Numerical Simulations of a PV Module with Phase Change Material (PV-PCM) under Variable Weather Conditions

The efficiency of PV cells is sturdily affected by the increase of their temperature, in fact, as the temperature of the cells increases, the energy yield decreases.

Theoretically, the temperature coefficient γ, which relates PV efficiency and cell temperature, ranges from -0.4 to -0.45% ℃. However, an experimental study has shown that this coefficient could rise to -0.65 % ℃ [1].

Furthermore, the PV panels heat up quickly as the layers have modes thermal inertia [2], so their efficiency decline as the solar irradiation grows.

Table 1. PV cooling techniques

Therefore, active and passive cooling techniques have been developed to cool photovoltaic panels to increase their efficiency [3, 4].

Active cooling techniques require the supply of energy, on the contrary, passive cooling does not require energy and also has lower maintenance requests.

Table 1 enumerates the different solar photovoltaic systems cooling technologies as proposed by Lupul et al. [5].

Hybrid PV/Thermal collectors allow to optimize and control the PV cell temperature [6], increase the overall energy conversion efficiency [7], as well as diminish the need for installation space [8].

The performances of PV/T nanofluid for cooling the PV cells have been evaluated in the study [9].

Among the passive cooling strategy, one of the most promising concerns the use of phase change materials (PCMs) to decrease the operative temperature of a PV panel.

PCMs act as a heat storage material where the thermal energy discharged by the cells is stored as latent heat of fusion, thus blocking the temperature increase. Hence these materials, whom temperature remains constant until the end of the melting process, allow for improved electrical conversion efficiency, creating a shift in temperature rise [10].

Therefore, the PCMs can accumulate thermal energy in the form of heat or cold with the possibility of using it later, this feature makes them extremely suitable for applications with electrical storages [11, 12].

Huang et al. [13] devised and validated a numerical PV-PCM model, they noticed that applying a tank, filled with 4.0 cm of PCM, to the rear of a photovoltaic panel, it’s possible to maintain a constant PV temperature under constant solar irradiation of 750 W m⁻² for about 150 min.

The potential of PCMs can be optimized by acting on the transition temperature, Kibria et al. [14] improved the PV-PCM system efficiency by 5% in comparison to the traditional PV panel, varying the PCM melting point.

It is also necessary to consider that the convective flow that arises inside the PCM in liquid phase negatively affects the performance of the photovoltaic system [15].

Khanna et al. [16] developed a CFD simulation in which they keep constant air temperature and solar radiation value, to establish that the greatest electrical producibility is obtained choosing PCMs which melts point at ambient temperature.

Ma et al. [17] analyzed many PCMs and they noticed that the PV-PCM system yields increase with latent heat capacity.

Various phenomena can affect the performance of the PV-PCM system. As regards the melting point, it is confirmed that temperatures close to the ambient one are to be preferred as they keep the panel at lower temperature values. Furthermore, ambient temperature affects the amount of PCM to employ, in fact, the higher this temperature the larger the amount of material to be used. Stropnik and Stritih [18] showed the optimum PCM volume to install to decrease the temperature of PV cells under various solar radiation levels. Another important parameter is the wind as its velocity increases the optimum depth decreases.

Therefore, an evaluation of a PV-PCM system under real temperature and radiation conditions is certainly of noticeable interest. Nouira and Sammouda [19] developed a CFD simulation in COMSOL to monitor the temperature of a PV panel, varying the solar irradiation, the ambient temperature and the type of PCM employed, during two days of summer. The result is very interesting it emerges that in the same environmental conditions the behavior of the system can be different. This is due to the incomplete solidification of the PCM during the night because of the high temperatures compared to the melting point. Not taking this phenomenon into account can therefore lead to results that are not entirely correct, which is an aspect not yet fully covered in the literature.

Therefore, several are the ideas on which to carry out studies on PV-PCM systems for the Mediterranean area where, despite the high temperatures reached during the year, these systems have not been deeply investigated.

For this reason, in this study, an unsteady CFD model is presented for analyzing the behaviour of a photovoltaic module equipped with two different PCMs.

The cell temperature and electrical efficiency of the two PV-PCM units are compared with those of a conventional PV panel. In particular, the outcomes at the winter and summer solstice, and the autumn equinox have been highlighted. One of the novelties of this study consists in the possibility to takes into account variable weather conditions in the developed numerical model. The hourly values for solar irradiation, ambient temperature, and wind velocity are used as input data.

In comparison with other literature studies, the proposed unsteady CFD analysis allows following the growth of the process of melting and successive solidification phase of the PCM. With this aim, the time of simulations has been extended at least for two days.

The analyses of the thermal and electrical behaviour for both of a conventional photovoltaic module (PV) and the same PV module with the addition of PCM (PV-PCM) is presented. The PCM material is placed into a chamber realized by thin aluminium foils.

The temperature of the cell temperature of PV-PCM module is determined by the energy balance with the surrounding environment and the heat stored into the PCM during the melting process.

The PV-PCM module consists of five layers, glass cover, PV cells and the two EVA sheet (EVA-PV-EVA), Tedlar, PCM material and the two plates of PCM tank.

The following conditions are assumed:

(i) the PV layers, as well as the PCM in solid and liquid phases, were assumed isotropic and homogenous.

(iii) the effects of the temperature were taken into account as variations in the electricity efficiency of the PV module.

(iii) the variations of the thermal properties of the PV layer and the PCM within the same phase with temperature were ignored.

(iv) the heat losses from the side walls were neglected.

(v) the flow in the melted PCM was considered laminar.

The heat fluxes on the PV-PCM module are (Figure 2):

• convection and thermal radiation between the glass panel’s top with the surrounding ambient;

• transmission and absorption of the solar irradiation;

• absorption of the transmitted solar irradiation through the glass by the PV cells:

• power generation;

• thermal conduction across the solid layers;

• storage or discharge of heat by the PCM during the phase changes;

• convection and thermal radiation between the back surface and the outdoor ambient.

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 Figure 2. Heat fluxes in PV-PCM unit

The fraction of the solar irradiance that hits the surface wasted into heat (G_eff) is calculated by:

$G_{e f f}=G \cdot \tau_{g} \cdot \alpha_{P V} \cdot\left(1-\eta_{e l}\right)$                 (1)

where, G is the total irradiance that hits the PV module, τ_g and α_PV are the transmission coefficient of the glass cover and the absorption coefficient of the cells.

The electrical efficiency of the module, η_el is calculated by:

$\eta_{e l}=\eta_{S T C}\left[1-\gamma\left(T_{P V}-T_{S T C}\right)\right]$                   (2)

where, η_STC is the efficiency at the temperature at Standard Test Condition (STC), T_PV and T_STC are the current cell temperature and the temperature at STC, and γ is the temperature coefficient of the PV module.

The heat dissipated via convection and radiation to the surroundings from the front q_T (Eq. (3)) and back q_B (Eq. (4)) surface of the PV-PCM system are calculated as follows:

$\dot{q}_{T}=h\left(T_{g}-T_{q a}\right)+\sigma_{0} \cdot \varepsilon \cdot F_{T, s}\left(T_{g}^{4}-T_{s k y}{ }^{4}\right)$             (3)

$\dot{q}_{B}=h\left(T_{a}-T_{b}\right)+\sigma_{0} \cdot \varepsilon \cdot F_{T b, g}\left(T_{b}^{4}-T_{s k y}^{4}\right)$           (4)

where, h is the convective heat transfer coefficient (a combination of natural and forced convection) between the top surface and the ambient, T_a is the ambient temperature, σ is the Stefan–Boltzmann constant, ε is the emissivity of the top/back surface for long-wavelength radiation,

F_T,s and F_b,s are the respective view factors of the top surface to sky and ground. T_sky and T_g are the sky and ground temperatures respectively.

The temperature of the sky is calculated by Eq. (5) and F_T,s and F_b,_s are calculated with Eqns. (6-7) and β represent the angle of inclination (tilt ) of the PV panel.

$T_{s k y}=0.0552 \cdot T_{a m b}^{1.5}$                  (5)

$\mathrm{F}_{\mathrm{T}, \mathrm{s}}=\frac{1+\cos \beta}{2}$         (6)

$\mathrm{F}_{\mathrm{Tb}, \mathrm{g}}=\frac{1+\cos \beta}{2}$               (7)

According to Skoplaki et al. [28] the convective heat transfer coefficient is calculated using a simplified formulation Eq. (8), where u is the wind velocity in m/s.

$h=5.70+3.80 \cdot u$                 (8)

It is worth to nothing that Kaplani and Kaplanis [29] had presented a more exhaustive expression for calculating convective heat transfer coefficient as a function the Grashof and Reynolds numbers.

Within the solid part of the system, the heat transfer process is governed by conduction, described as in Eq. (9)

$\frac{k_{i}}{\rho_{i} C_{i}} \frac{\partial^{2} T_{i}}{\partial^{2} y}=\frac{\partial T_{i}}{\partial \tau}$             (9)

ρ_i, C_i, T_i and k_i are the density, specific heat, temperature and thermal conductivity of the different layers.

The properties of the PCM were considered as a function of temperature for taking into account of its phase change.

The energy absorbed by phase change material from solid state at temperature T_s to complete melting at temperature T_l and beyond, (i.e. through the melting point T_m) is calculated by Eq. (10):

$Q=m\left\{\int_{T_{S}}^{T_{m}} C_{p s} d t+H+\int_{T_{m}}^{T_{l}} C_{p l} d t\right\}$                 (10)

where, C_ps and C_pl are the specific heat of the solid and liquid phases, T_s, T_l and T_m are the temperatures of the solid, liquid and melting/fusion of the material,

H is the phase change enthalpy or alternately, the latent heat of fusion/solidification (kJ/ kg^-1).

Assuming for each phase a constant specific heat, the temperature field is defined by Eq. (11) [13]:

$T=\left\{\begin{array}{ccc} T o+\frac{Q}{c_{p s}} ; T<T_{m}\text { (solid ph.) } \\ T_{m}; \quad T>T_{m} 0<Q<H \quad \text { (melt zone) } \\ T_{m}+\frac{(Q-H)}{c_{p l}} ; T>T_{m}\quad Q \geq H \text { (liquid ph.) }\end{array}\right.$             (11)

Q = energy absorbed by phase change material (kJ kg^-1).

3.1 Fluid dynamic simulation

The PV-PCM and the conventional PV module have been simulated using the ANSYS Fluent software under unsteady-state analysis [30]. The temperature of the melted PCM is calculated by solving the conservation equations for mass, momentum and energy [30, 31].

Conservation of mass (continuity) for the $i^{t h}$ direction

$\frac{\partial \rho}{\partial t}+\frac{\partial}{\partial x_{i}}\left(\rho \cdot u_{i}\right)=0$                  (12)

Conservation of momentum

$\begin{aligned} \frac{\partial}{\partial t}\left(\rho \cdot u_{j}\right)+\frac{\partial}{\partial x_{i}} &\left(\rho \cdot u_{i} \cdot u_{j}\right) =-\frac{\partial p}{\partial x_{i}}+\frac{\partial \tau_{i j}}{\partial x_{i}}+\rho \cdot g_{i}+F_{i} \end{aligned}$                (13)

Conservation of energy

$\begin{aligned} \frac{\partial}{\partial t}(\rho \cdot J)+\frac{\partial}{\partial x_{i}} \cdot &\left(\rho \cdot u_{i} \cdot J\right) =\frac{\partial}{\partial x_{i}}\left(k+k_{t}\right) \cdot \frac{\partial T}{\partial x_{i}}+S_{h} \end{aligned}$                       (14)

Among the available Reynolds Averaged Navier Stokes (RANS) turbulence models, a two-equation (k-ε) model has been applied. Such models are based on transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). For the standard k- ε model these equations are:

Turbulent kinetic energy (k) Eq. (15)

$\rho \frac{D k}{D t}=\frac{\partial}{\partial x_{i}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{h}}\right) \frac{\partial k}{\partial x_{i}}\right]+G_{h}+G_{b}-\rho \varepsilon$               (15)

Kinetic energy of turbulence dissipation (ε) Eq. (16)

$\rho \frac{D \varepsilon}{D t}=\frac{\partial}{\partial x_{i}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{t}}\right) \frac{\partial \varepsilon}{\partial x_{i}}\right]+C_{1 \varepsilon} \frac{\varepsilon}{k}\left(G_{k}+C_{3 \varepsilon} G_{b}\right)-C_{2 \varepsilon} \rho \frac{\varepsilon^{2}}{k}$                    (16)

where, $G_{k}$ represents the generation of turbulent kinetic energy due to the mean velocity gradients, $G_{b}$ is the generation of turbulent kinetic energy due to buoyancy, $C_{1 \varepsilon}, C_{2 \varepsilon}$ and $C_{3 \varepsilon}$ are constants. $\sigma_{h}$ and $\sigma_{t}$ are the turbulent Prandtl numbers for “k” and “ε” respectively. The turbulent dynamic for momentum μ_t, in the conservation equations and the k-ε turbulence model equations, is related to k and ε by Eq. (17).

$\mu_{t}=\rho C_{\mu} \frac{k^{2}}{\varepsilon}$              (17)

3.2 Geometry, mesh and boundary conditions

A bi-dimensional geometry, which includes the layers of the PV module was created by making distinct bodies for Glass, EVA-Silicon-EVA, Tedlar, Aluminium and PCM layers.

The mesh is of structured type, a quadrilateral grid was generated, with the smallest size of 0.1 per 0.3∙mm while the largest size was 0.7∙per 0.8∙mm. Further reduction of the size of the cell gives rise to change in the results of about ±0.2℃.

The quality of the mesh used is confirmed by its orthogonal quality and skewness, that resulted to be 1.0 and 0.0 respectively.

Then, wall boundary conditions (WBC) are chosen, selecting them among five different options, which are heat flux, temperature, convection, radiation and mixed (combined external radiation and external convective heat transfer).

This latter WBC was selected for taking into account for both convection and radiation heat fluxes.

Unsteady weather conditions for the air temperature, solar irradiance and wind velocity are defined through customized User Defined Functions (UDFs).

Thus, four User Defined Functions have been built for the variables outdoor temperature, solar irradiation, radiative heat fluxes between the glass and the sky and the radiative heat fluxes between the back of the panel and the ground. For each variable, a polynomial time-dependent function has been derived. In the polynomial function, time is expressed in seconds. The simulations have been carried out using a time step of 500 sec.

The numerical convergence of the model was based on the scaled numerical residuals of all the computed variables. The value of 10^-3 was chosen for continuity, velocity and turbulence residuals, while energy and radiation residuals were set at 10^-6. The solution converges after 200 iterations.

As regard the convergence analysis, in accordance with other literature studies [16, 32] it was observed that reduction of the space grid beyond 1mm does not lead to significant improvement in the results.

3.3 Electric yield

The temperature of the PV cells, calculated through the CFD simulation, were in turn used for calculating the electrical efficiency by Eq. (4). 

Thus, the power generated (P_el)is calculated by Eq. (18):

$P_{e l}=\eta_{e l} \cdot A_{P V} \cdot G$                 (18)

where, A_PV is the surface of the PV cells.

The daily energy yield product is determined from Eq. (19):

$E_{e l}=\int P_{e l} \cdot d t$                   (19)

In this section, the energy performances of a conventional PV module are compared with that of the two PV-PCM units, namely PV-RT 28 and PV- RT35.

Figure 4 shows the temperatures of the photovoltaic cells for the two PV-PCM units and conventional PV module at the summer solstice. The results are referred to the second day of simulation

The two PV-PCM units allow achieving PV cell temperature lower than that of the conventional PV.

4.png

Figure 4. PV cell temperatures - summer solstice

In particular, the PV-PCM_RT35 in comparison to the conventional module allows maintaining lower cell temperatures during the whole day. The maximum difference of 20℃ is verified at noon.

From 6:00 to about 10:00, PV-PCM_RT28 achieve the lowest cell temperature then the temperature rises abruptly as the PCM is completely melted. However, the maximum cell temperature remains about 8.0℃ lesser than the highest temperature reached by the conventional PV module.

It has to be highlighted that the cooling of the PV cell is less efficient in the PV-PCM units. Indeed on the late afternoon, the cell temperatures of the PV-PCM units are higher than the cell temperature of the conventional PV module.

In Figure 5 the rate of liquefaction for the two PCMs at 4:30 and 12:00 are depicted.

At noon the PV-PCM_RT28 is fully melted, instead of the PV-PCM_RT35, due to its higher melting temperature, (34-36℃), has a liquid fraction of 49.3% yet. Thus, the RT35 may store heat along with the whole daytime, reaching a liquid fraction of 93.8% at 16:30.

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Figure 5. Liquid fraction (LF) at the summer solstice

The PV-PCM_RT28 does not completely solidify overnight, it achieves a liquid fraction (LF) of 40.6% at 4:30, instead, the PV-PCM_RT35 achieves a total solidification during the night, LF of 0% at 4:30. So the entire the heat of fusion will be available along the day.

Figures 6 and 7 show the PV cell temperature for the three systems at the autumn equinox and winter solstice respectively.

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Figure 6. PV cell temperature - autumn equinox

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Figure 7. PV cell temperatures-winter solstice

At the autumn equinox, both the PV-PCM units have cell temperatures lower than those of the conventional PV unit for many parts of daytime.

Once again the cooling of the PV cell is less efficient in the PV-PCM units, especially the PV-PCM _RT35.

Such critical conditions deriving by the higher melting temperature the PV-PCM _RT35 that delay the transition from liquid to solid under the weather conditions during the autumn season.

Like happens at the summer solstice, on the late afternoon the cell temperatures of conventional PV module are lower than the cell temperatures of the two PV-PCM units. However, as the solar radiation on the late afternoon is weak, such drawback is of scarce significance in terms of energy yield.

At the winter solstice, any remarkable differences emerge between the three PV configurations. Indeed, the cell’s temperatures are always lower than 30℃ for the whole day, so the PV-PCM_RT35 cannot melt. The cell’s temperatures of the PV-PCM_RT28 are about 28℃, so close its melting state.

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Figure 8. Electrical efficiency and yields - summer solstice

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Figure 9. Electrical efficiency and yields - winter solstice

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Figure 10. Electrical efficiency and yields -autumn equinox

It has again observed that the cell temperature of the two PV-PCM units is higher than the cell temperatures of the conventional PV module. This behaviour deriving by the thermal insulation of the PCM layer that reduces the cooling of the PV cells. Thus, during the winter season, the addition of the PCM does not give useful contribute to increasing the energy yield of the PV module.

Figures 8, 9 and 10 depict the electrical efficiency (continuous lines) and power (dashed lines) at the solstices and the autumn equinox.

At the summer solstice and the autumn equinox, the two PV-PCM units attain efficiency and power production higher than the power production achieved by the conventional PV module.

The electrical efficiencies of the PV-PCM units are greater than 16% throughout the day, this means that the efficiency is close to the one at STC condition.

At the autumn equinox, the two PV-PCM have very similar performances with a slight prevalence for the PV-PCM _RT28 unit. Instead at the summer solstice, the PV-PCM_RT28 operates at the lowest efficiency in the afternoon of the summer solstice. Such critical condition is because such PV-PCM unit is totally melted and so is not able to further store heat.

A similar trend is observed for the power production which is a direct function of the electrical efficiency.

At noon of the summer solstice, the PV-PCM_RT35 allows achieving growth of power production of about 10.00 W/m², which corresponds to 10.0% of improvement in comparison to the conventional PV module.

At noon of the autumn equinox, the PV-PCM units allow attaining a growth of the peak of power production of about 9.1% for RT28 and 7.5% for RT35 in comparison to the conventional PV module.

At the winter solstice, the three PV modules do not give rise to remarkable differences for the electrical efficiency or power.

The daily electrical yields of the three PV-module configurations are depicted in Figure 11.

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Figure 11. Daily electrical yields

At the winter solstice, the three PV-module configurations produce the same electrical yields.

At the autumn equinox and summer solstice, the two PV-PCM units attain an energy yield higher than the conventional PV-module.

Table 4 reports the daily energy production for the three PV units.

The PV-PCM_RT28 and PV-PCM_RT35 units generate 4.6% and 5.6% more power in comparison to the conventional PV module, at the summer solstice.

Table 4. Properties of Rubitherm 28 and 35 HC

At the autumn equinox, the PV-PCM_RT28 give rises to an increase of energy production of about 5.7%, respect to the conventional PV-module.

As a general result the PV-PCM_RT28, which has a lower melting temperature, provide better performances during the spring and autumn season, while the PV-PCM_RT35 attains the better performances during the summer season.

Finally, it is possible to observe that the PV-PCM units give rises to the average growth of the daily yield production of 3.54% and 3.17% for PV-PCM_RT28 and PV-PCM_RT35 respectively.

This research is funded by the " research project PIACERI  2020" of the Department of Electric, Electronics and Computer Engineering of the University of Catania.