This optimized and upgraded system proposes classification based on five major parts: design configurations, integration system, application, heat extraction method, and energy storage. Each part also contains subparts based on their definition and characteristics. This classification system provides an extensive idea about the hybrid PVT technology. The most significant and comprehensive part of this classification is the heat extraction method, as the thermal efficiency depends mostly on it.
2.1. PVT Performance Analysis
Evaluation of a PVT system’s electrical performance is simple because storage is optional and electricity usage may happen instantaneously. When it comes to thermal performance, things are different. The PVT system is merely one component of a larger heat-supply system, which is composed of numerous subsystems, or the balance of the system, such as flow pipes, mechanical components, thermal storage, and auxiliary heaters, to mention a few. To achieve the highest overall benefits, the system designer must choose the right solar proportion and other design criteria [
29]. The overall efficiency of a PVT system is calculated as follows [
5,
18]:
Here, total efficiency is the summation of thermal efficiency
and electrical efficiency
. The PVT system’s thermal efficiency is calculated as follows [
30]:
where
is the useful heat,
is the solar irradiance, and
is the panel area. The PVT system’s thermal efficiency can be calculated as follows if it appears to be a typical flat plate solar collector [
3]:
Useful heat
is calculated as [
1]:
where
is the specific heat of the used fluid, mass flow rate of the fluid-like air/water is
, and the fluid temperature differential between the input and obtained output is represented by
. In conventional form, electrical efficiency is calculated as [
3]:
where
denotes the current,
denotes the voltage, the intensity of solar irradiance is
, and the panel/collector area is
. On the other hand, taking into account using the produced thermal energy inside the panel, panel-dependent electrical efficiency considering its temperature is formulated as [
3]:
where panel reference temperature is
, PV panel temperature is
, PV panel reference efficiency is
, and the temperature coefficient is
with a value of 0.0045 °C
−1. It shows that the simplest way to calculate thermal and electrical efficiency is by using the last equation instead of this one. These equations became more complex as mathematical and numerical modeling were advanced due to the inclusion of different variables. The PVT system’s electrical power can be calculated as [
31]:
Another method to obtain the PV cell’s total power is to measure the short circuit current
and open circuit voltage
and then multiply the obtained results. The module efficiency of electrical power is calculated as [
32]:
where
is the maximum obtained power,
is the irradiance, and
is the panel area. It is necessary to specify the electrical load demands in order to build a suitable PV system. Calculation of the battery storage and the PV panels number is also required [
33]. The values are calculated as:
where the energy consumption per day is
, peak sun hours is
PSH, systems components efficiency is
and
, and
is the safety factor reference for losses in PV temperature and resistive losses. The electrical energy generated by the PV system is measured in kWh and is determined by [
34]:
where the PV panel is
, daily irradiance is
, wire efficiency is
, and module efficiency is
.
This set of equations evaluates both the electrical and thermal performance, including the efficiency of a PVT system.
2.3. PVT System Thermal Modeling
The common practice is that the typical methods of measuring electronic junction temperature cannot be used to access the temperature inside and outside a PVT panel. Rather, the value is estimated using models. The popular approach uses a single thermal heat balance equation (HBE) and considers a PVT module as a single material block. The heat balance equation is formulated as [
37]:
where the absorbed energy is
, converted energy is
, and
is lost energy. The total energy input for the PVT system is represented by the absorbed energy from the incident solar irradiance collected by the front surface of the module. In the PVT module, thermal and electrical energy is obtained by converting this incident solar irradiance and generated heat. The amount of heat lost mentioned in the previous Equation (14) is the loss to the environment through various heat transfer processes. Heat losses can be classified into two parts. The primary factor influencing the first part is the temperature differential between the panel and its surroundings, while the second part can be due to various effects like the accumulation of dirt, diode losses, and wire contacts joule heat.
The PVT module’s total energy gained from the short wave irradiance that was captured is known as absorbed energy. There are various parameters and factors that influence the overall absorbed energy, including the following [
38,
39]:
- ▪
PVT panels supporting framework;
- ▪
Diffused radiation and direct radiation intensity when it strikes the panel;
- ▪
Defects in materials, its quality, and physical properties/limitations;
- ▪
The front layer’s optical characteristics, such as transmittance, scattering, reflectivity, and absorptivity.
The heat transfer method involves several mechanisms like conduction, convection, and radiation in the PVT module. Normally, the heat transfer between the structural interfaces of the module is known as conduction. As there is a very small part between the PVT module and the holding structure, and also minimal difference of temperature, conduction in this part is neglected. For the PVT module, each layer’s thermal capacity and thermal resistivity are considered to analyze heat transfer by conduction in each layer [
40].
Convection heat transfer occurs between the interfaces of the PVT module and the air that surrounds it, conforming to Newton’s cooling law [
41]. The related heat transfer coefficients are used to model it. The following formula is used to calculate the overall heat convection amount per unit area:
where the heat transfer coefficient is (
), module temperature is
, and air temperature is
. It normally occurs by both the forced and free convection methods.
Long-wave radiation is the element of radiation heat exchange in a PVT system. The Stefan–Boltzmann law is utilized to determine per unit area radiative energy:
where the surface emissivity is
, view factor is
, Stefan–Boltzmann constant is
, object temperature from radiation is
, and nearby temperature is
.
To investigate the PVT system’s thermal and electrical performance, a one-dimensional steady-state model can be used considering the flat plate collector. For this reason, the modified Hottel–Willier equations are considered [
42,
43]. The heat generated by the incident solar irradiation is obtained as [
16]:
Here, the incident solar radiation is
G,
is the solar absorbance, the glass cover transmittance is
, the electrical efficiency is
, and the packing factor is
. The PVT system’s total loss coefficient can be described as [
14]:
In the above equation, the collector heat loss coefficient from absorber to ambient is , is the reference temperature electrical efficiency of the module, and is the PV cell temperature coefficient.
The maximum heat transfer and the actual heat transfer ratio is considered as the heat removal factor
and can be calculated as [
16]:
Here,
is the surface area of the collector, the water mass flow rate is
, and
is the specific heat of water. The efficiency factor of the collector can be described as:
In the above equation, the tube distance is
W, the average bond width is a, the thermal conductance of the bond is
,
is the inner tube diameter, and
F is the fin efficiency. The general obtained equation for the useful heat gain is:
In the above equation, the collector outlet water temperature is
. Determination of the heat removal factor is achieved by the following equation:
where
is the efficiency factor of the collector, the surface area is
, the specific heat is
, and the total loss coefficient is
. The overall loss coefficient is described as:
where the top loss coefficient is
, the coefficient of edge loss is
, and the coefficient of bottom loss is
. The coefficient of bottom loss is formulated as:
The coefficient of edge loss is defined as:
The coefficient of top loss is defined as:
The equation that follows can be used to determine the mean plate temperature:
The total thermal energy input is calculated as:
The system’s thermal efficiency is calculated as:
Here, the obtained useful energy fraction is and the overall energy from input is .
If we consider from the optical perspective, the glass of the PVT panel has two parallel boundaries: air to glass and glass to air which transmits and reflects the light. Fresnel equations derive the coefficient of reflection in a boundary. P-polarization is formulated as:
The formula for s-polarization is:
Total reflection is calculated as:
Due to neglected absorption presence, the transmittance is calculated as:
Snell’s law is used to calculate the incidence angle on the second boundary, and it comes after the first boundary:
After entering the glass, a part of the light is absorbed by per unit length constant probability. It results in the transmittance coefficient of the glass decreasing exponentially with distance travelled:
Upon reaching the second boundary, it reflects and transmits using Fresnel equations again. The light is reflected and captured inside the glass and reflects back and forth between the two boundaries until it is totally absorbed. The sum of the infinite geometric series represents the system’s total reflection and transmission coefficients, yielding the following outcome:
For a counter flow heat exchanger, it can be evaluated by the hot and cold outlet temperatures. The analysis of the heat transfer unit (NTU-
) of an effective number is calculated as [
44]:
Here, the capacity ratio is defined as
and the heat exchange unit number is
. As a result, the solar energy received by the storage tank is:
The heat exchanger’s hot temperature at the outlet is calculated as:
The heat exchanger’s cold temperature at the outlet is calculated as:
For determining long-term performance, the energy balance should be integrated over time. The heat loss to the environment of the domestic water heater is:
The supplied energy of the domestic water heater is:
Here,
is the storage-tank-to-load extracted heat and
is the makeup temperature of the water. Finally, at any moment, the energy balance of a well-mixed storage tank is [
39]:
On the basis of the above PVT system modeling for parameters’ identification, mathematical modeling of a simulation is carried out to obtain the performance of a PVT system. The simulation model will provide the idea and relevance for the described mathematical and parameters model. The obtained results can be compared with the results of the available literature for validation purposes.