In remote areas such as deserts, islands, and mountainous regions where grid electricity is unavailable, solar energy has become a vital renewable resource due to its cleanliness and year-round availability. Photovoltaic water pumping systems are widely employed in these contexts, yet most utilize fixed-angle solar panels, which suffer from reduced solar energy utilization efficiency due to the cosine effect. To address this, we propose a novel sun-tracking device that adjusts the tilt angle of photovoltaic panels based on water level changes, specifically designed for photovoltaic water pumping systems. This device employs a three-point support structure, ensuring stability and automated tracking from east to west, while utilizing hydraulic principles for resetting. Our design integrates floating ball drive, constant current water inflow, siphon drainage, and secondary water replenishment units to achieve continuous and efficient solar tracking under various weather conditions.
The core innovation lies in leveraging the inherent water flow from photovoltaic pumps to drive the tracking mechanism, creating a self-sustaining system. The floating ball, connected to the photovoltaic panel via a steel rod, rises with increasing water level in a tank, causing the panel to rotate east to west. A constant inflow device maintains a linear water level rise using nozzle flow principles, while a siphon mechanism empties the tank at day’s end, resetting the panel. For intermittent cloudy conditions, a secondary water replenishment system, controlled by a PLC, ensures tracking continuity. Compared to fixed photovoltaic panels, our device significantly enhances solar radiation capture and water pumping capacity, as validated through theoretical modeling and experimental testing.
The overall structure of the photovoltaic sun-tracking device comprises several integrated units. The solar panel is mounted on a three-point support frame, connected to a floating ball inside a water tank through a steel rod. Water is supplied to the tank via a constant current inlet device, which draws from the main pipeline of the photovoltaic pump. The constant inflow unit consists of an overflow channel, a nozzle, and a drainage channel, ensuring a steady flow rate into the tank. The siphon drainage unit, attached to the tank bottom, triggers a siphon effect when the water level reaches a critical height, rapidly emptying the tank. The secondary water replenishment unit includes a PLC, solenoid valve, and liquid level sensor to adjust water levels during cloudy periods. This holistic design enables autonomous operation without external power, making it ideal for off-grid applications.
To establish the relationship between water level and solar position, we derived mathematical models for the photovoltaic panel’s rotation angle and the required water level changes. The rise height of the floating ball, denoted as H, is determined by the length of the photovoltaic panel L and its tilt angle ε. The rotation angle ψ ranges from ψ₁ (east) to ψ₂ (west), with the panel horizontal at 0°. The height H is given by:
$$H = \frac{1}{2} L \sin(\psi + \varepsilon), \quad -\psi_1 \leq \psi \leq \psi_2$$
At sunrise and sunset, the photovoltaic panel’s tilt angle ε complements the solar altitude angle α, expressed as cos ε = sin α. The solar altitude angle α depends on geographic latitude φ, solar hour angle ω, and declination angle δ, calculated as:
$$\sin \alpha = \cos \phi \cdot \cos \omega \cdot \cos \delta + \sin \phi \cdot \sin \delta$$
The solar hour angle ω and declination angle δ are derived from:
$$\omega = (t_s – 12) \times \frac{\pi}{12}$$
$$\delta = 23.45 \sin\left( \frac{2\pi (N + 284)}{365} \right)$$
where t_s is true solar time and N is the day of the year. The tracking duration Δt is the difference between pump start and stop times. The required water inflow rate Q into the tank, with radius r, is then:
$$Q = \frac{\pi r^2 H}{\Delta t}$$
This ensures the water level rises linearly, mirroring the sun’s apparent motion.
The constant current inlet device maintains a steady flow rate using nozzle outflow and constant pressure overflow. The nozzle flow rate Q₁ is governed by the Bernoulli equation:
$$Q_1 = \mu_n \cdot \frac{\pi d^2}{4} \cdot \sqrt{2g H_0}$$
where μ_n is the flow coefficient (0.61–0.63), d is the nozzle diameter, g is gravity, and H₀ is the height from the baffle top to the orifice center. Setting Q = Q₁ allows determination of H₀ and d for a given flow rate. For example, with H = 76.24 cm, Δt = 12 h, and r = 17.5 cm, Q ≈ 5.01 L/h. Using H₀ = 80 mm and d = 1.5 mm, the actual flow error is within 2%, meeting design requirements.
For cloudy weather, the secondary water replenishment unit adjusts the tank level to maintain tracking continuity. The replenishment flow rate Q_m, based on the level difference ΔH_m and time Δt_m, is:
$$Q_m = \frac{\pi r^2 \Delta H_m}{\Delta t_m}$$
The PLC monitors the water level via a sensor and opens a solenoid valve if the level falls below a set threshold, rapidly correcting the position. This ensures the photovoltaic panel resumes tracking after interruptions.
The floating ball’s mass and size are critical for generating sufficient torque to rotate and reset the photovoltaic panel. During descent, the ball’s gravity must overcome the friction torque and the panel’s moment of inertia. The maximum torque M_max is:
$$M_{\text{max}} = M_f + J \beta$$
where M_f is the friction torque, J is the moment of inertia, and β is the angular acceleration. The friction torque M_f = δ_m L q_N, with δ_m as the rolling resistance coefficient (80 mm for our frame), and q_N as the distributed load. The moment of inertia J = (1/12) m L², with m as the panel mass (29.45 kg). The gravitational torque M_G must satisfy:
$$M_G = G \cdot \frac{1}{2} L \cos \varepsilon \geq M_{\text{max}}$$
Thus, the floating ball mass m_f must be:
$$m_f \geq \frac{\delta_m q_N + \frac{1}{6} m L \beta}{g \cos \varepsilon}$$
For our setup, m_f ≥ 4164 g; we used a 4500 g stainless steel ball. During ascent, the buoyancy force F_f must provide adequate torque:
$$F_f = \rho g V_P$$
where V_P is the submerged volume, maximized when the ball is fully immersed. The net torque M_D during ascent is:
$$M_D = (F_f – G) \cdot \frac{1}{2} L \cos \varepsilon \geq M_{\text{max}}$$
The ball radius R is derived as:
$$R \geq \sqrt[3]{\frac{G}{\frac{4}{3} \pi \rho g} + \frac{\delta_m q_N + \frac{1}{6} m L \beta}{\frac{4}{3} \pi \rho g L \cos \varepsilon}}$$
With R ≥ 14.3 cm, we selected R = 15 cm to ensure reliable operation.
The siphon drainage unit empties the tank automatically when the water level reaches the siphon tube’s apex. The flow rate Q_siphon is calculated using the submerged outflow formula:
$$Q_{\text{siphon}} = \mu_c \cdot \frac{\pi d_c^2}{4} \cdot \sqrt{2g Z}$$
where d_c is the siphon tube diameter, Z is the water level difference, and μ_c is the flow coefficient, given by:
$$\mu_c = \frac{1}{\sqrt{\lambda \frac{l}{d_c} + \zeta_{\text{inlet}} + \zeta_{\text{bend}} + \zeta_{\text{outlet}}}}$$
Here, λ is the friction factor (using Blasius formula for smooth turbulence), l is the tube length, and ζ terms are local loss coefficients (2.5 for inlet, 0.5 for bend, 1 for outlet). For d_c = 4 mm and l = 2 m, the theoretical and measured flow rates align closely with water level changes.
We conducted experiments from October 21 to November 15, 2021, in Yangling, China (108°4’27.95″ E, 34°16’56.24″ N), comparing our tracking device with a fixed-angle photovoltaic system. Both systems used identical solar panels (CS5M32-260, 260 W peak) and DC pumps (M241.5T-5, 130 W). Parameters monitored included water tank level, photovoltaic panel tilt angle, steel rod force, solar radiation intensity, and cumulative water pumpage, with data logged每分钟 via a Kingview monitoring system.
Under clear sky conditions, the water level and photovoltaic panel tilt angle varied approximately linearly with time, as predicted. For instance, at 8:07, a rapid level adjustment occurred due to PLC intervention, correcting for seasonal variation in sunrise time. In cloudy weather, the secondary replenishment unit activated when pump operation stalled, quickly restoring the water level and panel angle to resume tracking. On overcast days, insufficient radiation prevented pump startup, so tracking was not feasible.
The force on the steel rod during ascent and descent was measured with a tension-compression sensor. During ascent, the rod pressure decreased with water level, peaking at 65.66 N, while the maximum buoyancy (138.47 N) exceeded the required force (109.76 N). During descent, the rod tension increased, reaching 40.08 N, less than the ball-chain weight (44.10 N), confirming adequate reset capability.
Siphon drainage flow rates were consistent with theoretical predictions, ensuring reliable tank emptying. Comparative analysis of radiation reception and water pumping under clear and cloudy conditions demonstrated the tracking device’s superiority. On clear days, the tracking photovoltaic panels received 28.56% more solar radiation than fixed panels, leading to a 34.74% increase in water pumpage (3.47 m³ additional). On cloudy days, radiation reception improved by 32.56%, with a 40.82% boost in pumpage (2.58 m³ additional).
| Weather Condition | Radiation Increase (%) | Water Pumping Increase (%) | Additional Water (m³) |
|---|---|---|---|
| Clear Sky | 28.56 | 34.74 | 3.47 |
| Cloudy | 32.56 | 40.82 | 2.58 |
Our discussion highlights the device’s advantages over motor-driven trackers, which are complex and costly. By using hydraulic principles, we achieve simplicity, stability, and energy autonomy. The three-point support enhances durability, while the modular design allows scalability—multiple photovoltaic panels can be synchronized using connected tanks, reducing costs for large-scale applications. However, further optimization is needed for ball size and material to minimize costs, and stability under diverse environmental loads requires additional study. Future work will focus on control algorithms for secondary replenishment, energy efficiency models, and predictive solar tracking to enhance applicability.
In conclusion, we have designed and tested a sun-tracking device that adjusts photovoltaic panel tilt angles via water level, integrating seamlessly with photovoltaic water pumping systems. The device employs a three-point support structure, floating ball drive, constant inflow, siphon reset, and secondary replenishment to achieve efficient solar tracking. Experimental results confirm significant improvements in radiation capture and water pumping under various weather conditions, outperforming fixed photovoltaic panels. This approach offers a practical, low-cost solution for enhancing solar energy utilization in remote areas, with potential for broader adoption in agricultural and off-grid settings.