**1. Introduction**

Solar photovoltaic energy is becoming the most popular renewable energy used in the world, at many caring of installations. Modeling and characterization are important topics that necessitate the determination of the exact solar photovoltaic (PV) cell's unknown parameters values and thus optimizing the PV power generated. Solar PV generator's performances are affected by many factors, where some of them are external, related to the environmental conditions like the weather's variations (irradiation and temperature), shading phenomenon, hotspot [1], dust, cell damage, wind velocity, and soiling [2]. Others are internal, related to the electrical, physical, and mathematical modeling. After the modeling step of any PV generator, their identified parameters values are used in the established model. Therefore, it is necessary to find the accurate values of the unknown electrical PV parameters by an appropriate approach. Besides, accurate parameter values of PV cells are essential for the development of good controlling techniques for Maximum Power Point Tracking (MPPT) based power electronic converters [3]. As shown in the **Figure 1** the importance of PV parameters' obtaining accurate values for a whole PV system.

**Figure 1.**

*Importance of determination of accurate PV parameter values in PV systems [3].*

With the complexity of the nonlinearity founded from the current-voltage relationship through the model used to represent the physical behavior of PV cells (Single Diode, Double Diode, Three Diode, and so on) [4]. The parameters to be found become more numerous, as the complexity of models increases. The PV parameters of a Single Diode Model (SDM), which are the most determined in literature, and which are the light and the diode saturation currents, the diode ideality factor, the series, and the shunt resistances. A challenge is to obtain the values of all the PV model's parameters value while keeping a reasonable compromise of some criteria, such as the fast speed of convergence, low implementation complexity, and so on.

Artificial intelligent (AI) algorithms have attracted attention lately, by the scientific community to be used for resolving many topic's problems. Among them solar photovoltaics' problems, such as modeling, identification, prediction, optimization, sizing, control, and many others [5]. The hybrid optimization-based methods have attracted more attention to achieve more efficiency and precision. For this reason, this paper presents a combination of the traditional Levenberg-Marquardt (LM) with the recent meta-heuristic Grey Wolf optimizer (GWO) method. This hybrid LMGWO method has seemed to be the most performing, which we finally have chosen to be used in this work.

The remaining of this chapter is structured as follow. After the introduction given in this Section 1. Section 2 presents a classification of the optimizationbased methods used in the literature to estimate the PV parameters values. In the Section 3, models are presented of the PV cell (single diode), and the problem of PV parameters obtaining values is presented. Section 4 gives some details about the hybrid used method to estimate the SDM parameters values. Moreover, this section provides the basic concept of the LM and the GWO. Finally, Section 5 shows some results comparing one method of each type proposed in the classification and the LMGWO. Some conclusions are given in Section 6.
