Performance analysis of perovskite and dye-sensitized solar cells under varying operating conditions and comparison with monocrystalline silicon cell

(cid:1) When perovskite reaches 53 (cid:1) C, dye-sensitized reaches 57 (cid:1) C and mono-Si reaches 61 (cid:1) C. (cid:1) Decrease in wind azimuth increases perovskite cell’s efﬁciency from 19.5% to 20.1%. (cid:1) Increase in wind velocity decreases perovskite cell’s temperature from 53 (cid:1) C to 44 (cid:1) C. The efﬁciency of solar cell is generally deﬁned at standard test conditions. However, wind direction, wind velocity, tilt angle of panel and solar radiation during operation differ from those at standard test conditions. The effects of operating conditions on the temperature and efﬁciency of silicon solar cells are widely analysed in literature. In the current work, the thermal performance of perovskite and dye-sensitized solar cells in operating conditions has been analysed and compared with monocrystalline sil- icon solar cell. The effects of wind direction (wind azimuth angle), wind velocity, tilt angle of panel and solar radiation on the temperature and efﬁciency of the cells have been analysed. The results show that as wind azimuth angle increases from 0 (cid:1) to 90 (cid:1) , the temperature of the cell increases from 51.8 (cid:1) C to 58.2 (cid:1) C for monocrystalline silicon, from 45.5 (cid:1) C to 50.7 (cid:1) C for perovskite and from 48.4 (cid:1) C to 53.9 (cid:1) C for dye- sensitized solar cell and the corresponding efﬁciency of the cell decreases from 22.3% to 21.5% for monocrystalline silicon, from 20.1% to 19.5% for perovskite and from 11.8% to 11.7% for dye-sensitized solar cell. (cid:3) 2017 The Authors. Published by Elsevier Ltd. ThisisanopenaccessarticleundertheCCBYlicense(http:// creativecommons.org/licenses/by/4.0/).


Introduction
Solar photovoltaic is one of the fastest growing renewable technologies. However, in solar cells, only a fraction of the incident solar radiation gets converted into electricity. Rest of the solar radiation gets converted into heat and raises the temperature of the cell. The temperature rise affects the efficiency (solar radiation to electricity conversion) of the cell. The efficiency of solar cells is generally defined at standard test conditions. However, ambient and operating conditions differ from those of standard test conditions.
For silicon solar cells, many studies are available in literature for finding the temperature of the cell in operating conditions and its effect on the efficiency of the cell which are as follows: Skoplaki and Palyvos [1] presented the available correlations for finding the temperature of the cell as function of solar radiation, ambient temperature and wind velocity. Kaplani and Kaplanis [2] incorporated the effect of wind direction and module tilt on the temperature of the cell. Skoplaki et al. [3] provided the correlations for cell temperature for various mounting conditions of the module, viz. free standing, flat roof, sloped roof and façade integrated. Skoplaki and Palyvos [4] presented the available correlations for finding the efficiency as function of temperature of the cell. Lu and Yao [5] presented the thermal analysis of the cell considering arbitrary number of glass layers. All the above studies consider steady state analysis whereas Jones and Underwood [6] and Armstrong and Hurley [7] carried out transient analysis in which the former considered lumped model for cell materials and the latter considered each layer of the cell separately.
For dye-sensitized solar cells (DSSC), Grätzel [8] reported that the temperature of the cell does not affect the solar to electricity conversion efficiency. Raga and Santiago [9] reported that the DSSC efficiency remains almost constant with maximum around 30-40°C. However, Sebastian et al. [10] reported that, above room temperature, DSSC efficiency decreases with increase in cell temperature and for very low temperatures (<0°C), efficiency increases with temperature. Pettersson et al. [11] presented the performance of low powered DSSC module and found that, below room temperature, efficiency increases with temperature and, above room temperature, it decreases with temperature. Chen et al. [12] presented the thermal analysis of the DSSC module. Pan et al. [13] analysed the performance of DSSC module integrated with cooling system for thermal management of the cells. Berginc et al. [14,15] studied the effects of temperature and iodine concentration on the performance of DSSC and reported the experimental measurements. Tripathi et al. [16] modelled the DSSC system and predicted the performance of DSSC under various levels of illumination and cell temperature. Zhang et al. [17] analysed the effect of temperature on the efficiency of perovskite solar cells. Cojocaru et al. [18] presented the effect of temperature on the crystal structure and the performance of perovskite cells.
Thus, it can be concluded that the performance of silicon solar cells in operating conditions is widely analysed. However, the study related to the effect of operating conditions on the temperature and efficiency of perovskite and dye-sensitized solar cells is not available in literature and, thus, it has been carried out in the current work.

Methodology
Solar cell having length L, width w and thickness t is considered in this work. The geometry of the cell is defined by cartesian coordinates (x, y, z) with centre at O (0, 0, 0) as shown in Fig. 1. Three types of solar cells: perovskite, dye-sensitized and monocrystalline silicon cells are considered. The perovskite cell is considered to be made up of five layers. 1 st layer (0 z t 1 ) is glass, 2 nd layer (t 1 z t 2 ) is TiO 2 , 3 rd layer (t 2 z t 3 ) is perovskite, 4 th layer (t 3 z t 4 ) is Spiro-OMeTAD and 5 th layer (t 4 z t 5 ) is silver. The layers of dye-sensitized solar cell are glass, dye sensitized TiO 2 , electrolyte, platinum and glass. The layers of monocrystalline silicon solar cell are glass, ethylene vinyl acetate (EVA), silicon, EVA and tedlar.
The following assumptions have been made in this work (i) The heat losses from the top and bottom surfaces are only considered and from the sides are neglected as the thickness of the cell is negligible compared to its length and width. (ii) Due to very small thickness of cell's layers (nm-lm), the contact resistances hardly affect the average temperature of the cell. Thus, they are not considered in the thermal analysis which helps in keeping the model simple. (iii) Since the thickness of the cell is very less, thermal capacity of the cell is neglected.
The fraction of the incident solar radiation (I T ) that gets transmitted through the glass cover and absorbed by the solar cell can be written as (sa) eff x I T where (sa) eff is the effective product of transmissivity of glass cover and absorptivity of solar cell. Out of the absorbed one, only a small portion gets converted into electricity and the rest of the solar radiation gets converted into heat (S h ) which can be written as where g cell is the solar radiation to electricity conversion efficiency of the cell. At the interface of the 2 nd and 3 rd layers (i.e. at z = t 2 ), the heat (S h ) flows towards the top and bottom of the cell. Thus, at z = t 2 , the sum of flow rates of heat entering the 2 nd and 3 rd layers can be written as follows where k 2 and k 3 are the thermal conductivities of the 2 nd and 3 rd layers respectively. During steady state, the heat conducts through each ith layer (i = 1 to 5) following the below equation At the interface of the i th and (i + 1) th layers (i.e. at z = t i ), the flow rate of heat leaving the i th layer is same as the flow rate entering the successive layer. Thus, the following energy balance can be written where k i is the thermal conductivity of the i th layer. Temperature of the i th and (i + 1) th layers at their interface (i.e. at z = t i ) is same. Thus, From the top and bottom surfaces, heat is lost to surroundings due to convective and radiative losses. Thus, at z = 0 and z = t 5 , the following energy balances can be written where k 1 and k 5 are the thermal conductivities of the 1 st and 5 th layers respectively. h t and h b are the convective heat transfer coefficients of the top and bottom surfaces respectively. T a is ambient temperature. r is Stefan-Boltzmann constant. e t and e b are the emissivities for long wavelength radiation of the top and bottom surfaces respectively. F t_s , F t_g , F b_s and F b_g , are the view factors between top surface and sky, top surface and ground, bottom surface and sky, and bottom surface and ground respectively. T s and T g are the sky and ground temperature respectively. Following Kaplani and Kaplanis [2], h t can be written as combination of natural and forced convection as follows where Gr is Grashof number, Re is Reynolds number and b is the tilt angle of the panel. h t_nat and h t_for are the heat transfer coefficients of the top surface due to natural and forced convection respectively and can be written as follows where Pr is Prandtl number of air, Gr c is the critical Grashof number = 1.327 Â 10 10 exp{À3.708(p/2-b)}, L ch is the characteristic length i.e. the length of surface along the direction of air flow, k a is the thermal conductivity of air, c w is the wind azimuth angle (the angle made by wind stream with the projection of surface normal on horizontal plane), v w is the wind velocity, t is kinematic viscosity of air. Following Kaplani and Kaplanis [2], h b can be written as combination of natural and forced convection as follows In the above equation, '+' is used when natural and forced flow are assisting each other and 'À' is used when they are opposing. Thus, if back side of the panel is leeward, '+' is used and if it is wind ward, 'À' is used. h b_nat and h b_for are the heat transfer coefficients of the bottom surface due to natural and forced convection respectively and can be written as follows   if Re c t=v w L ch P 0:95 where Ra is Rayleigh number, L ch is the characteristic length i.e. the length of surface along the direction of air flow and Re c is the critical Reynolds number (= 4 Â 10 5 ). By combining the convective and radiative heat transfer, overall heat transfer coefficients of the top and bottom surfaces (U t and U b ) are defined as follows The solution of Eq. (3) can be written as follows By putting Eq. (16) into Eqs. (2)- (7)), the following expressions of A i and B i (i = 1 to 5) are derived

Validation
Kaplani and Kaplanis [2] have reported the experimentally measured cell temperature as 46.1°C at tilt angle (b) = 30°, wind velocity (v w ) = 1 m/s, ambient temperature (T a ) = 20°C and solar radiation on tilted surface (I T ) = 800 W/m 2 for silicon solar cell. For comparison, the cell temperature has been calculated using the proposed methodology which is 45.6°C. Thus, the value computed using the proposed methodology differs from that of Kaplani and Kaplanis [2] by 0.5°C. The mismatch is within the acceptable range as cell efficiency hardly varies for this small temperature difference.

Results and discussion
The temperature and efficiency of monocrystalline silicon, dyesensitized and perovskite solar cells are calculated for various values of wind azimuth angle (wind direction), wind velocity, tilt angle of panel and solar radiation. The values of the parameters used for the calculations are presented in Table 1.
The optimum tilt angle is lower for places at lower latitudes and higher for higher latitudes. For building integration, tilt angle may kept as 90°. Thus, the variation of tilt angle (b) from 0°to 90°is shown in subsequent sections. However, while analysing the effect of other parameters, tilt angle is kept fixed as 45°which is near to optimum tilt angle for Cornwall, UK and is the mid value of the range of tilt angle (0° b 90°). Similarly, the variation in wind velocity (v w ) is shown in subsequent sections and while analysing the effect of other parameters, wind velocity is kept fixed as 4 m/s which is average wind velocity in sunny seasons at Cornwall, UK.

Effect of wind azimuth angle
The variations in temperature and efficiency of cells with wind azimuth angle (c w ) are plotted in Figs. 2 and 3 respectively keeping b = 45°, I T = 1000 W/m 2 and v w = 4 m/s. The results show that as the wind azimuth angle increases from 0°to 90°, the temperature of the cell increases from 51.8°C to 58.2°C for monocrystalline silicon solar cell, from 48.4°C to 53.9°C for dye-sensitized solar cell and from 45.5°C to 50.7°C for perovskite solar cell and the corresponding efficiency of the cell decreases from 22.3% to 21.5% for monocrystalline silicon, from 11.8% to 11.7% for dye-sensitized solar cell and from 20.1% to 19.5% for perovskite solar cell. This is due to the fact that when wind azimuth angle is 0°, the wind direction is normal to surface which leads to higher heat losses due to forced convection and thus lesser temperature and higher efficiency. The results also show that the temperature of monocrystalline silicon solar cell is higher than that of perovskite and dyesensitized solar cells due to higher heat generation.

Effect of wind velocity
The variations in temperature and efficiency of cells with wind velocity (v w ) are plotted in Figs. 4 and 5 respectively keeping b = 45°, I T = 1000 W/m 2 and c w = 0°. The results show that as the wind velocity increases from 0.5 m/s to 6 m/s, the temperature of the cell decreases from 61.4°C to 49.3°C for monocrystalline silicon solar cell, from 56.6°C to 46.3°C for dye-sensitized solar cell and from 53.3°C to 43.7°C for perovskite solar cell and the corresponding efficiency of the cell increases from 21.2% to 22.5% for monocrystalline silicon, from 11.7% to 11.8% for dye-sensitized and from 19.2% to 20.3% for perovskite solar cell. This is due to the fact that the increase in wind velocity leads to increment in heat losses which results in decrement in the temperature of the cell and, thus, increment in efficiency.

Effect of tilt angle of panel
The variations in temperature and efficiency of cells with tilt of panel (b) are plotted in Figs. 6 and 7 respectively keeping c w = 0°, I T = 1000 W/m 2 and v w = 4 m/s. If the change in incident solar radiation will be considered along with the change in tilt, it will result as combined effect of both. In that case, it will be hard to find the effect of individual that whether something is happened due to change in tilt angle or change in incident solar radiation. Thus, the effects of both are analysed separately in Sections 4.3 and 4.4 respectively. The results show that as tilt of panel increases from 0°to 90°, the temperature of the cell decreases from 57.8°C to 50.5°C for monocrystalline silicon solar cell, from 53.5°C to 47.3°C for dye-sensitized solar cell and from 50.3°C to 44.6°C for perovskite solar cell and the corresponding efficiency of the cell increases from 21.6% to 22.4% for monocrystalline silicon, from 11.7% to 11.8% for dye-sensitized solar cell and from 19.5% to 20.2% for perovskite solar cell. This is due to the fact that the higher tilt angle leads to larger heat losses due to forced convection which results in lesser temperature of the cell and, thus, higher efficiency.

Effect of incident solar radiation
The variations in temperature and efficiency of cells with incident solar radiation (I T ) are plotted in Figs. 8 and 9 respectively keeping b = 45°, c w = 0°and v w = 4 m/s. The results show that as the incident solar radiation increases from 200 to 1000 W/m 2 , the temperature of the cell increases from 33.8°C to 51.8°C for monocrystalline silicon solar cell, from 33.1°C to 48.4°C for dyesensitized solar cell and from 32.5°C to 45.5°C for perovskite solar cell and the corresponding efficiency of the cell increases from 20.8% to 22.3% for monocrystalline silicon, from 10.4% to 11.8% for dye-sensitized solar cell and from 18.5% to 20.1% for perovskite solar cell. This is due to the fact that the increase in solar radiation leads to increase in heat generation and, thus, increase in temperature of the cell. Increase in insolation has its own positive effect on efficiency which dominates over the negative effect of rise in temperature. Thus, efficiency increases with insolation. Since heat generation in monocrystalline silicon solar cell is higher than the other studied cells, the temperature of silicon cell remains higher in any operating condition. Thus, ranking of cells remains same in all the sections from 4.1 to 4.4.

Conclusions
In the current work, the performance of perovskite and dyesensitized solar cells in operating conditions has been analysed and compared with monocrystalline silicon solar cell. An analytical expression has been derived that gives correlation between cell's performance and operating conditions. For validation purpose, the values of temperature for silicon solar cell are computed using the proposed methodology and it is found that they differ from those of Kaplani and Kaplanis [2] by less than 0.5°C. The effects of wind direction (wind azimuth angle), wind velocity, tilt angle of panel and solar radiation on the temperature and efficiency of monocrystalline silicon, perovskite and dye-sensitized solar cells have been analysed. The conclusions are as follows (i) Higher heat generation in monocrystalline silicon solar cell leads to higher temperature as compared to perovskite and dye-sensitized solar cell.

Silicon
Dye-sensitized Perovskite     (iii) For perovskite solar cell, the increase in wind azimuth angle from 0°to 90°leads to increase in temperature of the cell from 45.5°C to 50.7°C and decrease in the efficiency from 20.1% to 19.5%. The increase in wind velocity from 0.5 m/s to 6 m/s leads to decrease in temperature of the cell from 53.3°C to 43.7°C and increase in the efficiency of cell from 19.2% to 20.3%. The increase in the tilt of panel from 0°to 90°leads to decrease in temperature of the cell from 50.3°C to 44.6°C and increase in the efficiency of cell from 19.5% to 20.2%. The increase in solar radiation from 200 to 1000 W/m 2 leads to increase in temperature of the cell from 32.5°C to 45.5°C and increase in the efficiency of cell from 18.5% to 20.1%. (iv) For dye-sensitized solar cell, the increase in wind azimuth angle from 0°to 90°leads to increase in temperature of the cell from 48.4°C to 53.9°C and decrease in the efficiency from 11.8% to 11.7%. The increase in wind velocity from 0.5 m/s to 6 m/s leads to decrease in temperature of the cell from 56.6°C to 46.3°C and increase in the efficiency of cell from 11.7% to 11.8%. The increase in the tilt of panel from 0°to 90°leads to decrease in temperature of the cell from 53.5°C to 47.3°C and increase in the efficiency of cell from 11.7% to 11.8%. The increase in solar radiation from 200 to 1000 W/m 2 leads to increase in temperature of the cell from 33.1°C to 48.4°C and increase in the efficiency of cell from 10.4% to 11.8%.
Thus, from the current work, the service providers can evaluate the performance of the system beforehand for the specific weather conditions of their respective locations which will help them calculate the area required to meet the demand. The analytical expression derived in the manuscript considers all the layers of the cells and this is its uniqueness. It will help researchers and manufacturers plug in the properties of different layers of their own cells to analyse them.