Analytical examination and comparison of synchronous machine model representation techniques

Synchronous Machines (SMs) are the corner stone of the power systems that have so far been dominantly studied. Considering high penetration of renewable energy sources, for example, wind energy conversion system; the Virtual SM concept is recently presented in the literature in order to inspire from SM to change the dynamic behavior of converter-based RESs. Accordingly, it is instructive to have insight into the different SM modeling approaches. In this paper, three most common SM parameter determination techniques within the framework of the well-known two-reaction theory are firstly discussed. Afterward, relationships between these techniques are addressed through their backgrounds and SM's time-constants comparisons. Furthermore, a new systematic approach is proposed to determine SM's time constants using rewriting SM's state-space equations on the basis of the path of the flux linkage penetration into the rotor core following a short-circuit fault occurrence. According to the proposed approach, an analytical method to approximate the time-domain variations of the machine variables during a three-phase short circuit fault is also derived. Last, numerical and simulation results are provided to investigate the effectiveness of the proposed method. For this purpose, two different SMs are taken into consideration.