This paper presents a systematic approach for a detailed positive sequence dq domain modeling and simulation of low inertia power systems for system stability and transients analysis. It aims to reduce the computational complexities while maintaining simulation accuracy comparable to electromagnetic transient (EMT) programs. The proposed approach integrates the detailed models of various components of inverter-based power systems. A computationally efficient voltage source model is proposed for the synchronous machine behind the sub-transient reactance considering stator transients, which makes the direct interface of SM model with the network feasible without affecting the accuracy. A method is presented to obtain explicit dynamic voltages of typical nodes that do not have a shunt capacitance. Furthermore, a method is proposed to simulate three-phase symmetrical faults in dq domain followed by the line tripping with and without current zero interruption. Matlab/Simulink numerical simulations with three bus and WSCC 9-bus test systems under various disturbances validate the  effectiveness and adequacy of the proposed method as compared to the EMT approach.