# Parameter Extraction of Photovoltaic Cells and Panels Using a PID-Based Metaheuristic Algorithm
## 1 Introduction  
In response to combating climate change and satisfying the requirements of sustainable development, countries are rapidly moving to renewable energy sources like solar power, which is converted using photovoltaic (PV) panels into electric energy [1]. The development of PV systems is crucial for nations to take advantage of the fact that solar energy is accessible in many regions of the world [2]. The European Commission has established goals for renewable energy, which will likely result in improvements to existing technology and the introduction of whole new approaches. The target is for 32% of total energy consumption to come from renewable sources by the end of the decade and a remarkable 100% by 2050 [3]. The move to clean energy sources is becoming critical due to rising environmental concerns, and solar technology has achieved significant advancements and has made continuous attempts to improve photovoltaic technology. In order to maximize the effectiveness of solar power generation systems in response to changing environmental conditions, accurate parameter extraction from PV models is required. \"Parameter extraction\" refers to identifying the key electrical parameters such as series resistance, shunt resistance, diode ideality factor, photocurrent, and saturation current in the single- and double-diode photovoltaic models, based on current-voltage (I-V) characteristics. Both analytical methods using complicated equations and metaheuristic algorithms have been used in this field. Both are especially useful when dealing with difficult issues like parameter extraction [4; 5]. Analytical methods provide a basic strategy, but they are extremely assumption-dependent. However, metaheuristic algorithms, such as genetic algorithms, perform very well when faced with complicated problems and do not require derivatives [6]. Improvements in clean energy technologies are made possible by combining these analytical methods and metaheuristic algorithms to release photovoltaic systems' full potential [7]. To illustrate the broader effectiveness of metaheuristic techniques in energy optimization problems, the War Strategy Optimization (WSO) algorithm has been successfully applied to optimal power flow in wind-integrated systems, achieving significant reductions in electricity generation costs and voltage fluctuations [8]. Although metaheuristic algorithms have many potential benefits, they can also have limitations, including a slower convergence rate and a higher calculation time [9]. The pros and cons of the various approaches to parameter extraction are addressed in a review by [PERSON] et al. [10]. Further information on these powerful optimization methods is provided by later review publications that categorize metaheuristic algorithms and their alternatives [11; 12]. While this study centers on photovoltaic systems, the importance of accurate modeling and parameter estimation extends across energy technologies. For instance, [PERSON] et al. [13] emphasized how structural understanding and redox behavior critically affect performance in sodium-ion batteries--highlighting the universal relevance of precise parameter extraction in optimizing next-generation energy systems. Despite extensive research in the domain of parameter optimization for photovoltaic systems, key challenges persist that limit the real-world applicability of existing algorithms. One notable issue is the computational intensity required for many of these algorithms to function optimally; they often necessitate large populations, a high number of iterations, and extended computational time [14; 15; 16; 17; 18]. This is particularly problematic as photovoltaic systems continue to grow in complexity, raising questions about the scalability and efficiency of current optimization techniques. This paper introduces a PID-based search algorithm (PSA) that directly addresses these limitations [19].