# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 1 Introduction
Inspired by PID control systems, PSA is engineered for efficiency, balancing both population size and the number of iterations to significantly reduce computational time. In tests involving both single- and double-diode models across six types of photovoltaic cells and panels, PSA has demonstrated not only effective scalability but also improved efficiency, making it well-suited for complex, real-world applications. Importantly, PSA requires fewer parameters to be configured, making it well-suited for real-world applications. PID controllers are widely used in control systems due to their simplicity, robustness, and effectiveness in correcting dynamic system deviations in real time. These properties make them well-suited as a foundation for optimization strategies. In the proposed PSA, the proportional, integral, and derivative components are reinterpreted as metaheuristic tuning mechanisms that adaptively adjust the exploration-exploitation balance. This control-inspired structure helps guide the search process more efficiently toward optimal solutions. By incorporating feedback-driven corrections instead of relying purely on stochastic behavior, PSA offers a more structured and dynamically responsive alternative to traditional metaheuristics, improving both convergence speed and robustness against stagnation. Another prevalent challenge in the existing literature is the susceptibility of optimization algorithms to local minima [20; 21; 22]. Many algorithms, while designed to seek optimal solutions, often converge to suboptimal points due to this limitation. PSA counters this challenge through its inherent resistance to disturbances and fluctuations, which allows it to avoid being stuck in local minima. The PID-inspired search mechanism in PSA ensures a more robust convergence to the global optimum, thereby elevating its efficacy over algorithms that are prone to local minima. Additionally, the PSA features a zero-output mechanism that adapts the search to prevent becoming stuck in local optima by using Levy flight in a probabilistic manner. In order to improve convergence towards the global optimum in later steps, the Levy flight enables the PSA to progressively shift focus towards the phase of exploitation despite larger diversity in the search space during earlier steps. The PSA's performance is evaluated through comparisons with twenty-six leading parameter extraction algorithms, each known for achieving optimal root mean square error (RMSE) in PV applications. However, computational efficiency and execution time scalability are the main weaknesses of the majority of these algorithms. To address these issues, this study significantly reduces execution time and iterations by using smaller population sizes under optimal RMSE. This will be achieved by determining preliminary error values outside the main iterative loop, hence providing a benchmark for further calculations in the incremental PSA. The PSA also applies a mechanism of zero-output with Levy flight that self-tunes probabilistically to avoid entrapment in local optima, which helps to enhance the efficiency of search and solution quality. Among the algorithms considered for comparison, the improved version of the snake optimization algorithm (ISOA) achieves a perfect balance between exploring and exploiting, proving possibilities with fewer variables and fewer iterations [23]. Reduced complexity makes it simpler to put into practice. While ISOA has optimized exploration-exploitation balance and accuracy, ISOA requires a high execution time to find the optimal RMSE, which took around 20.6 to 26.9 s per simulation to obtain the optimal RMSE value in the case of SDMs of the RTC France. For the RTC France DDM, it took around 26.87 s to reach the optimal RMSE.