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A long transmission line needs controllable series as well as shunt compensation for power flow control and voltage regulation. This can be achieved by suitable combination of passive elements and active FACTS controllers. In this paper, series passive compensation and shunt active compensation provided by a static synchronous compensator (STATCOM) connected at the electrical center of the transmission line are considered. It is possible to damp subsynchronous resonance (SSR) caused by series capacitors with the help of an auxiliary subsynchronous damping controller (SSDC) on STATCOM. The objective of this paper is to investigate the SSR characteristics of the system and propose a new design procedure for SSDC based on nonlinear optimization to meet the specifications on the damping torque in the range of critical torsional frequencies. The SSDC uses the Thevenin voltage signal to modulate the reactive current reference of STATCOM. The Thevenin voltage signal is derived from the locally available STATCOM bus voltage and reactive current signals. The STATCOM configurations considered in this paper are 12 pulse, two- and three-level voltage source converter with Type-2 and Type-1 control, respectively. The controller regulates either reactive current (supplied by the STATCOM) or the bus voltage. The 3-phase model of the STATCOM is based on switching functions. By neglecting harmonics in the switching function, D-Q model is derived which is combined with similar models of the other system components for linear analysis. The results of the linear analysis are validated by carrying out transient simulation based on the detailed nonlinear models. The study is performed on the system adapted from the IEEE First Benchmark Model.