This article investigated free cooling techniques for the wide range of thermal properties of the PCM layer installed on the backside of the PV cell

Available online 14 February 2022

2352-152X/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Faculty of Mechanical Engineering, Laboratory for Sustainable Technologies in Buildings, University of Ljubljana, Aˇskerˇceva 6, Ljubljana 1000, Slovenia

A R T I C L E I N F O Keywords:

Solar energy Photovoltaics Free cooling of PV Phase-change materials Evaporative cooling

A B S T R A C T

Free cooling of PV cells is a common research topic; it lowers the operating temperature of PV cells, resulting in higher electricity production. This article investigated free cooling techniques for the wide range of thermal properties of the PCM layer installed on the backside of the PV cell. Two options were assumed: micro- encapsulated PCM in which heat is transferred by conduction only, and macro-encapsulated PCM in which heat transfer is enhanced by convection. The effect of free cooling with PCM was compared with the evaporative cooling technique. The thermal response of virtual PV cells (vPV) was evaluated with in-situ experiments. One vPV was upgraded with a micro-encapsulated 5.2 mm thick PCM layer, another with an evaporative layer. Multi- parametric approximation models of the PV cell temperature and combined surface heat transfer coefficients were developed. Approximation models of temperatures were used for the determination of overheating hours (OHH) for the reference and evaporatively cooled vPV, while combined surface heat transfer coefficient models were used in the developed numerical model of thermal response of vPV with micro- and macro-encapsulated PCM. The required thermal properties of PCM were determined to provide the same efficacy of free cooling as an evaporative cooling technique for three selected climate conditions (Stockholm, Ljubljana, and Athens). The study shows that the free cooling of PV cells with PCM could be as efficient as evaporative cooling, but only in the hottest and coldest observed climates if the thermal conductivity of PCM is above 1.8 W/mK for micro- and above 1.2 W/mK for macro-encapsulated PCM, and the latent heat capacity is above 250 kJ/kg. In the milder climate, free cooling will not be as efficient as evaporative cooling (for the defined ranges of thermal properties).

It was determined that for such a climate, the additional heat transfer resistance of the PCM layer increases overheating of PV cells if the PCM’s thermal conductivity is below 0.4 W/mK and the latent heat capacity is below 150 kJ/kg.

1. Introduction

Photovoltaic systems are one of the most promising technologies to utilise renewable energy sources and, therefore, are a key technology for the transition into the post-fossil fuel era. Technological development in the previous decade enabled more reliable and cheaper products but with only a small increase in efficiency. Two directions can be observed to increase electricity production by photovoltaic systems: increasing the solar irradiation with tracking devices [1] or concentrators [2] and free or active cooling [3,4] of the PV modules. Even though PVT mod- ules have rapidly spread in the market [5], free colling of PV modules is a promising technique, considering the properties of semiconductor PV

cells. Free cooling can be achieved by increasing the cooling by natural (or mixed) convection, most commonly on the backside of PV modules.

The most common measure of increasing natural convection is by add- ing fins; Grubiˇsi´c-Cabo et al. [6] have reported an electrical efficiency ˇ increase of 2% with the addition of aluminium fins on the back. For better efficiency, an enhancement of forced convection is needed [7].

Solutions with heat storage that enable decreasing the temperature of PV cells during the operation phase (daytime) are even more frequently the subject of research. Phase change materials (PCM) appear to be the most efficient materials for the accumulation of latent (and sensible) heat [8]. Researchers report a decrease of peak temperature up to 35 ^◦C and an enhancement of efficiency up to 16% [9,10]. Furthermore, external fins can be added to enhance the heat transfer process [11].

Abbreviations: PV, photovoltaics; vPV, virtual PV; PCM, phase change material; PVT, photovoltaic thermal; CO2, carbon dioxide; CV(RMSE), coefficient of variation of the root mean square error; NMBE, normalized mean bias error.

* Corresponding author.

E-mail address: saso.medved@fs.uni-lj.si (S. Medved).

https://doi.org/10.1016/j.est.2022.104162

Received 6 September 2021; Received in revised form 6 November 2021; Accepted 3 February 2022

Because melting temperature (range) for the observed application is most suitable in the case of paraffin-based PCM, such materials are most often analyzed.

Nevertheless, many studies indicate disadvantages of such PCM, mostly low thermal conductivity [12–14] and relatively low thermal capacity. These shortcomings could be limited by adding heat-conductive ribs [15] or particles with high thermal conductivity, such as nano-graphite particles (741% increase of paraffin thermal conductivity to 0.9362 W/mK at 10% mass fraction [16]) or carbon fi- bres and extended graphite (enhanced thermal conductivity of paraffin to 2.09 W/mK [17]). Both measures reduce the heat capacity of the cooling insert (from 209.33 to 181.81 kJ/kg latent heat [16] and from 236.4 to 165.6 kJ/kg [17]) and decrease the sustainability of the PV systems due to the additional material use. Abdulmunem et al. [18] have combined a copper foam matrix with carbon nanotubes within phase change material and reported an effective thermal conductivity of 2.9 W/mK at 0.2% multi-walled carbon nanotubes concentration rate. PCM closed in cooling inserts can be microencapsulated or inserted in the gap of the assembly. In this case, convective heat transfer by liquid PCM can increase heat transfer from PV cells [19,20], and convection heat transfer must be taken into account in the numerical modeling. Addi- tionally, volume changes of PCM materials need to be considered in the cases of container encapsulation [21].

As the third principle of PV cell free cooling, evaporative cooling can be implemented. The most direct method is spraying the front of the PV module with water, with the additional advantage of cleaning the front surface. Elnozahy et al. [22] reported a decrease of peak temperature by 45.5% and an improvement of efficiency from 9 to 11.7%. Another option is a wetted surface on the back of the PV panel. Chandrasekar et al. [23] made a simple system with a cotton wick structure at the back of the module and achieved a 30% reduction in peak temperature and a 15.6% increase in output power. Evaporative cooling is especially effective in dry climates, where Alami [24] reported an increase of 19.4% of maximum power with clay as an evaporative cooling material on the back. Nevertheless, as assumed in the presented research, the process is based on a water supply without any water outflow. Especially in the case of PV modules installed on green roofs and facades, the apparatus for water supply already exists, and such a system will

increase sustainability due to the mitigation of heat islands and the decrease of CO2 emissions caused by electricity production.

The overview of research on the free cooling of PV cells showed that evaporative cooling has the highest efficiency; thus, it can be used as a benchmark for PV cell free cooling with PCM inserts. The present research aims to find the required thermo-technical properties of PCM, which will enable the cooling of PV cells with at least the same efficiency as evaporative cooling. It includes real and enhanced thermal conduc- tivity (λPCM), the temperature of peak thermal capacity (θPCM,m), ther- mal capacity (HPCM), and the mass of the PCM (expressed by the thickness of PCM insert dPCM). To fulfil this goal, (i) the 1-D transient numerical model of thermal response of PV cell with PCM insert was developed for micro-encapsulated PCM in which only conduction is assumed and macro-encapsulated PCM in which convective heat trans- fer in liquid PCM is considered; (ii) combined surface heat transfer co- efficients were determined by in-situ experiments in the form of multi- parametric models and integrated as boundary conditions in the nu- merical model; (iii) experimental data was used for the determination of the PV cell temperature of non-cooled (reference) and evaporatively cooled PV cell in the form of multi-parametric models that were used for the determination of all-year overheating hours (OHH), (iv) the devel- oped numerical model was validated for microencapsulated PCM, and (v) OHH was determined for the set of the range of the thermo-technical properties of PCM and compared with non-cooled and evaporatively cooled PV cells.

2. Research method

The research contains the experimental evaluation of virtual PV cell (vPV) temperature at different outdoor conditions. Three virtual PV cells were constructed in the size of 0.2 ×0.3 m using a material with a similar thermal conductivity as silicon and with solar absorptivity α_s 0.92, tightly covered by 2 mm thick glass with a low reflectance surface with a normal transmissivity τ_s of solar irradiation 0.96 (Fig. 1). During the first period of experiments, the thermal response of individual vPV was compared to prove that the samples and measuring sensors are adequate, and measurement results could be compared. During the first period of the experiment and for the reference vPV during the second Nomenclature

a, b, c parametric models’ coefficients cp specific heat capacity

d thickness fl liquid fraction

g gravitational acceleration Gglob global solar irradiation

hc+r combined heat transfer coefficient H latent heat capacity, height N number of data points Nu Nusselt number q ˙ heat flux

P number of adjustable model parameters Pr Prandtl number

Ra Rayleigh number

T time

U velocity x, y, z layer thicknesses α absorptivity

β thermal expansion coefficient θ temperature

κ thermal diffusivity

λ thermal conductivity, geographical longitude

ν kinematic viscosity

ρ density

τ transmissivity φ relative humidity Φ geographical latitude Index

a ambient air app approximate avg average bottom bottom surface enh enhanced exp experiment

g glass

l liquid

m melting, monthly num numeric opt optimal ref reference s solar, solid top top surface

w wind

β angle of incidence

period, the combined convective and radiative surface heat transfer coefficients hc+r,top, and hc+r,bottom were determined using measuring data and statistics. This was needed because of the specific size of vPV and the position of the experimental apparatus. In addition, the regression coefficients of the multi-parametric linear model of hc+r,top, and hc+r,bottom were needed as boundary conditions in the developed numerical transient simulation tool of the thermal response of PV.

During the second phase of experiments, one of the vPV was upgraded with a PCM layer and another with a water porous evaporative layer, both on the bottom surfaces of the vPV. One vPV was unchanged and served as the reference sample. The measuring data for this cell was used for validation of the developed transient simulation tool. Regarding the hypothesis that we set, the lowest vPV temperatures can be achieved in the case of evaporative cooling. Using the developed simulation tool, we want to verify which combination of PCM thermo-physical proper- ties can ‘compete’ with the best free cooling techniques. As mentioned above, during the second period of experiments, one of the vPV was equipped with a layer of microencapsulated PCM installed tightly on the backside of a vPV. The PCM has apparent specific heat determined by Arkar et al. [25], using data presented by Eddhahak-Ouni et al. [26].

From the DSC measurements, the latent heat of PCM used was estimated to be 72 kJ/kg. The producer [27] specified a peak melting temperature of 21.7 ^◦C, and the thermal conductivity is 0.18 W/mK in solid and 0.14 W/mK in a liquid state. In the case of the microencapsulated PCM, heat is transferred only by conduction. The apparent specific heat of the PCM was approximated by two polynomial equations:

10^∘C<θPCM<22^∘C: cp,app

=13,500− 2194⋅θPCM+147.3⋅θ²_PCM− 1.86⋅θ³_PCM (1) 22^∘C<θPCM<26^∘C: cp,app

=2,618,944− 298,007⋅θPCM+11,325.4⋅θ²_PCM− 143.5⋅θ³_PCM (2) For temperatures below 10 ^◦C and above 26 ^◦C, c_p,app was set to 2800 J/

kgK. Other specific PCM data used in numerical modeling are [28]:

thermal diffusivity κ=2⋅10⁻⁷ m²/s, kinematic viscosity ν= 1⋅10⁻⁵ m²/s, thermal expansion coefficient β=2⋅10⁻³⁷1/K and density ρ_PCM =

820 kg/m³.

At the bottom surface of the second vPV, a high water-porous/spread bio-based layer with a thickness of 1.5 mm was glued. The thin layer ensures low heat conductance resistance while providing sufficient water for free cooling by evaporation. Water was pouring by gravitation at a single point on the top-middle of the evaporative layer via a dis- tribution tube with a diameter of 4 mm. The mass flow rate was controlled by the position of a 500 ml water tank installed above the vPV. The position was controlled manually based on the temperature of the vPV 5 cm below the water inlet and at the middle of the sample. The increased temperature indicates a water shortage. Droplets of the water at the bottom of the evaporative layer were avoided by visual observa- tion. 3-D simulation using TRISCO software was used to determine the impact of the edge heat transfer (Fig. 1). The results were used for correction of the vPV temperature at the top (for water inflow control only); nevertheless, the edge heat losses do not cause significant tem- perature differences (<0.5 ^◦C at the point of temperature sensor).

The outdoor temperature, relative humidity, and global solar irra- diation on the surface of the vPV cells and wind velocity at the instal- lation were measured. All samples were equipped with heat flux sensors installed close to a surface temperature sensor. Hukseflux FHF02–02 sensors (measurement range ±10 kW/m², temperature range − 70 ^◦C to +120 ^◦C) were used. The total measurement uncertainty is ±15%, also considering dynamic measurement conditions. Calibrated T-type ther- mocouples (measurement uncertainty ± 0.5 ^◦C) were used for measuring surface and air temperatures; a capacity sensor AHLBORN FHAD46C41A (measurement uncertainty ±5%, measurement range 2 to 98% RH) was used for air humidity measurements; global solar irradiation was measured with a Kipp&Zonnes CMP3 Pyranometer (measurement uncertainty ±5%). In addition, sensors were connected to an AHLBORN MA5690-1 data acquisition system, while wind velocity Fig. 1. Experimental stand with vPV cells (left); schematic of thermocouples and heat flux sensors position on vPV cells (top right), boundary conditions and 3-D numerical simulation of the steady-state temperature indicating the low impact of edge thermal bridges (bottom right).

was measured with a Netatmo smart anemometer (measurement un- certainty ±0.2 m/s) and a Wi-Fi application. Data was stored at a 1 min time interval. vPV surface temperature sensors were installed on the backside of the vPV, between the bottom surface of the vPV and PCM layer and between the bottom surface of the vPV and evaporative cooling layer at the centre of the sample and 10 cm above the temper- ature sensor. The position of the vPV was not changed during the experiment; the tilt angle was 45^◦, south direction.

2.1. Experimental results

2.1.1. Temperature of reference and evaporatively cooled vPV cells During the first phase of the experiments, the temperatures of three equally designed vPV were measured and compared. This phase was conducted in May 2021. Such a design was assumed as a reference case.

As an example, the measured values for the period between 25 May and 29 May 2021 of three vPV are shown in Fig. 2. It can be seen that during the clear sky conditions, the temperature of vPV can reach up to 69.5 ^◦C (at solar irradiation on the plane of vPV Gglob,β >950 W/m² and ambient air temperature θ_a 27 ^◦C), which is adequate compared to experiments on real PV modules [29,30]. These findings also confirm that measure- ments and numerical simulations based on the vPV are adequate and can be extrapolated to the real PV products. Furthermore, the differences between each of the vPV temperatures are in the range of the thermo- couples’ measurement accuracy (±0.5 ^◦C); therefore, a vPV can be randomly equipped with free cooling additions (layer of PCM or evap- orative matrix).

In the second phase of the experiment (starting on 10 June 2021), one of the reference vPV cells was upgraded with an evaporative cooling layer. A bio-based cotton-cellulose fibre layer was glued on the bottom surface of the vPV cell. The selected material is sustainable and has excellent water spread-water content properties. Fig. 3 shows how water in the evaporative layer is spread from the point source at the top of the vPV cell with an inclination of 45^◦

The positions of temperature sensors and heat flux sensors remain the same: between the vPV and evaporative layer. The temperatures of the reference vPV cell θvPV,ref and evaporatively cooled vPV cell θvPV,evap

for three consecutive days are shown in Fig. 4. It should be mentioned that the saturated condition of the evaporative layer was maintained during the daytime, while the overflow of the water was maintained to be as little as possible.

The high efficacy of the evaporative cooling regarding the decreasing of the vPV cell daytime temperature can be clearly seen from Fig. 4, as the temperature decrease can be as much as 25.5 ^◦C. It is less than 18 ^◦C above the ambient air temperature, while at the same time, the reference

vPV cell has a temperature of more than 41 ^◦C above that of the ambient air.

For the development of vPV temperature approximation models, the measured temperatures of reference and evaporatively cooled vPV were arranged as 15 min average values, with the data reduction of values observed at changes of solar irradiation >50 W/m² within the time intervals. In this way, the impact of heat accumulation was avoided.

Furthermore, as the temperature of reference and evaporatively cooled vPVs depends on the meteorological conditions, regression models were developed with statistical methods within MS Excel using built-in T.

DIST.2T and LINEST functions for the determination of influence pa- rameters and regression coefficients.

The following linear approximation model was developed for the reference vPV temperature:

θvPV,ref,app=a1⋅θa+a2⋅(

τg⋅αvPV⋅Gglob,β

) (3)

where approximation coefficient a1 is equal to 1 and a2 is equal to 0.05057.

The linear approximation model of evaporatively cooled vPV was developed in the form:

θvPV,evap,app=b1⋅θa+b2⋅(100− φ_a) +b3⋅(

τg⋅αvPV⋅Gglob,β

) (4)

where approximation coefficient b1 is equal to 0.8725, b2 is equal to 0.0485, and b3 is equal to 0.02285. The measured and approximated temperatures of the vPVs are shown in Fig. 5.

Linear approximation models were validated with the following statistical metrics: the Coefficient of Variation of Root Mean Square Error CV(RMSE) and the Normalized Mean Bias Error NMBE:

CV(RMSE) = n

∑_n

i=1θvPV,i,exp

⋅

̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅

∑_n

i=1

(θvPV,i,exp− θvPV,i,app

)₂ n− p

2

√

⋅100 (5)

NMBE= n

∑_n

i=1θvPV,i,exp

⋅

∑_n

i=1

(θvPV,i,exp− θvPV,i,app

)

n− p ⋅100 (6)

where n is the number of observations and p is the number of adjustable model parameters; n is equal to 1, as suggested in [31]. According to the ASHRAE criteria [31], CV(RMSE) should be below 15% and NMBE within ± 5%. The statistical metrics presented in Table 1 shows the adequacy of developed approximation models.

2.2. Could free cooling with PCM be as efficient as evaporative cooling?

Among the researchers, the use of PCM for storing heat during the

Fig. 2.Temperature of three reference vPV cells and meteorological conditions (θ_a, Gglob,β and uw) for the five consecutive days of the first phase of the experiment.

daytime resulting in lower PV cell temperatures is a very popular research topic. Even though commonly used paraffin-based PCMs have low thermal conductivity and moderate latent heat capacity. Several measures to improve the thermal conductivity were mentioned in the

Introduction section and are available in other sources. To present the problem of poor material properties clearly, Fig. 6 shows the tempera- tures of the reference vPV cell: one that is evaporatively cooled and one with a layer of micro-encapsulated PCM with a thickness of 5.2 mm on the bottom side for three consecutive days. The properties of the PCM are shown in Section 2. The meteorological conditions at that period are shown in Fig. 4. Obviously, as a consequence of the poor thermal properties of the PCM used, the temperature of the vPV was even higher than for the reference one, by a maximum of 6.2 ^◦C in the worst case.

To determine if any combinations of PCM properties will make free cooling with PCM layer as efficient as evaporative cooling, a transient 1- D numerical tool was developed. In the present study, the micro- encapsulated PCM was used because of the simplicity of application;

nevertheless, macro-encapsulated PCM storage is worth investigating due to the higher efficiency caused by buoyancy-driven convection in- side the liquid phase [20]. The comparison of free cooling technique efficacy was determined with all year simulations in different climate Fig. 3.Spread of the water in an evaporative layer on the bottom surface of the vPV cell from dry to saturated state; the sample size equal to reference vPV cell (200

×300 mm).

Fig. 4. Measured temperatures θ_vPV,ref and θ_vPV,evap and meteorological pa- rameters (Gglob,β, uw) during the second phase of the experiment.

Fig. 5. Measured and approximated temperatures of reference vPV cell (left) and evaporatively cooled vPV cell (right).

Table 1

Statistical metrics of vPV cells’ temperature regression models.

CV(RMSE) (%) NMBE (%)

θ_vPV,ref,app 4.62 −0.98

θvPV,evap,app 5.23 −2.76

conditions and was based on annual overheating hours:

OHH=

∫₃₆₅

n=1

∫_sunset

sunrise

(θPV− 25^∘C)⁺dt=∑³⁶⁵

n=1

∑

sunset sunrise

(θPV− 25^∘C)⁺Δtnum (7) where n is the running day in the year and Δtnum is a computational time step in the numerical model. “+” indicates that only positive differences were summarised.

3. Transient numerical model of thermal response of free cooled PV cell with PCM

In addition to the material properties of the elements of free-cooled PV cells, two of the most influential parameters that define the tem- perature of PV cells are convective and radiative surface heat transfer coefficients. Newton’s cooling law and Stefan-Boltzman’s law for ther- mal emitters and dimensionless numbers (Pr, Nu, Ra) could be used for the determination of surface heat transfer coefficients [32]. In our research, however, we develop models for combined surface heat transfer coefficients using measured values of surface and air tempera- tures, as well as heat flux on the back surface of the vPV. As convective and radiative heat transfer cannot be separated in the case of in-situ experiments, the combined convective and radiative surface heat transfer coefficients were developed for the top (glass) and bottom

surface of vPV cells. Data measured in the reference vPV cells were used.

3.1. Combined surface heat transfer coefficients for vPV cells

Heat fluxes q˙_vPV,ref at the bottom surfaces of the reference vPV cells were measured in addition to temperatures to determine combined surface heat transfer coefficients h_c+r,top, and h_c+r,bottom . These co- efficients have a crucial impact on the temperature of the PV cells. Fig. 7 shows the measured heat fluxes of the reference vPV cells for five (5) consecutive days. A comparison of the heat fluxes measured on the in- dividual vPV shows that all samples have equal design and thermal properties.

The measurement data were arranged and filtered in the same manner as temperatures of reference vPV cells, as described in Section 2.1.1. Combining the measurements of surface temperature θvPV,i and heat fluxes q˙vPV,ref,i together with solar irradiation, the instantaneous combined surface heat transfer coefficients can be determined as follows:

hc+r,bottom=1 3⋅∑³

n=1

q˙_vPV,ref,n (θvPV,n− θa

) (8)

hc+r,top=1 3⋅∑³

n=1

τg⋅αvPV⋅Gglob,β,n− q˙_vPV,ref,n (θvPV,n− θa

) (9)

where n is the number of reference vPV cells (3). It should be pointed out that due to the thin layer of the glass, it was assumed that glass surface temperature is equal to the measured PV cell temperature. Heat flux at the top was not measured to avoid shading. Instead, it was determined from the energy balance. Fig. 8 shows the dependency of hc+r,top, and hc+r,bottom on temperature difference ΔθPV,ref between the reference vPV cell temperature θ_vPV,ref and surrounding air temperature θ_a and on wind velocity. The experimental results gathered in the period between 10 May and 8 July are shown.

From Fig. 8, it can be seen that combined surface heat transfer co- efficient h_c+r,top is in the range between 5 W/m²K at low Δθ_PV,ref (~ 2.5 K) and 7.5 W/m²K at ΔθPV,ref ~ 20 K in windless conditions (uw <0.5 m/

s) (a1), while it increases up to 12.5 W/m²K at wind speed 1.5 m/s. Note that this is the 15 min average value and that the experiment was per- formed in-situ. At wind velocities above 0.5 m/s, hc+r,top decreases with temperature difference (slope b1 is negative) because wind speed im- pacts the temperature difference Δθ_PV,ref (c1). The combined surface heat transfer coefficient at the back of the reference vPV hc+r,bottom is quite similar for non-wind conditions (uw <0.5 m/s), while it is less influential at higher wind speed than the top surface. The slope of line a2

and b2 is flatter. As a consequence, the maximum hc+r,bottom is around Fig. 6.Temperatures of vPV cells: reference, evaporatively cooled and vPV cell

with micro-encapsulated PCM layer.

Fig. 7.Heat fluxes measured at the bottom side of the reference vPV.

13 W/m²K.

For the purpose of numerical modeling, the approximation multi- parametric models of combined surface heat transfer coefficients were developed in the form:

hc+r,app=c1+c2⋅u^c_w³+c4⋅(

θvPV,ref− θa

)_c5

(10) where the approximation coefficient for the top (glass) surface are c1

2.44, c₂ 2.75, c₃ 1.001, c₄ 1.215 and c₅ 0.360, while for the bottom surface c1 2.39, c2 2.82, c3 1.054, c4 1.259 and c5 0.426. The statistical metric of models are: CV(RMSE) 17.9% and NMBE − 0.67% for the ‘top (glass) surface’ approximation model and CV(RMSE) 12.0% and NMBE 6.05% for the ‘bottom surface’ approximation model.

The same approximation model was used to determine the boundary conditions on the bottom surface of the vPV cell with a PCM layer. In this case, temperature θvPV,ref was replaced with the temperature of the outer surface of the PCM layer, which is determined in the iterative calculation procedure.

3.2. Numerical model of free cooled vPV cell with PCM

Taking into account the hypothesis that evaporative cooling is the most efficient free cooling technique of PV cells, the purpose of the numerical modeling of the thermal response of vPV cell with PCM was to determine the range of properties of PCM to reach the efficiency of evaporative cooling technique. For that, a transient numerical model was developed based on the energy balance and set of finite-difference equations, which were solved using the matrix inversion method within an MS Excel environment. Consequently, spatial discretization was done with a pre-defined number of nodes in a 1-D model: 5 for the glass layer, 3 for the PV cell and 19 for the PCM layer (Fig. 9). The following values of constant parameters were considered: the trans- missivity of solar radiation τ_g of glass is 0.96, and the absorptivity of PV cell α_s is 0.92; both properties do not depend on the incident angle of solar irradiation, thermal conductivity λg 0.76 W/mK, specific heat cp,g

840 J/kgK and density of glass ρ_g 2700 kg/m³, thermal conductivity λ_PV 230 W/mK, specific heat c_p,PV 896 J/kgK and density of PV cell ρ_PV 2700 kg/m³. The properties of PCM, including the approximation model for temperature dependant cp,PCM are stated in Section 2.

Simplification of the conductive heat flux at the border of the surface glass-PV and PV-PCM layer was done in such a way that the lower of two thermal conductivities was used in modeling (which will be for the glass and the PCM in practice). The energy balances for specific nodes A, B and C (Fig. 9) are as follows:

•for node A:

cp,g⋅ρ_g⋅Δx 2⋅Δθg,se

Δt = − λg

Δx⋅( θg,1− θg,2

)+hc+r,top,app⋅( θg,1− θa

) (11)

• for node B is:

cp,PV⋅ρPV⋅Δy⋅ΔθPV,1

Δt = − ( λg Δx

2+^Δy₂ )⋅(

θg,5− θPV,1

)− λPV

Δy⋅(

θPV,1− θPV,2

)

+τg⋅αs⋅Gglob,β

(12)

• for node C:

cp,PCM⋅ρPCM⋅Δz 2⋅ΔθPCM,19

Δt = − λPCM

Δz⋅(

θPCM,18− θPCM,19

) +hc+r,bottom,app⋅(

θPCM,19− θa

) (13)

Thermal conductivity in the liquid state of PCM, as presented in Section 2, is valid for the micro-encapsulated PCM layer. In the case of the macro-encapsulated PCM layer, which will also be studied, heat transfer is, in the case of the liquid state, enhanced due to natural con- vection. In our study, enhanced heat transfer in liquid PCM was modeled using the enhanced conductivity method presented by Bejan [33] and Souayfane et al. [34]. The procedure is as follows (according to Fig. 9):

• if all PCM nodes (19 in our case) have temperature θPCM,i <θ_m, the value of thermal conductivity λPCM =λ_PCM,s for solid PCM is used in modeling;

• if all PCM nodes have temperature θPCM ≥θ_m, the value of thermal conductivity λ_PCM,l is increased as corrected (enhanced) conductivity λ_PCM,enh considering t thickness of liquid PCM nodes zPCM (from Fig. 9) and boundary PCM temperatures θ_PV,3 and θ_PCM,19;

λPCM,enh=λPCM,l⋅(1+Nuz) (14)

where Nuz is the Nusselt number, defined by the thickness of the liquid PCM nodes zl =zPCM. In the present study, the Nu number for laminar natural convection in a rectangular enclosure heated or cooled from the side, presented by Berkovsky and Polevikov [33], was used:

Fig. 8.Combined convective and radiative surface heat transfer coefficient hc+r,top (left) and hc+r,bottom (right) of reference vPV cells; coefficients (yellow dots) were determined with 15 min averaging of variables.

Nuz=0.22⋅

( Pr

0.2+Pr⋅Raz

)_0.28

⋅ (zl

H )_0.09

(15)

where H is the height of the PCM enclosure. Rayleigh number is calcu- lated as a function of zliq:

Raz=gβ⋅β⋅z³_l⋅(

θsurface1− θsurface2

)

α⋅ν ⁽¹⁶⁾

where gβ is a component of gravitational acceleration (9.81 ×cos of tilt angle β), θ_surface1, θ_surface2 are the surface temperatures of boundary nodes of PCM liquid fraction. The relation is valid for 2 <

(zl

H

)〈10; Pr

<10⁵; Raz<10¹³.

•in the case of melting and one side solidification (it is assumed that melting occurs if θPV,3 >θ_m), thickness zl of all nodes in which θPV,3

>θ_m is determined and corrected conductivity is determined with θ_PV,3 and θ_m as boundary temperature conditions.

•in the case of solidification that occurs inside the PCM layer, the average thermal conductivity of PCM layer λPCM,avg is determined according to the liquid fraction of PCM, defined as:

fl= zl

zPCM (17)

The average thermal conductivity is assumed for all PCM nodes and is equal to:

λPCM,avg=λPCM,s⋅(1− fl) +λPCM,enh⋅fl (18)

To validate the numerical model, the measured data of meteoro- logical parameters were arranged in 15 min time intervals. The same time step was used in numerical analysis, for which linear interpolation of Typical Meteorological Year hourly values [35] was used.

3.3. Validation of the numerical model

The numerical model was validated for the case of reference vPV cell (without PCM) and vPV cell with the micro-encapsulated paraffin PCM layer. Thermal conductivity λPCM is λPCM,s in case of node i temperature θ_PCM,i <θ_m and λ_PCM is λ_PCM,l otherwise. Convection inside liquid PCM was not considered as the PCM is microencapsulated. For validation of the reference vPV cell, only the temperature nodes for the glass and vPV cell were considered. A comparison between the experimental and nu- merical model-determined temperatures of vPV cells are shown in

Fig. 10.

The results presented in Fig. 10 confirm that the numerical model, which is based on approximation multi-parametric models of combined surface heat transfer coefficients Eq. (10)), is adequate. Except at high changes of solar irradiation, the differences between measured and modeled PV cell temperatures are within ±1.6 ^◦C for the reference vPV cell. In the days presented in Fig. 10, the modeled temperatures are in general higher than measured ones, the main reason being desert sand deposition on the vPV glass. The modeled peak diurnal temperatures of the vPV cell with micro-encapsulated PCM are up to 3.7 ^◦C higher than the measured ones, an additional reason being the approximation model of apparent heat capacity of micro-encapsulated PCM (Eqs. (1) and ((2)).

A numerical model of transient heat transfer in the case of a vPV with macro-encapsulated PCM was validated by data presented by Kant et al.

[20].

4. Parametric study and overall efficiency of free cooling of vPV cell with PCM

With developed numerical tool, the free cooling efficiency indicator (overheating hours OHH) for sites with different climate conditions:

Stockholm (Φ 59.3326^◦N; λ 18.0649^◦E; average yearly temperature θ_a,

avg 6.6 ^◦C, average temperature in the hottest month θa,m,avg 18.8 ^◦C), Ljubljana (Φ 46.1139^◦N; λ 14.4669^◦E; 10.9 ^◦C; θ_a,m,avg 20.4 ^◦C) and Athens (Φ 37.9794^◦N, λ 23.7162^◦E; θ_a,avg 17.6 ^◦C; θ_a,m,avg 27.7 ^◦C) was determined. The design of PV cells with a PCM layer is shown in Fig. 11.

The first application is based on micro-encapsulated PCM, and the sec- ond on macro-encapsulated PCM. In the first case, heat transfer is limited to the conduction; nevertheless, adding particles or a conductive matrix, the apparent thermal conductivity λ_PCM can be significantly increased over intrinsic (paraffin) one, having thermal conductivity only up to 0.2 W/mK. In the case of macro-encapsulated PCM, the heat is transferred by conduction and convection inside a sealed container.

Fig. 11 shows the range of θm,PCM, HPCM, λPCM and the range of thickness of PCM layer dPCM considered in the study. Other properties are pre- sented in Section 2. The length of the PV module, which matters only in the case of the macro-encapsulated PCM layer, was 300 mm, assumed to be an adequate technical solution for the PCM container. The impact of the design and material properties of the PCM layer on the OHH for the observed site was compared with the reference (not cooled) and evap- oratively cooled PV cells. Later, the question of whether free cooling with a PCM layer can be as efficient as evaporative cooling will be answered.

The first parameter that was investigated was the melting tempera- ture of the PCM θ_m,PCM. The range of PCM thermal properties shown in Fig. 9. Temperature nodes defined in the numerical model.

Fig. 11 was considered in all-year simulations using Test Reference Year data [35] for specified locations. Results are shown in Fig. 12 for meteorological conditions of Ljubljana.

From Fig. 12, it can be seen that the optimal melting temperature θm, PCM, which gives minimum OHH, can be determined regardless of the considered PCM properties or the technique of PCM encapsulation. The influence of θm,PCM on OHH is more pronounced at latent heat capacity above 200 kJ/kg. The advantage of convection heat transfer can also be observed, as OHHs are significantly lower in the case of macro- encapsulation, by appr. 8000 Kh per year at the lower thermal con- ductivity of PCM to appr. 2500 Kh/a in case of increased thermal con- ductivity (above 1 W/mK), while the difference decreased due to the decreased latent heat capacity of PCM HPCM.

Nevertheless, it can be seen that optimum melting temperature θ_m,

PCM,opt does not differ significantly, despite the wide range of boundary conditions. It is approximately 2 K lower in the case of the macro- encapsulated PCM layer: 25.3 to 27.8 ^◦C for the micro-encapsulated and 22.5 to 27.5 ^◦C for the macro-encapsulated PCM. Fig. 13 shows that the same conclusion can also be drawn for other sites. Accordingly, the melting temperature of the PCM θ_m,PCM (25 ^◦C for Stockholm, 27.5 ^◦C for Ljubljana and 30 ^◦C for Athens) were considered in further research.

The second parameter that was investigated was the thickness of the PCM layer dPCM. Numerical simulations were performed to determine yearly OHH for three selected sites and the range of boundary conditions shown in Fig. 11. The results for the PV cell with a micro-encapsulated PCM layer for Ljubljana are presented in Fig. 14 (top). It can be esti- mated that optimal thickness d_PCM is 0.03 m for PCM with thermal conductivity λPCM below 0.35 W/mK (in case of HPCM 100 kJ/kg), 0.6 W/mK (HPCM 200 kJ/kg) and 1 W/mK (HPCM 300 kJ/kg). Higher λ_PCM leads to more efficient free cooling process; however, in our opinion, thickness of PCM above 3 cm cannot be justified as the OHH values decrease by only ~14% (dPCM 0.05 mm, λ_PCM 2 W/mK, HPCM 100 kJ/kg) and 9% (dPCM 0.05 mm, λ_PCM 2.0 W/mK, HPCM 300 kJ/kg). No signifi- cant differences between the sites were noticed in this case either.

Therefore, the thickness of the micro-encapsulated layer dPCM of 0.03 m for all sites was assumed in the further analysis.

Results for the case of the macro-encapsulated PCM layer are pre- sented in Fig. 14 (bottom) for PCM with thermal conductivity λPCM of 0.2 W/mK. The Pareto front of the optimum thickness of the PCM layer Fig. 10.In-situ measured and simulated temperatures of reference vPV cell and vPV cell with PCM.

Fig. 11.PV cells with micro- and macro-encapsulated PCM layers and ranges of material and construction parameters assumed in numerical modeling; the length of the PV cell is 300 mm.

Fig. 12.Annual overheating hours OHH of PV cells free cooled with PCM layer: micro-encapsulated (left), macro-encapsulated (right); site Ljubljana.

is indicated. Comparing the results for Ljubljana, the significant impact of convective heat transfer in the PCM layer can be observed, since all- year OHH is reduced by approximately 1/4 at the highest observed thermal capacity to 1/3 at the lowest one. The difference decreases in this case increased the thermal conductivity of micro-encapsulated PCM, as could be expected. Therefore, an additional conclusion can be made regarding the optimal thickness of the PCM layer. As shown in Fig. 14 (bottom), the optimum thickness decreased by increased latent heat capacity HPCM, but in the moderate range. Considering sustainability, the thickness dPCM of 0.03 m can be defined as optimum for the Stock- holm site as increases will result only in a marginal decrease of OHH. For the Ljubljana climate, the optimal thickness of the PCM layer is around 4 cm, but a thinner PCM layer (0.03 m) will cause an increase of OHH of less than 5%. Only in Athens will such a thickness increase all-year OHH, but only by a few percentage points. Consequently, the thickness of PCM

dPCM equal to 0.03 m will also be considered as optimum for macro- encapsulated PCM layers.

4.1. Free cooling with PCM layer vs evaporative cooling

To reject or confirm the main hypothesis (i.e., that evaporative cooling of PV cells (PV module) is the most effective free cooling tech- nique), values of all-year OHH were first determined for the reference and evaporatively cooled PV cells. The tilt angle of south orientated PV modules of 30^◦was assumed at all locations. The evaporative cooling was ‘activated’ at solar irradiation Gglob,β >20 W/m² and θ_a >15 ^◦C.

The results are presented in Table 2. As expected, due to the smaller incident angle of solar irradiation and higher ambient temperatures, the OHH for the reference PV cell in Athens are almost three times higher than for the Stockholm climate and more than two times higher than in Fig. 13.Annual overheating hours OHH of PV cells free cooled with PCM layer: micro-encapsulated (left), macro-encapsulated (right) for observed sites.

Fig. 14.Impact of design parameters (dPCM) and thermal properties (λPCM, HPCM) of PCM on all-year PV cell OHH; for micro-encapsulated PCM and Ljubljana climate data (top), for macro-encapsulated PCM and selected sites climate (bottom); pre-selected PCM melting temperatures θ_m,PCM were applied for each site.

the Ljubljana climate. In the case of evaporatively cooled PV cells, a significant decrease of OHH can be observed in all observed climate conditions. Despite less intense overheating in Stockholm, evaporative cooling is the most efficient among all observed sites, as OHH decreases by 76.5%. Nevertheless, evaporative cooling is also very efficient in other sites. A decrease of OHH by 71.9% can be observed in Ljubljana and almost 60% in Athens.

Another set of numerical analyzes was performed to determine the efficiency of free cooling with a PCM layer. PCM melting temperatures θ_m,PCM were adjusted to the local climate conditions, as summarised in Table 3. The thickness of the PCM layer was dPCM 0.03 m, regardless of the type of encapsulation. The all-year OHH are shown in Fig. 15 for the range of λPCM and HPCM. Black and red dashed lines, if they are within the range of calculated OHH, represent the OHH for the reference (non- cooled) PV cell and evaporatively cooled PV cell (Table 2), respectively.

It can be seen that, in general, OHHs for PV cells with PCM layers are lower than for the reference PV cell. This means that a PV cell can be free cooled with a PCM layer. The exception is the case study of a micro- encapsulated PCM layer in Ljubljana’s climate (Fig. 15 top middle), which turned out to be less efficient compared to reference case (without free cooling) in a ’triangle’ area λ_PCM <0.4 W/mK at H_PCM 50 kJ/kg to HPCM <150 kJ/kg at λPCM 0.2 W/mK.

Conversely, free cooling with PCM may be even more efficient than

evaporative cooling, but the top range of thermal properties of PCM must be provided: for micro-encapsulated PCM (Fig. 15 top) λ_PCM above 1.8 W/mK and H_PCM above 250 kJ/kg (Athens) or above 270 kJ/kg (Stockholm). The range of required PCM thermal properties is more favorable in the case of macro-encapsulated PCM layers (Fig. 15 bot- tom). In this case, thermal conductivity above 1.2 W/mK is required, with latent heat capacity above 225 kJ/kg (Athens) or above 270 kJ/kg (Stockholm). The required thermal properties are also summarised in Table 3.

5. Conclusions

Increasing electricity production with PV cells by decreasing its operating temperature is a popular research topic, especially regarding the daytime accumulation of heat with phase change materials. The presented research aimed to investigate the required thermal properties Fig. 15.All-year overheating hours OHH; for PV cell free cooled with micro-encapsulated PCM layer (top), and with macro-encapsulated PCM layer (bottom).

Table 2

All-year overheating hours OHH (Kh/a) for reference and evaporatively cooled PV cell.

Stockholm Ljubljana Athens

reference PV cell 24,950 30,870 67,220

evaporatively cooled PV cell 5850 8670 27,330

Table 3

Peak PCM melting temperature and thickness used in the numerical model and required PCM properties to achieve efficiency better than at evaporative cooling of PV cell.

Stockholm Ljubljana Athens

θ_m,PCM ( ^◦C) 25 27.5 30

dPCM (m) 0.03 0.03 0.03

Micro-encapsulated PCM λPCM (W/mK) : HPCM

(kJ/kg)

λPCM >1.8 : HPCM >

270 / λPCM >1.8 : HPCM

>250

Macro-encapsulated PCM

λ_PCM (W/mK) : HPCM

(kJ/kg)

λ_PCM >1.2 : HPCM >

270 / λ_PCM >1.2 : HPCM

>225

of PCM to achieve at least the same effect as by evaporative cooling, which we assume to be the most efficient free cooling technique for PV cells.

The simplified transient thermal response model was developed, which enables simulation of the temperature of PV cells for the case of micro- and macro-encapsulated PCM. The combined convective and radiative surface heat transfer coefficients on the top and bottom sides of the virtual PV module were determined with in-situ experiments and integrated into a developed numerical tool in the form of multi- parametric approximation models. Experimental results were also used for the development of approximation models of PV temperature, for reference (not cooled) and evaporatively cooled PV, which was used to determine yearly OHH for comparison.

Analysis of PV cell free cooling with micro- and macro-encapsulated PCM on the backside of the PV cell showed that:

•The PCM peak melting temperatures of 25 ^◦C for Stockholm, 27.5 ^◦C for Ljubljana, and 30 ^◦C for Athens gives the lowest OHH for most combinations of PCM thermo-technical properties;

•The thickness of PCM should be 3 cm in all three considered climatic conditions and both types of encapsulation;

•in Ljubljana’s climatic conditions, non-cooled PV cell can perform better (lower yearly OHH) than free-cooled with micro-encapsulated PCM in the case of pure PCM thermal properties: λ_PCM <0.4 W/mK and HPCM <150 kJ/kg;

•in Ljubljana’s climatic conditions, the efficiency of evaporative cooling cannot be reached even with the upper considered range of PCM thermal properties: λPCM =2 W/mK and HPCM =300 kJ/kg;

•free cooling of PV cells with PCM could be as efficient as evaporative cooling in the climates of Athens and Stockholm, but top range thermal properties are required: for micro-encapsulated PCM λ_PCM >

1.8 W/mK and HPCM >250 kJ/kg (Athens) or >270 kJ/kg (Stock- holm); for macro-encapsulated PCM λ_PCM >1.2 W/mK and HPCM >

225 kJ/kg (Athens) or >270 kJ/kg (Stockholm).

CRediT authorship contribution statement

Ciril Arkar: Investigation, Validation, Software, Formal analysis, Writing – original draft. Tej Ziˇˇzak: Investigation, Data curation, Vali- dation, Writing – original draft. Suzana Domjan: Investigation, Vali- dation, Visualization, Writing – review & editing. Saˇso Medved:

Conceptualization, Methodology, Writing – original draft, Writing – review & editing, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors acknowledge the financial support from the Slovenian Research Agency (research funding No. P2-0233 (C)).

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