# Biaxial-Type Concentrated Solar Tracking System with a Fresnel Lens for Solar-Thermal Applications
## 2 Experimental Methods and Apparatus  
The altitude-azimuth biaxial-type concentrated solar tracking system as shown in Figure 1 in this study contains the following sub-systems: (i) solar cells and battery; (ii) control system; (iii) structure mechanism; and (iv) Fresnel lens module. In order to track the sun trajectory accurately, we use the following Equation (1) as the sun tracking method in our experiment. In this equation, the altitude and azimuth trajectory formula use the hour angle (\(H\)) and declination (\(\delta\)) in the sun-tracking formula by [PERSON] and [PERSON] [24]. The horizontal coordinate is very convenient to define the sun position for prerequisite initial position of the solar tracker. The altitude and azimuth of sun can be measured through Equation (1). If the angles difference (\(\Delta\alpha\), \(\Delta\beta\)) is greater than the stepping motor step angle, the microprocessor will send a signal to the motor driver to actuate the solar tracker. \[\alpha=\sin^{-1}\left(\mathrm{sin}\mathrm{\varphi}\cdot\mathrm{sin}\delta+ \mathrm{cos}\mathrm{\varphi}\cdot\mathrm{cos}\delta\cdot\mathrm{cos}H\right) \tag{1}\]  
\[\beta=\pi-\cos^{-1}\left(\frac{\mathrm{sin}\alpha\cdot\mathrm{sin}\mathrm{ \varphi}-\mathrm{sin}\delta}{\mathrm{cos}\alpha\cdot\mathrm{cos}\mathrm{ \varphi}}\right),\mathrm{when}\ H\leq 0 \tag{2}\]  
\[\mathrm{If}\ \delta\geq\mathrm{\varphi},\beta=\cos^{-1}\left(\frac{\mathrm{ sin}\alpha\cdot\mathrm{sin}\mathrm{\varphi}-\mathrm{sin}\delta}{\mathrm{cos}\alpha \cdot\mathrm{cos}\mathrm{\varphi}}\right)-\pi,\mathrm{when}\ H>0 \tag{3}\]  
\[\mathrm{or}\ \beta=\pi+\cos^{-1}\left(\frac{\mathrm{sin}\alpha\cdot\mathrm{sin} \mathrm{\varphi}-\mathrm{sin}\delta}{\mathrm{cos}\alpha\cdot\mathrm{cos} \mathrm{\varphi}}\right),\mathrm{when}\ H>0\]  
The tracking system used in this study belongs to the concentrated solar type of structure. This system uses solar cells installed on both sides of the solar tracking system to convert the solar power and store the power in its battery. The battery storage energy from these two solar cells can supply themicroprocessor power sources (AT89552), GPS (SEN10752P), and two-step motors (TS3630N1210E3) (TAMAGAWA SEIKI CO., LTD, Matsusaka, Japan). Firstly, we use GPS to determine the tracking system location and then use the microprocessor (following Equations (1)-(3)) to control these two motors to rotate the azimuth angle and altitude angle to trace the sunlight, respectively. Besides, in our concentrated tracking system, the sunlight was concentrated by the microstructure of the Fresnel lens (area 1.3 m \(\times\) 0.9 m) to the heating head of the Stirling engine. The system block diagram is shown in Figure 2.  
Figure 1: Biaxial-type tracking system: (**a**) System photo; (**b**) Sunlight focused on the heating head of the Stirling engine at the center of solar tracker (arrow pointing). The focal length of the selected Fresnel lens is defined in its specification. When the sunlight is focused through the lens, it forms a focal area on the heating head of the Stirling engine. In this experiment the position of the heating head was moved to obtain the effect of the size of the focal point on the temperature change of the heating head at varying heating times. The function of the heating head can absorb external heat and supply this thermal energy to the gas inside the Stirling engine. Therefore, the materials of the heating head must have high thermal conductivity and be able to withstand large temperature changes (600 \({}^{\circ}\)C-1200 \({}^{\circ}\)C). In order to track the sun stability, the solar tracker needs to have sufficient mechanical strength and be suitable for machining operations. First, stainless steel, SUS304, was selected and the dimensions of the collector structure were unified for later side-by-side performance comparison. To reduce the weight, the main structure for the tracking system was made of aluminum alloy. The stepper motors, worm gears, and gear reducer were used to drive the overall tracking mechanism.