An Algorithm for Determining Optimum Tilt Angle and Orientation for Solar Collectors

Abstract

Proper installation, especially the tilt angle, directly affects the system’s output. Determination of the optimal tilt angle of a solar cell module depends on the solar radiation characteristics, season, and reflectivity in the local area. One of the important parameters that affect the performance of a solar collector is its tilt angle with the horizon. This is because of the variation of tilt angle changes the amount of solar radiation reaching the collector surface. A mathematical model is presented for determining the optimum tilt angle at different orientations (surface azimuth angle) for the solar collector, on a daily basis, as well as for a specific period such as monthly, seasonally and yearly basis. The optimum angle was computed by searching for the values for which the extraterrestrial solar radiation on the collector surface is a maximum for a particular day or a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthly optimum tilt angle) or even 4 times/year (i.e. using the seasonally optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation of 5.5% at 0o latitude to 78% at 60o latitude more than the case of a solar collector fixed on a horizontal surface.

Solar Receivers Optimum Tilt Angle at Southern Hemisphere

“…So, no need to compare the results of the present work with those of [10] and [11]. Figure 9 shows the results of applying Equation (2) and Equation (12) for determining B opt,d for 60˚S latitudes and Equation (2), the algorithm of [8] in addition to results of [1] for 60˚N. It is seen from Figure 9 that the results of the present work agree very well with those of [1] and the algorithm of [8].…”

“…When applying the algorithms proposed in [8] and [9] on the high latitude zones at Southern Hemisphere and analyzing the obtained results for each latitude as a function of δ, the following results were found.…”

“…Figure 9 shows the results of applying Equation (2) and Equation (12) for determining B opt,d for 60˚S latitudes and Equation (2), the algorithm of [8] in addition to results of [1] for 60˚N. It is seen from Figure 9 that the results of the present work agree very well with those of [1] and the algorithm of [8]. Moreover, Equation (12) gives an excellent fit of the calculated results of the algorithm in this work.…”

“…When applying Equation ( 12), that of [3], and the algorithm of [8] in calculating B opt,d for L = −50˚ the obtained results are given in Table 1. It is seen from Table 1 that regarding to the precise results of algorithm [8], a) For Southern Hemisphere, the equation in [3] underestimates B opt,d remarkably during the period starting from 22/9 to 21/3 and overestimates slightly B opt,d during the period starting from 22/3 to 21/9 with an absolute deviation < 5˚; and b) Equation (12) gives the results of the algorithm with an absolute deviation < 1˚; So Equation ( 12) could be applied with a very good accuracy with regard to the algorithm [8] while the equation in [3] gives an acceptable evaluation of daily optimum tilt angle during half a year only.…”