Theoretical approach model of building integrated photovoltaic thermal air collector

Received Mar 1, 2019 Revised Nov 8, 2019 Accepted Jan 23, 2020 Over recent years the photovoltaic technology has obtained significant development, especially in building integrated photovoltaic thermal (BIPVT) system. Photovoltaic thermal (PVT) air collectors are advantageous because of their efficiency. Various studies have been conducted to determine the ideal parameters of PVT air collectors. Few theoretical approach models of PVT air collector systems were used to help detect occurrences in a PVT collector system and calculate the optimal parameters. The heat transfer and energy balance of PVT air collectors were analysed and reviewed based on the model, quantity of cover, channels and forms of the collector. A mathematical model was developed to describe actual working situations and to examine new shut PVT collectors. The first law of thermodynamics is the principal equation in the model. Different analysis methods were utilised to evaluate PVT performances, which are generally based on energy and exergy analyses. This review focuses on theoretical approach model of single-pass PVT air collector.


INTRODUCTION
The depletion of conventional fossil fuel resources has revived the demand for utilisation of renewable energy resources. Therefore, an alternative energy source must be determined to satisfy our energy requirements and preserve conventional fossil fuels. One such renewable energy source is solar energy, which can potentially supply significant amount of the world's energy demand. Renewable energy sources, such as solar energy, provide environmental benefits and clean energy. In addition, solar energy is an ideal alternative source for impoverished or rural people who have no access to modern energy sources. Thermal and electrical energy can be generated from solar energy. Although these two energy sources are have different forms, they can be produced simultaneously by using hybrid collectors. This hybrid system consists of a combination of two types of collectors, namely, thermal collectors and photovoltaic-thermal (PVT) collectors. PVT collectors are designed to receive solar energy and convert it into thermal and electrical energy; in this device, thermal energy is transferred into fluid that flows into the collector. A PVT collector consists of a PV panel, an insulator and a frame as well as one or more cover (glass sheets) or a transparent material placed over the absorbing plate with air flowing around it. The efficiency of PVT collectors can be enhanced by using heat transfer area through the absorber with finned absorbers, corrugated surfaces and  [1][2][3][4][5][6][7][8][9][10][11][12][13]. The overall performance of the PVT system can be evaluated based on the thermodynamic, environmental and economic impacts analysis. Enviroeconomic and exergoeconomic analyses for PVT air collectors were studied [14]. Environmental-economic-exergy-energy analyses for different PVT air collector systems were studied [15][16][17]. Several types of PVT air collectors have been designed, evaluated and developed in various countries, thereby yielding varying degrees of technical performances based on energy-exergy analyses. In this review, we focused on the theoretical approach model of singlepass PVT air collector.

THEORETICAL APPROACH MODEL OF PVT AIR COLLECTORS WITHOUT GLASS COVER
Sarhaddi et al. [18,19] improved the thermal and electrical model for a PVT air collector, as shown in Figure 1. The figure shows the cross-sectional view of the PVT air collector, as well as its equivalent thermal resistant circuit and an element length 'dx' of the flow channel. The energy balance of the PVT collector is expressed as follows. For the PV module: For the back surface of a Tedlar: For the air flowing below a Tedlar: In the application of PVT system, Sahsavar et al. [20] developed a building integrated photovoltaic (BIPVT) collector by using the cooling potential of ventilation and exhaust air to refrigerate the PV panel and heating system in the ventilation of buildings. The energy balance of this PVT collector, as shown in Figure 2, is expressed as follows. For PV panels: For the air channel: For the bottom plate: Sohel et al. [21] proposed a dynamic model for PVT air collectors, as shown in Figure 3. The experimental data were similar with the modelled air temperature and electrical performance. The data from the PVT system were used to authenticate the theoretical approach in two buildings. The system energy balance for the heat loss from the top of the PVT is expressed as follows: From the PV panel to the air in the channel: From the PV panel to the roof top: The system energy balance for the heat loss from air to the roof and from roof to the room is determined as The energy balance of the air strip can be calculated as The energy balance around an infinitesimal control volume of the PV panel can be calculated as For the room air temperature:  Figure 5. The thermal efficiency of the two-inlet systems was 5% higher than that of a conventional one-inlet system. The thermal efficiency of the BIPVT system with a semi-transparent PV panel reached approximately 7.6%. This system can be easily applied and does not significantly increase cost. The energy balance of this PVT collector is expressed as follows.
For the top PV panel surface: For the fluid in the BIPVT: For the lining inner surface: For the PV panel bottom surface: For the solar radiation incident in the insulation:

THEORETICAL APPROACH MODEL OF PVT AIR COLLECTORS WITH GLASS COVER
Aste et al. [24] investigated a PVT air collector. A simulation model was developed to calculate the performance of the system. The simulated and experimental thermal and electrical performances of the PVT collector were consistent. The system has been applied to solar rooftops and buildings. The energy balance of this PVT air collector, as shown in Figure 6, is expressed as follows. For PV cells: For the glass part of the sandwich without PV cells inside: For the air gap: For the absorber plate: For the PV, the actual thermal-spectral efficiency is * , where is the temperature power coefficient of PV cells, and FS is the spectrum correction factor of PV efficiency.

Figure 6. Heat transfer coefficients and temperatures of a PVT air collector
Another heat transfer and energy modelling for PVT air collectors with glass cover were proposed in [25][26][27]. The analytical expression for the electrical efficiency of PVT hybrid air collectors was established. Case A is a glass-to-glass PV module with an air channel above the absorber plate, and Case B is a glass-to-glass PV module with air channel below the absorber plate. The energy balance of this PVT air collector, as shown in Figure 7, is expressed as follows: Case A: Glass-to-glass PV module with an air channel above the absorber plate For the PV module: For the blackened absorber plate: For the blackened absorber plate: For the air channel below the absorber plate:  Table 1 shows the comparation of Performance of air-based PVT systems.

CONCLUSIONS
PVT systems combine solar energy and PV collectors, which simultaneously produce heat and electrical energy. The efficiency and energy products from the combination of PV panels and collectors are higher than that of a separated system. Researchers and companies have proposed various designs to improve the overall efficiency of PVT systems. However, the lack of information on the commercial viability and long-term performance of a PVT system decreases its acceptance by the market.
Researchers have developed mathematical models to evaluate the performance of PVT systems with different collector designs. Energy balance is the basic concept in developing the mathematical models at a steady state. The performance of PVT systems is influenced by mass flow rates, collector geometry and other parameters. Model confirmation has been conducted to examine the behaviour of an actual system. To confirm the mathematical model, researchers have assessed either experimental or analytical results. Theoretical and experimental results have been generally consistent when the correct mathematical model is employed. Various approaches are limited because the precision of several key parameters is low and mistakes often occur in obtaining experimental results due to carelessness.