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Influence of the latitude on the orientation efficiency of a pseudo- equatorial solar tracking system.


The efficiency increase of solar systems is an important target set for the future. This goal can be reached through different paths; an important one is the use of tracking mechanisms with fixed-predefined or sensor-based orientation program. Literature widely analysis tracking systems referring to the fundamental aspects related to the orientation algorithms and to the input solar radiation on tracked solar systems, (Diaconescu et al. 2007; Abu-Khadera et al. 2008).

Previous work reported on the design and optimization of a novel pseudo-equatorial solar tracking systems (Fig. 1), using predefined orientation programs (Burduhos 2009). This paper further expands these results, aiming to determine the latitudes (locations) where the tracker could be optimally used.


2.1 Direct Solar Radiation

All simulations presented in this paper, for estimating the orientation efficiency, are based on the direct solar radiation (available and received).

As a prediction model for the solar radiation, the Meliss model was used, able to determine the direct solar radiation Rd [W/[m.sup.2]] based on the hour, the day of the year and the atmospheric conditions typical for the area:

[R.sub.d] = 1367* [1 + 0.0334 x cos(0,9856 [degrees] x N-2.72 [degrees])] x exp(-[T.sub.R]/0.9 + 9.4 x sin [alpha]) (1)



where: N is the day number of the year, [alpha] is the altitude angle depending on the hour, while [T.sub.R] is an atmospheric coefficient, with values between 1,..., 5.

Using this relation and considering the direct radiation measured in Braspv-Romania, the local atmospheric coefficient [T.sub.R] was evaluated having 3 as the mean annual value.

2.2 The Step Orientation Program

Considering relation (1) and a minimum acceptable orientation efficiency, based on Matlab numerical simulations for the Brasov-Romania conditions, the year was divided in 6 annual intervals (Fig. 2) having the orientation program as described in Table 1.


The locations for which the solar tracking system reaches an optimal efficiency were calculated based on numerical simulations using Matlab and (1); at different latitudes the variation of the orientation efficiency (energy of direct solar radiation normally received by the orientated surface / available energy of direct solar radiation) was further evaluated for an entire year.

The following simplified conditions were considered:

* a clear, cloudless sky;

* latitudes between 1[degrees]-89[degrees] N, because the northern and southern hemisphere are symmetrical;

* the optimal diurnal movements from Brasov were considered for all latitudes, while the elevation movement has been corrected according to the latitude;

* due to the fact that a comparative analysis is hardly influenced by the variation of the atmospheric coefficient [T.sub.R], this was considered for all latitudes 3.


Initially, due to the long simulation durations in Matlab, tests were done only for the first half of an year, with a temporary distance of 10 days and a latitude angular distance of 11[degrees]. These parameters could not sufficiently describe the variation in the orientation efficiency; this is why in the next step simulations were made throughout the whole year with a temporary distance of 5 days (Fig. 3).

As Fig. 3 shows, in the interval 67[degrees]-89[degrees] N the curve of the orientation efficiency modifies its bending. Further simulations with latitudes between 84[degrees]-89[degrees] N and a latitude angular distance of 1[degrees] (Fig. 4) show that this phenomenon occurs at 85[degrees]N; at this latitude the difference between the angular stroke of the tracking system and the duration of the day becomes evident.





From the global diagram (Fig. 5) and the interpretation of the obtained curves the following conclusions can be stated:

* the pseudo-equatorial tracking system is especially efficient at latitudes below 56[degrees]N because in this interval the orientation efficiency is higher than 95%;

* because the southern hemisphere is symmetrical to the northern one, the pseudo-equatorial orientation can be used in locations between 56[degrees]S and 56[degrees]N;

* at higher latitudes the use of the system is not justified, at least for two reasons: a) the system has high efficiency only during the spring and autumn and b) the polar night phenomenon which appears over 74[degrees]N.


This paper is supported by the Sectoral Operational Programme Human Resources Development (SOP HRD), Post Doctoral School, financed from the European Social Fund and by the Romanian Government under the contract number POSDRU 59323.


Burduhos, B., (2009). Optimization of Pseudo-Equatorial Tracking Mechanisms Used for Increasing the Conversion Efficiency of Individual Photovoltaic Modules, PhD. Thesis, Brasov

Diaconescu, D.; Visa, I.; Burduhos, B.; Popa, V. (2007). On the Sun-Earth Angles used in the Solar Trackers' Design. Part 2: Simulations, Annals of the Oradea University, Fascicle of Management and Technological Engineering, Vol. VI (XVI), pp. 842-849, ISSN:1583-0691

Meliss, M. (1997). Regenerative Energiequellen--Praktikum, Berlin Heidelberg, Springer, ISBN 3-540-63218-2

Mazen, M., Abu-Khadera; Omar, O., Badranb; Salah, Abdallah; (2008). Evaluating Multi-Axes Sun-Tracking System at Different Modes of Operation in Jordan, Renewable and Sustainable Energy Reviews 12, pp. 864-873

Olchowik, J.M.; Tomaszewski, R.; Adamczyk, J.; Gulkowski, S.; Cieslak, K.; Zabielski, K.; (2008). Four Years Exploitation Analysis of the Hybrid Solar System in South-Eastern Poland Conditions, Proceedings of 23rd European Photovoltaic Solar Energy Conference and Exhibition, pp. 3084-3087, Valencia

Sharan, A.M.; (2008). Variation of Energy Conversion Efficiencies of Stationary Photovoltaic Systems with Latitudes, Energy & Environment Vol. 19 Issue 5, pp. 679-689
Tab. 1. Optimal annual orientation program during one year

 morning local
 hours (the
Interval/number [[beta].sup.*] afternoon hours
[[beta].sup.*] steps in the are considered
steps [[gamma].sup.*] morning symmetrical)

N= 73...100 42.5[degrees] 63[degrees]; 8:39 (9:59);
N= 244...271 40[degrees]; 10:03 (11:23);
6 steps 19[degrees]; 11:24 (12:44)

N= 101...127 32.5[degrees] 64[degrees]; 8:13 (9:33);
N= 217...243 47[degrees]; 9:22 (10:42);
8 steps 31[degrees]; 10:24 (11:44);
 16[degrees]; 11:28 (12:48)

N= 128...216 24.5[degrees] 64[degrees]; 7:54 (9:14);
10 steps 50[degrees]; 8:54 (10:14);
 36[degrees]; 9:55 (11:15);
 24[degrees]; 10:43 (12:03);
 12[degrees]; 11:36

N= 272...724 54.5[degrees] 50[degrees]; 9:36 (9:55);
4 steps 24[degrees]; 11:18 (11:37);

 in the afternoon data are
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Author:Burduhos, Bogdan Gabriel; Visa, Ion; Diaconescu, Dorin Valentin; Ciobanu, Daniela
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Geographic Code:4EXRO
Date:Jan 1, 2010
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