In recent years, China has made significant breakthroughs in photovoltaic and hydroelectric power generation, effectively alleviating the problem of energy shortage. However, the high proportion of new energy access has led to an increase in power electronic devices, and has also exacerbated the problem of sub synchronous oscillations below the synchronous frequency caused by their interaction with the power grid. In order to reduce the impact of photovoltaic grid connection on the stability of the power system and avoid significant economic losses caused by sub synchronous oscillations, it is necessary to conduct research and analysis on photovoltaic grid connection systems. This article focuses on the problem of sub synchronous oscillation in photovoltaic grid connected systems. Firstly, a mathematical model of the photovoltaic power generation system is established, which includes photovoltaic arrays, inverters and their control systems, phase-locked loops, L-shaped filters, and transmission lines. Secondly, based on the mathematical model of the photovoltaic power generation system, modular modeling methods are used to derive and establish small signal models for each subsystem, and obtain the state space model of the photovoltaic power generation system. Finally, using the eigenvalue analysis method, the impact of different inverter and phase-locked loop control parameters, as well as the root locus of photovoltaic output changes, on system stability is studied and analyzed. The experimental results indicate that changes in control parameters and photovoltaic output will have varying degrees of impact on the sub synchronous oscillation generated by the photovoltaic power generation system.