In this paper, we proposed a new methodology that can improved and developed the faults detection and diagnosis methods of the photovoltaic generator, especially when it subjected to the impedance and reversed polarity defects. This proposed algorithm is based on the mathematical modeling of the IV characteristic, of the faulty photovoltaic generator hierarchies as: cell, cells group, module, string and the entire generator, when they submitted to one or more of: cells, bypass and blocking diodes in impedance and reversed polarity faults. This new methodology can facilitated the study of the faulty generator characteristics, and obtained a database for the learning phase and the classification of the new observations collected on the system during its operation. NOMENCLATURE I_phi = Photo-Current. N_Cells = Cells Number in Each Group. N_Groups = Groups Number in Each Module. N_Modules = Modules Number in Each String. N_Strings = Strings Number in the Generator. V_Cell_Imp = Cell Voltage Imposed. I_Cells = Cell Current. V_Cells = Cell Voltage. I_PV = Generator Current. V_PV = Generator Voltage. R_S = Cell Series Resistance. R_SH = Cell Shunt Resistance. I_S1 = Reverse Saturation Current of 1 st Diode. I_S2 = Reverse Saturation Current of 2 nd Diode. m1 = Ideality Factors of 1 st Diode. m2 = Ideality Factors of 2 nd Diode.