# Parameter Extraction of Solar Photovoltaic Model Based on Nutracker Optimization Algorithm
## 1 Introduction  
In order to tackle the well-known challenges of energy transition, a swift shift from fossil fuels to a wider renewable energy period is required; solar energy is the most abundant and easily accessible renewable energy resource. Annually, the total amount of solar radiation received by the Earth is 7500 times the global energy consumption (about 450 EJ), thus the utilization of solar energy is playing an increasingly important role in the global energy transformation [1]. Photovoltaic researchers have been striving to achieve reliable and accurate modeling of PV components for a better understanding of their operating principles, performance, and characteristics, as well as predicting their performance and lifespan under different environmental conditions. The single diode model (SDM) is the foundation of photovoltaic component modeling, while the double diode model (DDM) considers the recombination loss in the depletion region of the PN junction based on the SDM, and the triple diode model (TDM) is considered to be a more accurate model than the SDM and DDM [2]. It introduces a third diode to characterize solar cells under reverse current conditions [2, 3], and it contains nine parameters: \(I_{pb}\), \(I_{SD1}\), \(I_{SD2}\), \(I_{SD3}\), \(n_{1}\), \(n_{2}\), \(n_{3}\), \(Rs\), and \(Rp\). Due to the nonlinearity and complexity of the model, most mathematical and numerical analysis methods are simplified by certain approximation. Metaheuristic algorithms, well suited for solving complex optimization problems with large search spaces and non-linear objective functions, have been extensively studied in the field. In previous research, a diverse range of algorithms and their variants, including genetic algorithm (GA) [4], particle swarm optimization (PSO) [5], differential evolution (DE) [6],reinforcement learning neural network algorithm (RLNNA) [7], simplified bird mating optimization (SBMO) [8], firework algorithm (FWA) [9], artificial bee colony (ABC) [10], moth flame optimization (MFO) [11], harmony search algorithm (Hs) [12], mutative-scale parallel chaos optimization algorithm (MPCOA) [13], repairing self-adaptive differential evolution (Rcr-IJADE) [14], bee pollinator flower pollination algorithm (BPFPA) [15], free search differential evolution algorithm (FSDE) [16], teaching-learning based optimization (TLBO) [17], Generalized opposition-based learning teaching-learning based optimization (GOTLBO) [18], and evaporation rate-based water cycle algorithm (ER-WCA) [19], have been utilized for the parameter extraction of solar PV models. Recent trends in research also indicate an increasingly frequent pivot towards the exploration and utilization of novel metaheuristic algorithms. For example, [PERSON] et al. proposed the use of the atomic orbital search metaheuristic algorithm (AOS) for solar cell parameter identification [20], which simulates the mixing and recombination of atomic orbitals to search for the optimal solution. They also discussed more than 30 different RMSE calculation methods to achieve a novel and accurate RMSE calculation. [PERSON] et al. proposed an improved DE algorithm for parameter extraction of photovoltaic cells in 2022 [21]. He used a numerical method for the Lambert W function analytical equation to improve the local convergence characteristics of DE, which reduced the computation time to half of its original time. [PERSON] et al. proposed a two-stage identification method [22]. First, they preprocessed the experimental I-V curve by removing outliers, curve fitting, and the sparsification of the I-V data. Following this, they used maximum power matching (MPM) to roughly identify the parameters from the preprocessed data. Finally, they used the results as the initial values for the improved flow direction algorithm (IFDA) iteration to achieve the accurate identification of photovoltaic model parameters. [PERSON] et al.