A numerical modelling approach to optimising photovoltaic installations for thermal effects mitigation

Solar energy presents one of the best alternative sources of energy in the current bid to mitigate the negative impacts of global warming. The present study evaluated the influence of installation configuration together with the meteorological parameters on temperature characteristics of a solar photovoltaic array. Three dimensional simulation using Computational Fluid Dynamics was used in the numerical analysis of the temperature characteristics on solar PV arrays. The Shear Stress Transport k-ω model was employed to analyse the turbulent characteristics of the airstream near the photovoltaic array. A temperature prediction model was developed using Artificial Neural Networks and the model was found to be accurate with a coefficient of determination, R above 90 %. A Response Surface Methodology optimization model was developed to maximize energy generation while minimizing solar photovoltaic cell operating temperature. The models were able to reduce temperature and improve energy generated by 3.9 %. The optimized tilt and azimuth angles were found to be 28.2 tilt and 13.2 respectively yielding an average cell temperature of 29.3 C which gave 3.9 % increase in energy and revenue generated.


Introduction
Renewable energy sources have gained much traction in the last decade and can provide bulk of the global energy requirements. The issues to do with global warming and environmental degradation have necessitated the adoption of renewable energy sources particularly solar energy which is freely available in abundance (Kumar et al. 2014;Goel and Singh 2019a). As a result many countries have shifted their focus to clean and renewable energy sources (Goel and Singh 2019b). However, solar energy has its own shortcomings which include intermittency and its dependency on meteorological and environmental factors. There are three main factors affecting the performance of solar photovoltaics (PV) and these include irradiance, temperature and soiling (Lau et al. 2018). The current PV technology is dominated by crystalline silicone modules contributing 90 % to the global PV market (Kumar and Rosen 2011). However, these are greatly affected by temperatures above 25 o C (Vafaei et al. 2015;Ahadi et al. 2016). Although heat gain is desirable in solar thermal systems Singh 2017, 2020), it is definitely undesirable in solar PV systems. As the cell temperature increases, the PV array performance reduces considerably (Yadav and Bajpai 2018). In essence, there is a linear association between power loss and PV array temperature. Many correlations have been developed in studying the relationships between temperature and PV efficiency. For example, studies have indicated a performance loss between 0.1 %-0.65 %/K due to temperature (Kumar and Rosen 2011). This phenomenon justifies the importance of cooling in solar PV arrays mainly in hot climates (Zhang et al. 2017). Cooling of solar PV collectors is indispensable in improving the power output in solar PV plants (Siecker et al. 2017). Some temperature mitigation procedures have been proposed and these include water cooling, use of hybrid systems (PV-Thermal), forced air circulation and natural air circulation (Wole-Osho et al. 2020). Wind or air flow plays a significant role in lowering the array temperature thus improving the performance of the PV array. Mirzaei and Carmeliet (2015) evaluated the simultaneous airflow both underneath and above the PV modules to assess the temperature characteristics on the PV array using infrared thermography. It was noted that there was non-uniform distribution of surface temperature owing to the lateral eddies developed in the flow. In a different study, the role of cavity airflow on PV array performance was investigated using particle image velocimetry and it was found that the upstream velocity can be 1.26 to 1.35 times slower than the airflow in the cavity (Mirzaei et al. 2014). The results also indicated that turbulent mixing in a stepped configuration of PV modules yields better performance compared to a flat configuration. Studies have also shown that, air flow both in form of forced convection or natural convection has a cooling effect on the solar PV module (Goossens et al. 2019), thus wind-driven temperature mitigation is therefore widely accepted (Zhang et al. 2017). Al-Nimr et al. (2018) proposed a hybrid wind/PV system to minimise temperature rise on the PV cells through the use of a wind turbine. It was shown that through this hybrid system, more energy was generated by both the wind turbine and the PV system. Incorporating the major parameters influencing PV performance in optimising the installation configuration is of great importance. The effects of irradiance and temperature on PV performance have been widely studied (Kumar et al. 2020). However, these studies mainly concentrated on analysing the effects of these parameters on PV performance (Dubey et al. 2013). Many studies have only highlighted the importance of irradiance on optimisation of the installation configuration. Some studies have proposed the incorporation of other parameters such as soiling and shading in the optimisation of the installation configuration (Lau et al. 2018). However, the effect of temperature has not been fully investigated. Attempts have been made to evaluate the effects of cooling on PV array performance, and it was reported that increasing wind speeds improves the PV array performance (Kaldellis et al. 2014). Under normal circumstances factors which include wind speed and direction have a substantial contribution on the PV cell temperature although its analysis is complex due to the stochastic nature of wind. However, if the cooling effect of wind is taken into consideration, the optimum installation configuration can be different from the generally accepted configuration. The optimisation of installation configuration to utilise the cooling effect of wind is still yet to be investigated. Previous studies were mainly concerned with wind flow cooling effect on solar photovoltaics (PV) systems. The optimisation of such systems to maximise power generation while minimising the thermal effects has not been widely considered. The generally accepted optimum PV installation configuration only take the solar irradiance into consideration. The influence of other important factors such as temperature and the possible mitigation approaches for maximum energy yield have been generally overlooked. In optimisation of PV array installation configuration, there is need to consider other factors such as temperature effects. Although it is a complex approach, this will lead to a better optimisation model and higher energy yields. If installations are optimised, higher energy yields are obtained and this improves the revenues generated. This study therefore focuses on developing a predictive model for PV array temperature and establish an optimisation model to minimise temperature effects while maximising energy yield. The study is based on the premise that, of the major parameters influencing solar energy yield, i.e. irradiance, temperature and soiling, irradiance has been widely investigated and installation optimisation has been studied based on irradiance. However, temperature is also an important factor which need to be considered in determining optimal installation configuration. This research study is organised as follows; section 1 introduces the issues of thermal effects on PV performance. The related literature is also scanned in light of the present study. Section 2 presents the research approaches and methods used in this study. These include the experimental setup, the simulation approaches and techniques used. The data collection and validation mechanisms used are also discussed in this section. Section 3 outlines and discusses the results obtained from the simulation analysis. The techno-economic and optimisation analysis of the present study is also considered in this section leading to the conclusions in Section 4.

Materials and Methods
The initial step involved feature extraction from a wide array of meteorological parameters which was done to select the best parameters for predictive modelling and simulation. This was followed by the development of a temperature predictive model using selected meteorological parameters. The third step involved simulations on solar energy generated under varying tilt and azimuth (also known as orientation) angles. Having ascertained the implications on energy of varying the tilt and orientation, experimental design was performed to determine the minimum number of simulations that can be run in CFD. The simulations were run and on each simulation the average and maximum cell temperature were recorded and this was used to determine the thermal losses for each simulated configuration. These thermal losses were used as input in PVSyst for energy simulations. This was followed by optimisation for both temperature minimisation and energy maximisation. Finally, to determine the effectiveness of the optimisation model in financial terms, and economic analysis was done.

Parameter correlation and dimensionality reduction
Parameter correlation was performed to establish the relationships between the different meteorological parameters with temperature. Fourteen environmental and meteorological parameters were obtained from "NASA Solar Energy and Surface Meteorology" for use in temperature prediction and optimisation modelling. The meteorological parameters used are; precipitation (R), surface pressure (P), relative humidity (H), Diffuse Irradiance (DI), Global Horizontal Irradiance (GHI), Direct Normal Irradiance (DNI), minimum wind speed (Wmin), maximum wind speed (Wmax), wind speed (Ws), wind direction (Wd), wind speed range (Wrange), average temperature (Tavg), clearness index (C) and Downward Thermal Infrared radiative flux (IR). Software python v3.8 was used and these meteorological parameters were used in parameter correlation. Average temperature was taken as the response variable and the other parameters were used as the predictor variables. Selection of all relevant parameters was accomplished using Boruta algorithm in Python software. The selected parameters were used in developing the prediction model in Artificial Neural Networks (ANNs).

Artificial Neural Networks (ANNs) model
An Artificial Neural Network model was developed to establish the association between meteorological parameters against the ambient temperature which can be used to predict the temperature of PV collectors. Literature reveals that ANNs have been successfully used in situations where there is difficulty in establishing the relationship between the predictor and predicted variables both analytically and mathematically (Conceição et al. 2018). In this study, a feed forward backpropagation neural network was trained using the Levenberg-Marquardt algorithm. This training algorithm was selected due to its high computational speed notwithstanding that it also demands huge memory resources. The gradient descent learning algorithm with momentum was selected with input variables taken from the all-important variables obtained from the Boruta algorithm. All the values used in this study were normalised between the range 0 -1 as shown by Equation 1. Original non-normalised values were obtained by employing Where: Vn is the normalised value, Vmin is the minimum measured value, Vmax is the measured maximum value while Vp is the value predicted by the ANN model. All the relevant features obtained from Boruta algorithm were used as input parameters. The ANN had a single hidden layer having neurons which were varied between 10 and 50 with a step of five. The ANN also had a single output layer with temperature as the target value. Selection of the best performing combination of activation functions for both the hidden and output layer was done. All the different combinations of two of the three assessed activation functions were analysed for their performance in an ANN with a fixed number neurons equal to 25. The transfer functions evaluated were pure linear (purelin), hyperbolic tangent sigmoid (tansig) and logistic sigmoid (losig). One combination of transfer functions was used to select the best number of neurons to be used in the modelling process. There was random initialisation of the weights used in model development.
A ratio of 70:15:15 was used to assign data respectively for training, testing and validation. 3652 data sets obtained from NASA for the period 2009 to 2019, was thus split for training, testing and validation with respective number of datasets given by 2556, 548 and 548. The ANN toolbox in in MATLAB ® release R2018a was used in the modelling process.

Experimental design
Different variations of the installation configurations to analyse their effect on array temperature were obtained using face centred, central composite design of experiments implemented using Design Expert software v12.0 with a layout shown in Table 1 The wind direction and speed assumed values obtained from NASA through the use of User Defined Functions (UDFs). The results obtained from the CFD simulations with varying installation parameters were used to generate a response surface for mapping the relationship between installation parameters, temperature and energy generated by a solar PV module. -5 was adopted to compute the turbulent behaviour of the flowing fluid air.
Where; ρ (kg/m 3 ) is the density, while time taken is t (seconds) and the velocity vector is u (m/s). κ (W/mK) is the thermal conductivity and the independent flow variable is ∅. Γ ∅,eff (m 2 /s) represents the effective diffusion coefficient while S ∅ is the source term.
Where; gk is the turbulent kinetic energy generation term; gω is the specific dissipation rate generation term; ξω and ξk are respectively the effective diffusivity of ω and k. The dissipation rates of k and ω are respectively given by yk and yω; The cross diffusion term is given by dω; The user defined source terms taken as zero in this study are represented by sk and sω. The geometry used in the simulation was developed using ANSYS design Modeller v17.0 and it mimicked the geometry used by Abiola-Ogedengbe (2011) in his wind tunnel experiments. The ground mounted PV array had its tilt and orientation respectively varied from 8 o to 38 o and -22.5 o to 22.5 o while its height of installation hp was 1.5m. The UDFs (file) were used to provide the values of wind speed and wind direction. Respective dimensions of 21.4 hp, 6 hp and 9 hp were used for the length, height and width of the computational domain. 5hp and 15hp were respectively the distances from the inlet to the PV array and from the PV array to the outlet of the computational domain. These dimensions guaranteed no obstruction of air flow on the PV array surface. A mesh of structured grids was developed using ANSYS ICEM 17. This mesh had 600 000 nodes and was adopted after a mesh independence study. The Finite Volume Method (FVM) was adopted in resolving wind flow conservation equations. Pressure and velocity flow fields were decoupled by employing the SIMPLE algorithm. Diffusion and convection terms were discretised by making use of the second-order upwind scheme represented by Equation 6 (ANSYS FLUENT GUIDE 2013). , Where; the face value using second order upwind is given by γf,sou; The cell-centred value γ had its gradient γgrad in the cell upstream; The displacement vector r r is measured from the face centroid to upstream cell centroid. Simulations were done to compute airflow fields on the PV module. The pressure coefficient, Cp profile obtained in the simulations was validated against the pressure coefficient profile obtained by Tominaga et al. (2015). The Cp from simulations had a percentage difference of 1.03% with the Cp from experimental studies and hence the simulation model was concluded to be able to precisely compute the airflow fields around the PV collector.

Thermal Losses, temperature and radiation modelling
The solar ray tracing model was used for the selected location (Harare). Radiation flux was obtained from the Stefan-Boltzmann relationship given by Equation 7 where the Stefan-Boltzmann constant, As is the surface area, ε is the emissivity (assumed to be 1), Tp is the temperature of the sun while Ts is the temperature of the surroundings.
The thermal losses incorporated in PVsyst were determined using the relationship shown by Equation 8; Where, U is the thermal behaviour, Tc is the temperature of the solar cell, Ta is the ambient temperature, α is the absorption coefficient, H is the global horizontal irradiance while η is the PV cell efficiency.

Optimisation
The CFD simulation results were used to determine the optimum configuration for minimising temperature while maximising energy generated. Response Surface Methodology (RSM) was employed to generate a 2 nd order polynomial modelling the relationship between installation configurations, temperature and energy. The resulting temperatures from different simulations were used to simulate energy production using PVSyst for a full year. An empirical model (Equation 9) was used for predicting solar radiation availability on a tilted PV module surface. This radiation on a tilted PV module, It is obtained from the Global Horizontal Irradiance (GHI) which is obtained from Reflected Irradiance (Ir), Diffuse Irradiance and (Id) Beam Irradiance (Ib), where; rb, rr and rd are tilt factors for beam, reflected and diffuse irradiance.

Results and discussions Solar radiation and energy generated
The collectors were facing the general north direction i.e. North of North West (NNW), North (N) and North of North East (NNE) to harvest as much energy as possible. The different combinations of tilt (from 5 o to 44 o ) and orientation (from -22.5 o to 22.5 o ) were assessed. The simulations revealed that the maximum possible annual energy loss obtained after varying the parameters within the specified range was 5.1% as shown in Table 2 and 3. However, the range between 8 o and 38 o was chosen for optimisation in this study and the maximum energy loss within this range was found to be 2.5% which is reasonably low. This range was chosen based on the generally accepted deviation in tilt angle of ϕ ± 15 o where ϕ is the latitude of the location (Hartner et al. 2015).
It was found that when the orientation is facing due west, there is slightly more energy generated compared to orientations due east. It is also revealed that the variation of energy generated with respect to tilt angle can be modelled using a quadratic polynomial.

Parameter correlation analysis and selection of controllable parameters
Parameter correlation was performed in random forests applying the Boruta algorithm. The RandomizedSearchCV obtained from sklearn was used to optimise the hyper parameters. Four variables were selected by the algorithm and these were pressure, humidity, wind speed and wind direction. These parameters were selected with a test accuracy of 96.4%. The parameter selection indicate that wind direction, wind speed, humidity and pressure are closely correlated to ambient temperature. However, of these parameters, two are controllable and the other two are not controllable. Wind speed and direction are controllable parameters on installation configuration while pressure and humidity are non-controllable and hence cannot be used for temperature mitigation. However, these parameters are essential in predictive modelling of ambient temperature (See Fig. 1).

Fig. 1. Parameter correlation analysis using Boruta algorithm.
The correlation matrix used for variable selection shows that pressure has a very strong correlation with temperature. Other factors of influence include precipitation and clearness index as shown in Fig. 2. The relationship between pressure, relative humidity, wind speed and wind direction was analysed and the graphs are shown in Fig. 3. The correlation of each of the selected variables with temperature was analysed using regression analysis. As shown in Fig. 3. The coefficients of determination R 2 values of relative humidity, pressure, wind direction and wind speed are respectively 50.92%, 17.24%, 12.04% and 25.21%. The individual correlations show that relative humidity has the strongest correlation with temperature followed by wind speed.

Fig. 2. Correlation matrix for variable selection
From the parameter correlation analysis, some controllable parameters were selected. It was shown that the maximum and average wind speeds are respectively 9.22 m/s and 3.56 m/s. (See Fig. 4). The general wind direction is from the East especially from ENE to NNE. Such a phenomenon will make the collector facing NNE have more direct interactions with the wind while the NNW configuration has less direct interactions with the wind thereby experiencing less temperature reduction.   Fig. 3. Correlation of temperature with; relative humidity (a), pressure (b), wind direction (c) and wind speed (d).  Table 4). A total of 35 neurons were selected and used in the model as they gave the best results and this is outlined in Table 5. The ANN model was developed in Matlab and was found to perform well with R 2 values above 90%.  The velocity fields are different for different tilt angles with less obstructions occurring at lower tilt angles and higher obstructions being recorded on steeper tilt angles. Steeper tilt angles resulted in more wind-PV interactions thus causing more cooling in steeper tilt angles compared to less steep tilt angles. This was as a result of a larger effective surface area exposed to the flowing wind by steeper tilt angles. Lower impact wind velocities were recorded on lower tilt angles compared to the steeper tilt angles. An average of 9.99 m/s impact velocity was experienced on the 8 o tilt angle configuration against an average impact velocity of 10.03 m/s for steeper tilt angles. This is the reason for more cooling occuring on higher tilt angles while less cooling occurs on lower tilt angles. Both average temperatures (Tavg) and maximum temperatures (Tmax) were found to be increasingly lower with increasing tilt angle.

TKE profiles
The results indicate that higher tilt angles cause higher turbulences and hence TKE values increased with increasing tilt angles. As shown in Fig. 7, the results gave average TKE values of 0.264 m 2 /s 2 , 0.316 m 2 /s 2 and 0.395 m 2 /s 2 respectively for 8 o , 23 o , and 38 o . Higher turbulences experienced on higher tilt angles are the reason for the lower temperatures experienced on steeper tilt angles compared to lower tilt angles. This is because higher wind turbulences have a tendency of dissipating the heat generated on the PV collector. The orientation of installation also shows its importance in the cooling of the solar PV arrays as evident from the 22.5 o (Fig. 8) configuration which shows higher turbulences compared to other configurations. This is expected since more wind flow was expected in that direction compared to other directions.  Fig. 10. These streamlines characterise the path followed by fluid air particles and they describe flow in terms of velocity and direction. The flow velocity and the spacing between the streamlines are inversely proportional to each other. There are turbulent eddies behind the PV module for all configurations. These turbulent eddies were much closer to the PV module for the 38 o tilt and this had an effect of causing more cooling compared to the other tilt angles.

Response surface modelling
The values of average solar PV module temperature, maximum PV module temperature reached, TKE and average velocity were obtained from the simulations. Response Surface Methodology (RSM) was used to analyse these results and models were developed from these results. Temperature as the most important output variable was analysed against the installation variables used in this study. The results revealed that the tilt angle and the orientation had a strong relationship with PV module temperature. The simulation results were used to generate contours and response surfaces shown in Fig. 11 and the analysis of the contours generated was performed. The analysis of both the contours and the response surface revealed that both the tilt and the azimuth angle of installation had a significant contribution to the PV module temperature. It is evident that at the minimum azimuth of -22.5 o and a tilt of 8 o there is maximum temperature generation. This is validated by the fact that the wind direction in this study was found to be mainly concentrated on the eastern direction and hence more cooling was expected in the eastern orientation compared to the western orientation. The minimum temperatures were attained at an orientation (a) (b) Fig. 11. Average temperature contours Response surface for the average temperature.

Numerical optimization and economic analysis Minimising Temperature
Numerical optimisation was performed in Design Expert v.12.0 to determine the configuration that gives the minimum possible temperature rise on the solar PV array as shown by Fig. 12. The input parameters used were the tilt angle and the orientation while the output parameter was the temperature rise. The optimisation revealed a tilt of 35.4219 o and an orientation of 22.1484 o . This configuration gave an average temperature of 34.1 o C and a maximum temperature of 50.376 o C. On the other hand, the average velocity experienced was 10.0603 m/s while the TKE associated with such a configuration was 0.348912 m 2 /s 2 . The optimisation shows that for tilt angles above 20 o and orientations above 5 o , there is low temperature generated and hence the optimum solution lies in this region.
19 Fig. 12. Numerical optimisation of the installation configuration to minimise temperature.

Optimization for energy generation
The results from the simulation studies were used to run simulations in PVsyst to determine the annual energy generated on a hypothetical 25 kW solar PV array under different temperatures as obtained from CFD simulations as shown by Fig. 13 and 14. Different values of the thermal parameter (U) were obtained from CFD simulations and used in the PVsyst energy simulations. The values of ambient temperature and global irradiance were taken as the daily average and each day had its own values. The efficiency of the PV cells was taken as 18.9 % while the absorptivity was taken as 0.9. The simulations in PVsyst were used to select an optimum configuration for maximising the energy generated. The Installation configuration was optimised using the tilt, orientation and the cell temperature as the input parameters. The annual energy generated under these different parameters was taken as the output. RSM was used to optimise the configuration to select the one with the highest energy output. Energy gained due to temperature minimisation A comparison of the energy generated with and without optimisation was performed. The comparison revealed that installation optimisation using Response Surface Optimisation results in extra 1.5MWh of energy being generated and this is equivalent to 3.9 % more energy generated. Considering a Feed-in-Tariff of US$0.15, this translates to an additional annual income of US$225 which is a revenue of US$5625 in the expected lifetime of the 25 kW solar PV plant of 25 years The economic gain obtained from the different optimisation techniques is outlined in Table 3 where 'General' implies the generally accepted optimum configuration of 0 o N and 23 o tilt angle. It is shown that there is more power generated by temperature optimised configuration when compared to the general configuration. There are higher values of NPV, IRR and lower values of payback for the temperature optimised configuration.

Conclusions and recommendations
The study investigated the factors contributing to temperature characteristics of a solar photovoltaic cell. Up to 14 meteorological parameters were evaluated and out of these 4 were selected for predictive model development using Artificial Neural Networks. The model developed was found to be accurate with a coefficient of determination (R 2 ) above 90 %. Temperature distribution experienced on the PV collectors was also investigated. The turbulent air flow characteristic behaviour on a hypothetical 25 kW solar system was analyzed using a three dimensional computational fluid dynamics model. The impact of installation azimuth and tilt as well as meteorological parameters on temperature characteristics was analyzed. Response Surface Methodology based optimization model was developed and in this study, several observations were noted as follows:  Temperature can be accurately predicted using pressure, humidity, wind speed and direction with a coefficient of determination (R 2 ) above 90 %.  The air flow velocity fields and the temperature characteristics are dependent on the installation configuration and the meteorological parameters such as wind direction and speed.  Steep tilt angles experience higher impact wind velocities unlike less steep installation angles.
Low tilt angles experience a broader spectrum of impact velocities, henceforth higher temperatures were recorded.  Optimisation of the installation tilt was found to significantly reduce the temperature rise on the solar photovoltaic array while maximizing the energy generated by the solar photovoltaic array. The optimization performed was able to increase energy generated by 3.9 % thus increasing the total lifetime energy harvested by US$5625.  The generally agreed tilt and orientation of 23 o and 0 o North are not always the best configuration for solar photovoltaic installations in Zimbabwe. A configuration of 28.2 o tilt and 13.2 o azimuth gave the optimum energy generated with an average annual cell temperature of 29.3 o C. This resulted in 3.9 % extra energy being generated.