Parameter extraction of a solar photovoltaic system is a nonlinear problem. Many optimization algorithms are implemented for this purpose, which failed in giving better results at low irradiance levels. This article presents a novel method for parameter extraction using gravitational search algorithm. The proposed method evaluates the parameters of different PV panels at various irradiance levels. A critical evaluation and comparison of gravitational search algorithm with other optimization techniques such as genetic algorithm are given. Extensive simulation analyses are carried out on the proposed method and show that GSA is much suitable for parameter extraction problem.

Precise parameters extraction of solar photovoltaic cells is normally a vital part of a solar photovoltaic (PV) system, which can be interfaced with maximum power point tracker (MPPT) calculations and power electronic converters. This undertaking is vital for the device modelling, characterization, and simulation and for the device quality testing. Maximum power point tracker, ordinarily alluded to as MPPT, is an electronic framework that works the PV modules in a way that permits the modules to deliver all the force they are able to do [

The above addressed problem can be solved efficiently by many prominent techniques. But each prominent technique [

In the recent past, different heuristic advancement techniques have been created. Huge numbers of these strategies are propelled by swarm practices in nature. In this paper, another advancement calculation in light of the law of gravity and mass connections is presented [

Flowchart of gravitational search algorithm.

Current position: position of particles

Velocity: velocity

Force: the gravitational force between the particles

Acceleration: acceleration

Mass: mass

Dim: dimension of test functions

Low, up: search space limits

Read the parameters of the PV panel under consideration.

Agents that go out of the search space are returned to the boundaries.

The objective function is calculated for each iteration.

Mass of each agent is calculated.

Loop:

Force is updated for each mass.

Loop:

Update acceleration and velocity.

Loop:

Update agent’s position.

Repeat Step

Print the result.

The single diode condition accepts a steady esteem for the ideality factor

Double diode model of solar cell.

In this double diode model, the cell terminal current is calculated as follows:

The diode current equations and leakage current equation are given by

Thus the expression for cell terminal current is formulated as

The parameters _{L} or_{L}. The GSA optimization technique [

So, RHS is equated to zero.

The model parameters extracted are subsequently substituted in the MATLAB/SIMULINK model to plot the

Parameter extraction is performed for the 3 above mentioned solar panels. The optimal values of the parameters for respective panels are found out such that the variation of power with respect to voltage is minimum so that the overall power output is maximum. The convergence curves for shells S36 at standard temperature condition of 1000 W/m^{2} irradiation and temperature of 25°C are shown in Figure

Convergence graph for Shell S36.

Comparison of the optimized series resistance, shunt resistance, and ideality factor values of Shell S36 under different irradiance conditions is shown in Figures

Comparison of the optimized series resistance values of Shell S36 under different irradiance conditions.

Comparison of the optimized shunt resistance values of Shell S36 under different irradiance conditions.

Comparison of the optimized ideality factor values of Shell S36 under different irradiance conditions.

The simulated characteristics curves of the SIMULINK model for Shell S36 at different irradiations are shown in Figure

Optimization results of the algorithms GA and GSA at different irradiation levels for Shell S36, Shell ST40, and Shell SP70 are compared and tabulated in Tables

Comparison of optimization results of GA and GSA at different irradiation levels for Shell S36.

Parameters | Irradiation in Watt/m^{2} | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

200 | 400 | 600 | 800 | 1000 | ||||||

GA | GSA | GA | GSA | GA | GSA | GA | GSA | GA | GSA | |

| 0.825024 | 0.3069 | 0.8935 | 0.7996 | 0.7429 | 0.717498 | 0.656891 | 0.660802 | 0.59042 | 0.59824 |

| 200 | 319.6481 | 300.098 | 496.5787 | 390.029 | 212.121 | 200 | 234.6041 | 457.478 | 200 |

| 1.2 | 1.2 | 1.2 | 1.2 | 1.246 | 1.2 | 1.3489 | 1.2 | 1.2 | 1.24 |

| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

| 56.4 | 56.4 | 5.23 | 5.23 | 10.3 | 10.2 | 43.0 | 4.85 | 4.73 | 4.73 |

| 0.147 | 0.147 | 0.117 | 0.117 | 0.21 | 0.21 | 0.0933 | 0.0933 | 0.0867 | 0.0867 |

| 0.46 | 0.46 | 0.92 | 0.92 | 1.38 | 1.38 | 1.84 | 1.84 | 2.3 | 2.3 |

Comparison of optimization results of GA and GSA at different irradiation levels for Shell ST40.

Parameters | Irradiation in Watt/m^{2} | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

200 | 400 | 600 | 800 | 1000 | ||||||

GA | GSA | GA | GSA | GA | GSA | GA | GSA | GA | GSA | |

| 0.957967 | 0.940371 | 0.995112 | 0.983382 | 0.995112 | 0.995112 | 0.981427 | 0.981427 | 0.991202 | 0.999 |

| 480.9384 | 200 | 291.3001 | 200 | 295.2102 | 200 | 420.3324 | 200 | 333.33 | 200 |

| 1.480938 | 1.492669 | 1.2 | 1.404692 | 1.2 | 1.4604 | 1.2317 | 1.486804 | 1.2 | 1.4956 |

| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

| 52.0 | 57.2 | 1.10 | 22.4 | 1.05 | 1.05 | 1.77 | 68.6 | 0.996 | 72.8 |

| 0.022 | 0.022 | 0.0175 | 0.0175 | 0.0153 | 0.0153 | 0.0139 | 0.0134 | 0.0129 | 0.0129 |

| 0.536 | 0.536 | 1.072 | 1.072 | 1.608 | 1.608 | 2.144 | 2.144 | 2.68 | 2.68 |

Comparison of optimization results of GA and GSA at different irradiation levels for Shell SP70.

Parameters | Irradiation in Watt/m^{2} | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

200 | 400 | 600 | 800 | 1000 | ||||||

GA | GSA | GA | GSA | GA | GSA | GA | GSA | GA | GSA | |

| 0.01173 | 0.066471 | 0.197458 | 0.02346 | 0.250244 | 0.113392 | 0.26002 | 0.183773 | 0.26002 | 0.144673 |

| 255.132 | 499.5112 | 285.435 | 470.1857 | 260.016 | 487.781 | 200 | 237.5367 | 424.2424 | 385.1417 |

| 1.322 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.293255 |

| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

| 11.5 | 11.5 | 10.7 | 10.7 | 10.2 | 10.2 | 9.91 | 9.91 | 9.67 | 9.67 |

| 0.301 | 0.301 | 0.24 | 0.24 | 0.21 | 0.21 | 0.191 | 0.191 | 0.177 | 0.177 |

| 0.94 | 0.94 | 1.88 | 1.88 | 2.82 | 2.82 | 3.76 | 3.76 | 4.7 | 4.7 |

To predict the closeness of the results obtained, absolute error is estimated for the proposed and GA method. Absolute error is computed using the following equation:

The computed absolute error graph for Shell S36 is presented in Figure

Error graph for Shell S36.

In this work, the parameters of the PV module are determined using the proposed GSA. The simulated voltage-current characteristics for three different panels (Shell S36, Shell SP70, and Shell ST40), obtained from the simulation model, are validated with the extracted experimental data. Further, the absolute error curve is plotted for GSA in comparison with GA at different irradiance level (200 to 1000 W/m^{2}) at 25°C. It is observed that the error obtained in case of GSA is lesser. The extensive simulation results show that the proposed GSA method is superior to the existing GA in terms of speed of convergence, accuracy, computational efficiency, and consistency of solution.

The authors declare that there are no competing interests regarding the publication of this paper.