Integration of power electronic-based renewable energy sources into weak grids brings new concerns regarding the harmonic stability of modern power systems. This paper studies harmonic stability and impedance characteristics of power synchronization control (PSC) which has been introduced for control of converters under weak grid operating condition. Due to the varying grid impedance in weak grids, the harmonic stability of converters with LCL output filters would be a demanding prospect. Thus, this paper addresses this issue by studying the admittance characteristics of PSC based on the dynamics of the control scheme, the delay and the sampling frequency of the control system, and the linearized model of the grid-connected converter. Finally, the critical grid inductance and the sufficient conditions for achieving harmonic stability are introduced. Time-domain simulations are carried out to support the proposed harmonic stability analysis.