Abstract
The rise in the temperature severely affects photovoltaic cell efficiency and hence its power output. Moreover, it also causes the development of thermal stresses that may reduce their life span. Thus, there is a need for an accurate estimation of the cell’s working temperature. In this paper, a detailed thermal model based on various heat transfer modes involved and their governing equations has been presented to estimate the cell temperature of a PV module using MATLAB software under different climatic and solar insolation conditions. In order to validate the presented model, an experimental setup has been built and operated under actual outdoor conditions of Jodhpur, a city in the Thar Desert of Rajasthan. For the peak summer month of June, the predicted glass cover outer surface temperature has been found to be within 0.2–4.5°C of experimentally measured values and the back sheet temperature is found to be within 0.5–5.5°C. The predicted and measured power outputs have been found to be within 0.85–1.2 W while the efficiency values are within 0.17–0.38%. For the early summer month of April, the variations are 0.13–4.1°C, 0.2–4.1°C, 0.44–1.65 W, and 0.1–0.5% for glass cover temperature, back sheet temperature, power output, and efficiency, respectively. Thus, the predictions of the developed thermal model have exhibited a good agreement with the experimental results. The maximum glass cover temperatures recorded were 60°C and 65.5°C when the ambient temperatures were 35°C and 42°C near the noon for the early summer and peak summer day experiments, respectively. The presented model can be used to generate a year-round cell temperature data for the known environmental data of a location, which can help in the selection or development of appropriate cooling technology at the planning stage of the installation of a solar PV plant.
1. Introduction
The conventional systems of electric power generation are associated with high carbon dioxide emissions with a threat of global warming. Thus, there is a dire need for greater use of solar photovoltaic (SPV) systems for sustainable development. As reported by the International Renewable Energy Agency (IRENA) [1], the global cumulative installed capacity of SPV systems was 1047 GW in 2022 and there is an increase of about 11 times over the last decade. International Energy Agency (IEA) [2] has predicted that the installed power capacity of SPV plants will surpass other energy technologies by 2027 and its share will be 22% of the cumulative power capacity as shown in Table 1.
As per the IEA report, India ranks fourth globally in terms of installed capacity of SPV plants. Among the states of India, Rajasthan has the highest installed capacity. Jodhpur region, which is located in the Thar Desert (a tropical desert) of Rajasthan, has the highest number of sunny days and high solar radiation intensity. Hence, this region is making rapid progress in the installation of solar PV generation systems. The installed SPV plants in the Jodhpur region have increased from 71 MW in 2011-12 to 3832 MW in 2021-22 (up to 31.8.21) [3], and this region has a huge potential for the expansion.
Electrical power output and efficiency are the main performance parameters of a solar PV system, which primarily depend on numerous influencing parameters. Several electrical models of varying complexity have been developed for the simulation-based study of the performance of solar PV systems [4]. However, the electrical model alone is not sufficient to provide the correct prediction of the electrical power output of the system because the thermal behaviour of the PV panel and the working temperature of the cell have a major impact on the output power and electrical efficiency of a PV cell.
The solar PV panels convert only a part of the incident solar radiation on the panel surface into electricity. A major portion of the incident solar radiation is absorbed by the panel which leads to an increase in the operating temperature of the cell. With respect to the values at standard test conditions (STCs), Masters [5] specifies that the open circuit voltage drops by about 0.37% for each degree Celsius increase in cell temperature, while the short circuit current increases by approximately 0.05% for crystalline silicon cells resulting in the decrease in the maximum power availability by about 0.5%/°C. Looking at this significant effect of the cell temperature on the performance of the cell, a thermal model is required to make a reasonably accurate estimation of the PV cell temperature for the given environmental and operating conditions. Several researchers have carried out studies on the thermal modeling of solar PV panels. A brief account of the major studies is being presented here.
Among the initial works, Fuentes [6] has reported the nominal operating cell temperature. In their independent research works, both Schott [7] and Jones and Underwood [8] have developed the linear thermal model of PV panels based on the energy balance. Knaup [9] has experimented with panel heat capacity and heat transfer for non-steady-state conditions. Mattei et al. [10] have developed two models based on the convection heat transfer coefficient related to the nominal operating cell temperature and energy balance, respectively, and found that the energy balance model provides better results. Skoplaki and Palyvos [11] and Dubey et al. [12] have presented a summary of expressions of the conversion efficiency and the output power with a focus on the thermal aspect. Kaplani and Kaplanis [13] carried out theoretical and experimental studies on the effect of wind velocity and wind incidence angle on PV module temperature. Armstrong and Hurley [14] studied the effect of rapidly changing solar radiation and wind speed to determine the thermal response time of the PV panel.
Kant et al. [15] have developed and validated a thermal model of polycrystalline solar PV panels through experimentation and examined the effect of change in temperature. Jaszczur et al. [16] have analyzed the temperature distribution in the PV panel under varying environmental conditions. Notton et al. [17] have proposed an electrical analogy-based finite difference model for a double-glass multicrystalline photovoltaic module, which was validated by utilizing the experimental data.
Tsai and Tsai [18] and Belhadj et al. [19] have presented an integrated electrical and thermal model for PV panels based on MATLAB/Simulink. Recently, Yaman and Arslan [20] have included transient conditions in their mathematical model to correctly determine the thermal and electrical parameters of a PV module. They have validated the model by comparing the simulation results with those from outdoor experiments carried out for multicrystalline silicon PV modules in summer conditions of Mersin, Turkey having minimum and maximum ambient temperatures of 22°C and 30°C, respectively, and wind velocity of 5–10 m/s. Under these conditions, the maximum cell temperature has been reported to be 50°C.
King et al. [21] and Duffie and Beckman [22] have presented thermal models with simplifying assumptions. The model of King et al. underestimated the cell temperature and the model of Duffie and Beckman overestimated it.
Aly et al. [23] employed a one-dimensional finite difference numerical technique to solve their thermal model for monofacial PV panels with polycrystalline silicon cells using the energy balance approach for different layers. The experimentally measured back sheet temperature of the PV panel was compared with the modeled back sheet temperature for different days of the year at Doha, which is a dry and an arid place. In Doha, the rainfall is very scanty and the months of June and July are the hottest months with maximum temperature averaging around 42°C.
Bevilacqua et al. [24] proposed a transient one-dimensional thermal model based on the energy balance method for photovoltaic modules consisting of polycrystalline silicon cells. The model was validated by comparing the predicted results using the method of finite differences and experimental data of the module back surface temperature and the electric power output in different seasons at Calabria (Italy) where the average maximum ambient temperature in summer is about 30°C.
Nicoletti et al. [25] presented an experimentally validated finite difference solution of a simple one-dimensional thermal model of a photovoltaic panel with polycrystalline cells for summer conditions of Calabria (Italy) having ambient temperature of 20–35°C and wind speed of 5–14 m/s (reaching occasionally up to 20 m/s). They recorded a maximum penal temperature of 62.1°C.
Khanam et al. [26] have numerically solved one-dimensional, quasisteady state experimentally validated thermal models of four different types of PV cells, namely, monocrystalline, polycrystalline, and thin films PV modules with opaque (Tedlar) and semitransparent (glass) back cover plates for four different climatic locations of India with the basic objective of prediction and comparison of their electrical efficiencies. They found that despite having a high potential for solar irradiation (higher radiation and greater number of sunny days) in Jodhpur, the annual electrical output was higher in Bangalore for all PV technologies. Khyani et al. [27] carried out outdoor experimentation at Jodhpur to measure the solar panel temperature. They observed that, in the summer months of April, May, and June 2021 with a maximum ambient temperature of 42.2°C in the month of May, the temperature of the solar panel on the front side reached up to 58.6°C, 65.7°C, and 63.9°C, respectively. These studies establish the dire need of finding cooling solutions for the PV panels for hot climatic conditions which prevail in areas such as the Jodhpur region.
Though an accurate estimation of cell temperature is essential, the operating temperature of the cells in the PV panels cannot be directly measured because the cells are inside the panels with layers of other materials surrounding them and, thus, are not accessible from outside [15]. Nishioka et al. [28] have attempted to measure it by fabricating the panel with internal temperature sensors directly inserted and attached to the cells. However, this is useful only for limited experimental purposes as it is associated with higher costs and lower versatility. Moreover, peeling off the back sheet is not advisable for inserting the sensors because the back sheet is used for the protection of PV cells from moisture and dust. In several cases of experimental research, the temperature of PV panels is measured by attaching temperature sensors to the back surface of the panels and in some cases infrared sensors and thermographic cameras have been used. Therefore, it can be concluded that the prevalent methods of determining cell temperature lack accuracy and have practical difficulties.
Jodhpur is located in the Thar Desert of western Rajasthan where the daytime summer temperature normally ranges from 40 to 45°C. In between, week-long spells of extremely high day temperatures of 46−48° have also been observed. The sky is generally clear and wind velocity seldom exceeds 2-3 m/s. It is notable that a high wind velocity is advantageous because it tends to cool the PV panel because of the increased convective heat transfer and the clear sky conditions help in greater heat rejection by radiation to the sky. It is also to be noted that the environmental conditions in Jodhpur are such that, in general, the changes are gradual, especially the solar radiation intensity and ambient temperature except when a sandstorm occurs in the summer, which are also not frequent since the last 3 decades.
None of the presented models available in the open literature are suitable for the very harsh summer conditions of western Rajasthan with low wind velocity, high ambient temperature, and intense solar radiation. Hence, the objective of the present work is to present a thermal model, which can fulfil the following requirements:(i)It should be able to predict the cell temperature with reasonable accuracy even for extreme summer conditions and at the same time it should be simple enough for ease of application for the field engineers(ii)It must consider all the heat transfer modes involved(iii)It must be capable of predicting the cell temperature under different environmental and operating conditions because carrying out experiments covering all combinations of these parameters over a wide range is not a cost-effective and practical proposition(iv)It must also be capable of predicting the power output and electrical efficiency of the PV panel with good accuracy
It is to be noted that the prediction of year-round data of the cell temperature for any location corresponding to the available environmental data at the planning stage can help in establishing the cooling requirement and also in the development of a suitable cooling technology.
2. Heat Transfer
The absorbed solar radiation in the cell raises its temperature above the ambient temperature. The heat from the cell is transmitted to the top and bottom faces of the PV panel and is rejected from there to the environment by convection and radiation. The equilibrium operating temperature of the cell can be determined from a thermal model, and subsequently the electrical power output corresponding to a particular set of solar radiation and other environmental parameters can be predicted. Figure 1 shows the multilayered construction of a solar PV panel [29]. The thermal properties of different layers of the PV panel are given in Table 2.
Some other properties required for thermal modeling are as follows:(i)Transmissivity of glass, = 0.95 [30](ii)Emissivity of glass, = 0.88 [31](iii)Transmissivity of the front encapsulant, = 0.91 [32](iv)Absorptivity of the PV cells, α = 0.9 [33](v)Emissivity of back sheet, = 0.91 [34]
3. Energy Analysis of a Solar Photovoltaic Panel
The PV panel and the cell gain heat by absorbing a part of the incident solar radiation. The heated panel loses heat by convection and radiation to the environment. The heat from the cell flows through the various layers shown in Figure 1 above and below it by conduction and is finally lost from the panel’s top and bottom surfaces by convection and radiation.
Figure 2 shows the energy balance of a solar PV panel. For the solar cell, the energy balance gives the following equation:where P is the electric power output of the panel. For the incident solar radiation I over the unit panel area, IA (τ) reaches the cell surface after passing through the glass cover of transmissivity and front encapsulant E1 of transmissivity , where τ is the effective transmissivity and is equal to ().
The portion [IA (1 − τ)] is partly reflected back and a part of it is absorbed in the glass cover and front encapsulant E1. The power output P depends on the efficiency η of the cell at its operating condition. Energy portion [IA (τ) − P] α is absorbed in the cell, where α is the absorptivity of the cell, and it is converted into heat Qcell as given in equation (1). This absorbed heat causes a rise in the temperature of the cell. Since the absorptivity α is less than unity, a portion (1 − α) [IA (τ) − P] is reflected back from the cell surface. A part of this reflected radiation is also absorbed in the layers of the front encapsulant and glass cover. The efficiency of the cell is defined as
With the increasing ambient temperature, the stored heat in the multilayered structure of the module increases up to noon and this stored heat is released in the afternoon. The variations in the ambient temperature, wind velocity, and sky temperature affect the stored heat in the panel. Thus, basically, the panel experiences an unsteady state of operation. However, if these variations are gradual, a quasisteady state condition can be assumed when a short observation period of the order of 10 min is considered. For this assumption of quasisteady state condition, the variation in the stored heat is small. It is to be noted that ASHRAE Standard 93−77 [35] defines a quasisteady state with reference to the evaluation of the performance of solar collectors as the condition when the collector output changes gradually over a properly selected time period of 5–10 min. The standard permits the acceptance of such obtained results considering them to be of steady state.
The balance of energy is given by an equality in which the solar radiation that reaches the cell in the module will be equal to the sum of the electrical power that it delivers and the heat that it dissipates [36]. In the quasisteady state (treated as a steady state), the radiation absorbed in the cell as well as in the upper layers is rejected from the top and bottom surfaces of the panel, hence the energy balance can be written aswhere is termed as the top loss and is the back loss. Since a part of the incident solar radiation is also absorbed in the upper layers, the cell absorptivity α has been neglected in writing the energy balance equation. The modes of heat transfer involved are conduction, convection, and radiation.
The length and width of a PV panel are significantly larger than its thickness. Since the whole of the panel surface is subjected to a uniform flux of solar radiation, it can be expected that except near the edges, the variation in the temperature of the cell in the lengthwise and widthwise directions will be negligible. This gives a condition of one-dimensional conduction heat transfer across different layers in the direction of the thickness of the panel. The adoption of a one-dimensional (thicknesswise) variation of temperature approach can significantly simplify the thermal model. As mentioned earlier, Notton et al. [17] have proposed an electrical analogy-based one-dimensional finite difference model and Khanam et al. [26] in their numerical analysis of solar PV cells also considered one-dimensional heat conduction.
As discussed above, the absorbed heat raises the temperature of the cell above the ambient temperature and hence thermal gradients are established between different layers of the PV panel. The heat flows by conduction from the cell to the outer surface of the glass cover on the front side from where it is rejected by convection to the ambient air and by radiation to the sky. Similarly, heat flows by conduction to the outer surface of the back side from where it is rejected by convection to the ambient air and by radiation to the ground. Assuming the materials of different layers to be homogeneous and isotopic, the basic equation of conduction heat transfer as given by Fourier iswhere = heat flow rate by conduction, W, k = thermal conductivity of the layer, W/(m·K), A = area of the surface normal to the heat flow direction, m2, ΔT = temperature difference across the layer, °C or K, δ = thickness of the layer, m, and δ/(kA) = thermal resistance to the conduction heat transfer.
The fundamental equation of combined convection and radiation heat transfer from a surface is as follows [31]:where are the convective and radiative heat transfer coefficients, respectively, and and are the corresponding resistances.
Figure 3 shows the thermal network which helps in the heat transfer analysis for the estimation of top and back losses. As explained above in detail, since the thickness of the PV panel is very small in comparison to its length and width, the heat conduction that has been considered is one dimensional. The thickness of ARC is very small, and its conductivity is high. The resistance offered by this layer to conduction heat transfer is only 3.1 × 10−9 K/W, as given in Table 2. Hence, its resistance to conduction heat transfer has been neglected in the network presented in Figure 3. The effect of the frame has not been considered in the presented thermal model because it has a small surface area compared to the surface area of the panel and thus has a negligible effect on the temperature response of the PV panel [15]. The effect of metallic conductors has also been neglected.
Various temperatures indicated in the network are the equilibrium temperatures of (i) the cell (assumed to be uniform throughout its thickness because of the negligible conduction resistance of 1.5 × 10−6 K/W), (ii) glass side surface of encapsulant , (iii) inner and outer layers of the glass , respectively, (iv) back sheet side surface of encapsulant , and (v) the back sheet inner surface and outer surface , respectively. The thermal contact resistance between different layers has been neglected in the presented analysis, which is in line with Aly et al. [23]. Hence, . In the network, is the ambient temperature, is the sky temperature, and is the temperature of the ground facing the back sheet of the panel.
The thermal model presented in the next section deals with the various modes of heat transfer involved and presents the governing mathematical equations of these heat transfer modes and the power output equation.
4. Thermal Modeling of a Solar Photovoltaic Panel
A thermal model of the PV panel has been developed in this work. The simulation of the mathematical thermal model has been carried out using MATLAB. The major steps in the model-building strategy are as follows:(1)Presentation of the mathematical equations of the various modes of heat transfer involved in the top and back losses(2)Development of a computer program for the iterative solution of the set of mathematical equations to estimate the top and back losses, and the power output(3)Estimation of the equilibrium temperature of the cell(4)Validation of the mathematical model by comparing the predicted results with experimental data
4.1. Estimation of Top Loss
Top loss is estimated by the iterative solution of the mathematical model for the same. The heat flows by conduction from the cell to the outer surface of the glass cover on the top and from where it is rejected by convection to the ambient air and by radiation to the sky.
Since the heat flows by conduction across the encapsulant of thickness and thermal conductivity as depicted in Figures 2 and 3, the fundamental equation of conduction heat transfer, equation (4), giveswhere A is the area of the solar panel.
Similarly, the heat flows by conduction from the inner surface to the outer surface of the glass cover of thickness and thermal conductivity , hence we have
From the outer surface of the glass cover at temperature , the heat is lost by radiation to the sky at temperature . The convective heat transfer is due to the wind blowing over the surface of the panel. Hence, we have
By using the fundamental equation of the combined convection and radiation heat transfer, equation (5), the heat loss is given bywhere is the heat loss due to radiation to the sky from the top surface and is the heat loss by convection to the ambient air from the outer surface of the glass.
It is to be noted that the sky is considered as a blackbody at some fictitious temperature termed as sky temperature with which the outer surface of the glass cover exchanges heat by radiation. The sky temperature is a function of the relative humidity of air, atmospheric pollution including dust, the presence of clouds, and the ambient temperature, hence it is difficult to make a correct estimate of it. Investigators have estimated it using different correlations. A widely used equation for clear sky due to Swinbank [37] is = 0.0552 , which corresponds to the prevailing ambient temperature. In the Swinbank relation, both the temperatures are in Kelvin.
In equation (9), is the radiation heat transfer coefficient for the top side. It is given by the following expression [31]:where σ is Stefan and Boltzmann constant and its value is 5.67 × 10−8 W/(m2·K4) and is the emissivity of the glass cover.
In equation (9), is the wind heat transfer coefficient, which is a function of the wind velocity. It is determined by the following correlation given by McAdams [38]:
In the equilibrium, the top loss is calculated as
4.1.1. Conduction Heat Transfer through the Upper Layers
Since from the cell to the glass outer surface, the conduction resistances of their layers are in series, we refer to the thermal network given in Figure 3, where , and equations (6) and (7) give top loss as
4.1.2. Convection and Radiation Heat Transfer from the Top Side
From equations (9) and (10), we have
Hence, from equations (13) and (14), we get
The top loss is estimated by using the iterative solution of the governing equations and the main steps for the iteration are as follows:(1)Initialize the cell temperature = + ΔT for the known ambient temperature (2)Determine the wind heat transfer coefficient from the measured wind velocity (3)Calculate the top loss from equation (14) with a trial value for the glass cover outer surface temperature(4)With this first estimate of the top loss and after knowing the temperature of the cell, find the temperature of the outer surface of the glass cover from equation (13) and compare it with the trial value of (5)This calculated value of is likely to be different from the trial value of . Increase by a small amount and recalculate the top loss and from equations (14) and (13), respectively. This new value of is a trial value for the second iteration(6)Repeat steps 4 and 5 and find a new . This iteration will continue until the trial value of and the calculated value of are very close, say by 0.001°C
The flowchart for the iterative solution for the estimation of top loss is shown in Figure 4.
4.2. Estimation of Back Loss
Back loss is also estimated by using the iterative solution of the governing mathematical equations. The heat flows by conduction from the cell to the outer surface of the back sheet on the back side and the same is rejected by convection to the ambient air and by radiation to the ground.
Heat flows by conduction across the encapsulant of thickness and thermal conductivity , hence we have
Similarly, the heat flows by conduction from the inner to the outer surface of the back sheet of thickness and thermal conductivity , and hence we have
From the outer surface of the back sheet at temperature , the heat is lost by radiation to the ground at temperature . The ground surface behaves as a black surface because the surface of the back sheet sees a large area on the ground [18]. On the back side of the panel, basically free convection condition is encountered [15] in contrast to the front of the panel which experiences a forced convection condition because of the blowing wind. Hence, the back loss using equation (5) is given bywhere is the temperature of the ground which is usually taken equal to the ambient temperature [15], h is the convection heat transfer coefficient for the back side, and is the radiation heat transfer coefficient on the rear side. The radiation heat transfer coefficient is given by the following expression [31]:
In the equilibrium,
The free convection heat transfer coefficient h for the back side has been estimated from the mean Nusselt number correlation as follows:where Nu = Nusselt number, k = thermal conductivity of air at the mean film temperature , and L = length of back sheet.
Nusselt number has been determined from the following relation by Churchill and Chu (in reference [31]) as follows:where Ra is the Rayleigh number for an inclined surface. It is given by the following relation:where β = (1/) = coefficient of cubical expansion, = mean film temperature, K, ρ = density of air at mean film temperature, θ = angle of inclination of the back sheet with the vertical, and Pr = Prandtl number. It is given by the following relation as follows:where μ is the viscosity of air and is the specific heat of air at the mean film temperature.
4.2.1. Thermophysical Properties of Air
All thermophysical properties of the air (k, ρ, μ, and ) have been taken at the corresponding mean film temperature by using the following relations [31]:where all temperatures are in K.
4.2.2. Conduction Heat Transfer through Back Side Layers
The conduction resistances of the layers are in series hence, from equations (16) and (17), the top loss is calculated as
4.2.3. Convection and Radiation Heat Transfer from the Back Side
From equations (18) and (19), we have
From equations (26) and (27), we get
In order to solve equation (28), it is required to estimate the value of h and , hence an iterative process has been used. The major steps for the estimation of h and and hence the back losses are as follows:(1)We start with cell temperature initialized in step 1 of the iterative process for top loss estimation and a trial value of . We estimate and h and then calculate from equation (27) and from equation (26). This calculated value of is likely to be different from the trial value of .(2)We consider a new value of with a small change from the trial value of in step 1, which may be termed as (1). Again, we estimate and h and then calculate and from equations (27) and (26), respectively.(3)If the calculated value of in step 2 differs by more than 0.001°C from (1), then we consider a new value of with a small change from (1), say (2). This process is continued till the two successive values of do not differ by more than 0.001°C.
The flowchart for the iterative solution for the estimation of back loss is shown in Figure 5.
4.3. Estimation of Power Output P
The efficiency of a PV cell is given by the following fundamental expression as a function of operating cell temperature [39]:where = efficiency of the module at STC = 13.2%, = reference temperature of STC = 25°C, and = temperature coefficient = 0.5% per °C
Knowing the efficiency, the power output is calculated from
Since equation (3) of the energy balance must be satisfied, the LHS of this equation must be equal to or very close to the RHS, say LHS-RHS ≤1 W. If this condition is not satisfied, the cell temperature is increased by a small amount from its initial value of = + ΔT as mentioned in step 1 of the iterative process for top loss estimation. Then, new estimations of top loss , back loss , and power output P are made. This process is continued till the energy balance condition defined by equation (3) is satisfied.
To carry out the iterative process outlined above for the estimations of top and back losses, and power output, two functions have been created separately in MATLAB to estimate the top and back losses. The main iterative MATLAB program has been written to call these functions along with the initial value of and the measured values of the environmental data for the estimation of output power and checking the energy balance. If the energy balance condition is not satisfied, the initial value of cell temperature is increased by a small amount and the process of estimations of top loss, back loss, and power output is repeated till the condition of satisfaction of the energy balance equation is achieved.
5. Experimental Validation of the Thermal Model
In order to validate the thermal model, an experimental test facility has been set up on the rooftop of the Electrical Engineering Department of M.B.M. University, Jodhpur (India).
The setup consists of an equipment for the measurement of various environmental parameters, namely, solar radiation intensity I, ambient temperature , wind velocity , and sky temperature . Other parameters measured are the PV panel’s front glass cover and back sheet surface temperatures and , respectively, and output voltage and current. The validation is based on the accuracy of the prediction of the average temperatures of the top and back surfaces of the PV panel, power output, and efficiency with respect to their experimentally measured values.
The details of the experimental setup are given in the next section.
5.1. Experimental Setup
The details of the apparatus used for the experiment are given in Table 3. It consists of a digital solar radiation recorder, an automatic wind monitor, a contactless infrared thermometer, an ambient temperature measurement unit (Stevenson screen), and a programmable DC load. The solar radiation recorder and wind monitor were fixed at the height of the PV panel. The schematic diagram of the experimental setup and its photograph are given in Figures 6 and 7, respectively.
The manufacturer’s data for the REIL201129019 solar PV panel are given in Table 4. Since the yearly electrical energy output of a PV panel is maximum at an inclination of the latitude of the location, the panel was installed facing south (with no buildings or trees in view of the panel face) at an inclination of 26° with a horizontal inclination for 26.3° N latitude of Jodhpur.
5.2. Experimental Procedure
The solar radiation I at the plane of the panel was measured by using a digital solar radiation recorder, the wind velocity was measured with the help of an automatic wind monitor, a temperature measurement unit (Stevenson screen) was used for the measurement of ambient temperature, and the front and back surface temperatures of the PV panel and sky temperature were measured by means of a contactless infrared (IR) thermometer. The sky temperature has been taken as an average of the readings recorded by pointing the IR thermometer towards the sky at various angles from the zenith as suggested in reference [40]. The method of estimating the sky temperature adopted in the present study is also the same as described in reference [41]. The output voltage and current of the PV panels were measured with the help of a digital multimeter after connecting the programmable DC load operated in the constant resistance mode.
The day-long experiments have been conducted with PV panels installed on the rooftop as mentioned earlier, i.e., under real operating conditions. All readings as described above were recorded at an interval of 30 min. Early summer and peak summer days with nearly clear sky conditions have been selected for the results reported in the next section.
Experimentally, surface temperatures of the glass cover and the back plate were directly measured with uncertainty in the measurement of ±2°C. The power output of the panel has been calculated from the measured voltage and current values. The efficiency of the cell has been calculated from equation (2).
From the analysis of the uncertainties in the measurements, the uncertainties in the calculated values of various parameters using the method of Kline and McClintock [42] are as follows: Power = ±0.94% (odds of 20–1) Efficiency = ±4.1% (odds of 20–1)
The significant contributor to the uncertainty in the efficiency is the uncertainty in solar radiation measurement as depicted in Table 3.
Karwa et al. [43] have presented sensitivity analysis for their theoretical study by using a mathematical model. The sensitivity analysis for the present study shows that, typically at = 40°C, = 0.75 m/s, I = 725 W/m2, and = 20°C, +1°C change in the ambient temperature affects the cell temperature prediction by +0.7°C and the power output prediction by −0.4%. A change of +0.5 m/s in wind velocity affected prediction by −1.5°C and power output prediction by +0.9%. These values are about +0.4°C and +1.1%, respectively, for a +10 W/m2 change in solar radiation, while a +5°C change in the sky temperature affected these values by +1.0°C and −0.6%, respectively.
5.3. Validation of the Thermal Model
In order to validate the thermal model, the experiments have been conducted on April 23, 2023, and June 25, 2022, which are early summer and peak summer days, respectively. The days of experiments had nearly clear sky conditions. The comparison of the experimental results has been made with the predicted values from the model. It is to be mentioned that the measured value of sky temperature has been used in the mathematical model for its validation.
The recorded values of the environmental parameters are presented in parts (a) and (b), while experimental data and predicted values of temperatures of the penal front and back surfaces, and power output are presented in parts (c) and (d) of the plots of Figures 8 and 9 for April 23, 2023, and June 25, 2022, respectively.
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
In Figure 8, it can be seen that the predicted glass cover outer surface temperature values are within 0.13–4.1°C of experimentally measured values, while the predicted back sheet temperature values are within 1.2–4.1°C of the experimentally recorded values. The predicted and measured power output values are within 0.44–1.65 W. The RMSE values for top and bottom surface temperatures are found to be of 4.11°C and 2.03°C, respectively. For power output, RMSE is found to be of 1.19 W.
Figure 9, which refers to the peak summer day of June 2022, shows that the presented thermal model can predict the front glass cover outer surface temperature within 0.2–4.5°C of the experimental values and the predicted back sheet temperature values are within 0.5–5.5°C of the corresponding experimentally recorded values. The predicted and measured power output values can be seen to be within 0.85–1.2 W. The RMSE values for the top and bottom surface temperatures are found to be of 2.35°C and 3.57°C, respectively. For the power output, RSME is 1.09 W.
The predicted values of cell temperature have been used in equation (29) of the model to determine the power output of the panel as explained in Section 4. Experimentally, the power output is calculated from the observed values of voltage across and current through the load in the electrical circuit of the experimental setup.
The predicted and experimental electrical efficiencies of the PV panel are plotted versus the time of the day in Figure 10. The predicted and measured efficiencies are within 0.08–0.52% with a RMSE value of 0.27% for April 23, 2023, while the predicted and measured efficiency values for June 25, 2022, are within 0.17–0.38% with a RMSE value of 0.27%.
The variation of the efficiency with time of the day for both days of the experimentation is similar to those reported by Khanam et al. [26] and Elminshawy et al. [44]. As seen in Figures 8(d) and 9(d), the power output follows the trend of variation of the solar radiation intensity. The power output increases from morning hours to afternoon with the increase in the solar radiation intensity and then it is seen to decrease during the afternoon. From Figures 8(c) and 9(c), it can be seen that the PV penal temperatures increase with the time of the day up to the afternoon and then decrease, and, thus, this trend nearly follows the variation of the solar radiation intensity. It is to be noted that the ambient temperatures also affect the panel temperature, which increases in the forenoon period with the increase in the solar radiation but the decrease in the afternoon temperature does not follow the trend of solar radiation intensity and remains high. From the plots of efficiency in Figure 10, it can be seen that the efficiency variation shows a trend which is opposite to the trend of variation of the solar radiation intensity. Khanam et al. have explained the reason for this trend. The increase in the cell temperature excites the electrons which enhances the collisions between them and thereby increases the resistance, and hence the efficiency of the PV cell decreases in the middle hours.
The predicted and experimental values of various parameters discussed above can be considered to be in close agreement and practically acceptable. Hence, it can be inferred that the thermal model is validated to an acceptable degree of accuracy and the model can be used to predict the cell temperature as well, which is not possible to measure directly.
It is to be noted that the observed differences in the predicted and measured results are due to the fact that there are uncertainties in the estimates of sky temperature and wind heat transfer coefficient. The uncertainties in these parameters have been discussed in significant detail in reference [41]. Furthermore, it is mentioned that there is also an uncertainty in the estimate of the convective heat transfer coefficient on the back surface of the panel.
The fulfilment of the condition of one-dimensional conduction heat transfer mentioned earlier has been confirmed experimentally. The size of the PV panel used in the present study is 1200 mm in length, 535 mm in width, and 33 mm in thickness Along the length of the panel, the glass and back surface temperatures were measured at nine approximately equally spaced locations to find their average temperatures. The temperature at these locations was found to be within 2.5°C. In the spanwise direction, the temperature was measured at equally spaced 7 locations at the midheight of the panel. In the spanwise direction, the variation in the measured temperature was found to be less than 1.5°C. Since the variation of the temperature per unit distance is negligible in lengthwise and widthwise directions, so looking at the length and width of the panel, the assumption of one-dimensional conductive heat transfer across the thickness of the panel is justified. It is to be mentioned that the extreme locations for temperature measurements were kept about 50 mm away from the frame of the panel. This approach is also in line with Kant et al. [15] who did not consider the effect of the frame of the panel extending the logic that the frame has a low surface area with respect to the panel area and, thus, has a negligible effect on the temperature response of the PV panels. Aly et al. [23] have ignored the thermal conductance towards the frame in the analysis of their thermal model.
The cell temperature for the environmental condition of June experiment day has been found to vary from about 51°C at 10 am to a maximum of about 66.5°C at the noon and 53°C at 4:30 pm when the ambient temperature was 37−44°C giving the difference between the cell and ambient temperatures of about 14°C at 10 am, 25°C at noon, and 9°C at 4:30 pm. At noon, the experimental value of the glass cover temperature was found to be 65.5°C when the ambient temperature was 42°C. For the day of the experiment in April, the maximum cell temperature was found to be about 60°C when the ambient temperature was 35°C. The observed temperature difference between the glass cover and back sheet temperatures is found to be of the order of magnitude in line with Santiago et al. [36] who reported that the cell junction temperatures were typically 1–3°C higher than the temperature measured on the module’s rear surface depending on the module construction and material. It is also to be noted that the temperature of the back sheet of the panel is always higher than the temperature of the glass cover surface.
Since the operating conditions vary throughout the year, month, and even in a day, and they also depend on the location, so it is not cost-effective and practically possible to carry out experiments covering all combinations of these parameters over a wide range. The presented model can be used to generate a year-round data of the cell temperature, power output, and efficiency for any location for known values of ambient temperature, solar insolation, and wind velocity. This information can be utilized to select or develop appropriate cooling technology at the planning stage of the solar PV plant, which can significantly enhance the performance of the solar PV system. This aspect has a special significance in the tropics where the operating temperature of the PV cell is very high because of the high day time temperatures such as in the Thar Desert of Rajasthan where large solar PV generation systems are being installed. It has been mentioned earlier that the back sheet temperature is higher than the glass cover temperature, hence the back sheet can be targeted for the cooling of the panel without interfering with the incoming solar radiation on the front face.
6. Conclusions
A thermal model has been presented in this study to predict the cell temperature, power output, and efficiency under outdoor operating conditions. The presented model is based on the mathematical equations of various heat transfer modes involved and energy balance along with the equation for the prediction of the electrical power output.
The validation of the presented model has been carried out with experimental data. The predicted values of glass cover outer surface temperature, back sheet temperature, power output, and efficiency by the model are found to be within 0.2–4.5°C, 0.5–5.5°C, 0.85–1.2 W, and 0.17–0.38%, respectively, of the experimentally measured values for the peak summer month of June when the ambient temperature recorded was 37−44°C. The maximum glass cover temperatures recorded were 60°C and 65.5°C when the ambient temperatures were 35°C and 42°C near the noon for the early summer and peak summer day experiments, respectively. For the early summer month of April, these values were found to be of 0.13–4.1°C, 0.2–4.1°C, 0.44–1.65 W, and 0.1–0.5% for the glass cover outer surface temperature, back sheet temperature, power output, and efficiency, respectively. Thus, the predictions of the thermal model have exhibited a good agreement with the experimental results.
The presented model can be employed to generate a year-round cell temperature data for the available environmental data. This can help in the selection or development of an appropriate cooling technology at the planning stage of installation of a solar PV generation facility especially for the commercial-level solar PV plants.
6.1. Recommendations for Future Work
The study in this paper has been carried out on a single PV module of 1200 mm × 535 mm area. In actual field applications, the modules are arranged in series and parallel to form arrays of different areas depending on the power output requirements. This study may be extended to the arrays because the effect of the wind on larger areas of the arrays is significantly different. For the flow of any fluid over a flat surface (here, the fluid is air in the form of wind), the thermal boundary layer development and its characteristics, and the flow Reynolds number change with distance from the leading edge of the array surface in the direction of the flow. This causes significant changes in the value of the wind heat transfer coefficient for the same wind velocity, which is a definite variation from the McAdam’s relation presented in this study. It is to be noted that the wind velocity has a prominent effect on the cooling of a PV panel. On the other hand, the temperature of the blowing wind would increase as it moves along the surface of the array and its cooling effect reduces. Furthermore, in the city areas, the rooftop arrays experience different wind patterns than in the fields and the area of the arrays is also much smaller.
In the city areas, the sky temperature is much higher than predicted from Swinbank relation for clear sky due to the environmental pollution. The relative humidity also affects the sky temperature. The effects of these factors are needed to be investigated.
The information generated using the thermal model about the working temperature of the cell under different environmental conditions can help in the selection/development of an appropriate cooling technology at the planning stage of solar PV installations. The cooling of the solar PV panel is an area of great research interest. It has special significance especially for the arid regions such as that of the western Rajasthan where the water availability is very poor and the ambient temperatures are high.
Nomenclature
| A: | Area of the solar panel, m2 |
| : | Specific heat of air, J/(kg·K) |
| h: | Convection heat transfer coefficient for back side, W/(m2·K) |
| : | Radiation heat transfer coefficient for front as well back side, W/(m2·K) |
| : | Wind heat transfer coefficient, W/(m2·K) |
| I: | Solar radiation, W/m2 |
| k: | Thermal conductivity of air, W/(m·K) |
| : | Thermal conductivity of the back sheet, W/(m·K) |
| : | Thermal conductivity of the front encapsulant, W/(m·K) |
| : | Thermal conductivity of the back encapsulant, W/(m·K) |
| : | Thermal conductivity of the top glass cover, W/(m·K) |
| L: | Length of the PV Panel, m |
| Nu: | Nusselt number |
| P: | Power output of the PV Panel, W |
| Pr: | Prandtl number |
| : | Total heat loss from the back side, W |
| : | Heat loss due to convection to the ambient air from the back side, W |
| : | Heat absorbed in the solar cell, W |
| : | Heat loss due to convection to the ambient air from the outer side of the glass cover, W |
| : | Heat loss due to radiation to the ground from the back side, W |
| : | Heat loss due to radiation to the sky from the outer side of the glass cover, W |
| : | Total heat loss from the top side, W |
| Ra: | Rayleigh number |
| : | Ambient temperature, K |
| : | Temperature of the outer surface of the back sheet, K |
| : | Temperature of the solar cell, K |
| : | Temperature of the inner surface of the glass cover, K |
| : | Temperature of the outer surface of the glass cover, K |
| : | Temperature of the ground, K |
| : | Mean air film temperature, K |
| : | Sky temperature, K |
| : | Wind velocity, m/s |
| α: | Absorptivity of the PV cells |
| β: | Coefficient of cubical expansion, 1/K |
| : | Thickness of the back sheet, mm |
| : | Thickness of the front encapsulant, mm |
| : | Thickness of the back encapsulant, mm |
| : | Thickness of the glass cover, mm |
| θ: | Angle of inclination of the PV panel with the vertical, degree |
| : | Emissivity of glass |
| : | Emissivity of the back sheet |
| η: | Efficiency of the PV cell |
| μ: | Viscosity of air, kg/(m·s) |
| ρ: | Density of air, kg/m3 |
| σ: | Stefan and Boltzmann constant = 5.67 × 10−8 W/(m2·K4) |
| τ: | Transmissivity of glass |
| : | Transmittance-absorptance product |
| : | Transmissivity of the front encapsulant. |
Data Availability
The author elects to not share data, as this publication is an outcome of ongoing research work for Ph.D. thesis.
Conflicts of Interest
The authors declare that they have no conflicts of interest.