Accurately estimating the unknown parameters of the photovoltaic (PV) models based on the measured voltage-current data is a challenging optimization problem due to its high nonlinearity and multimodality. An accurate solution to this problem is essential for efficiently simulating, controlling, and evaluating PV systems. There are three different PV models, including the single-diode model, the double-diode model, and the triple-diode model, with five, seven, and nine unknown parameters, respectively, proposed to represent the electrical characteristics of PV systems with varying levels of complexity and accuracy. In the literature, several deterministic and metaheuristic algorithms have been used to accurately solve this hard problem. However, due to the high nonlinearity of this problem, the deterministic methods could not achieve accurate solutions. On the other side, the metaheuristic algorithms, also known as gradient-free methods, could achieve somewhat good solutions for this problem, but they still need further improvements to strengthen their performance against stuck-in local optima and slow convergence speed problems. Over the last two years, several recent metaheuristic algorithms with better characteristics to improve convergence speed and avoid local optima have been proposed to tackle continuous optimization problems. However, the performance of the majority of those algorithms for estimating the parameters of PV models has not been investigated. Therefore, in this paper, the performance of nineteen recently published metaheuristic algorithms, such as the Mantis search algorithm (MSA), spider wasp optimizer (SWO), light spectrum optimizer (LSO), growth optimizer (GO), walrus optimization algorithm (WAOA), hippopotamus optimization algorithm (HOA), black-winged kite algorithm (BKA), quadratic interpolation optimization (QIO), sinh cosh optimizer (SCHA), exponential distribution optimizer (EDO), optical microscope algorithm (OMA), secretary bird optimization algorithm (SBOA), Parrot Optimizer (PO), Newton-Raphson-based optimizer (NRBO), crested porcupine optimizer (CPO), differentiated creative search (DCS), propagation search algorithm (PSA), one-to-one based optimizer (OOBO), and triangulation topology aggregation optimizer (TTAO), are studied to clarify their effectiveness in estimating the unknown parameters of PV models. In addition, those algorithms collaborate with two deterministic functions, namely the Lambert W-Function and the Newton-Raphson Method, to aid in solving the I-V curve equations more accurately, thereby improving the performance of PV systems. Those algorithms are assessed using four well-known PV solar cells and modules and compared with each other using several performance metrics, including best fitness, average fitness, worst fitness, standard deviation (SD), Friedman mean rank, and convergence speed; and a multiple-comparison test to compare the difference between their mean ranks. Results of this comparison show that SWO is more efficient and effective for SDM, DDM, and TDM over the majority of the studied PV solar cells and modules, and the Newton-Raphson Method is more efficient for solving the I-V curve equations. In addition, this study reports that the majority of the recently published metaheuristic algorithms perform poorly when applied to this problem.