The pursuit of sustainable and energy-efficient solutions for domestic hot water production remains a critical challenge in building energy conservation. Conventional solar thermal systems, while beneficial, often grapple with issues like low collection efficiency and significant thermal losses, especially under non-ideal weather conditions. This work presents a comprehensive investigation into a novel integrated solar system designed to overcome these limitations. By synergistically combining photovoltaic/thermal (PV/T) collection, loop heat pipe (LHP) technology, and a heat pump (HP) cycle, this system, which we refer to as an advanced solar system, achieves high efficiency, operational flexibility, and significant energy savings. This article details the system’s design, mathematical modeling, simulated performance under various conditions, and experimental validation, highlighting its potential as a superior alternative to traditional water heating methods.
The core innovation of this solar system lies in its multi-modal operational strategy, which intelligently leverages available energy sources. The system comprises two primary loops: the solar photovoltaic-loop heat pipe (PV-LHP) loop and the heat pump loop. The PV-LHP loop features a glazed flat-plate PV/T collector-evaporator, a condenser coil immersed in a storage tank, and connecting tubing filled with refrigerant R22. The heat pump loop shares the same condenser tank but utilizes a separate unglazed finned-tube solar/air collector as its evaporator. This configuration allows the system to switch between three distinct modes based on solar irradiance and time of day, maximizing the utilization of ambient energy.
From 08:00 to 15:00, when solar irradiance is sufficient (typically >300 W/m²), the system operates in the PV-LHP mode. In this mode, the sun’s energy is captured by the PV/T collector. The absorbed heat vaporizes the refrigerant in the evaporator tubes. The vapor, driven by buoyancy, rises to the condenser located in the upper part of the water tank. There, it condenses, releasing its latent heat to the water. The condensed liquid then returns to the evaporator via gravity through a downcomer, completing a passive, pump-free cycle. Simultaneously, the photovoltaic cells generate electricity. After 15:00, or when solar radiation is insufficient, the system switches to a heat pump mode. If solar irradiance is still present, it operates as a dual-source (solar/air) heat pump; otherwise, it functions as a standard air-source heat pump. This intelligent orchestration ensures continuous hot water supply with minimized electrical energy consumption from the grid.
Mathematical Foundation of the Solar System Performance
To accurately predict and analyze the performance of this integrated solar system, a detailed mathematical model was developed. The model is based on energy conservation and thermodynamic principles, encompassing the PV/T collector-evaporator, the LHP condenser, and the heat pump unit.
The incident solar radiation on the tilted collector surface is calculated as:
$$I = I_{bt} \cos \theta + I_{dt} \cos^2\left(\frac{\beta}{2}\right)$$
where $I_{bt}$ and $I_{dt}$ are the beam and diffuse radiation, $\theta$ is the incident angle, and $\beta$ is the collector tilt angle.
The energy balance for the glass cover of the PV/T collector, assuming uniform temperature across its thickness, is given by:
$$\rho_g c_g l_{cg} \frac{\partial T_{cg}}{\partial t} = Q_{cg} – h_a (T_{cg} – T_a) – h_r (T_{cg} – T_a) + (h_{r,p-cg} + h_{c,p-cg})(T_p – T_{cg})$$
Here, $\rho_g$, $c_g$, $l_{cg}$ are the density, specific heat, and thickness of the glass; $h_a$ and $h_r$ are the convective and radiative heat transfer coefficients to the ambient; $h_{r,p-cg}$ and $h_{c,p-cg}$ are the radiative and convective coefficients between the PV panel and the glass cover.
The energy balance for the photovoltaic layer, assuming uniform temperature for the cells, Tedlar-Polyester-Tedlar (TPT) backsheet, and ethylene-vinyl acetate (EVA) encapsulant, is:
$$\xi \rho_p c_p l_p \frac{\partial T_p}{\partial t} = Q_p – (h_{c,p-cg} + h_{r,p-cg})(T_p – T_{cg}) – \frac{T_p – T_c}{R_{p,c}} – Q_e$$
where $\xi$ is the PV cell coverage factor, $R_{p,c}$ is the thermal resistance between the PV layer and the absorber plate, and $Q_e$ represents the electrical energy output.
The instantaneous electrical efficiency of the PV cells is correlated to their temperature:
$$\eta_p(j) = \eta_r [1 – B_r (T_p(j) – T_r)]$$
where $\eta_r$ is the reference efficiency at standard test temperature $T_r$, and $B_r$ is the temperature coefficient.
The heat transfer in the LHP’s evaporator and condenser sections is modeled considering thermal resistances. The overall thermal resistance from the evaporator to the condenser ($R_{e,c}$) includes the wall resistances of the evaporator and condenser tubes, while the interfacial and vapor flow resistances are neglected due to their relatively small magnitude:
$$R_{e,c} = R_{e,p} + R_{c,i} + R_{c,p}$$
The energy balance for the condenser wall and the water in the storage tank (assumed well-insulated) are:
$$M_{p,c} c_{p,c} \frac{\partial T_{p,c}}{\partial t} = \frac{T_{p,e} – T_{p,c}}{R_{e,c}} – \frac{T_{p,c} – T_w}{R_{c,w}}$$
$$c_w m_w \frac{dT_w}{dt} = \frac{T_{p,c} – T_w}{R_{c,w}}$$
where $R_{c,w}$ is the resistance between the condenser wall and the water, $m_w$ is the water mass, and $c_w$ is the specific heat of water.
The useful thermal energy gained by the water in the PV-LHP mode and the corresponding solar thermal efficiency are:
$$Q_c(j) = c_w m_w [T_w(j) – T_w(j-1)]$$
$$\eta_c(j) = \frac{Q_c(j)}{A_c I(j)}$$
The overall photovoltaic-thermal efficiency, a key performance metric for this solar system, is:
$$\eta_o(j) = \eta_c(j) + \zeta \cdot \eta_p(j)$$
where $\zeta$ is a weighting factor for the electrical output relative to thermal energy.
For the heat pump mode, simplified empirical models were developed based on manufacturer data and fitted as functions of ambient temperature ($T_a$), condenser inlet water temperature ($T_{w,in}$), and solar irradiance ($I$). For the dual-source mode:
$$\text{COP}_{\text{SASHP}}(j) = 10^{-3}[72.3 T_a(j) – 29.5 T_{w,in}(j) + 1.64 I(j) – 9.09]$$
For the air-source only mode:
$$\text{COP}_{\text{ASHP}}(j) = 10^{-3}[72.3 T_a(j) – 29.5 T_{w,in}(j) – 9.09]$$
These correlations allow for efficient annual simulations of the complete solar system.
Simulated Performance Analysis of the Integrated Solar System
Using the developed model, the performance of the solar system was simulated under various conditions to understand its characteristics and potential.
Performance in Typical Weather Conditions
The system was simulated for clear days in winter, summer, and spring/autumn. The initial water temperature was set to 10°C, 20°C, and 15°C for these seasons, respectively. The PV/T collector tilt was set to 50°, and the tube spacing was 110 mm with a PV coverage factor of 0.468.
| Season | Final Water Temp after PV-LHP Mode (°C) | Avg. Solar Thermal Efficiency, $\eta_c$ (%) | Avg. PV Efficiency, $\eta_p$ (%) | Avg. Overall PV/T Efficiency, $\eta_o$ (%) | HP Runtime Needed to Reach 45°C | Daily Solar Power Supply Fraction* |
|---|---|---|---|---|---|---|
| Winter | 31.5 | 44.1 | 12.5 | 50.2 | 1.0 hour (COP=1.90) | 38.0% |
| Spring/Autumn | 37.9 | 49.8 | 12.1 | 55.5 | 1.0 hour | ~100% |
| Summer | 42.9 | 49.5 | 11.7 | 55.0 | 0.5 hour | ~100% |
*Fraction of HP electricity consumption offset by PV generation during PV-LHP operation.
The results demonstrate that this solar system achieves solar thermal efficiencies comparable to conventional PV/T systems. The PV efficiency is highest in winter due to lower module temperatures. The overall PV/T efficiency is excellent across seasons. The solar system’s design ensures that in transitional and summer seasons, the PV generation during the daytime can fully cover the short heat pump operation needed to reach the target temperature.
Influence of Key Design and Operational Parameters
The performance of this solar system is sensitive to several parameters. Two critical ones are analyzed below.
1. Photovoltaic Coverage Factor ($\xi$): This factor determines the area ratio of PV cells to the total absorber plate. Simulations show that reducing $\xi$ increases the effective area for thermal absorption, thereby raising the final water temperature and the solar thermal efficiency. However, it decreases the electrical output. The overall PV/T efficiency remains relatively stable, indicating a trade-off. For instance, reducing $\xi$ from 0.668 to 0.268 increased the final water temperature from 36.9°C to 38.9°C and the average $\eta_c$ from 47.6% to 52.1%, while $\eta_o$ slightly decreased from 55.7% to 55.3%. This suggests that for a primarily thermal-driven application of this solar system, a lower PV coverage can be beneficial.
2. Initial Water Temperature ($T_{w,initial}$): The starting temperature of the water in the tank significantly impacts performance. A higher initial temperature leads to a higher final temperature but lowers the solar thermal efficiency because the system operates at a higher average temperature, increasing thermal losses to the environment. For example, increasing $T_{w,initial}$ from 18°C to 28°C decreased the average $\eta_c$ from 47.9% to 41.3% and $\eta_o$ from 53.5% to 46.7%. This highlights the advantage of operating the solar system in the PV-LHP mode starting from a lower water temperature to maximize solar gain.
Long-Term Annual Performance of the Solar System
An annual simulation was conducted using Typical Meteorological Year (TMY) data for Beijing, following the operational strategy of PV-LHP mode from 08:00-15:00 and heat pump mode thereafter. The results summarize the robust yearly performance of this solar system.
| Performance Metric | Value | Notes |
|---|---|---|
| Annual Average Solar Fraction | 50.9% | Percentage of total heating load met by solar (PV-LHP heat + HP’s solar-evaporator heat + PV electricity used for HP) |
| Daily Average Solar Power Supply Fraction | 13.7% | Average portion of the system’s daily electricity consumption offset by its own PV generation |
| Annual Net Electricity Consumption | 729.8 kWh | Total electricity drawn from the grid for the HP compressor |
| Annual Average Heat Pump COP | 3.06 | Weighted average COP across SASHP and ASHP modes |
| Energy Savings vs. Conventional Electric Heater | 71.3% | Based on comparing net electricity use to that needed by a resistive heater (COP=1) |
| Specific Electricity Consumption (Winter Avg.) | ~0.020 kWh/L | Highest in winter due to longer HP runtime and lower COP |
| Specific Electricity Consumption (Summer Avg.) | ~0.003 kWh/L | Lowest in summer due to high solar contribution and short HP runtime |
The annual simulation confirms the significant energy-saving potential of this integrated solar system. With a solar fraction exceeding 50% and substantial energy savings compared to direct electric heating, the system offers a compelling solution for sustainable hot water production. The self-consumption of PV electricity further enhances its economic and environmental profile.
Experimental Validation and Model Accuracy
To verify the accuracy of the mathematical model, an outdoor experiment was conducted for the PV-LHP operating mode. The test rig was set up with a PV/T collector at a 50° tilt, a 1m elevated water tank, and charged with R22. Temperatures and solar irradiance were meticulously recorded.
The comparison between simulated and experimental results for water temperature and solar thermal efficiency showed good agreement. The average relative error for water temperature was 0.66%, while for solar thermal efficiency it was 8.33%. The slightly higher error in thermal efficiency was attributed primarily to thermal losses from uninsulated connecting pipes in the experimental setup—a factor that can be minimized in an optimized installation. The errors for PV efficiency and overall PV/T efficiency were 1.49% and 7.15%, respectively. These results confirm that the developed model is sufficiently accurate for engineering analysis and performance prediction of this solar system, providing a reliable tool for its design and optimization.
Conclusions and Perspective on Solar System Development
This work has thoroughly investigated a novel, multi-modal solar system integrating photovoltaic/thermal collection, loop heat pipes, and heat pump technology. The key conclusions are:
- High and Stable Performance: The solar system demonstrates excellent solar thermal and overall PV/T efficiencies across different seasons, comparable or superior to conventional systems. The unique LHP-based heat transfer is passive and reliable.
- Operational Intelligence and Flexibility: The system’s ability to switch autonomously between PV-LHP, solar-assisted heat pump, and air-source heat pump modes ensures a continuous and efficient hot water supply under all weather conditions, maximizing the use of ambient solar and air energy.
- Significant Energy Savings: Annual simulation results are highly promising, showing a solar fraction of 50.9% and energy savings of over 71% compared to conventional electric water heating. The system’s own PV generation contributes meaningfully to offsetting its operating energy.
- Validated Modeling Tool: The developed mathematical model, validated by experiment, serves as an effective tool for analyzing and optimizing the performance of this solar system.
The design of this solar system represents a significant step forward in building-integrated renewable energy technology. Future work could focus on optimizing the control strategy for mode switching, conducting a detailed techno-economic analysis to evaluate payback periods, and exploring the use of more environmentally friendly refrigerants. Furthermore, integrating thermal energy storage or coupling the system with space heating could expand its applications. This integrated solar system offers a robust, efficient, and sustainable pathway for meeting domestic hot water demands, contributing to the reduction of building sector carbon emissions.