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This paper discusses the application of trajectory sensitivity analysis (TSA) of power systems containing FACTS compensators. Thyristor controlled series compensator (TCSC) and static synchronous compensator (STATCOM) are the devices considered. The TCSC is modeled by a variable capacitor, the value of which changes with the firing angle. The STATCOM is modeled by a voltage source connected to the system through a transformer. The effect of their individual and simultaneous use on the system transient stability is studied by applying TSA. Two different test systems are considered. It is shown that TSA can be used to determine the best possible locations of the two devices for transient stability improvement as well as to predict the critical clearing time. Index Terms-Optimal location, static synchronous compensator (STATCOM), thyristor controlled series compensator (TCSC), trajectory sensitivity analysis, transient stability margin.

A large signal voltage stability index is proposed in this study. Although the study focuses on a wind farm connected system, the index can predict instability of any power system. The index gives an idea about the stability margin of the power system under a given operating condition and can be used to predict emergency situations following a large disturbance such as line outage. The proposed index can be used effectively for systems with static as well as dynamic loads. The proposed index is verified in standard test systems. Matrix perturbation theory is used to verify the viability of the index.

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