Influence of Rotation Step Size on Incident Solar Irradiance in Flat-Plate Collectors with Single-Axis Tracking Under Clear-Sky Conditions

All solar systems, depending on their purpose, can be classified into three large groups: solar thermal collectors [1] convert solar energy into thermal energy, photovoltaic panels [2] convert solar energy into electricity and photovoltaic-thermal collectors [3] convert solar energy into thermal energy and electricity at the same time.

Regardless of their purpose, all solar systems can be classified, or into the non-tracking (fixed) [4] group, or into the tracking [5] group.

Among other things, the global scientific community has defined several sub-criteria for the classification of tracking solar systems [6] [7] [8] [9] [10] [11] [12] [13] [14]: control strategy (closed-loop, open-loop, hybrid), drive unit (active, passive), degree of freedom (SAT, DAT, Table 1) and strategy method (sensor, date and time, combined).

In the available literature, FPSC with tracking mechanisms, both SAT and DAT, were the subject of theoretical, numerical, experimental and combined research.

Neville [17] developed and presented two mathematical models. First, for describing the thermal performance of the FPSC with SAT, and the second one for describing the thermal performance of the FPSC with DAT. The results of the theoretical research presented by Drago [18] demonstrated the justification of the DAT concept, as this approach can improve thermal efficiency by over 20%. Thomson and Tamm [19], [20] compared the fixed FPSC and the FPSC with DAT. The results of theoretical and experimental research, in the climatic conditions of Estonia (city of Tallinn), indicated that the seasonal energy yield in the case of the tracking solar collector is higher by 10-20%. Depending on the tracking concept, FPSCs can reach the following thermal efficiency values [21]: 57.12% (sun tracking in the N-S direction around the E-W horizontal rotation axis), 62.17% (sun tracking in the E-W direction around the N-S horizontal rotation axis), 59.51% (sun tracking in the E-W direction around the vertical rotation axis), 64.36% (sun tracking in the E-W direction around the N-S inclined rotation axis) and 67.25% (sun tracking with two degrees of freedom). Different approaches in creating mathematical models for the fixed and tracking solar collectors can be found in references [22] [23] [24]. A review paper that, among other things, took into account the economic aspects of tracking FPSCs was presented in Bahrami et al. [25]. The isotropic and anisotropic diffuse (ground albedo and clouds effects) models to estimate the total solar energy received on the fixed and tracking (DAT) FPSCs are theoretically investigated by Kambezidis et al. [26].

The algorithm for adaptive tracking for FPSCs with experimental validation was developed by Neagoe et al. [27]. Their model was based on the new concept that considers inverse tracking as a viable option for protecting the collectors against overheating. For weather conditions in the city of Shtip (Northern Macedonia), Chekerovska and Filkoski experimentally (along with the development and verification of the 3D mathematical model) investigated the Sun tracking effect on the FPSC efficiency [28]. An interesting numerical study (using TRNSYS software) was conducted by Ajunwa et al. [29]. The subject of their study was an FPSC intended for solar drying. The solar collector was equipped with two side reflectors (on the east and west sides) and a manual SAT mechanism. The position of the reflectors could also be adjusted. The authors determined the optimal positions of the west and east reflectors for three months, respectively: 80° and 45° (for January), 80° and 40° (for February and March). Using the manual SAT mechanism, the total percentage of moisture loss increased by 5.11%.

This paper discusses the use of the EnergyPlus software in thermal analyses of solar tracking systems. The mentioned software is not primarily intended for such simulations because it does not have the appropriate tools. This numerical investigation continues the papers presented by Nešović et al. [30], [31], where the research subject was the FPSC with a specific SAT mechanism, more precisely, the FPSCs with SAT tracking in the E-W direction around the N-S rotation axis. For a specific location in Central Serbia (the city of Kragujevac), meteorological data for July 26 were used to determine the relationship between different rotation steps and incident solar radiation during one clear-sky day. Specifically, 8 different tracking scenarios (1°, 2°, 5°, 10°, 15°, 30°, 45° and 90°) were considered in this case. The obtained results are also compared with the performance of the fixed FPSC, which had a controlling role.

Geometric characteristics of the FPSC and main elements of the electro-mechanical transmission in the adopted tracking mechanism are described in Section 2.1. In Section 2.2, meteorological data (incident solar radiation on a horizontal surface, air temperature and wind speed) for the city of Kragujevac during July 26 are presented. The last sections are dedicated to the used software: Google SketchUp (Section 2.3) and EnergyPlus (Section 2.4).

Figure 1 shows the FPSC’s geometry designed in Google SketchUp software. The collector dimensions are 500×800 mm, meaning the collector surface is less than 0.5 $\mathrm{m}^2$. The optimal inclination angle (in the N-S direction) of the solar collector to the horizontal for the city of Kragujevac ($\beta$=34°) was determined according to the recommendations from reference [32]. The lower edge is located at a height of 700 mm from the ground. The given data determine the neutral position of the solar collector in space (Figure 1).

The FPSC is equipped with a specific SAT mechanism. Namely, sun tracking in the E-W direction around the N-S inclined rotation axis is enabled by the use of electro-mechanical transmission. The components of the mechanical transmission are shown in Figure 2, while the components of the electric transmission are shown in Figure 3.

The role of the drive unit, on which the drive chain is located, is played by the hybrid stepper servo motor (Figure 2). The stepper motor is placed under the FPSC. The planetary reducer enables a wide range of rotation step settings (its primary role). The torque, rotation step and mechanical power are transmitted from the drive chain to the chased sprocket via a chain transmission. The driven sprocket is integrated with the FPSC.

The role of the main executive element, during the day, has a microswitch. The microswitch operation is controlled by a logic controller with a predefined date and time schedule. The logic controller determines the stepper motor operation within the layout itself via the stepper motor controller.

Total $H_{{tot}}\left[\mathrm{W}. \mathrm{m}^{-2}\right]$, beam $H_{{beam}}\left[\mathrm{W}. \mathrm{m}^{-2}\right]$ and diffuse $H_\textit{diff}\left[\mathrm{W}. \mathrm{m}^{-2}\right]$ terrestrial solar radiation on the horizontal surface located in the city of Kragujevac $\left(\varphi=44.02^{\circ} \mathrm{N}\right.$ and $\left.\lambda=20.92^{\circ} \mathrm{E}\right)$ during July 26 are shown in Figure 4.

For July 26 (clear day, sunrise at 04:23 h, sunset at 19:03 h), the following average daily values were measured (Figure 4): $H_{\textit{tot,avg}}=667.61 \mathrm{~W} \cdot \mathrm{~m}^{-2}, H_{\textit {beam,avg}}=525.83 \mathrm{~W} \cdot \mathrm{~m}^{-2}$ and $H_{\textit{diff,avg}}=141.78 \mathrm{~W} \cdot \mathrm{~m}^{-2}$. The maximum values were recorded at 13:30 h ($\left.H_{\textit{tot,max}}=978 \mathrm{~W} \cdot \mathrm{~m}^{-2}\right), 14: 30 \mathrm{~h}\left(H_{\textit{beam,max}}=838 \mathrm{~W} \cdot \mathrm{~m}^{-2}\right)$ and $11: 30 \mathrm{~h}\left(H_{\textit{diff, max}}=258 \mathrm{~W} \cdot \mathrm{~m}^{-2}\right)$. The cloudy-sky periods (which can be concluded from the discontinuity of the terrestrial beam solar radiation curve) are present in the period from 07:30 h to 15:00 h.

During the mentioned period for the analyzed location, the wind speed c_w [m.s^-1] (Figure 5) is variable, but it is within the limits between c_w,min=0.4 m.s^-1 (07:00 h) and c_w,max=3.1 m.s^-1 (17:00 h). Average daily air temperature is t_o,avg=21.81°C (Figure 5). Minimum and maximum daily values are t_o,min=19.1°C (04:00 h) and t_o,max=24.7°C (15:00 h), respectively.

Google SketchUp software is primarily intended for the 3D modeling of buildings [34]. The interface provides faster and simpler work compared to other similar software. Models with a large number of details (shading elements, daylighting control, etc.) can be created in this software. It also provides many other possibilities, such as integration with Google Earth services and EnergyPlus software. Communication with EnergyPlus software is enabled by 2 tool palettes: Legacy OpenStudio and Legacy OpenStudio Rendering.

The EnergyPlus software is intended for numerical investigations of energy and ecological communication between buildings and the environment [35]. It was developed by Lawrence Berkeley, the National Laboratory, the US Army Construction Engineering Laboratory, and the University of Illinois [36]. The software is used in various thermo-technical analyses: heating, cooling, air conditioning, ventilation, solar systems, etc.

Since there are no models for analyzing tracking solar systems in the EnergyPlus software, the models were artificially created for the purposes of this study.

Namely, through a series of simulations, the total incident solar radiation was calculated during the day, for each FPSC rotation angle in the E-W direction around the inclined N-S rotation axis (Figure 6): from -90° (the moment of sunrise) to +90° (the moment of sunset). The rotation angle was 1°. For the results to be as accurate as possible, the one-minute time step was used (Figure 4 and Figure 5). The maximum numerical value for each rotation angle at a given time was used to form the daily curve of total incident solar radiation. In this way, a large database was created, which was then used to create different tracking scenarios, in this particular case, based on 8 rotation steps $\psi\left[^{\circ}\right]: \psi=1^{\circ}, \psi=2^{\circ}, \psi=5^{\circ}, \psi=10^{\circ}, \psi=15^{\circ}, \psi=30^{\circ}, \psi=45^{\circ}$ and $\psi=90^{\circ}$. All analyzed cases are graphically presented in Figure 7.

Total incident solar radiation $I_{tot}$ [W] on the tracking surface, i.e., FPSC with SAT, is determined by Eq. (1):

where, $I_\textit{beam}$ [W] is the beam incident solar radiation, $I_\textit{diff}$ [W] is the diffuse incident solar radiation Eq. (2) and $I_\textit{refl}$ [W] is the reflected incident solar radiation Eq. (3) [37].

where, $I_\textit{diff, cr}$ [W] is the diffuse incident solar radiation from the circumsolar region, $I_\textit{diff, sd}$ [W] is the diffuse incident solar radiation from the sky dome, $I_\textit{diff, sh}$ [W] is the diffuse incident solar radiation from the sky horizon, $I_\textit{refl, beam}$ [W] is the reflected beam incident solar radiation and $I_\textit{refl, diff}$ [W] is the reflected diffuse incident solar radiation [37].

In the following diagram (Figure 8), firstly are shown the numerical results of the average daily total incident solar radiation $I_{\textit{tot,avg}}\left[\mathrm{W}\right.$. day $\left.^{-1}\right]$ on the fixed FPSC for some cases of the angle $\psi_\textit{fix}\left[{ }^{\circ}\right]$. The results are based on the use of meteorological data for the city of Kragujevac during July 26, which was already mentioned in Sub-section 2.2. In all analyzed cases, the angle $\beta=34^{\circ}$ is the same. The angle $\psi_\textit{fix}=-90^{\circ}$ refers to the solar collector that is completely facing east during the day. When $\psi_\textit{fix}=0^{\circ}$, the solar collector is oriented towards the south during the day, which means that in the case of $\psi_\textit{fix}=90^{\circ}$ it is completely facing west.

As shown in Figure 8, $I_{\textit{tot,avg}}$ value is the highest when the fixed FPSC is oriented towards the south at an angle of $\beta=34^{\circ}$ ($I_\textit{tot,avg}=209.24 \mathrm{~W}$. day $^{-1}$). In cases where $\psi_\textit{fix}=-90^{\circ}$ and $\psi_\textit{fix}=90^{\circ}$, this value is reduced 1.78 times $\left(I_{\textit{tot, avg}}=117.55 \mathrm{~W}{. \text {day }^{-1}}\right)$ and 1.86 times $\left(I_\textit{tot, avg}=110.83 \mathrm{~W}{.\text {day}^{-1}}\right)$.

The orientation of the FPSC primarily affects the component $I_{\textit{beam, avg}}\left[\mathrm{W}\right.$. day $\left.^{-1}\right]$, because it is directly related to the solar incident angle [38]. Since the component $I_{\textit{diff, avg}}\left[\mathrm{W}\right.$. day $\left.^{-1}\right]$ originates from three sources (Section 3), its share in $I_{\textit{tot, avg}}\left[\mathrm{W}\right.$. day $\left.^{-1}\right]$ is much smaller and can be neglected in some cases. For the sake of comparison, the option $\psi_{f i x}=-60^{\circ}$ is 34.86% better than $\psi_{fix}=-90^{\circ}$, but also 24.24% worse than $\psi_{fix}=0^{\circ}$. The diagram shown in Figure 7 actually proves that the southern orientation of the fixed FPSC is the optimal solution.

The comparison of all 8 adopted tracking scenarios (Section 3, Figure 7) through the $I_{tot,avg}$ indicator during the same day (July 26) is shown in Figure 9 and Table 2.

If the mentioned values $I_{{tot,avg}}$ for FPSC with different rotation steps (Figure 9), are compared with the value $I_{{tot,avg}}$ for $\psi_{fix}=0^{\circ}$ (Figure 8), i.e., FPSC, the following SAT mechanism benefits can be seen: 35.923% for $(\left.\psi=1^{\circ}\right)$, 35.918% (for $\psi=2^{\circ}$), 35.85% (for $\psi=5^{\circ}$), 35.75% (for $\psi=10^{\circ}$), 35.51% (for $\psi=15^{\circ}$), 34.26% (for $\psi=30^{\circ}$), 32.95% (for $\psi=45^{\circ}$) and 23.04% (for $\psi=90^{\circ}$).

The next diagram (Figure 10) shows the $I_{{tot}}[\mathrm{W}]$ values, both for the fixed FPSC ($\psi_{f i x}=0^{\circ}$) and for some cases tracking FPSC ($\psi=1^{\circ}, \psi=30^{\circ}, \psi=45^{\circ}$ and $\psi=90^{\circ}$). Solar radiation curves, from sunrise to sunset (July 26), were created based on a sample with a one-minute measurement step.

The first thing that can be seen from Figure 10 is that the rotation step increases the area under the solar curve. Thus, for example, the area under the solar curve $\psi$=90° is greater than the area corresponding to the solar curve $\psi_\textit{fix}$=0°. The area under the solar curve $\psi$=1° is the largest, which is according to the Itot,avg values ($I_\textit{tot,avg}$=284.41 W . day${ }^{-1}$). Figure 10 also shows that the solar curves overlap to some extent during the day: $\psi$=90° and $\psi_\textit{fix}$=0° (for example, between 08:44 h and 14:41 h), $\psi$=1°, $\psi$=30°, $\psi$=45° and $\psi$=90° (for example, between sunrise and 06:14 h), etc. Another interesting effect can be observed from Figure 10, which is that there is a short period during the day when all the solar curves are tangent to each other. It is the period of solar noon (11:43 h). Then the sun is at its zenith (maximum altitude angle $\alpha_{\max}$=65.58°) for the analyzed day (in this case, July 26), so the solar incident angle is the same for all solar structures, regardless of whether the tracking mechanism is applied or not, regardless of the applied rotation step.

Tanging also occurs when the $I_{\textit{tot}}$ value decreases, that is, due to the reduction of the $I_{\textit{beam}}$ (moments of cloudiness, between 07:56 h and 09:31 h, Figure 10). Then the power of the solar collector for $\psi=90^{\circ}$ is close to the power of the solar collector for $\psi=0^{\circ}$, and the same phenomenon occurs at $\psi=1^{\circ}, \psi=30^{\circ}$ and $\psi=45^{\circ}$. This means that weather conditions affect the energy performance of tracking solar collectors.

In relation to $\psi_{f i x}=0^{\circ}$, the greatest benefits in the case of using $\psi=90^{\circ}$ are achieved in the morning and evening hours, concretely at 06:30 h ($I_{tot}$ is higher for 166.62 W). The advantage of using the remaining rotation steps ($\psi=1^{\circ}$, $\psi=30^{\circ}$ and $\psi=45^{\circ}$) in relation to $\psi=90^{\circ}$ is achieved precisely between the mentioned (morning and evening) periods and the moment of solar noon (Figure 10): $\psi=45^{\circ}$ ($I_\textit{tot}$ is higher for 102.76 W, 14:40 h), $\psi=30^{\circ}$ ($I_\textit{tot}$ is higher for 89.09 W, 14:41 h) and $\psi=1^{\circ}$ ($I_\textit{tot}$ is higher for 101.98 W, 14:39 h).

In this paper, the numerical method (tool) was applied to analyze the thermal performance of the FPSC with a specific tracking mechanism (SAT in the E-W direction around the N-S inclined rotation axis). For this purpose, the following software was used: Google SketchUp (for defining the geometry) and EnergyPlus (for conducting simulations). The simulations were conducted using weather data for the city of Kragujevac. The main goal of the paper was to determine the functional dependence between different rotation steps (1°, 2°, 5°, 10°, 15°, 0°, 45° and 90°) and incident solar radiation for a selected location during one clear-sky day (July 26). The control role is assigned to the fixed FPSC. All solar collectors (tracking and fixed) had the same inclination angle to the horizontal (34°).

Results showed that the total average incident solar radiation for the fixed FPSC is 209.24 W.day$^{-1}$. The same parameter in the case of the tracking FPSCs ranged between 257.45 W.day$^{-1}$ (for 90°) and 284.41 W.day$^{-1}$ (for 1°). In comparison with the fixed FPSC, the percentage benefits of the tracking FPSC were between 23.04-35.923%.

Taking into account adopted location parameters, investment costs, weather parameters that can be variable, as well as simulation results, the general practical recommendation is that a rotation step smaller than 15° has no practical sense because the impact on the total average incident solar radiation is almost negligible.

Following the research results, additional numerical simulations of the SAT solar collectors will be conducted in the coming period. They will take into account different locations in Serbia (1) and incident solar radiation in variable meteorological conditions, such as days with extremely clear-sky and cloudy-sky days (2).