The operating temperature is a critical factor affecting the performances of photovoltaic (PV) modules. In this work, relevant models are proposed for the prediction of this operating temperature using data (ambient temperature and solar irradiance) based on real measurements conducted in the tropical region. For each weather condition (categorized according to irradiance and temperature levels), the temperatures of the PV modules obtained using the proposed approach is compared with the corresponding experimentally measured value. The results show that the proposed models have a smaller Root Mean Squared Error than other models developed in the literature for all weather conditions, which confirms the reliability of the proposed framework.
As the PV power sector grows rapidly, favorable support policy and the cost of PV modules is becoming more and more affordable, the use of PV modules to generate electricity is increasing. PV modules are made up of multiple single solar cells that are connected in a series-parallel fashion to boost power and voltage over a single solar cell [
In the PV conversion process, the solar irradiance can only be absorbed in a particular range of wavelengths depending on the material of the cell. The rest is absorbed as heat, which increases the temperature of the PV cells [
The climate in Senegal is a tropical one, characterized by fast changes in radiation caused by large variations in the cloud cover. There is a Sahel zone in the north, characterized by fresh nights and hot days, and a hot and wet zone in the south. The daily maximum and minimum average temperatures are respectively 35°C and 23°C. The country has a high solar potential with an annual average sunshine duration of about 3000 h and an overall daily radiation average of 5.5 kWh/m2/day [
PV modules generally operate in an environmental condition that is different from the manufacturer’s optimal PV module conditions. Therefore, the use of PV modules in situ is often associated with losses in performance. The PV module temperature varies depending on various factors such as the irradiance, convection due to wind and air [
Several authors have shown the existence of a correlation between PV modules temperature and climatic conditions.
The impact of dust deposition, solar radiation, wind speed and ambient temperature on the temperature of PV modules were investigated in Iran by Rouholamini et al. [
Andrea et al. [
Jaszczu et al. [
Zhou et al. [
The recently studies mentioned above were investigated the influence of different environmental conditions on the PV module temperature. Solar irradiation and ambient temperature are the environmental parameters that are identified as most affecting the temperature of PV modules.
Several models for predicting the temperature of PV modules can be found in the literature [
Models | Correlations |
---|---|
Schott [ |
Tm = Tamb + 0.028 * (Gt − 1) |
Mondol | Tm = Tamb + 0.031 * (Gt − 0.058) |
Lasnier [ |
Tm = 30 + 0.0175 * (Gt − 300) + 1.14 * (Tamb − 25) |
Akhsassi [ |
|
NOCT [ |
|
Ross [ |
Tm = Tamb + 0.035 * (Gt) |
Models to predict PV module temperature as the available equations have been validated under given climatic conditions. Even if some studies are carried out in various climatic conditions, research in a tropical country like Senegal has not been exhaustively discussed in the published literature yet. Models to predict the best operating temperature of the PV module in this region are important on the PV performance modelling. The objective of this paper is to propose temperature models for PV modules in tropical regions using operational data.
Outdoor PV testing are located at solar power plants installed in Western Senegal. The temperatures in this zone differ from one region to the other, with the temperatures growing from coast to interior. The PV modules used to measure the operating temperature are of the polycrystalline type. They are mounted on support structures oriented to the south, inclined at 15 degrees to the horizon.
PV module temperature was measured with a single sensor placed at the back centre of the module of module, as shown in
The metrological data including the solar irradiance, and the ambient temperature of various weather conditions are measured and used as input parameters for the models. The
Weather conditions are categorized based on irradiance and temperature levels and defined in
Weather condition | Irradiance | Ambient temperature |
---|---|---|
HH | High | High |
HL | High | Low |
LH | Low | High |
LL | Low | Low |
HH and LL present high and low irradiance and ambient temperature, respectively. LH presents a low irradiance and high temperature. HL shows a high irradiance and low temperature.
The peak irradiance values take place in the dry season of November to June. This season is marked by a warmer period (March to June) and a cooler period (December to January).
The reduction in the irradiance value takes place during the wet season (July to October). This can be attributed to the majority of the days being overcast, reducing the amount of sunlight in this period.
This approach allows the assessment of the models for such a wide range of weather conditions.
A regression is used to finds a constrained minimum of models forms to forecast the PV module operating temperature of several variables starting at an initial estimate.
These models are examined and compared them against real data from outdoor PV testing. The optimal parameters to predicted PV module temperature are estimated for various weather conditions and named by Opt 1 and Opt 2.
Results show that Opt 1 and Opt 2 models have the smallest values of RMSE in all weather condition except HL weather condition. For this weather condition Lasnier is the best model. The models proposed in this study are therefore more suitable for modelling the temperature of modules in tropical zone.
The residual graphs for the models Opt 1 and Opt 2 are shown in
Scatterplots of the predicted
The residual histograms display the residual distribution for all the observations. The symmetry of the residual histograms (
The verification of the residuals for normality is provided by the normal residual probability plot. The residuals are normally distributed if the points on the graph are close to the straight line.
The residual value curves show that the adjustments obtained are acceptable, since the point clouds follow the theoretical curve. This confirms the reasonableness of the choice of our models.
In this work, PV module temperature models are proposed using constrained minimization based on the field monitored real data. The estimation temperature of PV module and the RMSE of the temperature models change according to weather conditions. The PV module temperature Opt 1 and Opt 2 models presented the smallest of RMSE in HH; LH and LL. Lasnier model has the smallest value of RMSE in HL. PV module temperature models Opt 1 and Opt 2 are closer to the PV module temperature measured for weather conditions HH, LL and LH. Lasnier model is closer to the PV module temperature measured for the weather condition HL.
The PV module temperature Opt 1 and Opt 2 models take the smallest values of RMSE followed by Lasnier and Schoot models for all weather conditions.
The residual value curves show that the adjustments obtained are acceptable, since the point clouds follow the theoretical curve. This confirms the reasonableness of the choice of our models. Models Opt 1 and Opt 2 can be used to estimate PV module temperature for that location and for locations of similar climatic conditions. We are also interested in the sensitivity of weather factors on the PV module temperatures.
Empirical coefficients
Nominal operating cell temperature (°C)
Proposed model 1
Proposed model 2
Plane of array
Root mean squared error
Ambient temperature (°C)
Module temperature (°C)
Reference temperature (°C)
Ambient temperature considered for NOCT conditions (°C)
Irradiance (W/m²)
Ten Merina SA and Senergy PV SA are gratefully acknowledged for supplying the information on the PV solar plants surveyed.