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This paper seeks to improve the photovoltaic (PV) system efficiency using metaheuristic, optimized fractional order incremental conductance (FO-INC) control. The proposed FO-INC controls the output voltage of the PV arrays to obtain maximum power point tracking (MPPT). Due to its simplicity and efficiency, the incremental conductance MPPT (INC-MPPT) is one of the most popular algorithms used in the PV scheme. However, owing to the nonlinearity and fractional order (FO) nature of both PV and DC-DC converters, the conventional INC algorithm provides a trade-off between monitoring velocity and tracking precision. Fractional calculus is used to provide an enhanced dynamical model of the PV system to describe nonlinear characteristics. Moreover, three metaheuristic optimization techniques are applied; Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and AntLion Optimizer (ALO) are used for tuning the FO parameters of the proposed INC-MPPT. A MATLAB-Simulink-based model of the PV and optimization have been developed and simulated for different INC-MPPT techniques. Different techniques aim to control the boost DC-DC converter towards the MPP. The proposed optimization algorithms are, also, developed and implemented in MATLAB to tune the target parameters. Four performance indices are also introduced in this research to show the reliability of the comparative analysis of the proposed FO-INC with metaheuristic optimization and the conventional INC-MPPT algorithms when applied to a dynamical PV system under rapidly changing weather conditions. The simulation results show the effective performance of the proposed metaheuristic optimized FO-INC as a MPPT control for different climatic conditions with disturbance rejection and robustness analysis.

Green energy sources are the primary research goal nowadays as they are viable, ecological, and cost-effective energy sources. Solar, wind, tidal, and biomass energy have penetrated the electric power production market in recent years due to the diverse methods and their renewable nature. The benefits of developing renewable power include reducing fossil fuel usage, mitigating the greenhouse impact, and reducing air pollution [

The proposed PV system is constituted by a PV module, the Buck–Boost converter as a DC-DC converter between the PV panel and the DC load, and the MPPT controller to achieve maximum power point of the PV panels. The model of the solar panels used in the proposed system will be illustrated, and the PV system is introduced [

Complete PV system model using MATLAB and Simscape.

The nonlinear equations of the PV system which describe the relationships between the different PV model parameters are developed and solved via MATLAB and Simulink tools where the PV cell electric circuit model is shown in Figure

PV cell equivalent electric circuit model.

The nonlinear equation of I-V characteristics of one-diode PV model was expressed by Milici et al. [

PV panel parameters.

Parameter value | Value |
---|---|

Max power _{max} |
735.72 W |

Open circuit voltage _{oc} |
65.9 V |

Short circuit current _{sh} |
15.21 A |

Temperature coefficient of |
–1.23 ^{−1} V/C |

Temperature coefficient of |
3.18 ^{−3} A/C |

The I-V and P-V nonlinear characteristic curves of the PV array simulated using MATLAB at different climatic conditions (temperature and irradiance) are shown in Figure

P-V and I-V characteristic curves at different climatic conditions.

Simulink and Simscape tools have been selected as platforms for modeling, implementation, and testing the Buck–Boost converter. The state space modeling is primarily represented by equation (

Figure _{1} = _{L}, _{2} = _{,} and

Buck–Boost Simscape model.

Buck–Boost output voltage at different duty cycles.

The proposed Buck–Boost has been designed and simulated using the parameters illustrated in Table

Buck–Boost design parameters.

Parameter value | Value |
---|---|

Load resistance | 4.5 |

Filter inductance | 1 mH |

Output filter capacitance | 4700 |

Input filter capacitance | 47 |

Switching frequency | 25000 Hz |

The primary feature of the PV system is the total energy monitoring in which the power of the PV modules can be extracted in a certain climatic situation. As shown in the literature, the most commonly used MPPT algorithm is INC. The INC algorithm is based on the reality that the PV output energy derivative for the output voltage at the MPP is zero (

The INC algorithm is used to detect the condition of MPP via the conductance (d

The voltage and current of the PV module are sensed by the MPPT controller

If (d

No change in the duty cycle occurs if

The duty cycle (PV reference voltage (

The INC variable step size algorithm proposed by Motahhir et al. [

Many computational requests for fractional order derivatives according to the definition have been suggested by Riemann–Liouville and Grunwald–Letnikov, [

The control procedure of the FO-INC algorithm can be expressed by the flowchart depicted in Figure

Fractional order INC MPPT flowchart.

The duty cycle of the Buck–Boost converter can be calculated based on the output of the FO-INC controller

Both fixed- and variable-step FO-INC MPPT have been implemented to improve the performance of the MPP tracking of the nonlinear PV system with Buck–Boost converter and resistive load. In case of fixed step, the effective parameter of MPPT performance is alpha

Genetic algorithms, Particle Swarm Optimization, and Ant Colony Optimization are among the most frequent algorithms in this field. However, these algorithms can solve many real and difficult problems. As one of the recent algorithms, the AntLion Optimizer Optimizer will be introduced along with its basic working principle, updated criteria, and pseudo algorithms. According to Pradhan et al. [

Initialize solution randomly

Specify the search direction

Specify the update criteria

Specify the stopping criteria

The inspiration of the particle swarm algorithm is to simulate the navigation and foraging of swarm of birds or school of fishes. PSO was developed by James Kennedy and Russel Eberhart in 1995 while studying the social behaviors of animals working in swarms [_{1} and _{2} are the acceleration coefficients, and _{min} and _{max} are the ranges of weight of particles. PSO uses fewer resources than the other optimization techniques. Usually, it does not require the problem to be differentiable as the gradient of the problem is not taken into consideration. As a result, there might be chances that PSO does not converge to optimal solution.

Initialize the PSO parameters (_{1}, _{2}, _{min}, _{max}, _{max})

For (each Particle

Simulate and calculate the MPP and the cost function.

The Best Cost (

The Best Solution (

The Best Cost (

The Best Solution (

(a) Update the velocity (

where

(b) Update the position of particles:

Ant Colony Optimization (ACO) introduces an artificial algorithm motivating actual ant colonies that solve discrete optimization problem. It was first presented by Marco Dorigo in 1992 as a major aspect of his Ph.D thesis and called it the ant system [

Initialize the ACO parameters

For (each ant

Simulate and calculate the MPP and the cost Function.

The Best Cost (

The Best Solution (

The Best Cost (

The Best Solution (

(a) Update pheromone for each ant:

(i) Calculate the solution

(b) Apply evaporation and globally update the ants position, according to the optimum solutions calculated earlier

In Algorithm

The primary motive of ALO is the running behavior of larvae of antlions. ALO is suggested based on the Emary and Zawbaa [

In Algorithm

Initialize the first population of ants and antlions randomly

For (each antlion (

Select an antlion using Roulette wheel algorithm [

Simulate and calculate the MPP and the cost Function.

The Best Cost (

The elite (

The Best Cost (

The elite (

(a) Update

(b) Create a random walk and normalize it using: _{,} where

(c) Update the position of antlions using

(d) Calculate the fitness of all ants according to the optimum solutions calculated earlier

The proposed system has been modeled and simulated using MATLAB and Simscape software environments in order to study the system behavior and MPPT performance with different metaheuristic optimization algorithms. The block diagram describing the total PV system with MPPT and optimizer is shown in Figure

The proposed PV system with metaheuristic optimization.

The operation sequence of PV with MPPT and optimization process is a closed loop as shown in Figure

The proposed system implementation flowchart.

The proposed MPPT contribution is generated by measuring the output energy of the PV system under different solar irradiances. Simulation was conducted when solar radiation and cell temperature change with a transient method of approximately 2 sec with 0.01 sec sampling. The characteristics of the PV array will be altered when the natural radiation and cell temperature alter, which causes the I-V curves of the PV array to change. In addition, the particular irradiance ranges from 400 to 1000

Comparative results between MPPT algorithms at 800

Climatic condition | ||||||||
---|---|---|---|---|---|---|---|---|

MPPT | 800 |
800 |
||||||

Max power (Watt) | MPP steps | Oscillation avg. (Watt) | No. of iterations | Max power (Watt) | MPP steps | Oscillation avg. (Watt) | No. of iterations | |

Fixed-step INC | 321.84 | 137 | 5.87 | — | 319.73 | 131 | 4.92 | — |

Variable-step INC | 324.63 | 125 | 4.89 | — | 319.90 | 127 | 4.17 | — |

FO-INC fixed step + PSO | 420.28 | 121 | 4.28 | 100 | 400.01 | 127 | 4.34 | 100 |

FO-INC fixed step + ACO | 470.62 | 115 | 4.067 | 100 | 462.24 | 121 | 3.089 | 100 |

FO-INC fixed step + ALO | 487.22 | 118 | 3.067 | 100 | 474.24 | 125 | 3.089 | 100 |

FO-INC variable step + PSO | 490.28 | 128 | 3.28 | 100 | 480.01 | 132 | 3.34 | 100 |

FO-INC variable step + ACO | 510.62 | 115 | 3.067 | 100 | 490.24 | 121 | 3.089 | 100 |

FO-INC variable step + ALO | 515.52 | 120 | 3.269 | 100 | 510.26 | 127 | 3.802 | 100 |

Comparative results between MPPT algorithms at 1000

Climatic condition | ||||||||
---|---|---|---|---|---|---|---|---|

MPPT | 1000 |
1000 |
||||||

Max power (Watt) | MPP steps | Oscillation avg. (Watt) | No. of iterations | Max power (Watt) | MPP steps | Oscillation avg. (Watt) | No. of iterations | |

Fixed-step INC | 428.84 | 145 | 4.87 | — | 419.73 | 153 | 5.92 | — |

Variable-step INC | 420.73 | 155 | 5.87 | — | 419.90 | 139 | 5.17 | — |

FO-INC fixed step + PSO | 436.88 | 120 | 4.88 | 100 | 410.51 | 121 | 4.84 | 100 |

FO-INC fixed step + ACO | 650.82 | 101 | 2.067 | 100 | 632.24 | 112 | 2.089 | 100 |

FO-INC fixed step + ALO | 667.32 | 118 | 3.87 | 100 | 664.24 | 120 | 3.889 | 100 |

FO-INC variable step + PSO | 590.28 | 86 | 2.28 | 100 | 580.23 | 92 | 2.34 | 100 |

FO-INC variable step + ACO | 720.62 | 65 | 2.067 | 100 | 705.24 | 71 | 2.079 | 100 |

FO-INC variable step + ALO | 725.32 | 80 | 2.369 | 100 | 710.63 | 96 | 2.802 | 100 |

Figure

Fixed-step INC I-V and P-V curves.

Variable-step INC I-V and P-V curves.

The objective of PSO, ACO, and ALO is to select the best value of

Optimization of fixed‐step FO-INC I-V and P-V curves.

Optimization of fixed FO-INC output response.

Optimization of variable-step FO-INC I-V and P-V curves.

Optimization of variable FO-INC output response.

The MPPT performance

MPPT algorithms efficiency.

MPPT method | Efficiency ( |
---|---|

Fixed-step INC | 75.9 |

Variable-step INC | 82.1 |

Fixed-step FO-INC + PSO | 90.2 |

Fixed-step FO-INC + ACO | 92.3 |

Fixed-step FO-INC + ALO | 93.2 |

Variable-step FO-INC + PSO | 94.7 |

Variable-step FO-INC + ACO | 97.5 |

Variable-step FO-INC + ALO | 98.1 |

The output power of the PV system will be changed by irradiance and temperature according to the simulation results of the system with different climatic conditions as illustrated in Tables

No data were used to support this study.

The authors declare that they have no conflicts of interest.

The authors would like to thank Prince Sultan University, Riyadh, Saudi Arabia for supporting and funding this work. Special acknowledgment to Robotics and Internet-of-Things Lab (RIOTU) at Prince Sultan University, Riyadh, SA.