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Opposition decided gradient-based optimizer with balance analysis and diversity maintenance for parameter identification of solar photovoltaic models

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Abstract

The solar photovoltaic (PV) parameter estimation/identification is a complicated optimization process that directly affects the performance of PV systems if the internal parameters of PV cells are not estimated accurately. Finding the precise and accurate parameters of PV models is the primary gateway to the PV system design to mimic their actual behavior. Numerous optimization algorithms are used to find the cell/module parameters, however, most of these algorithms suffer from the high computational burden, local optima trap, and frequent parameter tuning to get the best results. A metaheuristic algorithm called gradient-based optimization algorithm (GOA) is recently introduced to solve numerical optimization and engineering design problems. Nevertheless, the GOA appears to be trapped in sub-optimal locations, increasing computational time to get the best results. Thus, this paper recommends an enhanced GOA by employing an opposition-based learning mechanism to generate more precise solutions. Therefore, this paper proposes an enhanced variant, called opposition-based GOA (OBGOA), to identify the electrical parameters of various PV models, such as the single-diode model (SDM) and double-diode model (DDM). Numerous experimental data profiles are considered to classify the parameters of the SDM and DDM. The obtained results show that the OBGOA can estimate accurate and precise parameters than the other algorithms. In addition, statistical data analysis of various algorithms is presented for all the PV models. The results demonstrated that the proposed OBGOA could find circuit parameters of the cell and the modules accurately and effectively. This study is backed up by additional online guidance and support at https://premkumarmanoharan.wixsite.com/mysite.

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Abbreviations

I p :

Photocurrent in A

I d :

Diode current in A

I sh :

Current through the shunt resistor in A

I :

Output current of the cell/module in A

V :

Output voltage of the cell/module in V

I sd,  I sd 1, and I sd 2 :

Reverse saturation current of the diodes in A

R p  and  R s :

Ohmic resistance of the cell in Ω

n,  n 1, and  n 2 :

Ideality factor of diodes

D :

Problem dimension

\({X1}_{n}^{t}\) :

Updated position of the population

\({x}_{best}\) and \({x}_{\text{worst}}\) :

Best and worst solutions, respectively

\({r}_{1}\text{,} {r}_{2}\text{,} {r}_{3}\text{,}\mathrm{ and}\, {r}_{4}\) :

Random integers between [0, D]

\({P}_{r}\) :

Probability rate

q :

Electron charge in C

k :

Boltzmann constant in J/K

T :

Absolute temperature in K

N s  and  N sh :

Series- and parallel-connected cells, respectively

X :

Number of data samples

Y :

Number of decision variables

N p :

Population size

IT max :

Maximum number of iterations

\({X}_{ub}\)  and \({X}_{lb}\) :

Upper and lower boundary limit

\({x}_{p}^{t}\) :

Randomly selected solution

\(\overline{X }\) :

Random opposite solution

I exp :

Experimental current sample in A

I est :

Estimated current in A

PV:

Photovoltaic

GOA:

Gradient-based optimization algorithm

OBL:

Opposition-based learning

OBGOA:

Opposition-based GOA

SDM:

Single-diode model

DDM:

Double-diode model

RES:

Renewable energy systems

STC:

Standard test condition

TDM:

Three-diode model

IJAYA:

Improved Jaya algorithm

TLBO:

Teaching–learning-based optimization

PSO:

Particle swarm optimization

FPA:

Flower pollination algorithm

ALO:

Ant lion optimization

MFO:

Moth-flame optimization

BFA:

Bacterial foraging algorithm

SFLA:

Shuffled frog leaping algorithm

FFO:

Firefly optimization

GWO:

Grey wolf optimization

WOA:

Whale optimization algorithm

SCA:

Sine–cosine algorithm

SSA:

Salp-swarm algorithm

COA:

Coyote optimization algorithm

HHO:

Harris Hawks optimizer

SMA:

Slime mould algorithm

EO:

Equilibrium optimizer

DE:

Differential evolution

ABC:

Artificial Bee Colony

MPA:

Marine-predator algorithm

RMSE:

Root mean square error

GSR:

Gradient search rule

DM:

Direction of movement

LEO:

Local escaping operator

NFL:

No-free-lunch

RE:

Relative error

IAE:

Integral absolute error

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Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Dayananda Sagar College of Engineering, Bengaluru, Karnataka, 560078, India

    M. Premkumar

  2. Rajasthan Rajya Vidyut Prasaran Nigam Ltd., Sikar, Rajasthan, 332025, India

    Pradeep Jangir

  3. Department of Electrical and Electronics Engineering, Thiagarajar College of Engineering, Madurai, Tamil Nadu, 625015, India

    Rajvikram Madurai Elavarasan

  4. Department of Electrical and Electronics Engineering, National Institute of Technology, Tiruchirappalli, Tamil Nadu, 620015, India

    R. Sowmya

Authors
  1. M. Premkumar
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  2. Pradeep Jangir
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  3. Rajvikram Madurai Elavarasan
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  4. R. Sowmya
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Correspondence to M. Premkumar.

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Appendices

Appendix A

See Tables 13, 14, 15 and 16. IAEP denotes the integral absolute error with respect to the estimated power (Pest) and experimental power (Pexp) values.

Table 13 IAE and RE of OBGOA on SDM of the RTC France Si PV cell
Full size table
Table 14 IAE and RE of OBGOA on DDM of the RTC France Si PV cell
Full size table
Table 15 IAE and RE of OBGOA on SDM of the PhotoWatt-PWP201 PV module
Full size table
Table 16 IAE and RE of OBGOA on DDM of the PhotoWatt-PWP201 PV module
Full size table

Appendix B: control parameters of various algorithms

S. No.

Algorithm

Control parameters

Value

1

SSA

Number of search agents (Np)

30 (SDM), 50 (DDM and others)

Maximum number of iterations (ITmax)

1000

b

1

2

COA

Number of search agents (Np)

10 packs with 30 coyotes for all problems

Maximum number of iterations (ITmax)

1000

3

SMA

Number of search agents (Np)

30 (SDM), 50 (DDM and others)

Maximum number of iterations (ITmax)

1000

V b

− 1 to 1

4

EO

Number of search agents (Np)

30 (SDM), 50 (DDM and others)

Maximum number of iterations (ITmax)

1000

a1, a2, and RP

2, 1, and 0.5, respectively

5

HHO

Number of search agents (Np)

30 (SDM), 50 (DDM and others)

Maximum number of iterations (ITmax)

1000

β, F, and Q

1.5, 6, and 5, respectively

6

MPA

Number of search agents (Np)

30 (SDM), 50 (DDM and others)

Maximum number of iterations (ITmax)

1000

FADs, mutation probability, and p

0.5

7

GOA

Number of search agents (Np)

30 (SDM), 50 (DDM and others)

Maximum number of iterations (ITmax)

1000

P r

0.5

8

OBGOA

Number of search agents (Np)

30 (SDM), 50 (DDM and others)

Maximum number of iterations (ITmax)

1000

P r

0.5

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Premkumar, M., Jangir, P., Elavarasan, R.M. et al. Opposition decided gradient-based optimizer with balance analysis and diversity maintenance for parameter identification of solar photovoltaic models. J Ambient Intell Human Comput 14, 7109–7131 (2023). https://doi.org/10.1007/s12652-021-03564-4

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