In this paper, we discuss the single-machine infinite-bus system with one static synchronous compensator (STATCOM) asymmetrically installed as a current source. Together with a classical two order generator model, a simple power equation is drawn to give direct and clear physical concepts on synchronizing and damping torque coefficients. On the basis of the equations, some basic issues, such as the relationship of voltage gain control and damping control, operating conditions and installation of STATCOM, are investigated by detailed theoretical analysis. Then with proportional controller for voltage and damping control, the digital simulation proves the necessity of multi-objective control of STATCOM in damping power system oscillations and supplying fast voltage support. Finally, nonlinear simulation demonstrates how STATCOM improves the power transfer ability of the system after a severe fault.