Distinguishing features of natural and forced oscillations

Synchronous power systems often experience two types of oscillatory responses: natural and forced. Natural oscillations are a transient response characterized by the electromechanical oscillation modes. If one or more of these modes are undamped, a sustained oscillation occurs with the system in a near unstable condition. Alternatively, forced oscillations are typically caused by some rouge input driving the system into a sustained oscillation. An example is an ill-operating power-plant steam valve oscillating in a limit-cycle. This paper examines the unique features that may allow one to distinguish between a very lightly-damped (or undamped) natural oscillation and a forced oscillation. We first provide a unique mathematical representation for forced versus natural oscillations. The model is then used to show that the noise response of the system under the undamped natural case is considerably different than under the forced case. We show a spectral approach for using this difference to distinguish between the oscillation types.