Damping torque analysis (DTA) is a well-developed technique for understanding and studying power system oscillations. It is established on the basis of physical explanation of damping torque contribution of power system control to the rotor motion of generator. Hence when it is applied in a multi-machine power system, the DTA becomes complicated due to the involvement of large number of generators. In this paper, a graphical explanation of he DTA method is presented by using the small-signal equal-area criterion of power system stability analysis. The graphical explanation presented urns out to be completely independent of the physical concept of damping torque, indicating the significant potential to develop the graphical explanation into a general and simple approach for understanding and studying multi-machine power system oscillations. In the paper, an example of a multi-machine power system installed with a STATCOM (static synchronous compensator) is given to demonstrate how the potential of applying graphical explanation can be explored. Based on the conclusion drawn from the graphical explanation, it is shown why the STATCOM voltage control contributes little damping to power system oscillations and a simple method of designing a STATCOM stabilizer is proposed. Confirmation from simulation results of an example four-machine power system is presented in the paper.