General Formula for On-Axis Sun-Tracking System

Kok-Keong Chong, Chee-Woon Wong

Universiti Tunku Abdul Rahman Malaysia

1. Introduction

Sun-tracking system plays an important role in the development of solar energy applications, especially for the high solar concentration systems that directly convert the solar energy into thermal or electrical energy. High degree of sun-tracking accuracy is required to ensure that the solar collector is capable of harnessing the maximum solar energy throughout the day. High concentration solar power systems, such as central receiver system, parabolic trough, parabolic dish etc, are the common in the applications of collecting solar energy. In order to maintain high output power and stability of the solar power system, a high-precision sun-tracking system is necessary to follow the sun’s trajectory from dawn until dusk.

For achieving high degree of tracking accuracy, sun-tracking systems normally employ sensors to feedback error signals to the control system for continuously receiving maximum solar irradiation on the receiver. Over the past two decades, various strategies have been proposed and they can be classified into the following three categories, i. e. open-loop, closed-loop and hybrid sun-tracking (Lee et al., 2009). In the open-loop tracking approach, the control program will perform calculation to identify the sun’s path using a specific sun­tracking formula in order to drive the solar collector towards the sun. Open-loop sensors are employed to determine the rotational angles of the tracking axes and guarantee that the solar collector is positioned at the right angles. On the other hand, for the closed-loop tracking scheme, the solar collector normally will sense the direct solar radiation falling on a closed-loop sensor as a feedback signal to ensure that the solar collector is capable of tracking the sun all the time. Instead of the above options, some researchers have also designed a hybrid system that contains both the open-loop and closed-loop sensors to attain a good tracking accuracy. The above-mentioned tracking methods are operated by either a microcontroller based control system or a PC based control system in order to trace the position of the sun.

Azimuth-elevation and tilt-roll tracking mechanisms are among the most commonly used sun-tracking methods for aiming the solar collector towards the sun at all times. Each of these two sun-tracking methods has its own specific sun-tracking formula and they are not interrelated in many decades ago. In this chapter, the most general form of sun-tracking formula that embraces all the possible on-axis tracking approaches is derived and presented in details. The general sun-tracking formula not only can provide a general mathematical solution, but more significantly, it can improve the sun-tracking accuracy by tackling the

installation error of the solar collector. The precision of foundation alignment during the installation of solar collector becomes tolerable because any imprecise configuration in the tracking axes can be easily compensated by changing the parameters’ values in the general sun-tracking formula. By integrating the novel general formula into the open-loop sun­tracking system, this strategy is definitely a cost effective way to be capable of remedying the installation error of the solar collector with a significant improvement in the tracking accuracy.

2. Overview of sun-tracking systems

2.1 Sun-tracking approaches

A good sun-tracking system must be reliable and able to track the sun at the right angle even in the periods of cloud cover. Over the past two decades, various types of sun-tracking mechanisms have been proposed to enhance the solar energy harnessing performance of solar collectors. Although the degree of accuracy required depends on the specific characteristics of the solar concentrating system being analyzed, generally the higher the system concentration the higher the tracking accuracy will be needed (Blanco-Muriel et al., 2001).

In this section, we would like to briefly review the three categories of sun-tracking algorithms (i. e. open-loop, closed-loop and hybrid) with some relevant examples. For the closed-loop sun-tracking approach, various active sensor devices, such as CCD sensor or photodiode sensor are utilized to sense the position of the solar image on the receiver and a feedback signal is then generated to the controller if the solar image moves away from the receiver. Sun-tracking systems that employ active sensor devices are known as closed-loop sun trackers. Although the performance of the closed-loop tracking system is easily affected by weather conditions and environmental factors, it has allowed savings in terms of cost, time and effort by omitting more precise sun tracker alignment work. In addition, this strategy is capable of achieving a tracking accuracy in the range of a few milli-radians (mrad) during fine weather. For that reason, the closed-loop tracking approach has been traditionally used in the active sun-tracking scheme over the past 20 years (Arbab et al., 2009; Berenguel et al., 2004; Kalogirou, 1996; Lee et al., 2006). For example, Kribus et al. (2004) designed a closed-loop controller for heliostats, which improved the pointing error of the solar image up to 0.1 mrad, with the aid of four CCD cameras set on the target. However, this method is rather expensive and complicated because it requires four CCD cameras and four radiometers to be placed on the target. Then the solar images captured by CCD cameras must be analysed by a computer to generate the control correction feedback for correcting tracking errors. In 2006, Luque-Heredia et al. (2006) presented a sun-tracking error monitoring system that uses a monolithic optoelectronic sensor for a concentrator photovoltaic system. According to the results from the case study, this monitoring system achieved a tracking accuracy of better than 0.1°. However, the criterion is that this tracking system requires full clear sky days to operate, as the incident sunlight has to be above a certain threshold to ensure that the minimum required resolution is met. That same year, Aiuchi et al. (2006) developed a heliostat with an equatorial mount and a closed-loop photo­sensor control system. The experimental results showed that the tracking error of the heliostat was estimated to be 2 mrad during fine weather. Nevertheless, this tracking method is not popular and only can be used for sun trackers with an equatorial mount configuration, which is not a common tracker mechanical structure and is complicated because the centra! of gravity for the solar collector is far off the pedestal. Furthermore, Chen et al. (2006, 2007) presented studies of digital and analogue sun sensors based on the optical vernier and optical nonlinear compensation measuring principle respectively. The proposed digital and analogue sun sensors have accuracies of 0.02° and 0.2° correspondingly for the entire field of view of ±64° and ±62° respectively. The major disadvantage of these sensors is that the field of view, which is in the range of about ±64° for both elevation and azimuth directions, is rather small compared to the dynamic range of motion for a practical sun tracker that is about ±70° and ±140° for elevation and azimuth directions, respectively. Besides that, it is just implemented at the testing stage in precise sun sensors to measure the position of the sun and has not yet been applied in any closed-loop sun-tracking system so far.

Although closed-loop sun-tracking system can produce a much better tracking accuracy, this type of system will lose its feedback signal and subsequently its track to the sun position when the sensor is shaded or when the sun is blocked by clouds. As an alternative method to overcome the limitation of closed-loop sun trackers, open-loop sun trackers were introduced by using open-loop sensors that do not require any solar image as feedback. The open-loop sensor such as encoder will ensure that the solar collector is positioned at pre­calculated angles, which are obtained from a special formula or algorithm. Referring to the literatures (Blanco-Muriel et al., 2001; Grena, 2008; Meeus, 1991; Reda & Andreas, 2004; Sproul, 2007), the sun’s azimuth and elevation angles can be determined by the sun position formula or algorithm at the given date, time and geographical information. This tracking approach has the ability to achieve tracking error within ±0.2° when the mechanical structure is precisely made as well as the alignment work is perfectly done. Generally, these algorithms are integrated into the microprocessor based or computer based controller. In 2004, Abdallah and Nijmeh (2004) designed a two axes sun tracking system, which is operated by an open-loop control system. A programmable logic controller (PLC) was used to calculate the solar vector and to control the sun tracker so that it follows the sun’s trajectory. In addition, Shanmugam & Christraj (2005) presented a computer program written in Visual Basic that is capable of determining the sun’s position and thus drive a paraboloidal dish concentrator (PDS) along the East-West axis or North-South axis for receiving maximum solar radiation.

In general, both sun-tracking approaches mentioned above have both strengths and drawbacks, so some hybrid sun-tracking systems have been developed to include both the open-loop and closed-loop sensors for the sake of high tracking accuracy. Early in the 21st century, Nuwayhid et al. (2001) adopted both the open-loop and closed-loop tracking methods into a parabolic concentrator attached to a polar tracking system. In the open-loop scheme, a computer acts as controller to calculate two rotational angles, i. e. solar declination and hour angles, as well as to drive the concentrator along the declination and polar axes. In the closed – loop scheme, nine light-dependent resistors (LDR) are arranged in an array of a circular­shaped "iris" to facilitate sun-tracking with a high degree of accuracy. In 2004, Luque-Heredia et al. (2004) proposed a novel PI based hybrid sun-tracking algorithm for a concentrator photovoltaic system. In their design, the system can act in both open-loop and closed-loop mode. A mathematical model that involves a time and geographical coordinates function as well as a set of disturbances provides a feed-forward open-loop estimation of the sun’s position. To determine the sun’s position with high precision, a feedback loop was introduced according to the error correction routine, which is derived from the estimation of the error of the sun equations that are caused by external disturbances at the present stage based on its historical path. One year later, Rubio et al. (2007) fabricated and evaluated a new control strategy for a photovoltaic (PV) solar tracker that operated in two tracking modes, i. e. normal tracking mode and search mode. The normal tracking mode combines an open-loop tracking mode that is based on solar movement models and a closed-loop tracking mode that corresponds to the electro-optical controller to obtain a sun-tracking error, which is smaller than a specified boundary value and enough for solar radiation to produce electrical energy. Search mode will be started when the sun-tracking error is large or no electrical energy is produced. The solar tracker will move according to a square spiral pattern in the azimuth – elevation plane to sense the sun’s position until the tracking error is small enough.

Updated: July 1, 2015 — 5:59 am