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Photovoltaic (PV) system are the cleanest form of electricity generation and it is the only form with no effect on the environment at all. However, some environmental challenges persist, which must be overcome before solar energy may be used to represent a source of truly clean energy. This paper aims to study the stability and dynamic behavior of a grid-connected environmentally-friendly photovoltaic energy system using the bifurcation theory. This theory introduces a systematic method for stability analysis of dynamic systems, under changes in the system parameters. To produce bifurcation diagrams based on the bifurcation theory, a parameter is constantly changed in each step, using MATLAB and AUTO, and eigenvalues are monitored simultaneously. Considering how the eigenvalues approach the system's imaginary axis in accordance with the changes in the targeted parameter, the occurred saddle-node and Hopf bifurcations of the grid-connected PV system are extracted. Using the obtained bifurcations, the system's dynamic stability limits against changes in controlled (controller coefficients) and systematic parameters (such as Thevenin impedance network) are found.