This paper presents a practical method for calculating the electrical energy generated by a PV panel (kWhr) through MATLAB simulations based on the mathematical model of the cell, which obtains the “Mean Maximum Power Point” (MMPP) in the characteristic
According to the World Energy Outlook 2014, the global demand for electricity continues to rise at a high rate [
Renewable energy with the largest power generation capacity installed is wind power; however, solar energy is growing at a faster rate than any other form of renewable energy. Solar energy is available everywhere in the world; it is considered inexhaustible and has a higher annual generation potential than the annual electricity generation worldwide. The solar energy potential is harnessed by thermal and photovoltaic systems to generate electricity either on a large scale as a solar farm or on small scale as an autonomous or grid connected photovoltaic system (SFV) [
The first proposed works in the literature focus the efforts to calculate theoretically the energy potential radiated per square meter (kW/m^{2}) for a locality, due to the high cost associated with instruments measuring solar radiation. The proposed methods are based on solar radiation data, as C. Hotel’s model that is based on direct radiation [
Therefore, the methods stated above estimate the potential for solar radiant energy for a specific location, but they do not estimate the real electric energy generation of PV panel. In practice, the difference between the potential energy radiated regarding the electric power generated by a PV panel is significant; this is due to the panels only generating their maximum power peak, under conditions of 1000 W/m^{2} at a cell temperature of 25°C, known as standard test conditions (STC). It is known that there are locations around the world where STC is not reached and therefore the cell never reaches the maximum power point specified by the manufacturer.
Then, the electricity generated by PV cell is a function of the solar incident radiation (
The last two factors depend on the intrinsic characteristics of the cells and will be reflected in the
The aim of this paper is to provide a method using MATLAB to calculate the electrical energy generation of a cell based on its mathematical model and a reliable historical climate database.
The proposed method is based on a photovoltaic cell mathematical model and requires, as input, manufacturer cell data sheet and a climate database. As output, the efficiency and electrical energy generated by a PV panel are obtained.
The flowchart (Figure
Proposed method flowchart.
PV panels are sensitive to radiation and temperature variations. When the PN junction temperature of the cell is increased, the output voltage is reduced. Likewise when the incident radiation in the cell reduces, its current output reduces too. The reductions of voltage, current, or both are reflected directly in an output power reduction and therefore reduce the energy conversion efficiency [
Globally, there are several databases available that can be used such as the Center for Atmospheric Sciences NASA Langley Research Data (LaRC), which provide 22 years of historical data from any quadrant of the globe defined by longitude and latitude [
While a database for a location is more specific, the calculation of the method has major approximation to reality; therefore a local database is recommended.
In this case the proposed method was applied to a PV project in a Sewage Treatment Plant for a Group of Drinking Water and Sewerage of Yucatan (JAPAY) located at Merida, same place as CINVESTAV.
Temperature annual and monthly daily mean.
CINVESTAV database indicates that
Radiation annual and monthly daily mean.
Daylight hours annual and monthly daily mean.
The intrinsic characteristic of photovoltaic cells is that other factors determine the performance and efficiency conversion of radiant energy into electrical energy.
Therefore, it is important to identify in the manufacturer data sheet the following parameters: shortcircuit current (
Data sheet parameters of 250 Wp PV panel.
NOCT 







Area 


45  30.12  8.3  37.85  8.65  0.005  −0.17  60  1.62 
In order to determine the maximum electrical power point (
The simplest mathematical model reported includes one diode parallel to a current source [
Later it was suggested to add the effect of a parallel resistance (
The last two diodes’ mathematical model, represented by the equivalent circuit of the PV cell shown in Figure
Two diodes’ PV cell equivalent circuit.
The values of the series and parallel resistance (
Replacing
To obtain
Figure
MATLAB iteration result to calculate
In practice, it is a complex task to measure the cell junction temperature and other variables involved such as solar radiation, wind speed, the spectral distribution of the irradiation, the absorption capacity and heat dissipation, and the intrinsic construction material, as was reported by Lasnier and GangAng [
The value for NOCT of a cell is available on the manufacturer data sheet. The procedure for determining the junction temperature from NOCT is based on the fact that the difference between ambient temperature and the junction temperature is associated but is independent, and it also has a directly proportional relationship to the radiation for values between 400 and 1000 W/m^{2}. This allows for determining the junction temperature based on the following equation:
Using MATLAB Simulink language, the proposed method was implemented and integrated in a scheme that is shown in Figure
Implementation of proposed mathematical method in MATLAB Simulink.
Cell mathematical model inside of MATLAB Simulink mask.
To prove the mathematical model, the characteristic curve
The simulation result shows that, depending on the historical values of the temperature and radiation of a locality, the difference between
Using the same method implemented in MATLAB Simulink, Figure
Figure
Simulation of
The Py can be calculated under two conditions: for real values corresponding to a locality, as described by (
There is a loss of yield greater than 60%. So this fall should be attenuated or enhanced depending on the panel under test and the locality. A PV panel with high Py requires lower area than any other one with low Py. Therefore dimensioning the area with values at STC is not the most appropriate, because the MMPP varies from one locality to another, but this value is almost lower than
The real conversion efficiency (
The last step is to know the electric energy generated (EEG) by the PV panel. It can be obtained in two ways: by multiplying the instantaneous value of
The proposed method was applied to a project for the Sewage Treatment Plant for Group of Drinking Water and Sewerage of Yucatan (JAPAY), México, testing 250 Wp PV panels of five different manufacturers, to generate 95% of electric power consumption daily average. Table
250 Wp PV panel of different manufacturers.
Jinshi  Solartec  LDK  Canadian  Kewell 


NBJ250W  S60MC250  LDK250D2  VirtusII250  KWP250W 
250 Wp  250 Wp  250 Wp  250 Wp  250 Wp 
The aim of using the proposed method in this project is to determine the electricity generated for each PV panel tested, likewise, to evaluate and select the best efficiency option, to reduce the cost of investment, and to lower the installation area, providing greater certainty and reliability for investment return.
Applying the three first steps of proposed method the results are presented in Table
Results of three first steps in Merida city.
Manufac.  NOCT 










Jinshi  47  381.5  0.38  29.95  8.35  37.66  8.92  0.0051  −0.124  60 
Solartec  45  400.7  0.37  30.12  8.31  37.85  8.65  0.0053  −0.123  60 
LDK  45  550.1  0.4  29.9  8.38  37.8  8.92  0.0053  −0.118  60 
Candian  45  341.2  0.31  30.11  8.31  37.42  8.83  0.0035  −0.112  60 
Kewell  47  156.5  0.25  30.72  7.99  37.55  8.68  0.0017  −0.127  60 
To continue with the step there, the simulation results are evaluating simultaneously the 5 different PV panels to visualize and validate in the same graph the results of
Simulation result of
Table
Py and
Manufac.  MMPP (W) 

Area (m^{2}) 





Jinshi  99.5  250  1.63  61.04  153.37  15.34  14.34 
Solartec  101.5  250  1.62  62.65  154.32  15.43  14.72 
LDK  100.8  250  1.63  61.84  153.37  15.34  14.52 
Canadian  86.72  250  1.63  53.20  153.37  15.34  12.50 
Kewell  92.55  250  1.62  57.13  154.32  15.43  13.42 
Table
Finally, applying Step
EEG at Merida per day, month, and year.
Manufact. 






Jinshi  99.5  12.17  1.21  36.93  443.19 
Solartec  101.5  12.17  1.24  37.68  452.10 
LDK  100.8  12.17  1.23  37.42  448.99 
Canadian  86.72  12.17  1.06  32.19  386.27 
Kewell  92.55  12.17  1.13  34.35  412.24 
According to the simulation results of the method, the Solartec S60MC250 PV panel had the best yield and electrical energy production. However, for the JAPAY project, now it is important to know the PV panel investment and the area required for the project.
Therefore it is necessary to determine the number of PV panels needed for installation in order to cover the 95% of Sewage Treatment Plant consumption. Starting with the consumption annual daily mean (
Investment and total area required for JAPAY project at Merida.
Manufact. 

Cost ($USD) 

Investment ($USD)  Tot. area (m^{2}) 

Jinshi  1.21  337.5  490  $165,375  798.70 
Solartec  1.24  329.8  480  $158,304  777.60 
LDK  1.23  347.2  483  $167,698  787.29 
Candian  1.06  335.4  562  $188,495  916.06 
Kewell  1.13  347.1  526  $182,575  852.12 
The proposed method was the base of the study developed for the JAPAY project, which was implemented successfully, which ensured the projected electric power generation and ensured the planned investment. Figure
PV facilities of JAPAY in Merida city.
Nowadays the Sewage Treatment Plant produces its own electric energy, and it is an example of photovoltaics project for Merida city. Figure
Photovoltaic power generated.
CFE power delivered.
Power demand by Sewage Treatment Plant.
In this paper a practical fivestep method is presented to estimate the electrical energy generated by PV panel per day, month, and year, based on the MATLAB Simulink mathematical model of the PV cell and the evaluation of historic climatic variables for a specific locality.
Most of the literature works only estimate the energy potential by geographic information systems (GIS) and PVGIS, maps of solar radiation (W/m^{2}), digital surface models (DSM), and simulations of climate variables, but any reported method calculates the energy generated and considers any simultaneity to the response due to intrinsic characteristic between different PV panels and the historical climatic database, so the proposed method incorporates these conditions allowing for a more realistic calculation.
It has been demonstrated that there are significant differences in electric energy generation and power yield and its efficiency between the five different PV panels under test. These differences are always lower than STC and therefore are important and critical to estimate the number of panels, the facilities total area, and the PV panels investment required on a project.
The proposed method developed represents a powerful software tool for calculating the electric energy generated by a PV panel. The proposed method provides a good reliability and certainty for PV project investment and allows application in different geographical locations, different PV power peaks, and different panels manufacturers.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors thank CONAGUA Mérida for the assistance provided with the database. Likewise, the authors would like to express their gratitude to Dr. David Valdes Lozano, CINVESTAV, Mérida, for providing weather database. Finally, the authors acknowledge researchers and reviewers of Scientific Research Center of Yucatan A.C. (CICY).