Evaluating the Performance of Photovoltaic Thermal Systems in Varied Climate Conditions: An Exergy and Energy Analysis Approach

Global warming, predominantly attributed to the utilization of fossil fuels, presents a significant risk to the future. It is widely acknowledged that the transition to renewable energy sources is the most viable solution to this challenge. Solar energy, with its abundant and clean properties, has emerged as a crucial energy source worldwide, offering a sustainable alternative to the fossil fuel-dominated energy supply system, which has adversely impacted the environment and sustainability.

In scenarios of energy crises, solar energy, along with other renewable sources, is increasingly recognized as a viable and readily available solution for long-term energy security. Solar energy, in comparison to other renewable sources, excels in terms of accessibility, capacity, affordability, and efficiency. Consequently, the solar energy sector is poised to play a pivotal role in meeting future energy demands [1]. A notable innovation in this sector is the integration of thermal collectors with photovoltaic (PV) modules to form PV/T systems. These systems enable the concurrent collection of thermal and electrical energy from solar radiation using a single module. PV/T systems are commonly designed as either flat plate or concentrated collectors, depending on the fluid flow configuration [2]. The two primary working fluids in these systems are air and water. Water-based PV/T collectors are deemed more efficient due to water's higher heat capacity compared to air [2]. Moreover, the cooling effect of water can enhance the electrical efficiency of PV cells. Since the 1970s, PV/T technologies, including design modifications, working fluid configurations, and other factors influencing performance, have been extensively studied [3]. A notable challenge in PV/T system design is achieving optimal electrical and thermal efficiencies, as these efficiencies are inversely related to cell temperature, which is significantly influenced by ambient temperature, wind velocity, and the working fluid's mass flow rate and inlet temperature. These factors are critical in optimizing the overall performance of a PV/T module [4].

To ascertain the efficacy of PV/T systems, their physical characteristics are meticulously analyzed in both theoretical and experimental domains. Studies have investigated diverse water flow rates, ranging from 0.011 kg/s to 0.041 kg/s, corresponding to each level of solar radiation (500-800 W/m²). This variation in flow rates is instrumental in enhancing the heat transfer coefficient for water-based PV/T systems [3]. According to research examining PV/T systems under a spectrum of operational conditions and variable components, the overall efficiency of these systems fluctuates between 47.4% and 80% [3]. A detailed study by Brahim and Jemni [5] reported the average electrical, thermal, and total efficiencies of a PV/T module as approximately 12.52%, 43.75%, and 56.27%, respectively, particularly at lower inlet temperatures. The performance of PV/T systems is subject to geographical and temporal variations across different locales, influenced by fluctuating weather conditions where factors like irradiance and ambient temperature are beyond control. The pivotal elements affecting the thermal and electrical efficiency of PV/T systems are thoroughly explored using a mathematical model, which includes the analysis of the inner heat pipe [5]. In the realm of energy systems, energy represents the capacity to do work or produce heat within a system. Contrastingly, exergy signifies the quality or potential of energy in a system, defined as the maximal work achievable when the system attains equilibrium with its surroundings. Exergy analysis has become a fundamental tool in assessing the efficiency and sustainability of energy conversion processes. It elucidates the potential for useful work and identifies the losses or irreversibilities within a system. This analytical approach has been applied by several researchers in evaluating the energy and exergy efficiency of PV/T systems [6, 7]. An insightful study [8] delves into the analysis of experimental data from a water-based PV/T system, acquired through indoor experiments, utilizing MATLAB code for comprehensive analysis. Correspondingly, another research utilizing MATLAB modeling and simulation elucidated that the efficiency of photovoltaic panels diminishes as cell temperature escalates due to increased solar radiation, highlighting the intricate relationship between solar exposure and photovoltaic efficiency. Furthermore, the efficiency of a PV/T water collector has been rigorously evaluated through both experimental and numerical approaches [9]. This research juxtaposes the performance of the PV/T system with findings derived from both experimental data and numerical analyses, conducted through energy and exergy analysis of the system. In parallel, Gül and Akyüz [10] embarked on a study focusing on the electrical and thermal performance of a liquid flat-plate PV/T system, culminating in the model's validation against experimental results. Simulation outcomes indicated that thermal efficiency was adversely affected by elevated fluid inlet and ambient temperatures, achieving its zenith at a solar radiation intensity of 800 W/m².

This paper presents an in-depth analysis aimed at evaluating the performance of a PV/T household hot water system, utilizing both energy and exergy analysis under the climatic conditions of Tehran. The primary objective of this investigation is to pinpoint potential areas for enhancing the efficiency of the PV/T system. Through meticulous energy and exergy analysis, areas prone to inefficiency or energy loss within the PV/T system are identified. Such insights are pivotal for refining the design, operational tactics, and control strategies of the system, thereby augmenting overall performance and maximizing energy yield. A critical aspect of this study is its emphasis on the potential of specialized thermal absorber manufacturers to integrate their products into singular PV devices, transforming them into more efficient PV/T systems, particularly in terms of maximizing efficiency over a given roof area.

The research introduces an innovative experimental setup and employs a novel methodology integrating both energy and exergy analysis for a comprehensive evaluation of the PV/T system's efficacy. Furthermore, by juxtaposing numerical results with experimental data, the study validates the accuracy and reliability of the numerical model employed. This validation process significantly enhances the credibility of the numerical model, ensuring that the findings are both reliable and applicable to real-world scenarios.

The energy and exergy analyses are conducted to determine how the PV/T system works.

3.1 Energy analysis

The following assumptions are made to model the PV/T system:

1. The system is studied one-dimensionally.
2. The system is in a steady-state condition.
3. Ohmic losses in solar cells are assumed to be negligible.

The energy balance equations for each component of the PV/T system are as follows [14]:

For solar cells of PV module:

$\begin{gathered}\alpha_c \tau_c \beta_c I W d x=\left[U_{t c, a}\left(T_c-T_a\right)+h_{c, p}\left(T_c-\right.\right. \left.\left.T_p\right)\right] W d x+\eta_c \tau_c \beta_c I W d x\end{gathered}$          (4)

For blackened absorber plate temperature under the PV module:

$\alpha_p \tau_g^2\left(1-\beta_c\right) I+h_{c, p}\left(T_c-T_p\right)=h_{p, f}\left(T_p-T_f\right)$               (5)

The energy balance of flowing water through the absorber pipe under the PV module is given by:

$\grave{m}_f C_f \frac{d T_f}{d x} d x=F^{\prime} h_{p, f}\left(T_p-T_f\right) W d x$                (6)

where,

$F^{\prime}=\left(\frac{W \times U_L}{\pi D h}+\frac{W}{D+(W-D) F}\right)^{-1}$           (7)

$F=\frac{\tanh [m(W-D) / 2]}{m(W-D) / 2}$          (8)

$m=\left(\frac{U_L}{k \delta}\right)^{\frac{1}{2}}$             (9)

The initial conditions are given as follows:

$\begin{aligned}\left.T_f\right|_{x=0} & =T_{f i} \\ \left.T_f\right|_{x=L} & =T_{f o}\end{aligned}$

The solution of Eq. (7) can be found with the help of Eq. (6) and Eq. (5):

$\begin{gathered}T_{f o}=\left[\frac{P F_2(\alpha \tau)_{e f f} I}{U_L}+T_a\right]\left[1-\exp \left(-\frac{F^{\prime} \mathrm{A} U_L}{\grave{m}_f C_f}\right)\right]+ T_{f i} \exp \left(-\frac{F^{\prime} \mathrm{A} U_L}{\grave{m}_f C_f}\right)\end{gathered}$           (10)

The rate of thermal energy available at the end of a PV module absorber is evaluated as:

$\dot{Q}_u=\grave{m}_f C_f\left(T_{f o}-T_{f i}\right)$             (11)

After substituting the expression for $T_{f o}$ from Eq. (11), we get:

$\dot{Q}_u=\mathrm{A} F_R\left(P F_2\right)(\alpha \tau)_{e f f} I-U_L\left(T_{f i}-T_a\right)$                (12)

where, the flow rate factor, $F_R$ is given by:

$F_{R m}=\frac{\grave{m}_f C_f}{A U_L F^{\prime}}\left[1-\exp \left(-\frac{\mathrm{A} U_L F^{\prime}}{\grave{m}_f C_f}\right)\right]$                  (13)

An instantaneous thermal efficiency of the system can be obtained as:

$\eta_{t h}=\frac{\dot{Q}_u}{\mathrm{~A} I}$             (14)

The absorber is fully covered by a photovoltaic module. In this case, an instantaneous thermal efficiency can be obtained by using Eq. (13), and Eq. (14):

$\eta_{t h}=F_R\left(P F_2(\alpha \tau)_{e f f}-\frac{U_L\left(T_{f i}-T_a\right)}{I}\right)$               (15)

In modelling equations, we use the following relations for defining the design parameters:

$(\alpha \tau)_{e f f}=P F_1(\alpha \tau)_{1, \text { eff }}+(\alpha \tau)_{2, \text { eff }}$               (16)

where,

$(\alpha \tau)_{1, \text { eff }}=\left(\alpha_c-\eta_c\right) \tau_c \beta_c$            (17)

$(\alpha \tau)_{2, \text { eff }}=\alpha_p\left(1-\beta_c\right) \tau_g^2$                (18)

The penalty factors due to the glass cover of the PV module, $P F_1$ and absorber below $\mathrm{PV}$ module $P F_2$ are defined as:

$P F_1=\frac{h_{c, p}}{U_{t c, a}+h_{c, p}}$              (19)

$P F_2=\frac{h_{p, f}}{U_{L 1}+h_{p, f}}$          (20)

Also, the heat transfer coefficients are as:

$U_{t c, a}=5.7+3.8 v_w$                      (21)

$U_{L 1}=\frac{U_{t c, a} \cdot h_{c, p}}{U_{t c, a}+h_{c, p}}$              (22)

$U_L=\frac{U_{L 1} \cdot h_{p, f}}{U_{L 1}+h_{p, f}}$                             (23)

$h_{c, p}=5.7+3.8 v_w \quad v_w=0 \frac{\mathrm{m}}{\mathrm{s}}$              (24)

The electrical efficiency according to the data published by the manufacturer can be calculated as [11]:

$\eta_{e l}=0.1507-0.00045\left(T_c-25\right)$                        (25)

3.2 Exergy analysis

Exergy analysis takes into account exergy intake, exergy outflow, and exergy destroyed from the PV/T system, defined as follows [15]:

$\sum E x_i-\sum E x_o=\sum E x_d$             (26)

or it can be written as:

$\sum E x_i-\sum\left(E x_{\text {th }}+E x_{e l}\right)=\sum E x_d$                 (27)

where,

$E x_i=\mathrm{A} I\left[1-\frac{4}{3}\left(\frac{T_a}{T_S}+\frac{1}{3}\left(\frac{T_a}{T_S}\right)^4\right)\right]$       (28)

$E x_{t h}=\dot{Q}_u\left(1-\frac{T_a}{T_{f o}}\right)$                        (29)

$E x_{e l}=\eta_{e l} \mathrm{AI}$                (30)

The computed PV/T exergy is given as:

$E x_o=E x_{t h}+E x_{e l}$                        (31)

Finally, the exergy efficiency is calculated as:

$\eta_{e x}=\frac{E x_o}{E x_i}=1-\frac{E x_d}{E x_i}$              (32)

The PV/T system examined in this study is a renewable energy device that integrates solar photovoltaic (PV) and solar thermal components. This combination enables the simultaneous generation of electricity and thermal energy. The study involved a test conducted in Tehran, Iran on October 17, 2021. The parametric study was conducted using operational data values for four parameters: Global radiation, mass flow rate, ambient temperature, wind speed, and fluid inlet temperature. Energy and exergy analyses were performed to evaluate the system's performance. Validation of the numerical data was conducted to ensure the accuracy and reliability of the simulation. This validation process helped verify the experimental setup and procedures, ensuring the credibility of the results. The findings of the study can be summarized as follows:

1. The results indicate that as solar radiation increases, thermal efficiency and cell, plate, and fluid outlet temperatures increase. However, electrical efficiency decreases with increasing cell temperature. Energy and exergy efficiencies decrease with higher inlet fluid temperatures. The highest energy efficiency of 36.5% and exergy efficiency of 13% were observed at a fluid inlet temperature of 25℃.
2. Ambient temperature affects the heat loss rate from the system.
3. The analysis demonstrates the significant impact of wind speed on PV/T system performance. Increasing the wind speed from 0 to 9 m/s led to a 17% decline in energy efficiency, primarily due to an increase in the heat convective coefficient. However, this heat loss resulted in higher electrical exergy efficiency, outweighing the decrease in thermal efficiency and leading to a 15.5% improvement in exergy efficiency.
4. Higher mass flow rates contribute to lower cell temperatures and increased electrical efficiency.
5. The experiments were conducted with a fluid inlet temperature ranging from 25.1 to 62.2℃, an ambient temperature ranging from 23.3 to 25.7℃, and a radiation level ranging from 956 to 1016 W/m². The optical thermal efficiency of the system was measured to be 23.7%, and it produced 378.29 W of thermal energy during the first stage of the test.
6. The PV/T system demonstrated the highest overall exergy efficiency of around 13% when the irradiance varied between 956 and 1016 W/m². This efficiency was achieved at the manufacturer-recommended mass flow rate of 0.033 kg/s.
7. Observations from the experiments revealed that an increase in fluid inlet temperature had a negative impact on the thermal efficiency of the system.
8. A comparison between the experimental thermal efficiency and the numerical optical thermal efficiency showed that the experimental value was 23%, while the numerical value was 25.61%. This comparison indicates a reasonably good agreement between the experimental and theoretical results, with a small difference between the two values.

The findings of the study have significant implications for the design and optimization of PV/T systems. It is crucial to have effective cooling systems in place to maintain lower cell temperatures and enhance electrical efficiency. The research emphasizes the importance of designing efficient cooling mechanisms to prevent overheating and maximize system performance. Furthermore, monitoring and controlling the fluid inlet temperature can play a key role in optimizing the overall performance of PV/T systems. By continuously monitoring this parameter, appropriate adjustments can be made to ensure optimal energy and exergy efficiency.

Further research recommendations for evaluating PV/T system designs can involve conducting comparative studies to analyze the performance of different configurations. This includes comparing various types of PV cells, such as monocrystalline, polycrystalline, or thin-film cells, to assess their electrical output, efficiency, durability, and compatibility with the thermal absorber. Comparative analysis can also evaluate different thermal absorber materials, such as metals, alloys, or selective coatings, considering factors like thermal conductivity, heat absorption capacity, durability, and cost-effectiveness. Additionally, studying different system designs, including variations in the arrangement and configuration of PV cells, thermal absorbers, and other components, can be done. This includes comparing series and parallel configurations, different spacing and orientation of components, and variations in the flow path design. By conducting these comparative studies, valuable insights can be gained to determine the most efficient and effective setup for PV/T systems.