Computing the solar vector
Introduction
High-concentration solar thermal systems require the Sun to be tracked with great accuracy. Although the degree of accuracy required depends on the specific characteristics of the concentrating system being analyzed, in general, the higher the system concentration the higher the tracking accuracy needed. For a solar thermal central receiver system (CRS) with a concentration ratio of about 1000, Vant-Hull and Hildebrandt (1976) estimate this to be approximately 3.5 minutes of arc.
The current trend in solar concentrator tracking systems is to use an open-loop local controller that computes the direction of the solar vector based on geographical location and time. In a typical configuration, the local controller does everything necessary to ensure continuous automatic positioning of the concentrator in such a way that communication with the central controller is limited to setting aiming points, sending status data and accepting safety orders. This reduces the need for interaction with the central controller and minimizes data traffic. To keep down the price of the tracking system, the controller is based on a low-cost microprocessor, which, in addition to computing the Sun position, has to be able to control many other tracking system functions.
All this imposes important restrictions on the Sun-position algorithm to be used in the controller. It has to be highly accurate and efficiently computable at the same time. The greater the accuracy in computing the Sun position, the greater the margin of tolerance will be for other sources of error, such as optical or mechanical, that may arise within the concentrating system. It is therefore desirable for the accuracy of the Sun-position algorithm be as high as possible.
This paper reviews what has been published in the last 38 years in the solar literature concerning the determination of the Sun position, compares the different algorithms proposed and introduces a new, more accurate and simpler algorithm.
Section snippets
BIBLIOGRAPHIC REVIEW
The solar literature contains a wide range of papers referring to the calculation of the Sun position. These calculations can be classified into two groups. The first is a group of relatively simple formulae and algorithms that, given the day of the year, estimate basic Sun-position parameters, such as the solar declination or the equation of time (Cooper, 1969; Lamm, 1981; Spencer, 1971; Swift, 1976). The second consists of more complex algorithms (Michalsky, 1988; Pitman and Vant-Hull, 1978;
COMPARISON OF THE DIFFERENT ALGORITHMS
Of all the algorithms mentioned above, only four (Spencer, Pitmann and Vant-Hull, Walraven and Michalsky) are complete in the sense that, without the need for additional information, the true horizontal coordinates of the Sun can be estimate based on their results. To establish which is the best, their accuracy has been assessed and compared. Assessment of the accuracy of an algorithm is possible thanks to the Multiyear Interactive Computer Almanac (MICA). This software product of the United
THE PSA ALGORITHM
Even though the Michalsky algorithm may be considered good enough for most solar tracking applications, its accuracy, computing efficiency, and ease of use can still be improved. These tasks have been undertaken and, as a result, a new algorithm called the PSA algorithm, having the following characteristics, has been developed:
- 1.
Its ease of use has been improved by incorporating an efficient method of computing the Julian Day from the calendar date and Universal Time.
- 2.
Memory management has been
DESCRIPTION OF THE ALGORITHM
The input to the PSA Algorithm is time and location. The time for the instant under consideration is given as the date (year, month, and day) and the Universal Time (hours, minutes and seconds). The location is given as the longitude and latitude of the observer in degrees. Latitude is considered positive to the North and longitude to the East.
The Julian Day, jd, is computed from the input data by the following expression:
LONG-TERM VALIDATION OF THE PSA ALGORITHM
The MICA program only supplies Sun-related data for the interval between 1990 and 2005. However with the collaboration of the Real Observatorio de la Armada in San Fernando (Spain), it has been possible to test validity of the PSA Algorithm through the year 2015.
Following our request, the Real Observatorio generated 447 048 reference values of the true horizontal coordinates of the Sun, by evaluating such coordinates, using high precision formulae, every 20 minutes for the time period elapsed
CONCLUSIONS
High-concentration solar thermal systems require algorithms that are accurate and computationally inexpensive to determine the coordinates of the Sun.
The solar literature presents several examples of such algorithms, all of which are based on the use of simplified Nautical Almanac orbital equations.
A new algorithm, called the PSA Algorithm, has been developed, that constitutes an improvement over those in the literature. The new algorithm provides estimates of the true azimuth and zenith angle
NOMENCLATURE
- jd
Julian Day
- hour
Hour of the day in Universal Time and decimal format
- n
Difference between the current Julian Day and Julian Day 2 451 545.0 (noon 1 January 2000)
- L
Mean longitude of the Sun
- g
Mean anomaly of the Sun
- l
Ecliptic longitude of the Sun
- ep
Obliquity of the ecliptic
- ra
Right ascension
- δ
Declination
- gmst
Greenwich mean sidereal time
- lmst
Local mean sidereal time
- long
Geographical longitude
- Φ
Geographical latitude
- ω
Hour angle
- θz
Zenith distance
- γ
Solar azimuth
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