Solar Thermal Plant Design and Operational Suite of Tools



Solar Thermal Plant Design and Operational Suite of Tools

Final Report

Version

Faculty Advisor

Dr. Kwok-Bun Yue

Mentor

Dr. Michel Izygon

Team Members

Lakshmi Javvadi Yoguita

Sasya Kodali

Sukumar Bollineni

Deepa Borra

Acknowledgement

We are thankful to our instructor Dr. Kwok Bun Yue and mentor Dr. Michel Izygon for providing us their valuable guidance and encouragement in bringing out this project successfully.

We would like to thank the previous capstone (Team#5 Spring-07) for providing required information.

We are thankful to Ms. Abeysekera Krishani and Mr. Henning Seljenes for providing us with the resources required for our project.

We would also like to thank all the people who helped us in this project and whom we might not have mentioned here.

Table of Contents

1. Abstract………………………………………………………………………....4

2. Introduction……………………………………………………………………..4

3. Requirements of the project

3.1 Functional Requirements……………………….………….……………….6

3.2 User requirements……………………………………….………………….7

4. Required Technologies…..……………………………………….……………..8

5.Design and Implementation of the Solutiion

5.1 Design of an algorithm for Sharing and blocking…………….……….....9

5.2 Flow Chart Diagram………………………………………….…….…...13

5.3 System Architecture Diagram……….…………………………..……....15

5.4 Use Case Diagram……………………………………………...….……16

5.5 Implementation issues…………………………………………….….…16

6 Evaluation of solution

6.1 Solution to the problem……………………………………………..…....17

6.2 Design of solution………………………..…………………………........18

6.3 Functionality of the solution…………………………………………......18

6.4 Performance of Solution prototype…………………………………....…18

7. Lessons learnt…………………………………………………………………..18

8. Future enhancements……………………………………………………….…..19

9. Tasks we have completed…………………………………………………....…20

10. Comparison of other solutions………………………………………………...21

11. Screen Shorts………………………………………………………………….21

12. Conclusion……………….……………………………………………………26

13. References……………………..……………………………………………..27

Appendix - A

A.1. Glossary ………………………………………………….………………….27

A.2. Project Management

A.2.1 Time line of our project………………….……………………………...28

A.2.2 Team information……………………………………………………….28

Appendix - B

B.1. Downloaded Technologies…………………………….…………………..…29

B.2. Project Code……………………………………………… ………………....29

B.3. Read Me…………………………….…………………..…………………….20

Appendix - C

C.1 Classes developed……………………………………………………………..31

C.2 Algorithm……………………………………………………………………...32

1. Abstract:

A solar thermal plant uses various methods to generate electricity by using the energy from the sun. They use a field of thousands of movable mirrors called heliostats to reflect the sun rays onto a receiver located at the top of a tower. This energy is collected in the receiver and is then converted into electricity.

Our Project is an extension of the work done by the previous batch in last semester. They developed an application that calculates the Altitude, Azimuth, Normal of the sun and the Sun’s vector based on longitude and latitude of the plant location, time of day, position of heliostats and receiver.

Our aim is to improve the user interface of the previous capstone project and to add functionalities that will be helpful for solar plant designers. Heliostats suffer losses caused by shading and blocking by neighboring heliostats. Shading occurs at low sun angles when a heliostat casts its shadow on another heliostat located behind it and blocking occurs when a heliostat in front of another heliostat blocks the reflected suns energy on its way to the receiver. Our main task is to find the shading and blocking occurring between the heliostats. We consider heliostats are placed around the central mirror in a radial stagger way. By varying the distances between them i.e. radial spacing (ΔR) and the azimuthal spacing (ΔAz) we will find the shading and blocking.

2. Introduction:

Solar Thermal power plants are generating electricity from the energy of the sun. They generate heat by using lenses and reflectors to concentrate the sun's energy. This heat will be stored in the receiver and generate power whenever it is needed. They use a field of thousands of movable mirrors called heliostats to reflect the sun rays onto a receiver located at the top of a tower. This reflected sunlight is then converted into electricity.

The purpose of this project is to develop a set of software tools that will help the plant designers as well as operators to compute the optimal values for design factors of solar thermal power plants. The previous capstone batch computed the sun angle, optimal angles and position of the mirrors so that maximum energy is reflected towards the receiver.

A field of heliostats suffers losses caused by shading and blocking by neighboring heliostats. Shading occurs at low sun angles when a heliostat casts its shadow on another heliostat located behind it and blocking occurs when a heliostat in front of another heliostat blocks the reflected suns energy on its way to the receiver (Fig-1 illustrates the concept of shading and blocking losses).

We considered the values of the cell as heliostat values in the grid of the solar plant field to calculate the heliostat co-ordinates. Once we get the co-ordinates in heliostat co-ordinate system we have to change those to absolute co-ordinate systems assuming that the tower is placed at the origin. To find the shading and blocking we have to project the heliostat coordinates on to the plane of other heliostat with respect to the sun’s direction and calculate the intersection area. Once we find shading & blocking for a particular distance between the heliostats, we vary the distances between the heliostats and calculate the shading and blocking

[pic]

Fig-1: Shading and blocking losses

3. Requirements of the Project:

3.1 Functional Requirements:

1. To compute the shading between the central mirror and the neighbor mirror we need to follow few steps and these are listed below.

Steps to find the shading:

a) Find the equation of the plane of the mirror.

b) Find the absolute co-ordinates of center mirror and the surrounding eight mirrors, given the points in the heliostat co-ordinate system.

c) Project the points of the neighbor mirror (target mirror) on to the center mirror (source mirror) considering the sun’s vector.

d) Find the area of intersection between projected plane and the source mirror which results in shading.

2. Once we compute shading, the same steps will be used to compute blocking, but we will consider the direction of the reflected sun’s ray towards the receiver instead of the sun vector.

3. We compute the shading and blocking loss occurred by the neighboring mirrors on to the source mirror which are placed in a radial stagger way.

Fig-2: Radial Stagger

3.2 User Requirements:

It mainly focuses on the performance and the satisfaction of the user with the system. The user interface of the previous batch has navigated the data into several pages which is not user-friendly. Our application is an enhancement of the previous work and it is more like a professional web application.

We integrated all the pages into a single page and also we have populated the default values of the grid to make naive user more comfortable. The latitude and longitude of the plant are automatically populated when the user selects a particular location from the dropdown list and the user have an option to enter the latitude and longitude values of a new location and that will be dynamically stored in the database.

In our application, we find the losses due to shading and blocking between heliostats in the solar plant field. The application should be able to take the inputs and write computed values for the data into a text file.

4. Required Technologies:

We used Java 1.6, Java Servlets, JSP and Java 3D utilities. With the new features of Java 1.6 it is incredibly easy to add scripting capabilities to your programs. By using JavaScript we do not have to recompile our application every time we change something. We enhanced the user interface by changing the CSS styles and JavaScript code. By using JavaScript, We have provided strict input validation and added additional features like displaying calendar, today’s date etc. We used servlets and JSP which are powerful to develop dynamic web pages. We used JavaBeans for reusability. As you know, JavaBeans create reusable, platform-independent components. Also we used Java3D utilities like rayPlane and Clip to find shading and blocking. Java 3D is an interface that encapsulates the graphics programming using a real, object oriented concept.

5. Design and implementation of the solution:

5.1 Design of an algorithm for Shading and Blocking:

Inputs:

Mirror length – HL

Mirror width - HW

Mirror Position (Xm, Ym)

Azimuthal - Ө, Altitude- Ø

Sun’s vector (Xs, Ys, Zs)

Mirror Normal (Xn, Yn, Zn)

Algorithm:

1. For each mirror print Xm,Ym values

2. Print central mirror position Xm,Ym,Zm (Assuming Zm=0)

3. Print central mirror normal Xn,Yn,Zn

4. Calculate mirror co-ordinates in Heliostat co-ordinate system

[pic]

A (-HL/2,-HW/2, 0)

B (+HL/2,-HW/2, 0)

C (+HL/2, +HW/2, 0)

D (-HL/2, +HW/2, 0)

5. Calculate Central Mirror in absolute co-ordinate system:

For each point A, B, C, D, We need 2 rotations and 1 translation; For (X, Y, Z)

Ø rotation: (Elevation i.e. Altitude)

[pic]

Ө rotation: (Azimuthal)

[pic]

Translation:

[pic]

(XF, YF, ZF) are values driven with respect to each point A,B,C or D in absolute co-ordinate system.

6. Compute mirror co-ordinates in absolute co-ordinate system

A: XA YA ZA

B: XB YB ZB

C: XC YC ZC

D: XD YD ZD

7. Compute neighboring mirror absolute co-ordinates:

ΔR= 2*Diagonal

ΔA=1.5*Diagonal

Diagonal=√H²+W²

[pic]

Mirror-1 Co-ordinates:

A: (XA+ ΔA, YA, ZA)

B: (XB+ ΔA, YB, ZB)

C: (Xc+ ΔA, Yc, Zc)

D: (XD+ ΔA, YD, ZD)

Mirror-2 Co-ordinates:

A: (XA- ΔA, YA, ZA)

B: (XB- ΔA, YB, ZB)

C: (XC- ΔA, Yc, Zc)

D: (XD- ΔA, YD, ZD)

In the same way, we will calculate the co-ordinates for the rest of the mirrors. You can see the appendix for remaining mirror co-ordinates.

8. For each mirror, find the projections of mirror on to the center mirror plane. This can be done using the rayPlane utility offered by Java3D.

9. Find the intersection area of the central mirror and the projected plane, which is nothing but shading/blocking using the Clip function.

5.2 Flow Chart Diagram:

Select the heliostat

from the grid

if

Intersection No

Yes

Yes

No

Vary Yes

ΔR

No

Vary Yes

ΔAz

No

Radial spacing (ΔR) – The radius of the circular rings in the field is determined by the radial spacing (ΔR).

Azimuthal spacing (ΔAz) – The distance between the centers of two mirrors in a particular circular ring is determined by ΔAz .

5.3 System Architecture:

We followed 3-tier architecture. Our application contains 3 tiers such as presentation tier, business tier, and database tier. The presentation tier mainly concerns with presentation logic implemented by servlets and jsp. Business tier contains JavaBeans components contains business logic. Database tier contains data stored in MSAccess database.

Several users can use the system at the same time. The clients send the request to jsp/servlets. The jsp/servlet then requests JavaBeans to process the request. The JavaBeans gives the response to the jsp/servlets which is sent back to the client. The results are stored into the database.

[pic]

5.4 Use case diagram:

The user is a solar thermal plant designer. Here the user will generate the grid by entering the values of the heliostat and the grid size. Once the grid is generated, shading will be computed by taking the values of solar vector, altitude, azimuth and the normal of the mirror. Once the shading is computed the user can view the results.

[pic]

5.5 Implementation Issues:

We have faced few problems while implementing our application.

1. We were not able to start the server with the j3d jars as they are linked with some .dll files.

2. With the current environment setup we couldn’t run any applets on our web browser, although we were able to view our applets in the net beans viewer. We were getting exception in the server logs.

3. No real time testing can be done. Never had a chance to see the actual field or use any other related tools.

4. While using the Clip function for getting the shading and blocking values we observed that it takes only x and y values while we had z value too, we had trouble in converting from 3-dimensional to 2-dimensional so as we found the z values very less and negligible, we neglected the z value in the Clip utility.

5. We could not get sufficient help on Java 3D from the books and internet.

6. We had no ways to test Java3d libraries to check whether they were right or wrong and so we couldn’t test if the values are coming out right.

6. Evaluation of Solution:

6.1 Solution to the problem:

Our task is to find the shading and blocking between the mirrors which are placed around the central mirror and also to improve the user interface. We also need to find the location of the mirrors in radial stagger way. Once we find the shading & blocking occurred by the mirror then we have to implement it for the other neighboring mirrors and also we have to find the position of the mirrors by varying the distances between them.

6.2 Design of the solution:

We have divided our entire project into three steps namely:

1) User Interface Component

2) Arranging the mirrors in radial stagger way.

3) Compute Shading and Blocking

This division makes it very easy to maintain and enhance the code. It also enhances the flexibility in usage of the system even for the naïve users. In the third step (i.e.) for computing shading and blocking we divided the task into five steps for our convenience.

6.3 Functionality of the solution

The basic functionality of this project is to compute the projection and intersection areas between the mirrors by varying the distances between them.

6.4 Performance of the solution prototype

Our prototype has successfully been used to demonstrate the shading and blocking occurred due to sun’s vector in solar thermal plant and the future enhancement of our project is to optimize shading and blocking.

7. Lessons Learnt:

1. Importance of Research: As we are new to solar energy thermal plants, getting to know them in detail required a lot of research. We had done lot of research on mathematical formulas to compute shading and blocking. We understood how important it is to thoroughly research the topics on which we have no definitive idea before trying to implement them.

2. Time Management: Another important lesson we have learnt is the importance of time management. Meeting the various deadlines was challenging and gave us a valuable experience to complete the work on time.

3. Team Work: We also understood the importance of team work. Working together as a team with different people is very challenging and reaching a consensus might be tough in certain situations.

4. Gained valuable experience: We gained good knowledge and experience working on this project. We got thorough knowledge about the technologies like JSP, Servlets and JavaBeans by working on this project. Also we have learnt a new technology JAVA 3D.

8. Future Enhancements:

1. Assuming different geometrical shapes: We assumed the heliostats to be in a rectangular shape. The future work will be implementing for different geometrical shapes like concave and convex.

2. Mirrors in circular manner: Now we have considered that all the mirrors are parallel to each other in a grid in the future work we can considering the mirrors in a circular manner.

3. Minimizing shading and blocking: By varying the values of radial spacing and azimuthal spacing the losses caused due to the shading and blocking can be optimized.

9. Tasks we have completed:

1. Improved the User interface of the previous capstone project.

2. Populating the longitude and latitude of the selected location and also dynamically storing the longitude and latitude of new location which is entered by the user.

3. Finding the equation of the plane of source mirror.

4. Finding the coordinates of the source mirror in heliostat coordinate system

5. Converting the coordinates into absolute coordinate system.

6. Finding the coordinates of the neighboring mirrors in the absolute coordinate system.

7. Finding the Java3D utilities that helped in calculating shading and blocking.

8. Computed the projections of the neighboring mirror corners with respect to sun vector on to the central mirror plane.

9. Computed the intersection area of the source mirror and the projected plane.

10. Calculated the shading and blocking losses due to the neighboring mirrors on the central mirror which is the source mirror.

11. The distances between the central mirror and the neighboring mirrors can be changed.

12. The shading/blocking losses can be observed after changing the distances between them.

10. Comparison with other solutions:

We do not have any solution which could be used towards checking the correctness of our solution. We designed an algorithm for working towards our solution and we verified the correctness of our algorithm with help of our mentor and we implemented Java 3D utilities. We tested the Java 3D utilities to be working fine with the example values and then implemented them with our application. The solution we have got can be optimized by placing the heliostats in circular fields and considering the angle of placements of the heliostats with respect to the tower.

11. Screen Shots:

Step 1:

This is the home page where the users have an option to select a particular location and get the latitude and longitude values. We also have an option to add a new location, if the user does not find his desired location in the dropdown list. These values which are entered by the user are dynamically stored in the database.

[pic]

Step 2:

In the second step, the current date of the day will be displayed and in addition to this the user can also select the date, time and the interval.

[pic]

Step 3:

The user can enter the grid information and the heliostat (i.e.) the mirror information. Here the user can see the grid design and the position of the tower based on the information given by the user.

[pic]

We have populated the default values of the grid to make naïve user more comfortable

[pic]

Step 4:

By selecting the heliostat ID from the dropdown list, we can get the values of the altitude, azimuth, and normal.

[pic]

Step 5:

In this step the mirrors are arranged in a radial stagger way. When the mouse is hovered on any of the mirrors then the four co-ordinates of the mirror are shown.

[pic]

Step 6:

Here the user can see the shading and blocking occurred between the mirrors based on the sun’s vector.

[pic]

12. Conclusion:

We have developed professional web application for solar thermal plant designers which allows them to check how the placement of the heliostats in a solar plant field would result in the losses like shading and blocking and they have an option to change the distances between the heliostat and check the losses with the new positions. We have improved the UI of the previous capstone. Our current work enables to compute the absolute coordinates of the mirror and we are going to find the shading and blocking.

13. References:

The following references have been used in order to understand the underlying technologies used in developing this prototype.

1.

2.

3.

4.

5.

6.

Appendix A:

A.1. Glossary:

|Term |Definition |

|Heliostat |Movable mirrors that are used in the solar energy plants. |

|Grid |Pattern of mirrors represented in rows and columns |

|Azimuth |Azimuth is the angle, usually measured in degrees, between a reference plane and a point. |

|Altitude |The angular distance of a object above the horizon |

|Flux |The rate of flow of fluid, particles, or energy through a given surface. In your case, no |

| |fluid or particles. |

|Shading |Shading occurs at low sun angles when a heliostat casts its shadow on a heliostat located |

| |behind it. |

|Blocking |Blocking occurs when a heliostat in front of another heliostat blocks the reflected flux on |

| |its way to the receiver. |

|Angle of Elevation |It is the elevation angle of the sun, i.e. the angle between the direction of the sun and the|

| |horizon. |

A.2. Project Management:

A.2.1 Time Line of Our Project:

A.2.2 Team Information:

Lakshmi Yogitha Javvadi (Team Leader) – Coordinated team meetings and assigned tasks.Involved in research, design, coding, website maintenance and documentation.

Sasya Kodali – Involved in research, design, coding, debugging, website maintenance and documentation.

Sukumar Bollineni – Involved in research, design, coding, debugging, website maintenance and documentation.

Deepa Borra – Involved in research, coding, developing, testing, website Maintenance, and documentation.

Appendix B

B.1. Downloaded Technologies:

The following are the links provided to download the required technologies for free of cost:

1. Java jdk 1.6 from java.

2. Net Beans IDE 5.5 from

3. Java 3D from

B.2. Project code:

We have provided the project code on our project team website:



B.3. Read Me:

Step 1> Install the necessary applications:

Installing Net beans 5.5.1

Download it from .

1. Once you have downloaded the installer file, double-click the installer's icon to launch the installer.

2. In the install wizard, respond to the License Agreement, then click Next.

3. Specify an empty directory within which to install the IDE.

Note: This Net Beans IDE will not disrupt the settings of your other Net Beans installations because the IDE automatically creates a new user directory when launched (${HOME}/.netbeans/5.5.1).

4. On the same page of the wizard, specify an empty directory within which to install the Application Server and click Next.

5. Choose the JDK you want the IDE to use from the list of suitable choices in the list, and then click next.

6. Verify that the installation location is correct and that you have adequate space on your system for the installation.

7. Click Next to begin the installation.

You also need to download Net Beans 5.5.1 Visual Web pack to make use of upload package of java. You can download it from

Installing java3d

Download java3d from



Step 2 > To run the project:

1. Start the NetBeans5.5.1

2. Go to file(Open Project. Browse and select the project.

3. Press on f6 to run the project.

4. The application opens up in internet explorer browser by default.

5. The user/plant designers can fill in the values as follows:

5.1> Select the location from dropdown list or add new location

5.2> Enter the information required for date and time

5.3> Click on ‘Generate Grid’ and enter the grid information

5.4> Click on ‘Calculate’ and see the sun’s vector, altitude, azimuth and normal

5.5> Select the heliostat and get the shading and blocking values

5.6> Increment ∆R/∆A and observe new shading and blocking values

5.7> Observe the values written into text file

Note: We have two project folders, solarTower and uploadFile. Make sure you have both the project folder open in order to run the project and choose solarTower as the main project.

Appendix C:

C.1 Classes developed:

Java Class files to work with user interface and Calculation:

➢ Inputs.Java: The input file is just to initialize the user inputs.

➢ refazmalt.Java: This file calculates the reflectors altitude and azimuth.

➢ calculateServlet.Java: This is the main class file from where all the other class files are called. This will call different classes to compute the azimuth, Altitude and normal of the sun and the receiver.

➢ calculateAltAzm.Java: This java class file calculates Altitude and Azimuth of the Sun.

➢ doCalculateWith.Java: This class file calculates the Julian date. It calls another class file called Vect.Java which does the calculation of 2 vectors.

➢ helioData.Java: It holds the information of heliostats like helioId, x, y, z etc.

➢ Grid.java: This file computes the grid and writes the grid x and grid y to the file outputgrid.txt.

➢ Vect.Java: All the vector related computations are done year like calculating sun vector, finding normal, converting to vector

➢ J3DIntersectionUtils.java: This file calculates the intersection area using the co-ordinates, sun vector and normal.

➢ Index.jsp: This JSP file will upload the text file onto the server which can be later converted into XML and stored in the eXist database.

➢ gridCalculate.jsp: This calculates the grid size based on the values entered by the user.

c.2 Detailed algorithm for Shading and Blocking:

Inputs:

Mirror length – HL

Mirror width - HW

Mirror Position (Xm, Ym)

Azimuthal - Ө

Altitude- Ø

Sun’s vector (Xs, Ys, Zs)

Mirror Normal (Xn, Yn, Zn)

Algorithm:

1. For each mirror print Xm,Ym values

2. Print central mirror position Xm,Ym,Zm (Assuming Zm=0)

3. Print central mirror normal Xn,Yn,Zn

4. Calculate mirror co-ordinates in Heliostat co-ordinate system

A (-HL/2,-HW/2, 0)

B (+HL/2,-HW/2, 0)

C (+HL/2, +HW/2, 0)

D (-HL/2, +HW/2, 0)

5. Calculate Central Mirror in absolute co-ordinate system:

For each point A, B, C, D, We need 2 rotations and 1 translation; For (X, Y, Z)

Ø rotation: (Elevation i.e. Altitude)

[pic]

Ө rotation: (Azimuthal)

[pic]

Translation:

[pic]

(XF, YF, ZF) are values driven with respect to each point A,B,C or D in absolute co-ordinate system.

6. Compute mirror co-ordinates in absolute co-ordinate system

A: XA YA ZA

B: XB YB ZB

C: XC YC ZC

D: XD YD ZD

7. Compute neighboring mirror absolute co-ordinates:

ΔR= 2*Diagonal

ΔA=1.5*Diagonal

Diagonal=√H²+W²

[pic]

Mirror-1 Co-ordinates:

A: (XA+ ΔA, YA, ZA)

B: (XB+ ΔA, YB, ZB)

C: (Xc+ ΔA, Yc, Zc)

D: (XD+ ΔA, YD, ZD)

Mirror-2 Co-ordinates:

A: (XA- ΔA, YA, ZA)

B: (XB- ΔA, YB, ZB)

C: (XC- ΔA, Yc, Zc)

D: (XD- ΔA, YD, ZD)

Mirror-3 Co-ordinates:

A: (XA+1/2 ΔA, YA -ΔR, ZA)

B: (XB+1/2 ΔA, YB-ΔR, ZB)

C: (Xc+1/2 ΔA, Yc-ΔR, Zc)

D: (XD+1/2ΔA, YD-ΔR, ZD)

Mirror-4 Co-ordinates:

A: (XA-1/2 ΔA, YA -ΔR, ZA)

B: (XB-1/2 ΔA, YB-ΔR, ZB)

C: (Xc-1/2 ΔA, Yc-ΔR, Zc)

D: (XD-1/2ΔA, YD-ΔR, ZD)

Mirror-5 Co-ordinates:

A: (XA+1/2 ΔA, YA +ΔR, ZA)

B: (XB+1/2 ΔA, YB+ΔR, ZB)

C: (Xc+1/2 ΔA, Yc+ΔR, Zc)

D: (XD+1/2ΔA, YD+ΔR, ZD)

Mirror-6 Co-ordinates:

A: (XA-1/2 ΔA, YA +ΔR, ZA)

B: (XB-1/2 ΔA, YB+ΔR, ZB)

C: (Xc-1/2 ΔA, Yc+ΔR, Zc)

D: (XD-1/2ΔA, YD+ΔR, ZD)

Mirror-7 Co-ordinates:

A: (XA, YA -2ΔR, ZA)

B: (XB, YB-2ΔR, ZB)

C: (XC, Yc-2ΔR, Zc)

D: (XD, YD-2ΔR, ZD)

Mirror-8 Co-ordinates:

A: (XA, YA +2ΔR, ZA)

B: (XB, YB+2ΔR, ZB)

C: (XC, Yc+2ΔR, Zc)

D: (XD, YD+2ΔR, ZD)

8. For each mirror, find the projections of mirror on to the center mirror plane. This can be done using the rayPlane utility offered by Java3D.

9. Find the intersection area of the central mirror and the projected plane, which is nothing but shading/blocking using the Clip function.

-----------------------

Start

End

1

”R= ”R+10% *”R

Choose another adjacent heliostat Yes/No?

Store the values in a file

Compute the intersection area

No shading/blocking

Check if the heliostat projections are intersecting tΔR= ΔR+10% *ΔR

Choose another adjacent heliostat Yes/No?

Store the values in a file

Compute the intersection area

No shading/blocking

Check if the heliostat projections are intersecting the other heliostat.

Select any neighboring heliostat to compute the shading/blocking on central heliostat.

A

A

Compute the co-ordinates of the 8 adjacent heliostats.

1

Height-HL

Width-HW

Calculate central Heliostat position and central heliostat normal.

Calculate the co-ordinates of the central heliostat in heliostat co-ordinate systems

Perform 2 Rotations

Perform 1 Translation

We get the co-ordinates of the central heliostat in absolute co-ordinate systems

For a default ΔR and ΔAz, place the 8 heliostats around the central heliostat.

1

ΔAz= ΔAz+10%* ΔAz

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