Virtual synchronous generator (VSG) technology is widely used in the control of new energy grid-connected inverters because it provides damping and inertia. It is easy to cause frequency coupling when photovoltaic energy storage systems are connected to a weak grid, so analyzing the grid-connected stability of a VSG becomes more complicated. For photovoltaic energy storage systems connected to a weak grid, a multi-time scale VSG model based on harmonic state space (HSS) theory is established in the dq domain considering frequency coupling. The normalized parameter sensitivity analysis method is used to reveal the characteristics of root locus of key control parameters such as virtual inertia J, virtual damping Dp, droop coefficient Ku, proportional coefficient kpu and cut-off frequency c in power loop, voltage loop and low-pass filter, and the influence of power grid strength on system stability. The control parameters are adjusted and optimized to enhance system stability. Finally, the accuracy of the harmonic state space model and the root trajectory characteristics of the key parameters are verified on the Matlab/Simulink simulation platform.