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A Self-adaptive Algorithm with Newton Raphson Method for Parameters Identification of Photovoltaic Modules and Array

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Abstract

The word’s demand for renewable energy has be rinsing incrementally. One of the solutions for the energy crisis is photovoltaic. However, the design and development of better performing photovoltaic cells and modules requires accurate extraction of their intrinsic parameters. Metaheuristic algorithms have been reported to be the best methods for obtaining accurate values of these intrinsic parameters. However, local convergence goes against the recently devised heuristic methods and inhibits them from producing optimal result. This paper proposes a hybrid method that is based on the Newton Raphson method and a self-adaptive algorithm called the Drone Squadron Optimisation. The latter is an artifact technique inspired by the simulation of a drone squadron from a command centre. It is proposed that this hybrid method can help extract the best intrinsic parameters of photovoltaic cell and module. This study also provides insights and clarification on the reported approaches that have been recently proposed to formulate the objective function. Further, this study also computes and compares the ten best recently published heuristics algorithms in the domain of photovoltaic estimation. The study’s results obtain point to the difference between the two formulations and the accuracy of the best formulation. The results obtained from the six case studies covered in this study present the combined performance of the Newton Raphson method and Drone Squadron Optimisation to extract the accurate parameters of a photovoltaic module.

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Abbreviations

CBC :

The current best coordinates

CBOFV :

The current best coordinates objective function

D :

Dimension

ε :

Stopping criteria

E :

Solar irradiance

F (θ):

Objective function to minimize

I :

Cell output current (A)

I d, I d 1, I d 2 :

Diode currents (A)

I iext (θ):

Estimated current

I i :

Measured current (A)

I 0, I 01, I 02 :

Diode reverse saturation currents (μA)

I p :

Current through parallel resistor (A)

I ph :

Photoelectric current (A)

I sc :

Short-circuit current (A)

k:

Boltzman constant (J/K)

k i :

Temperature coefficient of Isc (A/K)

LB:

Lower bound

n, n 1, n 2 :

Diode ideality factors

N :

Number of the experimental I–V data pairs

N S :

Number of cells connected in series

OF :

Objective function

θ :

Vector of parameters

P :

Firmware perturbation

P acc :

Probability for the worst solution to be accepted

q :

Electron charge (C)

R P :

Parallel resistance (Ω)

R S :

Series resistance (Ω)

RMSE :

Root mean square error

STC :

Standard testing condition (1000 W/m2, 25 °C)

T :

Temperature (K)

TC :

Trial coordinates

TmOFV :

The team’s objective function

TmC :

The team’s coordinates

U (0, 1):

Random uniform distribution between 1 and 0

UB :

Upper bound

V :

Cell output voltage (V)

V d :

Voltage applied across the diode (V)

V i :

Measured voltage (V)

V mp :

Voltage at the maximum power point (V)

V oc :

Open-circuit voltage (V)

V t :

Thermal voltage (V)

ABC:

Artificial bee colony

ABSO:

Artificial bee swarm optimization

ABC-TRR:

Hybrid trust-region reflective algorithm

C-HCLPSO:

Chaotic heterogeneous comprehensive learning particle swarm optimizer

CAO:

Coyote optimization algorithm

CWOA:

Chaotic whale optimization algorithm

CPSO:

Chaos particle swarm optimization

CSO:

Cat swarm optimization

DE/WOA:

Hybrid differential evolution with whale optimization algorithm

DDM:

Double diode model

DSO:

Drone Squadron Optimization

EHA-NMS:

Hybrid adaptive Nelder-Mead simplex algorithm

ELPSO:

Enhanced leader particle swarm optimisation

ESCE-OBL:

Enhanced shuffled complex evolution algorithm improved by opposition-based learning

EVPS:

Enhanced vibrating particles system algorithm

FPSO:

Flexible particle swarm optimization

GOFPANM:

Hybrid flower pollination algorithm

HBCS:

Hybridizing cuckoo search algorithm

HFAPS:

Hybrid firefly and pattern search algorithms

IADE:

Improved adaptive differential evolution algorithm

IJAYA:

Improved Jaya

IMFO:

Improved moth-flame optimization

ISCA:

Opposition-based sine cosine algorithm

ISCE:

Improved shuffled complex evolution

ITLBO:

Improved teaching learning-based optimization

IWAO:

Improved whale optimization algorithm

MADE:

Memetic adaptive differential evolution

MLBSA:

Multiple learning backtracking search algorithm

MPSO:

Particle swarm optimisation with adaptive mutation

NoCuSa:

Nonhomogeneous cuckoo search algorithm

ORcr-IJADE:

Advanced onlooker-ranking-based adaptive differential evolution

PGJAYA:

Performance-guided JAYA

PV:

Photovoltaic

RcrIJADE:

Improved adaptive differential evolution with crossover rate repairing

SATLBO:

Self-adaptive teaching–learning-based optimization

SDA:

Successive discretization algorithm

SFO:

Sunflower optimization algorithm

SOS:

Symbiotic organisms search

Std:

Standard deviation

TLABC:

Teaching–learning-based artificial bee colony

tvACPSO:

Time-varying acceleration coefficients particle swarm optimisation

WDOWOAPSO:

Collaborative swarm intelligence

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Authors and Affiliations

  1. Laboratory of Technologies and Applied Sciences, University of Douala, Douala, Cameroon

    Patrick Juvet Gnetchejo, Salomé Ndjakomo Essiane, Pierre Ele & Steve Perabi Ngoffe

  2. Signal, Image and Systems Laboratory, Higher Technical Teacher Training College of Ebolowa, University of Yaounde 1, Yaoundé, Cameroon

    Salomé Ndjakomo Essiane

  3. School of Geology and Mining Engineering, University of Ngaoundéré, Ngaoundéré, Cameroon

    Abdouramani Dadjé

  4. Laboratory of Electrical Engineering, Mechatronic and Signal Treatment, National Advanced School of Engineering, University of Yaounde 1, Yaoundé, Cameroon

    Pierre Ele & Daniel Eutyche Mbadjoun Wapet

  5. College of Physics and Information Engineering, Fuzhou University, Fuzhou, China

    Zhicong Chen

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  1. Patrick Juvet Gnetchejo
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Gnetchejo, P.J., Ndjakomo Essiane, S., Dadjé, A. et al. A Self-adaptive Algorithm with Newton Raphson Method for Parameters Identification of Photovoltaic Modules and Array. Trans. Electr. Electron. Mater. 22, 869–888 (2021). https://doi.org/10.1007/s42341-021-00312-5

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