the same side of Ns, the azimuth difference between the direction to the sun and the direction of the normal of the mirror is the difference of the two angles found. If the two points are on opposite side the two angles have to be added.
The optically measured angle is an accurate difference of the azimuth angle of the sun and the azimuth angle of the normal of the mirror. The azimuth of the normal of the mirror is obtained by adding the azimuth of the sun, calculated from the ephemeris, to the azimuth difference angle found. Now an accurate azimuth position of the mirror is obtained.
It is possible to obtain information about the zenith angle of the sun by means of the optical measurement. This information is useful if at certain atmospheric conditions the observed position of the sun at large zenith angles is actually higher above the horizon than the calculated position of the sun, due to bending of light in the atmosphere. The actual observed zenith position of the sun can be used instead of the calculated zenith position of the sun, in case at large zenith angles there is a significant difference between the value that is calculated from ephemeris and the value that is measured by the system.
The combination of the optical measurement with the gravitational measurement that results in the observed zenith angle is shown in figure 10.
In figure 10, the directions Hr, Ha, g, N and Ns are all known 3 dimensional vectors in the coordinate system of the acceleration sensor. The only vector that has a relation to the coordinate system on the earth surface that uses azimuth and zenith angle is the vector g. That direction points towards the zenith. The acceleration sensor can only measure this reference direction. The projected spots Ns, N and S are all 2D positions on optical surface 123. The distance between the centre of the aperture A and the surface of the optical sensor ks was measured during the calibration process. The calibration process made that the direction Ns is perpendicular to the surface of the optical sensor. The calibration process made that the direction N is perpendicular to the surface of the mirror, or if the mirror is not flat this direction coincides to the optical axis of the mirror. The question to be answered is how the projected spot of the sun can be used to find the measured direction to the sun in the coordinate system of the acceleration sensor.
The triangle with sides k, ks and d exists in the optical system as well as in the acceleration system. With all the previous calculations the size of the vectors was only used when a vector was split up in a part that was parallel to the vertical acceleration and a part that was horizontal. The only property of concern has been the direction of those vectors. To answer the question about the direction of the vector S the length of the vectors Ns and N is relevant. That length is relevant for the ratio between the vector lengths. The length can be made equal to the factor ks and k by multiplying unity size vectors in the direction of these vectors with the factor k and ks. The directions are still original, but the difference of the two vectors represents a vector that is parallel to the line d on the surface of the optical sensor and that has the same length. This trick now makes it possible to use the direction and length of the line b on the optical surface of the sensor as a vector that can be added to the vector Ns to obtain the vector S. The rotated 2D coordinate system just gives the length of the vertical and horizontal components of the line b having Hr as the horizontal reference direction. The vertical component is perpendicular to Hr but is also in the plane of the optical surface, so it is perpendicular to Hr and Ns. A vector of length 1 in that direction can be obtained from the vector product of the two mentioned vectors. The horizontal component is parallel to Hr. Only a vector of size 1 in that direction is required for the next step.
It is possible to find the direction of a vector representing the direction and length of line b by adding vectors of the size of the vertical and horizontal coordinates of the transformed spot of S that are in the directions just described. This is possible by multiplying vectors of length 1 in those directions with the vertical and horizontal coordinate value of the spot in the 2D coordinate system.
After this is done the resulting vector is the sum of the two components. In turn this vector can be added to the vector Ns that was given the size of ks.
This results in the vector S as depicted in figure 5. The procedure made sure that the sizes of the vectors used matched the configuration indicated in figure 10. The direction of the vector S is now available in the coordinate system of the acceleration sensor. As a consequence it is possible to find the angle between the acceleration vector g and the vector S. The angle that can be calculated from the scalar product of the two vectors is the zenith angle of the direction towards the sun. This angle can be used for compensation of the atmospheric conditions.
The optical measurement will work only when the vision of the sun is not obstructed. This is the normal application of the heliostat. In case the vision to the sun is obstructed the heliostat cannot reflect sunlight to the receiver, so there is a relaxation of the accuracy requirements. It is still required to maintain the correct position, should the obstruction disappear (a cloud e.g.)
When an obstacle is covering the view of the sun the actual true north orientation and the actual zenith position of the mirror normal can be obtained from the acceleration sensor and the magnetic sensor. The method according this invention includes a decision on characteristics of the projected image of the sun to act as if the sun view is with or without obstruction. The characteristics that can be used are the size and the shape of the projected image as well as the brightness of the projected image. The measurement of the mirror orientation is the result of the magnetic and gravitation measurement or is the result of the gravitation measurement and the optical measurement, depending on the decision about the obstructed view of the sun.
The orientation requirements for a heliostat today are stringent. Obtaining the required low statistical variation of the measured orientation is possible by averaging a lot of gravitational measurements, while averaging is inherently done when calculating the geometric centre point of the projected image of the sun. The statistical variance of the calculated averages can be within the required accuracy limits.
The described calculations can be executed by a microcontroller that is part of the controller that is realizing the sun tracking operation. An advantage of the described approach is that this results in a closed loop system for maintaining a predefined angle to the sun’s direction that is calculated each time for a new position of the sun. As this acts as a closed loop system, it will automatically mitigate small deviations in the mechanical parts, thus enable cheap drive mechanics for the actuators and allowing a simple installation process, thereby reducing upfront investment for the power plant. The method will further reliably compensate for changes in orientation of the support due to settling of the soil in the underground. Typically, each heliostat can be powered from photovoltaic cells and the commands can be sent wirelessly to the heliostats.
The position determination unit and controller can be arranged as a single unit, possibly remote from the mirror. In an embodiment, the mirror, the actuation unit, the optical sensor, the gravitational sensor, and the magnetic sensor (if applicable), are deployed as a single heliostat unit. The controller and the position determination unit can be arranged in a server remote from the heliostat unit. This allows a plurality of heliostat units to be served using the same controller and position determination unit.
Figure 11 illustrates a method in accordance with the present invention. It assumes that a mirror is provided that has a mirror normal vector perpendicular to a surface of the mirror or corresponding to an optical axis of the mirror. Furthermore, an optical sensor and aperture are provided that are fixedly attached to the mirror, said optical sensor having an optical surface and an optical sensor normal vector arranged perpendicular to the optical surface.
In step S100, a position of the Sun is determined. In step S101, a direction of the Earth’s gravitational field is measured using a three-dimensional acceleration sensor fixedly attached to the mirror relative to a coordinate system of the acceleration sensor. In step SI02, the zenith angle is calculated using the measured direction of the Earth’s gravitational field. In step S103, a position of a spot of sunlight formed by the aperture on the optical surface is determined. This allows the azimuth angle to be calculated in step S104 using the measured direction of the Earth’s gravitational field and the position of the spot of sunlight. A difference between a desired and calculated azimuth and zenith angle of the mirror normal vector based on the determined position of the Sun and the position of the target is calculated in step SI05. Finally, an orientation of the mirror is controlled in step S106 in dependence of the calculated difference.
It should be obvious to the skilled person in the art that various modifications can be made to the embodiments discussed above without departing from the scope of the present invention which is defined in the appended claims.
Claims (25)
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| NL2013165A NL2013165B1 (en) | 2014-07-10 | 2014-07-10 | Heliostat system and method. |
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| US20110000478A1 (en) | 2009-07-02 | 2011-01-06 | Dan Reznik | Camera-based heliostat tracking controller |
| US9231141B2 (en) * | 2012-12-14 | 2016-01-05 | International Business Machines Corporation | Controlling a solar tracking system |
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