1. Introduction

In recent years, concentrator photovoltaic (CPV) system that uses relatively inexpensive optics such as mirrors or lenses to focus the sunlight on multi-junction solar cells has expanded rapidly. In order to maintain a high output power and stability of the CPV system, a high-precision of sun-tracking system is required to follow the sun’s trajectory throughout the day. In general, sun-tracking systems can be classified as one-axis and two-axis sun-tracking system[1]. For the one-axis tracking system, the system drives the tracker about an axis of rotation until the central ray and the aperture normal are coplanar. In contrast, the two-axis sun tracker tracks the sun in two axes such that the sun vector is normal to the aperture as to attain 100% collection efficiency.

At the present, the sun-tracking algorithms that are widely adopted to track the sun’s path are categorized into the three major groups, i.e. open-loop, closed-loop and hybrid tracking system[2]. The above-mentioned tracking methods are operated by either a micro-controller based control system or a PC based control system in order to trace the position of the sun. The open-loop sun-tracking method that employs special formula to predict the sun’sposition can continue to track the sun even when it is covered by cloud. Referring to the literatures[3-6], the azimuth and elevation angles can be determined by using the sun position formula or algorithm at the given date, time and geographical information. This tracking approach has the ability to achieve the tracking error of within ±0.2° when the mechanical structure is precisely made as well as the alignment work is perfectly done.

On the other hand, in the closed-loop sun-tracking system, various sensor devices, i.e. CCD sensor or photodiode sensor, are utilized to feedback an error signal to the control system for rotating the tracker towards the sun. Although the performance of the closed-loop tracker is easily affected by weather conditions and environmental factors, it has allowed great savings in terms of cost, time and effort by omitting precise alignment work of the sun tracker. In addition, this strategy is capable of achieving a tracking accuracy in the range of a few milli-radians (mrad) during fine weather[7-12]. For that reason, the closed-loop system has been widely used in the sun-tracking scheme over the past 20 years. In general, both sun-tracking methods stated above have their advantages and drawbacks respectively. As a result, some researchers have developed hybrid sun-tracking systems that include both the open-loop and closed-loop tracking schemes for the sake of high tracking accuracy[13-15].

In short, sun-tracking systems must be highly accurate and robust, but at the same time they must have minimum installation and maintenance costs. A novel on-axis general sun-tracking formula has been derived and integrated into the open-loop azimuth-elevation sun-tracking system in order to meet the aforementioned criteria[16-18]. With the use of new sun-tracking formula, any misalignments from the ideal azimuth-elevation configuration can be rectified without adding any closed-loop feedback controller or a flexible and complicated mechanical structure. The methodology of adopting the newly proposed on-axis general sun-tracking formula in the prototype of solar concentrator, which has been constructed in the campus of Universiti Tunku Abdul Rahman (UTAR), is presented in this paper.

2. Integration of On-Axis General Sun-Tracking Formula

In an ideal azimuth-elevation sun-tracking system, primary tracking axis or azimuth axis must be parallel to the zenith axis, and elevation axis or secondary tracking axis always orthogonal to the azimuth axis as well as parallel to the earth surface. Three orientation angles have been introduced in the general formula to compensate any alignment defects of the solar concentrator relative to the ideal azimuth-elevation sun-tracking system[16]:

(a) ζ and λ are the rotational angles about east axis and north axis respectively. These two angles show the real alignment work of the azimuth axis relative to the zenith axis.

(b) is a rotational angle about zenith axis. It determines the reference orientation of the azimuth axis. When ζ λ 0, it represents the offset angle relative to the real north.

The derivation of general formula for on-axis sun-tracking system has been presented in the previous paper[16]. According to the general formula, the sun-tracking accuracy of the system highly relies on the precision of the latitude angle (Φ), hour angle (ω), declination angle (δ) as well as the three orientation angles of the tracking axes of solar concentrator i.e. Φ, λ and ζAmong these values, Φ, ω and δ can be determined precisely with the availability of technology such as global positioning system (GPS) and precise clock, whereas the precision of , λ and ζare very much dependent on the effort paid during the on-site installation of solar collector, the alignment of tracking axes and the mechanical fabrication.

With the integration of general formula into the sun-tracking algorithm, we can control any on-axis sun-tracker with arbitrarily orientation of two orthogonal driving axes without the need of drastic modification in either hardware or software components of the tracking system. Nonetheless, we just simply change the input values for the three orientation angles , λ and ζ, and hence it has eased the installation work of solar collector with higher tolerance in term of the alignment. In other words, even though the alignments of the azimuth-elevation axes with respect to the zenith-axis and real north are not properly done, the new sun-tracking algorithm still can accommodate the misalignment through a direct change in the values of , λ and ζ, in the tracking program.

From our previous study[16], the unit vector of the sun,[S'], relative to the solar collector can be obtained from a multiplication of four successive coordinate transformation matrices, i.e.[Φ],[ Φ],[λ] and[ζ] with the unit vector of the sun,[S], relative to the earth and it is written as

(1)

where α is elevation angle, β is azimuth angle, ω is hour angle, δ is declination angle, Φ is latitude at which the solar collector is located as well as Φ, λ and ξ are the three orientation angles of two-orthogonal-driving axes of the solar collector. From the Eq. (1), let us multiply the first three transformation matrices[Φ],[λ] and[ζ], and then the last two matrices[Φ] with[S] as to obtain the following result:

(2)

From Eq. (2), we can further dissolve it into the following three equations:

(3a)

(3b)

(3c)

(4a)

(4b)

(4c)

In Eq. (3), it is found that only ω and δ are time dependant variables. Therefore, the instantaneous sun-tracking angles of the collector only vary with the angles ω and δ Given three different local times LCT₁, LCT₂ and LCT₃ on the same day, the corresponding three hours angles ω₁, ω₂ and ω₃ as well as three declination angles δ₁, δ₂ and δ₃ can result in three elevation angles α₁ α₂ and α₃ and three azimuth angles β₁, β₂ and β₃ accordingly as expressed in Eqs. (3a)-(3c). Considering three different local times, we can in fact rewrite each of the equation, Eqs. (3a)-(3c) into three linear equations. By arranging the three linear equations in a matrix form, the Eqs.(3a), (3b) and (3c) can subsequently form the matrices (4a), (4b) and (4c),

where the angles Φ, Φ, λ and are constants with respect to the local time.

In practice, we can measure the sun tracking angles i.e. (α₁,α_2α₃) and (β₁, β₂ β₃) during sun-tracking at three different local times via recorded solar image at the target using the CCD camera. With the recorded data, we can compute the three arbitrary orientation angles , λ and ζof the solar collector using the third-order determinants method to solve the three simultaneous equations as shown in Eqs. (4a)-(4c). From Eq.(4b), the orientation angle λ can be determined as follow:

Similarly, the other two remaining orientation angles, Φ and  can be resolved from Eq. (4b) and Eq. (4c) respectively as follow

(5a)

(5b)

(5c)

Figure 1 shows the flow chart of computational program designed to solve the three unknown orientation angles of the solar collector: , λ and ζusing Eqs. (5a)-(5c). By providing the three sets of actual sun tracking angles at different local times for a particular number of day as well as geographical information i.e. longitude and latitude, the computational process can be executed by the program to calculate the three unknown orientation angles.

Figure 1. Flow chart shows the algorithm of the computational program. The program has been designed for determining the three unknown orientation angles that we cannot precisely measure by tools in practice, i.e. Φ, λ and ζ.

3. Open-Loop Sun-Tracking System Design and Performance Study

For demonstrating the integration of general formula into sun-tracking algorithm to obtain a precise tracking accuracy, a prototype of Non-Imaging Planar Concentrator (NIPC) has been constructed in the campus of UTAR, Kuala Lumpur (located at latitude 3.22º and longitude 101.73º). The NIPC concentrator has been proposed to achieve a good uniformity of the solar irradiance with a reasonably high concentration ratio[19-20]. Instead of using a single piece of parabolic dish, the newly proposed on-axis solar concentrator employs 480 pieces of flat mirrors to form a total reflective area of about 25 m² (see Fig. 2). The target is fixed at a focal point with a distance of 4.5 m away from the centre of solar concentrator frame.

Figure 2. 25m2 prototype of Non-Imaging Planar Concentrator (NIPC) that has been constructed at Universiti Tunku Abdul Rahman (UTAR).

The prototype solar concentrator operates on the most common two-axis sun-tracking system, azimuth-elevation sun-tracking system, and is based on the open-loop system with the use of optical encoders to feedback the angular movements of the solar concentrator via serial port. Two units of 12-bit optical encoders, with a precision of 2,048 counts per revolution, are employed to get rid of the tracking errors caused by backlash, wind load and other external disturbances. A Windows-based sun-tracking control program run on the algorithm integrated with the general sun-tracking formula was developed for correcting any possible misalignment of azimuth-axis relative to zenith. In the algorithm, the sun-tracking angles, i.e. azimuth (β) and elevation (α) angles, are first calculated based on the given information, i.e. local time, date, geographical location, time zone and the newly introduced three orientation angles (, λ and ζ ). The control program then generates digital pulses and sends to the stepper motor driver through parallel port. Subsequently, the concentrator is directed by two stepper motors with 0.72° in full step, coupled to elevation and azimuth shafts via gear trains with gear ratio of 4,400:1 respectively and yielding an overall resolution of 1.64 × 10^–4°/step, to the pre-calculated angles along azimuth (AA’) and elevation (BB’) axes. Each time, the control program can only activate one of the stepper motors by using of relay switch. Fig. 3 shows the configuration of the open-loop control system of the prototype.

Figure 3. Configuration of the complete open-loop feedback system of the solar concentrator

3.1. Experimental Setup

According to the general formula, the major consideration of achieving high degree of sun-tracking accuracy is the precision of the input parameters to the sun-tracking algorithm, i.e. latitude angle (Φ), hour angle (ω), declination angle (δ), as well as the three orientation angles (, λ and ζ) of the solar concentrator. Experimental setup is required to ascertain that the collection of the sun-tracking data is reliable and accurate.

A suitable geographical location was selected for the installation of solar concentrator so that it is capable of receiving the maximum solar energy without the blocking of any buildings or plants. To avoid the sun-tracking errors by the wrong estimation of the prototype’s geographical

location, a global positioning system (GPS) was used to

determine the latitude (Φ) and longitude of the solar concentrator. In addition, the hour angle (ω) and the declination angle (δ) are both local time dependent parameters. With the synchronization between computer clock and Internet timeserver, these variables can be computed accurately with an input from precise computer clock all the time. An analytical equation based on the general sun-tracking formula and the tracking results has been derived and formulated as shown in Eqs. (5a)-(5c) where the three misaligned angles (, λ and ζ) can be calculated.

A CCD camera with a resolution of 640 480 pixels is utilized to capture the solar image cast on the target. The camera was connected to a computer via a Peripheral Component Interconnect (PCI) video card to have a real time transmission and recording of solar image. For the sake of accuracy, the CCD camera is placed directly facing the target to minimize the cosine effect. A polarizing filter was used to prevent the reflected or scattered sunlight from the target that could damage the CCD sensors of the camera. The actual sun-tracking angles, i.e. (α₁, α₂ , α₃) and (β₁, β₂, β₃) at three different local times, can be determined from the central point of solar image position relative to the central point of the target using the ray-tracing method.

3.2. Performance of the Sun-Tracking System

Before the performance of the sun-tracking system was tested, all the mirrors were covered with black plastic as shown in Fig. 2, except the one mirror located nearest to the centre of the concentrator frame. By observing the movement of the solar image with the CCD camera, the sun-tracking accuracy can be analysed and recorded in the computer database. Three different performance studies were carried out for the whole calendar year of 2009. Figs. 4 and 5 illustrate the recorded solar images and the plot of sun-tracking results respectively for three different performance studies.

Study no. 1: Initially, the alignment of solar concentrator was assumed to be perfectly done relative to the real north and zenith by setting the three orientation angles as = λ = ζ = 0° to the control program. According to the recorded results on 13 January 2009, the sun-tracking errors ranging from 12.12 to 17.54 mrad have confirmed that the solar concentrator azimuth axis is not well aligned with both the zenith and real north axes.

Study no. 2: Using the aforementioned analytical Eqs. (5a)-(5c), the three parameters of misalignment (, λ and ζ) were calculated based on the tracking results from the Study no. 1. With the calculated orientation angles ( = −0.1°, λ = 0°, and ζ = −0.5°), the performance of the prototype in sun-tracking has been successfully improved to the accuracy of below 2.99 mrad on 16 January 2009. It has reached the resolution limit of the optical encoder that is 4.13 mrad. To confirm the validation of the sun-tracking results, the sun-tracking system has been tested for a period of more than six months.

Figure 4. The recorded solar images cast on the target of the 25m2 prototype of Non-Imaging Planar Concentrator in the three performance studies.

Figure 5. The plot of pointing error (mrad) versus local time (hours) for the three performance studies.

Study no. 3: On top of that, additional effort has been made to improve the sun tracking accuracy beyond the resolution of the optical encoder by including the step count of stepper motor, 1.64 × 10^–4 °/step, in fine-tuning the position of the prototype solar concentrator. Referring to the algorithm flow as shown in Fig. 6, the initial concentrator’s azimuth and elevation angles are first defined by reading these angles from the optical encoders mounted along both the azimuth and elevation axes respectively. Subsequently, the sun position angles, i.e. azimuth and elevation angles are computed according to the general formula. The control program in succession compares the calculated sun position angles with the current encoders’ reading. If the absolute difference between the calculated azimuth or elevation angle and the encoder reading for azimuth or elevation axis (∆₁) is larger than or equal to the encoder resolution, i.e. 0.176°, the control program then generates digital pulses sending to the stepper motor driver. It will drive the solar concentrator to the pre-calculated angles along azimuth and elevation axes in sequence with the use of relay switch, and then store the current reading of encoders as the latest concentrator’s azimuth and elevation angles. In this case, the program operates in a feedback loop that is capable of making correction or compensation on any external disturbance like wind load and backlash so that the difference between the concentrator position and calculated sun angles is within the encoder resolution. Since the motor driving resolution (1.64 × 10^–4 °/step) is beyond the encoder resolution, a non-feedback loop has been introduced when the solar concentrator operating within the resolution of the optical encoder with ∆₁< 0.176° as shown in Fig. 6. In the non-feedback loop, we have made two assumptions in which the backlash and step loss are negligible for the resolution ranging from 0.05° to 0.176°. When the absolute difference between calculated azimuth or elevation angle and the concentrator’s azimuth or elevation angles (∆₂) is larger than or equal to 0.05° (Noted that this angle is sufficient for an on-axis solar concentrator to achieve a tracking accuracy of below 1 mrad), the control program will send the required pulses to motors for rotating the solar concentrator towards the sun along azimuth and elevation axes in order without any positioning feedback. After that, the timer is activated and the position of solar concentrator is updated with the sum of previous concentrator position and ∆₂. The solar concentrator is programmed to follow the sun at all times since the program is to run in repeated loops in every 10 seconds. This strategy has further improved the tracking accuracy to 0.96 mrad on 6 August 2009. Similarly, the performance of the sun-tracking has been observed for several months until the end of year 2009.

Figure 6. The algorithm flow of the sun-tracking control program that including motor step count, 1.64 × 10–4 °/step, in fine-tuning the position of solar concentrator prototype and improving the sun tracking accuracy beyond the resolution of the optical encoder.

4. Conclusions

Integration of general formula into the open-loop sun-tracking control system has been demonstrated. This approach allowed the on-axis solar concentrator to track the sun accurately and simplifies the fabrication and installation work of solar concentrator with higher tolerance in terms of the tracking axes alignment. In other words, the general sun-tracking formula is confirmed to be capable of remedying the installation error of the solar concentrator cost effectively with a significant improvement in the tracking accuracy to below 1 mrad in our 25 m2 prototype concentrator.

ACKNOWLEDGEMENTS

The authors would like to express their gratitude to Malaysia Energy Centre, Ministry of Energy, Green Technology & Water (AAIBE Trust Fund) and Ministry of Science, Technology & Innovation (e-Science Fund) for the financial support.