The synchronous signal tracking capability of Phase-Locked Loop (PLL) makes it widely used in grid-connected converter systems. However, the inherent nonlinearity of PLL will affect the stability of grid-connected converter systems. Based on the averaging method, the analytical solution of the second-order differential equation of the output phase angle of PLL is obtained, so that the operating state of the system can be judged directly from the analytical solution. The validity of the analytical solution is verified by comparing the analytical solution with the numerical solution and simulation results.