Analytic and Numerical Study of TCSC Devices: Unveiling the Crucial Role of Phase-Locked Loops

This paper proposes a hybrid dynamic model of thyristor controlled series compensators (TCSCs). The objective is to demonstrate, through advanced circuit theory tools and numerical simulations that some modeling aspects are not properly taken into account in the existing literature. In particular, we consider those related to the role of the TCSC impedance when the line current is polluted by harmonics and to the phase-locked loops (PLLs). Shooting methods and periodic small signal analyses are utilized to compute the impedance of the TCSC at sub-harmonics that are typical of the sub-synchronous resonance phenomenon. The case study focuses on the impact of sub-harmonics, on the behavior of the TCSC and on the synchronization of the firing angle through the PLL. Modeling recommendations are finally drawn based on the results presented in this paper.