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In this work, we present three methods to extract model physical parameters of a photovoltaic solar module modelled by a single-diode electronic circuit. The model physical parameters we are looking for are photocurrent Iph , saturation current Is , ideality factor η, series resistance Rs and shunt conductance Gp . The first method is based on exact solution of module characteristic equation, the second one uses exact expression of dynamic conductance and the third one makes use of exact expression of the integral of translated current-voltage characteristics (I-Isc ). In all these extraction methods, we achieve numerical fitting of experimental data of output current, differential conductance and area under translated characteristics with suitable analytical expressions to get model physical parameters at standard test conditions (STC). Then, we assume these values as initial conditions and derive exact analytical expressions reporting effects of module temperature and incident solar irradiance on photocurrent, saturation current and ideality factor using temperature coefficients provided as well as irradiance coefficients extracted from module manufacturer datasheet. We examine new analytical expressions of model physical parameters in the case of Shell SQ80 photovoltaic solar module at arbitrary operating conditions of module temperature and solar irradiance. We evidence good agreement between experimental characteristics and forecasted analytical characteristics generated by new analytical expressions.