On the problem formulation for parameter extraction of the photovoltaic model: Novel integration of hybrid evolutionary algorithm and Levenberg Marquardt based on adaptive damping parameter formula

•A new GCAOAAdLM is proposed to determine the parameters of the TD PV model at various climatic conditions.•A novel transition from localized to global strategy is offered to update exceeded solutions from the lower and upper boundaries.•The AdLM approach, which combines steepest descent and Gauss-Newton methods, is employed to predict the output PV current.•The nonlinear damping parameter formula is proposed to effectively steer the search direction of the LM method and mimic the natural behavior of the PV model, with greatly improved accuracy and stability. The estimation of the unknown parameters of the photovoltaic (PV) model is crucial for accurately verifying its real performance precisely under a wide range of climatic conditions. This paper presents an approach to determine the nine parameters of the three diode (TD) PV model based on the integration of the guaranteed convergence arithmetic optimization algorithm and Levenberg-Marquardt with adaptive damping nonlinear parameter method named as GCAOAAdLM. The keystone of the GCAOAAdLM model is accomplished by efficaciously enhancing the exploiter-explorer tendency with inclusion of various powerful hybrid strategies in terms the methodology itself. In addition, the objective function is newly designed leveraging on Levenberg-Marquardt with adaptive damping parameter method to accurately determine the initial roots parameters of the TD PV model. The experimental results demonstrate that the proposed GCAOAAdLM can reduce the root mean square error (RMSE), mean bias error (MBE), deviation of solar radiation’s levels (di), test statistical (TS), and absolute error (AE) to zero and the determination coefficient (R2) to 1 for all environmental conditions, with statistical reasons and comparisons against well-published approaches available in the literature.