An exergetic optimization is developed to determine the optimal performance and design parameters of a solar photovoltaic (PV) array. A detailed energy and exergy analysis is carried out to evaluate the electrical performance, exergy destruction components, and exergy efficiency of a typical PV array. The exergy efficiency of a PV array obtained in this paper is a function of climatic, operating, and design parameters such as ambient temperature, solar radiation intensity, PV array temperature, overall heat loss coefficient, open-circuit voltage, short-circuit current, maximum power point voltage, maximum power point current, and PV array area. A computer simulation program is also developed to estimate the electrical and operating parameters of a PV array. The results of numerical simulation are in good agreement with the experimental measurements noted in the previous literature. Finally, exergetic optimization has been carried out under given climatic, operating, and design parameters. The optimized values of the PV array temperature, the PV array area, and the maximum exergy efficiency have been found. Parametric studies have been also carried out.

Renewable energies are going to be a main substitute for fossil fuels in the coming years for their clean and renewable nature. A solar photovoltaic (PV) array is one of the most significant and rapidly developing renewable-energy technologies, and its potential future uses are notable.

PV array is a semiconductor device, which converts light energy directly into useful electricity. The energy payback time (EPBT) of a PV system lies between 10 and 15 years depending on insulation and the performance of it. If the performance of a PV array can be increased, the energy payback time can be reduced. Therefore, the optimized performance evaluation of a PV array is important.

PV array performance parametrically depends on climatic, operating, and design parameters such as ambient temperature, solar radiation intensity, PV array temperature, overall heat loss coefficient, open-circuit voltage, short-circuit current, maximum power point voltage, maximum power point current, and PV array area. It can be evaluated in terms of energy efficiency and exergy efficiency. Its evaluation based on the first and second laws of thermodynamics is known as energy efficiency and exergy efficiency, respectively.

The energy analysis has some deficiencies [

The energy conversion factor of a solar PV system sometimes is described as efficiency, but this usage sometimes leads to some difficulties such as follows [

A little work has been carried out in field of PV array exergy analysis or exergetic optimization of it.

Ross and Hsiao [

Landsberg and Markvart [

Würfel [

Smestad [

Bisquert et al. [

Gong and Kulkarni [

Černivec et al. [

Ghoneim [

Badescu [

Sahin et al. [

Skoplaki et al. [

Abdolzadeh and Ameri [

Joshi et al. [

Joshi et al. [

Sarhaddi, Farahat and Ajam investigated exergetic optimization of solar collector systems [

In this paper, a detailed energy and exergy analysis will be carried out to evaluate the electrical performance, exergy destruction components, and exergy efficiency of PV array. An equation for PV array exergy efficiency will be derived based on exergy destruction. A computer simulation program will be developed to predict the electrical and operating parameters of PV array. Finally, the exergetic optimization of PV array will be carried out; also, the effect of climatic, design, and operating parameters on exergy efficiency will be studied.

PV array exergy analysis is parametrically dependent on its energy analysis. Hence, firstly PV array energy analysis will be carried out. Then the exergy destruction components and exergy efficiency of PV array will be computed and optimized.

The proof of governing equations on PV array energy analysis is not included in order to have a brief note.

A PV array is nonlinear device and can be represented by its current-voltage (

Equivalent electrical circuit in the five-parameter photovoltaic model [

The second terms on the right-hand side of (

At short circuit current:

At open circuit voltage:

At the maximum power point:

At the maximum power point:

At short circuit:

Reference conditions or standard rated conditions (SRCs) are defined as follows [

The solar cell temperature at reference conditions is

The solar radiation intensity at reference conditions is

Substituting the above five pieces of information into (

Equations (

PV module manufacturers usually give temperature coefficients and NOCT conditions [

In the previous studies [

The convective heat transfer coefficient is given by [

The energy efficiency of a PV system can be defined as the ratio of the output energy of the system (i.e., electrical energy) to the input energy (i.e., solar energy) received on photovoltaic surface.

The maximum energy efficiency of a PV system is given by [

However, this definition of energy efficiency is restricted to theoretical cases. In (

For PV systems in practical cases, energy efficiency measures the ability of converting solar energy into electrical energy [_{GH} stands for the highest energy level of electron at maximum solar irradiation conditions.

Representation of a general current-voltage characteristic curve and its parameters [

_{GH} is equivalent to area under the _{L}_{L}

The energy efficiency of a PV system at maximum power is defined as the ratio of actual electrical output to input solar energy incident on PV surface area and it is given by [

This efficiency is also called actual electrical efficiency. The electrical efficiency of a PV array can also be defined in terms of fill factor (FF) as follows:

Exergy analysis is a technique that uses the conservation of mass and conservation of energy principles together with the second law of thermodynamics for the analysis, design, and improvement of energy and other systems. Exergy is defined as the maximum amount of work that can be produced by a system or a flow of mass or energy as it comes to equilibrium with a reference environment [

The specific heat capacity of silicon solar cell

The fourth term is electrical exergy destruction [

The electrical and exergetic models presented in the previous sections have been inserted into a MATLAB computational program. In this program, most of the geometric parameters and operating conditions can be variables. The formulation of optimization problem, considering the quantities

The experimental results of Barker and Norton [

The simulated values of PV array temperature, open-circuit voltage, maximum power point voltage, short-circuit current, and maximum power point current in present work have been validated by their corresponding experimental values in [

Climatic, operating, and design parameters of PV array during validation process are described in Table

Climatic, operating and design parameters of PV array [

Solar PV module parameters | Value in validation | Value in optimization |
---|---|---|

PV module type | Siemens SM55, | Siemens SM55, |

monocrystalline silicon | monocrystalline silicon | |

Number of modules in series per string, | 2 | From optimization |

Number of strings, | 6 | From optimization |

The solar radiation intensity at the reference conditions, | ||

The solar radiation intensity, | From experimental data | |

The ambient temperature, | From experimental data | 300 K |

The ambient temperature at NOCT conditions, | 293.15 K | 293.15 K |

The cell temperature at the reference conditions, | 298.15 K | 298.15 K |

The nominal operating cell temperature, | 318.15 K | 318.15 K |

The PV array temperature, | ( | From optimization |

The sun temperature, | 5760 K | 5760 K |

Wind speed, | 0.5 m/s | 0.5 m/s |

The short-circuit current at the reference conditions, | ||

(for total array) | (for total array) | |

The open-circuit voltage at the reference conditions, | ||

(for total array) | (for total array) | |

Maximum power point current at the reference conditions, | ||

(for total array) | (for total array) | |

Maximum power point voltage at the reference conditions, | ||

(for total array) | (for total array) | |

The electrical efficiency at the reference conditions, | 0.12 | 0.12 |

The current temperature coefficient, | ||

The voltage temperature coefficient, | ||

The efficiency correction coefficient for temperature, | ||

The semiconductor band gap energy, | 1.12 eV | 1.12 eV |

The effective product of transmittance–absorptance, | 0.9 | 0.9 |

The PV array emissivity, | 0.88 | 0.88 |

The length of solar module, | ||

The width of solar module, | ||

Time interval, | 900 seconds | 3600 seconds |

In order to compare the simulated results with the experimental measurements, a root mean square percentage deviation (RMS) has been evaluated by following equation [

The variations of solar radiation intensity, ambient temperature, and PV array temperature during the test day are shown in Figure

The variations of solar radiation intensity, ambient temperature, experimental PV array temperature, and simulated PV array temperature during the test day.

The simulated values of open-circuit voltage, maximum power point voltage, short-circuit current, maximum power point current, and the corresponding experimentally measured data during the test day are shown in Figure

The simulated values of open-circuit voltage, maximum power point voltage, short-circuit current, maximum power point current, and the corresponding experimentally measured data during the test day.

The simulated and experimental values of energy efficiency, exergy efficiency, and electrical efficiency during the test day are shown in Figure

The simulated and experimental values of energy efficiency, exergy efficiency, and electrical efficiency during the test day.

The good agreement between experiment and simulation values shown in the previous figures demonstrates that the choice of a wind speed of 0.5 m/s during our calculations is reasonable (Figures

The simulated parameters errors compared with those obtained by the experimental measurement are explained as follows.

The temperature coefficients of current and voltage are assumed constant. In practical cases, they have slight fluctuation due to the solar radiation intensity and PV array temperature variations.

The experimental measurements have been obtained from the figures of [

Wind speed is not constant and has a direct effect on the overall heat loss coefficient that can decrease the precision of calculated overall heat loss coefficient in the computer simulation.

The effective product of transmittance–absorptance is assumed constant while it is changing during the day with the change of solar incidence angle on PV array surface.

The type of PV array, its selected environmental, design conditions, and constant parameters during the optimization procedure are described in Table

Figure ^{2} and the PV array temperature from 300 to 350 K. It is observed from this figure that there is a global maximum point and the coordinate of this point shows the values of optimized parameters. The calculated values of global maximum point are

The variations of the exergy efficiency as a function of the PV array temperature and the PV array area.

In order to have maximum exergy efficiency, PV array temperature should be kept near the ambient temperature, or in other words, PV array temperature should be controlled. In order to control PV array temperature, there are some practical methods such as spraying water on the top surface of photovoltaic modules [

Figure

The variations of the exergy efficiency with respect to the solar radiation intensity.

The effect of ambient temperature on the exergy efficiency.

Figure

The average value of a function

On the basis of theoretical results obtained in the present paper, the following conclusions have been drawn.

The electrical and exergetic models of PV array presented in this study are in good agreement with the experimental results of Barker and Norton [

The PV array temperature has a great effect on the exergy efficiency. The exergy efficiency of a PV array can be improved if the heat can be removed from the PV array surface. In order to remove heat from the PV array surface, there are some practical methods such as spraying water on the top surface of photovoltaic modules [

Increasing the solar radiation intensity, the exergy efficiency of PV array increases initially and then decreases after attaining the solar radiation intensity of about a maximum point (Figure

While the ambient temperature is increasing, the exergy efficiency of PV array decreases (Figure

The design parameters such as PV array area have a little effect on the exergy efficiency (Figure

Ideality factor (eV)

Area (m^{2})

_{p}:

Heat capacity of the silicon material (J/g

Copper Indium Gallium Selenide

Electrical power (W)

Energy Payback Time

Exergy (W)

Fill Factor

Solar radiation intensity (W/m^{2})

Heat transfer coefficient (W/m^{2}

Circuit current (A)

Irreversibility in control volume (J)

Current-voltage

Dimensions of solar module (m)

PV array mass (g)

Time (hr)

Number of parameters

_{c}:

Number of cells in PV module

_{m}:

Number of modules in series per string

_{s}:

Number of string

Nominal operating Cell Temperature conditions

Photovoltaic

Photovoltaic/thermal collector

Resistance

Root Mean Square percentage deviation (%)

Solar absorbed flux (W)

Sequential Quadratic Programming

Standard Rated Conditions

Time interval (second)

Temperature (K)

_{L}:

Overall heat loss coefficient from the PV array to the environment (W/m^{2}

Circuit voltage

Experimental or simulated value of parameter.

Current temperature coefficient (mA/°C)

Voltage temperature coefficient (

Efficiency correction coefficient for temperature (

Difference in current, temperature, time, voltage

Global emissivity, semiconductor band gap energy (eV)

Efficiency (%)

Stefan-Boltzmann’s constant (W/m^{2}K^{4})

The effective product of transmittance-absorptance.

Length

Width

Array

Ambient

Cell, array

Convection

Destroyed

Diode

Electrical

Energy

Exergy

Experimental

Glass

The highest energy content of the electron

Inlet

The available energy content of the electron, light current

Loss

Maximum

Module

Maximum power point

New

At NOCT conditions

Reverse saturation

Open-circuit

Optical, optimum

Outlet

Radiative

Reference

Series

Short-circuit

Shunt

Simulated

Sky

Sun

Wind.

The authors acknowledge Professor. A. D. Sahin [