# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 1 Introduction
The improved simultaneous heat transfer search algorithm (ISHTS) demonstrates a high level of accuracy in PV parameter estimation because the balance between exploration and exploitation has been enhanced using simultaneous heat transfer along with elitist perturbation strategies, resulting in an optimal RMSE [24]. The algorithm operates efficiently at 50,000 iterations. However, while ISHTS is highly accurate and optimizes the exploration phase to achieve the optimal RMSE value, it requires substantial processing time, with an average execution time of about 23 s per simulation for SDMs and DDMs. The black widow optimization algorithm (BWOM), which takes its inspiration from the aggressive behaviors of black widow spiders, has certain distinct advantages over other optimization algorithms by using the cannibalism strategy and mating and reproduction mechanism. However, BWOM requires a higher number of search agents in order to obtain the optimal solution [25]. The enhanced generalized normal distribution optimization (NSGNDO) algorithm performs a balance between exploration and exploitation by means of neighborhood search strategies, which realize high accuracy in the PV parameter estimation [26]. In SDMs, NSGNDO achieves an optimal RMSE in 10,000 iterations and completes simulations in about 22 s. In DDMs, it is where NSGNDO yielded an optimal RMSE at about 38 s per run. However, in cases that are very large or highly nonlinear search spaces, the NSGNDO may face a long execution time. That is, the dual neighborhood search strategies make each iteration more complicated, possibly reflecting longer optimization times for high-dimensional problems. The gaining-sharing knowledge-based algorithm (GSK) proves to be advantageous due to its high accuracy and efficiency when it comes to extracting parameters for solar PV systems [27]. To achieve a good balance between exploration and exploitation, the GSK algorithm employs a pair of crucial stages known as the \"junior\" and \"senior\" phases. However, the iteration in the case of SDMs is 30,000, and the iteration in the case of DDMs is 50,000, both of which resulted in a significant amount of computing time. Improved shuffled complex evolution algorithm (ISCE) has major advantages include a basic yet effective global search, reliable performance, and less unpredictability [28]. This was performed by using the competitive complex evolution and reflection and contraction steps. However, when dealing with complicated situations that have multiple local low points, ISCE takes longer to make progress. ISCE achieved the optimal RMSE in the case of SDMs with 5000 iterations completing in approximately 19 s, while in the case of DDMs, it achieved an optimal RMSE with 10,000 iterations, averaging 24 s per simulation. The hybrid successive discretization algorithm (HSDA) offers a number of advantages, including increased accuracy and a strong capability for global searching [29]. This is achieved by using vicinity construction around seed solutions, successive discretization techniques, and adaptive adjustment of search radius. However, these benefits require a lot of processing power to fully realize them. The DIWJAYA algorithm relies on an improved JAYA with an individual weighting scheme, yielding high precision in PV parameter estimation, balancing between exploration and exploitation due to its adaptive weighting mechanism, population mean inclusions, and a Gaussian mutation strategy [30]. For the SDM, DIWJAYA reaches an optimal RMSE in 50,000 iterations, completing simulations in approximately 27 s. For the DDM, it achieves an optimal RMSE with reduced convergence times, averaging 30 s per run. While DIWJAYA's advanced features improve convergence speed and solution quality, its higher iteration demands limit scalability in PV parameter extraction, as the algorithm requires 50,000 iterations to reach the optimal RMSE. The atomic orbital search algorithm (AOS) is inspired by the quantum atomic model, whose concept is based on the movement of electrons around a nucleus's orbitals.