Research on Stochastic Bifurcation and Reliability of a Photovoltaic Power System Under Combined Additive and Multiplicative Random Excitation

The random impact of photovoltaic grid connection on the system has always attracted the attention of the academic community. Therefore, using some theories of stochastic differential equations, especially the stochastic averaging method, to study the bifurcation phenomena caused by random photovoltaic output has become a growing trend. This paper models a two-machine power system excited by stochastic photovoltaic output, based on a quasi-non-integrable Hamiltonian physical model, and analyzes its dynamic behavior from two aspects: stochastic bifurcation and stochastic reliability. First, the two-machine power system is transformed into a quasi-non-integrable Hamiltonian model, through which the system equations are simplified for the following calculations. In the subsequent stochastic bifurcation analysis, we study the effects of damping coefficient and noise intensity on the bifurcation evolution. We find that combined parameter and external excitations lead to more variable bifurcation evolution scenarios. Finally, through stochastic reliability analysis, the stochastic reliability analysis demonstrates the importance of mixed parameter adjustment in maintaining the system’s reliability level. Research shows that the stochastic bifurcation caused by photovoltaic grid connection can occur within a certain range of parameters, and we believe this phenomenon provides valuable insights for subsequent studies.