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Extraction of accurate Photo Voltaic (PV) model parameters is a challenging task for PV simulator developers. To mitigate this challenging task a novel approach using Gravitational Search Algorithm (GSA) for accurate extraction of PV model parameters is proposed in this paper. GSA is a population based heuristic optimization method which depends on the law of gravity and mass interactions. In this optimization method, the searcher agents are collection of masses which interact with each other using laws of gravity and motion of Newton. The developed PV model utilizes mathematical equations and is described through an equivalent circuit model comprising of a current source, a diode, a series resistor and a shunt resistor including the effect of changes in solar irradiation and ambient temperature. The optimal values of photo-current, diode ideality factor, ser ies resistance and shunt resistance of the developed PV model are obtained by using GSA. The simulations of the characteristic curves of PV modules ( SM55, ST36 and ST40 ) are carried out using MATLAB/Simulink environment. Results obtained using GSA are compared with Differential Evolution (DE), which shows that GSA based parameters are better optimal when compared to DE.

World’s primary energy consumption is increasing by about 2.5% in every year. Though most of the energy demand is shared by conventional energy sources, the environmental impact on usage of these sources has been disintegrative with the issues such as pollution, global warming, and excessive greenhouse effect. To overcome the above mentioned effects, finding sustainable alternatives is becoming increasingly urgent. To meet considerable percentage of demand, renewable energy sources are installed to share 3.9% of global power generation. The rapid growth of renewable power generation continues and this opens a new era for solar power generation. Solar energy is obviously environmentally advantageous relative to any other energy source. The increase in demand for solar industry over the past several years has expanded the importance of PV system design and application for more reliable and efficient operation.

PV module represents the fundamental power conversion unit of a PV generator system. PV module is a series connection of PV cells where each cell exhibits non-linear characteristics. To use PV module in the simulation environment, it is necessary that the model should produce the PV cell non-linear characteristics. For efficient design of the PV array in simulation environment, it is essential to use the accurate magnitudes of the panel parameters. But, these parameters are usually unknown to the user and hence the parameters are needed to be extracted by a proper extraction method before designing the PV array. Nowadays, a single diode PV model with a photo current source I, a single diode D, a series resistance R_{se} and a shunt resistance R_{sh} is used as the equivalent circuit of a PV cell [_{oc}, short circuit current I_{sc}, voltage at maximum power point V_{mpp}, current at maximum power point I_{mpp}, temperature coefficient of open circuit voltage K_{v}, temperature coefficient of short circuit current K_{i} and the maximum peak output power P_{mp} are necessary. Generally, all these values for a PV array are available in manufacturers’ data-sheet. Hence, most of the parameter extraction methods are based on manufacturers’ data-sheet. In single diode PV model, the unknown currents are obtained by nodal analysis. The other parameters R_{se} and R_{sh} are calculated from PV cell characteristics [_{se} and R_{sh} from characteristics curve may not be more accurate. In addition to that, the value of these resistances depends on solar irradiation and ambient temperature. To resolve these issues, optimization techniques are introduced to optimize accurately the value of photo-current, diode ideality factor, series resistance and shunt resistance.

Genetic algorithm based optimization of the circuit parameters is slow and takes larger computation time [_{se} and R_{sh}, a large number of iterations are to be evaluated, though the results are close to possible values [

Over the last two decades, many researches has to be done for various types of algorithms like Evolutionary Approach (EA), Differential Evolution (DE), Particle Swarm Optimization (PSO) and etc. [

In the proposed GS algorithm, agents are considered as objects and their performance is measured by their masses. All these objects attract each other by the gravitational force and this force causes a global movement of all objects towards each other with heavier masses. Hence, masses cooperate using a direct form of communication, through gravitational force. The heavy masses―which correspond to good solutions― move more slowly than lighter ones and this guarantees the exploitation step of the algorithm.

As per GS algorithm, each mass (agent) has four specifications:

1) Position;

2) Inertial mass;

3) Active gravitational mass and;

4) Passive gravitational mass.

The position of the mass corresponds to a solution of the problem and its gravitational and inertial masses are determined using a fitness function. In other words, each mass presents a solution and the algorithm is navigated by properly adjusting the gravitational and inertial masses. By lapse of time, we expect that the masses may be attracted by the heaviest mass. This mass will present an optimal solution in the search space.

The building block of PV array is the Solar cell, which is basically a PN semiconductor junction that directly coverts light energy into electricity. PV cells are grouped in larger units called PV modules which are further interconnected in a parallel-series configuration to form PV arrays or PV generators. _{pv}, a, R_{se} and R_{sh} a PV mathematical model is used according to the following set of equations [

The voltage-current characteristic equation of a solar cell is given as,

where, I_{pv} is a light-generated current or photocurrent, I_{o} is the cell saturation of dark current, q (=1.6 × 10^{−19} C) is an electron charge, K (=1.38 × 10^{−23} J/K) is a Boltzmann’s constant, T is the cell’s working temperature, “a” is an ideal factor, R_{sh} is a shunt resistance and R_{se} is a series resistance of solar cell. The photo-current I_{pv} mainly depends on the solar insolation and cell’s working temperature and is given by,

where, I_{SC} is the cell’s short-circuit current at 25˚C and 1 kW/m^{2}, K_{i} is the cell’s short- circuit current temperature coefficient, T_{n} is the cell’s reference temperature and H is the solar insolation in kW/m^{2}. The cell’s saturation current I_{o} varies with the cell temperature is

where, V_{OC} is the cell’s open circuit current at 25˚C and 1 kW/m^{2}, K_{V} is the cell’s open circuit voltage temperature coefficient, N_{S} is the number of cells connected in series per string and V_{t} is the thermal voltage given by, V_{t} = KT/q. The terminal equation of PV array for the current is given as,

where, N_{s} is number cells in series and N_{p} is the number cells in parallel.Hence the objective function using the Equations (1) to (4) is formulated as given below:

where

The detailed description of the algorithm to extract PV model parameters is presented below and the pictorial flowchart is shown in

A set of values for the I-V characteristics serves as the input data for the GSA. The parameters that are extracted by optimization are I_{pv}, R_{se}, R_{sh} and a are evaluated as X_{k}_{ }in GSA.

Considering a system with N agents (masses), Position of the K^{th} agent is defined by,

where^{th} agent in d^{th} dimension.

The fitness value of each agent

Gravitational constant (G) is initialized at the beginning and at the later stages and is calculated as a function of time (t) (to reduce the time control strategy).

During a time “t”, the force between the agents “k” and “l” with respect to mass is given as,

where, (all the values are with respect to specific time “t”);

The total force acting on a particle k at d^{th} dimension is given by,

where,

where,

Gravitational and Inertial masses are calculated by using the following equations (assuming gravitational mass is equal to inertial mass),

where,

By the law of motion, the acceleration of the agent k in

where,

Velocity can be updated by summing the current velocity and its acceleration. Similarly, the position of particles can be updated by adding its previous position and its velocity.

where,

To obtain the best solution for the global optima, this algorithm stops its searching for the best solution by maximum iterations given for the optimal PV design problem.

The PV modelling method accuracy is validated by measured parameters of selected PV modules. The experimental (I and V) data is extracted from the manufacturer’s datasheet [

Parameter | Mono-crystalline SM55 | Thin film ST40 | Thin film ST36 |
---|---|---|---|

I_{sc} | 3.45 | 2.59 | 2.68 |

V_{oc} | 21.7 | 22.2 | 22.9 |

I_{mp} | 3.15 | 2.41 | 2.279 |

V_{mp} | 17.4 | 16.6 | 15.8 |

K_{v} m/˚C | −0.077 | −0.1 | −0.1 |

K_{i} m/˚C | 1.38 × 10^{-3} | 0.26 mA | 0.32 mA |

N_{s} | 36 | 42 | 42 |

using MATLAB R2010b with Intel Core i3 CPU @ 2.53 GHz processor, 3 GB RAM under windows 7 environment. And the SM55, ST36 and ST40 PV modules are used for simulation study. The parameters settings in GSA are: Agents-100, Iterations-100 and Power of R-1. The results obtained using the proposed GSA method is compared with DE in a judicial way.

Fitness Value and Optimized Parameter Values by GSASimulation results are obtained by executing the proposed GSA method at 1000 W/m^{2} and 25˚C temperature for 25 times. The GSA method obtains the global optimal value of objective function as 5.847 × 10^{−12}, 9.6421 × 10^{−12} and 5.1656 × 10^{−12} for SM55, ST36 and ST40 PV modules respectively. Also, for experimental validation, the data is significantly fewer compared to the DE and R_{s}-model [

Figures 4(a)-(c) and Figures 5(a)-(c) show the I-V and P-V curves for SM55, ST36 and ST40 respectively, for different levels of irradiance and temperatures. It can be seen that the I-V and P-V curve obtained by proposed model strongly agrees to the experimental data for all types of modules. In particular, the proposed model is very accurate at all irradiance and temperature levels.

This paper presents a powerful GSA method for extracting solar cell parameters. Number of parameters extracted is limited to four i.e. I_{pv}, a, R_{se}, and R_{sh}. The GSA method has been successfully applied to the PV modules SM55, ST36 and ST40 under different temperatures and solar insolations. The results obtained using GSA are better when

Parameters | P-DE [ | B-E [ | PSO [ | GA [ | GSA |
---|---|---|---|---|---|

Time (Sec) | 119 | 119 | 148 | 601 | 32 |

Parameters/module | SM55 | ST36 | ST40 | |||
---|---|---|---|---|---|---|

GSA | P-DE [ | GSA | P-DE [ | GSA | P-DE [ | |

I_{pv} | 3.45 A^{ } | 3.45A^{ } | 2.689A^{ } | 2.71A^{ } | 2.6A^{ } | 2.68A |

a | 1.1182 | 0.86 | 1.2171 | 2 | 1.1136 | 1.06 |

R_{se} | 0.2458Ω | 0.56 Ω | 0.4109Ω | 1.46 Ω | 0.4610Ω | 1.42 Ω |

R_{sh} | 86.1164Ω | 4.9K Ω | 110.4652Ω | 182.6 Ω | 95.3439Ω | 440.6 Ω |

Fitness function J | 5.847 × 10^{−12} | 2.4 ×10^{−2} | 9.6421 × 10^{−12} | 2.6 ×10^{−2} | 5.1656 × 10^{−12} | 2.5 ×10^{−2} |

compared to DE and R_{s}-model. Further, the computational time is comparatively low using the proposed method which allows the possibility of real time application of the algorithm towards various modules under different environmental conditions.

Saravanan, C. and Srinivasan, K. (2016) Optimal Extraction of Photovoltaic Model Parameters Using Gravitational Search Algorithm Approach. Cir- cuits and Systems, 7, 3849-3861. http://dx.doi.org/10.4236/cs.2016.711321