**1. Introduction**

Recently, clean energy usage has increased significantly as demand for all other fuels declined because of environmental concerns. As a result" the scientific community made substantial efforts to harvest energy from different ambient sources [1–5]. Solar energy harvesting has become the most ideal option since it surpasses all traditional nonrenewable and renewable resources [6]. As a result, the worldwide solar electricity sector is expanding significantly, with a current value of more than \$10 billion each year [6–8].

Solar energy is converted into electrical energy by employing photovoltaic (PV) panels [9]. Numerous PV panels are linked together in serial and/or parallel arrangements to create bulky solar energy plants equipped with maximum power point tracking (MPPT) systems to increase power generation. The primary goal of MPPT systems is to regulate the parameters of the PV system to generate optimum power [9]. The rapid deviation of electrical energy production is a well-known property of solar plants [9]. Many solar facilities are linked to local grids, and their operation at the same time as the grids causes voltage instability in distribution lines [10]. Hence, stable and maximized power generation from

**Citation:** Singh, A.; Sharma, A.; Rajput, S.; Mondal, A.K.; Bose, A.; Ram, M. Parameter Extraction of Solar Module Using the Sooty Tern Optimization Algorithm. *Electronics* **2022**, *11*, 564. https://doi.org/ 10.3390/electronics11040564

Academic Editors: Enrique Rosales-Asensio and Amjad Anvari-Moghaddam

Received: 7 January 2022 Accepted: 11 February 2022 Published: 13 February 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

solar plants is an essential requirement of the green energy movement. To obtain maximum power density, both theoretical and experimental studies were performed to optimize the parameters of PV panels [4,11–13]. Single, double, and triple diode models of PV cells are widely employed to identify the current-voltage parameters [14–16]. These parameters are helpful for determining the accuracy and steadiness of the models. However, parameter assessment is not an easy task because of unbalanced operational cases such as faults and ageing. In most cases, the single diode model is employed because of ease and acceptance. On the other hand, the double diode model is anticipated to be more than the three-diode model accurate in case of lower solar irradiance.

Different types of algorithms were proposed and studied to get more accurate and precise parameters from nonlinear implicit equations with high accuracy [17–33]. The merits and demerits of these algorithms are categorized because of the trade-off between exploration and exploitation capabilities [17]. Some became caught in local optima solutions because of a lack of exploration capabilities for finding an optimal solution in the search space. Heuristic and deterministic are the two main groups of algorithms. Heuristic algorithms contain particle swarm optimization (PSO) [18], cuckoo search algorithm [19], harmony search [20], cat swarm optimization (CSO) [21], differential evolution (DE) [22], artificial bee colony [23], chaos CPSO [24], simulated annealing [25], biogeography-based optimization algorithm with mutation strategies [26], genetic algorithms [27], improved adaptive differential evolution [28], pattern search [29], generalized opposition-based teaching-learning-based optimization [30], and Nelder–Mead modified PSO [31]. The Lambert W-functions [32], least squares [33], iterative curve-fitting methods [34], conductivity method [35], Levenberg–Marquardt algorithm [36], Newton–Raphson, and nonlinear least square are categorized as deterministic algorithms. The applicability of deterministic algorithms is restricted because of continuity, differentiability, and convexity related to objective functions. These algorithms are likewise sensitive to the starting solution and settle at local optima in most cases. Because they do not include difficult mathematics, biorelated algorithms are more realistic and robust optimization methods for simplifying complex transcendental equations.

The sooty tern optimization (STO) algorithm mimics the attack and migration behavior of sooty terns (birds of tropical oceans). This algorithm provides a good balance between exploration and exploitation strategy and thus reaches optimal solution without getting trapped in a local solution. These benefits allow researchers to apply the STO for parameter extraction of a solar module. The key purposes of this research investigation are as follows:


This study utilizes the STO algorithm for the parameter assessment of PV cells/modules. Initially, the mathematical model for PV cell/module and problem formulation is discussed. At the second stage, the STO algorithm is briefly introduced and used to assess the optimal magnitude of undetermined parameters. Next, the output results are examined with a measured dataset, and the algorithm is compared to pre-existing metaheuristic algorithms. Section 5 contains the discussion and conclusion of manuscript.
