As an essential part of modern power systems, power electronics have improved system performance. They also brought new dynamic and transient problems and posed significant challenges to precise and efficient simulation. Traditional modeling and solving methods fail to balance between the simulation accuracy and efficiency, and they are not flexible enough to adapt to converters with various new topologies. This article proposed a widely applicable modeling and simulation method based on the unit switching circuit that greatly promote the simulation efficiency and modeling simplicity by converting switching circuits into constant sub-grid equations with injection functions. Critical issues for engineering applications, such as the blocking state and the triggering deadband of converters, were also discussed and addressed by boundary balance and conduction path estimation. The error and stability of the solving method were qualitatively analyzed, with further discussions on the validity and numerical features. Several cases, including common and general cases and a real project of power electronic microgrid, tested and verified the accuracy, generalization ability, and efficiency of the proposed method.