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78 Integrated system design (N) that bisects the angle between the vector formed by the sun and the heliostat center (SH) and the vector formed by the heliostat center and the receiver (HR). The incidence angle ω is the one between the normal of the surface and the other two vectors. Notice that the effective mirror area depends on this angle and corresponds to the area of the heliostat times the cosine of ω. The heliostat B has a surface located in the opposite side of the sun, which gives a lower incidence angle. On the other hand, the location of the heliostat A produces a higher incidence angle, reducing the effective area. This is why, for the solar power plants with a positive latitude (north hemisphere), the heliostats located at the north of the tower have a higher cosine efficiency and an better overall performance. The incidence angle can be obtained with the scalar product of the unit vectors of SH and HR, ω = 0.5cos−1(−SHU · HRU). (4-41) In order to obtain the solar ray unit vector it is necessary to set a reference system. Consider Figure 4-11, the unitary vector of the sun ray SH is a function of the position of Figure 4-11: Heliostat field, coordinate system. the sun, described by three angles, the solar hour angle ψ, the site latitude φ and the solar declination θ [78]. The solar hour angle is the angular displacement of the sun from a specific meridian due to the earth rotation. It is considered positive in the morning and negative in the afternoon, with each hour correspondent to 15◦of displacement (all the angles in radians in the following equations), ψ = (HOUR − 12)15π. (4-42) 180 The solar declination corresponds to the angle between the equatorial line and a line joining the center of the earth and the center of the sun. It depends on the day of the year, 23.45π 284 + DAY θ= 180 sin 2π 365 . (4-43) The variable DAY starts with 1 in January the 1st. The elevation of the solar ray is function of the mentioned angles, J.S. Bahamonde Noriega αSH = sin(φ)sin(θ) + cos(φ)cos(θ)cos(ψ). (4-44) Master of Science ThesisPDF Image | Design method for s-CO2 gas turbine power plants
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