Abstract: The fault characteristics of grid-connected inverter power sources are greatly affected by control strategies, and their nonlinear characteristics are significant, making traditional fault calculation methods unsuitable. To accurately calculate the faults of the grid-connected inverter system, this paper proposes a novel continuously solving method for time-domain system state variables. This method alternatingly solves the numerical solution of the control system and the analytical solution of the differential equation system of the main circuit. The proposed approach considers several factors, including the current capability of the power electronic converter, the control strategy switching after the fault, the nonlinearity of the control system, and the coupling of the state variables. This paper takes the grid-forming inverter as an example to establish the PSCAD simulation model and the mathematical model. By comparing and analyzing the simulation results with the calculation results of the proposed method, the effectiveness and correctness of the method are verified.