To improve the solar energy utilization in the photovoltaic power, the sun ray double axis tracking device is designed and its tracking method is introduced. Using the finite element method, the parameterized analysis model is built and the static calculation is performed in different conditions for the device. The design feasibility of the device is verified by evaluating the stress. The lightweight of the device is made on the premise that the design satisfies the intensity and this provides the basis for manufacturing the prototype. The sun's rays tracing experiment is carried out by the prototype. Results show that the device design is reasonable and meets the design requirements; the key working conditions for the solar tracking design are found; the lightweight is obvious and the weight is reduced by 14%; the average errors of azimuth angle and height angle are within 5 deg; compared with the fixed device, the increasing proportion of solar energy one day is up to 52.6%; and the device works steadily and has good mechanical properties.

## Introduction

With the growing consumption of fossil energy and the environmental pollution, developing sustainable and clean new energy is the common goal of all countries. As a new renewable energy, solar energy is infinite, producing clean and economic energy [1]. To improve the solar energy utilization of solar panels, one important method is to keeping the solar panels perpendicular to solar irradiation [2]. There are three types of the solar trackers by their degree-of-freedom: the fixed system, the single axis tracking system, and the double axis tracking system [3,4]. To maximize the solar energy utilization, the double axis tracking becomes a research hot spot [5,6]. Based on the control system, the solar trackers are divided into active and passive systems [7,8].

Active systems are generally an open-loop system without feedback, because the Sun's position is definite in a specific geographical location at different times, days, and seasons. They are three types of active systems: (1) based on sensor [9,10]; (2) based on time [11]; and (3) based on sensor and time [4]. Passive systems use the partial pressure produced by the sun heat to track the sun [12]. These systems are relatively cheap, but the rotation is not accurate and it takes a long time to orient it toward the Sun in the morning. So, they have not yet been accepted by the consumer.

The past research about solar trackers includes the control strategy, the tracking method, the and tracking sensor. But the economical systems are inappropriate for the concentrating photovoltaic power, and the accurate systems are mostly expensive and/or complicated. In addition, most of the solar trackers do not consider the structural performance and the light weight, especially for the large solar trackers. Since the form and structure of the tracking device is diverse, it requires mechanism to locate reliably and bear large load, so reasonable layout and design for the structure of the tracking device is essential. Another key point on the premise that the design satisfies the stress intensity and rigidity, the lightweight of the device is an important way to reduce the cost.

In this study, a double axis sun ray tracking device with low cost and high accuracy was presented. Solar cell sensor and DSP56F8346 microprocessor were used to track the sun. The tracking device was independent of the geographical location and initial settings. It has the advantages of stable and reliable operation, small tracking error, high strength, simple structure, and low cost.

## Materials and Methods

The Sun related to earth has two types of movement in the azimuth and altitude angle directions. The proposed system included tracking device and control system. The control system consists of hardware and software. The hardware is mainly composed of microprocessor control unit, power supply circuit, serial communication circuit, photoelectric detection unit, motor drive unit, proximity switch, and its corresponding peripheral circuit. The composition of the hardware is shown in Fig. 1. The system is directly driven by the photovoltaic module. Considering that the output of the photovoltaic module is DC, and the high cost of stepping motor, the system uses two brushless DC motors to drive the motor.

The photoelectric detection unit includes four solar cells sensor as shown in Fig. 2. The photoelectric detection unit mainly consists of four identical small photovoltaic cells. Two cells is a pair. One pair is responsible for detecting the altitude angle difference, and the other is responsible for detecting the azimuth angle difference. Each solar cell keeps the same angle with the below plane. Because the short-circuit current of the solar cell is directly proportional to the illumination intensity, the short-circuit current is usually used to measure the illumination intensity or the incidence angle of the sunlight. The relationship between short circuit current and incident angle is
$Isc=kSIn cos γ+qkSIn=(cos γ+q)kSIn$
(1)

where $k$ is the ratio coefficient of direct light, $q$ is the ratio coefficient of stray light, $S$ is the area of solar cell, $In$ is the irradiance on the vertical plane of sunlight, and $γ$ is the angle between sunlight and the plane of solar cell.

## Tracking Device Design

Taking a 1 kW sun ray double axis tracking device as an example, the mechanical structure of the sun ray double axis tracking device was developed. The parameterized model was established by using the finite element method. Considering different working conditions, the static analysis was carried out to obtain the displacement and stress distribution, and the stress assess was made. Under the foundation of satisfying the stress intensity, the lightweight was carried out and this provided the foundation for prototype test of the device. Finally, the prototype was manufactured and the tracing experiment was taken.

The 1 kW sun ray double axis tracking device is shown in Fig. 3. It is composed of the solar panels frame, the rotative bracket, the slewing bearing, the pillar, the support of the screw elevator, the screw elevator, and so on. The down-flange of the pillar is installed on the ground by bolts. The up-flange of the pillar is connected with the slewing bearing's outer ring by bolts. The slewing bearing's inner ring is connected with down-flange of the rotative bracket. The RV worm-gear reducer and the azimuth angle motor are installed on the rotative bracket. The input shaft of the reducer connects with the azimuth angle motor and the output shaft connects with the gear. The gear and slewing bearing's outer ring gear develop the gear transmission. The left side of the rotative bracket and the solar panels frame form the rotational connection by a pin. The right side of the rotative bracket and the elevator base form the rotational connection by a pin. The elevator is installed on the support of the screw elevator. The input shaft of the elevator connects with the altitude angle motor and the output shaft forms the rotational connection with the solar panels frame by a pin.

The detailed work process of the device is as follows: When it tracks the solar azimuth angle, the solar panels, the solar panels frame, the rotative bracket, two motors, the elevator, the support of the screw elevator and the RV worm-gear reducer rotates around the pillar by the gear transmission. And this can realize 0–360 deg sun tracking in the azimuth angle direction. When it tracks the solar altitude angle, the solar panels frame can realize 0–90 deg sun tracking in altitude angle direction under the thrust of the screw elevator.

## Mathematical Model

The displacement and stress distribution of the tracking device under different working conditions can be obtained by using the basic theory of elasticity, establishing the equilibrium equation, geometric equation, and physical property equation, and then verifying the feasibility of the design structure. The model is now divided into a finite number of microbody elements, each of which has a stress component: $σx$, $σy$, $σz$, $τxy$, $τyz$, $τzx$, a strain component: $εx$, $εy$, $εz$, $γxy$, $γyz$, $γzx$, a displacement component: $u$, $v$, $w$, and the equilibrium equation is
$∂σx∂x+∂τyx∂y+∂τzx∂z+X=0∂τxy∂x+∂σy∂y+∂τzy∂z+Y=0∂τxz∂x+∂τyz∂y+∂σz∂z+Z=0}$
(2)
The geometric equation is
$εx=∂u∂x,εy=∂v∂y,εx=∂w∂zγyz=∂w∂y+∂v∂zγxz=∂u∂z+∂w∂xγxy=∂v∂x+∂u∂y}$
(3)
The physical property equation is
$σx=λθ+2Gεxσy=λθ+2Gεyσz=λθ+2Gεzτyz=Gγyzτxz=Gγxzτxy=Gγxy}$
(4)
If the surface force on the surface of the object is $X¯$, $Y¯$, $Z¯$, and the displacement at the surface is $u¯$, $v¯$, $w¯$, then the static boundary condition is
$X¯=σxl+τyzm+τzxnY¯=τxyl+σym+τzynZ¯=τxzl+τyzm+σzn} at Sσ$
(5)
And displacement boundary condition is
$u=u¯, v=v¯, w=w¯, at Su, at Su$
(6)

where $θ=εx+εy+εz$, $λ=(Eμ)/((1+μ)(1−2μ))$, $G=(E)/(2(1+μ))$, with E being the elastic modulus. In Eq. (2), ($X$, $Y$, $Z$) is the force of the microbody. In Eq. (5), $Sσ$ is the boundary part of a given external force on the surface of an object. $(l,m,n)$ is the exterior normal of a point at $Sσ$.

($X¯$, $Y¯$, $Z¯$) is the known function of a point at the $Sσ$. In Eq. (6), $Su$ is the boundary part on the surface of an object. ($u¯$, $v¯$, $w¯$) is the known function of a point at $Su$.

Because of the complex structure of the tracking device, it is difficult to obtain the exact analytical solution of the differential equation. The finite element method is used to calculate its displacement and stress.

## Finite Element Model

The loads of the tracking device mainly include its own gravity, wind load, snow load, and earthquake load. In this design, the gravity and wind load were mainly considered. According to the theory of elastic mechanics, the finite element method was used, and the displacement and stress distribution of the device was obtained. And the feasibility of the design structure was verified by stress assessment [13]. The calculation considers four states of the two limit position in the condition of the downwind and headwind to find out the most dangerous working condition and evaluates the stress.

Considering the bearing capacity of the main components for the tracking device, the simplified finite element model is shown in Fig. 4. To reduce the number of grid and improve the efficiency of calculation, the solar panels frame, the rotative bracket, the support of the screw elevator, and the pillar are simulated by shell181 [14]. The slewing bearing is simulated by solid185 [15]. Without considering the stress and displacement of the elevator, the motor, and the reducer, their detailed structures are simulated by mass21 to consider the influence of the gravity to the stress and the displacement. The lead screw is simulated by beam188. The bolted and welded connecting parts are simulated by coupling nodes. The pin connecting is simulated by hinge element of mpc184 [16]. The material of the steel shapes is Q235 and the material of other components is No.45 steel.

## Boundary Condition

When the device is working, the combined loadings in four states of the two limit position under the condition of the downwind and headwind are as follows:

Condition 1: Fixed the bottom of the pillar + the solar panels frame is horizontal + gravity + 12 level downwind pressure ($P=0.613×v2$, v is the wind speed), as shown in Fig. 5.

Condition 2: Fixed the bottom of the pillar + the solar panels frame is horizontal + gravity + 12 level headwind pressure, as shown in Fig. 5.

Condition 3: Fixed the bottom of the pillar + the solar panels frame is vertical + gravity + 9 level downwind pressure, as shown in Fig. 6.

Condition 4: Fixed the bottom of the pillar + the solar panels frame is vertical + gravity + 9 level headwind pressure, as shown in Fig. 6.

## Stress Calculation and Evaluation

The displacement and stress distribution of the tracking device are shown in Figs. 710. Figure 7 shows that the maximum displacement of the device is on the edge of the solar panels frame, whose size is 9.47 mm. The maximum stress is occurred in the connection of the cylinder vertical axis on the base of the bracket and the steel plate, whose value is 113 MPa. Figure 8 shows that the maximum displacement of the device is on the edge of the solar panels frame, whose value is 6.32 mm. The maximum stress is occurred in the connection of the angle iron of the solar panels frame and the rectangular steel pipes, whose value is 69.1 MPa. Figure 8 shows that the maximum displacement of the device is on the edge of the solar panels frame, whose value is 9.28 mm. The maximum stress is occurred in the connecting base of the pillar, whose value is 69.8 MPa. Figure 8 shows that the maximum displacement of the device is on the edge of the solar panels frame, whose value is 16.15 mm. The maximum stress is occurred in the connecting base of the pillar, whose value is 119 MPa.

Because Q235 and 45 are plastic materials, strength assessment is made in accordance with the fourth strength theory [17]. The maximum stress, allowable stress, which is extracted in postprocessing under different conditions, is shown in Table 1. Evaluation results are in the allowable range, meeting the design requirements, having a certain optimization space.

## Lightweight of the Device

To reduce material costs and make device's weight minimum on the condition of meeting the mechanical properties of devices, it is necessary to carry out lightweight. The weight proportion of the frame, bracket, and pillar of the device is large. Therefore, lightweight is mainly to reduce the weight of the three parts.

The angle steel thickness $T1$ of the frame, the thickness $T2$ of the rectangular steel of the frame, the rectangular steel thickness $T3$ of the bracket, and the cylinder thickness $T4$ of the pillar were selected as design variables. Their range of the parameters is
$0.003≤T1≤0.0080.002≤T2≤0.0070.002≤T3≤0.0070.003≤T4≤0.008}$
(7)

The maximum stress SMAX was selected as state variables. And its value is $σmax≤[σ]=142$ MPa.

The overall mass of the device M was selected as the target function: M→min.

The structure of the device is complex, the number of elements and nodes is large, and the derivatives of the objective function and constraint function are not easy to obtain. Therefore, the zero-order method is used to optimize the solution [18]. For the zero-order method, because it is a random search, the convergence speed may be slow, so the number of iterations is set to 15 times.

Based on the static analysis, the most unsafe condition 4 was selected and the device was optimized. And then the device was checked in the other three conditions in order to lay the foundation for test of the prototype. By optimizing the thickness of steels, ultimately on the condition of meeting the strength given by design requirement, the weight of the device is minimized.

Figure 11 shows the relationship between the design variables, objective function M, and the iterations. Table 1 shows the stress assessment under different conditions after optimizing. Table 2 shows the contrast results for before and after optimizing. Results show that the angle steel thickness $T1$ of the frame and the cylinder thickness $T4$ of the pillar, respectively, reduce 1 mm. The rectangular steel thickness $T2$ of the frame reduces 0.5 mm. The rectangular steel thickness $T3$ of the bracket is not changed. Overall mass of the device reduces 40 kg and the effect of the lightweight is obvious. Because the maximum stress of condition 3 changes a little, the angle steel thickness $T1$ of the frame, the rectangular steel thickness $T2$ of the frame, and the cylinder thickness $T4$ of the pillar have little impact on it. Further optimization can reduce the rectangular steel thickness $T3$ of the bracket. In a word, the optimized device meets the strength requirement, and compared with original design, the weight is reduced by 14%.

## Device Tracking Test

The prototype of the tracking device is shown in Fig. 12. In order to test the operation effect of the two-axis solar ray tracking system in the actual environment, the sun tracking test is carried out. Testing environment: the weather is fine. Testing content: measure the average deviation of the azimuth and altitude angle between solar panel and sunlight. The test time ranges are from 9 a.m. to 15 p.m. The measuring interval time is 30 min and the total times of one day is 12. Figure 13 shows that the azimuth error between solar panels and solar rays fluctuates greatly with time, exceeding 5 deg in the first two measurements, and then ten measurements are within 5 deg; the altitude angle error varies smoothly with time, and the error is always within 5 deg; in a word, the average error of azimuth and altitude angle is within 5 deg, and the tracking device works steadily. Compared with 2 deg of the average error [19], although the average error is 3 deg larger, the price of solar cell is less than the camera. According to 12 h of sunshine per day and compared with the fixed device, the increasing proportion of solar energy one day is up to 52.6%. The solar tracking system is stable, reliable, and can meet the tracking requirements. It can greatly improve the solar ray reception rate.

## Conclusion

In this study, an inexpensive sun ray double axis tracking device is designed, and its tracking method uses four solar cells and DSP56F8346 microprocessor to track the azimuth and altitude angle. The mathematical model and finite element model are built and four conditions are considered. The stress calculation and evaluation, lightweight of the device are carried out. Results show that the device strength in four working conditions can meet the design requirement and the design of tracking device is reasonable; the dangerous conditions were conditions 1 and 4, which should be the key working conditions for the solar tracking design; on the basis of meeting the strength, the lightweight was obvious and the weight is reduced by 14%, and the key parameters are the angle steel thickness $T1$ of the frame, the rectangular steel thickness $T2$ of the frame, and the cylinder thickness $T4$ of the pillar; the average error of azimuth and altitude angle is within 5 deg; Compared with the fixed device, the increasing proportion of solar energy one day is up to 52.6%, and the tracking device works steadily.

## Funding Data

• National Natural Science Foundation of China (Grant No. 51672241, Funder ID. 10.13039/501100001809).

• The 14th batch High-level Talents Project for “Six Talents Peak” (Grant No. XCL-092).

• Province Postdoctoral Foundation of Jiangsu (Grant No. 1501164B).

• Technical Innovation Nurturing Foundation of Yangzhou University (Grant No. 2017CXJ024).

• China Postdoctoral Science Foundation (Grant No. 2016M600447).

• Yangzhou Innovative Capacity Building Plan Project (Grant No. YZ2017275).

• Yangzhou University Science Foundation Project (Grant No. x20180290).

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