SOLARIS CONFERENCE 2017   Sun tracking study and preliminary design of heliostat field in solar power towers Solaris 2017, 26 – 27 July 2017, Brunel University London, UK Alireza Asefikia Pouyan Talebizadeh Sirous Yasseri Roohollah Babaei Mahani   The heliostat layout is designed according to the efficiency and power of each individual heliostats. Then, heliostats from the highest to the lowest efficiency are positioned one by one and their input power is calculated and added to together to yield the desired input power. This study provides a guideline addressing both controlling and designing of solar power towers with the highest efficiency

Outline Sun tracking process Heliostat field parameters Results and discussion Conclusion References Solar power towers (SPT) is among the main concentrating solar power (CSP) systems which have good thermal efficiency and can help to reach a higher temperature of working fluid. SPT consists of an array of dual-axis tracking reflectors (heliostats) that reflect the sunrays onto the central receiver at the top of the tower and hence concentrate the power of sun on it. The cost of the surrounding heliostat field is almost 50% of the total costs and it accounts for 40% of the total losses. The aim of the present study is to develop a computer code for sun tracking and use it to design a surrounding heliostat field for a given absorbed power supplied on the receiver. For this purpose, the heliostats characteristic angles, the coordinate of each heliostat, the efficiency of the layout and the produced power should be specified for each set of the operating parameters.

Sun tracking process Since each heliostat surface has two degrees of freedom, therefore, at each instance, by obtaining two characteristic angles of each heliostat, i.e. the slope angle (β) and the azimuth angle (γ), the direction of each heliostat related to the tower at any time of a day and any day of the year can be determined. For determining the parameters β and γ, an algorithm is developed based on the vector geometry to pick an individual heliostat and calculate its characteristic angles at any time of the day and any day of the year. The unit vector along the reflected ray directed to the sun is defined by , the unit vector along the reflected ray directed to the receiver is defined by and the unit vector along the reflected ray normal to the reflective plane is defined by xx . The unit vector determines the orientation of the mirror plane with respect to the sun and should be positioned in such a way that the reflected ray strikes the receiver. The unit vector is a function of heliostat position with respect to the receiver defined in (Talebizadeh et al., 2013). The unit vector can be defined in terms of three angles including latitude , solar hour angle , and solar declination angle. Obtaining two characteristic angles of each heliostat i.e. the slope angle and the azimuth angle to fined the direction of each heliostat related to the tower at each moment.

Sun tracking process β: Slope Angle: the angle between the plane of the surface in question and the horizontal [2] γ: Surface azimuth angle, the deviation of the projection on a horizontal plane of the normal to the surface from the local meridian, with zero due south, east negative, and west positive [2]

Sun tracking process

Sun tracking process

Heliostat field parameters Local Heliostat Field efficiency The Produced power of each heliostat The input power on the receiver of each heliostat The input power on the receiver of each heliostat The total input power on the receiver The net absorbed power on the receiver

Results and discussion: Validation of incident angles Riaz [3] This study The computer code was verified by comparing our results with results of Riaz (1976). For the heliostats which are placed on a circle around the tower, the slope and azimuth angles as a function of time of the day and the location of heliostats on the circle are displayed in Figures 1-a and 1-b in comparison with (Riaz, 1976). The variation of the incident angle is shown in Figure 2. As shown, for the heliostats located in the north of the tower, the incident angle is lower than that located in the south of the tower for all heliostats. This is the reason that in the north hemisphere, more heliostats are located at the south of the tower. Furthermore, for the heliostats in the north of the tower, the incident angle has changed more significantly than those located at the south of the tower. Slope angle Azimuth angle

Results and discussion: Validation of heliostat field design The validation of the code for heliostat field design is studied first and then the layout of heliostat field is discussed for different Iranian cities. The layout of heliostat field for a 20MWt input power is also determined. For the validation, the results of the code are compared with the results of Collado (2009). In Table 1, the values of the constant parameters used in the design of the heliostat layout are listed. Note that the design is performed for the spring equinox (March 21) at noon. Colado [4] This study

Results and discussion The latitude and solar intensity of the selected Iranian cities Num City Latitude Solar intensity 1 Nehbandan (South of Khorasan) 32.3 970 2 Delgan (Sistan and Blochestan) 31 1030 3 Marvdasht (Fars) 30.24 981 4 Rafsanjan (Kerman) 30.28 885.7 5 Abarkouh (Yazd) 30.5 996 6 Jask (Hormozgan) 25.64 947

Results and discussion: Delgan city 20 MWt

Results and discussion The efficiency and heliostat number for different Iranian cities Num City Efficiency Number of heliostats 1 Nehbandan (South of Khorasan) 86.6114 288 2 Delgan (Sistan and Blochestan) 86.5368 271 3 Marvdasht (Fars) 86.4953 285 4 Rafsanjan (Kerman) 86.3317 316 5 Abarkouh (Yazd) 86.4861 281 6 Jask (Hormozgan) 86.1054 297

Conclusion The following results are achieved in this paper: Employing the vector geometry to control the heliostat’s direction at each moment and location Designing the heliostat field for high potential Iranian cities for constant input power Between the studied cities, Delgan with the latitude of 31° and solar intensities of 1030 W/m2 has the least heliostat number to reach a constant input power with an almost high efficiency of 86.5% We developed a computer code to control the heliostats’ direction using vector geometry. For each individual heliostat, the characteristics angles including the slope and azimuth angles was determined for every hour of a day and any day of the year. Then, for high potential Iranian cities, the heliostat layout was designed and the distribution of the heliostats is calculated in order to select the heliostat with higher efficiencies. This procedure is continued for the heliostat layout under the condition of constant absorbed power for finding the minimum number of heliostats. Due to the high cost of the surrounding heliostat field and also less dissipation of the energy, a more efficient design of the surrounding heliostat field is very important.

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References [1] Talebizadeh, P., Mehrabian, M.A., and Rahimzadeh, H., 2013, “Optimization of Heliostat Layout in Central Receiver Solar Power Plants, Joural of Energy engineering, 04014005-1. [2] J.A. Duffie, W.A. Beckman, Solar engineering of thermal processes, John Wiley & Sons, 2013. [3] Riaz, M.R., 1976, “A Theory of Concentrators of Solar Energy on a Central Receiver for Electric Power Generation”. ASME Journal of Engineering for Power, 98: 375-384. [4] Collado, F.J. 2009. “Preliminary design of surrounding heliostat fields”. Renewable Energy 34: 1359-1363.